^jhwwsitg 0( Division Range Shelf..., Received , K, : -'. -JA1.BANCROFT \ THE NEW PRACTICAL NAVIGATOR; BEING A Complete Cpttotne /t.'StfF T N A V IjfayT O N: TO WHICH AHE ADDED, T A B L BSU SITE FOR DETERMINING THE L E AND LONGITUDE AT SEAe CONTAINING, THE DIFFERENT KINDS OF SAILING, AND NECESSARY CORRECTIONS FOR LEE-WAY, VARIATION, Sec, EXEMPLIFIED IN A JOURNAL AT SEA: TOGETHER WITH All necefiary Inflru6Hons for determining the Latitude by DOUBLE ALTITUDES of the Sun, by the Moon, the Planets, and fixed Stars ; and for afcertaining the LONGITUDE by the LUNAR OB- SERVATIONS* and other Methods. The Manner of finding and knowing the Planets and fixed Stars, by Calcula- tion and Planifpheres. The Art of Surveying Sea-Coafts and Harbours. An Abftra,/,7>W nl \V /i /.',v, r ** TTf, 77 Printed by J. CROWDBR, Warwick-square. v K a TO THE Right Hon.^ GEORGE JOHN EARL SPENCER, VISCOUNT ALTHORP, AND MASTER OF THE TRINITT-HOUSE. THIS NEW AND MUCH-IMPROVED EDITION OF THE PRACTICAL NAVIGATOR, IS RESPECTFULLY DEDICATED, By his Lordfhip's much-obliged, And very humble Servant, JOHN HAMILTON MOORE. MAY ift, 1807, An Account of the Arrangement and Improvements in this Edition* '""PHE favourable reception which this Work has met with, embo!- 4- dens me to prefent before the Public the prefent Edition ; ia which, I truft, I have introduced fuch improvements as will continue to me the favour which I have fo long had the happinefs to enjoy. In my former Editions I had digefted the feveral Articles into a natural and fimple order, and endeavoured to mow how every thing might be deduced from the firft and moil fimpie principles of the Mathematics; in which, I truft, I had fo far fucceeded, as to render it eafy to the moft common capacity. How beneficial a work of this kind muft be to Learners cannot be doubted, when we reflect, that by being thus acquainted with the true principles of things, they will retain better what they have learned, and be enabled to make much greater progrefs in the art, than eould otherwife poffibly take place. Indeed, upon a careful perufal of the Work, I found the plan I had purfued, fo far as regards the parts of Navigation ufually taught and praclifed at fea f could not be amended -in the bulk, though fome improvements might be made in particular parts. It particularly occurred to me, that I had invariably found young Gentlemen, who attended me for a private e*j*. amination, previous to their paffing a public one, deficient in working an obfervation in all the variety of fituations which may take place. In this Work I have accordingly elucidated this important article, by- giving a Rule for every different iltuation, in which the obferver can poflibly find himfelf in refpecT: of the Sun; illuftrating each with a pro- jection on the Plane of the Meridian. There is introduced into this Edition, a Table for the near calcu- lating the Time of High Water, with the afliftance of the Nautical Almanack. I pafs over many others of fmallernote in the firft part of the Boolc t fuch as partial Amendments of the Style, &c. in hafte to give an ac- count of the Arrangements and Additions in the latter part of this WORK, which is for the moft part NEW. Previous to the year 1767, when the firft NAUTICAL ALMAXACK was publimed, the practice of finding the Longitude at Sea was aniver- fally by account. The mode of afcertaining it by taking the Moon's diftance from the Sun, or a fixed Star, commonly called the LUNAH. OBSERVATIONS, was attended with difficulties infurmountable to moft Mariners. By the unremitting affiduity of the Aftronomer lloyal, to xvhofe labours the Nautical Art is much indebted for its prefent high ftate of improvement ; and by the Rewards held out by Parliament, snd the confequent improvements injnftruments for meafuring the An~ gular Diftance, what before was confidered as nearly an impoflibility, is now come into almoft general practice. Proud of contributing my quota towards the facilitating this laudable purpofe, fo highly condu^ ciye fo the commercial intereils of this powerful Empire^ I have en- deavoured deavoured to render this part of the Nautical Art as fimple and plain as the nature of the fubject will admit. To the Defcription of HADLEY'SQUADRANTIS added the Defcription and Ufe of HADLEY'S SEXTANT, with an Account of the new Mode of dividing the Nonius, fo that the Diftance can be read off to fifteen feconds. The Method of adjufting the Sextant and Telefcope is fully enlarged upon, together with the ufe of this Instrument, in obferving the angular diftance. PARALLAX and REFRACTION are next defined, and illuftrated with a Plate. The Method of applying the Corrections for Parallax and Refraction to the obferved Diftance, in order to reduce it to the true, is next given. It being frequently complained to me by feamen, that it is next t* impoffible to find and know the Stars from which the Moon's diftance ' is computed in the Nautical Almanack, I have, to remedy this defect, fubjoined to this Work two plans of the Stars, one on the Plane of the Equator, the other on the Plane of the Meridian ; a defcription of the projection and ufe of thefe Plans is given at large in the Work, toge- ther with fome PRACTICAL DIRECTIONS for knowing the Stars. Next in order is the Method of finding the TRUE TIME, in order to regulate the going of the Watch. The Lunar Obfervations follow, arranged in a new, clear, and perfpicuous manner. The Examination of a YOUNG SEA OFFICER, being an Abftract of practical Seamanfhip, has been examined by two profeffional men, and large additions made. We have alfo added, what we conceive will be an acceptable article in the prefent times of hoftility, The Method of exercifing private Ships' Companies for War. In this article, the forms of two Quarter Bills are given, with the Exercife of the great Guns, according to the prefent practice, and fome approved manoeuvres in attacking and de- fending a fingle (hip. Two additional Tables will alfo be found, one exhibiting the Proportion of Powder for Sea. Guns, the other the Number of Shot contained .in Grapes of different Sizes. A variety of Methods of relieving Ships in Diftrefs ; the beft Means of faving people from Wrecks; and the Procefs recommended by the Royal Humane Society for recovering drowned Perfons, will alfo be found. To the Tables a felicitous attention has been paid. The Tables of Difference of Latitude and Departure for Points and Degrees, have been re. calculated with the greateft care. The Tables of Logarithms of Numbers, and of Artificial Sines, Tangents, and Secants, have been carefully compared with the third edition of Hodgfon's Tables, printed in the year 1738 ; xvith Gardner's third edition of Sherwin's, printed in the year 1742 ; and with Dr. Button's laft edition, by three per. fons ; fo that 1 truft the errors, if any, are few. The Tables which follow have undergone a firailar examination. To i he Tables of the Sun's Declination, a moft fcrupulous attention has been paid. The Table of Latitudes and Longitudes of Places is corrected by the lateft furveys and obfervations, and great additions made. Table XIII. For reducing the Sun's Declination to any given Me- ridian, and to any time under that Meridian, in the firft page of which which you have the Proportional Parts of the Daily Difference of the Sun's Declination to every Minute and every fix Seconds, anfwering to every five Minutes of Time, and to every Degree and fifteen Miles of Longitude. The fecond and third page contain the fame propor- tional Parts to every hour, and to every fifteen Degrees of Longitude. To the Table XVI. For turning Degrees and Minutes into Time, and the contrary, two columns are added on the right fide, for turning Minutes and Seconds (of an hour) into Longitude, and the reverfe. Table XVIII. contains the Decimal of every Minute in twelve Hours, being of ready ufe for finding the Proportion of the fmall Dif- ference (in twelve Hours) of the Moon's Parallax and Semi-diameter, by taking out the number from the Table anfwering to the Tii^e when the obfervation was taken, and multiply the differences therewith from the producl of each, cut off four figures from the right hand, the left hand figures are the Anfwers (if no Fraction remains) which muft be additive or fubtraclive, according as they are increafing or decreasing. The proportional Part of the Daily Difference of the Sun or Star's right Afcenfion is found by taking out the number, anfwering to half the time required, and multiply the difference therewith, from the producl, cut off four figures from the right hand, the remaining figures are the anfwer. Thus you avoid working by the the Rule of Three. In the precepts for finding tb* Longitude by Lunar Obfervation, page 238, you are told to make ufe of the Log Sine of 30 degrees*, half the fum of the apparent Altitudes, and half the apparent Diftance. This Edition has been carefully examined, improved, and corrected by my friend Captain JOSEPH DESSIOU, whcfe abilities as a Navigator, Mathematician, and Draughtfman, cannot be doubted. Therefore I may prefume to fay this is the moft correcl Edition that has been pre. fented to the Public's notice. * The Log Sine of 30 degrees is equal to the Natural Sine of half the Radius ; and, ac- cording to Euclid, Axiom 6, Book I. what things are each of them half of the same quan- tity, are equal among themselves* CONTENTS CONTENTS. "T^ECIMAL Arithmetic . ; . xii -*-"^ Geometrical Definitions . . i Geometrical Problems ... 5 Projection of the. Line of Sines y Tangents, and Secants^ on the Plane Scale . . .22 Defer iption and Ufe of Gunter's Seals . . 14 On the Ufe of the Settor . . 9 17 The Ufe of the Logai itbms . . i 9 Multiplication by Logarithms . * .22 Divifion of Logarithms . . . 22 V extract the Root in Logarithms . . 23 Y^ Application of Logarithms in meafuring all Kinds of Pack- ages taken on Board Ships . . 24 *lhe common Way of finding a Ship's Tonnage at London 26 To fad the Logarithm* of Sines, Tangents^ and Secants^ belong" ing to any Number of Degrees and Minutes required 26 Tofnd the Degrees^ Minutes and Seconds^ correfponding to any given Logarithm 27 *I'o]ind the Logarithm of the Sine or Co-Jine^for Degrees^ Mi- nutes and Seconds . . . 27 To find the Arithmetical Complement of any Logarithm ; 28 "Ufeful Proportions in Navigation . 29 Trigonometry . . . . 31 Introduction to Navigation . . .4^ Navigation . . . 50 Plane Sailing . . . . 53 Iraverfe Sailing , , , .62 Middle Latitude Sailing . ; 73 Msrcator's Sailing . . . .86 Conflruflion and Ufe of Mercator's Qjart . 107 Of Wind* . . . . 113 Of Tides . . . . 119 Table for finding the Time of High Water at any Place 128 Ditto . . . . 130 Of the Log- Line and Half- Minute Glafs . 132 Defcription and Ufe of Hartley's Quadrant and Sextant 135 To obferve the Angular Diflance between the Sun and Moon 143 To obferve the Angular Di/lance between the Moon and a Star 144. Parallax . . . * 145 Refraftion . 146 Semi-diameter - ... ibid* To work an Obfervation, or to find the Latitude of a Place^ by the Tables of the Sun and Star's Declination, and the Zenith Diflance . . . 147 n$ CONTENT*. J*X ' PAGE The Variation of the Compafs . * .152 T,; find the true Amplitude . . . *53 To -find the true 'Azimuth . . . 155 The Method of Keeping a Ship's Reckoning at Sea 161 Rules for correcting the Dead Reckoning . .167 Four Jepar ate Days' Work . . .175 Journal of a Voyage from London to Madeira and Teneriffe 379 Abftratf oft^e Journal . . . 197 The Method of Finding the Latitude- at Sea by two Altitudes ibid. To find the Latitude by one Altitude of the Sun^ when the Time is not more dtftant than one Hour from Noon . 207 To find the Latitude by the Meridian Altitude of the Moon 209 To find the Latitude by the Meridian Altitude of a Planet 2 1 r A Compendium of Nautical Aflronomy . .212 To find the apparent Time, and then by regulate the Going of the Watch . . . .218 To find the apparent Time by equal Altitudes of the Sun 219 To find the apparent Tune by the Sun's Altitude . ibid. Another Method of finding the apparent Time . 223 A Quejlionfor Exercife . , . 224 To find the apparent Time by the Altitude of a fixed Star ibid. The Method of Finding the Longitude by the Moon's Diftance from the Sun or a fixed Star , commonly called the Lur- nar Obfervations . . . 226 The tteceffary Preparations for working the Lunar Obfervations. ifl. To reduce the Titne at Ship to the Tune at Greenwich 22 7 id. To correct the obferved Altitude of the Sun or Star ibid. %d. To correft the obferved Altitude of the Moon . 228 4tb, To correft the obferved Diftance . . '229 Having the apparent Altitude of the Objefts and their apparent Di/iance, to find their true Dlflaace by A4r. Lyon's Method ibid. Having the true Diftance and Ti?ne^ to determine the Longitude 230 Examples of the Lunar Obfervations . . 231 Mr. Witcbel's Met hod' . . 235 Examples .... 236 Another Method and Examples . . '238 ^ue/i ions for Exercife . . . .239 To find the Sun's true Altitude , . 240 To find the Altitude of any of the known fixed Stars . 24.2 To find the true Altitude of the Moon's Centre 243 To find the Longitude by Jupiter's Satellites . 244 To find the Longitude by the Eclipfes of the Moon . 245 To find the Longitude by a Chronometer or Time-Keeper ibid. Oblique Trigonometry , . . 246 Oblique Sailing . . . , 349 Manner of Surveying ^Sea Coajls and Harbours ; 254 To take a Draft Sailing along Shore . . ibid. Tofarvey an Harbour by Obfervation on Shore . 257 t> To X CONTEXTS* To reduce a Draft to ofmaUer Scale . . 259 To find the Height and Di/hnce of Objetts at Sea . 260 Of the Curvature of the Earth . ; 262 Current Sailing . . . , 263 Explanation of the mojl ufefulSea Terms . 266 Explanation of the Riggtng of a Ship of War . . 292 Examination of a young Sea Officer . * 293 The Method of exercifing Ship's Companies for War . 312 On preparing for Exercife or rfclion . 313 Exercife of the Great Guns . . .314 he Method of attacking or defending a Ship . 317 On Ships in Diftrefs . . . 319 Onfaving Lives from a Ship loft on a Lee-Shore . 323 Directions for restoring the Drow ned, &c. . 325 Remarks calculated to ajjift Commanders when coming into the Britijh Channel " 326 INDEX TO THE TABLES. TABLE Difference of Latitude and Departure for Points . I, Difference of Latitude and Departure for Degrees . II. Logarithms of Sines, fangents^ and Secants to Quarter of Points III. Logarithms of Numbers . . IV. Artificial Sine?) ^Tangents, and Secants . V. Meridional Parts . . . VI. Mean Refraction of the Heavenly Bodies in Altitude, VII, Depreffion or Dip of the Horizon . VIIL The Sun's Parallax in Altitude . . IX. Moon's Augmentation . X. Dip of the S ^> f> |> i\> T 5 6> ftexvs that thefe numbers were their refpective remainders, after fuch divi- lions were made, and are read thus: one-half, three-fourths, two- thirds, four- fifths, nine- twelfths, and five-fixteentbs. . A Dt cimal Fraction is a part of an unit, or one, fuppofed to be di- vided into 10, 100, 1000, 10,000, &c. equal parts. If the unit is divided into ten parts, and each of thofe parts into ten more equal parts, we obtain the foundation of Decimal Fractions. In Vulgar Fractions the Numerator is fet over the Denominator ; but in Decimal Fractions the Numerator Is diftinguilhed by a comma, or point, placed before it, thus: ,5 ,75 ,125 is read thus, T 5 o T 7 o 5 oToVo* that is, the firtt figure is 5-tenths, the fecond 75-hundredths, and the third 1 2$-thoufandth parts of unity, or one. As whole Numbers increafe their value in tenfold proportion from the right hand to the left, fo Decimals decreafe in the fame proportion from the left hand towards the right : thus, ,5 ,05 ,005 ; or thus, -^ r S 5 T'QV' Too'o* To reduce a Vulgar Fraction to a Decimal. RULE. Add cyphers to the Numerator, and divide by theDeno- jiiir.ator. EXAMPLE I. EXAMPLE IV: Reduce | of a foot to a Decimal. Reduce J of an hour to a Decimal. 4) I >( 2 5 3) 8 20 10 20 9 10 EXAMPLE II. 9 Reduce | of a degree to a Decimal* - 28 9 20 10 20 9 Ex AMP BE III. EXAMPLE V. Reduce an hour to a Decimal. Reduce f of a degree to a Decimal. 2)i,o(,5 3)2,00000(666666 10 18 20 18 " 20 18 20 18 20 18 To find the value of a Decimal in the different denominations of the lame quantity, RULE. Multiply the Decimal by the parts of the integer, feparat- ing to the right hand as many Decimals as are in the multiplicand j and the figures to the left hand will be the parts of the integer re. quired. EXAMPLE I. EXAMPLE II. What is the proper quantity of What is the proper quantity of" ,25 of a foot ? ,5 of an hour ? ^5 >$ 12 60 Anfwer, 3,00 inches Anfwer, 30,0 minutes. x AMPLE EXAMPLE III. "What is the proper quantity of ,75 of a degree ? >75 60 Anfwer, 4^,00 minutes. EXAMPLE IV. What is the proper quantity of ,333 of an hour ? 60 Anfwer, 19,980 minutes. 3 EXAMPLE V. What is the proper quantity of ,666 of a degree ? ,666 60 Anfwer, 39,960 minutes. EXAMPLE VI. What is the proper quantity of ,2236 of a degree ? ,2236 60 Minutes, 13,4160 60 Seconds, 24,9600 Anfwer. Hence the parts of an integer, whether of coins, weights, or mea~ fares, may be reduced to a Decimal, by bringing the parts of an inte- ger into its loweft terms for a dividend, and the integer into the fame terms fora divifbr j the quotient will be the decimal parts of the inte- ger, the value of which may be found by multiplying it by the compo- nent parts of the integer, and feparating the number of decimal places towards the right hand, as above. Additw n of Decimals . Addition of Decimals is performed exactly as in whole numbers, only obferving to place the figures of the like denomination under each other, fo that the points which feparate the whole numbers from the Decimals ftand in a line under each other ; and as many Decimal places muft be cut otf from the product, as there are in the greatett number to-be added. EXAMPLES. Fathoms. Yards. Feet; Add 78,8 66,71 3720,45 34,56 148,9 25,0036 46,77 3 2 >?2* 4179,802 32,53 7,81 3*6284. 154,27 40,27 81,4 38,5 Sum 7928,8840 Sura 428,33 Add 15836,071 20,09 34>7 583,27008 Sum 334,912 Degree. 6.5 3*25 Sum 9.7$ Miles or Minutes. 6,4 Sum 10.35 800116473,50108 Subi* v r; or. r Subtraction of Decimal: -.: . * ^rformed as that of whole number*? alfb, only taking care to place. .. with the feparating point directly un* del each oilier. f *v ] EXAMPLES. Degrees. Minutes. From 9,75 10,35 Take 6,5 6,4 Remainder 3,25 Remainder 3,95 Multiplication of Decimals. Multiplication of Decimals is performed likewife as that of whole numbers, and as many places as there are in both the Multiplicand and Multiplier muft be cut off towards the right hand of the product, and the number- ftanding on the left hand of the point will be whole .numbers, and thofe on the right hand will be Decimals. EXAMPLE I. EXAMPLE II. Multiply 27,75 by 7,5. Multiply 39,25 by 6,5. 277S 39> 2 5 7>5 , 6 >5 19625 Anfwer 208,125 Anfwer 255,127 EXAMPLE III. EXAMPLE IV". Multiply 25,96 by 9,25 Multiply 49,96 by 20,36 20,36 13788 91920 Anfwer 240,1300 935>745 6 Dhnjion of Decimals. This Rule is alfo worked as in whole numbers ; the only difficulty 15 in valuing the quotient, which is done by the following; Rules: ift. If the Diviibr and Dividend have the fame number of Decimal parts, the quotient will be a whole number. 2d. If the Dividend has not fo many places of Decimals as are in the Divifor, then fo many cyphers twutt be annexed to the Dividend as will make thrm equal, and rhe quotient will be a whole number, jd. But when the divifidn is done, if the quotient has not fo many figures as it {hould have places of Decimals, then fo rpany cyphers mult be aff r >:ed as there are places wanting. EXAMPLE I. EXAMPLE II. Divide 208, 1 25 by 7, 5. Divide 2 ;^, 1 2 5 by 6,5. 7,5)208,125(27,75 ^5)255^25(30,25 150 Rule of Three in Decimals. Rule of Three in Decimals is worked in the fame manner as common Arithmetic, that is, by multiplying the fecond and third terms toge- ther, and dividing by the firfl, the quotietat will be the anfwer ; and of the fame denomination as the fecond term. EXAMPLE. Yards. Shillings. J f 3>5 6,75 3,5)82,6875(23,62$ 78 12 126 7,500 105 4 ,2l8 2,000 210 - 175 '75 Anf. il. ss. 7d. - y > In like manner may any other be worked, whether in coins, weights, meafure, or time, by reducing the parts of the integer into Decimals, and then find the value as above. The three laft Rules may be worked by Logarithms, which will be ihewn when we come to treat of their ufe. GEOMETRICAL GEOMETRICAL DEFINITIONS, EOMETRY is the Science which treats of the Defcnptiori* Properties, and Relations of Magnitudes in general 5 of which there are three Kinds or Species, viz. a Line, which has only Length without either Breadth or Thicknefs 3 a Superficies, comprehended by Length and Breadth 3 and a Solid, which has Length, Breadth, and Thicknefs. L A point confidered mathematically, is incapable of being divided, and therefore hath no parts, or it is the fmalleft part of fpace that can be affigned, and may be conceived A* fo infinitely fmall, as to be void of length, breadth^ or thicknefs, being always denoted by a dot, as at A* II. A right line is the neareft diftance between two points, which limits its length, without any fuppofed breadth, or thicknefs, as AB ; it A- may be fuppofed to be the flowing of a point* III. A -plane fuperficies is that which lies evenly between its extreme points, refembl ing a fmooth table, or polifhed glafs ; bounded by lines having length and breadth : but is conceived to have no depth or thicknefs, and may be conceived to be generated by the flowing of a right line. IV. Parallel lines are fuch as are equally diftant ^ in all their parts, which extended infinitely on A ~~~ the fame plane would never meet, as the lines AB, BC. B : C y. A plane angle is the inclination or meeting of two right lines in one point ; the point where they meet is called the angular point, and the lines AB and AC are called fides or legs; it is generally exprefied by three letters, the middle one always denotes the angular point, as A, and the other two the lees or fides that include it, as AB or AC. ; A ViAcircte GEOMETRICAL DEFINITIONS. VI. A circle is a plane figure, bounded by an uniform curve line; it is ordinarily defcribed by a right line, taken with a pair of com- pafles ; one point thereof being fixed, whilft the other is turned round to the place where the motion firft began ; the fixed point is called the centre, and the line defcribed by the other point is called the circumference. VII. The radius of a circle,or femidiameter, is a right line drawn from the centre to the circumference, as AC ; or it is that line which is taken between the points ef the compafTes to defcribe the circle ; and is half its diameter AB. VIII. An arch of a circle is any part or portion of the circumference, as DFE. IX. A chdrd of a circle is the fubtence of an arch, or it is a right line joining the ends of an arch ; it divides the circle into two unequal parts, called fegments, and is a chord to them both, as DE is the . chord of the arches DFE and DGE. X. A femicircle, or half a circle^ is a figure contained under the diameter, as AGB or AFB. XL A quadrant is half a femicircle, or one fourth part of the whole circle ; as the figure CAG. NOTE. All circles, whether great or fmall, are actually, or fuppofed to hav, their circumference divided 11110360 equal parts, called degrees, and each degree into 60 equal parts, called minutes, and each minute into 60 equal parts, called feconds, and fo on into thirds, fourths, &c. All angles are meafured by an arch of a circle, defcribed round their angular points, with the chord of 60 degrees, taken from the line of chords on the plane fcale, and are eftimated greater or lefs according to the number of degrees contained betwixt their legs ; and though legs be ma ie longer or fhorter, {till the angle between them continues the fame. XII. A right GEOMETRICAL DEFINITIONS, XII. A right line is faid to be PERPENDI- A CUL AR to another line, when it falls upon it fo as to make the angles on each fide of it equal, fuch as the figure ABCD, where the angle ACD is equal to the angle ACB, each a quadrant, or right angle, contain- ing 90 degrees. C~ (T~ ? . JB XIII. An ACUTE ANGLE is lefs than a right an- gle, and is that which contains lefs than 90 degrees, as ABC. XIV. An OBTUSE ANGLE is greaterthan a right angle, and is that which con- tains more than 90 degrees, as the an- gle GEH. The feweft number of right lin.es that can include a fpace are three, which form a figure called a triangle, or three-cornered figure, and confifts of fix {farts, viz. three fides and three angles ; it is diftinguifhed into three forts, viz. a right-angled triangle, an obtufe-angled triangle, and an acute-angled triangle. XV. A RIGHT-ANGLED TRIANGLE has one of its angles right, or containing 90 degrees ; the fide oppoflte the right angle is called the hypothenufe, and the other two fides are called legs ; that which {rands upright is called the perpendicular, and the other the bafe : thus BC is the hypothenufe, AC the perpendicular, and AB the bafe ; the angles oppofite the two legs are both acute. XVI. An ACUTE-ANGLED TRIANGLE has all its angles acute, or none of them cquaj to 90 degrees, as DEG. A 2 XV 7 II. An MARKS OR CHARACTERS* XVII. An OBTUSE-ANGLED TRIANGLE has one of its angles obtufe, or greater than 90 degrees, as RAF, the other two angles are acute, or lefs than 90 degrees, as in the triangle RAF. 3? NOTE. All triangles that are not right-angled, whether they arc acute or obtufe, are in general terms called oblique-angled triangles, without any other diftin&ion. The fum of the two acute angles of a right-angled triangle make 90, the fum of all the angles of any triangle 180. If from 1 80 you take the fum of the other two angles, the remaining angle will be found ; but in a right-angled triangle, if frqm 90 you fubtract the one angle, the other angle will remain. MARKS OR CHARACTERS. 4- Signifies more, or the Sign of Addition j it (hews that whatever numbers or quantity follow this Sign muft be added to thofe that go before it, thus 9 + 8, that is 9 added to 8. Or, A + B im- plies that the quantities reprefented by A and B are added. r Signifies lefs, and is ufed as the Sign of Subtra&ion ; it denotes that the number following it muft be fubtra&ed from thofe go- ing before it, as 7 5, or 5 fubtracted from 7. X The Sign of Multiplication, and (hews that the numbers placed be- fore and after are to be multiplied, thus 7X9, that is 7 multi- plied by 9, which makes 63, and 7x8x2 which makes 1 1 2. T- This mark ftands for Divifion, and fignifies that the number that Hands before it is to be divided by the number following it, as fz-riz ftiews that 72 is to be divided by 12. Or thus,^ r= The Sign of Equality: it (hews that the numbers or quantities placed before it are equal to thofe following it, thus, 8 X 1 2=96". Or 8 multiplied by 12 is equal to 96, and j-\- 2 x 436. : ;: i Proportion, and is read thus, 7 : 14:: 10 : 20, that is, as 7 is to 14, fo is 10 to 20. Or, A : B : : C : D, that is, as A is to B, to is Q toD. * Signifies Degrees, thus 45 mew the number 45 degrees. ' Signifies Minutes, thus 24' or minutes. w Signifies Seconds, thus 44" or 44 feconds. S Stands for Sine. Sec. for Secant. Tan.- Tangent. Each of thefe laft with Co. before them, fignifies the coinple, ment, as Co-fine, Co-tangent, Co-fecant. Signifies Angle. 4-d Angled, with an s at top Angles ^.s A Signifies Triangle, or AS. 1> Is frequently put to fignify the fum of any twe lines or numbers. Y Signifies the difterencc f ( 5 ) GEOMETRICAL PROBLEMS, USEFUL IN NAVIGATION. A PROBLEM is a practical PROPOSITION, in which Some- thing is propofed to be done or D A PROBLEM I. To draw a Right Line parallel to a given Right Line, to any given Diftance^ as at the Point D. WITH a pair of compafles take the neareft diftance between the point D and the given right line AB, with that diftance fet one foot of the compafles any whereon the line AB, as at A, and draw the arch C, from the point D draw a line fo as juft to touch the arch C, and it is done; for the line CD will be parallel to the line AB, and at the diftance of the point given D, as was required. PROBLEM II. To lifeEl or divide a given Line into two equal Parts. With any diftance in your compafles greater than half the line AB, with one foot in B, defcribe an arch with the fame diftance,, and one foot in A, de / icribe an arch that will cut the former A L_ arch in C and D ; through C and D draw a line, and that will cut AB iii \ E ; and the line AB will be divided at the point E into two equal parts. PROBLEM III. TO weft a Perpendicular on the End of a given R'ight With any diftance in your compafles, as from B to C, with one foot in C, defcribe che circle BDA, fo that it may juft touch the end of the given line at B ; from whence the cir- cle cuts the line as at D, draw a line through the points D and C, to cut the circle in A from A draw the line AB, which will be the perpendicular required. Qr thus. 6 GEOMETRICAL PROBLEMS. With any convenient diftance in your compafles, as from D to A, \rith one foot in D, defcribe the arch AFG, fet off the fame diftance from A to F, and from F to G ; upon F and G defcribe two arches in- terfedting one another in H j draw a li-ne L' from H to D, and it is done ; for HD will be the perpendicular required. I! PROBLEM IV. From a given Pointy as C, to let fall a Perpendicular in a given Right Line A B. With one foot in C, defcribe an arch to f; cut the given line AB m F and G, with one foot in G defcribe an arch, and with the fame diftance, and one foot in F, de- ^ fcribe an arch to cut the former in D, _jj^_ from C to D draw a line, and it is done ; A- '-.... for CD will be the perpendicular required. PROBLEM V. From a given Point to let fall a Perpendicular in a given Line, when tlfaid Perpendicular is to fall fo near the End of the given Line that it cannot be done as absve^ as at the Edge of a Sheet of Paper, &c* Let C be the point from which the perpendicular is to be let fall on the line AB, from any fbint in the line AB, as 3t A ; with the diftance AC, defcribe ...-'' an arch E, chufe any other point in the ..-*' line AB, as D, and with the diftance A - : ---.. 4- 0\ DC defcribe another arch interfering ''**-.,.. the former in E, join CE, and it is ****., done; for CB will be the perpendicular required. B PROBLEM USEFUL IN NAVIGATION. PROBLEM VI. To make Plane Angles, andfirjl a Right Angh^ containing go Degress. Draw the line CA on C, creel: a per- pendicular CD, and it is done ; for the angle DC A is an angle of 90. Ox thus, On the point C, with the chord of 60, defcribe an arch GH, and fet of? thereon from G to H, the diftance of the chord of 90, and from C through H draw CHD, which will form the angle DCA of 90 required. PROBLEM VII. To make an Acute Angle equal to any number of Degrees. Suppofe 36 30'. Draw the line BC, with the chord of 60 or radius, in your compaffes^ and one foot on C, draw the arch FB, on which fet off 36 30', or 36!, from B to F, through F and the centre C, draw the right line AC, and it is done ; for the angle ACB will be an angle of 36 30" as was required. PROBLEM To make an Obttife Angk^ that Jhall contain 127 20', Draw CB, take the chord of 60 in your compafTes,and with one foot on C defcribe an arch ; now, as we can take off only 90, fet off 90 from B to> G, and from G to E fet off the excefs above 90, which is 37 20', or 37^ ; draw the line CE, and it is done; for the angle ,'JT, ECB will be an angle of 1 27 20', PROBLEM 8 GEOMETRICAL PROBLEMS. PROBLEM IX. The Angles and Bypothenufe of a Right-angled Triangle given, to find either ofths Legs. Given the hypothenufe 250 leagues, the angle oppofite the bafe 54 30', confequently the other angle 35 30'; the bafe and perpen- dicular are required. Draw the line CB, and at C make an angle equal to 35 30' by drawing the line CA, take 250 from any convenient fcale of equal parts, and fet it off from C to A, from A let fall the perpendicular AB, to cut the line CB, and it is done ; for AB meafured on the fame fcale gives 145, and CB 203.6 leagues. NOTE. The two acute angles of a right-angled triangle make 90 degrees. PROBLEM X. 1 'he Angles and one Leg of a Right-angled Triangle being given, to find the Hypothenufe and the other Leg. The angle ACB 33 15', the leg AC 285 miles, to find the hypothenufe and the other leg AB. Draw the bafe AC, lay off on it 285 from your fcale of equal parts, from A to C j on A erecl: the perpendicular AB : with the chord of 60 fweep the arch AD, and on it fet off 33!, from your line of chords from A to D, through D and C, draw the right line BC, then BC will meafure 341 nearly, and BA 187 nearly, on the fame fcale of equal parts that AC was taken from. PROBLEM XI. The Plypothenufe and one Leg given, to find the Angles and the ether Leg. The les; A B 350, the hypothenufe 600 given, to find the angles, and leg BC. Draw the bafe CB, on B ere& the per- pendicular A B, on which fet off 350 from B to A, on the point A with an opening of 600. Draw an arch- to cut the line BC, in the point C draw AC, and it is done ; for the angle ACB will meafure 35 41' on the line of chords, and BC will meafure 487 nearly, on the fame fcale of equal parts before ufed. 90.^ C&./.5. BftUS &* USEFUL IN NAVIGATION* 9 Z.B 45 15' Z.D 108 30 PROBLEM XII. The Legs given^ to find the Angles and the Hypotbenufe. The leg AB 880 and BC 690 given, to find the angles A and C, and the hypothe- nufe AC. Draw the bafe BC; on B erect the per- pendicular AB, make BC equal to 690, and AB equal to 880 ; join AC, and it is done ; for the angle C being meafured as before, will be found as per figure, and the hypothe- nufe will meafure 1118,2. PROBLEM XIII. Two Angles and one Side of an Oblique-angled Triangle given^ to find either of the other Legs. The angle BDC 180 30', and CBD 45 15', and confequentlythe angle BCD 26 15', and the leg BC 98 given, to find the fides CD and BD. Draw the line BC, which make equal to 98, on the point B defcribe an angle of 45 15', then add 45 15' to 108 30' and the fum 153 45' taken from 1 80, the remainder is the angle BCDzi26 15'; from the point C defcribe an arch with the chord of 60, and fet off 26* 15', and it is done; for the fide BD will be 46 nearly, and DC 73,4, as was required. PROBLEM XIV. Two Sides and an Angle oppojite to one of them given, to find the other Angle and the third Side. The fide BC 160, and BD 79, and the angle C 29, 9' given, to find the angle D, and the fide CD. Draw the line BC equal to i6o,on C make the angle DCB equal to 29 9', take 79 in your compafTes, and with one foot on B, lay the other upon the line CD, draw the line BD, and it is done j for the angle D will be 99 25', the angle B 51 26', and the fide DC 127 nearly. B PROBLEM 79. 10 GEOMETRICAL PROBLEMS. Z.B aS 04' /.C 53. 08 Si 12 180 oo PROBLEM XV. 'Two Sides and their contained Angle given^ to find either of the other Angles , and the third Side. The fide BC 109, BD 76, and angle CBD 101 30' given, t find the angles BDC or BCD, and the fide CD. Draw the line BC, which make equal to p 109 ; on B defcribe an arch, on which fet off from BC towards D 101 30', then draw the line BD equal to 76, join DC, and it is done; for the angle BDC will be 47 32', the angle BCD 30 58', and the fide DC will be 145, as was required. PROBLEM XVI. Three Sides given, to find the Angles. " The fides BC 105, BD 85, and CD 50 miles given, to find the angles BDC, BCD,^and CBD. Draw the line BC equal to 105, take CD equal to 50 in your com- pafles, and with one foot in C, de- fcribe an arch as at D, then take BD 85 in your compafles, and with one foot in B cut the former arch in D, join BD and DC, and it is done ; & ^jo-T ' e? for the angle B being meafured, will be found 28 4', the angle C 53 8', which being added together is 8i 12', their fum fubtra&ecl from 1 80', leaves angle D 98 48', as was required. PROBLEM XVII. To find the Centre to a given Circle. With any radius, and one foot in the cir- cumference as at A, defcribe an arch of a circle, as CBD, then removing the foot from A to whence it cuts the given circle, as at B, on B defcribe another arch, cut- ting or croffing the former, as CAD, and through the points of interfe&ion draw the right line CD, which will give one right line paffing through the centre j in like manner may another right line be drawn, as- EFG, which will crofs the firft right Hne at the centre required, for any two diameters will always cut or crofs one ano- ther in the central point, PROBLEM USEFUL IN NAVIGATION. PROBLEM XVIII. II, -f To divide a Circle Into any Number of equal even Parts> as 4, 1 6, 32 Firft draw the diameter through the centre, which will divide it into two equal parts ; bifecl: the diame- ter with another right line perpen- dicular thereto, and the circle will be divided into four equal parts or quadrants ; bifect each of thefe qua- drants again by right lines drawn through the centre, and it will be divided into eight equal parts, and fo may you continue on your bifections any number of times, that is 4, 8, 1 6, 32, &c. doubling the number of even parts. This Problem is ufeful in conftru&ing the Mariner's Compafs. I. A chord or fubtenfe of an arch, is a right line that divides the circle into two unequal parts, and is a chord to them both, as FH, XI. II. A right fine of an arch is a line drawn from the end or termination of an arch, perpendicular to the ra- dius, or is half the chord of twice the arch, fo that XV is the fine of the arch XG, and of the arch XF, the fum of which arches together make 180, or a fern i- circle; III. Xhe verfed fine of an arch is part of the diameter intercepted be- tween the right fine and the arch, as VG. IV. Xhe tangent of an arch is a line drawn perpendicular to the end of the radius, or diameter, juft touching the ar~h, as DG. V. Xhe fecant of an arch is a right line drawn from the centre through the circumference, meeting the end of the tangent line to the fame arch, as OD is the fecant of the aich XG, to which DG is tangent 5 alfo OR is the fecant of the arch CX, to which CR is a tangent. NOTE. Sines, Xangents, Secants, are faid to be the meafure of fo many degrees as the arch contains parts of 360, fo that radius being the fine of a quadrant, or a fourth part of the circumference, contains 90 degrees ; thus the radius is always equal to the fine of 90, as is alfo the tangent of 45, and the chord of 60. 13 2 PROJECTION'. PRO J ECTI ON OF THE LINES OF SINES, TANGENTS, AND SECANTS, ON THE PLANE SCALE. ift.TTTrTITH the radius you intend for your fcale, defcribe a \ \ femi-circle ADBC, and upon the centre C raife the perpendicular CD, (which will divide the femi-circle into two quadrant?, AD, BD), continue CD directly to S, and upon B raifc the perpendicular BT, then draw the right lines BD and AD, 2dly. Divide the quadrant BD into 9 equal parts, then will each of thefe be 10 degrees. Again, you may fubdivide each of thefe parts into fingle degrees; and thefe again, if your radius admits it, into minutes, or fome aliquot parts of a degree greater than minutes. 3dly. Set one foot of the compafles in B, and transfer each of the divifions in the quadrant BD to the right line BD 5 then is BD a line of chords. 4thly. From the points 10, 20, 30, &c. in the quadrant BD, draw right lines parallel to CD, till they cut the radius CB, then is the line CB divided into a line of fines, which muft be number- ed from C towards B. 5thly. If the fame line of right fines be numbered from B to- wards C, it will become a line of verfed fines, which may be con- tinued to 180, if the fame divifions be transferred on the fame line on the other fide of the centre C. 6thly. From the centre C, through the feveral divifions in the quadrant BD, draw right lines till they cut the tangent BT, fo will the line BT become a line of tangents. ythly. Setting one foot of the compafTes in C, extend the other to the feveral divifions 10, 20, 30, &c. on the tangent line BT, and transfer thefe extents feveral ly into the right line CS, then will the line CS be a line of fecants. % Sthly. Right lines drawn from A to the feveral divifions, 10, 20, 30, &c. in the quadrant BD 5 will divide the radius CD into a line of femi-tangents. 9thly. Divide the quadrant AD into eight equal parts, and from A transfer thefe divifions feverally into the line AD, then is AD a line of rhumbsj each diviiioa anfwering to 11 15' upon the line f chords 9 The SCALE or EQUAL PARTS i _ :; 4 .; 6 r a :> n> i - ;< 'T^n , DlACOXAL SCALK OK Kgi'AL TAKT S . fer ' l z=r PROJECTION OF THE LINES OF SINES, &C. ON THE PLANE SCALE. 13 The ufe of this line is for protracting and meafuring of angles, according to the common divifion of the Mariner's Compafs. If the radius AC be divided into 100, or 1000, &c. equal parts, and the lengths of the feveral fines, tangents, and fecants, correfponding to the feveral arches of the quadrant be meafured thereby, and thefe numbers be fet down in a table, each in its proper column, you will, by thefe means, have a triangular canon of numbers, by which the feveral cafes in Trigonometry may be folved, the right lines, gra- duated as above, being placed feverally upon a ruler, form the in- ftrument called the Plane Scale ; by which the lines and angles of all triangles may be meafured. All right lines, as the fides of plane triangles, &c. when they are confidered fimply as fuch, without having any relation to a circle, are meafured by fcales of equal parts, one of which is fubdivided equally into 10, and this ferves as a common diviiion to all the reft. In moft fcales an inch is taken for a common meafure to determine their largenefs and number of parts ; what an inch is divided into is generally fet at the end of the fcale, as in the fcales A, H, and C ; the numbers 10, 20, 30,45, fhew that fo many parts of the fcales A, B, C, are contained in an inch. By any fcale of equal parts, divided as above, any number lefs than 100 may be readily taken ; but, if the number fhould con- fift of three places of figures, the value of the third figure can only be guefled at ; wherefore, in thefe fcales, it is better to ufe fuch a fcale as D, called a diagonal fcale, by which any number of three figures may be exadly found. Having prepared a ruler of convenient breadth for your fcale, (which may be an inch, more or lefs), firft, near the edges thereof, draw two right lines, af, eg, parallel to each other; then divide one of thefe lines, as af, into equal parts, according to the large- nefs you intend your fcale ; and through each of thefe divifion.s draw perpendicular right lines as far as the line c g ; next divide the breadth into zo equal parts, and through each of thefe divifions draw right lines parallel to the former af and c g ; again divide the length a, b, c, d, each into ip equal parts, and from the point to the firft divifion in the line d q, draw a right line ; then parallel to that line, draw right lines through all the other divifions, and the fcale is done. Befides the lines already mentioned, there is another on the plane fcale, marked ML, which is joined to a line of chords ; and {hews how many miles, eafting or wefting. make a degree of longitude in every latitude ; thefe feveral lines are generally put on one fide of a ruler, two feet long ; and on the other fide are laid down a fcale of the logarithms of the fines, tangents, and numbers, which is commonly called Gunter's Scale, and a$ it is of general ufe, it re- quires a particular (jefcription, INSCRIPTION ( '4 ) DESCRIPTION AND OF GUNTER's SCALE. WHILE the Reader is perilling the following, it is proper he fhould have a GUNTER'S SCALE before him. Gunter's Scale hath fet upon it thefe eight lines following : ift. Sine rhumbs, marked (SR) is a line which contains the lo- garithms of the natural fine of every point and quarter point of the Mariner's Compafs, figured from the left hand towards the right, with i, 2, 3, 4, 5, 6, 7, to 8, where is a brafs pin, and where it can be done, into halves and quarters. 2d. Tangent rhumbs, marked (TR) alfo correfponds to the lo- garithm of the tangent of every point of the compafs, and is figur- ed I, 2, 3, 4, where there is a pin, and from thence towards the left hand with 5, 6, 7. 3d. The line of numbers marked (Num.) contains the logarithms of the numbers, and is figured thus ; near the left hand it begins at j, and towards the right hand is 2, 3, 4, 5, 6, 7, 8, 9 ; and then i, at which is a brafs centre pin, going ftill on 2, 3,4, 5, 6, 7, 8, 9, and 10 at the end, where there is another brafs pin ; (as this line is generally much ufed, it requires a larger defcription.) The firft one may be counted for i, or 10, or 100, or 1000, and then the next 2 is accordingly 2, or 20, or 200, or 2000, &c. Again, the firft i may be reckoned i tenth, or I hundredth, or i thoufandth part, &c. then the next is 2 tenth, or 2 hundredth, or 2 thoufandth parts, &c. fo that if the firft one be cfteemed j, the middle i is then 10, and 2 to its right is 20, 3 is 30, 4 is 40, and 10 at the end is JOO; again, if the firft i is ic, the next 2 is 20, 3 is 30, fo on, making the middle i now 100, the next 2 is 200, 3 is 300, 4 is 400, and 10 at the end is now 1000. In like manner, if the firft i be efteemed i tenth part, the next 2 is 2 tenth parts, and the middle i is i, and the next 2 is 2, and 10 at the end is now 10. Again, if the firft i be counted i hundredth part, the next is 2 hundredth parts, the middle one is now fo hundredth parts, or i tenth part, and the next 2 is 2 tenth parts, and 10 at the end is now but one whole number or integer. As the figures are increafed or diminifhed in their value, fo, in like manner, muft all the intermediate ftrokes, or fubdivifions, be increafed or diminifhed ; that is, if the firft i at the left hand be counted I, then 2 (on the right hand of it) is 2, and each fubdivi- fion between them now is i tenth part, and fo all the way to the middle i, which now is 10, the next 2 is 20, now the longer ftrokes between i and 2 are to be counted from I 3 thus j i.i, 12, ( where DESCRIPTION AND USE OF GUNTER's SCALE. 15 (where is a brafs pin), then 13, 14, 15, fometimes a longer flroke than the reft, then 16, 17, 18, 19, 20, at the figure 2 ; and ait the fhorter ftrokes between them longer, are now each to be counted for i tenth part from the middle one to the next 2, now 20, from whence the longer ftrokes between the figures are units, thus 21, 22, 23, &c. to 3, which now is 30, and the fhorter ftrokes each between them, now is the tenth part of an integer; from 3, each fhort ftroke or divifion, is i tenth part of an unit. Again, if i at the left hand be 10, the figures between it and the middle i are common tens; and the fubdivifions between each figure are units ; from the middle I to I o at the end ; each figure is jfo many hundredths; and between thefe figures each longer divifion is 10'; from the middle i to 2, each lefs divifion is 2 units ; and, from 2 to the end, each fhorter divifion is 5 units. From this defcription it will be eafy to find the divifions reprefenting any given number, thus : Suppofe the point reprefenting the number 12 was required: Take the divifion at the figure i, in the middle, for the firft figure of 1 2 ; then, for the fecond figure, count 2 tenths, or longer ftrokes to the right hand, and this laft is the point reprefenting 12, where is the brafs pin. Again, Suppofe the number 22 were required, the firft figure be- ing 2, I take the divifion to the figure 2, and for the 2d figure 2, count 2 tenths onwards, and that is the point reprefenting 22. Again, Suppofe 1728 were required ; for the firft figure i, I take the middle i, for the fecond figure 7, count onwards as before, and $hat is 1700 ; then for the third 2 count 2 tenths from the laft, and it reprefents 1720; laftly, for the 4th figure 8, eftimate 8 parts out of 10 of the next fmaller divifion, or a little lefs than 10, this point, laft found, reprefents 1728. Required the point, reprefenting the number 435 : from the 4 in the 2d interval count towards 5 on the right, three of the larger divifions, and one of the fmaller, and that will be the divifion ex- preffing 43 5, and the like of other numbers, which by a little practice is readily done. All fractions found in this line muff be decimals ; and if they are not, they muft be reduced into decimals, which is eafily done by ex- tending the compalTes from the denominator to the numerator; that extent laid upon I in the middle will reach to the decimal required. Example. Required the decimal fraction equal to.|, extend from 4 to 3, that extent will reach from i on the middle to 75, towards the left hand ; the like may be obfervedof any other vulgar fraction, MULTIPLICATION is performed on this line, by extending from i to the multiplier ; that extent will reach from the multi- plicand to the product. Suppofe, for example, it was required to find the product of 16 multiplied by 4, extend from i to 4, that extent will reach from 16 to 64, the .produdt required. DIVISION l6 DESCRIPTION AND USE OF GUNTER/S SCALE. DIVISION being the reverfe of Multiplication, therefore extend from the divifor to unity, that extent will reach from the dividend to the quotient. Suppofe 64 to be divided by 4, extend from 4 to I, that extent will reach from 64 to 16, the quotient. N. B. This extent in Divifion is to be taken backwards from the dividend to the quotient,but in multiplication it is taken forward from the multiplicand to the product, they being contrary to one another. PROPORTION, or the RULE OF THREE, being performed by Multiplication and Divifion, therefore extend from the firft term ta the fecond, that extent will reach from the third term to the fourth. Example. If the diameter of a circle be 7 inches, and the cir- cumference 22, what is the circumference of another circle, the diameter of which is 14 inches? , Extend from 7 to 22, that extent will reach from 14 to 44 the fame way. In like manner may any other proportion, o r any denomination, be worked, which makes this line of general ufe, particularly in meafuring Superfices and Solids, which is done by extending rrom i to the breadth, that extent will reach from the length to the fu- perficial content. Example. Suppofe a plank or board 15 inches broad, and'27 feet lone;, the content of which is required. fixtend from i to I foot 3 inches, 1.25, that extent will reach from 27 feet to 33,75 feet, the fuperficial content. Or extend from 12 inches to 15, &c. The folid content of any bale, box, chefr, &c. is found by ex- tending from i to the breadth, that extent will reach from the depth to a fourth number, and the extent from I to that fourth number, will reach from the length to the folid content. Example I ft. What is the content of a fquare pillar, whofe length is 21 feet 9 inches, and breadth i foot 3 inches? The extent from i to 1,25, will reach from 1,25 to 1,56, the content of i foot in length; again, the extent from i to 1,50, will reach from the length 2 1,75 to 33,98 or 34, the folid content infect, Example 2d. Suppofe a fquare piece of timber, 1,25 feet broad, 56 deep, and 36 long, be given to find the content. Extend from i to 1,25, that extent will reach from ,56 to ,7, then extend from i to ,7, that extent will reach from 36 to 25,2 the folid content. In like manner may the contents of any bales, &c. be found, which, divided by 40, will give the tonnage. 3dly. The line of fines, marked (Sin.) begins at the left hand, and is figured thus: i, 2, 3, 4, 5, &c. to 10; then 20, 30, 40, &c. to 90, ending at the right hand, where is a brafs centre pin, here, and in all lines under it, are called degrees. 4thly.The line of verfed fines, marked (V.S.) begins at the right hand, againft 90 on the fines, and from thence figured towards the left hand, thus : 10,30,30,40, &c. ending at the left hand about ON THE DESCRIPTION AND USE OF THfc SECTOR. 17 169; each of the fubdivifions, from 10 to 30, are 2 degrees, and from thence to go, it is fingle degrees, and from thence to the end, each degree is divided into 15 minutes. 5thly. The line of tangents, marked (Tang.) begins at the left hand, as do the fines ; from thence it is figured to the right hand, thus : 1,2,3, &c. to 10, and fo on, 20, 30, 40, and 45, at the right hand, where is a little brafs pin, juft under and even with 90 in the fines ; from thence back again it is figured 50, 60, 70, 80, &c. to 89, ending at the left hand where it began at i degree. The fubdivifions of this line are the fame as thofe of the fines. 6thly. The line of the meridional parts, marked (Mer.) begins at the right hand, and is numbered thus : 10, 20, 30, to the left hand, where it ends at 87 degrees. This line, with the line of equal parts, marked (EP) under it, are ufed together, and only in Mercator's failing. The uppermoft line contains the degree of the meri- dians, or latitude, in a Mercator's chart ; and the lower is the equator, and contains the degrees of longitude. ON THE DESCRIPTION AND USE OF THE SECTOR. THfS inftrument confifts of two legs or rulers, reprefenting the radius of a circle, moveable round a joint in the centre; on each face are drawn feveral lines or fcales from the centre to almoft the end of the legs, and are drawn on both legs, that every fcale may have its fellow, and are called fe&oral lines. There are other lines drawn parallel to the edges of the legs, and muft be ufed with the feclor quite open, the ufe of which is explained in the defcription of the Gunter fca)e. On one face arc two lines of chords to 60 degrees, marked Cho. or C. two fcales of equal parts to 10, marked Lin. or L. two lines of fecants to 75 degrees, mark* ed Sec. or S. two lines of poligons marked p.;l. Upon the other face the fectoral lines are two* fcales of fines to 90 degrees, marked Sin. or S. two lines of tangents to 45 degrees, marked Tan. or T. two lines of upper tangents to lupply the defect of the former, ex- tending from 45 degrees to 75 degrees, and marked t. feveral pair of fecloral lines are numbered from the centre, and fo arranged as to make equal angles at the centre ; therefore, at whatever dif- tance the fector is opened, the angles will always correfpond ; that is, the diftance or radius from 60 to 60 on the line of chords, are equal to 10 and 10 on the line of lines, 45 and 45 on the line of tangents, and 90 and 90 on the line of fines. The lines of chords, fines, &c. are conftruted as thofe on the Gunter fcale, making 60 on the line of chords the radius of the circle. C - The l8 ON THE DESCRIPTION AND USE OF THE SECTOR. The fedloral lines are like fo many fimilar triangles, namely, that their correfponding fides are proportional, thus : let AC, AE, reprefent in plate I. fig. i. a pair of fe&oral lines,, forming the angle CAE, divide each leg into any number of equal parts (fav r 10) draw lines to any of the correfponding numbers, and each will be a fimilar triangle to CAE, and if the lines AC, AE, ; fhould re* prefent the line of chords, fines, or tangents, and CE the radius, and D on the chord, fine, or tangent, any propofed number, then the tranfverfe rneiifure BD will be the chord,, line, or tangent of that number. Indefcribing the ufe of the fecl:or, the term lateral dijlance is the diftance on one leg, only taken from the centre to any part of a fe&oral line; and the tranfverfe diftance is that taken between any two correfponding divifions on a fcale of the fame name. All are meafured on the lines of each fcale that aie nearest each other. Tbe Line o-f Ltnes^ or Prc-poriivnal Scale, The line of lines is ufed to divide a given line into any number of equal parts : fuppofe for example 8 deg. take the length of the line given in the compafles, and make it a tranfverfe diftance from 8 to 8, then will the tranfverfe diftance from 1 to i be one of the equal parts, or - s of the whole ; from 2 to 2 will be the 2d, &c. ; but if the line to be divided be too long for the legs of the lector, make any divillon fo that it may be applied to trie lector, mul- tiplying each tranfverfe diftance by the fame number you divided by. To find a fourth proportional to any 3 given lines or numbers, as fuppofe 6, 2, and 4, take the lateral diftance of 2 in your com- pafies, and make it the tranfverfe diltance at 6, then the tranfverfe, diftance of 4 will give the lateral diftance of i and ~\. Or if a fhip iailed 64 miles in 8 hours, how many miles did {he fail in 5 hours at the fame rate of failing ? lYJake the lateral diftance of 64 the tranfverfe diftance at 8 and 8, then the tranfverfe diftance of 5 and 5 will give the lateral diftance of 40, the fourth proportional. Having a chart conftru&eci upon a fcale of 5 miles to an inch, the feror i? adjufted to a correfponding fcale, by making the tranf- verfe diftance from 5 to 5 equal to one inch. And to reduce a chart of 6 inches to a degree, to one of 4 inches to a degree, make the tranfverfe diftance of 6, 6, equal to thj lateral diftance of 4, then any diftance from the chart let off latei ally the carrel- ponding tranfverfe diftance will be the diftance required. And if you have a chart of 3 inches to a mile, to enlarge to 5 inches to a mile, make the tranfverfe diftance of 3, 3, equal to the lateral dif- tance of 5, and proceed as before. A third proportional is found to two numbers ; thus having 6 and 4 given to find a third propor- tional, make the traiiiVerfe diftance at 4 and 4, the lateral diftance of LOGARITHMS. 1$ of 6, then the lateral diftance of 4 will give the tranfverfe diftance of 2,66 nearly. Ufe of the Line of Chords. The line or fcale of chords is ufed for protracting any angle ; you open the fe&or to any radius within compafs of the inftru merit, and the tranfverfe diftance of any degree required is to be laid down on the circumference of the circle; but if you want it to any particular radius, as, for inftance, to one inch, make the tranfverfe diftance between 60 and 60 equal to I inch, then you may take oit tranfverfly any degree under 60, but for any degree above 60, lay off the radius firft on the circumference, and the excefs above 60 taken tranfverfely, are to be laid off-on the circumference from the radius juft before laid down. The meafure of any angle is found by taking the diftance of the legs on the circumference, and applying it tranfverfely on the line of chords. Qf the Lines of Sines ^ Tangents^ and Secants. The tranfverfe diftancs on the line of fines {hews the decrees, &c. required ; and the tranfverfe diftance on the line of tangents to 45, do the fame. But to lay off a tangent 'above 45 degrees, you mull take the radius of the tangent 45, and open the fetor that the radius juft taken may juft reach to 45,45 on the line of upper tangents marked t, or on the beginning of the fcale of fecants, theut the fe&or is adjufted to take any tangent above 45 degrees, or any fecant to 75 degrees. The Line of Poligons. Open the fe&or tbat 6,6 be equal to the radius, then the tranf- v.erfe diftance of any of the numbers on the fcale will divide the circle into as many fided poliggns. LOGARITHMS. IOGAR1THMS are a .feries of numbers^ invented by Lord j Napier, Baron of iVfarchinfton, in Scotland, by which the work of multiplication may be performed by addition, and the ope- ration of divifion may be done by fubtra&ion ; fo that great time and trouble are faved thereby in the performance of all arithmetical operations; for if the logarithm of any two numbers be added to- gether, the fum will be the logarithm of the product; and if from the logarithm of the dividend you fubtra.} the logarithm of the di- vifor, the remainder will be the logarithm of the quotient. Again, if the logarithm of any number be divided by 2, the quotient will be the logarithm of the fquare root of that number; or, if the loga- rithm ot any number be divided by 3, the quotient will be the loga- rithm of the cube root of that number. C2 The 20 LOGARITHMS. The moft convenient feries now made ufe of is the following : Jl ' 2 3__ 4- 5 &c. index. i 10 100 IOGO 10000 jooooo, &c. logarithms. By which you perceive the index of any logarithm always one lefs than the number of figures the integer contains. To find the Logarithm of any Number containing lefs than 5 Figures. EXAMPLES. I would find the logarithm of 7 ? Look in the table for the number of 7 in the fide column, and againft it is 0.84510, This number having but one figure, the index thereto is o. I would find the logarithm of 79 ? Look in the table for the number of 79 in the fide column, and againft it is 1.89763 ; to which i is the index, becaufe the number contains two figures. I would find the logarithm of 763 ? Againft 763, in the firft fide column, is 2.88252 ; to which prefix the index 2, as the number contains 3 places of figures, 2.88252. To find the Logarithm of 7634. Find the logarithm of the three firft figures in the fide column as before ; and, cafting your eye on the numbers on the top line of the table, look for the remaining figure 4, bring your eye to bear down that column,and right againft 763 is the logarithm 88275, to which prefix the index 3, as it contains four places of figures, thus: 3.88275 is the logarithm of 7634. To find the Logarithm of any whole Number to 5 Places of Figures. Suppofe 76345 ? Look out the logarithm of the three firft figures 763 in the fide column, and the next figure 4 in the top column as before, and againft the angle of meeting is 88275, as before. Take the differ- ence between this logarithm and the next greater ; that is, the difference between 275 and 281, which is 6 j then fay, by the rule of three, if 10 gives 6, what will 5 give? that is its half or 3; which, adde as above ; then fay, if 100 gives 6 difference, what will 58 give i 1 Anfwer 3 ; which, added to 88275, makes 88278 ; to which prefix its index 5, makes the logarithm of 763458*10 be 5.88278. LOGARITHMS. tl To find the Logarithm of any mixed Number, #5763.458. 9 Where the integer is 763, or has only three places of figures, the rule is: Find the logarithm to all the figures, the fame as if they were whole numbers as before, to which prefix always the index of the integer, which in this number is 2 ; fo that the log. of 763.458 is 2.88278, nearly the fame as above, only differing in its index. To find the Number anfwering to any Logarithm to 4 Places of Figures. Seek under the column o, at the top of the table, the next lefs logarithm \ note the number againft it, and carry your eye along that line until you find the neareft logarithm next lefs than the given one, and you will have the fourth figure at the top of the ta- ble, which affix to the three given ones in the firfl fide column. What is the number to the logarithm 3.77342 ? I look in co- lumn o, and find under it, againft the number (93> the logarithm 7705 ; and, guiding my eye along that line, I find the given loga- rithm 77342 under the column, with 5 at the top; fo that the number is 5935. The Number^ if taken out ly tins precept^ will be either the Number required^ or the next lefs.- To find the Number anfwering any Logarithm to 5 Places of Figures nearly. Find the next lefs logarithm to the given one, and take the differ- ence betwixt it and the given one ; alfo take the difference betwixt the next greater logarithm, and next Jefs to the given one ; then fay, as the difference of the next greater and next lefs is to 10, fo is the former difference to the correction fought ; as, fuppofe you, would find the number to the logarithm 4.59632. 4.59632 4.59627 Theneareft next log. I can find is 59627115 num. 39470 The next greater ditto is 59638 5 - Difference ir 10 Then fay, n : 10 : : 5 : 5 nearly the correction ; which I add to the number 39470, makes the number fought to be 3947 5, anfwer- ing to the logarithm 4.59632. NOTE. Aliquot or even parts may be taken of the difference between the lefs and greater logarithms, where it can be done, thus : In this laft 5 is nearly the half of 1 1, as 5, the number fought, is of ro, the difference of the two numbers belonging to the greater and ]e> logarithms, which will often fave time and trouble. MULTI- LOGARITHMS. MULTIPLICATION BY LOGARITHMS. CASE I. To find the Produtt of two whole or mixed Numbers. Multiply 76 Log. = 1.88081 Multiply 76.4 Log. = i. 88309 b 7 54 i- 7 3 2 39 by 5.4 0.73239 Product 4104 =3.61320 j Product 4.12.56 =2.61548 CASE II. When both, or either, of the fractions are lefs than unity, as if 0.265 Log. 9.42325 Here the index of a fraction is 9, when 0.031 8.49136 the fir fl: decimal figure, as 2, ftands in _ the firft decimal place ; but if it fhould .008215 7-9 1 461 ihmd in the ieconr decimal place, as the 3 in .031, the index will be 8 ; if it Hood in the third decimal place, as .0031, the index would be 7. Thus the number of cyphers pre- fixed to any decimal, ar:d the index of that decimal, always together make 9 ; fo that if you take the number of cyphers prefixed to the decimal from, 9 remains its proper index. In the addition reject 10 in the fum of the indices ; and the proper product,, or value of the product, will be obtained : By reafon, if 9 reprefent the index of a fraction, 10 will reprefent, in this cafe, the index of unity. Indeed the index of unity maybe afTumed either o, 10, 100, &c as you pleafe ; but generally, for moft ufes, is not wanted to be more than 10, as in the line?, tangents, fecants, &c. As 7 or 8 places of de- cimals are generally fufficient for all purpofes, take thefe two more examples : Mntiply 3.72 Log. =0.57054 by 0.00064 6.80618 Produd. 0023808 7.5/672 Multiply 59.4 by .000031 5.49136. Product .0018414 7-265 Here the remainder to 9 is 2 in the index ; therefore piefix two cy phers to the number of the log. 23808 for the product required. DIVISION BY LOGARITHMS. CASE I. To divide a whole or mixed Number by a lefs whole or mixed Number \ RULE. From the logarithm of thedividend fubtract the logarithm of the divifor, and the remainder is the logarithm of the quotient. Divide 4104 by 54. 4104 Its logarithm is 3.61321 54 Its logarithm is 1.73239 76 Quotient ~ 1.88082 Divide 410.4 by 54. 410.4 Its logarithm is 2.61321 5.4 Its logarithm is 0.73239 76.0 Quotient = 1.88083 CASE LOGARITHMS. CASE II. When both, or either, fractions are lefs than unity ? As divide .008215 by .031 Its log. is Its log. is 7.91461 8.49136 .265 Product 9.42325 NOTE. In the indices here I borrow 10, in the fame manner as I flung it away in addition. Divide .0023808 by 3.72 .0023808. Its log. is 7.37672 3.72 Its log. is 0.57054 NOTE. -If I had afiumed the index of unity 100, then the index of the firft number would have been 97 or 97.91461, and.cji 98.49136 99.42325 So that 99 is the index of the firft decimal place under i coin this cafe. Divide 59.4 by .00003 1 . 59.4 Its log. is 1-77379 .000031 Its log. is 5 .49 136 .00064 Quotient 6.80618 ,0001915 Its quotient 6.26515 NOTE. Whatever index you make reprefent unity, omit it in the fum of the indices, and borrow it in the fubtra&ion of indices, the fum or remainder will be the true index required. To EXTRACT THE ROOTS IN LOGARITHMS. As- the multiplying the logarithm of any number by the index of its power produces the logarithm of that power ; fo the divifion of any logarithm by its propofed index, the quotient will be the lo- garithm of the root required. \Vhat is the fquare root of 324 ? 324 Its logarithm is 2)2.51054 1 8 Log. of the root is What is the cube root of 10648 ? 10648 Its log. is 3)4.02627 22 l^g. of the root is .34209 1.25527 To find any propofed root of any decimal fraction, you muft hrft prepare the index for the divifion of the propofed power, thus : .For the fquare you muft add 10 to th- index before you divide it ; for the cube you muft add 20 to its in ex before you divide it \ and .fo on for the root of any power propofed. ExAMfLE. What is the fquare root of 001849? ,001849 Its log. is 7.26694 Add jo. 2)17.26694 What is the cube root of 1 25 ? .125 The log. is 9.09691 Add 20. Sum 3)29.09691 .5 Its root 5= 9.69897 m i .04.3 The log, of thei , . rgot is / -.*** The LOGARITHMS. The APPLICATION of LOGARITHMS in meafuring Boards, Timber, Glafs, Stone, and all kinds of Pack- ages, ufualty taken on board Ships*. Required the content of a piece of glafs 2.9 foot long, and 1.75 broad ? Log. of 2. 91=0.46240 1.75-0.24304 Kequired the content of a board or plank 9f feet long and i| foot broad ? Log. of 9! or 9; 5 is 0.97772 if or 1.25 is 0.09691 5.075 =0.70544 The content is 5.075 feet. 11.88 nearly log ofcont. 1.07463 or ii feet io inches nearly. In like manner may any dimenfions be fquared, and the content be found. If the folid content be required of anyljox, bale, &c. add the lo- garithms of the length, breadth, and depth together, the fum will be the log. of the folid content. EXAMPLE. What is the folid content of a box whofe depth is 2. 7, Breadth 2. 3, and length 4. 5 feet. 2. 7 Its log. is 0.43136 2. 3 Its log. is 0.36173 4. 5 Its log, is 0.65321 Sum equal the log. of the content 1.44630:^4111^27.950128 feet nearly. The diameter of a cafk at the head and bung, slid alfo its length, being given, to find its content in beer and in wine meafure ? ill. Multiply the difference of the head and bung diameter by 0,7^ and add the product to the head diameter for a mean diameter. RULE FOR WINE MEASURE. Placedown the log. of the mean diameter twice the log. of the length, and under thefe two the content log. 7,53148, the fum of thefe four logarithms will be the log. of the content, abating 10 in the fum of the indices. RULE FOR BEER MEASURE. Put this conftant log. under the two former logs, always 7.44484 the fum of the four logs, will be the content for beer gallons, abat- ing 10 in the index. * The AUTHOR has lately publiftied an improved GUN TER'S SCALE, on which the foot is divided into ten equal parts, and -thefe parts fubdivided into ten equal parts, for the purpofe of taking dimenfions, and calculating by logarithms or de- cimal fractions. EXAM- LOGARITHMS. 2$ Ex AMP IF, What is the content of a cafk whofe heau diame- ter is 20, the bung diameter 28, and length 40 inches ? Bung diameter 28 Head diameter 20 8 Difference. _7 5.6 Number to be added to The head diameter 20.0 Mean diameter 25.6 FOR WINE. Lo. of meandiam.~ < ** { 1.40824 Length 40= 1.60206 Conftant log. 7.53148 FOR BEER. $1.40824 7 1.40824 7 A A A RA .44404 Anf. 73 gall. =1.86338 of beer Log. of 89.13 gallons 1.95002 the content for wine. The way thefe two conftant multiplying logarithms were found is thus : ift. The area of a cjrcle, whofe diameter is unity, is 7854 de- cimal parts of the fquare thereof; fo that if the fquare of the dia- meter of any circle be multiplied by ,7 854, the product wilt be the area of the given circle: hence ,7854 is always a cor.ftant quantity whofe logarithm is 9.89509. 2d. If the area of a circle be divided by 231, the number QI inches there are in a wine gallon, the quotient will be the number of gallons that circular area contains, at i inch deep: hence 231 is a conftant divifor. Its logarithm is 2.36361, the arithmetical com- plement of which is 7.63639, which I add to the former conftant logarithm 9.89509 The fum 7.53148 abating 10 in the indices, is the conftant loga- rithm to be added, as per rule, for wine meafure. For beer meafure the divifor is always 282, its log. is 2.45025, whofe arithmetical complement is 7.54975 Add the conftant log. 9.89509 Sum 7.44484, the conftant loga- rithm for beer meafure, as per rule, omitting 10 in the index, or fubtn\t 2.45025 from 9.89509 Take 2.45025 Remains 7.44484, the fame as above. D The ? LOGARITHMS. The common Way of finding a Ship's Tonnage at London, RULE. Multiply the length of the keel by the breadth of the beam, and that produft by half the breadth of the beam, and divide .the lad product by 94, and the quotient anting is the tonnage. EXAMPLE. Suppofe a fhip 72 feet by the keel, and 24 feet by the beam, what is the tonnage ? Length 72 - log. is 1.85733 greadth 24 r- do. 1.38021 Half-breadth 12 do. 1.07918 Arith. complement of log, of 94, do. 8.02687 Tonnage 220.6 2.34359 Anfwer. To find the Logarithm of the Situs, Tangents^ and Secants , belonging to any Number of Degrees and Minutes required. If the required degrees be lefs than 45, feek the degrees on the top, and the minutes in the left-hand column, marked M, againft which, in the column figned at the top with the propofed name, ftands the fine, tangent, .and fecant required ; but when the degrees given are more than 45, Jeek the degrees at the bottom, and the minutes in the right-hand column, marked M at the bottom, and the propofed name at the bottom. Here it may be obferved, that the degrees at the top, and minutes at the left-hand column, added to the degrees at the bottom and minutes in the right-hand column, always make 90 ; hence, if a fine be looked for, the co-fine or com- plement will be found in the adjoining column, the fame may be bferved of tangents and fecants. EXAMPLE I. Required the log. fmeof28 P 37'? Find 28 at the top of the page, and, in the left-hand column, marked M at the top, find 375 againft which, "in the column marked with the word Sine, ftands 9.68029, the logarithm of the fine of 28 37' required. The Ex AMPLE II. Required the log. tangent of 67 45' ? Find 67 at the bottom of the page, and 45' at the right-hand column marked M at the bottom; againft this, in the column mark- ed Tangent at the bottom, ftands 10 388 1 6,which is the logarithm^ required, fame maybe pbferved of tangents and fecants. Having the fine, tangent, and fecant, the co-fine, co-tangent, Co-fecant, are always found in the adjoining columns. The logarithm to any number of degrees above 90, is found by fubtrafting the given degrees from 180, and taking the logarithm pf the remainder ; or,, if 90 be fubtrafted from the given fine, and log. confine of the re,roajnde.r be taken, it will give the fame. LOGARITHMS. 2J fojind the Degrees^ Minutes^ and Seconds, correfponding to any given Logarithm. If the degrees, minutes, and feconds, be wanted to a given loga- rithmic fine, or co-fine thus found, and the next greater, and the next lefs than the given logarithm) and the difference between the given logarithm and the next lefs if a fine, and the next greater if a co-fine ; then fay, as the difference between the next greater and next lefs is to 60", fo is the difference between the next lefs, if a fine, and the next greater if a co-fine, to the number of feconds to be annexed to the degrees and minutes found before. EXAMPLE I Find the degrees, minutes, and feconds, corre- fponding to the log. fine 9.61405 ? Next lefs log. 9.61382 Next lefs log. 9.61382 Next greater 9,61411 Given log, 9.61405 29 23 Here the given log is found ftanding between 24 16', and 24 if-, then, as 29 is to 60, fo is 23 to 48, which, annexed to 24 16', gives 24 16' 48", anfwering to log. 9.61405. EXAMPLE II. Find the degrees, minutes, and fecends, corre- fponding to the log. co-fine 9.43297. ? The neareft found between 74 16', and 74 if. 74 1 6' Next greater log. 9.43323 Next greater log. 9.43323 74 if Next lefs 9-43 2 7 8 Given log. 9-43^97 Biff. 45 DifT. 26 Now, as 45 is to 60, fo is 26 to 34", which, annexed to 74 16 gives 74 16' 34", the degrees, minutes, and feconds required. To find the Logarithm of the Sine or Co~fme^ for Degrees^ Minute^ and Seconds. RULE. Find the logarithm to the degrees and minutes as be- fore ; take the difference between the logarithm and the next greater in the fine; but, if a co-fine, the next lefs ; multiply this difference by the odd feconds, and divide the product by 60 5 add the quotient to the right hand of the log. of the degrees and mi- nutes, if a fine, butfubtraft it if a co-fine, the fum or difference will be the logarithm, fuie, or co-fine required. D 2 EXAMPLE 28 GEOMETRICAL PROPOSITIONS. EXAMPLE!. Required the log. r* r - r\ s i r\t *k Sine of Sine of fine of 24 1 6' 48"? i6/ 9.61382 9.61411 Diff. 29 Now 29 multiplied by 48 gives 1392 ; this, divided by 60, the quotient, is 23, which, added to 9 61382, gives 9.61405, the lt>g. of 2 4 1 6' 48". EXAMPLE II. What is the log.-' co-fine of 74 16' 34"? Log. co-fine of 74 16' 9.43323 Log. co-fnre of 74 17' 9.43278 Diff. 45 Now 45 multiplied by 34= 1530; this, divided by 60, gives the quotient 26 nearly ; and 26 fubtra&ed from 9.43323, leaves 9.43297, the log. co-fine of 74 16', 34". If the giverUeconds be I, |, f, j, or |, or any other even parts of a minute, the like parts rnay be taken off the difference of the logarithms, and added or fubtracted as above, which may be fre- quently done by infpe&ion. To find the Arithmetical Complement of any Logarithm. The complement arithmetic of any logarithm, is what it wants of 10.00000 or 20.00000, and is ufed to avoid attraction. For finding it this is the rule: Take the refidue or remainder of the rirft figure from 9, and fo of the reft, till you come to the laft figure ; of which take its remainder from 10^ and it is done. EXAMPLE I. I would have the complement arithmetic of 9.62595 ? For the firil figure 9, write o ; for 6, 3 ; for 2, 7 ; for 5, 4 ; for 9, o ; and for the laft figure 5, write 5 ; arrd fo you have 0.37405 for the complement arithmetic fought. EXAMPLE II. The complement arithmetic of 10.33133 ? For o, write 9, and fo on as before directed, and then you will have 9.66867, which is the complement arithmetic of 20.33133. Or thus : From Take JO.COOOO 9.62595 From Take 20.00000 IO-33I33 0.37405 9.66867 It will be necefiary for the Reader to make himfelf well acquaint- ed with the following proportions, as he will find them uieful when he goes into Trigonometry, which are here rendered plain and eaiy to be undsrftopd : PROPOSITION I. If a right line frauds upon, or meets with another right line, and makes angles with it, the two angles taken together will be two right angles, or two angles equal to two right angles, GEOMETRICAL PROPOSITIONS. Let the line CD meet AB in D; on D ere<9" the perpendicular DE 5 with the chord of 60 in your compares, and one foot in D defcribe the arch AEB, which will be a femicircle or 180; of which AB is the diameter, and the angles ADE and BDE are quadrants, each 90, becaufe ED is perpendicular to AB ; now the angle BDC is lefs than 90, fince the two angles together make neither more nor lefs than 180 or a femicircle ; confequently any number of right lines ftanding upoa the fame fide oFthe line AB, and coming from the fame point D, the fum of all the angles formed by fuch right lines, cannot exceed 1 80. If the angle BDC be fubtracted from 180, the remainder will be the angle CDA ; or if the angle ADC is given, the angle BDC is found in the fame manner. PROPOSITION IT. If two right lines crofs each other, the an- gles which are oppofite are equal one to the other. Let the two lines AD and CB crofs each other in the point E. With the chord of 60, or any convenient radius, in your com- pafles, and one foot in E, defcribe a circle ; then, by meafuring the angles, it will be found that the angle AEB is equal to the angle CED, and that the angle AEC is equal to the angle BED; for the angle AEB, added to the angle AEC, makes a femicircle ; and fo do the angles BED and DEC ; and all the angles taken together, make 360. PROPOSITION III. If a right line crofs two parallel lines, the outward angles will be each equal to the inward and oppolke onei. Let the lines AB and CDbe parallel lines, and EF the line that cuts them in the points G and H. With the chord of 60 in your compares, and one foot on G and H, defcribe the arches BEA and DFC, which will bs each a femicircle ; now, by meafuring the angles BGE and AGE, they will be found equal to the angles DHE and EHC, and each equal to 1 80, by the firft proposition. In like manner it may be proved, that the two outward angles are c to the two inward and oppofite ones. PRO* 3^ GEOMETRICAL PROPOSITIONS* PROPOSITION IV. In every plane triangle, whether right of oblique, the three angles are equal to two right angles, or 1 80. In trie triangle A G B draw C D parallel to A B through the point G ; on which point, with the chord of 60, or any- convenient radius,' defcribe a circle ; and, with the fame radius^ on A and B defcribe arches ; now, by the laft proportion, the angle AGB will be equal to the angles FGE, and the angle ABG will be equal to the angles CGE, and the angle BAG is equal to the angle DGF : now, fince the oppofite angles are equal, the angles DGF, FGE, and EGC, together, make a fe- micircle, or i8o 9 ; therefore it is plain that the three angles of a plane triangle, whether right, acute, or obtufe, together, are equal to two right angles or 180; hence it follows that, as the right angle BAG, Fig. 2, is 90, the other two acute angles, ABG, and AGB, taken together, can be no more than 90; therefore, if one of the acute angles, in a right-angled triangle, be given, the other is found by fubtra&ing the given angle from 90. And in any oblique-angled triangle, if one of the angles be given, the fum of the other two is found by fubtra&ing the given angle from 1 80; and if two angles are given, the third is found by fub- tracling the fum of the two angles from 180. PROPOSITION V. In every plane triangle, if one of its fides be produced, the outward angle will be equal to the two inward oppofite angles, Let ABC be the triangle, and CD the fide produced, with the chord of 60, or any other radius, defcribe arches on AB and C, draw CE parallel to A B ; then, by the third propofition, the angle ACE muft be equal to the angle BAG, and the angle DCE equal to the angle CBA; therefore the outward angle DCA is equal to the two inward oppofite angles ACB, and BAC; which may be eafily proved by meafuring the angles by the line of chords on the plane fcale. NOTE. I hope the learned Mathematician will excufe the me- thod here taken of demonflrating the above propofitions in a me- chanical manner, judging it befl adapted to the capacity of thofe for D TRIGONOMETRY. for whofe ufe this book is intended, not doubting but the Teacher will, as I always do, demonftrate them in a more geometrical manner to thofe v/ho are capable of receiving fuch. TRIGONOMETRY. PLAIN Trigonometry is the art of meafuring plane triangles, by comparing the fides and angles together by known analo- gies; whereby three things being given, a fourth may be found, on condition that one of them be a fide : but as angles are rneafured by the arch of a circle, defcribed upon their angular points, and the proportions that thefe arches bear to right lines cannot be ex- actly found ; therefore the writers on Trigonometry have applied right lines to thefe arches, that the proportion they bear to the fides of a plane triangle may be found. The right lines applied to a circle are: ift. A CHORD, or the fub- tenfe of an arch, is a right line that divides the circle into two unequal parts, and is a chord to them both, as DH is the chord of the arches DH and DAH. 2d. A RIGHT SINE of an arch is, a right line drawn from one end or termination of an arch perpendicular to the ra^ dius ; or it is half the chord of twice the arch ; fo that RS is the fine of the arch AS, and SZ the co- fine. 3d. A VERSED SINE is that part of the diameter contained between the right fine, and* the arch, as RA and RCD, is the verfed fine of SHD, or DEP, its equal. 4th. A TANGENT of an arch is a right line drawn perpendicu- lar to the end of the diameter, jufl touching the arch } as AT is the tangent of the arch AS, and HG the co-tangent. 5th. A SECANT of an arch isa right line drawn from the centre through the circumference, and produced until it cuts the tangent as CT. NOTE. -The fine, tangent, and fecant of the complement of through where that cuts the arch draw AC to cut AB in A, and it is done; for BA being meafured on the fame fcale that BC was, will be 213,1, and AC 308,6 miles. By making the Hypothenufe AC Radius, it will be, r t / > . 1 52X 3 "325 c To find the perpendicular AB. As fine ang. A 56 45' 99223;; Js tothe bafe BC 325 2.51188 So is fine ang. C 33 15' 9-73901 12 2C Totheperpen.AB2i3,i 2.32854 To find the hypothenufe AC. As fine ang. A 56 45' 9.92235 Is to the bafe BC 325 2.51188 So is radius 90 10.00000 12.51188 9.92235 Tothe hypoth. AC388,6 2.58953 By making the Bafe BC Radius, it will be, To find the perpendicular AB. As radius 90 10.00000 Is to the bafe BC 325 2.51188 So is tang. ang. C 33 15' 9.81666 12.32854 10.00000 To the perpen, AB 313,1 2,32854 To find the hypothenufe AC. As radius 90 10.00000 Is to the bafe BC 325 2.51188 So is fee. ang. C 33^ 15' 10.07765 12.58953 IO.OOOOO Tothehypoth, AC 388,6 TRIGONOMETRY. By making the Perpendicular AB Radius, it will be, To find the perpendicular AB. As tang. ang. A 56 45' 10.18334 Is to the bale BC 235 So is radius 90 2.51188 12.51188 10.18334 Tothe'perpen, ABzij,! 2.32854 To find the hypo'henufe AC. As tang. ang. A 56=45' 10. * Is to the bafe BC 325 . So is fee. ang. A 56 ^y 10.26099 12.77287 _' 0.1 8334 To the hypoth. AC 388,6 2.58953 By GUNTER. < Extend from 56 degrees 45 minutes, to 33 degrees 15 minutes, on the line of fines, that extent will reach from the bafe 325, to the perpendicular 213,1, on the line of numbers. 4 2dly. c Extend from 50 degrees 45 minutes to radius on the line of fines, that extent will reach from the bafe 325, to the hy- pothenufe 388,6 on the line of numbers.' CASES IV. and V. The Hypothenufe and one Leg givcn^ to find the Angles and the other Leg. The Lea; AB 91, the hypothenufe 170 given, to find the angle ACB, or BAG, and the leg BC. By CONSTRUCTION. Draw BC at pleafure, on B A, erect the perpendicular BA, which make equal to 91, take 1 70 in your compafies, and, with one foot on A, lay the other on the line BC, and join A and C, and it is done ; for the angle C will be 32 22', the angle A 57 38', and BC 143,6. U3.6 By making the Hypothenufe Radius, it will be, To find angle C. As the hypoth. 170 2.23045 Is to the radius, So is the perpend. 91 TO-OOOOO i.-9594 11.95904 2 23045 To fine ang, C 32 22' 9.72859 To find the bafe CB. As radius 10.00000 Is to the hypoth. 170 2.23045 So is line ang. A 57 38' 9.92667 To the bitfs 143,6 12.15712 IO.OOOOO 2.15712 TRIGONOMETRY, By making the Perpendicular Radius, it Will To find the angle A* As the perpendicular 91 1.95 904 Is to the radius 10.00000 So is the hypoth. 170 2.23045 12,23045 1,95904 To fee. ang. A 57 38' 10.27141 To find the bafe BC. As the radius lo.coooo Is to the perpend. 91 1.95904 Sois tang. ang. 57^38' 10.19005 To the bafe H3>6 12.15709 10.0000 2*15709 By GUNTER* c Extend from hypothenufe 170 to the perpendicular 91 on the line of numbers 5 that extent will reach from radius to fine angle C, the complement of angle A 32 degrees, 22 minutes, on the line of fines. 2dly. * Extend from radius to fine angle A 57 degrees, 38 mi- nutes ; that extent will reach from the hypothenufe 170, to the bafe 143.6 on the line of numbers.* CASE VI. The Legs given, to find the Angle and tiypotbenufe. The legs AB 890, BC 787 given, to find the angle BAG, or ACB, and the hypothenufe AC. By CONSTRUCTION. Make BC~787, and on B erect the perpen- dicular BA, which make equal to 890; join AC, and it is done ; for the angle C will be 48 31'; confequently, the angle A 41 29', and hypothenufe 1188. By making the Bafe Radius, it will be, To find angle C. As the bafe 787 2.89594 Is to rad. tan. 45^ 10.00000 So is the perpend. 890 2.94939 To find the hypoth. AC. As rad. tan. 45 io.ooooo Is to the bafe 787 2.89597 So is fee. ang. C 48 3*1 ' 10.17888 12.94939 2.89597 * 3-74 8 5 IO.OOOOO To tan. ang. =48 31' 10.05342 To the hyp. AC=s 1 182 3.07485 By TRIGONOMETRY, 41 By making the perpendicular radius, it will be, To find anle A. As the perpend. 890 Is to rad. tan. 45 So is the bafe BC=;S7 2.94939 10.00000 2.89597 12.89597 2.94939 To find the hypoth. AC. As rad. tan. 45 10.00000 Is to the perpend. 890 2.94939 So is fee. ang. A 41 29' 10.12543 13.07482 IC.OOOOO To tan. ang. A 41 29' 9.94658 To the hyp. AC 1 1 88 3.07482 By GUNTER. * The extent from 787 to 890 on the line of numbers will reach from radius (or 45 degrees) to 41 29' on the line of tangents. 2dly. 4 The extent from fine angle C 48 degrees, 31 minutes, to radius, or 90 degrees, will reach from the bafe 890 to the hy- pothenufe 1188, on the line of numbers/ ^hie/lions to exercife the Learner in Trigonometry* Queft. I. The hypothenufe 496 miles, and the angle oppofite to the bafe 56 15' given, to find the bale and perpendicular. Anf. Bafe 41 2,4, and the perpendicular 275,6 miles. Quejl. 2. The perpendicular 275 leagues, and the angle oppofite* to the bafe 56 15' given, to find the hypothenufe and bafe. Anf, The hypothenufe 495, and bafe 41 1,6 leagues. Queft. 3. The bafe 33 yards, and the angle oppofite to the per- pendicular 53 26' given, to find the hypothenufe and perpendi- cular. Anf. Hypothenufe 55,39, and the perpendicular 44,49 7 ar ds. Queft. 4. The hypothenufe 575, and perpendicular 50 miles given, to find the bafe. Anf. Bafe 572,8 miles. Queft. 5. The hypothenufe 59, and the bafe 33 miles given, to find the perpendicular. Anf. Perpendicular 48,9 miles. Queft. 6, The bafe 33, and perpendicular 52 leagues given, to find the hypothenufe. Anf. Hypothenufe 61,59 leagues. AH INTRODUCTION TO THE ART OF NAVIGATION. BEFORE we begin Navigation, it may not be improper to give the Learner fome idea of the Syftem of the Univerfe, commonly called the Solar, or Copernican Syftem, which is as follows >~ The Sun, that immenfe and amazing fountain of heat and light of the whole fyftem, is placed near the common centre of the or* bits of feven opaque fpherical bodies, which make their revolutions round it, in lefs or more time, according to their feveral diftances from it, Mercury is neareft to the Sun, and receives its light and heat from it, and revolves round it in ellipfts in two months and twen- ty-eight days, Venus is fomewhat higher in the fyftem,and defcribes its ellipfis found the Sun in feven months and fifteen days, and becomes our evening and morning ftar by turns. The Earth is next to Venus, and defcribes an ellipfis round the Sun in 365! days, or one year, which being at a greater diftance from the Sun than the former planets, and therefore receiving lefs of its light and heat, to make up the deficiency, the wife Author of Nature has eaufed a fecondary planet, called the Moon, to move round it in 27 days, 1 2 hours, and 44 minutes ; it receive* its light and heat from the Sun, and reflects it upon the Earth, which, in fomemeafure, compensates for the abfence of the Sun, during the winter feafons, in the North and South. Mars is ftill higher in the Syitem, and takes a larger circuit, re- volving round the Sun in I year, 10 months, and 22 days. Jupiter is the largeft of all the planets, and defcribes a large el- llpns round the Sun in u years, 10 months, 27 days; there are four Satellites, or Moons, moving round it ; they receive their light from the Sun, and refle.cl: it upon their primary planet, as the Moon does upon the Earth. Saturn revolves round the Sun in 29! years, has 5 Moons which move rouncj him, and is alfo furrounded with a prodigious ring or gtmofphere. The Georgium Bidus is the moft remote of all the planets, and is attended by two Satellites : the firft or neareft of which performs fynodical revolution in about 8 days and three quarters, * Thf SYSTEM An. Xclipse /" rtr Moon . I'uhli.tfuJ In' J.,.inhn* -ng. is fhe in ? / Long, left 15 . 40 E. Diff. of long. 27 . i5\V. Long, in u.^W. EXAM. X. A /hip from longitude i6q 20' W. lails weftward until Ihe differs her long. 41 20', what long, is Ihe in ? o , Long, left 160 . 20 W, Diff. of long, 41 . 2oVV r . Long. in 201 . 40 360 , oo 158 .2oE, Here it is plain, that the fhip has crolfed the opposite meridian, and, therefore, has come into a longitude of a different name. In failing due north or fouth, the fhip changes her latitude only ; and failing eaft or weft, her longitude ; but failing upon any other courfe, {lie muft change both latitude and longitude. Eaftina: or welting, in PJane Sailing, is called Departure or Me-, ridian Diftance. The inftrument ufed in meafuiing a fhip's way at fea, is the Log, Ships at fea are directed from one place to another by means of an inftrument called the Mariner's Ccmpafs, which is an artificial repreientatiori of the horizon uf every placa, by the means of a cir- cular piece ofpapsr, called a card, divided like the horizon into de- grees and points, which are called Rhumbs. Now the card being prope'rly fixed to a piece of- fteel, called the Needle, that has been touched with a loadftone, (whofe property is fuch as to caufe one end of the needle k> touched to point towards the north, when turn- ing freel, on fomething (upporting it) all the points of the card will "be directed towards the correfpcwding points of the horizon : Hence NAVIGATION. 53 Hence it follows, that in every place the north point of the card fhews the pofition of the meridian of that place, and fome one rhumb or point of the card will coincide with, or be directed along the track that makes any given angle with the meridian ; confe- quently, by the help of the card or compafs, a {hip may be kept in any propofed track or courfe. A rhumb line, or point, is a right line drawn from the centre of the compafs to the horizon, and is named from that point of the horizon it falls in with. The courfe is the angle which any rhumb line makes with the meridian, and is fometimes reckoned in degrees, and fometimes in points of the compafs ; fo that if a {hip fails upon the fecond rhumb, or N. N. E. the courfe is 22 degrees 30 minutes : and fo for any other. One Magnus, a (hepherd, nrft difcovered the loadftone by its flicking to the iron of his fend u Is ; whence the name Magnet was given to the ftone, or Magnetic Needle. Gio, of Naples, about 300 years ago, firft difcovered that a piece of iron rubbed on it, and then fijfpended, had the property of pointing to the north and fouth, and thence applied it to navigation. How to touch the Compafs Needle. Having two ftrong magnetical bars, lay the corrvpafs needle as nearly north and fouth as you can, with the intended north north- ward; join the two magnets in a line conliderably above the nee- dle, the north end of which being northward (round which end of each a notch is made) bring them down upon the needle, that the junction may be on its centre ; then draw them afun 'er along on each half of the needle, and continue the motion till they are eight inches clear of the needle's e; d, and, by a circular motion, join them, and bring them, to the centre as before, then fep^rate them, repeating the operation feven or eight times, taking care not to put the magnets out of their paralielifmj and the needle will be Sufficiently magnetical. PLANE SAILING. PLANE SAILING is the art of navigating a fhi-p upon princi- ples deduced from the notion of the"earth*s being an extended Plane, and is no more than the application of Plane Trigonometry to the folution of the feveral variations, or cafes ; where the h po- thenufe, or longeft fide, is always the rhumb that the (hip iai s upon. The perpendicular is the diRVence of latitude counted on the meridian, and the bale the departure ; which is eaftiug or wefting, counted from the meridian.. The 54 PLANE SAILING. The angle crppofite the bafe is the courfe or angle that the Ihip makes with the meridian ; and the angle oppofite the perpendicular is the complement of the courfe, which being taken together, make always eight points or rhumbs, which is 90 degrees. In contracting figures relating to a (hip's courfe, let the upper part, on what the figure is drawn upon, always reprefent the north ; the lower part fouth 5 the right hand eaft , and the left weft. Draw the north and fouth line to reprefent the meridian of the place the fhip fails from ; then, if the ihip's courfe is to be fouth- wardj take the upper end of the line for the place failed from ; bat, if the courfe is northward, take the lower end for that place. When the courfe is eafterly, deicribe the arch, and lay aff the courfe and departure on the right-hand fide of the meridian ; but when wefterly, on the left-hand fide. When the courfe is given in degrees, the degrees exprefling it muft be taken from the line of chords ; but when in points, from the line of rhumbs; and is always to be laid off upon the arch 3 be- ginning at the meridian. When the courfe is given in points, it may be fet down with its correfponding logarithm in the calculation, as found in Table III. of the logarithms, without reducing it into degrees. In all cafes, wherever the complement of the courfe, or- co-fine, &c. is ufed, the degrees or points put down is the courfe itfelf ; yet the logarithm belonging to the complement, or co-fine, &c. of that courfe is taken. CASE I. Courfe and Di/lance failed given^ to find the Difference of Latitude and Departure from the Meridian. A {hip from the Lizard, in lat. 49 57' N. fails S. W. by W. 488 miles. Required the latitude fhe is in, and her departure from the me- ridian flie failed from ? By CONSTRUCTION. Draw the line CA to reprefent the meridian of the Lizard, and C the Lizard point. With the chord of 60 in your compaffes, and one foot in C, defcribe the co?npafs N. W. S. E. Take 5 points in your compaiTes from the line of rhumbs on the plane fcale, and fet it off on the arch from S. towards W. for the couife; draw the line CB, which make equal to the dift. 488 ; draw B A parallel to E. and W . to cut the meridian in A. Then will AC be the difference of latitude 27I 3 J 3 and AB the departue 405,8. PLANE SAILING, By making the Diftance Radius, it will be by Axiom I. The conrfe <; points 56 15' To find the Departure. As radius 90 Is to the dift. o.ooooo 2.68842 So is the fine cou. 5 pts. 9.91985 To the dep. 405,8 2.60827 The com. courfe 3 points 33$ 45' To find the Diff. of Latitude. As radius 90 o.ooooo Is to the dift. 488 2.^68842 So is co-linecou. 5 pts. 9.744/4 To the diff. of lat. 271 2.43316 Now as the fhip is in north latitude failing foutherly from the latitude left 49 57' N. Take the difF. of lat. 27i,i-*-6o~ 4 31 S. Gives the lat. in 45 26 N, And the departure from the meridian is 405,8 miles, To render the following work more eafy, and that the Learner, by being initiated in this other method, will be the better able to underftand many things in the following work, (as well as in fe- veral modern authors, ) where the proportion of oppoiite fides, and oppofite angles, do not appear, and where radius is not intro- duced. Obferve. In the defcription of the logarithm (p. 22 x you are (hewn, that by- adding the logarithm of two numbers together, their fum produces the fame number in the logarithms, as the pro- duct of the fame two numbers when multiplied. And by fub- tradting the logarithm of two numbers from each other, the re- maining logarithm produces the fame number as the quotient of the fame number j or the complement arithmetic (p. 28; of the loga- rithm $6 PLANE SAILING. rithm of the divifor added to the logarithm of the dividend., ifejecl- ing (radius) or 10 in the index (p. 35) the refult is the very fame* Again, when the proportion begins with a fine or a co-fine, the complement arithmetic added to the other two terms, their fum rejecting, 10 in the index will be the logarithm of the number fought. Now as the logarithm co-fecant of any angle is equal to the complement arithmetic of the logarithm fine of that angle, and the logarithm fecant is equal to the arithmetic complement of the loga- rithm co-fine of that angle : omitting radius, therefore, the co-ar. may be taken out of the tables by infpe&ion. Here all the three fides may be made radius, t find the difference of latitude and departure ; therefore, the Learner may make which fide he pleafes radius j but as for my part I fhall make the flrfr, where thejjiftance is made radius, whenever the courfe is given. ff** Though. iloWnethod of working by logarithms is certain, yet the fame may be wrought by Gunter's Scale and Compaffes, and by fcveral other methods. NOTE. When the courfe is given in points, make ufe of the line marked fine rhumbs, and tang. rhum. on the upper fide of the fcale ; when in degrees, make ufe of the lines marked fine and tang. By GUNTER. Now+to perform the lafr cafe, extend from rad. or 8 points to 5 points on the line marked SR ; that extent will reach from the dift. 488 to the dep. 405,8 on the line of num. 2dly. * Extend from rad. or 8 points to 3 points (the comp. of the cou. on the line SR ;) that extent will reach from the dift. 488 to the difFof lat. 271 on the line of numbers. Thus may all the operations be performed in the feveral cafes of Navigation. By this cafe is calculated the Table of Latitude and Departure for every degree, point, and quarter point of the Mariner's Compafs, to the diifc. of 300 iniles, which is of excellent ufe in working day's works at fea, and may be applied both to middle latitude and Mer- cator's (ailing, as fhali be (hewn hereafter ; we fhall only proceed now to the working of the laft cafe by the Table of Diff. of Lati- tude and Departure. By INSPECTION. Find the given cou. at the top or bottom of the tables, either among the points or degree?, and in that page, and right againft the dirt, taken in its column, ftarid the difFof lat. and dep. in their columns. Thus the cou. is S. W. by W. or five points, which is found at the bottom ofthe Table of Diff. of Lat. and Dep. for points: and as the dift. 488 is too great to be found in the Tables, divide it by 2 (or any PLANE SAILING. 57 any other convenient number) and that gives 244, which look for in the dift. column, and right againft it ftands 135,5 for the difF. of lat. and 202,8 for the dep. which being doubled (becaufe divided by 2) gives 271 for the difF. of lat. and 405,6 for the dep. the fame as before. Any of thefe methods will do, but the laft is chiefly pradtifed at fea. NOTE. All points or degrees above 45, are to be looked for at bottom of Table I. and all lefs at top j and the miles on the left hand. CASE II. Courfe and Difference of Latitude given^ to find the Diftance run^and Departure from the Meridian. If afhip runs S. E. by E. from i 45' north latitude^ and then by obfervation is in 2 46' fouth latitude, what is her diftance, and departure. Now, in this cafe, as the {hip has crofled the Equator, there- fore the lat. 1 45' N. added to 2 46' S. is 4 31', which multiplied by 60 gives 271 miles for the difF. of lat. Conftru&ed the fame as Pro- B blem X. in Geometry. Draw BC 271, and BA making an angle with BC~5 points, or 56^ 15'; upon C erect the perp. CA to join BA in A and it is done 5 then will CA=4o6, and * AB=488. C By CALCULATION. By making the Diftance AB Radius, it will be, Courfe S. E. by E. 5 pts.=56 15' To find the Departure. Ascofinecbu. 5 pts.co.ar. 0.25526 Is to the difF. of lat. 271 2.43297 bo is fine cou. 5 points 9.91985 To the dep. 405.6 2.60808 Complement 3 pojnts=33 c> 45' To find the Diftance. A co-fine cou 5 pts-co: ar. 0.25526 Is to the difF. of lat. 271 2.43297 So is rad. 10.00000 To the dift- 487.8 2.68823 Hence the {hip's dift. run is 487,8 miles, ami her dep. trom the merid. is 405,6 eafterly. By GUNTER. c Extend from 3 to 5 points on the line marked SR, that extent will reach from the difF. of lat. 271 to the dep. 405,6 on the line of numbers.' 2dly. ' Extend from rad. or 8 points to points, that extent will reach from the difF of lat. 27 1 to the dift, 488 on the line of numbers/ H By 5 PLANE SAILING. By INSPECTION. Find the cou. among the points or degrees, and the diff. oflar. in its column, right againft which ftand the dill, and dep. in their columns. Now as the diff. of lat. 271 is too great to be found in the Tables, I divide it by 2, and that gives 135,5 which I find over five points in the lat. column ; againtt that Hands 244, for the dift. and 202,8 for the dep. which multiplied by 2 gives the did. 488, and the dep. 405.6. CASE III. Courfe and Departure from the Meridian given^ to find the D'iflance and Difference of Latitude. If a (hip fails N. E. by E. f E. from a port in 3 15' fouth lati- tude, until fhe depart from her firft meridian 406 miles, I demand her distance, and what latitude {he is in ? By CONSTRUCTION. B Dep. 406 E. C .Draw the mer. AB, upon which erect the perp. BC, and fet ofFthere- 011 from B her dep. 406 eafterly from B to C, with the chord of 60, on C defcribe an arch, and fet off ' thereon the comp. of the cou. as A DE, and through D and C draw the line CDA, cutting the mer, in the point A; then the dift. AC, meafured on the fame fcale before ufed, gives 449, and AB 192 the diff. of lat. By CALCULATION. By making the Diftance AC radius, it will be, Thecourfe5| points =64 41' To find the Diff. of Lat. As fine cou. 5 J pts. co.ar. 0.04384 Is to the dep. 406 2.60853 So is c,o-fine cou. 5 j pts. 9.63099 To the diff. of lat. 192 2.28336 The compl. zf points=25 19' To find the As fine cou. 5.?. pts. co.ar. 0.04384 Is to the dep. 406 2.60853 So is fad. io.occoo To tfce dift. 449.1 2^5237 From the lat. left 3 15' S, Subtract the diff. of lat. 192 miles, or 3 12 N. The remainder being 3, {hews the fhip is in o 03 S. By GUNTER. c Extend from 5j points to 2| on the line marked SR, that ex- tent will reach frgm the dep. 4,06 tg the diff. of lat. 192 on the line of number?.* adljr. PLANE SAILING. 59 zrdly. Extend from rad. to 5 J points, that extent will reach from the dep. 406 to the dift. 449 miles.' By INSPECTION. Find the cou. either among the points or decrees, and the dep. in its column ; right againft which {rands the dift. and diff. of lat. in their refpeclive columns. Thus, with the cou. 5^ points, and half the dep. I find 224,5 for the dift. and 9$, 8 for the diff. of lat. which being doubled, gives the dift. 449, and the diff of lat. 191,6 nearly as before. CASE IV. Dijlance and Difference of Latitude given^ to find the Courfe and Departure. Suppofe a fhip fails 488 miles, between the fouth and the eaft, from a port in 2 W 52' fouth latitude, and then by obfervation is in 7 23' fouth latitude j what courfe has fhe fteered, and what depar- ture has fhe made ? From the latitude by obfervation 7 23' take 2 52' the latitude left, the remainder 4 31' multiply by 60 = 27 1 miles or minutes of difference of latitude. Conftru&ed as Problem XI. in Geo- metry. Draw the mer. AB = 2/J ; upon B ere& the perp. BC ; take 4.88 in your compafTes, and with one foot on A, lay the other on the line BCj join A and C ; then will B C be the dep. 406, and the angle B A C the cou. = 56 16', or 5 points nearly. To find the Courfe. | To find the Departure. At the dift. 488 co. ar. 7.31 158 j As rad. 10.00000 B Is to the rad. o is the diff. lat. 271 10.00000 2.43297 To co-fine cou. 56 16' 9. 7 4455 Is to the dift. 488 2.68842- So is fine cou. 56 16' 9.91993 To the dep. 405.8 2.60835 Hence the cou. is S. E. by E. and the dep. 405,8. By GUNTER. ' The extent, from the dift. 488 to the diff. of lat. 271, on the line of numb, will reach from rad. or 90, to 33 44' the co-cou. on the line of fines. ' And the extent, from rad. to 56 16' on the line of fines, will reach from the dift. 488 to the dap, 405,8 on the line of num- bers/ H 2 By 6o PLANE SAILING. By INSPECTION. Seek in the Tables till againft the dift. taken in its column be found the given diff. of lat in one of the following columns ; and adjoining to it (lands the dep. which, if lefs than the diff of lat. the cou. is found at the top ; but, if greater, the cou. is found at the bottom. Now, with half the dift. 244, and half the diff. of lat. 135,5 look in the Tables till they are found to agree in their refpeciive columns, which they do nearly over 5 points ; againft them ftands 202,8 for the dep. which, being doubled, gives 405,6 nearly, as before. CASE V. Dijlance and Departure given^ to find the Courfe and Difference of Latitude. Admit a (hip fails 488 miles between the north and weft from the iflarid of Bermuda, in lat. 32 35' north, until her dep. is 405 miles ; what courfe has fhe fleered, and what lat is fhe in ? NOTE. This cafe is conftruted much the fame as the laft. By CALCULATION. Dep. 405. To find the Courfe. As the dift. 488 co ar. 7.31158 Is to radius lo.coooo So is dep. 405 2.60746 To the fine of cou. |6 6' 9.91904 To find the Diff. of Lat. As radius 10.00000 Is to the dift. 488 2.68842 So is co-line co. 56 6 r 9.74644 To the diff. of lat. 272,2 2.43486 ' Hence the courfe is N. 56 6' W. or N. W. by W. nearly. To the lat. failed from 32 35' add the diff. of lat. 272, or 4 32', gives 37 07', the lat. the (hip is in. By GUNTER. c Extend from the dift. 488 to the dep. 405 on the line of num- bers, that extent Will reach from rad. to the cou. 56 6' on the line of fines, 2dly. c Extend from rad. to the comp. of the cou. 33 54' on the line of fines, that extent will reach from the dift. 488 to the diff. of lat. 272 on the line of numbers. By INSPECTION. Seek in the Tables till againft the dift. taken in its column, be found the given dep. in one of the following columns > and ad- joining PLANE SAILING. 6l joining to it ftands the dift". of lat. which, if greater than the dep, the coii. is found at the top ; but if lefs, the cou. is found at the bottom. Now, with half the dift. 244, and half the dep. 202,5, I look in the Fables, and find them to agree in their columns, nearly over 5 points, againft which is lat. 135,5, which being doubled, is 27 1, the difF. of lat. nearly, as before. CASE VI. Difference of Latitude and Departure given^ to find the Courfe and Dljlance. A fhip fails between the north and weft till her difference of latitude is 271 miles, and her dep. is 406 miles; I demand her courfe and diftance? Conftruaed as Problem XII. in Geo- metry. Draw A 8 27 1, and perp. to it BC ^1406 ; join C and A; then will the angle CAB be the cou. =56 17', and AC the dift. 11:488 miles. Dep. 406. B To find the Courfe. As the diff.of lat. 27 1 co ar. 7.56703 Is to rad. 10,00000 So is the dep. 406 2.60853 To the tan. of cou. 56 1 7' 10.17556 To find the Diftance. As fin. -cou 56 I7'co ar. 0.07998 Dep. 406 : : Rad. : Dift. 488.1 2.60873 10.00000 2.68851 Hence her cou. is N. 56 17' W. or N. W. by W. and the dift. failed 488,1 miles. By GUNTER. c Extend from the difF. of lat. 271 to the dep. 406 on the line of num. that extent will reach from rad, to 56 17' the cou. on the line of tan. 2dly. For the dift. we muft confider it as rad. (there being no line of fee. on the fcale) and extend from rad. or 90 to the cou. 5 points on the line of fines, that extent will reach from the dep. 406, to the dift. 488 on the line of numbers. By INSPECTION. Seek in the Tables till half the given diff. of lat. 135,5, and dep. 20 j are found together in their refpeiiive columns; then right againft them will be found ( half the dift. 244, in its column, and the cou. ftand in degrees either at the top or bottom of the column where the difF. of lat. and dep, *vas found, which in this cafe is 56 15', or 5 points the cou. required. The fix foregoing Problems are the common cafe of Plane Sail- ing* PLANE SAILING. ing, which the learner ought to be well acquainted with ; and for that end I here add fix more for pra&ice, whofe anfwers may be found by the foregoing rules: gtueftion I. A Slip in 2 10' fouth lat. fails N. by E. 89 leagues : what lat. is fhe in, and what is her dep. ? Anfwer. Lat. in 2 i2'N. and dep. 17.36 leagues. Queftion II. A fhip fails S. S. W. from a port in 41 30' north lat. and then by obfervation the faid fhip is in 36 57' north lat. I demand the dift. run and dep. ? Anfwer. Dift. run 98,5 leagues, dep. 37,7 leagues. gueflion III. A fhip fails S. S. W. half W. from a port 2 30' fouth lat. until her dep. be 59 leagues ; I demand her dift. run and lat. in ? Anfwer. Dift. run 125,2 leagues, lat. in 8 i' fouth. Qyeftion IV. If a fhip fails 360 miles fouth weftward from 21 59' fouth lat. until by obfervation fhe be in 24 49' fouth lat. what is her cou. and dep. ? jfrfaer. The cou. is S. W. by W. halfW. or S, 6i P 4/ W. and her dep. from the mer. is 317,3 miles. >ueftion V. Suppofe a fhip fails 354 miles north eaftward from 2 9' fouth lat. until her dep. be 150 miles; what is her cou. and lat. in ? Anfwer. Her cou. is N. 25 4' E. orN. N. E. half E. nearly, and fhe is in lat. 3 11' North. ^ueftion VI. Sailing between the north and the weft, from a port in i 59' fouth lat. and then arriving at another port in 4 8' north lat. which is 209 miles to the weftward of the firft port ; I demand the cou. and dift. from the firft port to the fecond ? Anfwer. The cou. is N. 29 40' W. or N. N. W. J W. nearly ; and the dift. of the ports is 422,3 miles, or 140,7 leagues. TRAVERSE SAILING. "TTT" AV ING learned thofe necefTary problems concerning a Single \ 1 Courfe, the next is a Compound Courfe, commonly called a Traverfe; in order to the right underftanding of which, obferve the following definitions : A Traverfe is when a fhip, meeting with contrary winds, fails on feveral courfes. When the wind is directly or partly againft a fhip's direct courfe to the place fne is bound to, fhe reaches her port by a kind of Z like courfe ; which is made by failing with the wind, firft on one fide of the fhip, and then on the other fide. In a fhip, when looking towards the ftem, head^ or fore-part ; Starboard fignifies the right-hand fidej Larboard or Port the left-hand fide i Aft PLANE SAILING, 63 Aft or abaft is towards the hinder part, or ftern ; The Beam fignifies athwart or acrofs the middle of the (hip* When the (hip fails the fame way the wind blows, (he is faid to fail or run before the wind ; and the wind is right aft, or right. aiiern ; and her courfe is then 1 6 points from the wind. When a (hip fails with the wind blowing dire&ly acrofs her, (he is faid to have the wind on the beam j and her courfe is eight points from the wind. When the wind blows obliquely acrofs the fhip, the wind is faid to be abaft the beam, or afore the beam, according as her courfe is more or lefi than 8 points from the wind. When a {hip endeavours, to fail towards that part of the compafe from whence the wind blows, (he is faid to fail on a wind, or toply to windward, orclofe hauled, or on a bowling. A veffel failing as near as (he can to the point from whence the wind blows, is laid to be clofe- hauled. The generality of (hips will lie within about 6 points of the wind, but Hoops and other veflels will lie much nearer. The Windward, or Weather-fide, is that fide of the (hip on which the wind blows ; and the other is called the Leeward or Lee- iide. Tacks and (beets are large ropes made faft to the lower corners of the fore and main fails, by which either of thefe corners are hauled fore and aft. When a (hip fails by or on a wind, the windward tacks are al- ways hauled forwards, and leeward, or lee-(heets aft. The (larboard tacks are aboard when the (larboard fide is to windward, and the larboard to leeward ; and the larboard tacks are aboard when the larboard fide is to windward, and the (larboard to leeward, either tacks the yards are braced up. To know how near the wind a (hip will lie, obferve the courfe (lie goes on each tack when (he is clofe hauled, then half the num- ber of points between the two courfes will (hew how near the wind that (hip will lie. The mod common cafes, in turning to windward, may becon- flruted by the following precepts : - Having drawn the meridian, or north and Couth, and parallel of latitude (or eaft and weft line) in a circle, reprefenting the horizon of the place, mark, in the circumference, the place of the wind ; draw the rhumb, pafiing through the place bound to, and lay thereon the di fiance of that place from the centre. On each fide of the wind lay off in the circumference the points or degrees (hewing how near the wind the (hip can lie, and draw the rhumbs. Now, the firft courfe will be on one of thofe rhumbs, according to the tack the (hip leads with ; draw a line through the place bound to, parallel to the other point, to meet with the firit, and this will the courfe and diilance on the other tack. TQ 64 TRAVERSE SAILING. To refolve a Traverfe, is to reduce and bring feveral courfes into one; the courfes are known by the compafs, and the diftance by the Jog, which in common voyages is hove once in two hours, but in {hips of war, or in Eaft-Indiamen, every hour. In the fteerage, or fome convenient place in the (hip, there is generally kept a table, called the log-board, divided into feven co- lumns ; in the firft is written the hours of the day, in the fecond, the knots the (hip runs during half a minute; each of thefe knots bear the fame proportion to a fea mile that half a minute does to an hour; confequently, fo many knots as the fhip runs iu half a mi- nute, (the time allowed for trying the experiment) fo manv miles {he runs in an hour. In the third the fathoms, 10 of which ought to make a knot; in the fourth the courfes fleered by the compafs ; in the fifth the winds ; in the fixth the lee-way, or how far the fhip is drove to the leeward of the courfe fleered by the compafs ; in the feventh the tranfaclions of the day, as in the following Table. Every day at noon the contents are tranfcribed into the log-book, which is divided into columns, exactly like the log-board, and the feveral courfes being corrected by allowing for the lee-way \ and variations, and the diftance run upon each being fetdown in a Tra- verfe-table, fhews what difference of latitude and departure the {hip has made during the lafl 24 hours ; and from thence is found the latitude and longitude the fhip is in, &c. This operation is called doing a day's work. ^ The LOG-BOARD. H. K. F. Courfes. Winds. Lee- Tranfa&ions. way. 2 6 S. W. by S. N. 4 5 5 6 5 N.W. 8 5 Moderate gales 10 4 5 N.E. N. N. W. & fair weather, J2 4 5 at 8 A.M. faw 2 4 5 a fhip to the 4 4 5 northward. 6 4 5 8 5 S. W.byS. W. N. W. 10 4 5 J No obferva- 12 4 tion. Having placed the feveral courfes and diflances run upon each, begin with the firft courfe S. W. by S. which is 3 points, and the diffancerun upon it being fummecTup, is 21,5, or an half, which being doubled (becaufe the log is hove every two hours) is 43. In like TRAVERSE SAILING, 6$ Sike manner proceed with the other courfe.s, and then find the difF. of lat. and dep. for each con. and dilh When the cou is to the fbuthwanJ, the difF. of lat. rmjft be fet in the column marked S, but if to the northward, in that marked N ; likewife, when the courfe is to the eaftward, the dep. muft be fet in the column marked E ; but if to the weftward, in that marked W. Thus the firft courfe being S, W. by S. 3 points, the difF. of lat. belonging to it is fet under S. and the dep, under W. as in the following table : TRAVERSE TABLE. COURSES. DIST. 43 45 2 7 N. 3',* S. E. 3i,8' W. 2 3>9 15,0 S. W. bv.S. N. E: S. W. by S. 35,8 22,4 ^7 3<>8 26,4 S. 3'>8 D. Lat 31,8 38,Q 3i,8 Dep. W. 7> T Here the weftings being greater than the eaftings, the difF. fhews how far the (hip has got to the weftward ; and the fouthings being greater than the northings fhew how far (he is got to the fouth- ward of the place fhe fet out from. Now the difF. of lat. 26,4 and dep. 7,1 being looked for in the Tables, will be found nearly {landing together under 15 and againft dift. 27. Hence the courfe made good upon the feveral c&urfes is S. 15 W, and the dift 27 miles. EXAMPLE 66 TRAVERSE SAILING. EXAMPLE I. Suppofe a fhip takes her departure from the Lizard in latitude 49 57' N. it bearing N. N. W. diftance, by eftimation, 5 league^ fails' S E. 34, W. by S. i6,W. N.W. 39, and S. by E. 40 miles; required the latitude fhe is in, and her bearing and diftance from the Lizard ? By CONSTRUCTION. Dep, 14,2 M Draw the line L M to reprefent the meridian of the Lizard, and L the Lizaid point ; on L defcribe the compafs ; then fet off the oppofite point to the bearing of the Lizard ; the S, S, E. line L A, which make equal to 15 miles; parallel to the S. E. line draw the line AB equal to 34 miles: again, from B parallel to W. by S. draw BC equal to 16 miles ; next, through C, draw a line parallel to W. N W. which make equal to 39 miles ; from D draw DE, parallel to the S* by E-. line, equal to 40 miles ; then is E the place of the fhip at the end of her feveral courfes, EL the diHance, LM the dilF, of lat EM her departure, and the angle ELM the cour-fe fhe has made good. To TRAVERSE SAILING* 6 7 To find the fame by CALCULATION.' For the Firft Courfe, S. S. E. 15 Miles. To find the'Diff. of Lat. As rad. 90 10.00000 Is to dift. 15 1.17609 So is co-fine cou. 2 pts. 9.96562 To diff. lat. 13,9 1.14171 For Departure. As rad. 90 10.00000 Is to did. 15 So is fine cou. 2 pts. To dep. 5,7 1.17609 9-58284 -75 8 93 Second Courfe S. E. 34 Miles. For Difference of Latitude. As rad. 90 Is to co fine cou. 45' So is dill, 34 To diff. lat. 24 10.00000 9,84948 '53*48 1.38096 As rad. 90 Is to fine cou. So is dill. 34 To dep. 24 For Departure. JO.OCOOO 9 84948 1.53148 1.38096 Third Courfe W. by S. 16 Miles. For Difference of Latitude. As rad. 90 10.00000 Is to co fine cou. 78 45' 9.29024 So is dift. 16 To diff. lat. 3,1 1.20412 0.49436 For Departure. As rad. 90* Is to fine cou. 78 45' So is dift. 1 6 To dep. 15,7 IO.OOOOO 999157 1.20412 1.19569. Fourth Courfe W. N. W. 39 Miles. For Difference of Latitude. As rad. 90 10.00000 Is tg co- fine cou. 67 30' 9.58284 So is dift. 39 To diff. lat. 14,9 1.59106 I.I7390 For Departure. As rad. 90 Is to fine cou. 67 30' So is dift. 39 To dep. 36 IO.OOOOO 9.96562 1.59106 1,55668 Fifth Courfe S. by E. 40 Miles. For Difference of Latitude. As rad. 90 10.00000 Is to co-fine cou. 11 15' 9.99157 So is dift. 40 To diff. lat. 39,2 1.60206 For Departure. As rad. 90 10.00000 Is to fine cou. n 15 ' 9.29024 So is the dift. 40 1.60206 To the dep. 7,8 0.89230 Though this method of finding the diff. of lat. and dep. by loga- rithms is certain, yet the fame may be more readily found by the Tables of DifT. of Lat. and Dep. ; that is, to find the diff. of lat. 1 2 and TRAVERSE SAILING. 68 and dep. for each courfe and dift. by infpe&ion, and placing them down as in the following TRAVERSE TABLE : COURSES. DIST. DIFF. LAT. DEPARTURE. N. S. E. W. S. S. E. '5 J 3>9 5,7 S. E. 34- 24,0 24,0 W. by S. 16 3>* !5,7 W. N. W. 39 H>9 3 6 > S. by E. 40 39>* 7,8 From fum 49 80,2 37)5 51,7 take *4>9 37>5 Refts 65v3 14,2 - Having placed them as above, add up all the wettings, eaftings, northings, and fouthtngs feparately, and fet down their refpcclive Aims at the bottom of each column ; and as the wefting is greater than the eafting^ fubtracl: the eafling therefrom, and the difT. 14,2 fnews that theihip's dep. is i"o much weft of v her firft meridian. Again, the fouthing being greater than the northing, fubtracl: the nurthing from it, and the remainder Ihews how far the fliip is to the fouthward of her firil place, or difF. of lat. fhe has made* To find the direct Courfe or Bear- ing of the Lizard from the Ship. As thediiT. lat. 6^5,300. ar. 8.18509 Is to rad. 90 lo.oooco So is the dep. 14,2 1.15229 To tang. cou. 12 :6 ; 9.33738 Which, becaufe the diff. of lat. is foutherly, and the dep. wef- terly, is S. 12 16' W. Whence the Lizard bears from the {hip N. 12 i6'E. orN. by E. and To find the direcl Diftance. Asfineof cou. 12*16' co. 3^0.67272 Is to the dep. 14,2 1.15229 So is rad. 90 10.00000 To the dift. 66,84 1.82501 The cou. and dift. may be found fufficiently near under 12 degrees in Tables, where the dift. is 67 mile*. EXAMPLE II. Suppofe a fhip from the Lizard 49 57' is bound to Cork in lat, 5i4i'N. whole dep. from the mer. of the Lizard is 120 miles weft, but by reafoa of contrary winds is obliged to fail on the fol- lowing courfesj viz. S, S. W. 54 miles, W. by S. 39, N. W. by TRAVERSE SAILING. 6$ N. 40, N. E. by E. 69, and N. N. W. 60 miles; I demand the direct GOU. dill, diff of lat. and dep. made good upon the feveral courfes, with the lat. {he is in, and what courfe {he muft after- wards fleer, and how far, to gain her intended port ? By PROJECTION. Latitude of Cork 51 41' Latitude of Lizard 49 57 Cork i 44 Difference of latitude 104 Departure 120 13, I D 4& 1 TT 'o **v, ''''-*& "*/ * >c X '*'./ ^ c? *% **"* "'( 3)<>p. 4$. 7 fc- With the chord of 60 defcribe a circle, through which draw the mer. north and fouth, and, eroding- that at right angles, draw the eaft and weft points ; the centre reprefents the Lizard ; then fet ofFtwo points from the fouth wefterly; through which draw aline to the centre for the iirft cou. S. S. W . upon that fet off the ftrft dilr. run 54 miles, which is the {hip's place at the end of her firft courfe. Draw the W. by S. rhumb; and parallel to it a line, pafling through the (hip's lair* place ; and upon it fet off 39 for the fecond diiL -, draw the N, VV. by N, rhumb; and parallel to it, as before, . draw JO TRAVERSE SAILING. draw a line, pa/Ting through the {hip's laft place; upon it fet off 40, and that will be the place of the (hip at the end of her third cou. ; then draw the N. K. by E. rhumb ; and parallel to it a line^ paffing through the (hip's laft place ; and upon it fet ofF69 for the fourth did. ; then draw a N. N. W. rhumb ; and parallel to it a line as before, through the (hip's laft pla.ce; and upon it fet orFthe laft dift. 60, which is the fhip's place at the end of her feveral courfes ; from which draw a line parallel to the eaft and weft line, until it cuts the mer. ; for the whole dep, from this to the centre, being meafured on the fame fcale, will g^ve her dirF. of lat. made good upon the feveral courfes ; and a line drawn from the (hip's laft place to her firft, will give the whole dift. ; and the angle which this line makes with the meridian will be the (hip's courfe made good. Now, to find what courfe (he muft fteer, and how far (he muft run, from the centre of the compafs, or the Lizard point, fet off the whole diff. of lat. of the two ports, viz. 104, to F; through F draw an E. and W, line wefterly, and fet off thereon the whole dep 1 20 from F to E ; then will E reprefent the fituation of Cork ; join AE, and draw AD parallel to the mer. ; then will AE be the o 22,4 W. S.VV.^W. 3 >7 **,? W. by S. 25 4>9 24,5 W. by N. iS 3>5 '7>7 S. S. E. 3 2 29,6 12,2 S. S. E..JE. 27 2j,2 *3>9 S. by E. 25 24,5 4)9 South 3 1 3'^ S. S. E. 39 3 6 > H-9 3>5 *7 2 ,9 45*9 93,3 3>5 45,9 'Diff. Lat. 169,48 Depar. ! 47>4-W. The MIDDLE LATITUDE SAILING, 73 The fhip is in lat. 34 2 *' N. the dep. is 47,4 W. The cou. made good is S. 1 5 38' W. and d ft. 175,9. The cou. to the intende-i port is S. 58 35' W. or S.W. by W. one quarter weft nearly, diftance 155,4. MIDDLE LATITUDE SAILING. IN Plane Sailing the earth was confidered as a plane, reprefenting a bowling-green, having the meridians parallel to each other, and confequently the degrees of longitude equal in all places ; but this cannot be true, as the earth is a globe or fphere ; for, As the meridians are circles on the terraqueous globe, meeting in the poles, (as may be feen in the Plate page 45) it is obvious, that any two of thofe circles muft recede more at greater diftances from the poles ; and at equal diftances from each pole, or at the equator, the diftance between the meridians is greateft. The true place of a fhip at Tea depends upon its diftance from the equator, and fome noted meridian ; and fince the meridional dif- tance, that is, the^diftance between any two meridians, varies in every latitude, it is therefore conv nient this diftance (ho >ld be reckoned in a fixed latitude, and where the degrees are of the fame magnitude with thofe of the meridian, which can be no where but on the equator, where 60 geographical miles make a degree. The circumference of all circles are in direcl: proportion to each other, as their radii ; and fince the earth turns once round its axis in 24 hours, every point upon its furface muft defcribe circles pa- rallel to the equator : hence it follows, that the circumference of any parallel of latitude, in milegj is to the circumference of the equator, in miles, as the co-fine of that latitude is to radius; and, that the breadth of a degree, in any parallel of latitude, is to the breadth of a degree upon the equator, as the fine complement of that latitude is to radius. By the laft proportion was the following Table calculated, which {hews the breadth of a degree of longitude in every latitude j and may be made to .anfwer for any degrees or minutes by taking pro- portional parts. K MIDDLE LATITUDE SAILING. The following Table Jhews how many Miles anfiver to a Degree of fa gitude at every Degree of Latitude. D.L. MILES. D.L M-ILES. D.L. MILES. D. L MILES. D. L. MILES. I 59 -99 19 S^,. 73 37 47 - -9' 2 55 34 41 73 17- -54 2 59 . .96 20 56.. 38 38 47 - -38 56 33 --55 74 I6..53 3 59 -92 21 56 . .01 39 46 . .62 57 32 . .68 75 15.. 52 4 59 .86 22 55-63 40 45 -95 58 3' 79 76 14. .51 5 59- -77 23 55-. 23 41 45 - -28 59 33 -90 77 '3-5o 6 59 - - 6 7 24 54-. 8 r 42 44 -59 60 30 . .00 78 12.. 48 7 59.. 56 25 54 .-3 8 43 43-. 88 61 29.. 19 79 i . .45 8 59 -4* 26 53 - -93 44 43.. 16 62 28.. 17 80 10 . .42 9 59 . .26 27 53 "56 45 42.. 13 63 27 . .24 81 9.- 38 10 59 -8 28 52.. 97 46 41 ..68 64 26 . .30 82 8.. 35 ji 58.. 89 2C; 52 . 47 47 40 . .92 65 25 . .36 83 7--3 2 12 58 . .68 30 51.. 96 48 40.. 15 66 24 ..4 J 84 6.. 28 *3 58 . .46 3 1 5i .-43 49 39 -3 6 67 23 45 85 5-23 14 58.. 22 3 2 50 . .88 50 38.. 57 68 22 . .48 86 4 ..i8 IS 57 -95 33 50 . .32 5i 37 - -7 6 69 21 .. 5 87 3.. 14 16 57.. 67 34 49 -74 52 3 6 - -94 70 2O . .52 88 2 . .09 17 57 -37 35 49.. 15 53 36 . .11 7 1 9 --54 89 I.. 5 18 57 . .06 36 4-8 . -54 54 35-. 26 72 '8.. 55 Hence it follows, that As radius, or fine 90 *\ Is to the diff. of long, in miles, / So is co-fine of any paral. of lat. > To thedift.in miles between any i Two mer. in that paral. of lat... ) As co-fine of any paral. of lat. Is to the diftance run in miles in that lat. So is the radius, or fine of 90* .To the diff. of long, in miles. From what has been faid, arifes the folution of the following Problems, PROBLEM I. The Difference of Longitude between two Places^ both In one Parallel of Latitude, being ghen^ to find the Diflance between the?n. Suppofe a fhip in the lat. 49 30' N. or S. fails directly E. or W. until her diff. of long, be 3 30', and the dift. failed be re- quired * By MIDDLE LATITUDE SAILING. 75 ^Q By PROJECTION. With the fine of 90 in your compafles, taken from the Plane Scale, and with one foot in P, defcribe the arch EQ, and upon it fet off the diff. of long. 210 miles, and draw the .lines PE and PQ_ to reprefent the two meridians ; and then EQ_reprefents the equa- tor, and P the pole. Again, with the fine com. of the lar. 49 30', viz. 40 30' in your compafles, taken from the line of fines on the PJane Scale, and with one foot in P defcribe an arch, and the dift. between the points, where it cuts the two meridians, be- ing meafured upon the fame fcale of equal parts that the difF. of long, was, will be the dep. 136,4 miles. Or, thus: Draw the men AB,and with the chord of 60 in yoiir compafles defcribe an arch, and upon it fet off the comp. of the iat. 40 30' (taken from the line of chords) and fet it off upon the arch as a cou. in Plane Sailing, and draw the line AC as.a dift. which make equal to the diff. of long. 2io miles ; then will the departure CD be the diftance 136,4 miles as before: tbis laft method is preferable to the former, as we are not confined to any particular fcale. Reverfe this Problem, and fuppofe the dift. failed in any parallel of Iat. given, to find the diff. of long. With the fine com. of Iat. in your compafles defcribe an arch, upon which fet off the dep. 136,4 miles, and through the points where it cuts the arch draw the lines PE and PQj then, with the fine of 9'o in your compafles, and one foot in the former centre P, defcribe an arch to cut PE and PQj then EQJbeing meafured upon the fmall fcale of equal parts that the dep. was, will be the diff. of long. 210 miles. By 76 MIDDLE LATITUDE SAILING. By CALCULATION. To find the Departure. Asrad. 90* . 10,00000 Is to the diff, of long. 210 2,32222 So is co-fine lat. 49 30' 9*81254 To the dift, or dep. 136,4 2,13476 By GUNTER. * The extent from rad. to fine com. lat. 40 30' on the line of fines, will reach from the diff, of long. 210 to the dift. 136,4 on the line of numbers/ By INSPECTION. Find the fine com. of the lat. among the degrees, and in the dift. column the diff. of long, oppofite to which, in the column of dep. is the dift. required ; but as the co-lat. is 40 30', therefore, For 40 degrees you will find 135 For 41 degrees you will find The fum is Half the dift. required This is done becaufe the Table of Diff. of Lat. and Dep. is cal- culated only for fingle degrees. By the reverfe of the laft problem, having the dift. run in any parallel to find the diff. of long. Suppofe a fhip in lat. 49 30' N, or S. fails dire&ly E, or W, 136,4 miles, and her diff. of long, be required ? As co-fine of lat. 49 30' co. ar. 0,18746 Is to the dift. 136,4 2,13481 So is rad. i *-* 10,00000 To the diff. of long, 2IO 2,32227 By INSPECTION. Look for the comp. of the lat. among the degs. as if it was a cou, and the dep. in its column ; right againft which ftands the diff. of long, in the dift, column. In the laft Problem the fhip is fuppofed to have failed due eaft or weft, in the fame parallel of lat. but in her courfe ftie generally croffes feveral meridians and parallels, and then arrives at a different lat. from that (he left} and 3 as it is plain by MIDDLE LATITUDE SAILING. 77 by the foregoing Table, that the miles which make a degree in one parallel, wtil not be the fame as thofe ihat make a degree in any other parallel, lyiiv^ on the fame fide of the equator ; there- fore add both iats. together, and take ha-f their fum for a mean or mid. lat. ; which may -o conceived as if the {hip had failed in one lat. ; with which the diff. of long, may be turned into dep and dep. into cliff, of long, in the fame manner as has been already fhewn, for it will be As the co. fine of the mid. lat." la to the departure, So is radius To the difference of longitude. As radius Js to the difference of longitude, So is the co fine of the mid. lat. To the departure. Having the diff. of lat. and dep. the cou. and din:, are found by Cafe the Sixth, in Plain Sailing, . CASE I. Required the bearing and diir.. between the Lizard, in lat. 49 5/' N 6 long. 5 1 2' W, a r:j the ifland of St. Mary, one of the Weftern idands, in lat. 37 N. and long. 25 12' W ? Lizard's lat. 49 57' N. St. Mary's lat. 36 58 N. 49*57' Long, 5 12' W. 36 58 Long. 25 12 W. 12 59 Sum 2)86 55 Mid. lat. 43 25 Diff. in miles 779 90 oo Co-mid, lat. 46 32 By PROJECTION. S jf&&Ltzara 1 2oo diff. long* St. Mary's Draw the mer. AE, with the chord of 60 defcribe the arch PS j upon which fet off 46 32', the comp. of mid. lat. from Q_to S ; through S draw the line AC = i 192, the diff. of long, let fall the perpendicular CE, which will be the dep. 865 ; upon AE fet off AD 777, the diff. of lat, j and upon D erecl: the perp. DG, and upon 78 MIDDLE LATITUDE SAILING. upon it fet off the dep. 865 ; join G and A, and it is done ; for GA will be the dift. 1168 miles, and the angle GAD the cou. S. 48 4' W. The CALCULATION. To find the Departure. As radius 10.00000 Is todiff. of long. 1200 3.07918 Soisco line mid. lat.4328' 9.86080 To the dep. 870,9 2.93998 To find the Diftance, As fine cou. 48 1 1' co, ar. 0.12768 Is to deg. 870,9 2.93998 So is radius 90* o.ooooo To the dift. 1168 3.06766 To find the Courfe. As diff. of lat. 779 co. ar. 7.10846 Is to radius I o.ooooo So is dep. 870,9 2.93998 To tang, of cou. 48 1 i' 10.04844 NOTE. The courfe may be found without the departure, by Middle Latitude Sailing, thus : Asthediff.oflat.779co.ar. 7.10846 Is to the diff. long. 1200 3.07918 So is co fi. mid. lat. 43 28' 9.86080 To tang. cou. 48 1 1' 10,04844 By GUNTER. ift. c The extent from 46 32', the comp. of the mid. lat. to rad. on the line of fines, will reach from 1200 to 870,9 on the line of numbers. 2dly. 'The extent from rad. or 90 to 41 49', the comp. of the cou. on the line of fines, will reach from 779 to 1168 on the line of numbers. 3dly. c The extent from 779 to 870,9 on the line of numbers, will reach from 45 to 48 on the line of tangents/ By INSPECTION. Look for the comp. of mid. lat. as if it was a cou. in Plane Sail- ing, and difF. of long, in the dift. column; oppofite to which ftands the dep. in its column. Having the diff. of lat. and dep. the cou. and dift. are found as in Cafe VI. in Plane Sailing. Thus, taking J of the diff. of long. 120011:300, and as the comp. of the mid. lat. is 46 32', or nearly 46!, I look over 46 and 47, and againft the dift. ftands 215,8 and 219,4 in the dep. columns; which, added together, gives 435,2, half is 217,6 ; this multiplied by 4 gives 870,4 the dep. Again, taking -J the difF. of lat. and ^ of the dep. 194,7, and 217,6 ; the neareft number to thefe ftanding together are 216,2 and 194,7 over 48 and againft the dift. 292; this, multiplied by 4, gives 1168 miles : hence the cou. is S. 48 W. ; and diftance 1168. CASE MIDDLE LATITUDE SAILING. 79 CASE II. Both Latitudes and Departure from the Meridian glven^ to find tire Courfe and Diftance^ and Difference of Longitude. A fhip in lat. 49 57' N. and long. 5 24' W. fails fouth wef- terly, till her dep. is 789 miles, and fhe be in lat. 39 20'N. ; I demand the cou. dift. and long, fhe is in ? Latitude left Latitude in Diff. of latitude In miles 49 57' N. 39 20 N. Latitude left Latitude in Sum of latitude Middle latitude 10 37 60 49 57' N - 39 20 N. 89 17 637 44 90 38 oo Comp. of mid. lat, 45 22 By PROJECTION. Draw the mer. AD, from A to D, fet off the diff. of lat. 637 miles, and on D erect the perp. DG, which make equal to the dep. 789 miles. Draw the line AG, and that will be the diih 1014 miles, and the angle DAG the cou. 51 5'. Again, draw EK parallel to AD, making the dift. from AD equal to the dep. DG 789, pn A defcribe an arch ; take thecomp. of the mid. lat. 45 22' in your compafTes from the line of chords, and fet that off on the arch on the oppofite fide of the mer. AD, through where that cuts the arch draw the line AE to cut the line KE in E, from E let fall the perp. EB, and it is- done; for AE will be the diff. of long. 1109 miles. By CALCULATION. To find the Courfe it will be, Asthediff.oflat,637 co.ar. 7.19586 Is to radius 90$ 10.00000 So is dep. 789 2.89708 To tan, cou, 51^5' 10,09294 To find theDiftance it will be, As the fine cou. 51 5'co.ar. o.i 0899 Is to the dep. 789 2.89708 So is radius qo^ 10.00000 To the dift, 1014 3.00607 So MIDDLE LATITUDE SAILING. To find the Difference of Longitude it will be, As co fine mid. lat. 44 38' co. ar. o. 14775 Is to departure 789 . 2,89708 So is radius 90 10.00000 To diff. of long. 1109 3.04483 Long, the fhip failed from 5 2^ f W. Diff. long. 1 109 miles, or ~6o= 18 29 W. Longitude in 23 53 W. By GUNTER. ift. < The extent from the diff. of lat. 637 to the dep. 789 on the Hne of numbers, will reach from rad. or 45 backward to 51* 5', thecou. on the line of tangents. 2dly. c The extent from 51 5' to radius or 90 on the line of fines, will reach from the dep. 789 to thedift. 1014 on the line of numbers. 3dly, c The extent from the comp, of mid-, lat. 45 22 r to rad. or 90 on the line of fines, will reach from the dep. 789, to the diff. of long. 1109 on the line of numbers.' By INSPECTION. RULE. With the diff. of lat. and dep. find the cou. and dift, as in Cafe VI. in Plane Sailing. 2dly. Taking the comp. of mid. lat. as a cou. and the dep. in its column, and the dift correfponding to thefe will be the diff. of long. Thus, taking a tenth of the diff. of lat. 637, and dep. 789, that is, 63,7 and 78,9, the neareft numbers to thefe are 63,6 and 78,5 Handing together over 51, againft the dift. 101, which mul- tiplied by 10 gives 1010; hence the cou. by infpe&ion, is S. 51 W. and the dift. 1010. Taking 45 22' or 45 as a cou. and a tenth of the dep. 78,9 in its column, the neareft is 78,5, in the dift column ftands in, which multiplied by 10 gives mo for the diff. of long, nearly, as before. CASE III. One Latitude^ Courfe and Diftance given, to find the Difference of La- titude and Difference of Longitude. A fhip in latitude 42 30' N. and longitude i8 Q 31' W. fails S. E. by 8.591 miles, O f 197 leagues 5 I demand the latitude and longitude the (hip is ii> { By MIDDLE LATITUDE SAILING- "81 d& $%? O'-- Vep. 322.3 By PROJECTION. As Cafe I. in Plane Sailing, viz. Draw the mer. AD, and on A defcribe an arch with the chord of 60, and upon it fet off the courfe S. E. by S. or 3 points, through where that cuts the arch draw the line AC ; making it equal to the dift. 591, from C let fall the perp. CD ; then will CD be the dep. and AD the diff. of lat. 491 miles. Draw the line EF parallel to AD, making the dift, from it equal to the dep. Take the comp. of mid. lat. 51 36' from the line of chords in your compaffes, and fet it off on the arch on the other fide of the mer. AD, and through where that cuts the arch draw the line AB to cut the line EF in B, from B let fall a pefp. and it is done \ for AB will be the diff. of long. 419 miles. Lat. left Diff. of lat. Lat. in Lat. left 42 3, the proper. diff. of lat. which is 77,9, the neareft is 77,6, againft this ftands 117 in the dift. column, which multiplied by 10 gives 1 170 nearly, the fame as that found by calculation. CASE II. Both Latitude and the Departure from the Meridian given^ to find the Courfc, Diflance^ 'and Difference of Longitude. A {hip in lat. 49 57' N. and long. 5 Q . 14 W. fails S. weft- ward, until her departure from the meridian be 789 miles, and then by obfervation is in the lat. 39 20' N. required her courfe ft- ered, diftance run, and longitude in ? Lat. left 49. 57' Merid. parts 3470 Lat. in 39 . 20 Merid. parts 2571 Diff, of lat. 10. 37 637 miles Diff. 899 By PROJECTION. With the proper diff of lat. and dep. project the fame as in Cafe VI. in Plane Sailing; extend the mer. Ai to B r and make A8 equal to the meridional diff. of lat. and draw a line parallel to the dep. DE ; produce the dift, AD to cut this -parallel ; and CB will be the diff. of long. Hence the angle B AC will be the con, S. 50 5' W. DA the dift. 1.0:4, and JBC the. diff. of long, miles. To find the fame by CALCULATION. As p. difF. lat. co. ar. 7.01586 Is to rad. po 9 lo.ooqoo So is ^he dep. 789 / 2.8^708 To tang. cou. 51 5*~ 10.09294 As rad. 90' ro.cocop Is to mer. difF. lat, 899 .2.95376 As fine cou. 31 5'co. ar. 0.10^99 Is- to dep, 7^9 y7o8 So i rad. po^.o' o.oo^oo So the dift. 1014 3.00607 Lopgitude left 5. n'.W. Dift. pf long. 1114=18 . 34-AV* So is tang. cou. 51,5 10.09292 Longitude in 23 To difF. of long. 1114 3.04668 , Met cou r fe. is S. 1 5'' W. and dillance 1014 miles. ' r NOTE. The dhf. of long, may ba found by faying, As prop. of lat. : dep. : : merid. difF. of.} pi; ;. difi^.cf loog. 92 MERCATOR'S SAILING. By GUNTER. ift. c The extent from diff. lat. 637, to dep. 789, on the line of numbers, will reach from rad. or 45, to 5^5', the cou. ontheline^ of tangents. 2dly. * The extent from rad. to com. cou. 38 55', on the line of fines, will reach from diff. lat, 637, to 1014, the diir. on the line of numbers. 3dly. * The extent from co-cou. 38 55', to fine cou. 51 5' on the line of fines, will reach from mer. diff. lat. 899, to 1114, the diff. of long, on the line of numbers.' By INSPECTION. The diff. of lat. anddep. being found together in their refpective columns will give the cou. among the degrees or points, and the dift. in its column j in the lat. column belonging to the cou. look for the meridional diff of lat. and againft it will ftand the diff. of long, in the dep. column. Now i-fixth of diff. of lat. and of dep. are 106,1 and 131,5, the nearer numbers to thefe are 106, 4 and 131,3, ftanding together over 51 the cou. and againft dift. 1695 this, multiplied by 6, gives 1014 the dift. Again, over 51 look for i-tenth of mer. diff. of lat. 89,9 in the lat. column, the neareft is 90.0, and againft which ftand iu,i in the dep. column j this, multiplied by IQ, gives zui for the diff. of long. CASE III. Both Latitudes and Courfes given^ to find the Dlflance and Difference of Longitude* A Clip from the Lizard makes her courfe S. 39 W. and then, by obfervation, is in lat. 453i'N. j required her dift. run, and long, in ? Lat, of the Lizard 49 57' N. Mer. parts 3470 Lat. by obfer. 45 31 N. Mer. parts 3074 Diff. 4 26 =22601. diff. 396M, By CONSTRUCTION. Draw a mer. AB, the upper end A will reprefent the (hip's place in her firft lat. Take the proper diff. of lat. 266 in your compaffes, and with one foot in A, the fhip's place, lay the other upon the meridian j from MERCATOR'S SAILING. 93 from A to E ; take the mer. diff. of lat. 396 in your companies, and with one foot in A, the {hip's place, as before, lay the other upon the mer. at B ; and upon thefe two points r.-uie the perp. DE and CB; a line drawn from the (hip's phce, making an angle with the mer. equal to 39, the ihip's cou. will cut the two perps at D and C ; the firft will be the dep. which terminates the dift. AD 342, and the other will be the diff of long 08 321 miles. From what has been faid, it is plain, that any cafe in Mercator's Sailing may be projected as a right-angled triangle, by only confi- dering the diff, of long, or dep. as the bafe ; the meridional, or proper diff. of lat. as the perp. ; the hypothenufe cut by the dep. as dift. ; and the angle which that makes with the perp. the cou. ; for in all cafes in Mercatot's Sailing, the meridional diff. of lat. bears the fame proportion to the diff. of long, that the proper diff. of lat. does to the dep. Thefe inftructions being well underftood, will be fufficient to inform the Learner how to conftrudt any of the following cafes : By CALCULATION. To find the Diftance. | To find the Diff. of Longitude. Asco-fi.cou. 39 co. ar. 0,109(50 | Astheco-fi. cou. 39co.ar. 0.10950 Is to the diff. ot lat. 266 2.42488 j Is to mer. diff. of lat. 396 2.59770 So is radius lo.coooo So is fine cou. 39 9-798B7 To the dift. 342,3 2.53438 Todif.lon.32O,7~52i'W.2. 50607 I Lizard's longitude left 5. 12' W. Longitude in 10 . 33 W. By GUNTER. ift. c The extent from co-fine cou. 51, to rad. on the line of fines, will reach from the proper diff. of lat. 266, to the dift. 342,3 on the line of numbers. 2dly. 'The extent from co-fine cou. 51, to fine cou. 39 on the line of fines, will reach from the mer. diff. of lat. 396, to the diff. of long. 321, on the line of numbers.' By INSPECTION. Under the cou. 39, and agaiaft half the diff. of lat. 133, ftand.? 171 in the dill, column, which being doubled is 342, the d;ir. ; under the fame degrees, and in the lat. column, looic for half the mer. diff. of lat. I98,againft that, in the dep. column, ftands 160,5, doubled is 321, the diff. of long, nearly, as before. CASE IV. One Latitude^ Courfe^ and Diftance given, to fnd the Difference of Latitude^ and Difference of Longitude. A fhip in latitude 42 -50' N. and longitude 18 31' W. fails S. W. by S. 94 MERCATOR'S SAILING. W. by S. 591 miles ; I demand the latitude and longitude the fhip is in ? To find the Difference of Latitude it will be, As rad. 90 JO-ooooo Js to the diftance 591 2.77159 So is co-fine cou. 3 pts. 9.91985 To the difF. of lat. 491,4 12.69144 Lat left 423o'N. Diff.lat.49 1 8 11 M.pts. 2822 2194 Lat. in 34 i9N.M.diff.oflat.628 To find the Difference of Longitude it will be, Asco-fi. co. 3pts.co.ar.c. 08015 Lon. left Istom.difF.oflat. 628 2.79796 So is S. cou. 3 pts. 9.74474 To diiT. of Ion. 419,6 2.62285 Di.lo. 420 7,00 W. Long, in 25 By GUNTER. ift. c The extent from rad. or 5 points, the com. of the cou. on the line marked SR, will reach from the dift. 591, to the diff. of Ut 4 491,4 on the line of numbers. 2dly. l The extent from co-cou. 5 points, to the cou. 3 points, on the line marked SR, will reach from the mer. difF. of lat, 628 to the difF. of long. 419,6 on the line of numbers.' By INSPECTION. Under the cou. 3 points, and oppofite a tenth of the dift. 59,1 in the lat. column ftands 49,1, which, multiplied by 10, is 491, the difF. of lat. ; then find $ of the mer. difF. of lat. 157-, in the fat. co- lumn^ againft which ftands 105 in the dep. column, which, mul- tiplied by 4, gives 420, the difF. of long. CASE v. Beth Latitudes and Dijlance given, to find ibe Courfe and Difference of Longliu *'e. If a (hip runs 300 miles N. wefterly from a port in lar. 37 N. and long. 10 25' W, un- til (he be in lat. 41 N.; required the courfe {leered and long, in ? Lat left 37 N. Mer. parts 2393 Lat. in 41 N. A4er. parts 2702 Diff. lat 4-240 M diff. lat. 309 M. MERCATOR'S SAILING. By CALCULATION. To find the Courfe. As the dift. 300 C0. ar. 7.52288 Is to rad. 90 10.00000 So is pro. difT. of lat. 240 2.3802 1 To the co- line cou. 36" 52' 9.90309 Longitude left Diff. of long. 232, or Longitude in To find the Diff, of Long. Asco-fi.cou.36$2'co.ar. 0.09639 Is to mer. diff. of lat. 309 2.48996 So is fine courfe 36? 52' 9.77812 To the diff. of long. 231,7 2.36497 10 25' W. 3 52 W. 14 17 W. By GUNTER. ift. c The extent from the dift. 300, to the proper diff. of lat. 240, on the line of numbers, will reach from rad. or 90, to 53* 8', the comp. of the cou. on the line of fines. 2dly. c The extent from co-cou. 53 8', to cou. 36 52', on the line of fines, will reach from the mer. diff. of lat. 309, to the diff. of long. 231,7, on the line of numbers.' By INSPECTION. With the dift. and diff. of lat. find the cou. then in the lat. co- lumn belonging to this cou. find the mer. diff. of lat. ; againft which, in the dep. column, will ftand the diff. of long. Thus, half the dift. 150, and half the diff. of lat. 120, will be found {landing together in their columns, nearly under 37, the cou. ; and, in the lat. column, find half the mer. diff. of lat. 154,5, the neareft to it is 154,1 ; againft which, in the dep. co- lumn, ftands 116,1, which doubled is 232,2 the diff. of long, nearly as before. CASE VI. One Latitude, Courfe, and Departure given, to find the Difference of Latitude^ and Difference of Longitude* A (hip fails E. S. E. from a certain port in latitude 50 10' S. and longitude 10 1 6' E. until her departure from the meridian be 957 miles ; I demand the dil- tance failed, and the latitude and longitude fhe is in? MERCATOR's SAILING. To find the Diftance it will be, As fine cou. 6 pts. co. ar. 0.03438 Is to the dep. 957 So is radius. 2.98091 10.00000 To the diftance 1036 3.01529 To find the Diff. of Long. Asco Hnecou. 6pts. co.ar. 0.41716 Is to mer. dill', of lat. 667 2.8241 3 So is line courfe 6 pts. 9.96562 To din", of long. 1610 3.20691 To find the DifF. of Lat. it wi As fine cou. 6 p(s co. ar. 0.03438 Is to the departure 957 2.98091 So is co-line cou. 6 pts. 9.58284 To diff. lat. 3961=6 36' 2.59813 Lat. left. 50 xo'S. mer. pts. 3490 Lat. in 56 46 S. mer. pts. 4157 Mer, difference Jat. 667 Longitude, left 10 i5'E. Diff. of long. 1610 = 26 50 E. Longitude in 37 6 E. By GUNTER. i ft. c The extent from 6 points to rad. on the line marked SR, will reach from the dep. 957, to the dift. 1036, on the line of numbers. 2dly. c The extent from 6 points to 2 points, on the line marked SR, will reach from the dep. 957, to the diff. of lat. 396, on the line of numbers. 3dly. c The extent from 2 points to 6 points on the line marked SR, will reach from the mer. diff. of lat. 667, to the diff. of long. 1610, on the line of numbers.' By INSPECTION. Over the cou. of 6 points, and againft a fifth of the dep. 191,4 {lands 79,2 and 207, which, multiplied by 5, gives 396, the diff. of lat. and 1035 for the dift. Then, in the lat. column, find a tenth of the mer. diff. of lat. 66,7, the neareft to that is 66,6 ; againft which, in the dep. co- lumn, ftands j6Oj8, which, multiplied by JO, is 1608, the diff. of long. CASE VII. One Latitude, Diftance failed, and Departure from the Meridian, given, to find the Courje, Difference of Latitude, and Difference of Longi- tude. A (hip in latitude 49 ?o f N. and longitude J44o'W. fails S. eaft- ward 645 miles, until her depar- ture from the meridian be 500 miles. Required the courfe fteer- ed, and the latitude and longitude ihe is in ? 8. To MERCATOR'S SAILING. 97 To find the Courfe it will be, As the diflance 645 co.ar. 7.19044 Is to rad. 10.00000 So is the departure 500 2.69897 To fine cou. 5o5o' 9.88941 To find DifF. of Long, it will be, Asco-li.con. 50 50' co. at, 0.19957 Is to m. diff. of lat. 588 2.76938 So is fine courfe 50* 50' 9.88948 Todiff.lon.' 721,8= 12 2' 2.85843 Long, left Long, in Tofind the DifF. of Lat. it will be, As fine con. 50 50' co. ar. o.i 1052 Is to the departure 500 2 69897 So is co fine cou. 50 50' 9.80043 Todiff. lat. 407,3 6 47' 2.60992 Lat. left 49 30' N. Lat. in 42 4 N. Mer. diff. lat. M. pts. 3428 M. pts. 2840 588 As pro. diff. of lat. 407,3 co. ar. 7.39008 Is to departure 500 2.69897 So is m. diff. ot lat. 588 2.76938 To diff. of long. 271,8 2.85843 Hence the fhip's cou. is S. 50 50' E. or S. E. eaft nearly, and foe is in the lat. of 42 43' N. and long. 2 38' W. By GUNTER. ift. < The extent from the dift. 645, to the dep. 500 on the line of numbers, will reach from radius to 50 50' on the line of fines. 2dly. < That extent from 50 50' to 39 10', on the line of fines, will reach from the dep. 500, to the diff. of lat. 407, on the line of numbers. 3dly. ' The extent from 39' 10' to 50 50', on the line of fines, will reach from the mer. diff. of lat, 588, to the diff. of long. 732, on the line of number?/ By INSPECTION. Now a 5th of the dift. and dep. are 129 and 100, and are found together over 51; and in the lat. column Hands 81,2, which, mul- tiplied by 5, is 406, the diff. of lat. Then, in the lat. column, feek | of the meridional diff. of lat. 147, the neareft is 1466; againft which, in the dep. column, ftands 181,1, which, multiplied by 4, is 724,4 the diff. of long. Having, in the preceding parts, (hewn how to work the moil ufeful problems in Middle Latitude and Mercator's Sailing; I {hall now work the three following cafes both by Middle Latitude and Mercator's Sailing, in a manner I generally teach perfons who are of age, and youth of good abilities ; efpecjally if they are limited to a Jlhort time. N C)B MERCATOR/S SAILING. The Difference of Latitude and Departure given, to find the Courft, Diflanc,:^ and Difference of Longitude^ by Middle Latitude and Mer - cator's Sailing. A fhip from latitude of 37 N. and longitude 48 20' W. fails between the north andeaft, until {he be in latitude 51 15' N. and finds that fhe has made 564 miles of departure \ what was her di- rect courfe, diftance run, and longitude in ? Lat. left 37. o' N. Mer. parts 2393 A "Oi-7 V, Lat'. in MMMM 14. 15 mmmmv 15 N. Mer. parts 55 miles difF. 3593 1200 ] ^ 1 P Is ^ 8 = 8 / -4PMMM Sum lat. f)88 . 15 3U^f ^ A* ^ N> .- jf" o Mid. lat 44. 7 90. o' T ^v:r JMMMHMi * 44 7 F ^l) Comp. mid. lat. 45 .53 Draw the mer. DP, make it equal to 855 the difF. of lat. j on P ere& the perp. PN, and make ^ 564 the dep. ; join D and N, then will the angle PDN be, the cou. N. 33 25' K. and DN the dift. 1024 miles. At the dift. of the dep. 564, draw EF parallel to DP ; with the chord of6odefcribe the arch TS, and upon it fet off the comp. of the mid. lat. 45 55' from S to T, through T draw DOj and cut EF in O ? then will OD be the difF. of long, $85,6 miles, by Mid. i,at. Sailing. Again, produce DP to A, and make DA zz 1200 the mer. difF. of lat. ; draw AB parallel to PN, and produce DN until it cuts AB in B ; then will AB be 791,7 miles, the difF. of long, by Mer- cator's Sailing. By CALCULATION. As diif. of lat. 855 co. ar. 7.06803 Is to radius 10.00000 So is the departure 564 2,75128 To tang, of cou. 53 25' 9.81931 As line cou. 35 25^0. ar. 0.25907 Is to the dep. 564 So is radius To the dift. 1024 2.75128 o.oocoo 3.01035 To find the DifFerenceof Longitude. By Middle Latitude Sailing. Asco fi. m. lat. 44- 7' co. ar. 0.14392 Is to thedepaiture 564 2.75128 So is rad. 90 lo.oooeo . 89520 Lon. left 20 W. Long, in 35 I4\V. byM. Lt.Sail. By Mercator's Sailing. Asco-fi.cou. 33 25'co.ar. 0.07848 Is to mer. diff. lat. i?co 3.07918 So is the fine cou. 33 25' 9-74093 Todiff.lon.79i,7=ri3 12' 2.89859 Long, left 48 20 Long, in 35 8 W. by Mer. Sail Her direct courfe is N, 33 25' E. or N. h, by N. nearly, diftance 1024 miles. MRCATOR*S SAILING. 99 By GUNTER. ift. c Extend from 855 to 564 on the line of numbers, that ex- tent will reach from rad. or 45, to 33 25' the cou. on the line of tangents. adly. c Extend from rad. or 90, to the cou. 33 25' on the line of fines, that extent will reach from the dep. 564, to the dift. 1024, on the line of numbers. 3dly. c Ex-end from rad. or 90, to the comp. of mid. lat. 45 53', on the line of fines, that extent will reach from the dep. 564, to 786 miles, the difT. of long, by Mid. Lat. Sailing. 4thly. ' Extend from the fine of the cou. 33 25' to the co-fine of the cou. 56 35', on the line of fines, that extent will reach from the meridional diff. of lat. 1200 to 792 miles, the diff. of long, by Mercator. Or, ' The extent from the diff. of lat. 855, to the dep. 564, will reach from the meridional diff. of lat. 1200, to 792, on the line of numbers/ By INSPECTION. With the diff. of lat. and dep. find the cou. and dift. as in Cafe VI. in Plane Sailing. Take the comg. of mid. lat, as a cou. and the dep. in its column, the correfponding dift. will be the diff. of long, by Mid. Lat. Sailing. And, Having found the cou. inftead of the proper diff. of lat. find the meridional diff. of lat. in the lat. column belonging to the cou. ; the correfponding dep. will be the diff. of long, by Mercator's Sailing. Now, taking i-tenth of the diff. of lat. i-tenth of the dep. viz. 85,5 and 56,4, the neareft numbers ftanding together in the Tables to thefe are 85,5, and 55,5 under 33 againft dift. 102, and 85, 4* and 57,6 under 34 againft dift. 103 ; now 33 added to 34 is 67% half is 33 30' the cou, ; and 102 added to 103 gives 205, half is 102,5, which, multiplied by 10, gives 1025 the dift. To find the Difference of Longitude. Over the comp. of mid. lat. 46, find I of the dep. viz. 141 in. its column, and againft it ftands 190 in the dift. column, this, mul- tiplied by 4, gives 784 miles, the diff. of long, by Mid. Lat. Sail- ing. Again, the cou. being 33 25', or nearly 33 f > look for i-tenth of meridional diff. of Iat.=ri2o in the "lat. columns, under 33 and 34, the neareft numbers to thefe are 110,9 and 120,2, the dep. correfponding are 77,9, and 81,1, their fum is 159, half is 79,5, which, multiplied by 10, gives 795, the diff. of long, by M creator's Sailing, nearly as before. From what has been faid, it is eafy to perceive thaf all the Cafes (fave the firft) in Mid. Lat: and Mercator's Sailing, are projected and worked in the fame manner as in Plane Sailing ; and N 2 to 1OO MfiRCATOR's SAILING. to obtain the difF. of long, by Mid. Lat. Sailing ; the cornp. of the mid. lat. is taken as a cou. in Plane Sailing, and with this cou. and the dep. the dift. is found, which will be the difF. oflong. by Mid. Lat. Sailing. And having the cou. take the meridional difF. of lat. as if it was the proper difF. of lat. the correfponding dep. will be the difF. of long, by Mercator's Sailing. The Courfe and Diftance given, to find the Difference of Latitude , and Difference of Longitude. Afhip from the latitude 51 15' N. and longitude 9 50' W. fails S. W. by S. until fhe has run 1022 miles, what latitude and longitude is fhe in ? To find the Latitude. To find the Departure. As rad. 90 c.oocoo Is to the diftance 1022 3*00945 So is fine courfe 3 pts. 9.74474 To the departure 567,8 2.75419 As rad. 90 o.ooooo Is to the diftance 1022 3-00945 So is co-line courfe 3 pts. 9.91985 To the difF. of lat. 849,8 2.92930 Now 849,8 or 850 divided by 60, gives 14 lo'S. and being fubtrafted from the latitude left, leaves 37 5' the latitude in : hence the middle latitude is found to be 44 10', and meridional difference of latitude 1 194. Whence, To find the DifFerence of Longi- tude by Mid. Lat. Sailing. As co Ii.m.lat.44io'co.ar.o.i4429 Is to the departure 567,8 2.75420 So is radius oo w 10.00000 To find the DifFerence of Longi- tude by Mercator's Sailing. As ce-fi . cou. 3 pts . co, ar. 0.080 1 5 Istomer. difF. of. lat. 11943.07700 So is fine courfe 3 pts. 9.74474 To difF. oflong. 797,8 2.90189 Longitude left 9- 50' W, DifF.of long. 798 =13 18 W. Long, in, by Mercator 23 8 W. To the dhT. of Ion. 791,6 2.89849 Longitude left ueft. ift. Required the bearing and diftance of Hang. Cliff in Shetland, in lat. 60 7' N. and long. 50' W. and the North Cape of Lapland, in lac. 71 10' N. long. 26 i' E ? Anf. 934> ! Mercator's Sailing. A r > N. 45 4 E. dift. 941,2 miles, by Mid, Lat. Sailing. >ueft. 2d. A (hip in Jat. 37 N. and long. 48 20' W. fails be- tween the N. and E. until /he is in the lat. of 51 18' N. and finds {he has made 564 miles of dep. ; jequired her direct cou. dift. run, and long, in ? 'N. 33 38' E. dift. 1018 miles, long, in 34 42' W.by Middle Latitude Sailing. . 33 38' E. dift. 1018 miles, long, in 35 9' by Mer- cator's Sailing. gueft. 3d. A {hip from the lat. of 50" 30' N. fails S. S. W. 150 leagues] what lat. is fhe in, and how much has ihe differed her long. ? Lat. in 43 34'NT. diff.-of long. 252,9 miles, by Mer- cator's Sailing. Lat. in 43 3^.' N, diff. of long. 252,3 miles, by Mid- dle Latitude Sailing. A (hip from lat. 20 40' N. fails N. E. by E. until (he be in the lat. of 27 i6'N. ; required her dift. run, and diff. of long. .? f Dift. run 712,8 miles, diff. of long. 648,1 miles, by * r ) M creator. ) Dift. run 712,8 miles, diff. of long. 648,6 miles, by C Mid. Lat, 102 MERC ATOP. ? S SAILING. 5th, Suppofe a fnip from the lat. of 45 40' N. fails be- tween the S. and E. 6co miles, and then her deo. is computed to be 308 miles ; required the cou. lat. and diff. of ione. ? CourfeS. 30 53' . lac. in 37 5' N. diff. of longitude 411,5 by Mercator. Courfe S. 30 53' E. lat. in 37 5' N. diff. of longitude 412,0, by Mid. Lat. Qefl. 6th. A fhip from the lat. 45 30' S. fails N, N. W. until her'diff. of Jong, be 7 40'; required the lat. flie is in, and her dift. failed ? NOTE. This mu ft be worked by Merca tor's Sailing, thus : As the fine cou 22 30' if. to the diff. of long. 4(10, fo is the co-fine cou. 22 30' to the mer diff. cf lat. 1 1 10. Now, from the mer. parts of lat. left 3073, take the mer. diff. of lat. mo, the remainder 1963 is the mer. parts, of the lat. come to 31 4' S. Having the cou. and proper diff. of lat. the reft is found by Cafe II. in Plane Sailing. Anf. The (hip is in lat. 3 4 ; S. dift. 937,4 miles. ^veft. 7th. A fhip in the lat. 51 I5*N, and long. 22 W. fails between S. and W. until {he has made 564. miles of dep. and 786 miles of diff. of long. ; required her cou. dift. lat. and long, in ? Note. This muft be worked by Mid. Lat. Sailing, as thus : As diff. of long. 786 : rad : : the dep. 564 : co-fine of mid, lat. 44 9', -|- 44 9':=r88 18' the fum lat. and 88 i8'-5i 6 i5'=lat. in 37 3'N. Having the diff. of lat. and dep. the cou. is found to be S. 34 7' W. and the dift. 1006 miles. It may now be fuppofed that the Learner is capable of working any fingle courfe, either by Mid Lat. or Mercator's Sailing; we ihall now proceed to Compound Couries. commonly called Tra- verfe Sailing, which may be worked by Mid. Lat. and Mer- cator's Sailing, either by projection, calculation, Gunter's fcale, or infpelion. How to folve compound courfes, or a traverfe, has already been fhewn in Plane Sailing ; but it is neceffary alfo to fhew, how pro- per allowances for the longitude {hould be introduced into fuch ac- counts, which is eafily done by any of the following methods : i ft. Complete the Traverfe Table to each cou. and dift. as iri Plane Sailing ; and find the whole diff. of lat. dep. and lat. in. 2dly. With the whole diff, of iat. and dep. hud the direct cou. and dift. 3(ily. With the latitude left and latitude in, find the complement of the middle latitude ; with which, and the departure, find the difference of longitude by Middle Latitude Sailing. Or, with the courfe and meridional difference of latitude, find the difference of longitude by Mercator's Sailing. Thefe methods are generally ufed in working a day's work at fea ; but thofe that want a greater degree of accuracy may work bv the following methods, efpecially in high latitudes : By MERCATOR'S SAILING. 103 By the feveral differences of latitudes and departures, found in the Tables of Difference of Latitude and Departure, find the lati- tudes come to, middle latitudes, and complements of middle lati- tudes ; with each complement of middle latitude and correfpond- ing departure, find the difference of longitude to each courfe anddif- tance, and fet them down in two additional columns, marked differ- ence of longitude eaft and weft, according to the departure ufed ; add up the eaft and weft columns, and their difference will be the whole difference of longitude, by Middle Latitude Sailing, But if you work by Mercator's Sailing, find the Meridional dif- ference of latitude for each courfe and diftance ; with each courfe and meridional difference of latitude, find the difference of longi- tude ; which fet down as above directed, and the difference between the eaft and weft columns will be the difference of longitude by Mercator's Sailing. By this method the (hip's place may be found at the end of each coUife and diftance run, and pricked off on a Mercator's chart. EXAMPLE I. Suppofe a fhip from the Land's End, in latitude 50 4' N. and longitude 5 41' 31", 5 W. is bound to the Ifland ot Sc. Mary, in latitude 37 N, and longitude 25^ 6' W. but by reafon of con- trary winds is obliged to fteer the following courfe", viz. S. by W. 24 miles; W. S. W. 32, N. W. \ W. 41, S. S. E I E. 49, E. N.E.I E. 19, W.2i, N. E. | E. 36, S. 41, S. S. W. 92, and N. 30 miles; and it be required the latitude and longitude (he is in, with the direcl: courfe and diftance to her intended port. With the feveral courfes and diftances, find their differences of latitude and departure, and fet them down as in the folio wing I TRAVERSE TABLE. 1 COURSES. DIST. DIFF. OF LAT. D I- P A R T U R E . N. S. E. W. S. by W. H *3>5 4.7 W. S. W. 3 2 12,2 29,6 N. W.| W. 4i 26,0 31,7 S. S.E.I E. 49 44.3 2I,O E.N.E.fE 19 4,6 is,4 Weft 21 21,0 N. E. i E. 36 22,8 27,8 South 41 41,0 S. S. W. 92 85,0 35> 2 North 36 3 6 > 89,4 K'6,O 67,2 122,2 J 89,4 07,2 JDif. lat.S. 116,6 Dej ar. 55 It 104 MERCATOR'S SAILING. It is plain by the Traverfe Table, that the fhiphas made 116,6 miles of fouthing, and 55 miles of wefting. Now from latitude left 50 . 4' Meridian parts Take diff. of lat. 117 = i . 57 348! Latitude in Sum latitudes Middle latitude 48 . 7 N. Meridian parts 2)98 .11 49 . 5 Mer. diff. lat. 33 2 179 Whence, to find the Difference of Longitude it will be, By Mid. Lat. Sailing. As co-fine mid lat. 49 5' 0.18378 Is to the dep. 55 So is rad. 90* .74036 JO.COOOC To diff. oflong.84=i24' 1.92414 Long, left Long, in 7 . 6 by m. lat. By Mercator's Sailing. As p. diff. of lat. 1 16,6 7*93330 Is to the dep. 55 1.74036 So is m. difF. of lat. 179 2,23285 Todiff long. 84,4=1 24' 1.96251 Long left Long, in 5 4* 7 6 by mer. W. By INSPECTION. Taking the comp. of mid. lat. 41 as a cou. and the dep. 55 in its col. the neareft is ;5,i againft which {lands 84 in the ditt. col. the diff. of long, by Mid. Lat. Sailing. And, With the proper ditf. of lat. and dep. j the cou. found nearly 25 and dift. 129 under the cou. ; in the lat. col. look for the mer. diff. of lat. ; 179, the neareft is 180,4 againft which ftands 84,1, in the dep. col. which is the diff. of long, by Mercator's Sailing. To find the direct Courfe and Diftance to St. Mary's. Lat of (hip 48 7' N. Mer. pts 3302 Lon. of (hip 7 6'W. Lat. St. Mary's 36 58 N. Mer. pts. 2390 L. St. Mary's 25 12 W. DifF. lat. ii 9 669ms. DifF. 9 12 Diff. of long 18.61086 Sum lat. 2)85 5 Mid. lat. 42 32 By Middle Latitude Sailing;. As the diff. of lat. 669 7-17457 Is to diff. long. 1086 3.035 8 3 to is co.fi mid. lat. 42 3 2' 9. 86740 To tang. cou. 50 . 7 10.07780 As co. fi. courfe 50 7' 0.19299 Is to prop, diff, of lat. 669 2.82543 So is rad. 90 To the dift. 1043 IO.OOOOO 3.01842 Ty MERCATOR'S SAILING. 105 By Mercator's Sailing. As mer. diff. of lat. 91 2- 7.04001 Is to rad. go* 10.00000 So diff. of long. 1086 3.03583 To tang. cou. 49 59' 10,07584 As rad. 90 o.ooooo Is to p. diff. lat. 699 2.82543 So is fee. cou. 49 59' 0.19178 To the dift. 1041 3.01721 Hence the direct courfe from the (hip to St. Mary's is S. 50 f W. anddiftance 104.3 miles, by Middle Latitude Sailing; and S. 49 V 59' W. and diflancc 1041 miles by Mercator's Sailing. The fame may be found By INSPECTION. Take | of the diff. of long. 1086, viz. 271,5 nearly, and look for that in the dift. column over the comp. middle lat. 47 nearly, arid in the dep. column ftands 198,5-! of the dcp. Then look for | of the diff. of lat. 167,2, and of dep. 198,5 until they are found (landing together in their refpe&ive columns, the neareft are found over 50, viz. 199,2, 167,5; the dift. correfponding to thefe is 260, this multiplied by 4 gives 1040 miles. Hence the courfe is S. 50 W. dift. 1040 miles, by Mid. Lat. Sailing. Again, talcing T V of the meridional diff. of lat. and T ^ of the diff. of longitude, viz. 91,2, and 108,6, the neareft numbers to thefe are 108,8, 91,3 ftanding over 50 in the lat. column, be- longing to the above degree ; look for T % of the proper diff, of lat. viz. 66,9, the neareft is 66,8, the diftance is 104, which being multiplied by 10, gives 1040 miles. Hence the cou. is S. 50 W. and dift. 1040 miles, by Mercator's Sailing, the fame as by calculation. Here, to have gone to geometrical ftriclnefs, the diff. of long, fhould have been found to every cou. and dift. run, by Mid. Lat. or Mercator's Sailing, which would have given the (hip's true place at the end of each cou. and dift. but fhall leave the doing of that to the Reader ; and as all traverfes are worked in the manner fhewn above, which is fuffiqiently exa& for a (hip's run in 24. hours, I (hall therefore only add a few queftions for the Learner's exercife. Suppofe a (hip from the lat. 68' 38' N. and long. 8* 40' E. is bound to the North Cape, in 7 1 10' N. and long. 26 o' E. fails as in the following Table j required the lat. and long, (he is in, and her direct cou. and dift. to the Cape. Q COURSES, io6 MERCATOR'S SAILING. COURSES. D. N. S. E. W. LAT. IN DilT. 1 *- E. >ong. W. 68 38 N. E. by N. N.. E. 63 3* 5 2 >4 26,9 3v 26,9 69 3 69 57 97* 78,0 N.N.E. 56 5i7 21,4 70 49 64,2 North. 3 a 30,0 71 19 N. W. by N. 25 20.8 "3-9 71 40 44> N.N.W.fW. 3" 3i*7 i;>o 72 J2 5S> N. by IS. 40 39>2 7,8 7 2 5 I 2 5>9 N.E.byE.lE. 2 2 33,9 63,5 73 *5 219,1 S.'E. 5 35>4 35-4 72 50 121,0 E. N. E. $5 24,9 60, i 73 *5 207,7 31 M 35=4 250-3 3>9 812,9 99* 35-4 3>9 99> ii Diff. oflat. 276,1 Dep. 219,4 Diff. Ion. 7 '-3*9 E. In working the above, the dirf. of long, is found by the cou. and mer. dift. between each par. oflat. ; or, it may be done by tak- ing the comps. of each mid. lat. and the dep. for each courfe. Now the lat. left was 68 .38' N. Lon. 8 4o'E. The d. ofl. 276ms. 4 36 N. DirF. Ion. 714 m. = u 54 h.. Lat. in Lat. of N. Cape 73 14 M. p. 6583. Lon. in 20 34 E. 71 10 M. p. 6177. Lon. of Cape 26 o E. The diff. lat. 2 .4' Mcr. dift, 1! 406. Diff. of long. 5 . 26'^ 326 mile,, With the mer. difF. oflat. 406, and diff. of IOD.T. 326, the cou. between the {hip and the Cape is S 38. 44' E. dift. 159 miles by Mercator ; and S,. 38 47' E, dift. 159,1 by Mid. Lat. Sailing. By INSPECTION. With.-} of diffof lat. 276, and | of dep. 219, viz. 92 and 73, the cou,. made good is 38 30' and dift. 354 miles. And with T Vof mer. dift". of lat* 849, and the cou. 38 30', the diff. of long, is 676, by Mercator's Sailing. And with the comp. of mid. lat. 19,2, and the dep. 219, the diff. of long, is 675, nearly, by Mid. Lat. Sailing; diff. from that above 38 miles, by Mercator, and 39 miles by Mid Lat. Sailing. But as (hips never run fuch dift in 24 hours, the firft methcd of finding the diff, of long, will be fufficiently exact for any day's run. The bearing and diflance to the North Cape may be either found hy . I. -l-Il :,.". n .( ,/-/ /,../ ,.////, /Vv././v.V.vw .In MERCATOR'S SAILING. 107 found by Mid. Lat. or Mercator, by Infpe&iori, which will be nearly as above. A {hip from the Lizard, In lat. 49 57' N. and long. 5 12' W. is bound to Funchal in Madeira, in lat. 32 38' N. and long. 17 5' W. fleers the following cou. S..S. W. 250 miles, W. 156, S. h. by S. 300, W. by N. 180, and S. 185 miles j required the lat. and long, {he is in, and her direct cou. and dift. to the intended port? By rinding the diff. of long, for each cou. by calculation, the fliip i? in lat. 39 27' N. and long. 1 1 i5 /T vV, by Mercator s Sail- ing ; but by working by the whole diff. of lat. and dep. the long, will be 11 1.9' W. The cou. from the fhip to Funchal is S. 34. 19' W. dift. 495,2 miles by Mercator' s Sailing : And S. 34 ,23' W. dilt. 495,3 miles, by Mid. Lat. Sailing'. A {hip from lat. 38 14' N, and long. 25 56' W. runs the fol- lowing courfes and diftances, viz. N. E. by N. | E. 56 miles, N. N. W. 38^ N. W.by W. 46, S. S. E. 30, S, by W. 20, and N. E. by N. 60 miles; required the diredt cou. and dift. made good, and the lat. and long, ihe is in ? The cou. is N. 14 E. difK 108 miles, lat. in 39 59' N. long, in 25 22' W. Suppofe a fhip in lat. 67 30' N. and Jong. 8 46' W. fails the following courfes, N. E. 64 miles, N. N. E. 50, N. W.by N. 58, W. N. W. 72, W. 48, S. S. W. 38, S by E. 45, and E. S. E. 40 miles ; what lat. and long, is (he in ? By working; by the whole diff. of ; at. and dep. the {hip is in lat. 68 44.' N - and long. 1 1 4' W. But By finding the diff. of long, for each cou. and dift.. (he- is in long. 11 37' W. by Mid. Lat. Sailing, and 11 44 W. by Mer- cator 's Sailing. Having gone through the neceflary Problems in Mercatoi's Sailing, we fhail now proceed to {hew how the true chart, com- monly called Mercator*s Chart, may be conftru&ed either for the whole, or any part of the Terraqueous Globe. J/Phw a Chart is to commence from the Equator, or if the Equator /'; to run throng') it. Having provided a fcale of convenient length, draw a line to re- prefent the Equator, and, crofting that at right angles, another to reprefent the meridian of fome krvown p'ace, fuch as .London, Paris, the Lizard, or any other place whofe longitude is known j the upper end of which will reprefent the north, and the lower the fouth. From the fcale take 60 in your compafles, and with i foot upon the meridian, fet off that diirance on both fides of it upon the equa- tor, if the chart is to contain eaft and weft longitude; but, if it is only to contain weft longitude, lay it off upon the left-hand fide of the meridian i but if eaiierly, on the right-hand fide, and that O 2 will io8 MERCATOR'S SAILING. will point out the degrees of longitude, which may be divided into halves, quarters, or minutes, if required. Having fet off as many degrees of longitude as you intend the chart mould contain, through the laft draw a line (or lines) pa- rallel to the meridian, which will be the bounds of the chart eaft and weft. Having divided the equator as above, proceed to fet off upon the two extreme meridians from the equator, the meridional parts (as found in the Table) belonging to each degree of latitude ; that is, take from the fcale in your companies the miles anfwering to one degree in the Table, and, with one foot in the equator, fet off that diftance on each fide of it upon the extreme meridians, if the chart is to contain north and fouth latitude ; but if only north or fouth, upon one fide of the equator. Again, take the meridional parts anfwering to 2 degrees and 3 degree?, &c. in your compaffes, and fet them off upon the meridian, from the equator, as before. In like manner proceed to fet off as many degrees as you intend the chart mould contain ; or, which will be the fame thing, take the meridional difference of latitude between any 2 parallels, and fet them off federally from the leaft latitude. Lay a ruler on each of thefe divifions, and draw lines parallel to the equator, and they will be parallels of latitude, each of which will be enlarged towards the poles, in proportion as the degrees of longitude are. Parallel to the meridian, draw lines through the point?, expref- fing the degrees of longitude, to cut the parallels of latitude, which bound the chart north and fouth. The parallels of latitude may alfo be divided into halves, quar- ters, or minutes, by taking the meridional parts for degrees and minutes, and fetting them off as before. Draw double lines on the borders of the chart, and mark out the degrees of latitude and longitude; and, in fome convenient place, draw the compafs. In like manner may a chart be made that {hall contain any number of degrees and minutes required. When the chart is not to commence from the equator, but is only to ferve from a certain diftance on the meridian, between two parallels on the fame fide of the equator, then the meridians are to be drawn as before, and for the parallels of latitude you are to proceed thus :- From the meridional parts anfwering to each point of latitude in your chart, fubtraft the meridional parts anfwering to the leatfc latitude, and fet off the difference -feverally from the parallels of the leaft latitude upon the two extreme meridians, and the lines joining thefe points of the meridian will reprefent the feveral parallels upon the chart. Let it be required to draw a chart that fhall ferve from the lati- tude of 14 Degrees north, to 52 degrees north, and that mail con- tain, 25 degrees of longitude weft of the meridian of Greenwich, gee the Chart, page no, Draw SAILING. 109 Draw a line to reprefentthe meridian of Greenwich, from which fet off towards the left hand 25 degrees of welt longitude, as before directed; ihrough the two laft points draw lines parallel to the meridian of London, and thefe will be the extreme meridians, or eaft and weft bounds of your chart. Having drawn the two meridians on the lower* edge of the paper, draw a line perpendicular to the meridians, to reprefent the parallel of 14 degrees north ; then, from the meridional parts anfwering to 15 degrees 910, fubtracl: the meridional parts anfwering to 14 de- grees 849, and take the difference, 61, in your companies, and fet it off from the parallel on both the meridians from you, and that will reprefent the parallel of 15 degrees. Again, take the meridional parts of 15 degrees 910, from the meridional parts of 16 degrees 973, and fet off the difference 63, upon the meridians from the point reprefenting the parallel of 15 degrees, and that will reprefent the parallel of 16 degrees. In like manner proceed to fet off the parallels upon the meridians. Or, if the meridional parts of 14 degrees be fubtracled from the meridional parts of every fucceeding parallel, and the difference be fet off from the parallel of 14 degrees upon the meridians, theje points will reprefent the feveral enlarged parallels of latitude, the fame as before j and, if it be required that the meridians ihould be "divided into degrees and minutes, the meridional parts for fuch muft be taken from the Table, and fet off a> above. Having fet off as many parallels as you intend the chart fhould contain, through each point draw parallels ; or if you think draw- ing lines through every degree will crowd your chart too flinch, you may divide the borders only into fmgle degrees, &c. and draw lines through every 5 degrees of latitude and longitude, as in the chart. Take from the Table of Latitude and Longitude of Places, the latitude and longitude of each particular place contained within the bounds of the chart, and lay a ruler over its latitude, and another croffing that over its longitude; the points where thcfe crofs will reprefent the propofed place upon the chart. In like manner may any place be readily rrarkcd. Hence the particular points of a fea- coaft may be laid down as above, and lines properly drawn from point to point will form the outlines of the fea-coafts, i (lands, &c. to which may be annexed, the depths of water, Setting of currents, and whatever elfe may be thought convenient for the chart to con- tain. This map or chart is not to, be confiderecl as a iufr or (Imilar re- prefentation of the earth's furface, for in it the figures of iilauds and countries are diftorted near the poles. For Siippofe an ifland in the latitude 60 N. or S. where the breadth of a degree of longitude is juft half as large a? a degree upon the equator. Now, as the degrees of latitude are e.t, larked in propor- tion as the degrees of longitude are expanded cowards the poles, it is plain, that every point of that ifland or country, being laicidown no MERCATOR'S SAILING. in its proper latitude and longitude, will be reprefented twice as large as it really is. Hence it follows, that as the degrees of latitude are every where increafed, like thofe of longitude, it is plain the bearing between places will be the fame on this chart as on the globe; and the pro- portions between the latitude and longitude and nautical diftances, will be the fame upon this chart as upon the globe. * And fince the meridians in this projection are right lines, it fol- lows, that th'e rhumbs, which form equal angles with the meri- dians, will be ftraight lines, which render this projection of the earth's furface much more eafy and proper for the mariner's ufe than any other. Gunter's Scales have drawn upon them two lines, one marked N M, fignifying the Nautical A4eridian ; and the other, directly under it, marked E P, fignifying Equal Parts, or degrees of lon- gitude upon a JvtercatorV Chart. Thofe are equal parts, or degrees of longitude, to which the de- gree's of the nautical meridian are fitted, by increafing them, in their true proportion; hence the limits or bounds of a Mercator's Chart by thefe lines are eafily made, by transferring the divifions correfponding to the degrees to be ufed from the fcale to the paper the chart is to be drawn upon : but as the degrees drawn by thefe lines are too frnall for the feaman's ufe, it is much better to ufe a fcale of equal parts as before, and, confequently, the degrees may be made of any propofed length. By the Latitude and Longitude it? y to prick off the Ship on the Chart. RULE. Lay the ruler acrofs the chart in the latitude your {hip is in, then look upo^ the equator, or line marked with the degrees of longitude, for the longitude ydur (hip is in by your reckoning, and. letting one foot of your compafies in that longitude, take the neareft dilhnce to fome north and fouth line, and from where that line crofles the edge of the Riler that lies in the given latitude, lay off that fame diltance along the edge in the ruler to the right hand, if the longitude you are in was to the right hand of the north and fouth line; or to the left hand, if it was to the left hand; where this falls will be the place of the {hip ; but this will only do" when the longitude marked on the chart, and your reckoning of longi- tude in, are both counted from the fame meridian. Therefore, jor a general rule, take the following, viz. By the Latitude in and Longitude made, to prick off the Sbip*s Place. RULE. Set one foot of your compafies in the place you take your departure from, and take the neareft difhince to fome north or fouth line, and from where that falls upon the equator, or the Jine marked with the degrees of longitude, fet off that diftance the fame way the place lies from it ; that is, to the right hand, if the place MERCATOH'S SAILING. Ill place lies to the right hand of the north and fouth Jine, or to the left hand if it lies to the weft ; and make a mark with a black lead pencil ; this mark will ferve to prick off by, till you come to take a new departure; and then rub it out, and make a new one as before. Then lay a ruler acrofs the chart in the latitude you are in, and taking fo many degrees in your compafTes from the line of longi- tude, as your longitude made comes to, fet them off from your black-lead mark along the edge of the ruler to the eaftward; if the longitude made be eaft, or to the weftward if it be weft; where this falls will be the longitude the Ihip is in by the chart; from which take the neareft diftance to fome north and fouth line, and from where that line, &c. as in the iirft cafe. The {hip's place on the chart being found, as before taught, it remains in the next to {hew how to find the bearing and diftance of any place from the (hip ; and firft, 7Ts find how (wy Place bears from the Skip. RULE. Lay a ruler from the place of thefhip to the pdace you would know the bearing of; then fee one foot of your compafies in the centre of fome compafs near the ruler, and take the neareft diftance to the edge of the ruler :. then run one foot of your com- pafTes along by the edge of the ruler, and obferve what point of the compafs the other comes neareft to, which will be the bearing Required. To find the Diftance of any Place from thg Ship. If the place be in the fame longitude that the (hip is in ; that is, if it bears due 1 north or fouth, then the difference of latitude be- tween them, turned into miles or leagues, will be the diftance. CASE II. If the place be in the fame* latitude the {hip is in ; that is, if in bears due eaft or due weft, then take half the diftance between the {hip and the place in your compaffes ; and, letting one foot on the line marked with the degrees of latitude, in the latitude the {hip is in, fee what latitudes the other foot will reach to, both above and below it ; the difference between thefe two latitudes will be the diftance required. CASE III. When they arc neither m the fame Latitude nsr in the fame Longitude with the Ship. RULE. Take the difference of latitude between both places in your compaffes from the equator, or graduated parallel ; and hy- ing a ruler over both places, put one foot upon the (hip's place, and flide in MERCATOR'S SAILING. Hide vour compaffes along the edge of the ruler (holding both pomts parallel to the meridian) until the other cuts the parallel of latitude palling through the phice (or any E. and W. line cut by the ruler) then ftay the companies. Take the diftance between where the point retted by the edge of the ruler and the place (or where the ruler croiTed the aforefaid eaft and weft line) in your compares, and apply it to the equator, or graduated parallel, and that will give their diftance in degrees, which may be turned into miles or leagues ; and in the fame manner as you find the bearing and diftance be- tween the fhip and any place, you may alfo find the bearing and diftance of one place from another ; or if the diftance between the dtp and place be taken in your compaffes, and applied to the fide of the chart, or graduated meridian, nearly in the parallels of the fhip and place, it will give the diftance in degrees as before ; and for this purpofe there are generally marked on the fides of charts fcales of leagues, by which the diftance between the places may be readily found. Or the diftance between two places upon a Mercator's Chart may be eafily found, thus : Take half the diftance between any two places, and with one foot of the compaffes in the middle parallel, extend both ways upon the graduated meridian; count the number of degrees between both points, which will be your diftance, eithtr in leagues or miles, ac- cording as the icale is divided ; or take the diftanee in your corn- pa fles, and fet one foot as much above the one place as the other point is below the other place, on the meridian : the number of degrees between the points of the compares will be the diftance* EXAMPLE. Required the Bearing and Diftance between Cape St. Vincent and Teneriffe ? Lay a ruler over both places, and take their difference of latitude 8 30', from the equator or graduated parallel, in your compaffes ; and fiiJe one foot along the edge of the ruler from Teneriffe, hold- ing the other point in the direction of the line CB, until the other point juft touches the eaft and weft line, (AB) paffing through St. Vincent, as at B, from C, where the foot of the compaffes refted, by the edge of the ruler, and St. Vincent being meafured, and ap- plied to' the graduated parallel, gives 10 two-third degrees, or 640 miles the diftance. Again, take the neareft diftance between the centre of the com- pafs in your compaiTes, and Hiding them along the edge of the ruler, as before directed, you will find the courfe to be S. W. by S. | W. nearly. Hence the direct courfe between Cape St.Vincent and Teneriffe is S, W. by S. -I W. diitance 640 miles, or 213 one-third leagues ; and the fame wuh other places. OF ( "3 ) OF WINDS. THE earth is endued with a wonderful principle of gravitation, whereby all its parts are ftrictly united together ; and all bo- dies that are loofe upon it clofely adhere to its furface, tending di- reUy towards its centre. Hence it is, that (hips are able to fail with the fame facility every where (void of impediments) upon the furface of the fea, quite round the terraqueous globe ; and that (as tofenfe) there is no fuch thing as an upper or lower part of the earth; for let the inhabitant be in what part foever, he will there gravitate towards the earth's centre, and imagine himfelf tobe on the higheft point of its furface; from whence he will obferve the heavens like a large vault over his head, and his antipodes he will imagine to be directly under him, as they will alfo theirs, for the like reafons. According to this law of gravity, if the earth was at reft, (and not acted upon by any other power) and its parts loofe, or its furface alt over covered with a deep fluid, it would naturally form itfelf into a true fphere, or globe. Notwithftanding this power of attraction, yet the fun, whofe rays upon the earth caufe vapours or fumes to be continually riling from it, which muft partake of the quality of thofe parts from whence they are evaporated ; a collection of which form what we call our air or atmofphere, furrounding the earth, and cxtendjng fame miles above its furface, and is liable to be put in motion by various caufes. Hence, air is a fine elaftic fluid, and h found ca- pable of being comprefled or condenfed by cold, and expanded or rarefied by he^t. Confequently, an alteration of heat or cold happening in any part of the atmofphere, the air in that part will be either condenfed or rarefied, and the neighbouring parts will thereby be put into mo- tion, thVough the endeavour which the air by its elafticity or fpringinefs always makes to reftore itfelf to its former ftate, or come to an equilibrium. Wind is a ftream or current of air, which generally blows from one part of the horizon to its oppofite. The following obfervations have been made on it, particularly , by Dr. Halley, which are not unworthy the Seaman's notice. Between 30 degrees north latitude, and 30 fouth latitude, there is a conftant eaft wind throughout the yeaj, blowing on the At- lantic and Pacific oceans, and this is called the Trade Winds. ^or as the fun, in moving from eaft to weft, heats the air more immediately under him, and thereby expands it; the air to the eaft- ward is conftantly ruftiing towards the weft to reftore the equili- brium or natural ftate of the atmofpherej whkh occafions a perpe- tual eaft wind in thofe limits. P The OF WINDS. The trade winds, near thefe northern limits, blow between the north and eaft; and, near the fouthern limits, they blow between the fouth and eaft. For as the air is expanded by the heat of the fun near the equator, therefore the air from the northward and fouthward will both tend toward the equator to reftore the equilibrium : now thefe motions from the north and fouth, joined with the foregoing eafterly mo- tions, will produce the motions obferved nen ofe limits, between the noTth and eaft, and between the foath ana weft. Thefe winds, if the whole furface of the globe were fea, would undoubtedly blow quite round it_ as they are found to do in the Atlantic and Ethiopic oceans ; but feeing fuch great continents in- terpofe and break the continuity of the ocean, regard muft be had to the nature of foils, and the poiitions of high mountains, which are the principal casfes of the variety of winds differing from the former general one. , In fome parts of the Indian ocean ^here are periodical winds,, which are called Monfoons : that is, fuc"h as blow half the year one way, and the other half the contrary way. For air that is cool and denfe will force the warm and rarefied air into a continual frream upwards, where it muft fpread itfelf to preferve the equilibrium ; fo that the x irpper courfe or current of the air {hall be contrary to the under current ; for the upper air muft move from thofe parts where the greateft heat is, and fo by a kind of circulation the N. E. trade wind below will be attended with a S. W. above ; and a S..E. below, with a N. W. .above : -* And this is confirmed by the experience of feamen, who, as foon as they get out of the trade winds, immediately find a. wind blow- ing from the oppofite quarter. In the Atlantic ocean, near the coafts of Africa, at about 100 leagues from fhore, between the latitudes of 28 and 10 north, feamen conftantly meet with a frefh gale of wind blowing from the N.I. Thofe bound to the Caribbee I/lands, acrofs the Atlantic, find, as tfeey approach the American fide, that the N . E. wind becomes eafterly, or feldom blows more than a point from the eaft, cither to the northward or fouthward. The trade winds on the American fide are extended to 30/3i, or even to 32 of north lat. ; which is about ^farther than what they extend to on the African fide ; alfo, to the fouthward of the equator, the trade winds extend 3 or 4 degrees farther, towards the coaft of Brafil on the American fide, than they do near the Cape of Good Hope OTI the African fide. Between the latitudes of four degrees north, and four fouth, the wind always blows between the fouth and eaft : On the African iide the winds are neareft the fouth, and on the American fide jieareft the eaft. In thefe feas Dr. Hatlev obferved^ that when the wind was eaftward, the weather was gloomy, dark, and rainy, with hard gales of wind - a but when the wind, veered to the fouth- OF WINDS, Warclj the weather generally became ferene, with gentle breezes, next to a calm. Thefe winds are fomewhat changed by the feafon of the year ; for when the fun is far northward, the Brafil S. E. wind gets to the fouth, and the N. E. wind to the eaff ; and when the fun is far fouth, the S. E. wind gets to the eaft, and the N. E wind on this fide of the equator veers more to the north. Along the coaft of Guinea, from Sierra Leon to the ifland of St. Thomas, under the equator, which is above 500 leagues, the foutherly and S. W. winds blow perpetually; for the S. E. trade wind having patted the equator, and approaching the Guinea coaft, within Boor 100 leagues, inclines towards the There, and becomes S. S. E. then fouth, and by degrees, as it comes near the land, it veers about to S. S. W. and within the land it is S. W. andfome- times W. S. W. This track is troubled with frequent calms, and violent fudden gufts of wind, called Tornadoes, blowing from all points of the horizon. The reafon of the wind fetting in weft on the coaft of Guinea is, in all probability, owing to the nature of the coaft, which be- ing greatly heated by the furi, rarefies the air exceedingly, and confequently the cool air, from off the fea, will keep rufhing in to reftorethe equilibrium. Between the 4th and loth degrees of north latitude, and between the longitude of Cape Verd, and the eaftmoft of the Cape Verd Iflands, there is a traft of fea which feems to be condemned to per- petual cairns, attended with terrible thunder and lightning, and fuch frequent rains, that this part of the fea is called The Plains. Ships in faring thefe 6 degrees have been fometimes detained whole months, as is reported. The caufe of this feems to be, that the wefterly winds fetting in on this coaft, and meeting the general eafterly winds in this track, balance each other, and io caufe the calms ; and the vapours carried thither by each wind meeting and condenfing, occafion the almoft conftant rains. The laft three obfervations {hew the reafon of the two follow- ing, which mariners experience in failing from Europe to India, and in the Guinea trade. The difficulty which {hips in going to the fouth ward, efpeciaily in the months of July and Auguft, find in paffing between the coafts of Guinea and Brazil, notwithftand- ing the width of the fea is not more than 500 leagues. This hap- pened becaufe the S. E. winds at that time of the year commonly extend fome degrees beyond the ordinary limits of 4N. latitude; and befides, coming fo much foutherly, as to be fometimes fouth, fometimes a point or two to the weft : it then only remains to ply to windward. And if, on the one fide, they fteer W. S.. W. they get a wind more and more eafterly ; but then there is danger of falling in with the Brazilian coaft, or {hoals , ?nd if they fteer E. S. E. they fall into the neighbourhood of the^coaft of Guinea, irom whence they cannot depart without ru-nn ing eafterly as far as P 2 the OF WINDS. the ifland of St. Thomas ; and this is the con-flan t pracYrce of ai* the Guinea ihips. All {hips departing from Guinea for Europe, their direct courfe is northward} but on this courfe they cannot go, becaufe the coaft bending nearly eaft and weft, the land is to the northward; therefore as the winds on this coaft are generally between the S. and \y. S. W. they are obliged to fteer S. S. E. or S. and with thefe courfes they run off the more; but in fo doing they always find the wind more and more contrary, fo that when near the {here they can lie fouth ; at a creat diftance they can make no, better than S. E. and afterwards E. S. E. with which coarfes they generally fetch the ifiand of St. Thomas, and Cape Lopez, where ^finding the winds to the eaftward of the fouth, they fail wefterly with it, till coming to the latitude of four degrees fouth, where they find the S. E. wind blowing perpetually. On account of thefe general winds, all thofe that ufe the Weft- India trade, even thofe bound to Virginia, reckon it their beft courfe to get as foon as they can to the fouthward, that fo they may be certain of a fair and frefh gaJe to run before it to the weft- ward ; and for the fame reafon thofe homeward bound from Ame- rica endeavour to gain the latitude of 30, where they firft find the wind begin to be variable, though the moil ordinary winds in the North Atlantic ocean come between the fouth and weft. Between the fouthern lats. of 10 and 30 in the Indian ocean, the general trade-wind, about S. E. by S. is found to blow all the y-ar round in the fame manner as in the like lats. in the Ethiopic ocean, and during tiie fix months, from May to December, thefe winds reach to within 2 of the equator ; but during the other fix months, from November to June, a N. W. wind blows in the track lying between the 33 and loth degrees of fouthern lat. in the meridian of the north end of Madagafcar ; and between the 2J and I2th degrees of fouth lat. near the lone, of Sumatra and Java* In the track between Sumatra and the African coaft, and from 3ofS. lat. quite northward to the Afiatic coaft,, including the .Arabian fea and the Gulph of Bengal, the monfoons blow from September to April on the N. E. and from March to O&obej o^i the S. W. In the former half year, the, wind is more fteady and gentle, and the weather clearer than in the latter fix months : and .the wind is more ftrong and fteauy in the Arabian fea than in the Gulph of Bengal, lie twee n the ifiand of Madagafcar and the coaft of Africa, and hence northward as far as the equator, there is a track wherein, from April to October, there is a conitant frefh S. S. W. wind, which, to the northward, changes into the VV. S. W. wind blow- ing, at that t;me, in the Arabian fea. To the eaftward of Sumatra and Malacca, an the north of the equator, and along the coafts of Cambodia and China, quite through the Philippines, as far as Japan, the monfoons blow northerly nnd ; uie northern fettibg in about October or November, and OF WINDS. IIJ arid the ibuthern about May. 'Thefe winds are not quite fo cer- tain as thofe in the Arabian Tea. Between Sumatra and Java to the weft, and New Guinea to the eaft, the fame northerly and foutherly winds are obferved; but the firft half year the monfoons incline to the N. W. and the latter to the S. E. Thefe winds begin a month or fix weeks after thofe in the Chinefe feas fet in, and are quite as variable. Thefe contrary winds do not fhift from one point to its oppofite all at once: in fome places the time of the change is attended with calms ; in others by variable winds ; and it often happens on the fhores of Coromandel and China, towards the end of themonfoon, that there are moft violent ftorms, greatly refembling the hurricanes in the Weft Indies, wherein tbe wmd is ib vaftly ftrong, that hardly any thing can refift its force. All navigation in the Indian ocean muft neceffarily be regulated by thofe winds ; for if mariners ihould delay their voyages till the contrary monfoon begins, they muft either fail back, or go into harbour, and wait for the changing of the trade winds. Vapours rifing from the fea, and by the wind carried over low lands to the ridges of mountains, and compelled to mount up with the ftream of the air to the tops, where the water prefently preci- pitates, gliding down by the chinks and cliffs of the ftones, and part of the water entering into the caverns of hills, and gathering into bafons, which being once filled begin to run over, and form fubter- raneous paflages through the earth, breaking out in fprings by the fides of hills; feveral oF thofe meeting tog-ther form a rivulet ; feveral of thefe rivulets meeting together make a river. This, to- gether with what is incorporated into vegetables, renders it impof- fible for all the water evaporated from the fea to return to it again. Hence the evaporations arifing from the Mediterranean are fuch, that notwithftanding there are nine capital rivers, which empty themfelves intoit, beiidefmaller ones, there is aconftant current run- ning through the Straits of Gibraltar from the Atlantic ocean, to make up the deficiency. R. Mean, M. D. and F. R. S. obferves, i. That fome difeafes are probably the effects of the influence of the heavenly bodies. 2. That the moft windy feafons of the year are about the vernal and autumnal equinoxes. 3. All the changes we have enumerated in the atmofphere do fall out at the fame times when thofe happen in the ocean; and, as both the waters of the fea and the air of our earth or fluids are fubjecr. in a great me ifure to the fame laws of motion, fo that natural effe&s of the fame kind are owing to the fame caufe?. 4. The alteration made by the fun and moon in the atmofphere muft thereby have influence on the animal body. 5. The elafticity of the air k of great moment, and it is reciprocally as the prefTure, fo that the incumbent weight be- ing diminimed by the attradlk>n, the air underneath will be much^ expanded 5 thefe, and fuch like caufes, will make the tides "in the air to be rruich greater than thofe of the ocean ; and there is no doubt to be made, but~that tfte fame infinitely wife Being, who contrived ti'- Il8 OF WINDS. the flux and reflux of the Teas, to fecure that vaft collection of ivaters from ftagnation and 'corruption, has ordered this ebb and flood of the air of our atmofphere with the like good defign ; that is, to preferve it fweet, and a brifk temper of this fluid fo neceflary to life, by a continual circulation. 6. Two contrary winds blowing towards the fame place, may accumulate the air there, "fo as to increafe the height and the weight of the incumbent cylinder; in like manner the direction of two winds may be fuch, as meeting at certain angles, may keep the gravity of the air in a middle flate ; but if the wind blows different ways from the fame pla^e (which may be occafionetl by thunder and lightning) the height and weight of the air may be much decreafed. 7. The changes in our atmo- fphere at high water, new and full moon, the equinoxes, &c. muft occaiion alterations in all animal bodies, for all living creatures re- quire air of a determined gravity to perform refpiration eafily; for it is by its weight that this fluid infmuates itfelf into the cavity of the bread and lungs : by a flow circulation the fecretion of the fpi- rits is diminifhed ; and by the want of the force of elafticity and gravity, the juices begin to ferment, change the union of their parts, break their canals, and difeafes follow. Befides the above caufes, the atmofphere may be put in motion by the elaftic vapours forced from the bowels of the earth by fuk- terraneous heats, and condenfed by whatever caufes in the atmo- fphere. A mixture of effluvia in different qualities in the air may, by rarefaction, fermentation, &c. produce winds and other effeds like thofe refulting from the combination of fome chemical liquors ; and that fuch things happen, we are afiured from the nature of thunder, lightning, and meteors. From the eruption of volcanoes and earthquakes in diftant places, wind may be propagated to re- moter countries. The divided or united force? of the other planets, and of the comets, may varioufly difturb the influence of the fun and moon, &c. We know that there happen violent tempers in the upper region of the air, when we below enjoy a calm, and how many ridges of mountains there are on our globe which interrupt and check the propagation of the winds, fo that it is no wonder that the phcenomena we have afcribed to the action of the fun and moon, are not always conftant and uniform, and that every effect does not hereupon follow ; which, were there no other powers in nature able to alter th? influence of, this might, in a very regular and uniform manner, be expedled from it. That the rarefied air afrends is fufficiently demonftrated by the aeroftatic globe, or air balloon, lately invented : this is a globe made of filk, or other light fluff, irvade air tight with gum ; which, being filled with inflammable or rarefied air, will, when let loofe, afc.end, until it comes to that part of the atmofphere that is nearly as light as the air within it, where it will continue fome time. OF OF TIDES. A TIDE is that motion of the water in the Teas and rivers, br which they regularly rife and fafl : the general caufe of which was difcovered by Sir ISAAC NEWTON, and is deduced from the following confiderations: Daily experience (hews, that all bo- dies, when thrown upwards from the earth, fall down to its fur- face in perpendicular lines 5 and as lines perpendicular to the fur- face of any fphere tend towards its centre, the lines, along which all heavy bodies fall, muft be directed towards the earth's centre. As bodies appear to fall by their weight or gravity, the law, by which they defcend, is called the law of gravitation : and as a magnet or loadftone will draw fmall portions of iron or fteel, and as a piece of glafs, amber, or fealing-wax, when warmed by rub- bing, will draw fmall bits of paper, and other light fubflances, the law, by which fuch bodies fly to thofe which draw them, is called the law of attraction. Hence it is not improper to fay, that bodies, when falling by their gravity towards the earth, are attracted by the earth; and therefore the words gravitation and attraction may, refpecting the earth, be ufed indifferently, as by them is only meant that power, or law, by which all bodies tend towards its centre. Sir ISAAC difcovered, by a great number of obfervations, that this law of gravitation or attraction was univerfally diffufed throughout the folar fyftem 5 and that the regular morions, ob- ferved among the heavenly bodies, were governed by it -, fo that the earth and moon attract each other, and both of them are at- tracted by the fun. He alfo difcovered, that the force of attrac- tion, mutually exerted by thefe bodies, was leffened as the diftance increafed, in proportion to the fquares of thofe diftances ; that is, the power of attraction, at* double the diftance, was four times lefs j at triple the diftance nine times lefs 5 at quadruple the di-f- tance, fixteen times lefs, and fo on. As the earth is attracted by the fun and moon, it follows, that all the parts of the earth will not gravitate towards its centre in the fame manner as they would do, if thofe parts were not affected by fuch attractions. And it is evident, that were the earth en- tirely free from fuch actions of the fun and moon, the ocean, be* ing on all fides equally inclined towards its centre by the force of gravity, would continue in a perfect itagnant {rate, without ever ebbing or flowing.- But, as the cafe is otherwife, the water in the ocean rnuft needs rife higher in thofe places where the fun and rnoon diminish its gravity, or where they have the greateft at- tra&ioru As 120 OF TIDES. As the force of gravity muft be diminifhed moft in thofe parts of the earth to which the moon is neareft, or in the zenith, becaufe her attraction will there be moft powerful ; therefore the waters, in fuch places, will rife higher, and it will in them he full fea or high- water. The parts of the earth directly under the moon, and alto thofe in the nadir, viz. fuch places as are diametrically oppo- flte to thofe where the moon is in the zenith, will have high-water at the fame time. For either half of the earth would gravitate equally towards the other half, were they fuperfluous free from all attraction. But by the a&ion of the moon, the gravitation of one half of the earth towards its centre is diminifhed, and that of the other increafed. In the half-earth next the moon, the parts di- rectly under her being moft attracted, and confequently their gra- vitation towards the earth's centre moft diminifhed, the waters in thefe parts muft be higher than in any other part of this half-earth. And in the half-earth, fartheft from the moon, the parts in the na- dir being Icfs attracted by her than thofe which are nearer, gra- vitate lefs to wards the earth's centre, and confequently, the waters in thofe parts mult be higher than they are in any other part of this half- earth. Thofe parts of the eaith where the moon appears in the hori- zon, or is go degrees diftant from the zenith and nadir, will have their loweft waters. For as the waters in the zenith and nadir rife at the fame time, the adjacent waters xvill prefs towards thofe places to reftore the equilibrium ; and, to fupply the places of thefe, others will move the fame way, and foon to 90 diftant from the find zenith and nadir : confequently the waters, in tho'fe places \vrrere the moon appears in the horizon, will have moft liberty to defcend towards the centre ; and therefore they will, in fuch places, be the loweft. Hence it plainly follows, that the ocean, if it covered the furface of the earth, would put on a fpheioidal, or egg-like figure, in which the longeft diameter would pafs through the place where the moon is vertical ; and the fhorteft where (he is In the horizon. And as the moon apparently fhifts her pojltion from caft to weft in going round the earth every day, the long dia- meter of the fpheroid, following that motion, would occafion the 'two floods and ebbs in about every 25 hours, which is about the length of a lunar day, or the time fpent between the moon's leav- ing the meridian of ar.y place, and her coming to it again. Hence, the greater the moon^s meridian altitude is at any place, the greater will thofe tides be which happen when (he is above the horizon ; and the greater her meridian depreiiion is, the greater will thofe tidts be, which happen when {he is below the horizon. The fummer day, and the w'inter night, tides, have a tendency to be the higheft \ becaufe the fun's fummer elevation, and his winter depieflion are greateft : this is more efpecially to be obferved when the moon has north declination in fummer and fouth declination in winter. f The time of high -water is not precifely at the time of the moon's coming OF TIDES. Il2 coming to the meridian, but about an hour after. For the moon continues to a<5t with fome force after (he has pafTed the meridian, and by that means adds to the libratory, or waving motion, which fhe put the water into whilft fhe was on the meiidiaji ; in the fame manner as a fmall force applied upwards to a ball, already raifed to fome height, will raife it ftill higher. The tides are greater than ordinary twice every month ; that is, about the times of new and full moon : they are called fpring tides. At thefe times the fun and moon concur to draw in the fame right line ; and therefore the fea muft, under fuch joint influences, be more elevated than at other times. During the time of their conjunction, or whilft they are on the fame fide of the earth, they both confpire to raife the water in the zenith, and confequently in the nadir: and when the fun and moon are in oppofition, that is, when the earth is between them, whilft one makes high-water in the zenith and nadir, the other does the fame in the nadir and zenith. The tides are lefs than ordinary twice every month ; that is, about the times of the firft and laft quarters of the moon ; thefe are called neap-tides : be- caufe in the quarters of the moon, the fun raiies the water where the moon depreffes it, and depreffes where the moon raifes the wa- ter ; fo that the tides are then caufed only by the difference of their actions. Hence it is neceflary to obferve, that the fpring- tides happen not exa&ly at the new and full moon, but generally three days after, when the attracting powers of the fun and moon have confpired for a confiderable time. In like manner the neap-tides happen about three days after the quarters, when the moon's at- traction has been leffeneJ by that of the fun for feveral days to- gether. When the moon is in her per'tgium^ or neareft approach to the earth, the tides rife higher than they do under the fame circum- ftance at other times ; for, according to the laws of gravitation, the moon muft attract moft when fhe is neareft the earth. 7 A he fpring-tides are greater about the time of the equinoxes, that is, about the latter end of March and September, than at other times of the year ; and the neap-tides are then lefs; becaufe the longer diameter of the fpheroid, or'the two oppofite floods, being then in the earth's equator, will defcribe a great circle of the earth ^ by the diurnal rotation of which, thofe floods will move fwifter, defcribing a great circle in the fame time they ufed to defcribe a Jefs one, parallel to the equator ; and confequently the waters be- % ing thrown more forcibly againft the fhores, muft caufe them to rife higher. The following obfervations have been made on the rife of the tides: namely, the morning tides generally differ in their rife from the evening tides. The new and full moon fpring tides rife to different heights. In winter the morning tides are higheft. In iummer the evening tides are higheft. Thus it appears, that, after a period of about fix months, the order of the higheft tides are in- verted j that is, the rife of the morning and evening tides will Q, change jrd 122 OF TIDES. change places, the winter morning high-tides becoming the fame .as the fummer evening high-tides. Some of thefe effedls arife from the different diftances of the moon from the earth after a period of fix months, when fhe is in the fame iltuation with refpect. to the fun ; for, if fhe be in perigee at the time of the new moon, fhe will, in about fix months after, be in perigee about the time of full moon. Thefe particulars being well known, a pilot may chufe that time which will prove moft convenient for conducting a {hip out of any port, where there is not a fuflicient depth of wa- ter on common fpring tides. Small inland feas, fach as the Mediterranean and Baltic, are little fubjecl: to tides ; becaufe the action of the fun and moon is always nearly equal to the extremities of fuch feas. The tides, in very high latitudes alfo, are very inconfiderable ; for the fun and moon acting towards the equator, and always raifing the war ter towards the middle of the torrid zone, the neighbourhood of the poles muft confequently be deprived of the waters, and the fea within the frigid zones muft be low in comparifon to the other parts. All the things hitherto explained would be exactly obtained, were the whole furface of the earth covered with fea. But fince there are a multitude of iflands, befides continents, lying in the way of the tide which interrupt its courfe; therefore there arife, in many places near the (here?, a great variety of other appearances, befides the foregoing ones, which require particular folutions, in which the fituations of the fhores, ftraits, Ihoals, winds, and other things, muft neceflarily be confidered. For inftance; s.?, the fea has no vifible paflage between Europe and Africa, let them be fup- pofed one continent, extending from 79 north, to 34 fouth : the middle of thofe two would be in latitude 19 north, near Cape Blanco, on the weft coaft of Africa. But it is impoffible the flood tide fliould fet to the weft ward, upon the weftern coaft of Africa (for the general tide, following the courfe of the moon, muft fet from eaft to weft*, becaufe the continent, for above 60, both northward and fouthward, bounds that fea on the eaft} and there- fore, if any regular tide, proceeding from the motion of the fea, from eaft to weft, fhould reach this place, it muft be either from the North of Europe fouthward, or from the South of Africa north- ^yard. This opinion is further corroborated, or rather fully confirmed, by common experience, which fliews that the flood -tide fets to the fou'hward along the weft coaft of Norway from the North Cape to the Naze, or entrance of the Baltic Sea, and fo proceeds to the fotithward along the eaft coaft of Great Britain, and in its pafTage fupplies all thofe ports which lie in its way, one after another. The coaft of Scotland has the tide firft, becaufe it comes from the northward to the fouthward. On the full and change days, it is high- water at Aberdeen at I2h. 45m. but at Tinmouth-bar not fill jh, Rolling thence to the fouthward, it makes high- wat^r at the OF TIDES. 123 th? Spurn a little after 5)1. at Yarmouth Roads a little after 8h at Harwich at loh. 33m. at the Nore J2h. and at London 2h. 3001. all in the fame day. And although this may feem to contradict the hypothecs of the natural motion of the tides being from eaft to weft, yet as no tide can come weft from the main continent of Norway or Holland, it is evident that the tide we have been trac- ing, by its feveral ftages from Scotland to London, is fupplied by that tide, the original motion of which is from eaft to weft. As \vater always inclines to the level, it will in its pafla^e fall to any other point of the compafsj to fill up vacancies where it finds them ; and yet not contradict, but rather confirm, the hy- pothefis. While the flood tide is thus gliding to the fouthward along the eaft coaft of England, it alfo lets to the fouthward along the weft coafts of Scotland and Ireland ; one branch of it falls back north- eaft into St. George's Channel ; and another runs between Ufhant and the Lizard, into the Britifh Channel. Some may object that this courfe of the flood-tide, eaft up the Channel, is quite contrary to the h-.-pothefis of the general motions of the tides being from eaft to weft; and confequently of its being high- water where the moon is vertical, or any where elle on the meridian. But it may be anfvvered, that this particular direction of the tides does not con- tradict the general direction of the whole. A river with a weftern courfe may fupply canals which wind north, fouth, or even eaft, and yet the river keep its natural courfe; and if the river ebbs and flow?, the canals fupplied by it would alfo do the fame, al- though they did not keep exact time with the river; becaufe it would be flood, and the water advanced to fome height in the ri- ver, before it reached the fartheft part of the canals ; and the more remote the extremity of the canals are, the longer time it would require; it may alfo be added, that if it were high-water in the river juft when the moon was on the meridian, fhe would be far paft it before it could be high -water in the remoteft part of thofe canals ; and the flood would fet according to the courfe of the ca- rials that received i}, and could not fet welt upon a canal of a dif- ferent pofition. As St. George's Channel, the Britifli Channel, &c. are no more in proportion to the vaft ocean, than fuch canals would be to a large navigable river ; it will evidently follow that the flood-tide may, among thofe obftru6tions and confinements, fet upon any other point of the compafs, as well as weft ; and may make high- water at aiiy other time, as well as when the moon is- upon the meridian, without any wife contradicting the general theory of the tides. Among pilots it is cuftomary to reckon the time of high-water by the point of the compafs the moon bears on at that time, allow- ing three quarters of an hour for each point. Thus, in places \ where it is high-water at noon, on the full and change days,, the tide is faid to flow north and fouth, or 12 o'clock. In places where the moon bears i, 2, 3, 4, or more points to the eaft ward or Q. 2 weftwaxd 124 OF TIDES. weftward of the meridian, when it is high water on fuch days, the tide is faid to flow on fuch a point ; fo, if the moon bear Ibuth- eail, at high- water, it is faid to How ibuth-eaft and north- weft, or Q o'clock:; if (he bears fouth-weft, it flows fouth-weft and north-eafr., or 3 o'clock 3 and in like manner for every other point of the moon's bearing, From the obfer vat ions of many perfons, the time of high- wa- ter on the days of the new and full moon on mod of the coafts of Europe, and feveral other places, have been collected ; and thofe are generally put in a table, againfl the names of their re- fpedtive places, in an alphabetical order ; hence it is called the Tide Table, which is at the end of the Book. The method generally prcfcribed for finding the time of high water at any place, is contained in the following particulars : To find the Leap Year. Divide the given year by 4, if nothing remains, it is leap-year, but if I, 2, or 3 remains, they fhew that it is fo many years after- Biflextile or Leap-year, as the remainder is : thus, in the year 1806, divided by 4, gives 451, and the remainder [2] (hews it is the fecond year after BifFextile, or Leap-year. To find tbf Golden Number for any Tear. RULE. Add one to the given year, and divide the fum by ig, the remainder will be the Goldeii Number. EXAMPLE. Required the Gsldin Number of 1 8 06 ? By adding one to that year, it gives 1807; this divided by 19 gives 95 for the quotient, and the remainder is 2 3 the Golden Num- ber for 1806. Tofnd the Epaflfor any Tear. NOTE. The Epat is the moon's age at the beginning of the year, or rather the ift of March. The Epaft advances 1 1 every year to 30, becaufe the folar year is 1 1 days -longer than the lunar' year, and as the Epacl increafes, it fhews the moon's age at the beginning of the year ; it is here fuppofed that at the end of 19 years, the fun and moon make all the variety of fituations they poffibly can with one another, and thence begin, and go over the lame again. The Golden Number at the birth of Chrifr was J, which is the reafon that one is added to the given year, to rind the Golden Number. RULE. Divide the given year by 19, the remainder multiply by 1 1, and the product will be the Epact, if it does not exceed 29 ; but if it does, fubtract ^o from it as often as you can, and the re- mainder will be the Kparr, for i: never exceeds 29. EXAMPLE, OF TIDES, EXAMPLE. What is the Epafi of the Tear 1806-? 1806 divided by 19, gives 95 for the quotient, and I remaining fhews the Epact is(ii) for 1806. To find the Morris Age. To the Epa& add the day of the month, and the Epa& or num- ber for the mo/ith j the fum, if it does not exceed 30, is her age ; but if it does, fubtracl 30 from it as often as you can, and the re- mainder is her age. NOTE. The Epa&, or number for each month, is found thus: divide the number of days contained between the ift of January and the ift day of any month, by 29!, the remainder will be the number for that month. Required the Number or Epacl: for Sept. 1806 ? The number of days contained between the ift of January, 1806, and the ift of Sept. are 243 days, divided by 29!, gives 8 for the quotient, and 7 for the remainder, which is the number fought ; and fo for any other month. EXAMPLE. Required the Moon's Age, April 29, 1806 ? Day of the month 29 Epaft u Number for the month 2 Moon's age 12 Numbers for the months are nearly as follow : Jan. Feb. Mar. Apr. May June July Aug. Sept. O&. Nov. Dec, In com. years 0202244678910 Jn leap years 021*3 3 55 7 8 91011 To find the Moon's Southing on any Day cf her Age, Since the fun returns to the meridian he has left in the fpace of 24 hours, and the moon in about 24 hours 4^111 in utes ; therefore, if the moon leaves the meridian at the fame time, that the fun does, on any day, the next day {he will come to the .meridian 49 mi- nutes after him, falling back about 49 minutes every day ; whence, to 6nd the time of the moon's fouthing, or coming to the meridian on any day, we have this eafy RULE : Multiply the day of her age by 49, and divide the product by 60, the quotient is the hours, and the remainder the minutes after- noon when {he fouths. Or, which is rather eafier, and in many refpects fufEcjemly exact for the manner'? purpofe j multiply the 126 OF TIDES. moon's age by 4, and divide the product by 5, the quotient is the hours, and the remainder multiplied by 12, gives the minutes after- noon when (he is upon the Meridian; but if this time exceeds 12, fubtraft 12 hours from it, and the remainder is the time of her Southing in the morning. N. B. From the fui! moon to the change (he comes to the me- ridian, or fouths, in the morning; but from the change to the fuil^ in the afternoon. EXAMPLE. Required the Moon's Southing, Aug. 14, 1896? The EpacT: is 1 1 Number for the month is - 6 Day of the month 14 Moon's Age I = 49 min. Hence it appears that the moon comes to the fouth at 49 mi- nutes afternoon. To find the Time of High Wa+er on any Day of the Moon's dge at any Place. RULE. To the time of the moon's fouthingon the given day, add the time of high-water at the full and change, at the given place, taken from the Table ; the fum is the hour paft noon on the given day when it is high-water at that place ; and if this hour exceeds 12, fubtracl: 12 from it, and the remainder (hews the time of high water in the morning ; but if it exceeds 24, fub- tracl: 24 from it, and the remainder fhews the time of high-water in the afternoon. Required the Time of HighWater at Milford on the 29th Jan. 1806. EXAMPLE I. Epact 1 1 No. of Month o Day of Month 29 30) 40 (* Moon'; Age 10 x by ' 49 -T- by 60)490 ( 10 Moon's South. 8 10 afternoon. Time at Milford 6 14 10 12 H. \V. Morning 2 i o EXAMPLE. OF TIDES. EXAMPLE II. At what time will it be High Water at London, Auguft . 29, 1809? 19)1809(95 X by 99 m - m 4 II Epjra No. of Month Day of Month Subtraa Moon's Age Multiply by 3) 44 ( H 7 29 5 30 20 4 Divide by 5) 80 ( Moon's Southing 16 Hours Time at London 2 46 Afternoon 8 lib t raft In the Morning 6 46 So that it is High Water at 46 min. after 6 in the morning ; and by adding 12 hours 24 mi- nutes, the fum gives the time of the next High Water. EXAMPLE III. Required the Time of High Water at Dover,Ocl:. i, 1806. I 9 )i8o6 v9 5 X by 96 I II No. of Month 8 Day of Month I 20 Multiplied by 49 -r- by 60)980(20 Dover 26 . 36 .24 Afternoon 2 . 36 Here it is 36 min. part two o'clock in the afternoon. EXAMPLE IV. Required the Time of High Wa- ter at Aberdeen on the 2d of June, 1806. EpadT ii No. of Month 4 Day of Month 2 Moon's Age X by -by 17 . . J2 In the Mornjng 13 . 36 Time at Aberdeen 12,45 H. W. Morning 26 . 21 21 Co?ning int-3 a Port and finding that it iV High Watei at a certain Hottr^ to know when it is High Water there on Full and Change D.ays. RULE. Subtract the time of high-water from the moon's feu th- ing on that dav, but if required add 12 hours, the remainder will . jbe the time of 'the flowing, on the full and change, at that place. This OF TIDES. This method of finding the time of high-water, at times, will differ hours wide of the truth ; even if the moon's fouthing beex- aclly found ; for the floods do. not always happen at the fame dif- tance of time from each other, but at different diftances, accord- ing to the times of the moon's age, or as the waters are a&ed upon by the fum or difference of the attractive forces of the fun and moon, and alfo on account of winds and ftorms, even when out of hearing; therefore pilots, and all concerned, would do well to ufe the following method, which will in general give the time of high-water nearer the truth, when the tides are not greatly in- fluenced by the wind. A Table (hewing the Day of the Month and Hour of the Day when it is New Moon hy Astronomical Calculation. A Tableof Corrections to be added to the Moon'b Age to find her South- in; . Month?. 1806. 1807. 1808. 1 h09. Ds. ' H. M. Ds. H. M. D. H. D. II. D. II. D. II. 1 o 3 4 5 6 1 8 9 10 11 12 13 14 15 . 36 1.11 1 . 46 2 . 21 3 . 1 3 . 44 4 .37 5 . 40 6 . 58 8 . 14 9. 17 10. 9 10 . 53 11 . 33 12. S 16 17 18 39 20 21 22 23 24 25 26' 27 28 29 29i . 45 1 . I*/ I . 54 2 . 30 3 . 11 3 . 56 4 . 51 6. 7 . 18 8 . 31 9 31 10 . 21 11 . 3 1 1 . 42 12 . 00 Jan. 19- 18 8 . 8 7 . 2 8 . 21 27 . 4 15 . 13 14 . 2 15 . 1C 14 . 8 Feb. IS . 3 25 . 21 March. 19- 19 26' . 14 25 . 7 April. 18 . 9 7 . 14 May. 17 . 20 7 . 5 24 . 23 14 . June. 16 . 4 5 . 17 23 . 13 12 . 16 12 . 6 July. 15 . 12 5 . 3 23 . Auguft, 13 . l v q 3.11 21 . 10 19 - 19 10 . 20 9- 8 Sept. 12 . 2 1 . 19 Oclober, 11 . 12 1 . 5 30 . 13 10 . 5 8 . 20 7 - 7 6. 17 Nov. 9 . 24 28 . 24 17 . 15 17 . 2 Dec. 9 . U 2 54 2 . 3 9 . 2 9 44 3- ^ 3 12 2 3 2 . 21 9 . 17 9 -3 1 3 . 12 3V 18 2 . 12 2 . 12 9- 3i 9 . 16 3.18 4 . o 2 . 21 2 3 Q 44 9- * 4 . o To find the Time of High From page i. of the month in the Nau. Aim. take out the time of the phaie of the moon anfwering nearer! to the given day, v/hich reduce to the meridian of the place by fubtracliing the long. of the place in time, if it be weft, and adding it if it be Eaft : then, under the neareft phafe, at the top of the Table, and oppofite the difference OF TIDES. 131 difference between this reduced time and the noon of the given day, is the Correction to be added to the time of high water on the new and fall moon at the given place, to find the time of high water on the given day. EXAMPLE I. Required the Time of High Water at Portfmoutb, on the iyh cf June^ 1808. D. H. M. The neareft pbafe to the i3th of June is 3d quarter 1510 8 Day of month 13 Diff. of time before the 3*1 quarter 2 10 8 Between zd. 6ho. and zd. izho. the equation is -|~ 35 Flows at Portfmoufh - 11 36 'As it is paft the full gives high water 2h. 41 min. A. M. = 1441 EXAMPLE II. IVcat lime is it High Water at P or if mouth the ^d of July ^ 1808. D. H. M. To July the 3d the neareft phafe is ift quarter June 30 17 45 July the 3d may be called June 33 Diff. of time after the i ft quarter 2 6 15 The equation for" 22d. 6 ho. is -J- 7 5" Flows at Portfmouth n 36 High water 7 Ho. 32 P. M. =s 19 3* EXAMPLE III. Required tie Time of High Water the lOfh of July , 1808, at Hali- fax, Nova Scotia^ Long. 63 28' \V. where it flows yH. joM. P. H. M. S. Time from noon of full moon at Greenwich 71-33: Long, of Halifax 63 28 in time = - 4 13 52 Time of full moon at Halifax 7 7 49 8 Given day 10 Interval of time paft the full moon 2 16 10 52 Correction from the Table for the interval _|_ { 33 Time of high water new and full at Halifax 7 30 High water at Halifax the loth of July 93A.M. But to find the time of the next high water find the difF. of equa- tion for the next 12 hours, which added to the time of the lail high water, gives you the time required. K 2 OF ( 13* ) OF THE LOG-LINE AND HALF-MINUTE GLASS, AND HOW TO CORRECT THE DISTANCE GIVEN BY THEM. THE log is a flat piece of wood like a flounder, or of the figure of a quarter of a circle, having its circular fide loaded with lead fufficient to make it fwim upright in the water .To this log is fafteneda long line of about 150 fathoms, called the log-line, which is divided into certain equal fpaces, called knots, each of which ought to bear the fame proportion to a nautical mile (60 of which make a degree) that half a minute does to an hour, that being the time allowed for the experiment. They are called knots, becaufe at the end of each of them there is a piece of twine with knots in it, reeved between the ftrands of the line; thefe pieces of twine fhew how many knots run out, in half a minute, and confequently the fhip's rate of failing per hour, Mr. NORWOOD, and feveral other able mathematicians, have found that a degree of a great circle upon the earth contains about 367,200 Englifh feet, therefore a nautical mile bein - 6 V part of 367,200 feet, that is, 6120 feet, and fince half a minute is T l rs part of an hour, the length of the knot on the log-line ought to be the -rJio part of 6120 feet, or 51 feet. (In the requisite Tables pub- liihed in 1802, the fea mile is accounted 6078 feet.) But as for themoft part, the fhip's way is found, by experience, to be really more than that given by the log, and as it is fafer to have the rec- koning before the fhip than after it, therefore 50 feet may b.e taken as the proper length of each knot, and thefe knots fubdivided into ten fathom?, each of five feet, which is certainly the beft adapted for practice, and will correfpond with ail the tables and inftru- ments ufed in navigation, as they are decimally divided, and con- fequently, the {hip's run determined with greater eafe and cer- tainty. But Come experienced commanders find, that the allow- ing 50 feet to a knot generally makes the ftiip a-head of the reckon- ing ; and to avoid danger moftly divide the log-line into knots of 7 or 7! fathoms of 6 feet each, to correfpond with a glafs that runs 28 feconds. Others again divide the feconds the giafs runs by 4, and take the quotient for trie diflance in fathoms bet ween the knots : which laft method I have ufed for 40 years, and always found it anf- wered ; but-certain it is, that whatever length the knots are, the jaofr. convenient way is to divide them into tenths. Jn hot or dry weather, the glafs runs out fauer than in mcift or rainy OF THE LOG-LINE AND HALF MINUTE GLASS, &C. 133 rainy weather ; therefore care fhould be taken to try what number of feconds the giafs runs. The knots commonly begin to be counted at 'the diftanceof ro, 12, or 15 fathoms from the log, according to the largenefs of the {hip, that fo the log may be out of the (hip's wake when it is thrown overboard before they begin to count, lelt the eddies fliould fuck the log after the ftiip ; and for the mod ready difcovery of this point of commencement, there is commonly fattened at it a piece of red rag ; that part of the line between the red rag and the log is called the ft ray-line. The log and log-line being duly prepared and hove overboard from the lee quarter, and the line veered out (by the help of a reel, which turns eafy, and about which it is wound) as fa ft as the log; will carry it away, or rather as raft as the fhip fails from it, will fhow how faft the {hip has failed in the given time, or rate of fail- ing per hour. The experiment for finding the velocity of the (nip is called heav- ing the log. Care mould be taken to veer out the line as fa ft as the log takes it, for if the log is left to turn the reel of itfelf, the log will cpme home and deceive, you in the reckoning. In King's (hips, India {hips, and fome others, the log is hove every hour, but in coafters, and thofe ufing fhort voyages, every two hours, Here the (hip is fuppofed to move with equal velocity between the times of trying the experiment. But if the gale has not been the fame during the whole hour, or time between heaving the log, or if there have been more fail fet, or any handed, that fo the (hip has run more or lefs in any part of the hour than (lie did at the time of the experiment; or if it fhould fall little or more wind at that time, there muft be allowance made for it according to the difcre- tion of the artift : Sometimes, too, when the (hip is before the wind, and a great fea fetting after her, it will bring home the log; in fuch cafes it is cuftomary to allow one mile in ten, and lefs in proportion, if the fea be not/o great. Care ihould alfo be taken to meafure the log-line pretty often, left ic ftretch, and deceive you in the diftance. The like regard muft be had, that the half-minute glafsbe juft 30 feconds, otherwife no account of the {hip's way can be kept; to prove which, if there be no (top watch at hand, let a plummet, of any form or weight, he fattened to a ftlk firing or thread, with a loop to hang on a fmall pin or nail fattened in any ptace, fo that the plummet may fvving freely ; let it be 39! inches from the end of the loop .to the middle of the plummet, and the plummet caufed to fvving; each of thofe fwings will be a true fecond of time, al- ways counting every time it pafles the perpendicular let fall from the pin, and every time it pafles from the perpendicular to the ut- '' iV/inpf will be half-a-foamd. 134- F THE LOG-LINE AND HALF-MINUTE GLASS, &C. How to correft the Dtjlance given by the Lot-Line and Half- Minute Glafs. The diftance given by the log may be wrong on three accounts. viz. by an error in the glafs, an error in the lag-line, or an error in both j for correcting of which take the folio wing cafes : CASE I. When the log-line is truly divided, and f the glafs is faulty. RULE. Say, as the feconds run by the g'lafs are to 30 feconds, (b is the diflance given by the log to the true diftance. EXAMPLE. I. Suppofe a (hip runs at the rate of 7$ knots in the time the glafs runs out, but meafu ring the glafs I find it runs 34 feconds ; what is the true rate of failing ? As 34. : 30 : : 7,5 : 6,6 miles, the true diftance failed in an hour. EXAMPLE II. Suppofe a fhip runs at the rate of 6 J knots, but meafuring the glafs I find it runs only 25 feconds j required the true rate cf jailing ? As 25 : 30 : : 6,5 : 7,8 miles, the true diftance failed in an hour. CASE II. When the glafs is true and log line faulty. RULE. Say, as 50 feet is to the diftance meafured between knot and knot, fo is tffe diftance run by the log to the true diftance. EXAMPLE I. Suppofe a fhip runs at the rate of 6 J knots in half a minute, but meafuring the fpace between knot and knot, I find it to be 56 feet; required the true rate of failing ? As 50 : 56 : : 6,25 ; 7 miles, the true diftance failed in an hour. EXAMPLE II. Suppofe a (hip runs at the rate of 6f knots in half a minute, but meafuring the fpace between knot and knot, I find it to be only 44 feet ; required the true rate of failing ? As 50 : 44 : '. 6,5 : 5,72 miles, the true diftance failed in an hour. CASE III, ' When both the log-line and glafs are faulty. RULE. Multiply Thrice the meafured length of a knot by the diftance run by the log, the product divided by 5 times the mea- fured time of the glafs will give the true diftance run. EXAMPLE DESCRIPTION AND USE, &C, 35 EXAMPLE. Suppofe a ftiip runs 5 knots of a log-line of 45 feet to a knot, while a glafs of 25 feconds is running out j what is the true rate of failing ? The meafured length of a knot 45 Multiplied by Gives thrice the meafured length of a knot 135 Which multiplied by the diftance run per log 5 Product 675 And dividing the product by 5 times the time the glafs runs, that is 5-4-25:1=125, the quotient is 5,4, the number of miles the fhip runs per hour. This rule is only a compound of the two former fimple ones, which is con- traded a little. When the glafs is faulty, the log-line may be divided as in the annexed Table, {hewing the length of the knots of the log-line of different glafles. Second of Glafs. Length of Knots in Feet.; 24 40,0 25 41,8' 2(> 43>4 2 7 45> 28 46,8 29 48,4 30 50,0 31 5i>8 3* 53.4 33 55,0 34 56,8 35 58,1- 36 60,0 j THE DESCRIPTION AXD USE OF HADLEY's QUADRANT AND SEXTANT Fig. I. The principal Parts of the Injlrummis are, The Index D The Index Glafs E The Horizon Glafles G and F The Dark Glades, or Screens, H. The Sight Vanes K and G The graduated arch of the Quadrant contains only 45 de III. DESCRIPTION AND USE &C. grces, or thsSth part of a circle, but it is to be counted as 90, and fo divided, becaufe, by the double reflection, the angle is doubled. The divifions run o^ 10, 20, &c. to 90, as in the figure ; each degree is divided into 3 parts, of 20 minutes each, which, by the help of the vernier, or divifions on the index, is again fubdivided into minutes of a degree, thus : The index D is a flat bar moveable on the centre of the inftru- ment ; that part of the index that fltdes over the graduated arch, having the firfl: and lad divifions thereon correfponding to thofe on the arch, is called the Vernier or Nonius, and which divides every fub-divilion on the arch in minutes : thus, 7 divifions on the nonius being divided into 20 parts, it is evident the difference between the fir ft divifionon the arch and on the nonius is -^ of one of the fub-divifions on the arch, or i minute, becaufe 7^ there is divided into 21 parts, being I in 20 more than on the arch. The dif- ference of the two firfl divifions will be 2', and the difference of the three firfl 3, and fo on ; hence it will arife, that in whatever divi- jion.s on the vernier and arch cut one another the neareft, the ver- nier will indicate how many minutes above the next fub-divifion according as it is numbered to right or left thereof. On the hot* torn of the index, againft the back of the arch, is a fcrew, made to fix faft the index when required. The arch, as before obferved, is divided into 90 degrees, num- bered, 10, 23, 30, &c. and each degree into 3 parts, each 20 mi- nutes, and is tobc read thus : id. id. 2om. ld.4Cm. 2d. 2d. 20iTi. 2d. 4Cm. 3d. S:c. obfcrving to read to the divifion that the (]), or diamond like point of the nonius lad palled over ; then the nonius will give the number of minutes more, to be added to the divifion laft puffed by the nonius. Thus, fuppofe the 0, or A of the nonius has paffed over 15 degrees and two parts, or i5d. 4.001. and Hands fomc where between I5d. 4001. and i6d. then obferve what divifion or line on the nonius coincides with any divifion or line on the arch, that number on the nonius will be the minutes to be added to ifd. 40 m. Suppofe 15 on the nonius touches fome ciivifion on the arch, then 1501. muft be added to I5d.40min. and the angle or altitude n.eafurcd will be I5d. 55m. The index glafs E. is a piece of glafs truly ground, filvered on tho back, and fixed in a brafs frame, perpendicular to the index; its ufe is to receive the rays proceeding from any object, and reflect them to the horizon glaffcs F and G ; at the back of the brafs frame of this glafs are two Icrev/s, ferving to adjuft the frame perpendicu- lar to the index. The horizon glafles F F are fmaller pieces of ground glafs, one part of which is filvered, and the other part open or un filvered, in order to look at an object through it ; thefe are let in frames and placed perpendicular on the limb at F and F ; their ufe is to re- ceive the rays of any object refle6ted from the index glafr, and again to refiedl thofe rays to the eye through the holes of the fight vanes K and G. To HADLEY'S QUADRANT AND SEXTANT. 137 *To adjuft the Quadrant or Sextant for the Fore Obfervatlon. Firft, the index glafs muft be perpendicular to the plane -of the quadrant, which, if not, you may thus difcover : hold the plane of the quadrant in an horizontal pofition, with the index glafs near the eye ; look right down the quadrant in fuch a manner as to fee, the arch of the quadrant direct, and at the fame time reflected by the index glafs; then, if the arch feen direct, together with its reflected image, appear to be in one line; the index glafs is truly adjufted ; if not, it muft be rectified by means of the fcrews placed at the back of the index glafs : it is eafy to difcover which way ths inclination is, by prefTing the index glafs with your thumb while you obferve the arch. Secondly, The axis of the horizon glafs muft be parallel to the axis of the index glafs, if not the error is eafily difcovered and rec- tified in the fore horizon glafs when the index is adjufted, thus : bring on the nonius nearly to on the graduated arch, and look directly through the fight vane at the moon or any bright ftar, fo as to fee the reflected image in the horizontal glafs, and the object at the fame time through the unfilvered part ; then move the index backwards and forwards (lowly, and obferve if both images coincide or pafs behind one another, which, if they do, the axis of both are parallel ; which if not, you fhould nicely adjuft by the two fcrews placed on the top block of the horizon glais, and by the lever on the back of the quadrant or fextant. But to adjuft the inflruments by the horizon, hold the inftru- jnent horizontal, if the real horizon and that reflected in the quickfilvered part of the horizon glafs coincide, it i.s adjufted; if not, adjuft by the two fcrews on the top of ths block of the horizon glafs, and then with the inftrument vertical by the lever on the back Fig. II. remembering to place on the graduated arch to (Q on the inftrument before you begin. If a fmall piece of coloured glafs fet in brafs (which I firft fixed to a quadrant in 179") be made to turn round to the fight vane oc- cafionally to guard the eye, and the fcreens turned back, the fame correction may be macte by ufmg the fun inftead of the moon of ftar. To adjuft the Q uadranl for tbt Back Observation. Find the dip of the horizon for the elevation of your eye in Table VIII. double the dip, and advance the index D as many mi- nutes before o degrees on the arch of the quadrant, as are equal to double the dip: fcrew your index faft : Ihift the fcreens for the back obfervation : hold the plane of the inftrument upright with the arch downwards look through the vane G, and if the hori- zon line feen through the unfilvered part of the back horizon glafs G coincide with the reflected image of the fame, feeiuhrough the filvered part of the glafs, the quadrant is rightly adjufted ; if not, fbcken the fcrew in the middle of the lever behind the back * and turn the glafs backward* or forwards, as re^ S quired. ^8 DESCRIPTION AND USE OF quired, till the horizon lines coincide, then tighten the fcrewyand the quadrant is adjufted. Another way to adjuft fir the Back Obfervation. Take the altitude of the fun's lower limb, by the fore obferva- tion, when he is nearly on the meridian ; then fhift the fcreens as quick as pofliblc for the back obfervation : if the upper limb of the -fun be level with the horizon (allowing for double the dip) the quadrant is rightly adjufted ; if not, move the fcreens of the back horizon glafs G till it is fo ; repeating the operation till you find the quadrant truty adjufted. 5T0 take the Altitude of the Sun by the Fore Obfervation. The fun's image at any time, when not much obfcuredby clouds, may be feen as reflected from the unfilvered part of the horizon glafs, by looking through the hele in the light vane ; having put the fcreens down to guard the eye, hold the inftrument vertical, and, turning towards the fun, direct the fight to that part of the horizon beneath the fun, and moving the index, you may bring down the red image of the fun towards the horizon : if the fun's image fhould be faint you may turn back the fcreens, and you can- not mifs it. Having brought down the fun's image near the horizon, fwing the quadrant backwards and forwards, making your eye the centre of motion, and keep moving the index, at the fame time, till the fun's lower edge juft touches the horizon, and you will have the apparent altitude of the fun's lower limb upon the arch of the qua- drant at that inftant. But this altitude is greateft at twelve o'clock, when the fun is on the meridian, from which the latitude is de- termined ; but this apparent altitude requires the following cor- rections : The index error, if any, to be added or fubtracted. The dip of the horizon. The fun's femi- diameter and refraction. Thefe corrections are neccflary to find the true altitude of the fun's centre nearly, the correction of the fun's parallax being fo fmall, that it may always be neglected in determining the latitude. The back obfervation is managed the fame as the fore obfervation, only your back muft be turned towards the fun, and the fcreens fhifted to the back horizon glafs, remembering to fubtract the fun's femi-diameter (if the apparent lower limb be taken) and add the dip, fubtracting the effect of refraction, and you will have the al- titude of the-fun's centre. The correction for the index error is thus : Turn down the fmall knob of brafs placed on the limb, to hinder the index from going off the arch, as it may be in the way. This correction may be accurately eftimated by taking the diameter of the fun, or any object before and behind on the arch ; that is, "bring the upper limb of the object to coincide with the low^r, and note HADLEY'S QJJADRANT AND SEXTANT. 139 note the angle, then take it on the extra arch, as it is called ; that is, bring the lower limb to coincide with the upper, and note the angle, half the difference of thefe two angles will be the true cor- rection of the index error. EXAMPLE. Suppofe the fun's diameter meafures 36 on the arch, and 28 on the extra arch. The difference is 8', half which is the error to be fubtracted, becaufe the diameter meafures more on the arch, or gives the fun's diameter too much, but had the extra arch given the greater angle, the error would have been additive. To take the Altitude of the Moon. The moon's altitude may be either taken by the fore or backob- fervation, exactly in the fame manner as the fun's altitude, only here you muft bring the edge of the moon into contact with the horizon, which is round and well defined, whether that be the upper or under edge : the corrections to be applied to the obferved altitude are as follow : The index error, as before directed, if any ; the dip to be fub- tracted in the fore obfervation, and to be added in the backob- fervation ; the femidiameter to be found in the nautical ephemeris- for every noon and midnight, at Greenwich ; if very great accu- racy is required, this femi-diameter muft be corrected for the in- termediate time : which being a Ided to, or fubtracted from, the obferved altitude, will give the apparent altitude of the centre; and the moon's horizontal parallax for every noon and midnight r at Greenwich, is to be found in the Nautical Ephemeris. This muft be corrected for the intermediate time ; then take the proi portional logarithm of the moon's horizontal parallax out of the Nautical Almanac, increafe its index by 10, and fubtradt the log. co-fine of the moon's apparent altitude from the fun ; the remain- der will be the proportional logarithm of her parallax in altitude; from which take the moon's refraction (Table VII.) and the re- mainder will be the correction of the moon's altitude, which be- ing added to her apparent altitude, will give the true altitude of her center. To take the Altitude of a Star by the Fore Qlfervation. Set the index at (D, and holding the plane of the quadrant ver- tical, direct the fight to the ftar, and at the fame time look for the reflected image of the ftar in the filvered part of the horizon glafs ; move the index a little, which will feparate the reflected image from the direct image, the former will be eafily diftinguifhed from the latter by its motion, when you ftir the index ; continue to ad- vance the index, and at the fame time follow the reflected image of the ftar with your eye, directing your fight lower and lower, and changing the pofition of the quadrant or fextant, as the image S 2 of 140 DESCRIPTION AND USE OF of the ftar defceftds, till you have brought it down to the horizon^ the index will then (hew the obferved altitude of the liar. The Corre&ions to be applied to the obferved altitude of the ftar are : the index error, the dip (thefe two give the apparent altitude) ; the refraction gives the true altitude ; the fixed {tars have neither femi- diameter nor parallax worth notice. In taking the altitude of a ftar, or the moan, by night, always get as near the water as pofftble ; in moderate weather a grating may be flung over the {hip's fide, and an obferver fit upon it to take the altitudes ; the fame may be done to take the altitude of the fun in an hazy horizon; for the nearer the eye is to the furface of the water, the nearer the true horizon will be to the eye. Advice to Seamen in the Choice of their Quadrants and Sextants. The joints of the frame muft be clofe, without the leaft open- ing or loofenefs, and the ivory on the arch and nonius inlaid and fixed, fo as not to rife at the ends, nor above the plane of the in- ftrument; all the divifions on the arch and nonius muft be exceed- ing fine and ftraight, fo that when the index or nonius is fet to any divifion on the arch, the divifions on the line that coincide may appear diftincl:, for only the firft and laft line on the nonius will coincide with the other lines upon the arch, if the quadrant is well divided ; likewife try in different parts of the arch, if the no- nius, or index plate, cuts regularly in rder with thofe on the arch : if they do not, the divifions are bad, and the quadrant ought to be rejected. Again, look into the great fpecwlum or index glafs fiant-ways, holding it about ten o'r twelve inches from the eye, and obferve the image of fome diftant object ; if the image appears clear and diftindt in every part of the glafs, the fpeculum is good ; but if it appears notched, or drawn with fmall lines, the glafs is veiny, and muft be rejected, if more images thin one of the fame object ire feen, it ftiews that the two furfaces are not ground parallel the' other fpeculum may be examined in the fame manner. Obferve the fun, or a candle, through the dark glalTes feverally, holding the glafs about eight or ten inches from the eye; if they are veiny, the object will appear notched at the edges, but if clear and well defined, the glafTes are good. Quad rants, like watches, may appear well to the eye, and yet be good for little ; it is therefore much better to give two guineas and an half^ or three guineas, for a good one, that will laft a man for life, than purchafe thofe wretched inftruments, made up at 4 low price, which cannot be depended on. The furprizing improvements made in Navigation fince the vear 1767, when the firft Nautical Almanack was published by 'Dr. Maflcelyne, the prefent .Aftronomer Royal, are beyond the moft fanguine expectations ; and though feveral nations have con- tributed towards this important end, the Englilh have (by the en- couragement held out by Parliament, and the great improvements HADLEY'S QUADRANT AND SEXTANT 141 made in nautical inftruments and calculations) furpaffed them all; fo that by the help of the improved fextant, the Nautical Alma- nack, and the Tables contained in this book, a fkilful and expert obferver can determine the longitude to a degree of accuracy that people unacquainted with the operation would fcarcely thi.ik pof- j&ble. Hadley's fextant is conftruded on the fame principles as the quadrant 5 but as it is ufed to meafure the angular diftance between the fun and moon, or the moon and a ftar, in order to determine the longitude > the arch is extended to 120, for the purpofe of meafuring their diftance when greater than 90; it is alfo pro- vided with fome appendages not generally annexed to a quadrant, in order to take the obfervation with greater accuracy. On the adjoining plate is reprefented a fextant, the frame of which is generally made of brafs ; the arch BB is divided into 120% each degree into three parts, of courfe equal to 2o minutes, which are again fubdivided by the nonius into every half minute, or 30 feconds ; every fecond divifion, or minute, on the nonius, is cut Jonger than the intermediate ones ; the nonius is numbered at every fifth of thefe longer divifions, from the right towards the left, with 5, jo, 15, and 20, the firft divifion towards the right hand bein< to be confidered as the index divifion. This is the general way of graduating fextants ; but for obtain- ing greater accuracy, fome are divided as follow : the arch contains 120; each degree is fubdivided into 4, of courfe equal to 15', which are again fubdivided by the nonius into 15"; every fourth tfivifion or minute of the nonius, is longer than the intermediate ones ; the nonius is numbered at every fifth of thefe long divifions, from the right towards the left, with 5, 10, 15; the firft divifion towards the right hand is to be confidered as the index divifion. The prefent mode of dividing the nonius of the fextant is thus : (beginning from the right hand towards the left) by taking fifteen divifions on the nonius, equal to fourteen on the arch, confequently one divifion on the arch will exceed one on the nonius by .'-, that is, by | of a minute, where- the degrees on the arch are fubdivided into |, equal to 15 minutes. The nonius, till very lately, was divided as the quadrant. In order to obferve with accuracy the contaci: of the lirnbs of any two objects, an ndjuftino-icrew, L 9 is added to the index, by which it may be moved with greater regularity than it can by the hand; but this fcrew does not act until the index is fixed by the ftnger-fcrew M. Caie fhould be taken not to force the aujurHng- fcrew when it arrives at either extremity of its adjuftmcnt. When the index is to be moved any confjderable quantity, the fcrew Al, at the back of the fextant, muft be loofened ; but when the index is brought nearly to the divifion required, this back fcrew ihould be tightened^ and the index moved gradually by the adjufting- fcrew. N. B. Many quadrants have an adjufting-fcrew. In 14-2 DESCRIPTION AND USE OF In many fextants the lower part of the index glafs, or that neareft the frame, is,filvered as ufual, and the back furface of the upper part painted black ; alfo a fcreen is fixed at the bafe of the index glafs, turning on its axis, and may be placed over the filver part when the fun's rays are ftrong, in which cafe the image is reflected from the poliflied furface of the upper part, and the error, which might probably arife from the planes of the glafles not being pa- rallel, is thereby avoided. There are feveral coloured glafles at H, each of which is fet in a different frame,, turning on a centre ; they are ufed to fcreen the eye from the brightnefs of the folar rays, and the glare of the moon, and may be ufed feparately or together, as occafion re- quires. There are other fuch glalFes- placed behind the horizon glafs at F. to weaken the rays of the fun or moon when they are viewed direclly through the horizon glafs ; the paler glafs is fometimes ufed in obferving altitudes at fea, to take off the ftrong glare of the horizon. The fextant is furnifhed with a plain tube, without any glafles ; and to render the objects ftill more diftinct, it has two telefcopes, one reprefenting the objects erect, or in their natural pofition, the otherfhewing them inverted; it has a large field of view, and other advantages ; a little ufe will foon accuftom the obferver to the inverted pofition, and the inftrument will be as readily ma- naged by it as the plain tube alone. By a telefcope the contact of the images is more perfect ly diftinguifhed ; and by the place of the images in the field of the telefcope it is eafy to perceive whether the fextant is held in the proper plane for obferving. By fliding the tube that contains the eye-glafles in the infide of the other tube, the object is fuited to different eyes, and made to appear per- fectly diftinct and well defined. The telefcopes are to be fere wed into a circular ring, at K ; this ring refts on two points againft an exterior ring, and is held thereto by two fcrew* ; by turning one and tightening the other, the axis of the telefcope may be let parallel to the plane of the fextant. The exterior rin^ is fixed on a brafs ftem that flides in a focket, and by means of the fcrew S, at the back of the fextant, it may be raifed or lowered fo as to move the centre of the telefcopa to point to that part of the horizon glats which {hall be judged the moil fit for obfervation. A circular head, containing a plate, in which there are thre coloured glalTes, and a fourth that is open, fometimes accompa- nies this fextant. This head is to be fcrewed on the eye-end of the tube, or on that of either telefcope. The edge of the plate projects a little beyond the head on one fide, and is moveable by the finder, fo that the open ring, or any of the coloured glafles, may be" brought between the eye glafles of the telefcope and the eye. To thefe are added, a fmall fcrew-driver to adjufj the fcrews, and HADLEY'S QUADRANT AND SEXTANT. 143 and a magnifying glafs to read off the obfervation with greater accuracy. The Atljuftments of a Sextant are to fet the index and horizon- glafles perpendicular to the plane of the inftrument, and their planes parallel to each other ; by the fame method as the quadrant, only fcrewing on the plain tube or telefcope ; alfo to fet the axis of the telefcope parallel to the plane of the inflruoient ; each of thefe par- ticulars muft be examined before an obfervation is taken, and the adjuftments, if requifite, be made,, For correcting the index error, fee the rules foradjufting Hadlev's Quadrant. ( v To fet the Axis of the Telefcope parallel to the Planfyf the Sextant. In meafuring angular diftances, the Hae of fight, or axis of the telefcope, (houlci be parallel to the ptwi&i^'fne inftrument, as a deviation in that refpeit will occafion a confiderable error in the obfervation ; and this is moil fenfible in large angles. To avoid which, an inverted telefcope is ufed, in whole field there are placed two wires parallel to each other, and equidiftant from the centre; to which are fometimes added two others, at right angles to thefe, but parallel to each other. By means of thefe wires the adjuft- ment may be made thus : fcrew on the telefcope, and turn the tube containing the eye glafs, till the wires are parallel to the plane of the iaftrument ; then take two obje&s, as the fun and moon, or the moon and a ftar,whofe angular diftance mull not be lefs than 90, becaufe the error is more eafily difcovered when the diftance is great ; bring them exactly into contact ou the wire which is neareft the plane of the inftrument, and fix the index ; then, by altering a little the pofition of the fextant, bring them to appear on the wire fartheft from the plane of the inftrument ; if they remain ftill in contact:, the axis of the telefcope is parallel to the plane of tha fextant } but if the limbs of the two objects appear to feparate at the further wire, it ftiews that the object-end of the telefcope in- clines towards the plane of the fextant ; this muft be reciified by tightening the fcrew neareft the fextant, which is attached to th ring that holds the telefcope, having previoufly flackened the (cre<# fartheft from it. If the images overtop each other when brought to the wire fartheft from the fextant, the object end of the tei^ fcope is inclined from the plane of the fextant, and rnuft be relti- fied by flackening the fcrew neareft the fextant, aiui tightening the other. Repeat this operation till the contarfc be rendered per- fet on both wires, the axis of the teiefccpc will then be truly ad- jufted. To obferve the angular Diftance benvcn tht Sun and Mion. Screw on the inverted telefcope, placing the wires parallel to the plane of the inftrument ; then turn down the fcreens, according to the brightnefs of the fun ; place the index at O on the arch, and if the fan's image be very bright, turn up th fqreen before tnehori- 144 DESCRIPTION AND USE OF z-on glafs, and with the fcrew S, raife the telefcope to the tranfpa- lent part of the horizon glafs. Having done this, hold the fex- tant fo that its plane may pafs through the two objects : if the fun be to the right hand of the moon, the fextant is to be held with its face upwards ', but if it be to the left hand, the face is to be held downwards. With the inir.ru ment in this poiition, look directly at the moon through the telefcope, and move the index forward, till the fun's image is brought nearly in contact with the moon's neareft limb ; then fix the index by the fcrew under the fextant, ans! make the contact perfect by means of the adjtifting-fcrew ; at the fame time move the fextant flowiy, making the axis of the telefcope the centre of motion, by which means the objects will pafs each other, and the contact be more accurately difcriminated. The index will {hew the obferved diftance of the fun and moon's neareft limbs, which you will read off with a magnifying glafs, Second Method. It will perhaps be more eafy for thofe who are not accuftomed to make obfervations of this kind, to find the diftance nearly, and fetting the index forward to it, to look 'directly towards the moon holding the inftrument as before ; the fun will then appear nearly in contact with it, and is to be made perfect by the method above- mentioned. In the Nautical Enhemeris, the diftance of the fun and moon is fet down for every ihiee hours of time at Greenwich on fuch days as the moon is not more than 120, nor lefs than 40* diftant from the fun, and may be found for any intermediate time by taking proportional pans ; from thefe diftances you may com- pute roughly their diftance at the time of obfervation, thus : Turn the (hip's longitude into time by Tab. XVI. and add it to the time of obfervation, if the longitude be weir, but fubtract it if the lon- gitude be eaft, the funi or difference will give the time at Green- wich j then, by the Ephemeris, find the diftance nearly at that time, fiom which fubtract 30 minutes for the fun and moon's fe- mi-diameters, and the remainder will give the diftance of their neareft limbs at the time of obfervation. If a number of obfervations are to betaken, the following method will not be found unacceptable : Having brought the objects into contact, as before directed, and noted down their apparent ano-ular diftance, advance or draw back your index two or three minutes, according as the objedls are receding or approaching, and wait till they again come into contact, repeating the operation as often as j idg.ed necefiary, ufmg the mean of all the obfervations to de- termine the longitude. This method will be found eafy and ac* curate. NOTE. The contafr. of the limbs mud always be obferved in the middle, between the parallel wires. To cbftrvc ike Diftance between the Moon and a Star. Turn down the lighted: fcreen before the index glafs, and direfi the tele -cope to the #ar, holding the fextant in its proper petition^ HADLEY'S QIJADRANT AND SEXTANT* 143 as before directed ; then move the index forward, till the reflected image of the moon is feen in the telefcope ; by moving the inftru- ment flowly up and down, the moon will appear to rife and fall by the flar. The round and well defined limb of the moon, whether it be neareft or furtheft from the ftar, muft be brought into contact with it. When the object to be feen by reflexion is to the right hand of that to be feen by direct vifion, the inftrumeru is held with its face upwards ; but when the object to be feen by reflection is to the left hand of that feen directly, the inftrument is held with its face downwards. Having brought the objects into contact, the no- nius will fhew the obferved angular diftance. If the diftance between the moon and one of the ftars fet down in the Ephemeris for rinding the longitude, is to be obferved, their diftance maybe roughly calculated as before directed, to which fet the index ; then look through the telefcope, and direct the fight to theftar, which is generally a bright one, and lies in a line nearly perpendicular to the horns of the moon, either to the eaftward or weftward, as denoted in the Ephemeris; then, holding the inftru- ment in the plane of the two objects, give it a flow motion up and down, and if the moon's image come in the field of the telefcope, it is a proof you have taken the right ftar, as no other in that di- rection will correfpond in diftance to it. After the diftance is obferved between the fun and moon, by a fextant or quadrant, there ftill remains to be made feme corrections to obtain the true diftance ; the corrections are thofe for pa- rallax, refraction, and femi-diameter. The dip of the horizon is an angle made with the height of the eye of the obferver and the vifible horizon, and which makes the 1 angle of celeftial objects appear higher than they really are by the amount of the correction found in Table VIII. and which is to b fubtracted from all altitudes. PARALLAX. The parallax of the fun and moon is the difference, of the altitude of either object, if obferved at the fame moment of time from the centre^ and from the furface of the earth. The parallax of the heavenly bodies is greateft when in the horizon j hence called the horizontal parallax. That of the moon is let down in the Nauti- cal Almanack for every noon and midnight, but may be found for any intermediate time by taking proportion.:! parts. The fun's mean parallax being only 8".6, is feldom attended to in nautical cal- culation, except when his altitude is taken to determine the true time, or the angular diftance to determine the longitude. The ftars, on account of their great diftance from the earth, have no fenfible parallax ; the parallax of the fun and moon caufmg them to appear lower than they really are, it is evident this corrosion muft be added to the apparent altitude of the fun and moon, in order to obtain their true altitude. This will be belter illuftrated by the plate facing page 146. Let C reprefent the centre of the T earth 146 DESCRIPTION AND USE OF earth ; a, o, e, part of the moon's orbit; b, d, g, part of the fun's orbit; 1, k, part ofthe ftarry heavens. Now, to a fpecrator at m, upon the furface of the earth, let the moon.^ppear at e, in the ho- rizon of m, and it will be referred to f ; but if viewed from the centre c, it will be referred to h. The difference between thefe places, or the arch f, h, is called the horizontal parallax, and the angle m, e, c, the parala&ic angle. The parallax will be greater or lefs, according to the diftance of the objeds from the earth; thus, the parallax f, h, of e, is greater than the parallax f, n, of g, and with refpecl: to the fame object, it is evident when it is in the horizon, the parallax is greateft, and that it diminifh.es as the ob- ject approaches the zenith, where it vanifhes. Thus the hori- zontal parallax of e and g is greater than the parallax in altitude of and d ; but the objecls a and b, as feen from m, the furface, or c, the centre, appear in the fame place, 1, or the zenith. Having the earth's femi-diameter, and the parallax of any ofthe planets, their diftance may be found thus : As the tangent of the parallax : is to the earth's femi-diameter in miles : : fo is radius : to the diftance. Having the diftance, the parallax in altitude is found thus : As the diftance : is to radius : : fo is the earth's femi-diameter : to the tangent ofthe parallax. REFRACTION. From various experiments it hath been found that the rays of light palHng through the atmofphere, are bent out of their ftrait courfe into an elliptic curve-line, from whence it follows, that all heavenly bodies, except when they are in the zenith, appear higher than they ought to do, and the more fo the nearer they are to the horizon, where they are nearly 33 miles. This apparent eleva- tion of the heavenly bodies above their true height is called the Refraclion, therefore all apparent altitudes obferved, muft (after the dip has been allowed for) be reduced to their true altitudes by the corre^lion found in Table VII. which muft be fubtra&ed from the apparent altitude, or added to the zenith diftance, in order to obtain the true altitude. Now, fince parallax makes all objecls appear lower than they really are, and refraction makes them appear higher than they are, it is evident that the true altitude of an object cannot be ob- tained without correcting the obferved altitude for the difference of thefe*two fums. SEMI-DIAMETER. T*he moon's feroi diameter is fmalleft when in the horizon, and Hicreafmg as fhe approaches the zenith, wh;re it is greateft ; as fhe is then nearer the fpeclator by the earth's femi-diameter. This augmentation is fet down in Table X. Another reafon of thtf" apparent augmentation and diminution of the moon's femi-diame- ter is, that fhe moves round the earth in an orbit not circular, bat elliptic^ Tlic Jtityj of Liijlit - iHif.ti'Hff t/m> K Annosfilnvc tmikf Object,* i' liitfht'i' tlnin tht'V fire . ^_ / !",......,.... *b- "b- Object*' oppciir "'^x /<>n'('/' /////.v tlicv tire . ; ; ,;l l,y,l.,l,>liii,>n \-tli,- r,t ,,,'lJt.- /'/.;;//. //. .Inly i.j.fi*!. HADLEY'S QJJABRANT AND SEXTANT. 147 elliptic, and is confequently, at different parts of her orbit, nearer to, or farther from the earth, which occafions an apparent aug- mentation or diminution of her femi-diameter ; on which account her femi-diameter and horizontal parallax for every noon and mid- night are fet down, page 7, of the month, in the Nautical Alma- nack, and may be found for any intermediate time by taking pro- portional parts. It is evident, that to obtain the true angular diftance, the ob- ferved diftance muft be corrected for the femi-diameter of the ob- jects. If the neareft limbs of the fun and moon are obferved, the furn of the femi-diameters muft be added \ if the furthefl limbs are obferved, the fum mull kefubtraftidhom the obferved diftance, to obtain the diftance of their centres. The fame rules hold good in, refpect to adding or fubtracting the moon's feni-diameter, accord- ing as her neareft or furtheft limb is ufed when the obfervation is made between the moon and a ftar, obferving that the ftar has no ferrii- diameter. To work an O'.frvation, or to find the Latitude of a Place, by the Tables of the Sun or Star's DeulinatiQn, and the Zenith Dljlancc. The latitude of any place is its diftance from the equator, either north or fouth, counted in degrees, &c. upon an arch of the meri- dian, contained between the zenith and the equator. . The zenith is that point directly over our heads, and is 90 de- grees diftant from the horizon. The zenith diftance is the diftance of any object from the point directly over our heads, which is always the complement of the altitude; it is faid to be fouth, if the fun or ftar be fouth, and north, if the fun or ftar be north of the obferver. To the obferved altitude add the difference between the fe- mi-diameter and the dip, the fum will be the apparent altitude of the fun's centre \ but muft be fubtradted if a back obfervation is ufed. From the apparent altitude fub*ra?i the refraction, the remainder will be the true altitude of the fun's center: this being iubtra. c ,ied from 90 degrees, gives the true zenith diftance, with which, and the declination, the latitude is found by the following rules. See Globe, facing page 45. NOT?. For the dip and refraclion, fee Tables 8 and 7. I ft. When the fun or ftar is in the zenith, the declination is the latitude ; and is of the fame name as the declination, north or fouth. 2d. When the fun or ftar is on the equator, confequently hath no declination, the zenitn diftance is the latitude of the place : if the zenith diftance be fouth the latitude is north j but if north, the latitude fouth. 3d. When the zenith diftance is north, and declination north, if they be both equal, you are on the equator, therefore in no la- titude. . T 2 4 th. 148 DESCRIPTION AND USE OF 4th. When the zenith diftance is fouth, and declination fouth, then, if the zenith diftance is equal with the declination, you arc on the equator, The foregoing need no examples. ift. But, when the zenith diftance is fouth, and the declination north, the declination added to the zenith diftance gives the lati- tude north. 2d. When the zenith diftance is north, and the declination fouth, the declination added to the zenith diftance gives the lati- tude fouth. 3d. When the zenith diftance is fouth, and the declination fouth, if th> zenith diitance is more than the declination, fubtraft the declination from it, and the remainder gives the latitude north. 4th. When the zenith diftance is north, and the declination north, if the zenith diftance be more than the declination, fubtra<5t the declination from the zenith diftance, the remainder is the lati- tude fouth. 5th, When the ienith diftance is north, and the fun hath north declination, the zenith diftance being lefs than the declination, fubtra&ing the z,enith diftance from the declination, gives the lati- tude north. 6th. When the zenith diftance is fouth, and declination fouth, if the zenith diftance is lefs than the declination, the zenith dif- tance fubtracted from the declination gives the latitude fouth ; for it is plain in thefe two laft cafes, the obferver is .between the fu and equator. The preceding fix rules are exemplified in their regular order below. EXAMPLE I. Suppofe, on the 4th May, 1806, the al- titude of the fun's lower limb to be 56 30' ibuth, the eye being elevated 16 feet above the furface of the fea. Required the lat, ', n ? o ' " 56 30 . o iz o Obf. alt. fun's 1. 1. Jjemi-dia. '* o? p Dip - 4P$ Sun's apparent altitude 56 42 o Refraaion fubtrad. o i o Sun's true altitude enith diftance Declination added 33 19 o South. 15 51 o North. With the chord of 60 defcribe a circle to reprefent the meridian ; through the Latitude - - - 4? i -"> o North. centc r draw the diameter EQ, to repre- fent the equator, and at right angles thereto, another diameter ; mark the upper end, NP. for the north pole, and the lower, SP. for the fouth pole ; fet off the declina- tion, 15 55', taken from the line of chords, from E to I) ; take from the line of chords the zenith diftance, 3*3 19', and fet it off from D to Z. Then will EZ mea- fure on the line of chords, 49 10', the latitude, required. EXAMFLS HADLEV'S QUADRANT AND SEXTANT EXAMPLE Suppofe, on the T4th Jan. 1806, the me- 2Mdian altitude of the fun's lower limb was foun 4 to be 46 20' north, the elevation of the eye '-"ing 1 6 feet. Required the lati- tude? ' " Sun's obferved altitude 46 20 O North. Semi-dia 16' c Pip - 40 > Add o 14 O 46 31 o North, oio Diff. 11 o Apparent altitude Refraction - Sun's true altitude Zenith diftance - 43 29 o North* Draw the figure as before ; take the Declination 21 23 o South, declination, ai" ao', from the line of - chords; fet off from E towards thefouth Latitude - - 64 5$ o South, pole, to D; take the zenith diftance on the line of chords, and fet it from D to Z ; then will EZ,meafared on the fame line of chords, be the latitude required* EXAMPLE III. Suppofe, on the aoth Jan. 1806, the meri- dian altitude of the fun's lower limb to ba 42* 3O 7 fouth, the eye being elevated ao feet above the water. Required the lat. Sun's obferved altitude 42 30 o South. Semi-dia. 16' o' 1 Dip - 40 Sun's apparent altitude 42 42 o Refraction - - - - o i o MM Sun's true altitude Zenith diftance 47 19 o South, peclination - - ao ia o South, Draw the figure as before ; fet off the Latitude - - 27 7 o North, declination, 20 i a', from E towards the fouth pole to D. Secondly, % off the zenith diftance, 47 19', contra from D towards the north, to Z; then wilKEZ meafure on the line of chords 27"* 7', the la- titude, EXAMPLE IV. Suppofe, Jn 1806, the altitude of the ftar Aldebaran, when on the meridian, be found - 40 a7' north, when the decl. is 16" 6*35" north, the eye being elevated ao feet above the fea. Required the lat ? ' " Qbferved altitude - 40 27 o Dip for 20 feet - 040 Apparent altitude Refra&ion Star's true altitude * Zenith diftance Star's declination Latitude 4^ z* o North. 90 o o 49386 16635 ' Draw the figure as before ; fet off tnc 33 31 *S South, ftar's declination, 16 6' 3 .5" from E to D; 150 DESCRIPTION AND USE OF I); next fet cff the zenith diftance 49 38', from D to Z ; then will ZJ^ meafured on the line of chords, be 33 32' 25", the latitude required, which is fout EXAMPLE V. Suppofe the fun's true meridian altitude to be 64 20' fouth, and his declination 14 icf fouth, the latitude is required? Sun's true merid. alt. Zenith diftance Sun's declin. fubtract ' /' / 64 20 o Vrj 1$ 40 o South. I 14 200 South, [jr, I a Latitude ii ao o North. EXAMPLE VI ' Given, the true altitude of the fun's cen- ter, 64* 20' north, and the fun's declination, 14 20' north. Required the latitude ? Sun's true merid. alt. Zenith diftance Sun's declinat. north Latitude 64 20 o 25 40 o North. 14 20 o ii 200 South. EXAMPLE VII < Given, the trne meridian altitude of the fun's center 82 TO' north, and the de- clination 23 north. Required the lati- tude? ' " Obferved altitude 82 10 o 90 o o Zenith diftance Declination Latitude 7 50 o North. 33 o o North. 15 10 o North. ^***^^^* 1 ' IX V -*"'^ In tke two laft examples it is plain the obferver is between the fun and the equator. Suppofe on the I2th of March 1806, by a back obfervation, the pbferved altitude of the fun is 25 12' fouth, the eye being 40 feet above 25 12'S. Sum + 22 25 34 2 Sun's obf. alt. Semi-dia. 16 \ Uip 6 ) Su App. alti. Refrac. True alti. True zenith dif. Dec. 12 3 Cor. for 64W. long. By Table 25I2'S. n -f 22 25 34 2 3 25 32 90 oo 2 5 3 2 90 oo 64 28N. 28 1 4 J332S 64 28 N 28! 4 J 68 ooN Lat. in 67 52 N HADLEY'S QUADRANT AND SEXTANT. i$i tabove the horizon, required the latitude in the longitude of 64^ eaft and 64 weft. Sun's obf. alt. Semi-dia. 16 1 Dip 6 J App. alti. Refraction True alti. True zenith dill. Dec. 12 Cor. for 64 E, long. From Table Lat. in As the declination in the tables is calculated for the meridian of Greenwich, it is plain that when a (hip is to the eaftward, and the declination decreafmg, it rnuft be more at the (typ than at Green- wich ; confequently the proportional parts of the daily difference muft be added to the declination of that day; but when the'^hip is to the weftward of London, the proportional parts muft be fub- tra&ed, to find the true declination at the place of obfervatiori ; but had the declination been increafmg, the proportional parts muft have been fubtra&sd when to the eaftward, and added when to the weftward, to obtain the true declination at the fliip ; whence it follows, that no latitude can be truly afcertained without find- ing the fun's declination at the place of obfervation, as above, which is but too often neglected. Here it may be obferved alfo, that in a back obfervation, the fun being brought over theobferver's head, the upper edge appears to him the lower one ; and though the fun appears to the Ibuth of him, yet the zenith diftance* is north. The fame may be obferved if he is north of the fun. The back obfervation is feidom aied, unlefs there is a high land, or other oMr.ru6r.ions, between the ob- ferver and the fun. The foregoing rules are for obferving the fun, or a ftar, when they are at the greateft altitude, or upon the meridian above the pole ; but as in fome parts of the earth the fun does not fet for fe- veral days, and fome ftars never fet, in that caie they msy be ob- ferved when they are at the loweft, or upon the meridian below the pole. To work which obfervation, take the following RULE, Add the complement of declination to the true meri- dian altitude, the fum is the latitude, of the fame name that the declination is of, Suppofe, on the I2th of June, 1806, an obferver in a high northern 15* OF HADLEY'S QUADRANT. northern latitude, 65 weft of Greenwich, his eye being'28 feet above the level of the fea, fhould obferve the altitude of the fun's lower limb on the meridian below the pole, to be 8* 15' fouth, by a fore obfervation. Required the latitude ? The fun being obferved below the pole, it muft have been at 12 hours paft noon, at the place of obfervation ; and that place being 65? welt of London =4 hours 20' later than at London, it muft be 1 6 hours 20 minutes paft noon at London. Sun's declin. I2th June, 23 8' N. 1 3th ditto, 23 12 N. Diff. -04 Correc. for 65 weft of Greenwich, Tab. 18. oc'53'S A , 4 Decl. i2th June 23 8 o } Correct, declin. 23 8 53 North, Sun's obferved alt. 8 15' o" From femi-dia. 16 5 dip, difF. o n o add. Apparent altitude Refraction fubtr. True merid. alt. 8 20 o Compl.of S.'sdec. 66 51 7 75 ii 7 North. At fea I took the altitude of the north pole-ftar, when on the meridian below the pole, and found it 46 21'. Required the lat. ? Mer. alt. . - 46"2i'o'' Compl. of decl. i 43 50 North. Latitude in 48 4 50 North. The pole ftar is the laft in the tail of the Little Bear, and is known by two ftars always pointing to it, commonly called the Pointers. How to find and know the ftars, will be further elu- cidated when we come to treat of finding the longitude at fea. OF THE VARIATION OF THE COMPASS. THE variation of the compafs is an arch of the horizon con- tained between the meridian of the place and the magnetic meridian, and is either eaft or weft ; or it is the number of degrees, &c, the needle's point ftands from the true north or fouth points TO FIND THE TRUE AMPLITUDE. 153 of the horizon* reckoned to the eaftward or weft ward, and is rea- dily found from the fun's amplitude or azimuth. 70 find the true Amplitude. The fun's true amplitude is an arch of the horizon, compre- hended between the true eaft or weft points thereof, and the center of the fua at its rifing or fetting ; or it is the number of degrees, &c. the fun rifes or lets to the northward or fouthward of the eaft or weft point of the horizon. The fun's magnetic amplitude is the number of degrees, &c. the center is northward or fouthward of the eaft or weft points of the compafs at his rifing or fetting, and is found with an azimuth com pafs in the following manner : Having placed the azimuth compafs in a convenient part of the ihip, look direftly through the fight vanes at the fun's center j and when the fun's lower edge juft touches the horizon, ftop the card, by a ftop which is placed on the compafs for that purpofe ; then the quantity of degrees and minutes contained between the eaft or weft, and the north or fouth, points of the compafs, will be the magnetic amplitude. The true amplitude is found either by infpe&ion in the Tables of the Sun's Amplitude, or by calculation, as follows : RULE. As the fine compl. of the lat. or fee. lefs radius Is to radius, So is the fine of the fun or ftar's declination To the fine of the true amplitude. Which is always of the fame name with the declination, whe- ther north or fouth. EXAMPLE I. Suppofe the fun's declination to be 10 43' S. in lat. 51 32' N. I demand the true amplitude? As fine com. lat. 51* 32' 9.79383 Is to radius < 10.00000 So is fi. fun's dec. i o 43' 8.9 26940 Ton*, of true amp. 1 7 24' 9.47557 Or thus : Lat. 51 32' N. fecant 0.20617 Decl. 10 40 S. log. fine 9.26940 True amp. 17 24' S. =: 9.47557 EXAMPLE II. In latitude 38 25' N. what is the fun's true amplitude when the declination is 18 59 N. ? As fine com. lat. 38 25' 9.89405 Is to radius 10.00000 So is fine declin. 18 59' 9.51227 To fun's true amp. 24 32' 9.61822 Or thus : Lat. 38 25' N. fecant. 0.10595 Decl. 18 59' N. log. fine 9.51227 Log. fi, 24 32' true am. N. 9.61822 U To 154 TO FIND TkE TRtfE AMPLITUDE. 'To f >id the true AmpUtv.de by the Table of Amplitudes. Look for the given declination at the top of the table, and the laiitucle in the firft column on the left hand, in the common angle of meeting, will be the degrees and minutes of the amplitude required. EXAMPLE. I. Tn latitude 40 N. when the declination was 17 N. required the fun's true amplitude at rifing? Under declination 17, and right againft the latitude 40 ftand 22* 26' the true amplitude, and is to be counted from the eaft to- wards the north, becaufe it is at the fun's riling, and the declina- tion is north; that is, E. 22 26' N. But when the latitude is given in degrees, and the declination in degrees and minutes, find the declination at the top as before, and the neareft degrees to the given latitude in the left-hand co- jumn, againft which, and under the given declination, ftands the true amplitude; cr, if the minutes of the declination be near 30, or half a degree, find the amplitude for the given degrees of decli- nation, and the amplitude for one degree above it; add thefe two amplitudes together, half the fum will be the true amplitude, fuf- ficiently ex-act for practice at fea. EXAMPLE II. Suppofe I woulc! knew the fun's true amplitude at his fetting, in latitude 57, his declination being 11 34' S, Find the ampli. as before for the C 1 1 j j . h iu . f 20- 30' Lat. 57, and the declination \ 12 J w >e [ 22 26 Their fum 42 56 Half the fum 21 28 is the true amplitude : that is, W. 21 28' S. becaufe at fun fetting, and the declination fouth. In like manner, if the declination be in degrees, and the latitude in degrees and minutes, as in EXAMPLE III. Suppofe it were required to find the fun's true amplitude at fet- VHSJ, in latitude 49 27', when his declination was 21 north. Now 27 minutes being nearly half a degree, therefore, r *at .J49 ^ and declination 21 V 33 f 1 5 i ^ amplitudes are 33 53 Sum 67 oo Half the fum is 33 30, the true am- plitude required ; that is, W. 33- 30' N. because the fun was let- ting, and the declination N. When the latitude and declination are both given in degrees and minutes,, take the neareft degrt-js to both, unJefs they are rf ear 30 as obici cu before, and End the amplitude as in Example I. EXAMPLE TO FIND THE TRUE AZIMUTH. 155 EXAMPLE IV. Suppofe it were required to find the fun's true amplitude at fit- ting, in latitude 49 20', his declination being 19 40' N. Now as the latitude is neareft to 49 and the declination neareff 20, therefore againft latitude 49 and under declination 20, ftands 3i25'N. the true amplitude; that is, W. 31 25' N. the decli- nation being north, and at the fun's letting. To find the true Azimuth. The true azimuth is an arch of the horizon contained between the meridian of the place and the azimuth circle patting through the center of the fun or ftar at the time of observation ; or it is the true diftance of the fun or ftar from the true north or ibuth points of the compafc. The magnetic azimuth is ao arch of the horizon contained be- tween the magnetic meridian and the azimuth circle patting through the center of the fun or ftar when obf.rved; or it is the apparent diftance of the fun or ftar from the north or ibuth points of the compafs, either in the forenoon, or in the afternoon, when they are 5, 10, 15% &c. above the horizon, and the lefs the altitude is, the more exait you may perform the ohfervation. The magnetic azimuth is found by the compafs, in the follow- ing manner : Place the compafs in a convenient part of the fhip; then move it fo that the fights may be directed to the fun's center ; and the fha- dow of the firing will fall directly on the line marked on the plain which joins the fights; then the degree, &c, in the arch intercept- ed between the end of the index, and north point of the card, will give the magnet azimuth required. If the fun does not thine ftrong enough to give a ftrong fhadow, look through one of the fights, and move the compafs till one of the firings cuts the fun's centtr, and then the intercepted arch,, as before, {hews the fun's azimuth, and the like of the ftar's. When there is a rough fea, the obfervation is befl made by two perfons, and if the card vibrates much, take the middle degree be- tween the limits which the vibration reaches. Whn the azimuth is obferved, the altitude of the o6jet. muft be obferved at the fame time. Having the latitude of the place of obf rvation, and the fun or ftar's declination with the true altitude at the time of obfervation, the true azimuth is found as follows : RULE. From the half fum of the complement of the latitude, the complement of the altitude and the fun or liar's polar diftance: 1'ubtrad the polar diftance, noting the half fum and the remainder. Then add together The log. fine of the I at. co ar ~ co fee. lefs rad. or complement of the. Air, co ar = co fee. indexes. U2 U 156 TO FIND THE TRUE AZIMUTH, The log. fine of the half fum, And the log. fine of the remainder, into one fum. Half the fum of thefe four logarithms will give the log. co-fine of half the true azimuth, which being doubled, gives the true azU muth, reckoned from the north in north latitude, and from the fouth in fouth latitude. N. B. The polar diflancc of the fun or flar, is their diftance from the neareft, or elevated pole, and if the latitude of the place, and the declination of the fun or ftar, be both north, or both fouth, then the complement of the declination is the polar diftance ; but if the latitude and declination be one north and the other fouth, the declination added to 90 gives the polar diftance. EXAMPLE. I. In latitude 51 32' N. the fun's altitude was obferved to be 39 28', his declinatipn being then 16 37' N. required the true azimuth. 90 oo' 90 oo' 90 op' Lat, 51 3* Alt. 39 28 Dec. 16 37 Com. Alt. 50 32 Fol. dift. 73 23 Co Lat. 38 28 Sine co ar =z f Co Secant "I 0,20617 Co Alt. 5032 Sine co ar = [lefsrad. J 0,11239 Pol. dift. 73 23 Sum 162 23 1 Sum 81 ii Sine 9,99484 Pol. dift. 73 23 Rem. 7 48 Sine 9,13263 2)19,44603 Log. co li of | the Azimuth = 58 06' 9,72301 2 True Aaimuth Ji6 -12 from the North. EXAMPLE II. Jn latitude 42 16' N. the fun's altitude was obferved to be 18 40', ty declination being then f 38' S. j required the true azimuth? 90 op'" 90 oo' 90 oo' J-,atifrjdp 42 16 N. Altitude 18 40 Declination 7 388. (Co-rait 71 20 Polar dift. 97 38 po-lat. TO FIND THE TRUE AZIMUTH, 157 Co-lat. 47 44 Co fecant 0,13076 Co-lat. 7 1 20 Co fecant 0^2347 Polar dift. 97 38 Sum 2i6 42 108 21 Log. fine 9,97733 Polar dift. 97 38 Remainder 10 43 Log. fine 9,26940 Sum 19,40096 f-Surn log. co-fi. 59, 53 == 9,70048 2 . . . True azimuth 119 46 from the north. The following queftions are fet down for the Learner's ,rcife : Queft. I, Being at fea, in latitude 40 38' N. in the afternoon, the fun's altitude was obferved to be 20 46', when his declination jvas j 7 10' S. what was the fun's azimuth at that time r Am. 137 50' from the north. >ueft* II. What is the fun's true azimuth in lat. 26 30' N. in the forenoon, when his altitude is 24 28', and his declination 22, 40' N. ? Am. 75 44' from the north point of the compafr. Queft. III. At the ifland of St. Helena, the fun's altitude was .obferved to be 30 22' in the forenoon, his declination being then 22 58' S. required the azimuth #t that time? Am. 72 22' from the fouth, or 107 38' from the north, *htfft. IV. What is the bearing of the ftar Aldebaran at the Cape of Good Hope, when its altitude is 22 25' ? Ans. 130 20' from the fouth, or 49 40' from the north. Having found the fun's true amplitude or azimuth by the pre~ ceding methods, &c. magnetic amplitude or azimuth by obferva- tion, it is evident, that when they agree there is no variation ; but when they difagree, then, if the true and obferved amplitudes be both of the fame name, that is, both north or both fouth, their difference is the variation ; but if the true and obferved amplitudes be of different names, that is, one north and the other fouth, their fum is the variation. Again, if the true and obferved azimuths be both on the eaft, or both on the weft fide of the meridian, their difference is the variation ; but if the true and obferved azimuths be one on the eaft and one on the well fide of the meridian, their fum gives the variation ; and to know \yhether the variation i$ eafterly or wefterly, obferve tteis general .153 TO FIND THE TRUE AZIMUTH. RULE. Let the obferver's face be turned to the fun ; then, if the true am- plitude or azimuth be to the right hand of the magnetic, or obferved, the variation is eafterly; but if to the left hand, weilerly. EXAMPLE I. Suppofe the fun's magnetic amplitude at riling is found to be E. 26 12' N. but the true is found to be E. 14 20' N. j required the variation ? From the greater E. 26 12' NT. Take the leifer .14 20 N. Remains the variation n 52 E. Which is eafterly, becaufe in this cafe the true amplitude is to the right of the obferved. N With the chord of 60 defcribe a circle to reprefent the compafr, through which draw the north, fouth, eaft, and weft lines ; take the amplitude at riling, 26 12' from the line of chords, and fetting it from E. towards N. and likewife the true amplitude 14 20', and Fet it from E. towards N. as r before, the difference of thefe two angles, or between the true and magnetic amplitude, viz. n 52' is the variation. Now fuppofe yourfelf placed at the centre of the horizon reprefented by the compafs, and looking towards the mag- netic amplitude at the fun's rifing, it is plain that the true ampli- tude found by calculation is towards the right hand of the obferved, which fhews the variation is u 52' E. and muft be allowed to Sie right hand in -all courfes fteered, before they can be put in the Traverfe Table or bearings, taken by the compafs. EXAMPLE II. Suppofe the fun's true amplitude at fetting be W. 34 26' S. and his magnetic amplitude W. 23 13' S. required the variation, fmce they are both of the fame name ? From TO FIND THE TRUE AZIMUTH. From the true W. 33. 26* S. Take the magnetic W. 23 138. '59 Remains the variation ii 13 W. Which is wefterly, becaufe the true amplitude is to the left of the obferved in this cafe. N EXAMPLE in. Suppofe the true azi- The mag. az. 101 15 \\\ * Variation 16 35 * Let JJ. E. S. and W. reprefent the horizon ^ C, D, F, an azimuth - circle, paffing through the fun's centre; now an obferver, placed at the centre, will fee the fun at rifing, in the line i, but when he gets a greater altitude, and arrives at E, he will fee the fun in the line O *> andasjthe fun alters its altitude, willbefeen in the line 3, O 4> G 5> at length will arrive at its meridian, Z, S, and the figures, 2, 5, 4, 5, will reprefent the different magnetic azimuth ; the difference between any of thefe and the true azimuth found by calculation, is the varia- tion. EXAMPLE IV. . Suppofe the fun's true amplitude at rifing is li. 13* 24' N. and his magnetic amplitude E. iz'^z'S. required the variation, and which way ? Since the true amplitude and ob- ferved have different names, To the true amplitude K. 13 24' N. Addthemagneticamp.E.i2 328. Their fum is the variation 25 56W. Which is wefterly, becaufe the true amplitude is to the left of the obferved. EXAMPLE V. Suppofe the fun's true azimuth in the forenoon isN.864o'eaiterly > but by the compafs it is N. 73 24' eafterly; required the variation, and which way ? Since the true and obferved szi- muths are both on the fame fide ot the meridian, From the greater N. 86* 40' E, Take the leifer . N. 73 24 E. Remainder variation 13 16 E. Which is eafterly, becaufe the true azimuth is to the right of the obferved. EXAMPLE i6o FIND THfc TRUE EXAMPI/E VI. Suppofe the fun's true azimuth is N. 32 28'ea(lerly,andhis magnetic azimutft N.8 50' weft; required the variation*, and which way ? Since they are on the different fides of the meridian, To the true azimuth, N. 32 28' E. Addtothemag.azim. N. 8 5oW. Sum is tht variation 41 18 E. Which is eafterly, becaufe the true azimuth is to the right of the obferved. AZIMUTH. EXAMPLE VII. Suppofe the fun's true azimuth S. 17 45' E. and the magnetic azi- muth S. 5 48' W. required the va- riation, and which way ? Since they are on different fides the meridian, To the true azimuth, S. 17 45' E. Add the obferved az. S< 5 48W. Sum is the variation 23 33 \V is weft, becaufe the true azimuth is to the left of the ob- ferved. The ufe of the variation is to correct, the courfe fleered by the compafs ; when the variation is earl, it muft be allowed to the right hand upon every courfe fleered quite round the compafs; but when the variation is weft, to the left hand. NOTE. The variation may be eafily found by taking the fun's altitude in the morning, and obferving what point of the compafs he bears upon ; and in the afternoon when the altitude is the fame, the middle point will be the true meridian, the difference between which and the north or fouth points of the compafs is the variation. If the altitudes are taken at 5, 6, or 7 o'clock in the morning, you will have the fame altitude at 5, 6, or 7 o'clock in the evening, being equally diftant from noon. The variation of the compafs was firft obferved at London, in the year 1580, to be ri 15' eafterly ; and in the year 1622, it was 6 o' E. ftill decreafing, and the needle approaching the true me- ridian, until it coincided with it in the year 1662, fmce that time the variation ftill continues at London to increafe wefterly, at the rate of about !i or 12 minutes every year; and is at this time about 23 30' wefterly, and in the Englifh channel about 28 oo' wefterly ; but how far it will go that way, time and obfervations will probably be the only means to difcover. The variation at Paris in the year 1640, was 3 E. but in the year 1681 it was 2 21' XV. and is now about 22 20' wefterly, ilill continuing to go wefterly. In (hort, from obfervations made in different parts of the world, it appears, that in different places the variation differs, both as to its quantity and denomination, it being eaft in one place, and weft in another; the true caufe and theory of which has not yet been difcovered, and therefore in long voyages it is abfolutely neccflary that the mariner fhould find the variation of the compafs by ob- fervation as often as pofEble. THE THE METHOD OF KEEPING A SHIP'S RECKONING OR JOURNAL AT SEA. BY keeping a Ship's Reckoning, or Journal, is meant keeping an account of the (hip's way, that the manner may be able at any time to afcertain the latitude and longitude the fhip is in ; it therefore fhould be the great concern of every perfon who takes upon them the navigating of fhips to remote parts, to be expert therein, as the lives and fortunes of fo many men are committed to their charge. When a fhip is bound from one place to another, which lies fo far from her that fhe is obliged to go out of fight of land for any confiderable time, as from England to Jamaica; at the time of her leaving fight of land, {he is faid to take her departure, and that part of the land fhe then leaves is faid to be the place fhc takes her departure from ; fuch as the LandVend, Lizard, &c. and at the time of taking fuch departure, the captain or mate generally takes the bearing or diftance of that land, (according to his judgment,) and fets it down on the iog-board, or in the log-book, againft the time it was taken, thus, Land's-end, N. N. E. dift. 7 leagues, or Lizard N. by W. dift. 5 leagues, &c. In the fame manner may the departure from any place be taken, as may be feen in the firft day's log of the following journal, where the log book is marked in columns for hours, knots, fathoms, courfes, winds, lee-way, tran fact ion s ; and under it the columns for courfes, diftances, northings, or fouthings, eaftings, or weft- ings, the latitude by dead reckoning, latitude by obfervation, meri- dian diftance, difference of longitude, longitude in, and in the laft, bearing and diftance of the land. Notice niuft be taken, that in the column for courfe, you are al- ways to fet down the courfe you have made by your reckoning for that twenty- four hours ; that is, from the noon of the day before to the noon of the day you work on, thefea account being always kept from noon to noon. Dead reckoning is that account deduced from occurrences which are written on the log-board. In the columns for diftance you are to fet down the diftance made by your reckoning for that twenty-four hours. In the columns of northing and fouthing, you are to fet down the difference of latitude made in that twenty-tour hours, marking the column with north, if the difference of latitude be north; and fouth, if fouth. In the column of eaftingor wefting, you are to fet down the de- parture made that twenty-four hours, marking the column with eaft, if the departure be eaft, and with weft, if wefterly. 'In the column marked latitude by D. R. you are to fet down the latitude you reckon yourfejf in on that day ; and in the column marked lat. by gb, you are to fet .down the latitude found by qbier- X vation ; 162- THE METHOD OF vation; alfo the difference of longitude made in the 24 hours in the column marked diff. long.; the longitude in, in the column marked long, in ; and in the laft, the bearing and diftance from the land, The variation, if any, muft be allowed upon all courfes fteered, and upon all bearings that are taken by the compafs ; that is, if it be eafterly variation, it muft be allowed to the right hand ; if wefterly, to the left of the courfe or bearing. Suppofmg yourfelf placed in the centre of the compafs, and looking diredly forward to the point you are to allow the variation upon. EXAMPLE. Suppofel fleer S. W. and there is one point wefterly variation, then my true courfe is S. W. by S. ; or fuppofe 1 fet a point of land, and find it to bear by the compafs E. S. E. and I know there is half a point eafterly variation, then the true bearing is S. E% by E. \ E. Leeway muft be allowed upon all Courfes fteered, which is the difference between the point which the fhip endeavours to fail up- on, and the point fhe really fails upon, and is caufed by the foree of the wind or furge of the fea, when fhe is clofe hauled or ply- ing to windward, which makes her fall off and glide fidewaysfrom the point of the compafs fhe capes at, and muft be allowed on the right hand of the courfe fteered when the larboard tacks are on board, and to the left hand when the ftarboard tacks are on board. The allowances that are generally made are as follow : I ft. When a fhip is clofe hauled, if all her fails be fet, the water fmooth, and a moderate gale of wind, fhe is then fuppofed to make little or no leeway. 2dly. The fhip being upon a wind, and the fmall fails in, allow one point for leeway. 3dly. The wind blowing hard, fo as to caufe one top-fail to be taken in, allow two points for leeway. 4thly. When it blows fo hard that both top-fails are taken in, and the fea runs high, allow then three points for leeway. 5thly. The fore- fail being furled, and the fhip tries under a main- fail and mizen, allow four points for leeway ; for fhe then makes her way about four points before the beam, as the fea phrafe is. 6thly. When the fhip tries under the main-fail only, fhe then makes her way about three points before the beam, that is, allow near five points leeway. ythly, If the fhip tries under the rnizen only, the way is about two points before the beam, that is, allow fix points for her lee- way. 8thly. When fhe lies hull, that is, with all her fails furled, her ^vay is one point before the beam, and then feven points is her lee- way. Qthly. When a fhip is lying to under a main-fail, mizen, &c. then obferve how fhe comes up and falls off, and take the middle be- tween th^two points, and from that allow the leeway and varia- NOTE KEEPING A JOURNAL AT SEA. l6j NOTE. In all cafes refpe& muft be had to the fmoothnefs of the water, or to the fea's running high, and the mould and trim of the ihip, and then the allowances may be afcertained with the greater certainty, by fetting the fhip's wake by a compafs placed on each rail of the fhip's quarter,which is ufually fet there for that purpofe. For it is well known that fome {hips, with the fame quantity of fail, and with the fame gale, will make more or lefs leeway than others ; and alfo the fame (hip, when flie is out of her trim, or differently loaded, will make different leeways : for it is obferv- able, that the more water a fhip draws, the lefs leeway fhe makes ; becaufe fhe then meets with a greater refiftance in fplitting the water with her fide, than otherwife fhe would The leeway may be eafily found by the azimuth compafs, by turning the inftrument about until you fee the wake of the (hip either over the fights or parallel to them; then the point of the card, which is cut by the vertical line in the box, which is neareft to you, is the true courfe ; the difference between that and the courfe given by the compafs in the binnacle, is the leeway required, which ought to be accordingly entered upon the log-board. There is another way of finding the leeway, by fixing a compafs cut in lead (or other metal) on the poop, or fome other convenient part of the fhip's ftern, with the meridian parallel to the fhip's keel. By fome of the above methods, the leeway (if there be any) ought to be carefully obferved as often as may be judged neceflary ; and thefe obfervations fhould be punctually fet down by the officer of the refpe&ive watch ; at leaft, if no obfervation be made, he ought to fet down the leeway according to his judgment once or twice in the watch, and by this means the courfe made good may be found to a much greater certainty and exa&nefs than by the common method of allowing for leeway, when the day's account comes to be worked (which is generally once in 24 hours) ; for an observation muft certainly be better than any guefs. But if no obfervation be made, the perfon who is upon deck, and has the care of the watch, is better able to make proper allowances, while things are frefh in his memory, and while he is an eye-witnefs of the 'feveral occurrences that happen ; and certainly much more capable than another who was not upon the deck during the whole watch. I have often admired to fee how particularly every thing is ftated upon the log-board, excepting the leeway : and yet that (which is one of the moft material articles, fince the courfe, according to the compafs, muft be corrected by it) only allowed for the next day, according to every one's fancy, thereby, as it were, keeping as many different journals as there are artifts (fo called) on board the fhip, and yet not one regular journal properly kept amongft thsffi allj fince one of the moft material articles is only guefled at. X z EXAMPLE 164 THE METHOD OF EXAMPLE I. Suppofe I fteer N. E. by E. with my Larboard Tacks o Board, and make one Point Leeway, then my Courfe made good is E. N. E. Leeway and Variation, when they are both to be allowed one Way, that is, both to the right Hand, or both to the left, acid them together, and allow their Sum the fame way they were to be allowed. But if they are to be allowed, one to the Right Hand and the other to the Left, fubtract the lefs from the greater, and allow the Remain- der the fame Way the greater was to be allowed. EXAMPLE II. Suppofe I fteer N. N. W. with my Starboard Tacks on Board, and make one Point Leeway, there being at the Time Half a Point Weft- erly Variation j I would know my true Courfe ? Leeway to the Left Hand I Point. Variation to ditto 1 Point. Their Sum to be allowed to the Left Hand ii Point Whence the true Courfe is N. W. by N. k W. EXAMPLE III. Suppofe I fteer S. W. by W. with my Larboard Tacks on Board, find make two Points and a Half Leeway, and I have one Point and d Quarter Wefterly Variation, what is my true Courfe ? Leeway to the Right Hand 2! Points. Variation to the Left K i J Point W. The Remainder to be allowed to the Right JIand i| Whence the true Courfe W. S. W. I Wefterly. E X A M. P L E IV. Suppofe a Ship lying to under a Main-fail, with her Starboard Tacks on Board, comes up K. by S. and falls off to N. E by E. there being one Point Wefterly Variation, and (he makes 5 Points Leeway, what Courfe does fhe make good. The Middle between E. by S. and N. E. by E. is E. by N. for which allowing 6 Points to the Left Hand, the true Courfe wiJl be N. by E. It is plain by the preceding Examples, that if the Leeway is made towards the Meridian, it is taken from the Courfe fteered ; but when it is made from the Meridian, it muft add to the Courfe fteered, tq find the true Courfe. The fame may be obferved of the Sum or Difference of the Leeway and Variation, as mr*y be feen by the fol- lowing Table, which is here fet down to exercife the young Naviga- tor in the foregoing Rules, THE KEEPING A JOURNAL AT SEA. THE TABLE. 165 Courfes fleered. Winds. Lee- way. Varia- tion. Courfes corrected. N. W. \ W- W N. N. E-- N. N. W. 1 i JW. N. 5 | W. S. 6^ W. w. s.w. S. i ~ S. 6| W. w. s.s.w. I J. 4- \V. W. by N. s. w. NbyW. W. N. W. ii ff 3. 4 S. 7 W r S. i i W. s. W. S. W. I| S.S.E. s. s. w. w. i li S 4- E. s.w. w. N. W. by W. s.s.w. 1 if Jf s. s. w. i w. W. by N. A W. W by N. S. N. by W. E.S. E. i 2 ii a W. S. W. 1 W. S|W. E. by S. SI 1? "T *-* JL 4- ii E. by N. E. N. E. " N. a E. N. E. 4 E. E. N. JL u E. by N.4 E. E. S. 4- a E.N. E.|E. S. E.S. E I i^ S.by E. * E. E. S.E. N. E. 1 ii EbyS.-|E. W. S. W. S. 1 S. W. by W. W. by N. S. W. by S. 1 W. .* N. N. W. w. s. w. I 4 N . VV.|W. S. w.s.w. I oi E. S. -IE. N. by E. N.W.byW. T i N.N. E. {E. N. W. by N. W.by S. If i N. l W. N.W.byW. N. by E. I* i$ N.W.by W'W. W by S. N.W. by N. II 2 W. 4. S. NOTE. In failing in the Channel, or along a Coail in a Stream Tide or Current, particular Care muft be taken to take its fetting for aCourfe, and its drift for a Diliance, if pailible, which mud be en- tered among the Cqurfes and Diitances in the Table of th;it Day's Reckoning. And where the Yetting of ths Stream Tide and Drift are not known, you muft attain the Point it muit fet upon, from the Chart of the Coaft you are failing along, by the times the Stream ends at dif- ferent Places en the Coaft, and by the Principles of Fluids againll fuch Rocks, Shoals, Sand-Banks, &c. By a llrict regard to thefe, both the drift and letting of the Stream-Tide;? may be pretty nearly afcertained and allowed for. Currents, the Way they fet you, and the Difhnce you fuppofe you arc driven by them, is to be fet in the Traverfe Table for the Day, as any other Cuurfe and Pittance. EXAMPLE V. Suppofe I try the Current, and find it to fet W. by N. per Compafs one Mile per Hour, the Variation being One Point Kafterly ; then if fail in that Current 24 Hours, I fet down in the Traverfe Table, as a Courfe, W. N. W. Diftance 24 Miles. Heave THE METHOD OF, &C. Heave of the Sea is to be accounted for in the fame Manner as Cur- rents : As, fuppofe there is a great fea heaving towards the S. \V W by my Compafs, there being Half a Point Wefterly Variation, I then fet down in my Traverfe Table S. W. by S. half WeOerly, with fo much Diftance as I judge the Sea has heaved the Ship. At leaving the Land, the oppofne Point of the Bearing, with the Variation allowed upon it, and the Diftance you judge yourfelf from it, muft be fet down in the Trarerfe Table as a Courie and Diftance. EXAMPLE VI. Suppofe, having Two Points and a Half Wefterly Variation, the Start bearing by my Compafs N. E. dift. 4 Leagues ; the oppofite Point to N. E. is S. W. which, with the Variation, makes S. by W. W. for the Cou. to be fet in the Traverfe Table did. 12 Miles. When you make the Land the Bearing, itfelf (with the Variation allowed upon it) and the Dift. you judge yourfelf from it) is to be fet down in the Traverfe Table as a Cou. and Dift. This needs no Ex- ample, The Courfes marked on the Log-board are the Courfes fteered by the Compafs. In order to obtain the true Courfe, it is neceifary to al- low both for the Variation of the Compafs, and for the Leeway, upon each Courfe on the Log- board, as has been fhewn, before they are put into the Tvaverfe Table. Every Day at Noon the Lng-board is to be tranfcribed into the Log-book, which is ruled exactly like the Log-board. Mariners keep the Reckoning for the Chip's Place. From Noon to Midnight they mark with P. M. fignifying after Mid-day; and the fecond twelve Hours with A. M. iignifying af-er Midnight; ending their Day's Work at the Noon of the civil Day. Hence, their Ship's Account is twelve Hours earlier than thcir$hore Account of .Time. And, as UK Sun's Declination ufed for determining the Latitude at the End of the Sea day i* calculated for the Noon of the Common-day at Greenwich, therefore the Declination for the Noon of the civil Day, muft be taken for determining the Latitude, &c. at finishing their Day's Account. Thus, a Day's Work marked Tuefday, May 6th, be- gan on Monday at Noon, and ends 00 Tuefday Nooa, fo that the Sun's Declination for the 6th of May is ufed for Tuefday, and fitted to the Meridian of the b-hip, according as fhe is E. or W. of Greenwich. There are various Methods of keeping a Sea Journal, according to the Sentiments of various Perfons with regard to what deferves being recorded : forne approve of a Journal including the Log-book, each day's work at fume length, and fuch occurrences as feem of moft im- portance 3 while others prefer a fhort Abftract of* this long Journal> containing little more, than theCourferun, the Latitude and Longitude jn, and fometimes the Bearing and Diftance of the intended Port, for each Day. In the following Journal thelong Form isufed, as reprefentingmore fully each day's work, and the neeeflary Corre&jons j and an Abftract jof this may be drawn out in the fhorteft Form that feems confident with Diftinctnefs. The Learner ought to be thoroughly acquainted with the long Form, and when he does that, he may either continue it, or take the morteft form ; or retrenching from the firft, and adding to the fecond what Particulars he thinks proper, and may thereby make out a Form adapted to his own particular Tafte, RULE-: RULES for corre&ing the DEAD RECKONING by an Obfervation. I^TOTWITHSTANDING the Rules already laic! down for keeping J^ a Ship's Way at Sea, yet by reafon of the feveral accidents that may attend a Ship in one Day's Run, fuch as fwelling Seas, differ- ent Rates of failing between the Times of heaving the Log, want of C'ire at the Helm in letting the Ship fall off, or come to accidental Cur- rents, fudden fqualls.. when no Account can be kept, &c. the Latitude by Account and Latitude by Obfervation may very often differ, th-n it is necrffary that proper Corrections be made in the Difference of Longitude. Vi hen you hnve mnde all proper allowances you can, fuch as for Leeway, Variation, Currents, &c. and flill rind that your latitude by- Account will not agree with your Latitude by Obfervation, then you mull correct as follows : FirrK confider whether you have made proper Allowances for Cur- rents Heave of the -^'ea, if the Courfe of the Helm has been carefully attended to, if the Log- line and, Half-minute Glafs be juil, and the Log properly hove, or any fudden fqualls, or proper Allowances made for the eeway, &c. which of thefe you conjecture your error is in ; make what Allowances you think meet to your Difference of Latitude and Departure by Dead Reckoning, and fee if that will reform your Lati- tude by Account, fo as to make it agree with your 1 atitude by Ob- fervation ; if it does, you have gueiTed right j (for you muft always keep to the atitude by Obfervation, it being the only thing to be de- pended on 5) but if it will not agree with the obfcrved Latitude, it is to be fuppofed that there are Miltakes in your Conjecture, or fome other Caufe, which produces the Error in the Reckoning, -and ftands m need of being corrected. Jn this Cafe, you are rlrft co examine your Log-line ad Half-minute GLils, and if there be an Error in them, al- low for it, as in the following Examples: EXAMPLE. I. Yefterday at noon, we were in latitude 48 20' N. and till this day at noon we have failed 5S. S.W. 48 miles, b. V. 7 . by S. 36 miles, N. E. 34 miles, and find by good obfervation that we are in latitude 47 14'. TRAVERSE TABLE. COURSES. DIST. ~ 3 6 24 N. S. E. W. S. S. W S. W. by S. N.E. I?>o I7> 44>3 29,9 17,0 18,4 20,0 3^4 74 2 i7> 9 4*,5 N. E. bv N. 20 1 6,6 n,i W. S. W. 7 - 26,8 <>47 S. by \V. | W. 20 19,1 S>* 16,6 80,8 53* 6 7>5 16,6 53>6 Diff.Lat. 64,2 Dep. l6,q By the Traverfe Table it appears, that by Account the DifY. of Lat. is 64.2 S. and ihe Departure 16.9 W. Latitude RULES FOR CORRECTING, &C. 169 Latitude failed from 36 15' N. 36 15' N. Difference of latitude by account I 4 S. Lat. obf. 34 56 Latitude in by account 35 1 1 N. Diff. lati I 19 Differing 15 miles from the latitude by obfervatioa. I now examine the log- line and half-minute-glafs, and find them both right. Next I confider whether there be any current, and I think I have reafon to fufpeft one ; upon trial I find there is one fetting S. S. V$\ W. at the rate of 7 fathoms an hour, and judge I have been in it thefe 24 hours. Then 7 fathoms (or tenths of a knot) per hour, in 24 hours, makes about 17 miles: and to the dift. 17 miles, and courfe S. S. W. |. W. the dirF. of lat. is 14,6 S. and departure 8,7 W. Diff. lat. Now by tra. table 64,2 S. And by current 1 4,6 S. Latitude failed from 36 15' N. Diff. of lat, cor. tor cur. i 19 S. Correct for cur. 78,8 S. 25,6W. Lat. in, correct for cur. 34 56 N. Which agreeing with my latitude by obfervation, I conclude that my reckoning is right ; then having the latitude left, and la- titude come to, the difference of longitude may be found either by Middle Latitude or Mercator's Sailing, as before. If, after all proper allowances are made for errors in difhmce, currents, &c. the latitude by account and obferved latitude fhould difagree, then the reckoning muft yet be further corrected ; and'to do which, the following are the common, and feem to be the moft rational, methods : CASE I. If the Courfe found by Dead Reckoning be lefs than three Points^ or thirty-three Degree:. RULE. To the difference of latitude and departure by account find a courfe ; with this courfe and the difference of latitude by obfervation, find the difference of longitude, either by Middle Latitude, or Mercator's Sailing. EXAMPLE. Yefterday at noon we were in lat. 39* 18' N. by an obfervation, this noon we are in lat. 37 48' N. and our dead reckoning gives 107 miles of fouthing, and 64 of wefting; required the true dif- ference of longitude ? To the difference of latitude 107, and departure 64, I find the courfe 2 T points ; then with the meridional difference of latitude between the two obfervations 115, and tiae fame courfe, I find the true difference of longitude 69 miles. CASJ; RULES * Jl C R R L C J 1 N .., CASE II.- If the Courfe found by Dead R.eckoniny be msre than three Pointy ' "or t/jirty-tbtee Dagrct^ and It fi than five Pointy or fifty -fix Degrees. RULE. With the cliff, of lat. and dep. by account, find the dlilance; with this diftance, and din 1 ', of lat. by obfervation, find another departure. Take half the Turn of this dep. and dep. by ac- count, for the true dep. with which, and the diff. of lat. by obfer- vation, find the diff, of longitude. EXAMPLE. YeftenJay at noon we were in lat, 52 40' N. and are this noon in lat. 54 22' N. having by account made 84 miles of northing, and 76 mile? of welling; required the true difference of longitude? To the diff. of lat. #4, and dep. 7^, the diftance is 113 miles, and the coii rfe 42. To did. 113, and diff. of lat. between the two obfervations 102, the dep. is 49,5; then 76 added to 49,5 is 1*5,5, half of which is 62,7, the true dep. To dep. 62,7, and diff. of lat. by obfervation 102, the courfe is 31, and with the courfe 31 and the meridional diff. of lat. be- tween the two obfcrvations J/i, I find the diff. of long, is 103 miles. CASE III. If the Coirfs by Dead Reckoning be more than fve Points^ or fifty -fix Degrees. RULE. With the diff. of lat. and departure by account find the diftance ; then with this dift. and diff. of lat. by obfervation find the diff. of long. EXAMPLE. Yefterday at noon we were in lat. 3$ 52' N. to-day at noon we are in lat. 40 I b' N. and by account have made 68 miles north- ing, and 112 miles of weflmg \ required the true dift. oi longi- tude ? With the diff. of latitude 68, and departure 1 12, I find thedif- Jam-e 131 miles, and to diftance 131, and difference of latitude by oWervanon 86, the courfe is 49, nearly; whh this courfe, and (he meridional difference of latitude between the two obfervations I ii, the difference of longitude is 128 miles. The reafon of the above rule is plain, if we confider, tint when a fhip fails near the meridian, it will require a fenfible error in tne rourfe, to make any coniiuerable error in the difference of latitude ; h c;in hardly happen if proper care is tuken at the helm ; and therefore it is mo't likely that 'the error is in the diftance run; but ivfcen the cotirle is near the middle of the quadrant, or between 3 points from the meridian, it is then probable the error may be in THE DEAD RECKONING. 1/1 in both courfe and diftance ; and when the courfe is more than five points from the meridian, it is then rroft likely the error is in the courfe, as it will require a great error in the diftance to make any confiderable one in the difference of latitude. NOTE. As the true place of a fhip depends upon h-r latitude and longitude being truly ascertained, I have fet thefe down only, the reft being of lefs confequence to the mariner. To correEi for fever 'al Days. By help of the three preceding rules, the longitude may always be corrected for a fingle day, but if an observation has been wanted for one or more days, then mark the latitude and longitude at la it obfervation, or if this be your firft obfervation fince leaving the land, mark the latitude and longitude of the land you left ; this is the only latitude and longitude you can call certain ; all the fol- lowing part of the reckoning muft undergo a correction, which is made as follows: Take the northings, fouthings, eaftings, and wefting*, that you have made fince your laft obfervation; or, if this be your firft ob- fervation, then for every day from your leaving the land, minding not to leave out the difference of latitude and departure of the day you correct on, and bring them into the Traverte Table, by which you will have the whole difference of latitude and departure by ac- count fince the laft obfervation ; and with that fame difference of latitude and departure find the courfe by dead reckoning ; cben ob- ferve which of the foregoing cafes that courfe fall-s under, and cor- rect by the rule for that cafe. But when an obfervation has been wanting for feveral days, then mark the latitude and longitude you were in at your laft obfervation, or on leaving the land as before, and then you may correct with a greater degree of certainty, eipe- daily in high latitudes, by the following rules : CASE I. Reckoning from the laft certain latitude and longitude. When the courfe given by the meridional difference of latitude and difference of longitude by account, taken as difference of lati- tude and departure, is lefs than three points, or 33 degrees. RULE. To the meridian difference of latitude and difference of longitude by account (taken as difference of latitude and departure, as fhewn in M creator's Sailing), find a courfe ; with this courfe, and'the meridian difference of latitude by obfervation, find a cor- refponding departure, which will be the correct difference of lon- gitude. EXAMPLE I. Having failed three days ago from latitude 49 57' N. and got no obfervation till this day at noon, and find I am in latitude 45 23' N. and by dead reckoning lam in 45 i2'N. having differed my longitude 173 miles ; required my difference o/ lon- gitude ? Y 2 Lat. RULES FOR CORRECTING Lar. failed from Lat. by account M. Parts. 49 57' N. 347 4$ 12 N. 3047 4 45 . diff. of lat. by ace. Lat. failed from Lat. by obfer. M. Parts. 49 5 7' 347 45 23 .3063 4 34 423 Mer. diff. of lat. by obf. 407 To meridian difference of latitude by account 423, and differ- ence of longitude by account 173, the courfe is 22 45'. Then with the courfe 22 15, and meridional difference of latitude be^ tween the obfervations 407, I find the difference of longitude is 167 miles. CASE II, When the courfe given by the meridional difference of latitude and difference of longitude by account (taken as before) is greater than three points, and leis than five points. RULE. To the meridian difference of latitude and difference of longitude by account, taken as difference of latitude and departure, find a diflance ; with this distance, and meridian difference of lati- tude by obfervation, find a correfponding departure; half the fum of this departure, and the difference of longitude by account, is the correct difference of the longitude. EXAMPLE II. Three days ago we were in latitude 45 23' N. and have fince that time failed between fouth and weft, have, by dead reckoning altered our latitude 94 miles, and our longitude 147 miles ; but by an obfer vat ion this day, we find we are in latitude 43 34'; re- quired the correct difference of longitude ? M. Parts. Lat. failed from 45; 23' N. 3063 Lat. by bier. 43 34 N. 2910 M. Parts. Lat. failed from 45 23' N. 3063 Lat. by ace. 43 49 N. 2931 34 Mer. diff. of lat. by account. 132 i 49 Mer. diff. by obfervation f 153 With the meridian difference of" latitude by ace. 132, and differ- ence of longitude by ace. 147, I find the diflance 198, and courfe 48. Then with the diftance 198, and meridian difference of la- titude by obferyation 15?, the dep. is 125; now 125 added to 147 is 272, and half this fum, viz. 136, is the correct diff of longitude. CASE III. When the courfe given by the meridian difference of latitude and difference of longitude by account (taken as before) is more than five points, or 56 degrees. RULE. To the meridian difference of latitude and difference pf longitude by account, taken as difference of latitude a,nd depar- ture, find a diftance. THE DEAD RECKONING. 173 To this diilanceand meridian difference of latitude by obferva- don, find a cor refponding departure, this departure will be the cor- rect difference of longitude. EXAMPLE III. Two days ago I was in latitude 43 34' N. and have fince then made by account 50 miles by fouthing, and 256 miles difference of longitude weft, but find by obfervation that lam in 42 30' N. ; what is my true difference of longitude ? M. Parts. M. Parts. 1, at. failed from 4334'N. 2910 Lat, by account 42 4^. N. 2841 Lat. failed from 43 3^.' 2910 Lar. by obfer. 42 30 2823 J 04 JMer diff. of ht. by account 69 j Mer. diff. of lat. by obfer. 8S Then to meridian difference of latitude by account 69, and diff, of longitude by account 256 (taken as difference of latitude and departure), the diftance is 265, and courfe 75 degrees. And to diftance 265, and difference of latitude 88 (the meri- dian difference of latitude by obfervation), the departure is 25, which is the correct difference of longitude. Here we have given, at feme length, the different methods of correcting the dead reckoning by an obfervation, which are rea- dily done by the Table of Difference of Latitude and Departure. The {hip's way is generally greater than the diftance given by the log, and it is always fafeft to have the reckoning a- head cf the {hip, that the mariner may be looking out for land, and not make it before he is aware of it. When a great fea fets after the mip, it is common to allow one mile over for every ten given by the log, for the beave of the fea; but if the fea be athwart or againft her, her diftance mufl be lefs than that given by the log. The error in the {hip's reckoning is frequently attributed to un- Jcnown currents; for by various caufes, yet undetermined, there are many counter motions of the water in the open feas, as well as thofe obferved near the ihores, where the motions may be to- Jerably well accounted for. Some of the obferved currents in the great leas may perhaps be owing to the tides following the moon, and to the libratory motion the waters may have thereby, and the unfettled fetting and drift of thefe currents may poiTibly'depend on the change in the moon's declination. However, it is well known from cbfervations, that the trader-wines occafion a confiderable current within their limits, particularly within the Torrid Zone, where tie motion is perpetually towards the weft, at the rate of eight or ten miles a day, butat the extremities of the trade- winds, or near the latitudes of 30 N. or S. it is likely that the currents are compounded of the laid weftern motion, and or" one towards the equator; therefore all {hips failing within thefe limits ihould allow acpu/fe each day for this current, 174 RULES FOR CORRECTING, &C. NOTE. When the difference of latitude by account is lefs than the difference of latitude by obfervation, the (hip is a-head of the reckoning, but if lefs, the reckoning is a-head of the {hip. When the mariner is dubious of his account of longitude, he ge- nerally runs into the latitude of the intended port, and then fails E. or W. if there be fea -room, according as -it is fituated, and keeps a good look -out for the land. The method I have chofen to introduce the young mariner into the moft capital part of navigation is, by (hewing him firft how to work a few feparate days' works, independent of each other, and then proceed to a continued Journal from London to Madeira and Teneriffe, in which will be inferted moll of the occurrences that commonly happen at fea or in harbour. I have feen many young navigators, who have been taught the principles of Navigation on fhore, very deficient in keeping a jour- nal at fea ; and therefore muft requeft the tea4 7 c 4?i 58,8 ii,9 32,8 35>3 1 9>5 M*7 no,/ Dep. 42,0 iff. L 112,9 42,0 at. 70,9 Lat. left Diff. lat. Lat. in 46 2*' N. M. i ii 1 S. Par.^3i 5 6 Par. 1=3054 45 17 N. M. jSum lat. 2)91 45 Mer. D, Lat.= iO2: iVlid. lat- 45 52 Co. M. lat. 44 08 JLong. left 22 18 W. ! Diff. of Ion. 2 39 F,or 2 40'. Long, in 19 .?g W. IJirea Cou. S. 57 22' h.. Dift. 131 m. "]\''C courfcs and winds on the log-board being examined, it appears that the fhip fails and has no lee-\vay ; therefore the feveral courles from the log-board are entered into tlic Traverfe Table \vitliout alteration. Kext the fathoms and knots belonging to each courfe are fummed up, and the refults are put in the column of di fiance's in the Traverfe 7V>ble : and to thefc ccurfes and diitances, the whole difference of latitude, departure, courfe, and diftance made good, are found .as above. Then, having the latitude left, and the latitude come to, find the complement of the middle latitude, and'with that and tHfe dcpdrture, find the longitude, &c. by middle latitude failing. Or, with the courfe, and meridional difference of latitude, find the difference of fongktt&j by M creator's Sailing 1 . NOTE. \Vhenthe cdd fat heirs arc above five, we allow one knot, ! ut, if voder five, nothing is ajlovvd. ?J E FOR KEEPING A EXAMPLE II. Jane 29, 1806^; being yerterday noon in latitude ^s 3 0/s - a Couries. Lhtt. N. 6. E. W. i 6 SiW. W.N.VV. I S.by W. i-W. 3^ 28,7 8,7 7 6 2 S.byE. - E. 32 3 6 9*3 6 ^ S. t E. 30 29,9 2 >9 3 4. 6 S.E.byE.^E 39 18,4 344- 5 5 3 S.byE. IE. 60 574 ^7.4 6 7 8 6 5 5 c i 4 S. by W, W. by S. I DifF. Lat. 165,0 64,0 8,7 8,7 9 ro 5 $ 2 S .? Dep. r T c C DifF. iat. 2"45'6. 21 5 2 S. S. W. W. I Lat.Ietc 25 308. Mer. parts 1583 I 2 5 9 2 C Lat. in 28 158. Mer. parts 1768 3 4 4 5 6 c Sura Iat. 53 45 M.diff.lat. 185 6 5 5 i 2 S.E.byS. S.W.bjS. 1 Mid. Iat. 26 52 *? 5 4 8 9 4 Co.m.Iat. 63 08 <^ 6 C .... . .. .. |0 1 1 6 5 C -! Long. left 10 15 E. Dif. Long, i 02 E. or i oi'f E. 12 $ 5 TT 1 Jou- is-x 1 8 30 E. -Lfift. 174 miles. Long, in u 17 r,. 'The courfes and winds on the log-board being examined, it appears that the (hip is clofe hauled, and one point lee-way being allowed, reduces the courfes, and taking a courfe for the current S. thefe feveral courfes being corrected by the variation i | point weft, give thofe in the traverle table, to which the whole difference of latitude and departure is to be found as above. And hence the latitude and longitude in may be found, either by middle latitude or Mercator's failing. NOTE. In the two following examples, the courfes are corrected to the neareft de- grees, asfetdown in the Traverle Table, and the odd minutes are rejected. RULES FOR KEEPING A JOURNAL. I 77 EXAMPLE III. Yefterday at noon we were in latitude 33 4o'N. longitude 16 20' weft, the fun was obferved to fet 50* 18' from the north point of the compafs; we have failed this day noon, as per log-board, in a current fetting W. S. W. if mile per hour ; required the flap's place, and her courfe and diftance to the weft end of the Jfland of Madeira ? LOG-BOARD. , TRAVERSE 1 ABLE. H K. F Courles. Winds. L. Vvav Courfes. Dilt. N. S. E. W. i 6 2 S. by W, W. O S.oiE. 40 40,0 '7 2 6 O S, 10 W. 70 68,9 12,2 3 6 3 S. 44 W. 58 41*7 4 r 7 2 s. 55 w. 20,6 *9>S 6 3 Diff. lat. 171,2 0,7 82,0 7 7 2 S.W.byS. W. by N.' I 0,7 8 7 2 9 7 4 Dcp. 81,3 10 7 6 Before the courfes can be corrected to ii 7 4 put into the Traverfe Table, the variation of 12 8 i the compafs muft be found from the fun's I 8 o true amplitude. 2 8 5 The declination is 22* 30' N. 3 4 8 7 2 5 S.WbyW. N. W. o As cof. lat. 33 40' : rad. : : fin. 22^30' : fine 27 22'. Comp. = 62 38'. 5 7 7 6 6 4 So that the true amplitude rr N. 62^8'W. Mag. amplitude ~ N. 50 i8W. 6 Variation = 12 20 W. 9 10 6 6 2 I The courfes on the log-board being cor- reded by this variation and the lee-way, will ii 6 3 give the courfes fitted tor the Traverfe Ta- 12 6 r hie. Lat. left Diff. lat. Lat. in Sum lat. Mid. lat. Co. mid. lat. 33 4o'N. 30 49 N. 64 3 2 57 29 - 57 46 R Long, left Diff. long. 16 Long, in 20 W, 36 w. 56 W. Madeira's lat. Lat. in Diff. lat. Sum lats. Mid lat. 32 30 38'N. 49 N. M. parts 2073 M. P. 1945 I 49 ~ 109 miles 128 63 31 19 39 Co. mid. lat. 58 21 Madeira's long. Long, in 5 W. 56 W. Diff. long o 51 E. The courfe N. 21 44 E. dift. 1 17 miles. In the work for the amplitude, the latitude at fun-fet was taken the fame as at noon ; for although there were about 46 miles of fouthing in that time, and fo the latitude at fun-fet, was about 34 52', yet the amplitude being only ic' lefs, the alteration in variation would fc rcely affect the difference ef latitude and departure found from the courfes fo cone&ed. Z IT* RULES FOR KEEPING A JOURNAL, EXAMPLE IV. Yefterday at Noon we were in Latitude 19 30'$. and Longitude OIO'E. This forenoon weobferved the Sun's Altitude to be io4o' when he was Sc 355793 1 1 12 i o 2)19,48389 Diff. Lat. ao6 N. M. Parts Co. S.True Azimu , = 56*30' 9, 74*9 4 Lat. left 19 308. 119 z Lat. in 17 248. 106 Sum Lat. a) 36 54Mer.dif.L. 13 Mid.Lat. 18 27 90 oo Co. Mid. Lat. 71 33 Longitude left ooio'5. Dhl~. Long. i 3 w - 113 oo from the S. 1 80 oo i 67 oo from the N. 80 True Azimuth True ditto Mag. Azimuth Variation 13 30 W. Lat.in 17*24 S.MfP. 1060 Long. in 55S.M.P. 9 6$St.Hel.lo.5 43 W. Prefent long. I a/W. Diff. lat. i 29M.D.Lat. 60 Diff. long. 4 16 60 In Miles 89 In Miles 256 With the Meridional Difference of Latitude aid Difference of Longitude, the direct Courfe to St. Helena is found S. 70 i^'W. and with that Courfe and the proper Difference of Latitude the Diftance is found a&3 Miles. ( '79 ) JOURNALOF A VOYAGE FROM LONDON TO MADEIRA, A N p T E N E R I F F E, IN THE ENDEAVOR, of London ; WILLIAM CLEAR, COMMANDER; KEPT BY JOSEPH BRIGHT Mate. Departure taken from the Lizard in Latitude 49 5?'N. Longitude 5 !2 ; W. bound for Funchal, in Madeira, in Latitude 32 38' N. Longitude 17 5' W. and to Santa Cruz, in TenerirFe, in Lati- tude 18 s 28' N. Long ; turie 10 16' W. bearing from the Lizard- Point S. 27 20' W. tliftance 1170 Miles. Begun April 25, 1806. In the following JOURNAL is 'exemplified, the Manner of al- lowing for the Variation, Lee- way, Lying to, Calms, Currents, Heave of the Sea, &c. and to correct the Dead Reckoning, by an Observation, in all Cafes ; with mofl of the Occurrences that com- monly happen at Sea, and the Ship's Way pricked off on MERCA- TOR'S CHART. Z a A JOURNAL OF A VOYAGE Friday April 25, 1806. Saturday 26. At5 A.M. the pilot came onboard; thenweighed and failed from Tower Wharf 5 at i j came to with the beft bower at Blackwjjll. Wind S. S. W. ' refh gales and cloudy weather, with rain. At 5 A. M. \veighed and failed, at 9 came to an anchor at Gfavefend, and cleared fliip. Wind fromS. S, W. toN.N. W. Sunday 27. At 4 P. M. weighed and failed, moderate weather ; at 9 came to with the beft bower at the Nore in 9! fathoms, frefh gales; at 4 A. M. weighed and failed ; at 1 1 came to anchor in the Downs 7 fathoms, Deal Caftle bearing W. S. in diftant 3 miles. Wind W. by S. Monday 28. At i P. M. fet the Pilot on fhore. Thefe 24 hours, the firft and middle parts moderate and fair, the latter part ftrong gales and cloudy ; hoifted the boats in. Tuefday 29- Strong gales and cloudy; at 2 P. M. veered out the long fervice of the beft bower, got top- gallant yards and maft down; at 4 P. M. ftruck yards and top-mafts. Thefe 24 hours had very hard gales of wind. Wind W. by S. Wednefday 30. rhefe 24 hours, for the moft part, frefh gales : a 4 A. M. hove up the beft bower, and let go thefmall bower: at 9 hove up the fmail bower and let go the beft bower again j all hands employed righting the anchors. Thurfday May i. At 6 P.M. ftrong gales with heavy rain; at 8 veerec out the long fervice, and let go the fheet anchor under foot ; at 9 A. M. hove up the fheet an- chor. -Wind variable from S. by W. to W Friday 2. The firft and middle parts moderate and fair ;..th latter part ftrong gales. Wind W. by S. Saturday 3- Thefe 24 hours, frefh gales and fair ; at 10 A. M got up yards, top-maft ? and top-gallant mafts Wind E. S. E. FROM LONDON TO MADEIRA. H K. F. Courfes. Winds. Lee- vay. k/. .MARKS on board, Sunday, JVi-t) 4th, 18 so. a S.byW4W. N.iW. At 2 P.M. hove fhort. 4 At. 4 weighed and f.;i!cd in Co. with a 6 40 Gun Man of War, and 20 full oi S Merchantmen. 10 W. N.byW. At 6 S. Foreland bore N.N.W.dlflr^M 1 HZ S.W.byVvMV/. A.I 2 A.M. Fairlrc bore N. dill. 6 !!. 1 At. 6 Beachy bore N. by W. 6 Miles 4 W.N.W.UV N. * W. At 3 Beachy bore N.E.byE. " miles. 6 \V. s.w. N. by E. Frefh Gales and clear, levernl fhips s landing up Channel; clol'ercefcdbocb IO Topfajls. 13 At 12 Bembridire P.bcrcV/.N.W.a" M. r..;!l in Company with the Fleet. ! * I ! 1 I 1 1 j H. K. F. Courfes. Winds. Lee- way. REMARKS .. -V,-ji,vi y, May 5 a W I s - N. E. 4 6 4 < 6 Frefh galrs and clear. 8 IO 5 5 At 4 P.M, parted u-irh the Fleet, they being bound to Spithead. Jninnoiq 12 4 6 bearing V> .N.\Y. diiuuit i.\ miles. i 4 5 4 4 At 5 let out one reef of e i h Top-lail. At 7 A.M. Portland light bore W .N. 4 5 W. 9 MiU.3. 8 4 At 10 A.M. it bore N.E. n Miles, 14 10 4 2 W. by S. W. N.N.E. Sail in Sight. 12 5 I 1 i 1 | 1 i Being Tipon the Coafl this laft D.iy, tlie Log is hove, and the Bearings and Diftances of Lands, Rocks, Sands, &:c* as you approach them, muit always b Get down, and are of the greateft confequcnce, elpecially in bad Weather, or when you are in Danger of being drove out of your true Courle, in the Night, or in a Fog ; fo that you may at any Time determine, by your Reckoning, or the Chart, the Ship's Place, and to {'ail Courfes am! Diftances as Circumibinces require, in order to pals Places of Danger, and to have it always in y So't in the Night or in foggy Weather, when no Land can be leen. For it tome times happens, that in working to Windward in the Englifh Channel, K. of Dummie. S'aips by making too long a Board, have got upon a Sand called the Ow t i,s,, on which there is now a floating LigV'f. It is therefore abibluteiy nf-ccfiary to have good Draughts of the Coafts you thilupcn, unlefs you are well acq 1 with them wdeed. A JOURNAL CF A VOYAGE, . j-Lee- RE MARKS on board, Tuefday, May 6, H. K. F. Courfes Winds [way. 18:6. 2 Thffe 24 Hours moderate Gales and 4 fair Weather. 6 8 4 W. S. W. N. E. At 6 P. M. (he Lizard bore N. N. E. 10 4 ; Diftance 6 Leagues, from which I take 12 2 J my Dcpar.it being in the Lat.of 49^57' N. and Lon Leagues or 18 Miles upon the oppofite, or S.S.VV. Point half E. wing <"f the Compafs, and allowing for the Variation, as before taught, makes it S. h: dift. -8 M. xvhich is tobeftt down as the firft Courfe and Diitance in the folio Traverfe Table. The firft Courfe fleered by Compafs is W. S. W. which, allowing for the Varia- tion, makes S.W. by S. half W. and the Sum of all the Diftances failed on lhat Courfe till two o'clock, when it alters, is 18 Miles and an half, which being- doubled, becaufe the Log is heaved every twr hours, gives 37 Miles ; fo the fecond Courfe and Dift. to be fet down in the Traverfe Table is b. W. by S. half W. 37 Miles. In like manner the fe- cond Courfe fleered is S. W.byW. and the Variation -allowed makes it S.S.W. half W. and the Dift. on that Courfe fummed up and doubled, gives 56 Miles; therefore the third Courfe and Dift. to be fet down in the Traverfe Table is S.S.W. half W. 56 Miles. Hav- ing ffflund the whole Difference of Latitude and Departure made upon the feveral Courf.es, I then mark down upon my Slate cr Paper what every thing that is to be found comes to, and afterwards fet them clown in their proper Columns a? under. 1~ "TRAVEUSE TABLE. H Now to Diff. of Lat. 9 ;. 9 S. andDcp. 41. I W. the Courfe is S. 26 * iW. Dift. i o?Miles; Conrfes. Dift. N. S. E. 1.8 "11 W. S,* E. S.W.hyS. ' W. s. s. w. i w. 18 37 56 Dif. Lat. 17.9 28 f 49-4 *35 !L 4 i 49 9 i 2 95 9 Dep. 48 i 4051 then Lat. failed from, Diff. of Lat. 95 9 zz Lat. in, or Ship's Lat. Sum. of Lats. [Middle Lat. Com. of Middle LaN Then with this Com. of Mid. Lat. or 4 i found as a Courfe among the Degrees, and the Dep. 48. i in its Column, in the Dift. Col. {lands 74, which is the Diff. of Long. Or, with the Courfe a6 30 and Meridional Diff. of Lat. 147, the Diff. of Long, is found to be nearly 74 by Mercator's failing. Longitude failed from, or Lizard's Longitude 5' li'W. j) This being the firft Day fince Difference of Longitude 74 Miles i 14 W. > leaving the Land, the De- Longitude in, r Ship's Longitude 6 26 W. ) parture is the Mer. Dift. find the Rearing and Diftance of Ufhant 48 2i'N. Mer Parts 3323 Longitude in Ufhant's Long. Latitude in Ufhant's Lat. 48 28 N. Mer. Parts 33*3 3334 4'W. Difference of Lat, 7 Mer. Diff. of Lat. u Diff. of Long. T 22 With the Mer. Diff. and Diff. Long. Ufhant is found to bear N. 82 22 y E. and with that Bearing, taken as a Courfe, and the proper Difference of Latitude, the Diftance is found 53 Miles. The Bearing and Diftance to Funchal is found in the fame manner. FROM LONDON TO MADEIRA. Lee- REMARKS on b >ard, Wednesday, H. K. F. Courfes. Winds. way. May 7, 1826. 2 6 SWbyW4W N. Thefe 24 hours moderate gales, and 4 5 5 cloudy weather. 6 5 N. W. At 4 P.M. fpoke the CharmirigNunry, 8 5 from South Carolina, bound to Lou- 10 3 6 s. w. | w. don. 12 3 4 2 3 4 At 6A.M.got the bower anchors on the 4 4 5 gunnel, and unbent the cables and 6 4 6 {lowed them. 8 5 S.W.byS|W W. N. W. At noon C. Ortega! bore S. o z;'E 10 4 5 dift. i8r miles. 12 4 Variation 24 points wefterly. Diff. I, at. by Lat. bylMer. Diff. Bearings and Courfe. Dift. Lat. !Dep. D. R. Obf. JDift.:long. Long, in Ditlance. S. W. 1 N. W. W.' ; W. iFunchalS.z644'W. S. 300 W. 108 93 53 '46 48! i 41 IH/! 7 45 Difttmce 951 Miles. The Variation being allowed on each Courfe, and the Diftances fummed up, as be- fore taught, the Traverfe Table will ftand thus : With the difference of latitude and depar- ture the courfe is found S. 30 o' W. and the diftance roS miles. Diff. of latitude i* 33' S. ' Mer. parts. Latitude left 48 21 N. 3323 Latitude in 46 48 N. 3181 Sum lat. 65 oo Mer. Diff. L.I 58 Middle latitude 4? 3 0,0 oo Com. mid. lat. 42 26 TRAVERSE TABLE. COURSES. Dift N. S. E. W. S.WbyS : .W. S.S.W.4W. S.by W. ',W. 43 39 27 33-2 34 4 25 9 *7 .? 18 A 7.8 Diff lat. 93-5 Dep. 53- The Diff. o{ Long, is found by MercatorV, or Middle Latitude Sailing, to be i i<)'W. Yefterday's Longitude 6 i \V. Longitude in 7 4/W. This Day's Departure being added to the Mer. Diftanec Yeflerday, gives i 41', the Mcr. Dift. to-day. To find the E earing and Dijlance of Cape Qrtegal. Latitude in Cape's latitude Difference of lat. 46 48 N. Mer. parts 43 47 N. Mer. parts 1 i Mer. dif. lat. 3185 Longitude in 293^ Cape's long* 257 Dif. long, 7 45' 7 43 In Miles 181 With the merid. diff. of lat. and diff. of long, the direc* courfe to C?pe Ortojral is S. 27' E. and with that courfe, and Jie pn j.er di&rtnceof Utitude, the is i Si miles. NOTE. As the Table of Difference of Latitude and Departure are only calculated to fingle Degrees, the neurell Degree, to the Com. of Middle Latitude is to he talu-n iu working by InfpedHon to iind the Difference of Longitude by : t!';r,s the Com, of Mid. Latitude is 42" 26', for which I take 42 to find the Difference of Longitude, The fame may be obferved in finding the Courfe ninde good, tac ue.ire.Tt iJiri-:- .: ' De- gree to the Courfe is always fet down, and will be found fuiTici A JOURNAL OF A VOYAGE, Courfcs. Lee- REMARKS on board, Tkurfday, H. K. F. "Winds. way. May 8, 1806. 2 5 W.S.W.'jS. N.W. 6 Thefe 24 hours moderate gales and clear 4 4 5 weather. 6 4 5 At 6 P. M. fa\v a fhip to the weft ward. 8 4 1 S. \V. by S . \V. by N. i 00 10 4 5 Obferved fun's mer. alt. at noon 6 1 35 11 4 6 , a 4 5 Zenith diftance 28 25 S. 4 4 S. S. W. Weft. i Declina tion 16 58 N. 6 4 8 4 Latitude 45 23 N. ro 4 At noon C.OrtegalS.ioai'E.dift.QoM. 12 4 Variation i l point wefterly. Dit. | Lat. bylLat. by!Mcr.'Dif. cf I Courfe, ! Dift. 'lat. JDep. D. R. 1 Ohf. |Dift.| Long. Long, in. j Bearing and dift. I S. 1 W. N. i N. 1 W. | W. W. FunchalS.28u' w S.I3 C W. 97 96 1 " 45.T2J 45.23! 51 1*0.30 8.6. Dift. 871 Miles* By allowing for variation and Ice-way the work will be as follows : With the difF. of lat. and dep. the courfe is found S. 8 30' W. and the dift. 97 miles. Dif.oflat. Lat. left Lat. in by D.R. 46 36'S. 8N. Mer. parts. 35 3047 Sum lat. 2)92 Mid. lat. 46 90 n oo 00 Mer. diff. lat. 138 TaAVEasE TABLE. Courfes. S. W. I S. .S. by W. S.iE. Dift. 23 36 40 Dif. N. lat. S. E. W. 20.7 35-3 39-8 3-9 3-9 18.3 7*0 ~ 3-9 (21.9 96-3 Dep Longitude left 7 45' W. Difference of longitude 30 W. Com. mid. ht. 44 cc Longitude in by account 8 i5\V. Here the latitude, by obfervation, differing from the latitude by account, I correcz for the true longitude ; and as this is the firft obfervation got fincc leaving the land, I correct by Cafe I. as follows : Lizard's lat. Lat. by D. R. 4957'N. Mer. paints 3470 45 ii N. Mer. parts 3047 Mer. did*, lat. by account Lizard's long. Long, in by account DifF. of iong. by account 42 8 6 W. 2 54 60 Tn miles Lizard's lat. 4957'N. Obi. lat, 45 23 N. J74 Mer. parts 347 Mer. parts 3063 With the mer. diff.of lat.and diff-of long, by account, the fhip's direct courfe from the Lizard is found to be S. 23 C W. With that courfe, and the mer. diff. of lat, by obfervation, the diff. of long, fince leaving the Lizard is found 174 miles, c^ual to 2 C 54'W^ Lizard's longitude 5 \% W. Longitude in 8 c6 W. With the courfe 23, the proper diff. qf lat. 274 miles, the true mer. dift. is found 113 miles, . diff. lat. by obfervation 407 To find the direft Courfe and Dlfiance \o Cape Ortegal. I, at. in 45 2i'N. Mer. parts 3063 Longitude in Cape's lat, 43 <:N. Mer. parts 2926 Cape's longitude Dif. lat. t ;6 Mer. dif. 135 Dif longitude With the mer. diff. of lat. and diff. of long, the direct coutfe to Cape Ort.-^al is found S. 10 K. and with th*t courfe and the proper cif f t.f l,:tA96, the dl;Uiice is .. to be 98 miles. FROM LONDON TO MADEIRA. 185 H. K. F. Courfes. Winds. Lee- way REMARKS on bo/fird, Friday, AI.;y 9, 1806. ^ 3 5 S,byW.|W. Weft. I Thefe 2-1- hours moderate gales and clear 4 3 5 Vf eatner. 6 3 5 8 10 i 3 5 At 8 P. ?vf, fet up tbe mizcn top-maft fhrouds, and back-frays. 12 2 At noon Cape Ortegal S. 12 E. diftancc 2 3 22 miles. 4 2 6 8 3 4 S. by W. W. b] r s. i Variation i| point wefterly, per amp. 10 4 Thick hazy weather. 12 4 Down top-gallant yard=. Dif. j Lat. by Lat. bv .ler. Dif. of I Courfe. ] Dift. lat. Dep.i D. R. Obf. J Dift. Longf. ! Long. in. j Bearing and (lift. N. W. FunchalS 2 10' S. 9 E. 76 ,758. iE. 44.08 Ii.46 17 E. 7* 49' W. W.difc.Si,-milef. With the difF. of lat. and dep. the courfe is found S. 9 E. and the dift. 76 miles. Dif. of lat. i 15'. S. Mer. parts Yefterday's lat. 45 23 N. 3063 Lat. in ' 44 08 N. Sum lats. Mid. lat. Com. mid, lat. 45 15 31 Mer. 'diff. iat. ic< I RAVEKSE TABLE. Courfes. Dift. N. S. W. S. 4E. 46 3 DhT. Lat. 45-8 29.1 4-5 7-3 Dep. 74-9 ii. 8 Yefterday's longitude 8 06' W. Difference of longitude o 17 E. , . . Longitude in 7 40 W. This day's departure being fubtra&ed from the meridional diflance of yefterday, g;vr 1 46', the meridional diftance or "to -u ay. To find tbe Bearing and.&ijlance of Cabt OrtegaL atitudein 44 08' N. Mer. prts 2957 Longitude in 7 49 W. Cape's lat. 43 47 N\ Mer. parts 2928 Capes longitude 7 43 W. DifF. lat. 2 r Mer. diff. lat. 29 DifF. long. 6 B;. With the mer. difference of latitude and difference of longitude, Cape Ortegal is found to bear S. 12 o' E. and with that bearing taken as a Courfe, and the proper difference of latitude, the diflance is found 22 miles. NOTE. When the tenths on any fide are more than 5, or half a mile, you n-uft call that fide one more than you found it to be; but when they arc lei's than 5, then you need not take notice of them ; as in the above th, .'iffeience of latitude and ?ie- panure are 74.9 and n.8, which I call 75 and 12, Waule the Tenths are above 5. But when you take the. difference of latitude and departure to find the Courfe, then take them in Miles and Tenths j the fame may be ob!c;ved in calling up the Knots and fathoms. If, when doubled, the Tenths are more, than 5, fet one mile more in the Traverfe Table ; but if lels, emit them, as there are no Tenths in the diitance column. Aa 1 86 A JOURNAL OF A VOYAGfe i Lte- REMARKS on Board, Satur^y, May 1 H. K. F. Courfes. ( Win l. way. jo, 1806. 2 3 5 Weft. S.S.W. 3 Thefe 24 hours hard gales and fqualiy, 4 3 .S with .irMli raini.. HandeJ the tore 6 3 S and n .i 1 "- courts. 8 Lav to up N.W. by N. off N. byE. 5 At 8 : . M faw a fliip to windward 10 Djuft i mile per hour W. under jury mafts. 12 a Up N. W. off North. W. by S. 5 MOi'e moderate* 4 Drift I f mile per hour. Wore fliip. 6 Sec the reefed courfes. 8 4 IS. W. N.W.bj'W.iW. li Set the top-fails clofe reefed. 10 S C.Finifterrt 8.31 24'VV.dirt.?3 m. It 5 Variation i ^ point wefterly. |J5iff. Lat. by Lat. by Mer. Dift. of 1 Tourfe. Dift jLat. Dep i\ R- Obf. Dift Long. Long, in | bearing and Dift. W. 1 S ' W. i N. W. jFuDchjIS^n^'W. S-79 20 1 4 25 Ivo4' 2. IT :I S.io W. | Dift. "90 - iles. Taking the middle points (viz. N. by W. and N.N.W.) between the point to which the fhip corres up, and the point ihe r'ei'- off to for the fecond and third courfes, as taught in the rules for lying to, and then allowing as b, 'ore for variation and leeway, the Traverfc Table wii! ftand as follows : With the difF. of lat. and dep. the courfe i found S. 8i* 4i r W. and the dift. 25 miles. Uift. of Lat. 00 04'S, Men parts. Yefteiday"slat. 44 08 N. 2957 Latitude in 44 04 N. 2951 Sum Lats. 88 12 Mer.diff.lat. 6 Middle Latitude 44 06 90 oo tom.Mid.Lat. 45 54 TRAVERSE TABLE. Courfes. Dift. 21 9 9 28 N. 7-i 7-7 8.5 S. 17.2 E. W ~ 6.8 W.N.W.iW. NiN.E.'iE. N.byE. ^E. S. by W. |W. 4.6 3.0 23.3 27. 2 ^3-3 7.6 26.6 7.6 Diff. Lat. ^9 Dap. I9-- The departure to-day being added to the mer. dill.yefleiday, gives n', the iner. dift to-day. With the courfe and mer diff of lat. the diff. oflong. is found by Mercatorto be gi miles. Or, with the mid. lat. and dep. the diff. of long, is found by mid. lat. felling a; miles weft. Diff. longitude o* 3!' Yefterday's longitude 7 49 W- JLongitude in 8 20 W. Heret!?*dif. of long, found by mid. lat. differs confiderably from that found by Mercator's failing, but if the mer. parts were taken from a table of miles and tenths it would prre nearer with mid. lat. failing; but in all cafes where the courfe is To great, a vwi the difference of latitude is in miles and tenths, middle latitude fhould be depended on. df To find the Bearing and Dijlance of Cape Fintflerre. Latitudein 44c4'N'. Mer. paits 2951 Longitudein 8 7 2o'W. Cape's latitude 42 -53 N. Mer. parts 2854 Cape'slong. 9 i& w Diff. latitude 71 ~ i n Mer.diiF.oflat. 97 Diff. long. 5 8 With the mer. cliff, of lat. and diff. of long. Cape Finiflerre is found to bear S. 31* 14' W, and with that bearing and the proper diff of lat. the diftance is found &$ toilet. FROM LONDON TO MADEIRA. i8 7 ,Lce- REMARKS on Board, Sunday, May nth, H. K. F. Courfes. Winds. way. 1806. 2 Calm ( The fnft 8 hours calm and fot^gy. 4 Up T. G. Y. out reels, fetT. G. S. 6 iHuifted the boat out, and tried the cur- 8 rent, found it to fet N. W. by N. I mile 10 3 5 w.s.w. South, I per hour. 12 4 4 Moderate and clear. 2 4 6 4 6 4 4 8 6 Variation if point wefterly. 8 4 8 10 12 4 4 8 5 Cape Finiftene S. 38 lo'dift. 53 Mile?. Dift. "1 Lat. by Lat. by j IVJer. Diff. ofj Long, i Courfe. jD.ft. Lat. Dep.l D. R. Obf. 1 Dift. Long. 1 in. |Bearing&dift. S. W. S. W. I N. N. I W. W. 1 W. |Fundi.S.ib49 80. 84 15 83 1 43.49 45.34 1 3.26 1.55 1 10.2 |W. oirt. 7?<;M. The variation and lee-way being allowed n the courfe iteered, and the fetting of t ic cur- rent and its crift in 2.4 hours being made a courfe and ciift. the work, will be as follows: With the diff. of iat. and dep. the courf is found 8.79* 57'W. and the dift. 84 M. Diff. of latitude oo 13 if'S. Mer. parts. Lat. left 44 4N. Lat in 43 49N. 493 1 Sumoflats. 87 53 Mer.dif. Iat. 20 Middle Iat. I R'AVKKSE TABLE. Courfes. ; i N. S. 30.8 E. W. N. W.$W. S.W.byVV4W. 24 72 16.1 17- S 65.1 16.1 3^7* 16.1 Jep. 8 TT 9 Diff. Lat 14.7 Com. mid. lat. 46 04 The diffv of long, found by Mercator's failing is 1 13 miles, but by mid. Iat. is found 1 1 5 miles, equal to i 55' W. Longitude left 8 20 W. Longitude in by account 10 15 W. The diff. of long, found by mid. Iat. ftill differs from that found by Mercator's failing; the caufe is the fame as before, and as the {hip has made fp great a courfe, we ftill depend, on mid. Iat. The Iat. by obfervation differing from the Iat. by account, I correct for the true lon- gitude as follows (it being three claysuncel had an obfervation before) by Cafe II. p. 182. Laft obf. Iat. 45 23* X Ship's Iat. by ace. 43 M. pts. Mer. diff. Iat. by accounf Ship's long, at laft obferv. Ship's long, in by ace. to-day Diff. long, fmce laft obf. Laft obf. Iat. 4523'N. Ship's Iat. by obf. 43 34 N. Mer. diff. by obf. With the mer. diff. Iat. by aec. 132 and, diff. of long, by account 129, the direct courfe fmce laft obf. is found S. 44 2i'W. and the dift. 132 miles. With that dift. andthe mer. diftVof Iat. by obf. 153, the dif. long, is found 104, this added to the diff. of long, by account 129, gives 233, \vhich dU vided by 2, gives the true diff. of long-, fmce laft obf. 116 M. nearly equal to j 56' W. Long in laft obfervation 8 6 W. Long, in IP a W. The courfe feund fmce laft obfervation 44 a i' is of no farther ufe than to know what Cafe to corre& by. With the true courfe fmce laft obf. 37 10' and the proper diff, of Iat. ico.the dep. is i*3'-t-* 3'W.-326^. To find the Bearing and Diftance of Cape Fmifierre. Latitude in 43 34 ; N. Mer, Parts 2910 Longitude in ic c 02'W. Cape's Lat. 4^ 5*N. Mer. parts ^2852 Cape's Long. 9 I4'W. Difference of Lat, " 42 Mer. Diff. of Lat. 5~DifF. of Long. 48 With the mer. diff. of Iat. and diff. of long, th e direct courfe to Cape Finifterre is found 5. 38 10' E. and with that courfe and proper diff, of lat. the diftance J found j ; miles. A ft Z 1 88 A JOURNAL OF A VOYAGE Lee- REMARKS on board, Monday, M v 12, H. K. F Courfes. Wind'. way. 1806. 2 4 s S.'WbyW. 3. byE. I rhefe 24 hours moderate gales, with fmal! 4 4 5 ftiowers of rain. 6 4 5 8 4 JO 4 i ^ 4 2 3 5 4 3 5 S.W. S.S.E. I 6 8 3 1 5 Var. per. Az. I point weft. 10 \ A great fwell from the S. W. for which ] 12 -! allow 6 miles. Hazy weather. j Diff[ Lat. bylLat. by Mtr. D:ff. ILoig. Courfe |Dift. Lat. Dep D.R. j Obf. Dift. Long. 1 ia. Bearing and Dift. *$$ fC' j S. W. N j W. W. j W. FunchaiS.23l5'V\ W. J 84 5 67 4^-44 1 4-14 '33 1 lf -3- 1 Dift^6< 5 M.les In this day's work the i'well is confidered as a current, whole drift in 24 hours is 6 miles, the allowance made for the fwell ; and as it comes from the S.W. it heaves the {hip to- wards the N. E. ard the variation allowed upc^n it makes the laft courfe N.E. by N. as in the Trave r fe Table. With the diff.of lat.and dep. the courfe is found S. 53 3o'W.and the dift. 84 miles. Dift". lat. o 50'$. Mer. parts. Lai. left 43 So'S. 34 N, Lat. in Sum lat. Middle ia 42 44 2910 2841 86 18 Mer.diff.lat. 69 43 90 09 oo TR AVERSE i'ABI. K. Courfes. i Dift, ~ 3 6 N. 5.0 ! 1'P S. 32.2 12.6 54^ 5*f E. W. S. W. l.y W. S. W. N.E. byN. 3-3 3-3 48. 2 22. 6 70.8 3 3 DirY. lat. 49 De;, 07. t The dep. 68 being added to yefterday's mer. Com. mi|j-. Jit. 46 51 (> dift. gives 4 34' themer.dift. this day. The difference of longitude is found as before to be 1 33'W. Yefteiday'b longitude 10 2W. Longitude in this dsy n 35 W. To find the Bearings and Di/tance of FunchaL Latitude in 42' 44/N. Mrr. rarts 2?4l longitude in li c Funchal's lat. 32 38N. Mer. parts 2073 funchal's long, 17 35'W. 5 W. Dif lat. 606 rr 10 6 Mer. dif. lat. 768 Dif. lorg.33orr 5 30 With the mer. d'f. of la', and dif. long. Funchal is fuund to bear S. 23 15' W. and with that bearing t^ktn as before, and the proper dif. of lat. the diftance is 655 miles. Tofndtbc Bearing and Dljiance of the intended Port on Mercator's Chart, Lay a ruler acrofs Mercatcr's Chart, in lat. 42 44', and fet one foot of the compiles on the tn:rif the ruh r, and that will fl-iew you the fhip's place. Then l.'y the ruler over the fnip's place and Funchal, and take the ncarelt diilance between the ruler and the centre of the ccrr.pafs; flide one foot along the fide of the ruler, and the other foot wili {hew the courfe to be S. S.W. Again, (keeping the ruler as before) take .from the graduated paraiiel the dif}". of lat. between the lliip and port (10 is/) in your ccrrpaffes, ar-d Hide ore r'cot along t}>e ruler, ho:dn-g both points parallel to the N. and S lines', till the other cuts the E. and W. lines 5 paUing through the Slip's place; the diftance between where the point refted, by tTie edge of the ruler, and Funchal, being meafured upon tfce graduated parallel, gives nearly i j, or 660 miles for ths diftance. In like manner find the bearing and rfiftaj.ct of any other place fiom the fhip; or fake the diftance between Funchal ana the iVip in .y&ur Compares, and iay it on the meridiir, placing one foot as rrairh above Furjchal HS the other is below the fhip's pi^ce, aud that wiii be the iift in de grees or in leagues, U the meriJ, "s marked ib ROM LONDON TO MADEIRA. Lcc- REMARKS on board, Tueiday, May \ H. ,::. F. Gou rfta. Win cis. W. y- i3 1806. 2 4 5 W. S.S. W. i Thefe 24 hours frefh gales, and clear 4 4 5 weather. 6 4 5 8 5 10 5 12 5 2 '5 S 4 5 5 W. -| N. s.s.w.-i\v. i 6 5 5 8 5 5 10 5 5 12 4 Variation i point wefterly. Diff. Lat. by Lat. by Me.r. Diff. Courfe. Dift. Lat. Dep. D. R. Obf. Did., long. Long, in Bearing and Dift. W. N. N. W. ; W. W. I''unchaIS.i2 tl 48'W. W. rzo 120 42 44' 42 30 6.30 2.43 M-I5 Diftance6o7 Miles. The variation being allowed on both the courfes, and the leeway upon the fecond, it will be found that the fhip has failed due Weft thefe laft 24 hours, and by fumming up the diftances her whole difUnce is found to be 120 miles, which is alfo her departure ; it is evident fhe has made no difference of latitude, therefore her latitude by account is the fame as yeflerdiy. As the fhip has failed upon a parallel with the Equator, her difference of longitude Is found by parallel failing 2 43 f W. Yefterday's longitude II 35 W. Longitude in by account 14 i8W. The latitude byobfervation not agreeing with the latitude by account, and it being two days fince my laft obfcrvation, I correct as follows, by Cafe III. Pa^e 182: Laft obf. lat. 43 34' Mer. parts 2910 With the tner. dif. of lat. and clif. long Lat. in by ace. 42 44 Mer. parts 2^41 by account, the courfe fince hit obf. is found to be S. 75 W. and the diitancc Mer. dif. lat, by account fince laft obf. 69 266 miles. J.ong. in at laft obfcrvation Ship's long, by account Dif. long, by ace. fince laft obf. 43 - C2\ 14 i6W. JLaft obf, lat. Thisday'slat.byobf. M. parts 2910 With that dift. and the mer. dif. of lat. by obi", the true dif. of long, fince kit cb- fervation is found to be 25 j : 4 J^'W. Long, in at laft obfcrvatioa 10 M. parts 2822 Longitude in 2 W '5 Mer. dif. lat. by obf. fince laft obf. With the courfe fince laft o-^fervation S. 70 49'W. and the prcper dif. of lat. 64 miles, . parture (or Mer, dift.) fince Uft obfcrvation is found 184 miles, tquai to 3 O4'W. Mer. dift. at laft obf. 3 26 W. True Mer. dift. this day 6 30 W, To find the Bearing an I Dijlance of Punch al In Madeira. Latitude in Funchai's lat. 42 3C/N. Mer. parts 32 38 N. Mer. parts 282^ Longitude in Dif. lat. 592 n: 9 52 2073 Funchal's long, i . dif, lat. 749 Dif. Jcrgittide a 5orzi;o With the mer. difference of latitude and difference of longitude the bearing of Fur.chal is found to be S. 12 4^'W. and with ;hat beaiir.g ukeu u* before, and ths proper djf. of latitude, the diftanos is found 1^07 miles. 193 A JOURNAL OF A VOYAGE H. K. F. Courfes. Winds. Lee. way. REMARKS on boa'd, Wednefday, May I4th, 1806. a, 8 S. S. W. N. W. St'ff" gales, with fliowers of rain. 4 8 Frefh gales. 6 8 S 8 8 S 10 8 S 12 8 5 t 9 Ditto weather. 4 6 o S.iE. S.W.byW.fYV. \ More moderate. 6 5 5 Var. p. amp. i point weflerly. 8 5 5 10 5 Tl 5 IDift j Lat. bvjLat. by Mer. Dirt. Long. Courfe. IpmJ Lat. iDep. D.R.j Obf. Dift. Lon. in. Bearings and Dift. I I S. 1 j N. I N. t W. ' w. Funcnai S. 17" cn'VV Snuth. J 170 | 170) | 39.46! 39-AOJ 6.30 '4 15 Diftant 44.4 miles. Yefterday'slat. 4** 3C/N. Diff. lat. z 448. Lac. in by ace. 39 46 N TgAVERE TABLE. Courfes. Dift. N. .Lat. S. E. W. 23-0 S. byW. S, S.E. $E. ri8 54 Dift 115.7 48-8 164.5 *3' J 23.! 33.0 0. I 23.0 De P . Proper allowance* being made for variation and lee- way, it appears from the Traverfe Table that the ihip h^s failed due South- 164$ miles, ar.d as (he ma^e no departure, her lon- gitude in and mer. dift. is the fame as yefterday j but as by obfervation the fhip is found to be in lat. 39 40' N. it is plain firft courfe in the next Traverfe Table muft ^e the oppoiite Pcint t;f the Bearings of the Deferta's allowing t c Variation and ih FROM J.ONDON TO MADKIRA. '95 Courfes Lee- RKMARK-.. on U.'^ni, vYcdiK-j'day, H. K. F, Winds. way. June ', 18^6. | 2 6 a S. S.W. N. N. E. Lig ht Breezes and clear. Variation 4 6 3 s.s. \v~4w per amplitude iS' 1 3 1 -' ^ 8 2 10 2 12 4 4 Calm. S, S.W. J W. W. N. W. Made and fhortened fail occafionally. 4' J 4 6 6 8 6 -, 10 5 6 N. W. Frefh breezes and clear. Set ftudding 12 4 fails. Lat. by obi'. 30 3 ' N. Dim Courfe. |Dift. Lat Dtp. Lat by. Lat. by, Mer. D. R. Qbf j Diff Piff. .Long.j I.on.i in. !f><*ari'-i;r stid D1H -met. E. J E. (>- V} Salvages, i. j ' -,o" i.. S. i3o'F,. Til T I I 2.5 3">..VN 3-3'Ni 2.5 E. 1 W. :Dilla.!u-c 2 miles. Courfes Lat. Dckr. -s2 22 N. All' 20 -, corrected. Dift N. S. E. W. X Lat. i r> S. S 55 E. 23 1 8.8 13.2 Lat. in. 30 3 i N. M P 192^ S. 4 W 12 12.0 0,8 __^ S. 7 W 8l 80.4 9,9 Sum a;6z 53 M X Lat. 130 111.2 13.2 10,7 Mid. Lat. 37 20 107 Lat. jSal. 30 8 N M P i898.Long. 15. 53^'. Lat. in. 30 3iK'MP 19241.01);'. 10 33 25 X .at. 2^ MP 2(> K^j.uny. 40 With the M. diff. lat. and dirt, oi long, the Salvage bears as above. H. K. F. Courfes. Wind*. Lee- 1 vvay.:RKMARi;s -n 1'hurfday, June , 2 6 4 South Weft. Frefh Breeze and clear, all fails let. ! 4 6 2 6 5 Q Var. 18 W. H , 2 ic 6 3 ! 12 .T 4 I 2 5 S . by W. V.'.b \V. Do. Weather, two fails in fight. 4 5 6 3 8 3 1 10 2 ! 4 i.'rM Bree/es 10 2 I W. by S. * 'lu ILU Iding- fails. Courfe. JDiltJX L.it. Dep.j Lat. by Lat. by Obf. M. 1 Diftj X |Long. - Long.j in. [Bearings md Dii,. I 1 S< 1 K ' N. N. E. E. 'v\' . IS. (J;-u. i c S. T 4 E. i -7 | 704 I 2f? 2". /'/ 28 47 29 2-) |- 16 4 |S27 C 33W.22M. j Lat. .it. 30 31 NMP 19 2-; i.:n. 6t.Cru.r6 i6W Courfes ; I)ift. N. f- S. E . W X Lat. 144 S correiled. s. ]':. 6? |63-7 7 Lat. in. -8 47 MP 1805 Long-, in. TG 4W* , E. 4 T 14 7 .') ! -)59 l8 1:9 l>i/T. Long. , 5 i ! -4-^i 2 '.; M. Lat. 29 30 Lat. S.Cru. s^z ?'Kl\r.P. "r ------- L^ in. L. 6 - i --- DiJF. of ------- L^ in. 215 -7 N.'M.P.J? .J C.iM.L. 6 ___ , Witl>the Mer. D.ifF. of Liit. nn-1 Ditf. oi'Loug. Cruz, in Tcucnite, btuib a.s above. 196 A JOURNAL OF A VOYAGEj &C. Lee- REMARKS on board, Friday, H. K. F. Courfes. Winds. way. June 6, 1806. a 3 4 S. S.E. S.W. i Frefti breeze and cloudy. 4 3 6 a 4 Handed top-gallant fails, and in firft reef 8 3 top-fails. At 6, the Peak of Teneriffe 10 3 bore by compafs W. S.W. i a 2 4 w. N.W. Ditto. 1 Frefli breezes and clear. Variation iS W. a a 4 4 a Set top-gallant fails. Hazy with rain. No 6 a land in fight. 8 S Light breezes and clear. IO a 4 S. S. E. Ditto, At noon made Teneriffe, bearing W. by 12 a 4 N. dift. 6 or 7 leagues. Dzf. 1 ILat. byjLat. bylMer. Dii'. of Courfe. [Dift. lat. iDep.f D. R. 1 Obf. Dlfc.j Long. [Long. in. Bearing and dift. S. E. | N. i 1 S. Cruz, Teneriffe, S. 25 E. Z 3 18 8 | a8 30! J37E. icm.E. 15 54 W. S.Sai4\V.D*oM. The eourfes being corrected for one point leeway, and 18* W. variation all thefe 24 hours, I find by the Tmverfe Tibls the di- rect courfe of the (hip to be S. aj E. dift. ao miles. Dif. of lat. o 1 8 S. Lat. left 28 47 N. Lat. in Sum lat. Mid. lat. Courfes corrected. Diit. 30 4 IO N. 6 6 6 6 lat. S. E. w. S.5iE. N. 74 W. S.52E. 18.5 6 2 23 6 7 9 23.1 Dif.> 24 7 6 6 18 I 5 1 5 *3 * 23.1 Dep. 8.4 Com. mid. lat. 61 aa With the comp. of mid. lat. the diff. of long, is found to be 10 miles; and the bear- ing and diftance of Santa Cruz by mid. lat. is found to be S. 82 14' W. dift. 20 miles. L - REMARKS on board, Saturday, |une H. K. f7 . Courfes. Winds. wi . 7, 1826. 2 3 W. byN. N N.E. Light breezes and clear.Made all fail. 4 3 6 3 At 5 the eaft end of Teneriffe N.W. 4 g miles; at "j anchored in 9 fathom 10 in Sanra Cruz Road, the town of 12 Variable. Santa Cruz W.'tjy N. . a mile. 2 Variation 17 10' weft. 4 Weft. At 8 A. M. hoifted out theboats nnd 6 went on fhore to wait on the Gov. 8 Moored (hip with the fmall bower to 1C 'Calm. the S.W. in 19 fathom, and ftream T 2 South. anchor to the N. E. in 10 fathom. ,D.f . L>- b- jLac. bj Me-.l tt. Conrf-. DHL; !ar. Dep. DR. 1 Obf. Dift.j Lor p. Long . in . Bearing and dift. S. W. I At anchor in San. s, 81 w. JQ 3 1 Z.t7N 1 5? E '2iinW. 16 i;W. CruzRd.Tenerif. The Courfes being corredled for W. variation, I find by the Traverfe Table th- j true courfe to be S. 82 W. dift. 19 miles. Dif. lat. o 3 S. Lat. left 28 30 N. Latitude Com. mid. lat. With 23 27 1 31 the com. of raid. lat. the diff. of long, is 21 miles. Courfe corrected. Dm. N. S. E. W. S. 82 W. J 9 Diff, lat. 2J 5 Dep. 18 S i8>8 ( '97 ) An Abdradl of the foregoing JournaL Day. re 44 u 5 Lat. by Lat. by Bearings Dift. ffj o Courfe. Dist. Ac. Obs. Long. in. of Funchai. Miles, j 6 S. 2 633'W. 107 48 2iN. 6 26VV 8.24 W. 1148 g 7 ^.30 W. 108 46 48N. 7 45 W S. 26 44'W 952 "U 8 S.8 3 o' W. 97 45 12 4.5 23 N. 8 6 8.28 34 8 7 I j 9 S. 4 E. 76 44 8 7 49 *>. 32 10 815 ]-, 10 S. 79 W. 20 44 4 8 20 $.30 53 799 1 1 S. 80 W. 8 4 43 49 43 34 10 2 S. 26 49 735 12 S. 53030' W. 84 42 44 if 3? S. 23 if 655 # 13 West, 12042 44 42 30 14 15: S. 12 48 \ v 607 "4 15 jouth. S.bW.fW. 17039 46 192136 149 .39 4 36 36 14 15 15 26 S. 17 59 w S. 18 5-1 w 444 16 S. 68 W. 1 19 35 5 2 35 4 7 3Q S. 8 29 W 190 T? i / S. 35 20' E. 135 34 OI .33 5 6 16 6 8.32 7 W) 92 G 18 Anchored in Funchai road, and failed 3d June forTenerifFe. Defer tors N.W. |N 2 2 $ 2 32 10 Salvages. 9 4 S. i3o' E. in 30 3 1 30 31 16 33 ^, 56 5.8 E. 42 Santa Cruz it r S. 14 E. 107 28 47 28 47 16 4 S. 2? 33 W. 22 $ 6 S. 2$ E. 20 28 30 15 ?4 3.82 14 W. 2O b 7 S. 82 W. >9 Anchor in Santa Cruz road, | mile off (bore. The Method of finding the LATITUDE tf/SEA,/?;/ tubing two Attitudes^ either in the Forenoon or Afternoon , leaving the intermediate Time meafured by a common Watch, with Eafe and Accuracy^ independent of the Sun's Meridian Altitude. GENERAL RULES. I-ft. '"T^O the fecant of the latitude by account, add the fecant of JL the fun's declination, (rejecting their indexes) and call that fum the logarithm ratio*. 2d. From the natural fine of the greareft a]titude } fubtracl the natural fine of the leaft altitude, and rind the logarithm of their dif- ference, and write it under the logarithm ratio. feca 50 m The arithmetical comp. of the co-fine of sny angle is cqur,! to tljr ant of that angle, omitliag tlie firft 6gure in the index ; thus tho fecan min is 10.16487, and omitting the firft figure !, leaves U.U-^7, ;'u , or tue arithnjet. comp, of co-fine 4C dog. 5'. aiim 'ue fecaat it f| M. H 198 THE METHOD OF FINDING THE LATITUDE 3d. Subtract the hours and minutes when the altitudes were taken from each other, and half the difference call half-elapfed time. 4th. With half the elapfed time enter the tables, and from the column of half-elapfed time take out the logarithm anfwering thereto, and fet it down under the logarithm ratio. 5th. Add thefe three logarithms together, and with their fum en- ter the tables in the column of middle time, where, having found the logarithm neareft thereto, take out the time correfponding to it, and put it down under half the elapfed time. 6th. Subtract the lefs from the greater, and the difference will be the time from noon, when the grea eft altitude was taken. 7th. With this time enter the tables, and from the column of rifing, take out the logarithm correfponding to it ; from this loga- rithm fubtracl: the logarithm ratio, the remainder will be the loga- rithm of a natural number which, being found in a common table of logarithms, and added to the natural (me of the greacefc altitude, will give the natural fmeofthe fun's meridian altitude. Having the meridian altitude of the fun at noon, the latitude is found by the ufual method. N. ]3. If the latitude, found by the above prccefs, fhould differ widely from the latitude by account, it TV ill be proper to repeat the operation, ufmg the latitude laft found inftead of the latitude by ac- count, till the refult gives a latitude nearly agreeing with the lati- tude ufed in the computation. * EXAMPLE. I. Being at fea in latitude 46 50' north by account, when the fun's declination was ii b 17' N. at 10 K. 2 M. in the forenoon, the fun's altitude was 46 55', and at 1 1 H, 27 M. in the forenoon, the fe- cond altitude was 54 9'. Required the true latitude, and true time of the day when the greateft altitude was taken ? H. M. Nat. Sines Lat. 46 co'Sec. 0,16487 ii 27 o Gr. Alt. 54 9' 81055 Dec. Ji *7'Sec. 0,00848 10 2 o lea Alt.49 55' 73036 Log Ratio >I7335 Ela.T.i 25 o 8019 Com. Log 3,90412 | Ela.T. 42 30 in the column of I- elapfed Time 0,73429 i 15 30 in the column of middle Time 4,81176 T.f.noon 33 o in the column of Log rifmg 3,01488 From which fubtracl: the Log ratio . o> 1 ' 7 335 The natural Number in the Logarithms = 694 2,84153* to which the nat. fine of the greateil Alt. 81055 90 GO gives the r.at. fmeofthe Sun's mer. Air, =8 1749 54-5 35 io BY DOUBLE ALTITUDES. Sun'3 Zenith Diftance Sun's Declination Latitude The obfervation at Noon was 33 as the time agrees with the obfervation, the watch is right EXAMPLE II. ' Being at Tea in lat. 47 19' N. by account, when the fun's de- clination was 12 1 6' N. at 10 H. 24 M. A. M. per watch, the fun's alt. was 4.9 9' at I H. 14 M. P. M. his alt. was 51 59'. Required the latitude ? Ela. T. H. 12 10 I I M. O 24 36 J4 S. o o Alt 49 5* '9' 59 N. Nat. 75642 78783 S. 3141 S. Lat. 47* IQ' Sun's decl. 12 16 Log. ratio Its log. c o ,16880 ,01003 3 17883 ,49707 2 50 Diff. \ El. T. i 25 o Its log. in col. of half elapf. time is 044077 Sub. o 15 o Col. of mid. time correrponding to 4,11667 Tr. Ti i 10 o Its log. in col. of rifmg is ' 3,66542 Ti. p. W. i 14 o Log. ratio fub. 0,17883 Wat. faft 040 3066 the nat. num. of this log. 3,48659 N. S. Sun's gr. alt, 78*783 90 OO N. S. S. mer. alt. 81849 = 54 56 Sun's zen. dift 35 4 South Sun's decl. 12 16 North Lat. in - 47 20 North. Here the Latitude found by computation may be relied on, as it differs but one mile from that ufed in the operation. EXAMPLE III. Being at fea in lat. 50 40' North per account, when the fun's declination was 20 o' South, at 10 H. 17 M. A. M. per watch, the fun's alt. was found 17 13', at 1 1 H. 17 M. A. M. per watch, it was found 19 41'. Required the latitude I Times 2CO THE METHOD OF FINDING THE LATITUDE Times Alt. Nat. S. Lat. 50 40' 0,19803 H. M. s. Decl.20 oo 0,02701 10 17 o 17 I3'=r29599 n 17 a 1941=33682 Log. ratio 0,22504 100 Diff.N.S. 4083 Itscom.log. 3,61098 o Its log. from col. half elap. time is 0,88430 In col. o'f mid. time correfponding ^4,72032 Tr, time o 31 o From noon, its log.from col of rifing 2,96067 T. p. W. o 43 o log. ratio fub. 0,22504 W. flow o 12 o 544 N. num. of 2 >735 6 3 33682 N. S. greateft alt. 20 i 34226 N. S. the fun's mer. alt. 20 i'. Zen.dift.69 59 Decl. 20 o S. Lat. 49 59 N. But as this latitude differs 41 miles from that by account, it will be proper to repeat the operation, ufing the lat. laft found inftead of the lat. by account. H. M. s. Lat. 49 59 0,19178 | Elapfed time o 30 o Peel. Log. ratio True time 30 O Time per v^atch o 43 O H. M. Watch flow o 13 o In col. mid. T. i o 4)7*407 True time o 30 o Its log. in col. of rifing is 2,93223 Log. ratio 0,21879 5 1 7 Nat. num. of 2,71 344 33682 Nat. S. gr. alt. Nat. S. fun's mer. alt. 34199=20 o' Zen.'dirV Declin. The lat. 50 o North. The latitude laft found, differing only one mile from that ufe< in the operation, may be depended on as the true latitude, it is plain, that the operation is repeated with very little add trouble, few alterations being neceflary. BY DOUBLE ALTITUDES. 2OI EXAMPLE IV. Being at Tea in latitude 60 o' north by account, when the fun was on the equator, and confequently had no declination at i H. o M. P. M. per watch, his altitude was 28 53', and at 3 H. o M. P.. M. per watch, it was 20 42'. Required the true latitude ? Times. Lat. i H. M. s. Alt. N. S. Dec. i o 0-28 53=4^303 3 o o 20 42 = 35347 _ Log. Elap. T. 2OO 12956 Its la - El. T. i o o Its log. in col. of Elap. tim 2 O O Its log. in col. of mid. tirre T. fr. N. i o o Its log. from col. of rifing D.perW. i o o Log. )o o'= 0,301 03 o rr O,OOOOO ratio 0,30103 g. 4,11247 e. 0,58700 5,00050 ratio 0,30103 1704 N. num. 3> 2 3i4-0 48303 90 Q o' Nat. S. Sun's mer. alt. 50007 = 30 o Sun's merid. alt. 60 O Latitude The latitude by computation, coming the fame with the latitude by account, fhews that the latitude by account was right. From the foregoing examples it is plain, that the operatign is the fame, whether the fun hath north or fouth declination. And it will be the fame whether the dip is in a north or fouth latitude. It is alfo clear, that when the fun has no declination, the fecant, rejecting the index of the latitude is the log. ratio. EXAMPLE. V. Wanting to go through the N. Channel among the Maldives, and by account being in latitude 7 40' N. the declihation being then 22 47' N. at 7!!. 25 M. 408. A.M. the true altitude of the fun's centre was 22 30', and at 10 H. 31 M. 48. S. A. M. it was found 63 40'. Required the (hip's true latitude? H. M. s. Alt. .Nat. S. Lat byac. 7*4o'o, 00300 Times 10 31 48 6 3 40' 89623 Declinl 22 47 0,03528 7 25 40 22 30 38268 Log. ratio. 0,039*8 Elap.T. 368 51355 Irs log. 47 I0 58 | El. T. i 33 04 Its log. in col. of | elap time is 0,40368 H. M. S. .3 * 3 5>*5H4 TrueT. i 2826 Its log. in col. of fifing is 3,86709 T. p. W". i 28 12 Log. ratio 0,0391*$ W. flow o o 14 6728 Nat. num. 3)82791 90 op 89623 -N. S . gr. alt. Mgr. alt. 74 29 0355 N. S. Sun's mer. alt. = 42a/. C c^ 2Q2 THE METHOD OF FINDING THE LATITUDE Zen.dist. 15 31 N. Decl. 22 47 N. Lat. in 7 16 North. N. B. As the Tables are only calculated to 10 feconds, the log. for any intermediate fecond is found by taking the difference be- tween the log, next greater and next lefs ; and faying, as TO fe- conds is to that difference, fo is the given feconds to the difference of the logarithms ; or, if it be any even part, take fuch a part of the difference, and apply it to the next lefs logarithm j but in thefc operations a few feconds are not rt-garded. SECOND OPERATION. Lat. 7" 16' 0,00350 Dec. 22 47 0,03528 ratio 0,03878 4,71058 0,4.0368 H. M. 5. * 2 i 20 5i'534 True time i 28 26 ^ 3,86709 N. S. gr. alt. ^~ 89623 Log. ratio 0,03878 6735 N. num. -. . Log. 3,82831 N. S. Sun's m. alt, 96358=74 29. Hence thelat. inis7i6'N, The latitude laft found, agreeing with that ufed in the operation, it may be taken as the true latitude ; and the operation is repeated with very little additional trouble, few alterations being neceflary. Hence it is plain, that if you are miftaken in the latitude by ac- count, yet by repeating the work two or three times, making ufc of the latitude laft found in the next operation, it will at laft dif- cover itfelf to be true, by being equal to the laft fuppofition, which evidently fhews the excellency of thfe Tables. in the former examples we have confidered both altitudes taken at the fame place or ftation ; but as that is felciom the cafe at fea, the neceffary correction for any alteration of ftation may be readily made as follows: H. M. Suppofe the firft altitude in the forenoon, at 10 26 The fecond altitude in the afternoon, at ah. 43 m, 14 43 Difference of longitude made is 30 miles W, equal to o 2 14 4t 10 16 Subtra&ed is the elapfed time -^ ^ 4 '15 If a fhip has been failing to the Eaftward, the above two mi- nutes muft be added; but unlefs the difference of longitude be confiderable, it is not worth notice, a's it will make a very incon* ftderable error in the latitude. Again, BY DOUBLE ALTITUCES. 203 Again, if the fhip fails or makes towards that point of the com- pafs which the fun bears upon, fhe muft raife the fun's altitude as many minutes as the miles {he has run towards it ; therefore the miles run towards the fun muft be added to the firft altitude ; but if failing from the fun, the fame muft be fubtraled ; if they are but few, they are not worth minding : and then the feaman may make a very good eftimation by looking at the log-board only, who by that will be able to afcertain the diftance failed to, or from the fun, between the obfervations, which will be of fufficient exadtnefs in the practice of navigation; and if the fhip makes an angle with the fun's bearing, it may be readily found by the Table of Difference of Latitude and Departure, and then either add or fubtracr, according as the cafe requires ; as may be feen in the following examples, which are inferted for the benefit of thofe who require a greater degree of accuracy. EXAMPLE VI. Suppofe a (hip from the Bay of Bifcay, bound to the Englifh Channel, in a brilk gale running N. by E. f E. per compafs, at the rate of nine knots per hour, at i o H.oM. A.M. per watch i obferved the fun's altitude 13^ 18' bearing S. J E. by compafs, and at i H. 40 M. P. M. per watch, the fun's altitude again was found 14 15, the latitude by account being 49 ij'N. and the fun's declination 23 28' S. Required the true latitude ? Correction ofthefirjl Altitude. The time of the firft obfervation is 10 H. o M. A. M. and of the fecond i H. 40 M. P.M. the elapfed time is 3H.4oM. and the rate of failing is 9 miles per hour ; then fay, by the Rule of Three, as i H. is to nine miles, fo is 3 H. 40 M. to 33 miles, the diftance run in the elapfed time. Again, the fun's bearing at the firft obfervation is fouth J E. the oppofite to which is N. | \V or -J- point, and the fhip's courfe du- ring the ehp.. time is N. by E. 4 E. i| points, fo the angle of fhipV courfe with the fun's bearing is'2j points. Now in the Tableof Difference of Latitude and Departure,tothe courfe 2-j points, and diftance 33, the difference of latitude is 29 miles, the (hip fails from the fun : therefore from the firft obferved altitude 13 18' take 29', the remainder 12 49', is the firft altitude corrc&edj which is to be ufed in; th operation, as follows : Cca THE METHOD Ql FINDING THE LATITUDE G $04 Let the circle reprefe : it tfce compafs N, S, E, W, and A the {hip's place. Take the fhip's courfe N, by E. | E. or i | point, and fet it off from the north towards the eaft; take the fun's bearing S. 1 E. or of a point, and fet it off from the fouth towards the call ; the oppofite point fc A G, N. VV. then will G A C be the angle the (hip has made during the elapfed time, which angle being fet off from the north, (or meridian) to the ear!, will be the true coi>rfe the fhip has made from the fun, as the angle BAD. From A to D fet off 33 miles, the diftance failed in the elapfed time i from D draw a line parallel to the E. and W. to cut the north or meridian line at B, then AB will be the difference of latitude 29 miles^ that the fhip has failed from the fun during the elapfed time. mes Ela. T, H. M. 10 1 4 340 S. o Alt. Nat. S. Lat. 49 17' J2%9'=:22i83 Decl. 23 28 0,18554 0,03749 I 5 2 4 1C 5 Log. ratio Diff. N. S. 2432 Its log. Its log. Time correfponding to 0,22303 iO o 3,94458 40 o Its log. in col of rifmg is Log. ratio 0,22303 o o 7 35 5606 Nat. num. of 3,74867 Zen. difL 72 25 N. S. M. Alt. 30221 = 17 35 O'smer.alt, Declination 23 28 Latitude 48 57 N. But as the latitude by computation differe confiderably from that by account, the work mufl be repeated. Latitude 48 57^=10,18262 Declination 23 28 0,03749 Log. ratio o ? 220ii BY DOUBLE ALTITUDES. 205 .Log. ratio 0, 22011 H. M. s. Diff. N. S. 2432 Its log. 3,38 59^ j 50 o Its log. 0,33559 o 10 o Time anfwering to 3,94166 ~o Its log. in col. of rifmg 3>97*7O Log. ratio 0,22011 Zen. did. 72 238. 5644 Nat. num. of 3,75 , 59 Declina. 23 2& S. 24615 Tr. lat. 48 55 N. 30259 N. S. men alt. 17 37'. This latitude differing only two miles from that in the above computation, it may be depended upon as the true latitude. EXAMPLE til. A fhip failing N E. half E. by compafs, at the rate of nine knots an hour, at o H. 31 M. 40 S. P. M. per watch, I found the alti.ude of the fun's lower limb 28 23 ; above the horizon of the fea, the eye being elevated twenty feet above the furface of the water, and the fun's bearing by compafs being at the fame time S, by W. and at 2 H. 58 M. 20 S. P. M. by watch, the altitude of the fun's lower limb was 16 41' above the horizon, the eye being elevated as be- fore, and the latitude by account, at the time of the laft obferva- tion, was 48 5' uorth, and the declination 13 ly'fouth. Re- quired thetiue latitude at taking the laft obfervation ? Firft obferved alt. fun's lower limb 28 20' Second ditto 16 41' Refraction to be fubtraeled 2 Correction for refraction Dip of the horizon fubt rafted A pp. alt. Sun's femidiameter added Correct altitude of fun's centre 28 30 16 53 Csr region for the firft Aliltudt. The time of the firft obfsrvation o H. 31 M. 40 S. P M. of the fecond 2 H. 58 M. 20 S P. M. fo the elapfed time is 2. H. 26 M. 40 S : the rate of failing is nine miles per hour. Then as i H. : 4 miles ; ;2 H. 16 M. 40 S. : 22 miles, the diftance run in the elapled time. Again, the fun's bearing at the firft obfervation is S. by W. the oppoiite point to which is &. by E. or j point. The (hip's courfe during the ela. time is N. E. 4- E. or 4^ pts. So the angle of the ihij/s courfe with ) f T the fun's bearing In J06 THE METHOD OF FINDING THE LATITUDE In the table of difference of latitude and departure, to the courfc 3 points, and diftance 22 miles, the difference of latitude is 17 miles, which the (hip fails from the fun. Wherefore, firft obferved altitude 28 30' 17' 28 1 3' the firft corredt altitude to be ufed in the operation. H. M. s. Alt. N.S. Lat. byac.48 5' 0,17519 Times 03140 28 13' 47281 Declin. 1317 0,01178 2 58 20 16 50 28959 -- -- Log. ratio 0,18697 Ela. T, 2 26 40 Diff. N.S. 18322 Its log. 4,26297 ^Ela.T.i 1320 Its log. from col. of lelapf. time. 0,50232 j 46 27 In col. of mid. time-correfponding to 4,95226 c 33 7 Its log. from col. of rifing 3,01794 Log. ratio. 0,18697 N.S. gr. alt. 47281 90 o 678 N. numb, of 2,83097 Mer. alt. 28 40 N. S. 47959 Zen. difc 61 20 Decl. 13 17 Lat. 48 3 N. And as it differs but two miles from the latitude by account, it may be taken as the true latitude. s f& Exercife. ift. Being at fea in latitude by account 3928'N. when the fun's declination was 20 41' N at 1 1 H. 30 M. 15 S. A. 1VL per watch, the altitude of the fun's lower limb was obferved to be 68 j 8' 45", and at 12 H. 26 M. 28 S.P.M. it was 70 58', the height of the eye being 21 feet above the furface of the fea. Required the true latitude of the fhip ? Anfwer, 39 28' N. 2d. Being at fea, in lat. 50 4' N. by account, at 10 H". 17 M. 30 S A.M. per watch, the altitude of the fun's lower limb was ob- ierved to be 17 4' J, and at n H. 17 M. 30 S. it was 19 31', the declination being then 20 S. and the height of the eye 21 feet above the fea Required the latitude in ? Anfwer 50 2 f N. 3d. Suppofe a (hip at fea in lat. 47 i ;' N. by account, at 9 H, 55 M. 30 5. by watch, the altitude of the fun's lower limb was 17* 24', bearing by compafs 8. by E. iE. and at 12 H. 54 M, 10 S. his altitude was 21 45' f , the declin. being then 19 30' S. the height of the eye 20 feet above the fea, and the {hip's courfe by compafs was E. | S. at the rate of 7 knots per hour. What was the lati- tude ? Anfwer 47 2 j'N. 4th. At ii H. 28 M. 20 S. A. M. per watch, the altitude of the fun's lower limb was 2& ib' a the fun bearing then S. by W. by compafe, BY ONE ALTITUDE OF THE SUN, compafs. At 2 H. 58 M. 20 S.P.M. his a'titude was 16 40', the height of the eye 20 feet, his declination being then i 'f jy'S. and the latitude then by account 48 08' N. the fhip'scourfe during the elapied time was N.E. with her larboard tacks on board failing at the rate of fix knots, and made half a point lee- way. What latitude was fhe in when the lad altitude was taken ? Anfvver 48 9'N. By the fhip's courfe per compafs is to be underftood its courfe made good j lee-way, if any, being fir ft allowed ; or the courfe, by compafs, corrected for the lee -way only, but not for the variation. Had the variation of the compafs been applied, both to the fhip's courfe and the fun's bearing, it would not have made any difference in the operation or rtfult, as the angle formed by them will always be the fame, whether they are both eftimated by the compafs s or when the variation is allowed on both. This method of finding the latitude is of excellent ufe, iince there are fo many circumftances at fea, which deny the opportunity of having the fun's meridian altitude ; and as the knowing the true latitude is of the greateft confequence, efpecially in coming into the EngHfh channel, &c. where there are frequent obftrudions of clouds, every feaman ought to be ready at determining his latitude, by trrs method, whenever an opportunity offers, left he (hould not fee the fun upon the meridian. NOTE. The nearer to noon the obfervations are taken the better; provided the elapfed time be not much lefs than half the interval of time, when they are both taken on the fame fide of noon, nor much greater than once and half the greater interval, when taken on dif- ferent fides of noon. To find the LATITUDE by one ALTITUDE of the Sun* when the Time is not more dijlant than one Hour from Noon. RULE. To fin 4 the true Time. WHEN the fun's declination and complement of the latitude are both north or both (buth, their Him, but if one be north 2nd the other fouth, their difference, is the meridian altitude. From the natural fine of the fun's meridian altitude, fubtracl the natural fine of the obferved althude. Then add together, The log. co-fecant of the comp. of the lat. } . a The log Cxantof the fun's declination, f &* thclr " li];>xe <> and the common logarithm of the difference of natural fines into one fum. The fum of thefe three logarithms being found in the column of rifing, the hours, minutes, and fecoiv.ls correfporuling to it, will be the true time from noon when the altitude was taken. EXAMPLE. at fea in latitude 50 4' N. by account when the fun'* de- clination 208 THE METHOD OF FINDING THE LATITUDE BY clination was 20 fouth, at n H. 17 M. A. M. per watch, fun's alt. was 19 41'. Required the true time ? Comp. lat. 39. 56 N. . Co-fee. 0.19254 Declination 20. CO S. Sec. 0.02701 Sup. m. alt. 19. 56 Nat. fine 34120 L. ra. 0.21955 Obfer. alt. 19. 41 Nat. fine 33656 464 Co.L. 2.66652 H. M. s. . 12. oo. oo Log in col. of rifing 2.88607 ' IS == < 2 ^- 2 5 True time at fea 11.31.35 Having the true time previous to the obfervation, to find the change of altitude. Add together the logarithm found in the col. of riling, anfwering to the minutes and feconds the fun had to rife when the altitude ,was taken, and the fecant of the fuppofed meridian altitude from this fum, (the index being increafed by 5*) fubtracl the log ratio, the remainder is the log. fine of the change of altitude from the time of obfervation to noon ; which, being added to the obferved altitude, gives the fun's meridian altitude. Log. in col of rifing of $8 :VI. 258. 2.88607 Obfer. alt. 19.41 Log. fee. m. alt. 19 20' -f- 5 Index 5.02683 Cha. of alt. -f 20 . Tr. m. alt. 20.01 7.91290 Subtract log. ratio 0.21955 Log. fine chan. of alt. 20 min. 7-69395 EXAMPLE. Being at fea in lat. 60 north by account when the fun was on the equator, at i H. o M. P. M. per watch, the fun's alt. was 28 5 3'. Required the true time and latitude in ? Com. Jat. 1 30 oo N. Nat. fine 50000 C. fee o.3Oio3fLog. ratio. Mer. alt. J Ob. alt. 28.53 Nat. fine 48303 Ch. of alt. 1.08 j6o7Comlog. 3.22968 T.m.ak. 30.01 Log. in col. of rifing 15^=35307 in i. ooTrT gen.dift. 59.99^ Log fcc.mer. alt. -f5in. 5.06247 The S, bemg on the equator. 8.593*8 Subtract log. ratio 0.30103 Log fine chan. of alt. io8'8.292 1 5 * The 5 is the inoVx of fix hours in the column of rifing. f The fun being on the equatrr, and having no declination, the eo-fec. of tht tornp. of the lat. gives the log. rario. THE MERIDIAN ALTITUDE OF THE MOON. 209 EXAMPLE III. Being at fea in lat. 39 28' north by account, fun's declination 20 4i'north at 26 M. 28 S.P.M. fun's alt. was 71 10'. Required the true time and latitude at the fliip? Comp. lat. 5o-3aN. Co.fec. 0.11239 Declination 20,41 N. Nat. 611694674 Secant 0.02895 Sup. m. alt. 71.13 Nat. fine 94646 0.14132 28 Com, log. 1.44716 """*" L - , $ S' Obfer.alt. 71.10 Log. in col. of rifing 13=1.58848 630 T.T. Chan. alt. 3 Log.fec.fup.mer.alt. -|- 549216 [atih. Tmer.alt. 71.13 Zen.dift. 18.478. 7.08064 Declination 20. 41 N. Subtract log. ratio 0.14132 Lat. in 39.28^ L. fine chan. of alt. 3 m. 6.93932 NOTES. i ft. The altitudes for determining how much the watch differs from apparent time had better be taken in the morning, or evening, when the fun's altitude dots not exceed 1 8 degrees. 2d. An error in the fuppofed latitude can make very fmall difference in the change of altitude ; and the nearer the altitude is taken to noon the better to find the change of altitude. 3d. This method is not to be depended on mould the apparent time exceed an hour from noon, and, in fome inftances, not then ; fuch as altitudes taken near the equator; or when the meridian altitude exceeds 60 degrees; nor is there much oc- cafion for this method, or that of the double altitudes there, fince there is generally a clear horizon, and confequently a meridian altitude iseafily obtained. To find the Latitude by the Meridian Altitude of ike Moon. To the Longitude of the given place in time add the number from (F. XVII.) correfponding to that Longitude, and the daily- variation of the moon's pafTage over the meridian on the given day, (Nau. Aim. p. vi.) if the Longitude be weft; but fubtraci the fum if the Longitude be eaft: the fum or difference will be the time at Greenwicn when the moon was on the meridian of the given place. In page 7th of the month in the Almanack, find the moon's femi-diameter, and horizontal parallax, at the neareft noon, or midnight, to the reduced time, which will be fufficiently accurate for the purpofe of finding the latitude. For Parallax, fee the ufe of the fextant. Take the difference between the moon's femidiameter and dip, and add it to the obferved altitude, if the lower limb was bbferved, but fubtta-ft their fum if the upper limb was obferved; the fum or cTifFerence will be the apparent altitude of her centre. From the proportional logarithm of the moon's horizontal paral- lax, increafmg its index by 10, fubtradt the log. co-fine of Dd the 2IO THE METHOD OF FINDING THE LATITUDE BY the moon's apparent alt. the remainder will be the prop. log. of the moon's parallax in altitude, from which take her refrac- tion, the difference will be a correction, which, being added to the apparent altitude, will give the true altitude of her centre : hence the zenith cfiftance, to which apply her decimation, and you will have the latitude. NOTE. The moon's declination is fet down in page the 6th of the month for every noon and midnight in the Nautical Almanack. Therefore find the declination for the neareft noon and midnight, both before and after the reduced time, and take the difference. From (T. XVIII.) take out the number correfponding to the hours at top, and the minutes in the left hand column,with the time at Greenwich, with which multiply the difference; from the pro- duel: cut off four figures from the right hand, the remainder is a correction to be added to the declination, if increafing, but fubtracl:- ed if decreafing; the refult will be the declination at the given time. EXAMPLE I. Suppofe, On Oct. I, 1806, in longitude 45 W. the altitude of the moon's lower limb, when on the meridian, fouth of the ob- ferver, fhould be 60 43' o'', the eye being 23 feet above the fea. Required the latitude ? The longitude 45 weft turned into time equal to 3 hours, and the correaion 7 M. from (T. XVII.) added to 15 H. 13 M. the time the moon paffes over the meridian on the given day, gives 18 H. 40 M. time at Greenwich. Hor. par. 57' 10" P. L. 10,4981 Moon's ob. alt. 60 43' cf App.alt. 6O54L. co-fi 9,6869 M.fem.dia. 15 35 ) + n I Dip 4 34 3 Par. in alt. zz 27 48 P. L. 8ii2 6054 I Refrac. 23 27 25 Cor. of the moon's alt. -f Moon's dec. midnight 2i3i'N. True alt. Do. at noon 22 24N. Dec. 21 31' 27 25 6l 21 26 9 Diff. in 12 hours 53 -f Zen. difl. Then 53 X by, 5278 (T, XVIII.) gives +28 28 38 34 S Moon's dec. at reduced time 2 1 59 Latitude EX AMPLE II. Suppofe, on Dec. 27, 1806, in longitude 60 cafl^ the altitude of the moon's upper limb mould be obferved, when on the meridian, being then fouth, 54 30', the eye 20 feet above the fea. Required she latitude ? The THE MERIDIAN ALTITUDE OF A PLANET. 211 The longitude 60 eaft in time equal to 4 hours, lefs the cor- reaion 9 M. found in (T. XVI'I.) fubtrafted from 14 H. 18 M. the time the moon pafles over the meridian on the given day, leaves 10 H. 27 M. time at Greenwich? Hor. par. 60' 28* P.L. 10,4738 Moon's ob. alt. 54 30' d App. alt. 549 o co-fi. 9,7676 M.fem.dia. j6'29 /f \ Dip 4 16 /- 2 4 5 Par. in alt. 36 25 P.L. 7062 - Refraction 41 54 9 15 35 44 Moon's cor. to be added -f. 35 44 Moon's dec. at noon 1 6 37' N. 16 37' o* N. 54 44 59 Do. at midnight 14 26 N. 90 2 n Zen. dift. 35 15 iS 2' 1 1'' = 131" x by 8708 I gives i i 4 "-i' 54" (T. XVIII.) I- I 54 16 35 6N Moon's dec. at reduced time 1635 6N. Lat5i 50 ;N Tofndthe Latitude by the Meridian Altitude of a Planet. In page 4th of the month in the Nautical Almanack, are given the declinations and times of the planet's paflage over the meridian of Greenwich every fix days. Reduce the longitude into time, and add it to, or fubtracl it from, the times of their paflage over the meridian of Greenwich, according as the longitude is eaft or weft : the fum or difference will be the time they pafs the meridian of the place of obferva- tion : correct the obferved altitude for the dip and refraction, with this corrected altitude and declination find the latitude, EXAMPLE L Suppofe, in longitude 15 Weft, on Oc~L 7, 1806, the meridian altitude of Jupiter, when South of the obferver, fhould be 29 12', the eye being elevated -22 feet above the furface of the fea, and the latitude be required? By the Nautical Almanack, Jupiter pafles the meridian of Greenwich that day at 5 h. 14 m. afternoon ; and i h. the longi* tude in time added to it, gives 6 h. 14 m. the time of his paflage over the meridian of the place of obfervatioiu Mer. alt. 29 i2'oo" Dip 4' 28" -f Refra. i' 41" oo 6 9 29 5 51 90 oo oo Zen. dift. 60 54 9 S. Peel. 23 32 ,00 S, Lat. 37 22 9N, 2 EXAMPLE ( 212 ) EXAMPLE II. Suppofe, in lat. by account, 47 12' N. and Ion. 15 W. bound for the Englifh Channel, and having had no obfervation for feveral days, I find the meridian altitude of Venus, bearing fouth of me, is i8 15', the eye being elevated 22 feet above the horizon, and the declination 23 5 1' 60'' S. Required the latitude ? Mer. alt. 1 8 15*00'' Dip 4' 28" + Refra. 2' 54" oo 7 22 True alt. Zen. dift. Decl, 18 7 38 90 o 71 52 22 S. 23 51 oo S. Lat. 48 i 22 N. A COMPENDIUM OF NAUTICAL ASTRONOMY, IT is a complaint frequently made by feamen, that it is a thing impraaicable to find and know the flars. Recurring to the exiftins Treatifes on the fubjea of Nautical Aftronomy, the com, plaint does not feem altogether ill-founded, if we confider that feamen have but little time to acquire thofe fciences which are necefTary for the undemanding a regular fyftem of aftronomy. It has, therefore, been attempted to fimplify and render praaicable, the method of finding and knowing the ftars. For the attainment of which purpofe, we beg leave to introduce the following methods : Look for the right afcenfion of the fun and flar in Tables XIV. and XV. and fubtraa the fun's right afcenfion from the ftar's ; bu^ if the fun's right afcenfion be greateft, add 24 hours to the ftar>s>, : right afcenfion, and then fubtra& the fun's from it, the remainder *wiilbe the time of th? ftar's coming to the meridian, When the fun's right afcenfion is leair, the ftar comes to the meridian in the afternoon : but before noon, when the fun's is the greateft/ A COMPENDIUM OF NAUTICAL ASTRONOMY. EXAMPLE I. At what time will the ftar Arc. turus be on the meridian of Greenwich, Dec. I, 1806 ? H. M. s. Arclurus right afc. Sun's right afc. 14 24 6 48 38 6 48 1 6 27 46 EXAMPLE II. At what time will the ftar Vir- gin's Spike be on the mer. of Greenwich, Sept. i, 1806? H. M. S. Virgin'sSpike right afc, 13 14 59 Sun's right afc. 10 39 49 The ftar culminates 2 35 10 So that the ftarSpica Virginus, or Virgin's Spike, comes to the meridian of Greenwich at 35 minutes after two in the after- noon. In the morning 9 39 That is, the ftar Arclurus will be on the nruer. of Greenwich 39 min. after nine in the morning. To find what Star comes on the Meridian at a given RULE. Add the time from noon to the fun's right afcenfion, the fum will be the right afcenfion of the ftar required to be known ; look in the Table of the ftar's right afcenfion, and find what ftar's right afcenfion agrees with, or comes neareft to it ; and that is the ftar required. EXAMPLE I. J would know what ftar will be on the meridian of Greenwich about ,ten at night, Jan. 26, 3806? H. M. s. Gafc. for noon. Jan, 2 6 20 33 19 And for 10 h.more 2 given time 10 P.M. 10 o o 30 35 19 24 OO GO Nearly anfw. to Sirius 6 35 19 EXAMPLE II. What ftar will be upon the mer. of Greenwich 30 minutes paft 4 A. M. May 10, 1806 ? H. M. ?. G right afc. May i o at 3 6 31 noon and for 16 H. 3 more given time 16 hours 30 min. from noon of the ioth 16 30 o Anfwcring nearly to Altair 19 39 31 Having found the time of the ftar's coming to the meridian by the foregoing method ; in oider to determine whether you have obferved by the right ftar, obferve the following rules : ift. If the latitude in and declination be of the fame name, fub- traft the declination from the latitude, the diff. fubtra&ed from 90 gives the altitude. 2d. If the lat. and dec. be of contrary names, add the dec. to the lat. the fum fubtracled from 90 gives the alt. of the ftar required, EXAMPLE 214 A COMPENDIUM OF NAUTICAL ASTRONOMV. EXAMPLE I. What will be the altitude of Arrurus at Greenwich when on the meridian Jan. 25, 1806 ? H. M. S. Lat. of Greenwich 51 28 4oN. _v Declination 20 u 5oN. ~v Altitude EXAMPLE II. What will be the altitude of the ftar Virgin's Spike at Green- wich, Sept. I, 1806 ? H. M. s. Lat. of Greenwich 51 28 4oN. /' Declination 10 8 39 S. 58 43 jo I* Altitude 28 22 41 Of the Celeflial Globe, The Celeftial Globe is a round body, upon the furfece of which is 'reprefented the concavity of the heavens ; that is to fay, a right line. being drawn from the eye of the Spectator, placed at its centre through any ftar thereon reprefented, will point to the fame ftar in the heavens ; whence it follows, that the celeftial globe being elevated to the latitude of a given place, the fun's place in the ecliptic brought to the brazen meridian, and the hour index fet to the upper twelve, by turning the globe round to any given hour, all the ftars reprefented on the globe will point to their corre- fponding ftars in the heavens ; thus exhibiting all the ftars at that time vifible above the horizon. From thefe data the following problems may be folved. PROBLEM I. Required the time of rifing, paflage over the meridian, and fetting, of the ftar Regulus, on the 6th of Jan. 1805, in lat, 52 north ? Pirft, elevate the pole as many degrees above the horizon as correfpond with the given latitude, which, in this inftance, is 52 north : then look in the horizon for the day of the month, which is the 6th of Jan. oppofite to which ftands 16 of Capricorn -, find 16 of Capricorn on the ecliptic, and bring it to the eaftern fide of the brazen meridian ; fet the hour index to the upper twelve ; then, by turning the globe round, you will find the ftar Regulus rifes at a quarter before eight in the afternoon, comes to the meri- dian at a quarter before three in the morning, and fets at a quarter before ten in the forenoon. PROBLEM II. Required the altitude and azimuth of the ftar Regulus, at eleven o'clock in the afternoon of the 6th of January ? The fun's place being brought to the brazen meridian, as before, and the hour index fet at twelve; fcrew the quadrant of altitude in the zenith, or over 52, counted on the brazen meridian, from the equinoctial ; turn the globe to the weftward, till the hour index points to eleven ; then lay the quadrant of altitude over the A COMPENDIUM OF NAUTICAL ASTRONOMY 215 the centre of the ftar, and you will find its altitude, counted on the graduated edge of the quadrant, 30, and its azimuth 18 eaft, foutherly 5 that is, io8 Q , reckoned from the north point of the compafs. Thus may the time of rifing, paffage over the meridian, and fetting, of any ftar, together with ifs altitude and azimuth, be found. But r.s fhips are feldom provided with globes, we fliall endeavour to work fuch problems as are neceflary for feamen to know, by the plans fubjoined to this lyth edition. The firft plan divides the celeftial globe into two equal parts, the northern and the fouthern hemifphere, extending from the equinoctial to each pole. Upon the equinoctial is marked in time and degrees, the right afcenfion, beginning at the firft point of Aries, and reckoning to the eaft ward, including 360, or 24 hours. The declination is reckoned in degrees, beginning at the equi- noctial, and counting towards each pole, ending at 90. The ecliptic begins alfo at the firft point of Aries, and ends at Libra, extending in the northern hemifphere nearly 23 28'. The other part of it begins at Libra, extends nearly 23 28' foutherly, and ends at Aries again. On this circle are marked the twelve figns of the zodiac, in which may be found the fun's place for every day in the year. From this it is clear, any ftar may be found, whofe right afcenfion and declination are known. EXAMPLE I. Required to find the ftar Regulus ? Enter Table XV. where you will find the ftar's riht afcenfion is 149 30' 15", and declination i254' 38" N. nearly. Lay a ruler from the pole over the right afcenfion ; take the declination in your compafies, and fet it oir by the fide of the ruler from theequinoaial, and that will give the place of the ftar required. EXAMPLE II. Required to find the ftar Aldebaran ? Enter Table XV. where you will find the ftar's right afcenfion is 66 12', and declination 16 6' 35" N. nearly. Lay a ruler from the pole over the right afcenfion ; take the de- clination in your compafies, and fet it off by the fide of the ruler from the equinoctial, and that will give the place of the ftar required. EXAMPLE. III. Required to find the ftar Antares ? In ''ab. XV. before direded, find the ftar's right afcenfion and decimation, which in this inftantfe is 244 22'45"'right afcenfion, and declination 25 59' i6"S. nearly. Lay a ruler from the pole over the right afcenfion ; take the de- clination in your compares ; let it off along the ruler from the equinoaial, and it will give the ftar's place as required. This 2l6 A COMPENDIUM OF NAUTICAL ASTRONOMY. This projection of the celeftial globe upon the plane of the equator, is fufficient for the purpofe of finding the ftars in either hemifphere, independent of the other. But as it may in\many inftances he neceflary to trace the relative fituation of the ftars in both hemifphereSj another plan has been fubjoined, which, it is trufted, will, together with the foregoing one, anfwer every fituation the mariner may find himfelf in. As it is very difficult to lay down a fphere on a plane, the fol- lowing method has been fuggefted : that is, by laying down the equinoctial on a plane, and the hour circles extended in the fame proportion as the degrees on the equinoctial, having the diftance both to the norrh and fouth expanded fo as to correfpond nearly with thofe circles upon the globe itfelf, by which means the right afcenfion and declination will cut each other at right angles ; the firft reckoned from the firft point of Aries, and the laiter fiom the equinoiliai, either north or fouth, having the ecliptic laid down as in the former plan. This plan being laid flat, pointing N. S. E. W. will {hew the face of the heavens. The right afcenfion and declination of a ftar being given, it may eafily be found by laying a ruler over the right afcenfion, and taking the degree of declination in the compafles, and laying it off from the equinoc- tial alongfide the ruler. To prove which, let us make ufe of the firft of the three foregoing examples. Thus, by laying a ruh-r over the right afcenfion of Regulus, which is 149 30' 15", and taking the declination 12 54' 38'' N, in yowr compafTes, and laying it off by the ruler, counting from the equinodtial, you will have the fhir's place as required. Any other ftar may be found by the fame method. The n'o;ht afcenfion in thefe examples is given in degrees, but may eafily be converted into time by Tab. XVI. Sompta&lcal Directions far knowing the Stars. Having {hewn how to find the ftars by their right afcenfion and declination, we {hall next proceed to fhew how they may be known by their mutual bearings and diftances from each other. It was judged better adapted to the practice of feamen, to enable them to know the ftars from which the moon's diftance is com- puted in the Nautical Almanack, to give the bearings and diftances of the brighteft ftars furrounding each of them, than by following the ufual method of delineating the conftellations, which are ar- bitrary appellations, there being no marks in the heavens bearing any refemblance to the forms in which they are ufually exhibited. I ft. Required to know the ftar a Arietis, Jan. 6, 1806 ? By the foregoing rules I find that a Arietis comes to the meri- dian at 7 h. ii m. afternoon; and to be certain of this, I take his altitude, and find it correfpond with my latitude, as before directed. For further conviction, I find the bright ftar Algol, bearing N. E. by N. diftant about 23; the ftar Menkar, S. E. by S. difiant about 26; the ftar Mirach, N. W. by W. 21; and the ftar Shedir, N. N, W. 38; as exhibited by dotted lines on the plan. 2d. Re- A COMPENDIUM OF NAUTICAL ASTRONOMY. ?l' 2d. Required to know the ftar Aldebaran, Nov. 25, 1806? By the foregoing rules, I find that the ftar Aldebaran comes to the meridian at o h. 2 m. 48 f. in the morning. For further fatis- fadlion, 1 compare his altitude with my latitude; and further, I find the ftar Capella hearing N. by E. ~ E. diliant about 30; Bc~ telgeux, E.S.E. 29; Bellatrix, S. K. *E. 21; and Pleiades, W. N.W. i6 6 . 3d. To know the ftar Pollux. Find the time of his com ir, to the meridian as before, when you will fee the following ftar:., viz. Aizubens, bearing S. E. eafteriy, diftant 28; Procvon S. 23 ' and Caftor N. W. by W. 5. 4th. To know the ftar Regulus. Find the time of his cul- minating, as before; and further, you will fee the two ihrs in the confteliationof the Great Bear, called the Pointers, in the fol- lowing bearings, viz. the Lower Pointer, N. hy E. 46 ; Dubhe, or the Upper Pointer, N. 4 E. 51 N. B. A line drawn direcl- 3y through the Pointers leads within a degree of the north poie liar. 5th. To know the ftar. Virgin's Spike. Find the time of her culminating; and further, you will fee the ftar marked der; then add together, The log. co-fecant of the comp. of the lat. "J The log. co-fecant of the polar diftance, I Rejecting their The log. fine of the half-fum, and f indices. The log. fine of the difference into one fum, ) Find the log. fine of half the fum of the four logarithms, which being doubled, and brought into time, as before, will give the time from the midnight before the altitude was taken. Half the fum of thefe four logarithms will give the log. co-fine of half the hour angle, which being doubled and turned into time, by allowing fifteen degrees for every hour, &c. or more briefly by the table, will give the true time, if the altitude was taken in the afternoon ; but if in the forenoon, its complement to 24 hours will be the true time, reckoned from the preceding, or noon before'. KUTP. The refraction is found in Table VII of this book; The dip of the horizon, Table VIII. in ditto; The fun's, parallax in alt. Table IX. in ditto; The fun's declination in page 2, of the month; and, Ti-e fun's fcmi-di. in .page 3, of the -mouth, in the Nautical Almanac!.. KX AMPLE I. Suppole., on thr 7th May, i8w6> r.t 5h.^30m, 32 f P. A'!, per Watch; in hit. ?,r) 54' N. and Ion. '35 30' weft .of Greenwich, by account^ THE TIME AT SEA 221 account, the altitude of the fun's lower limb fhould be found to be 15 45', the eye being 18 feet above the fur face of the-fea, and the true apparent time when the observation was made were re- quired ? Obf. ah. fun's 1. 1. 15 45' o" Lat, - . ^9 {4' o" Semi.i/ja"7 Diffa ; o g( 90 'o o Dip 443 , Co. lat. - 50 6 o Ap. alt. fun's 1.1. 155648 Refra.3'i7" ? o:fr Sun's decl. May ?th 1641 c6N Par. o 8 J * y Ditto - Srh 16 ^8 " Sun's true alt. 15 5J 39 Diff, in 24 hours - 0163^ 90 o o Zenith dift. ' 74 6 21 16' 33" X ,3182 gives 5 26 Sun's decl. /th May - 16 46 5 Timeatlhip J 30 32 True dec. for Ion. and time 16 51 31 Long. \\ r . in time -}- 2 22 o 90 o o Reduced time ~ 52 32 Polar di^. 73 8 29 Co. lat. ) 6 o ~ - - Co. fee. ? . / . Polar dift, 73. 8 2? - - - Co. fee. f . *. eisr * d ' . Oj oioo Zen. dift. 74 6 21 2)197 -20 50 T r Sutn 98 40 2> I. o^. ne - - oo-co Zen. dift. 74 -6 21 Remainder 24 34 4 Log. fine - 9,61 S? 5 Sum 4 log. 2) '9 4 1 34 o log. co-fi. 2 Horary angle - - ' 9 ,^7402 *3 8 o in time Time B 5 5 . M. S, 3 5 a 3 3* at (hip per watch Hour kngle Watch flow - - - - 02. NOTE. Ry turning the long. W. into time, and adding it to the timeat the iTiip, gives the reduced time, 7 h. 5201, 32!", anJ the difference of declination between the yth and 8th of May, if. 16' 33'' 993\ which multiplied by 3282,3 number found ia T.. XVIi[ corrfvfponding to 3h. 56111. i6f. half the reduced time from the product ; cut ofF four figures from the right, the remainder 5' /042 gives 16 6 J D;ff< _ J 3 44 59 Tr.dec.forlon.&t.6 22 31 13 41 20 Polar dill. 90 o o 96 22 31 Zenith difh Co-lat. P. dift. 76 i 8 40 ' 38 3 Co-fee. 1 , ... ,.{ 0,20585 96 22 3 z Co-fee. J U ^0,0027^ Sum, I Sum Zenith dift. Remainder 2)211 ii jj 105 35 35 Log. fine 76 18 40 9>9 8 37' 9,68910 29 j 6 55 Log. fine Sum *lo Co 39 log. fine \ hor. angle 9,94033 2 Hour angle 121 18 THE TIME AT SEA. Hour angle 121 i8 H. M. in time from Iaft mid. 8 5 Time per watch $ 21 Watch fall s. 12 O o 15 4# As the time is before noon, the fine of half the fum of the logs, is taken and doubled, which gives the hour angle, reckoned from the iaft midnight ; for there feems to be no neceflity for taking the co.fine of half the four logs, unlefs the obfervation be made in the afternoon. Anstber Method of finding the apparent Time. RULE. When the fun or ftar's declination and complement of latitude are both north, or ooth fouth, their fum*, but if one be north, and the other fouth, their difference is the meridian altitude. From the natural line of the fun or (tar's meridian altitude, fub- trac^ the natural fine of the true altitude. Then, the fum of ihe log. co-fee, of the comp. of the lat, the log. fee. of the fun or ftars decl. reje&ing their indices, and the log. of the difference of the natural fines being found in the co- lumn of riimg, the hour?, minutes, and feeonds correfponding to it, will be the true rime from the noon wh- n the altitude was t&ken. We ihall work the two foregoing examples by this method. EXAMPLE I. 0,11511 0,0 1 908 Co-latitude 50 6' o" N. Log. co-fee. Sun's decl. 16 51 30 N. Log. fee. left, rad. Meridian alt. 66 57 30 True alt. 15 54 39 N. fine 92022 N.fine 27386 Diff. nat. fines 64636 Its log. 4,81047 In col. of riling gives true time 50. 32' 3^" theapp. 1 time P. M. of the given day differing 2'' from the > 4,944.66' other method. ) EXAMPLE II. Co-latitude 38 30' o" N. Log. co-fee. Sun's decl. 6 27 57 S ^og & lefs rao. ^,20585 Meridian alt. 32 2 3 True alt. 13 4.1 23 DiiT nat. fines N. fine 5304.2 N. fine 23665 29377 Its log. 4,46803 4,67662 If the fum exceeds 90, fubtrad it frqm iJ?c% snJ the remalndtr will be tl* itude. 224 NEW METHOD OF FINDING Correfponding to 3h. 53' iS'', the apparent time from noon, which fubtra&ed from 12, leaver 8h. 6' 42", the apparent time on the morning obfervation. A Queftion fa Exercije. .At fea, April 18, 1806, in lat. 4.5 37' N. and Ion. 50 19' W. from Greenwich, at 4 h. 20' 30", P. iVl. per watch, the alt, of the fun's lower limb was found 25 20' 30", the eye of the obferver being 20 feet above the fur face of the fea. Required the apparent lime of obfervation ? True time Ship's time Watch too faft o To find the apparent 7 inn by the -Altitude of a fixed Star. Correct the ohferved altitude for the dip and refraction. Find the {hip's latitude by account, at the time of > bfervation. Find the-ftar's right afceufion arid declination in T. XV. From half the fum of the zenith diftance, co-latitude, and polar diftance, labtradt the ^e'nith diftance, noting the half fum and re- juainder. Then half the fum of the log, co-fee, of co-latitude ; log. co-fec,- of polar diftance; log. fine of the half fum , and the log. fine of the remainder will be the log. co-fine of half-hour angle, and when doubled, you will have the hour angle. Turn this hour angle into time, and apply it to the ftar's right alcenfion by fubtraiiing it when the ftar is eaft of the meridian, or adding it when it is weit of the meridian, their fum or difference will be the right afcenfion of the mid- heaven, or meridian. From the right afcenfion of the merdian (incrcafed by 24 if ncceflary) fubtract the fun's right afcenfion the preceding noon 93787 Halffum 119 54 13 Zen. dift. 61 49 50 Rem. f H < 30 15' 20" 2 Sine 9,92877 Sum 4 logs. 2)19,87281 Co-fine , 9,93640 H. M. S. H. M. S. Ho.ang.6o 30 40= 423 S.'s right afc. Sept. 7, n i 32 Ditto Do. 8, 1 1 5 8 Star's right afcenfion 7 29 8 . _^. Daily difference Right afcen. of mer. 3 27 5 Jncreafed by 24 o o 3,36X56009 gives o 3 36 2 10 16 25 33 O 2 10 16 23 23 12 Q" O 4 23 23 27 27 5 Time at (hip S.'s right afc. at noon 1 1 i 31 Cor. fubtra&ed Time at (hip nearly 16 25 33 True time Ship's Ion. 30 i 8' E. in time 2 I 12 After midnight Ti.atGreenw.nearlyi4 24 21 .1 ......... EXAMPLE II. Suppofe, on April 14, 1 806, in lat. 48* 56' N. Ion. 66 W. the obferved alt. of Aldebaran, when weft of the meridian, fhould be 22 Q 24' 29'', the height of the obferver's eye 2 1 feet above the fur- face of the fea. Required the true apparent time at fhip ? Obf.alt.ftarAldebar.22 24' 29" - 639 &ar's dec. 1806 16^ 6' jjT Ff 226 THE LUNAR OBSERVATIONS. H. M. S. Star's true alt, 22 17 50 Star's ri^ht afc. 1806 4 24 48 90 o' o" 90 o' o" 90 o" o> Lat. 48 56 o Dsc. 1 6 6 35 Alt. 22 17 50 Polar dirt. 73 53 25 Zen. difh 67 42 13 Co-lat. 41 40 Co-fee, 0,18248 Pol.dif. 73 53 25 Co-fee. 0,01740 Zcn.dif.O; 42 10 Sum 2)182 39 35 | Sum gi 19 47 Sins 9*99988 2en.dif.67 4 2 1O Rem. 23 37 37 Sine 9,60290 0's right afc. 1 4th I 29 9 Di^to 1 5th i 32 51 Sum 4 logs. 1)19,80266' Daily difference -o 3 41 Hi. < 37 to' 40" Co.fine 9,90133 2 Ho.ang. 74 21 20=n 4 57 25 3' 41" X , 5124 gives i' 53" Stir's right afc. 4 24 48 H. M. s. Right afc. of mcr. 9 22 13 App. time atiliip 7 52 50 Sun's right afc. ' 1 28 16 Correction O i 53 App. time at fhip 7 53 57 True time at fhip 7 50 57 Loru 66 W. in time 4 24 o - App. time at Green w.i 2 17 57 NOTE. This method of finding the time is certain, could a irood horizon be obtained in the night ; but as that is feldom the cafe, it is beft to regulate*thc watch by the fun. The A'Lti~d sffnd:nv the LONGITUDE by the M-JOt^s "Difl the Sun or a fixed Star, commonly called. THE LUNAR O ance from OBSERVA- TIONS. A VARIETY of methods for difcovering the longitude have at different times been brought forward, the rnoft celebrated and practicable of wh;ch is that by means of mcafurincr the angular diftance of the moon from the fun or a fixed fear. This method was. originally propofed by John Werner, but owing to the imper- fection THE LUNAR OBSERVATIONS. 227 fe&ion of inflruments for meafuring the angular diftance, and the insufficient knowledge of the moon's, true place, it could not, /in his time, be brought to the degree of accuiacy to which it is at prefent arrived. Thefe difficulties are at length happily furmountedby the inven- tion of Mr. .Hadley, in producing his Quadrant and Sextant ; and by the ingenuity of Profeflbr Mayer, of Gottingen, who has fuc- ceededin conftfu&iiig tables agreeing to the moon's motion in every part of her orbit, with furprifing exa&nefr, Finding the difference of longitude between any two places, may be reduced to the problem of finding the difference of lime between two places. For, as it is evident that the fun paiTes over a whrols circle of the earth, or 36^, in 24 hours, it follows that the dif* ference of time between the noon of one place and another, will always be the fame proportional part of 24 hour?, as the difference of their longitude is of 360. And the difference between any two given inftanis of time iv'i! b: in like preptiftfan. For if an obfc-rvcr knew that at the fame inftant that it was two o'clock in the after- noon under the meridian where he was, it was only mid-day at another place, it would be clear he was 30 to the eastward of the given place : fince 24 h. : 2 h. : : 360 : 30, and the longitude is eafr, fince the time at the place of observation is Jatelt. To afceriiain the, difference of longitude between the firft meri- dian and a given place, the angular diilance of the moon fiom the fun or a fixed ftar is to be obferved. For as- the dlftartce of the moon from the fun and feveral fixed flars eafi and weft of her is given in the Nautical Almanack, for every three hous, calculated for the ^meridian of the Royal Obfervatory ac Greenwich, it is clear that the di fiance between the fame objects being obfervel at any other place, the time- at Greenwich miy be deduced therefrom'j which, compared with the apparent time, points out the difference of time, a"ndj confequently, the difference or longitude between the two places. As the angular diftance of .objects is conceive-] to be me;' from their centre?, the obferved diitance muft be cleared i effects of parallax and rsfra -tion, in order to obtain the true tance. For effecting which purpofe, tha following methods, by_ Mi". Ly^ns and Mr. Wiuchell, arc iLc uu.ti: ia uie. ike nfcc/fu/y Preparations for working a L rtna r O fc^ iff. To reduce the time at fliip. to the tin^e at jCJreeawichr, r l"urn t!ie longitude of the fliip, carried forward to the time of obf.rva'ion, into time, by allowing 15^ for frvery hcur, a> to the time at ihip, if the longitude be weir, or iubtra-*< ii eait; the fumor difference v/ili be the fuppolsd time at Green v.'icli, which call reduced time. ad. To correct the ubkrved altitude of the fun or ilar. Take '' Ff2 228 THE LUNAR OBSERVATIONS* Take the fun's femi-diameter from pige 2 of the month in the Nautical Almanack, from which fubtract the dip of the horizon ; the remainder, added to the obfer ed altitude of the lower limb, or the fum fubtradted from the obflrved altitude of the upper limbj will give the true altitude of the fyji'j centre. From the fun's refraction take his parallax in altitude, the re- mainder will be the eorrelion of the fun's altitude. This cor- rection, fubtracted from the apparent altitude, will give the true al- titude of the fun's centre. If a ftar has been obferved, from the obferved altitude fubtradl: the dip of the horizon, the remainder is the ftar's apparent ki- tude, from which take the refraction anfwering to that altitude, the remainder is the liar's true altitude. 3d. To correct the obferved altitude of the moon* Take the moon's femi-diameter and horizontal parallax from page 7 of the month in the Nautical Almanack, for the neareft noon and midnight before and after the reduced time, and rind their difference, which multiplied by the number found in Table XVIII, correfponding to the hours and minutes of reduced time, gives a number of feconds, which being added to the moon's fei-i -diameter at the noon or midnight immediately preceding the reouced time, if it be increafmg, but fubtracted therefrom, if de- creafing, the fum or difference will be the moon's femi-diameter at the time of obfer vation. To the moon's femi-diameter, thus corrected, add the augmentation anfwering to her obferved alti- tude, the fum will be the moon's true femi-diameter : when the reduced time is any even part of 12 hours, as f , }, |, or ; fuch parts of the difference of the femi-diameter and horizontal parallax may be taken and applied as above, without being at the trouble of working by the numbers in Table X VIII. From the moon's true ieiiii-diameter fubtract the dip of the horizon, the remainder, added to the obferved altitude of the lower limb, or their fum fubtracted from the obferved altitude of the upper limb, gives the apparent altitude of her centre. To obtain the correction of the moon's altitude, proceed as follows : Having taken out the horizontal parallax at the noon and mid- night immediat ly before and after the reduced time, and having found their difference, as before directed, Multiply it by the number found in Table XVIII, corre- fponding to the hours and minutes of reduced time, gives a num* ber of minutes and feconds, which, being added or fubtracted from the horizontal parallax, at the noon or midnight immediately pre- ceding the reduced time, according as it is increafing or decreafing 5 the fum or difference will be the moon's horizontal parallax at the ducri time. To the prop, log of the moon's horizontal parallax add the Jo*, fecant kfs radius of the moon's apparent altitude, the Aim will THE LUNAR OBSERVATIONS. will be the prop. log. of the moon's parallax in altitudes from which take the refraction, the remainder will be the correc- tion for the moon's altitude* 4th. To correct the obferved diftance, To the obferved diftance of the fun and moon's neareft lirnbs, add both their femi -diameters, and the fum will be the apparent diftance of their centres. To the obferved diftance of the monn from a ftar, add the moon's femi-diameter, if her neareft limb was taken, but fubtradt it if her fartheft limb was taken, the fum er difference wili be the apparent diilance. NOTE. There are 12 pages in each month in the Nautical Almanack. The Tun's dedication is found in page II, The fun's femi-diameter III. The moon's fcmi-dia. and horizont. parallax VII. The diftance of the moon from the fun, &c. VIII. IX. X. XI XIL Having the apparent Altitude of the Qbjcft^ and their apparent to find their true Diflance^ by Mr. L vow's Method. I ft. Add together the prop, log of the corr ction of the fun of #ar's altitude, die log. to-fine of the fun or liar's apparent alti- tude, rhc log fine of the apparent diflance, and the log co-fecant of the moon's apparent altitude ; their fum (rejecting 30 irt the in- dex) will be the prop, log of the firft arch. 2d. Add together the prop log. of the corre to determine the Longitude. IN the Nautical Almanack, among the distances of the objects, look for the computed diftance between the moon and the other object, obferved on the given day ; if it be found there, the time at Greenwich will be at the top of the column, but if it falls between two diftances, as it generally will, take the difference between the diftances that ftand immediately before and after the computed dif- tance, and alto the difference between the diftance {landing before it and the computed diftance. . Then take the proportional logarithm of the firft difference, which is the difference in three hours, and the proportional loga- rithm of the fecond difference, which is the difference between the computed diftance and the diirance before it. The difference between thefe two logarithms will be the propor- tional logarithm of a number of hours, minutes, and feconds, which being added to the time Handing over the fir ft diftance in theNau* tical Almanack, will give the true time at Greenwich. The difference between Greenwich-time and that at the {hip turned into longitude, will be the longitude in, at the time the obfer vat ions were made, which will be eaft if the time at the (hip be greater than that at Greenwich, but if it be lefs, the longitude will be weft. Or the proportional part of time may be found by faying ; As the firft. difference : is to 3 hours : : fo is the fecond difference : to a proportional part of time, which being added as above directed will give the true time at Greenwich. NOTE. In working the following examples, it will fave feme time, if all the lopa- tithrnic fines, ungcnts, fecants, and proportional logarithms, which ftill at the fame opening THE LUNAR OBSERVATIONS. opening of the book, he taken out at the lame time, both in the Cut andfecond part oi the operation. Thus, the co-fine and co-tangent of the ftar's apparent altitude, and co-fccant of its altitude, may all be taker, out at the fame tim?, and written down in different parts of the paper (or in a formul, .y the- :o-f U K>, co-tangent, md co-fecant of the moon's apparent altitude, the fine andtangrat of the apparent diilance. and the fine and tangent of the diftacce corrected, for the refraction of the fun or fkr. EXAMPLE!. ^Suppofe, on the 23d of May, 1809, in longitude 13 13' weft of Greenwich by account at Oh. iom. P. M. by a watch well regu- lated, the diftance of the fun and moon's nearcPc limbs were ob- ferved to be 104 38' 14", when the mtx Vs altitude of her lower limb was 43 20' 2o'', the altitude of the fun's low-er limb 12 39' 28'', the eye of the obferver 20 feet above the fur face of the fea. Required the true longitude? II. M. M. S. M g; Time by watch 6 10 T ; 'sfemi-dia.n. 15 41 V- > ; , her. pnr. at noon ^7 .;; Long, in time 4- 54 Do. midnight 15 49 Do. midnight Vft ' 'I Red. time i 4 Diff. in ?2 hours -f 8 Diff. in 12 hours'" -f l3 ' *> -i- 5 a8 x 5888 gives -f 16 G'sobf.alt.ia39'i3' ;;' t r-nu-du.naon5 41 \. ' s par. at noon 5- -3 Dip 4 17 i" 3Z 15 46 ).- *s par. at red. ti. 57 49F.L. ,. ^Augmentation n) 'sap. alt. 43 3 2 Sec. App. alt. iz 5^ o * ' G'^"ef.46 ? __ w ^ 7) 's femi-dia. 15 57 D '* par. 'in alt. G'spar. 95 ''Dip 4 17 Refraction G'struealt. 12 47 3 n 40 I 's correction '4 v-bs. alt. 43 20 20 Ap. dill, of Q aod }) ' . GandJ, J sfemi.d:a. 15 ^9 + 1547 3 r ^ Vf }; 'sap. alt. 47 32 o ,^ . i's App. dilc. ice To find the Diflance by. Mr. L vow's ALi'h*:'. D, M. S. Cor.f rG'sap. alt. 3 57 P.L. .1 6587 p. j,. l 6587 G'sap, alt. 1251 o Co-fmcp <;. Co-tang. 0-641* App. Dift. 105 10 o Sine 9 9846 TaiJ'spar. 23 31 Dift. correc. for 0's refradticn 105 13 7 THE LUNAR OBSERVATIONS. Dift. cor. for 0's ret. and prin. ef. of ]J 's par. 104 49 36 To determine the Longitude. True diftance 1044933 Dift. at 6 hours 104 13 8 104 13 8 l)o. at 9 hours 105 46 19 36 25 P.L, 6940 i 33 ii P.L. 1859 Time over firft dift. 6 - - J TO 20 P.L. 4081 N.B. The longitude is True time at Greenwich 7 xo 20 Weft, bccaufe the time Time at ihip 6 10 at the fhlp i* leaft. ' " Long, in time . i o 2,0 ~ 15 5* W* EXAMPLE II. Suppofe^ on the ioth of March, 1809, in longitude 23 eaft of Greenwich, at 5 h. 36 m. P. M. by a watch well regulated, the diftance of the fun's neareft limb to the fun was 68 9' 57", when the altitude of the fun's lower limb was 31 48' 9", the alt. of the moon's lower limb 23 41' 7", the height of the eye of the ob* ferver 18 feet above the lea, the true longitude is required ? K. M. M. S. M. S. Time at Ship 5 36 D femi dia. at noon 16 i hor. par. noon 58 48 Long, m time I 32 Do: at midnight 15 58 Do. midnight 58 35 Ked. time 4 4 diff. in n hours 3 diff. in 12 hours n 3 X ,338S gives i n X ,3388 gives 4 Obf.alt.of0 LL 31 48 9 femi-dia. at n. 16 i hor par. noon 58 46 Qfemi-dia.t6 7 ? . ' I)ip. 44 S 3 femi-dia. 16 o H. P. red. time 58 42 P L 4866 Augmentation 7 )) app. alt. 24 o 10 Sec. 0393 Rtfrac. 131? . 44 D femi-dia. 16 7 }) par, in alt. 53 3 8 ar ^"* di. icr 1 8 feet refrac. - a 8 . alt. 31 o 12 ac. 131? . 44 par. ^5"* dip. icr 1 8 feet 4 4 refrac. (i) true alt. 31 58 49 iz 3 cor. D alt. 51 36 ; - . D Obf. alt. 13 41 7 - -- Ohf, dift. and D 68 9' 57" j) App. alt, 24 10 dia. and ]) 16 7 + 16 7 + 32- 14 . dift. of centres 68 4211 To find the Dlftance fa Mr, Lyorfs Method. Cor. f*r^'a. alt. i' 23" P.L. a 1143 p - L - * . 0'sapp. alt. 32 012 Co-fme 9 92^4 Co-tang, o 2042 . diftance 684211 Sine 99693 Tang. 04091 },'sapp.uh, 24 to Co-fee, o 3907 . , 2darc. ai"PX.2 7270 JPiifl are, 43 P. L. 2 4027 ift arc. 43 Correlion for 0's refrac. App. dift. Corrected dift, 63 42 33 for 0's ref. THE LUNAR OBSERVATIONS. 233 Cor. for J) 's app. alt. 5 r 30 l)'s app. alt, 24 o 10 Corrected diftance 68 42 33 G's true altitude 31 58 49 Third arc. P. L. Co-fine Sine Co-fee. P. L. P. L. 5435 Co-tang, o 3514 Tang. o 4093 O 5435 9 9607 9 9693 o 1761 4th arc. 8' 56'' P. L. I 3043 O 7496 3d. arc. 32 % Principal effe&s of }) 's par. 23 6 Dift. corrected for Q's refradion 68 42 33 Firft corrcaion in Table XXVI 9 7 ..- Second ditto ditto *J d ' fferencc True dift. To determine the longitude True diftance By Nau. Aim. the dift. at three hours 68 49' 8" Ditto at fix hours 67 13 6 H. M. s. diff. i 40 35 diff. i 36 * + 5 8 M 55 + 3 time at (hip diff. long in time 68 19 34 68 19' 34 " 68 49 8 29 34 P. L. 7845 P. L. 2729 H. M. S. ... . 3 55 25 P.L 5116 5 36 i 40 35 *5 0i/ 45"E 25 8 45 Long. eaft. EXAMPLE III. Suppofe that about f paft four P. M. on the 26th Nov. 1809, in lat. 54 V 25'S. long, by account 10 E. fix obfervactons were made, the mean of which were taken at 4hs. 44m. arid the altitude was 27 42' 35'' the error of the inftrument, 24", to be added, the eye of the obferver 21 feet above the furface of the fea, required the true time ? " M * o / // o / // Mean time at fhip 444obf. alt. Q L. L. 274235 zen. dift. 62 6 49 Long. 10 E. 40 error of quad. + 2400. lat 3535 o co-fee, o 23" 16 Ti. at Greenwich 4 4 0'sfe.di. 16 14 ) 27 4259 Dip 4235 + 1151 1664445 >9 2 56 co-fee, o 02971 Ditto 27th 21 75zref. Diff. in 24 hours 1113 n'i3"X,i695gives-f- 47 true alt. Long. 10 E. gives 22 G's dec. Pol. dift. 2057 44 zen. dift. 90 latitude 69 256 832222 fine 9 99708 62 6 49, Co. lat. 3535 H. M. o in time 4 44 On the fame evening the following ebfervations were made of the diftance of the ftar Regulus from the moon's fartheft limb, Ion. by account as before, and the error of the inftruments by which the moon's altitude and dirtance were taken was 7' 30' 25'' to be added; the true longitude Is required? G g Times ., THE LUMAR OBSERVATIONS. Mean Time at (hip Long, in time . Reduced time "J ' ie- dia. noon Ditto midnight Diff. in Ti hours J's femi-dia: Augmentation ) 's fcmi-dia. Dip ;, 'a Obf. alt. 's ap-p. ult. Times. Alt. of Regulus. Alt. of D's Low. Limb. Dift. of ) and * H. M. S. 10 44 37 10 27 29 10 33 4 10 3z 8 10 34 16 o / A 19 5 30 2O i o 20 15 o 20 29 20 40 o / // 19 54 43 '9 9 43 19 28 13 19 48 43 19 57 43 o / // 3* 30 43 3i 3 3 3i 33 3 1 34 o 3 r 35 45 js 3834 101 16 30 97 M 5 157 44 58 10 33 43 20 15 18 T? 29 49 + 7 30 31 3^ 59 + 25 10 33 43 20 15 18 19 34 19 3i 33 2 4 H. M. 10 33 i 40 3 I 's h Ditto or. par. noor midnight t 54 16 54 23 9 53 * n 14 i t 14 4 ,3 Diff. J tf 7X8 9 U 's h n 12 hours 25 gives or. par. noon + 7 + 6 54 16 )'sapp. alt. 54 2: 19 44,50 P. L. o 5*9.9 Sec. O 020-:; 19 44 5 Obf. dift of),, and-/: 31 33 24 Hor. p;r. rtd. ti. 51 10 Refradtion 2 37 )'s co reel ion #'sobf. alt. Dip. **s app. alt. Refraction i dia. 14 54 20 821 #'s true alt. Ap.dift.ofQ& D centre 18 30 To find the Diflance by Mr. LYON'S Method. }c'scorrec. 234?-!- 18459 P-L. 18459 , ff -^;'s app. alt. 20 1055 co-fine 9 9725 co-tang. 04347 tr.dift.3i 13 43 App. dift. 3 1 1830 fine 97157 * tan g- 9 784odift 9)1.31 41 D^s app. alt. 19 44 50 co-fee. 04713 f /y . 2d arc. i 33 P. L. 2 0646 Firft arc. i 46 P. L. a 0054 ift.arc i 46 firftdiff. 27 19 + 13 31 18 30 dift. at9h-3i 41 a diftati2h-30 13 9 Diftance correAed for the -,< J s refrac. 31 18 43 o / // ^'ecorrec. 48 33 P.L. 95691 P.L. o 5691 2d diff. i *7 53 V 's ap. alt 1944 50 co fi. 9 9737 co-tan. 04449 ift diff. 27 i9p.l.Si8S Cor. dift. 31 1843 fine 9 7 ] 57 tang. 9 7841 2d diiF. i 27 53p-1.37 r. alt. 20 821 co-fe. 0463 1 4th ar. 38 39 P.L. 07981 Third arc. 34 u P.L. 7zj6 3d arc. 34 n Pnn . effects of the \ >s par. 532 ti. i ft diiF. 9 Cor. Tab. XXVI, 33" Ditto 33" J i 5 diff. True dift. 3 IJ 343 3 1 ^3" + 3* Greenwich time 9 55 58 Time at fhip 10 33 43 Ltng. in time 37 45:1:926 ijE, THE LUNAR OBSERVATIONS. 3$ Here I have given one method of finding the longitude, illuf- trated by a fufficient number of examples, all of which are reduced to the year 1809, in order that the reader, or teacher, may have fuf- ficient time to furnifh himfelf with a N. A. for that year, which is now printed. But as many would wifh to have fome other me- thod of reducing Ihe diftance, that, by comparing them together, they may not only have the advantage of proving their calculations, but alfo of making choice of which they prefer to work by; the fe- cond method I fhall prefent the Reader with, is chiefly deduced from that invented by Mr. Witchell, late Mailer of the Royal Academy at Portfmouth, as it is fhort, and requires but four places of figures in the logarithms, befides the index j the preparations in both me- ,thods being exactly the fame, RULE. Firft. Add the fun, or ftar's amd moon's apparent altitudes to- gether, half the fum; fubtract the lefs from the greater, and half the difference; then add together, the co tang, of half the fum, the tang, of half the difference, and the co-tang, of half the apparent diftance; their fum (rejecting 20 in the index) will be the log. tang, of an angle, which call A. Secondly. When the fun or ftar's altitude is greater than the moon's, take the difference between angle A, and half the appa- rent diftance ; but if lefs, take their fum. Then add together the co-tang, of this fum or difference, the co-tang, of fun or ftar's ap- parent altitude, and the prop. log. of the correction of the fun or ftar's altitude; their fum (rejecting 20 in the index) will be the prop. log. of the hrft correction. Thirdly. If the fum of ang'e A and half the diftance was taken in the laft article, take now their difference, but if their difference, now take their fum ; then adu together the co-ta,;g. of the fum, or difference, the co-tang, of the moon's apparent altitude, and the prop. log. of the correction of the moon's apparent altitude; their fum (rejecting 20 in the index) will be the proportional loga- rithm of the fecund correction. Fourthly. When the an^le A is lefs than half the apparent dif- tance, the firft correction mult be added to., and the fecond fubtracted from, the apparent diftance; but when the angle A is greateft, their fum muft be added to the apparent diftance,. when the fun or ftar's altitude is lefs than the moon's ; but when the moon's altitude is leaft, their fum muft be fubtracted to give the corrected diftance. Fifthly. In Table XXVI. look for the correfted dift. in the top column, and the correction of moon's alt. in the left-hand fide column ; take out the number of feconds that Hand under the for- mer and oppofite to the latter. Look again in the fame Table for the corrected diftance in top column, and the fecond correction in the left-hand fide column ; take out the number of feconds that ftand under the former and oppofite the latter, the difference be-- 2 G 2 tweaii 236 THE LUNAR OBSERVATIONS. tween thefe two numbers will be the third correction, which muft be added to the corrected diftance, if lefs than 90, but fubtradted from it, if more than 90; the fum, or difference, will be the true diftance. To illuftrate this laft method of reducing the apparent diftance to the true diftance, I (hall take the apparent altitudes and diftancesas they ftand in the firft examples, worked by the former method. EXAMPLE I. See Example I. p. 231. Given, the apparent diftance of the fun and moon's centres, 105 10' o", the fun*s apparent altitude 1 2 5 i f , that of the moon 4^ 32', and horizontal parallax at reduced time 57' 49". Required the true diftance of their centres by Mr. Witchell's method . ? M. s. O's refrac. 4 6 D's hor. par. at red. ti. 57 49 P.L. o 4932 r O.'s parallax 9 D's ap. alt. 42 32 Sec. o 1397 's correc. 3 57 )> 's par. in alt. 41 55 P.L. 6329 Refraction i D 's correction 40 55 O'sap. alt. 1 2 51' o 3)'s ap. alt. 43 31 o Sum 56 23 o Half fum 28 IT Co-tang. 10 2710 DifF. 30 41 o HalfdifF. 15 20 Tang. 9 4381 Ap. dift. 105 10 o Half dift. 52 35 Co-tang. 9 8837 ift. cor. -f- 38 _. Arc A 21 23 Tang. 9 5928 2d cor. 23 33 Sum 73 58 Co-tang. 9 4584 O'sap. alt.12 51 Co tang. 10 6418 104 49 35 O's cor. 3 57 P.L, J 6587 3d cor. 3 _ ift. cor. 3 8 P.L. i 7589 t Tr. dift. 104 49 32 DifF. 31 12 Co-tang, o 2178 }) J sap.alt43 32 Co-tang. O 0222 >'scor.4o 55 P.L. o 6434 2dcor. 23 33 P.L. o 8834 EXAMPLE II. See Example p. 232. Given, the apparent diftance of the fun and moon's centres 68 Q 4'2' n", the fun's apparent altitude 32 o' 12", apparent altitude of the moon 24 o' 10", the fun's correction i' 23", the moon's correc- tion 51' 30". What is the true diftance of their centres by Mr. Witchell's method? fun's THE LUNAR OBSERVATIONS. 237 0*sap.alt 32 o 12" 2/'s ap. alt. 24. o 10 Sum 56 o 22 Half Turn 28 o' 1 1' 1 Co-tang, o 2743 Diff. 802 HalfdifF. 4 o I Tang. 8 844.7 Ap. dift. 68 42 Ji Half dift. 34 21 5 Co-tang, o 1653 jft. cor. -f 22 Arc A 10 53 30 Tang. 9 2843 68 42 33 2d cor. 23 8 Diff. 23 27 35 Co-tang, o 3625 _P Q's ap. alt 32 o 12 Co-tang, o 2042 68 19 25 0's cor, i 23 P.L. 2 1143 3d cor. % -f- 7 . , _ i ft. cor. 22 P.L. 2 6809 Trusdift.68 19 32 Sum 45 14 35 Co-tang. 9 9963 D 'sap. alt. 24 o JO Co-tang, o 3514 I'scor. 51 30 P.L. o 5435 5>d correc, 23 8 P.L. O 8912 EXAMPLE III, See Example p. 233. Given, the apparent diftance of the moon's centre from the ftar Regulus 31 i8 ; 30", the apparent altitude of the Oar 20 10' 55", that of the moon 3i Q 18' 30'', the ftar's correction 2' 34", that of the moon's correction 48' 33''. What is the true diftance of their centres by Mr. Witchell's method ? #'sap. alt. 20 io'55 7 J) 7 sap. alt. 19 44 50 Sum 39 55 45 Halffum 19 57' 52'' Co-tang, o 4398 DifF. % ' 26 5 HalfdifF. 13 2 Tang. 7 5788 Ap. dift. 31 18 30 Halfdift. 15 39 15 Co-tang o 5525 ift. cor. -f 14 - Arch A 2 7 59 Tang. 8 5711 2d cor, 5 36 DifF. 13 31 16 Co-tang, o 6790 -/c'sap.alt. 20 10 55 Co-tang, o 4347 31 13 8 -X'scor. 2 34 P.L. i 8459 3d cor. -f 34 ift. cor. 14 P.L. 2 8996 True dift, 31 13 42 Sum 17 47 14 Co-tang, o 4937 D'sap.alt. 19 44 50 Co-tang, o 4450 J'scorrec. 48 33 P.L. o 5691 adcorrec. 5 36 P.L. 238 THE LUNAR OBSERVATIONS. Another Method. Firft. From half the fum of the apparent altitudes of the fun and moon, or moon and ftar, and the apparent diftance, fubtract the fun pr ftar's apparent altitude ; the difference call the firft remain- der, the moon's apparent altitude taken from the half fum leaves the fecond remainder. Secondly. To the log. fine of thirty degrees add the log. fine of the apparent diftance, the log. co-fine of the moon's apparent al- titude, the log. ft cant of the half fum, the log. co-fecant of the firft remainder, and the prop. log. of the moon's correction; reject the tens in the index, the remainder will be the prop. log. of the firft correction. Thirdly. To the log. fine of thirty degrees add the log. fine of the apparent diftance, the log. co-fine of the fun or ftar's apparent altitude, the log, fecant of the half fum, the log. co-fecant of the fecond remainder, and the prop. log. of the fun or ftar's correriion ; rejecl: the tens in the index, the remainder will be the prop. log. of the fecond correftion. The difference between the correction of the moon's altitude, and the fit ft correction, call the difference of corrections. ' Enter Table XXV 7 !. with the apparent diftance at the top, and the moon's correction in the left-hand fide column, the correfpond- ino; number will be the third correction ; in the fame column, and correfponding to the difference of corrections, you may find the fourth corredtion. Fifthly. Subtract the moon's, the fecond, and fourth corrections from the apparent diftance, to the remainder add the fun or ftar's, the firft and third correction; the fum will be the true diftance. EXAMPLE. I. See Example p.- 231. Given, the apparent diftance of the fun and moon's centres 105 10 ; , the fun's apparent altitude 12 51', that of the moon 43 32', the. fun's correction 3' 57'', and the moon's correction 40' 55". Required the true diftance ? 30 o' Sine 9 6990 9 6990 2'scor. 40' 55'' Ap. dift. 105 10 Sine 9 9846 9 9846 2d cor. 49 D'sap alt. 43 32 Co-fine 9 8603 4th cor. 19 G'sap.alt. 12 51 Co-fine 9 9890 Sum 161 33 105 10 o Half fum 80 46 Secant o 7946 o 7946 ift. rem. 67 55 Co- fee, o 0331 104 27 57 2d rem. 37 14 Co-fee. O 2182 G's cor. 3 57 G'scor. 3 57 P.L. 2d i 6587 ift. cor. 17 23 i'scor. 40 55 P.L. 9 6434 cor. 3d cor. 16 - 49"PL,2 3441 ift. cor. 17 23 P.L. i 0150 Truedift. 104 49 33 Dif. cor. 23 32 EXAMPLE THE LUNAR OBS LR V AT ION S. 239 EXAMPLE II. See Example p. 2- Given, the apparent diftance of the fun and moon's centres 68 42' 1 1", the fun's apparent altitude 32 o' 12", apparent altitude of the moon 74 o' 10", the fun's correction i' 23", the moon's 5 t' 30. Required the true diftance ? Ap. dift. i 'sap. alt G'sap.alt Sum Half fum ift. rem. 2d rein. G's cor. D J s cor. ift. cor. 33 68 .24 3* o' 42 o o o" Sine ri Sine io Co-fi. 12 Cc-fl. 9 9 9 6990 9 6 93 9607 3335 2964 5435 8024 9 9 9 o 2 2d - cor- ?. i'o"P. 6990 D'scor. 57' 9693 ad cor. i 4th cor. o 9284 Sum 52 8 42 3335 6 7 49 2073 >s cor - "*" l 1143 ift. cor. + 28 3d cor. 4- 2518 L. True dift. 8 19 so- o r 3 ii 40 2 3 22 9 34 124 62 3 38 42 21 21 21 I 51 28 33 16 4 6 23 30 22 Secan'O Co-fe.o t^o-fec. P.L. P,L. o P.L. DirF. of cor. 23 8 EXAMPLE III. See Example p. 233. Given, the apparent diftance of the moon's centre from the ftar Regulus 31 18' 30", the Apparent altitude of the moon 19 44' 50", the apparent altitude of the ftar 20 ic' 55'', the ftar's correction 2 ' 34" ? the moon's correction 48' 33". What is the true diftance of their centres ? 30 o' o" Sine 9 6990 ^9 6990 D's cor. 48'33" Ap. dift. 31 18 30 Sine 9 7157 9 7157 2d cor. 2 2$ Fsap.alt.iQ 44- 5 Co-fmeg 9737 4th cor. o v^sap.alt.20 10 55 Co-fmeg 9725 --- _ Sum 50 53 Sum 71 14 15 Ap. dift. 31 18 30 Half fum 35 37 7 Secant o 0900 0900 -- - ift.difF. 15 26 12 Co-fec.o 5748 30 27 37 2d. difF. 15 52 17 Co-fee. . o 5631 ->'s cor. -f 2 34 -v^'scor. 2 34 P.L. 2d i 8459 i ft. cor. -4-42 57 D'scor. 48 33 P.L. o 569100^ --- 3d cor. 4- 34 --- ,'2GJ 8862 --- jft. cor. 42 57 P.L. 622 2 P.L. True dift. 31 13 42 DifF. of cor. 5 36 The difference in th& Jaft method is that there is no variety of cafes. jueftious for Exercife* Suppofe, on the 23d of May 1805, in longitude 9 weft of Greenwich, by account at 3 h. 41 m. 15 f. P.M. by a watch well regulated, the diftance of the fun and moon's neareft limbs (hould be 24O THE LUNAR OBSERVATIONS. be obferved to be 67 5' 36'', at the fame time the altitude of the fun's lower limb fhould be 31 48' 15'', the moon's 23 48' j 5'', the eye of the obferver being 18 feet above the furface of the fea. Required the true longitude of the place ? dnjwtr. u"20 l 15" weft. Suppofe, at fea in longitude of 10 weft by account, on June the 5th, 1805, the mean of five obfervations were taken; viz. at 3 h. 17 m. 20 f. P.M. the diftance of the fun and moon's neareft limbs were 106 18 m. 12 f. the error of the fextant 2 m. 37 f. the al- titude of the moon's upper limb 20 4' 6'', the error of the quadrant I m. the altitude of the fun's lower limb 45' 22' 3'', the error of the inftrument 48 f. the eye being 21 feet above the fea. Re- quired the true longitude ? Jin fiver. 5 59' weft. Suppofe, on the ift. of January 1806, in longitude 8 eaft of Greenwich, by account at 5 h. 56 m. A.M. per watch well regu- lated, the diftance of the moon's fartheft limb from the ftar Pollux fliould be 62 52' 28'', the altitude of the moon's lower limb being 15 19' 14'', and the ftar's altitude 29 51' 39", the eye of the ob- ferver being 1 8 feet above the furface of the fea, and the true lon- gitude fhould be required ? Anfwer. 7 36' 30'' eaft. NOTE. In veflels which afford only one obferver, it will be found fufficiently exact for practice to have a quadrant at hand, in order to take the altitudes of the objects immediately after the diftance is obferved, as the difference of altitudes which take place during the time fpent in the operation will be nearly infenfible. It is recommended to take the altitude of the fun firft. But as it may fometimes happen, owing to the obfcurity of the horizon, that the altitudes cannot bq taken, the following methods are given to ob- tain them by calculation : To find the Sun's true Altitude. It fometimes happens that the diftance of the celeftial obje&s may be taken, but for want of a good horizon, or affiftants, their altitudes cannot be taken at the fame time; to fupply fuch defi- ciencies, obferve the three following cafes. CASE I. The apparent time, the {hip's latitude, longitude, and the fun's declination given, to find the true altitude of his centre. RULE. If the (hip's co- latitude, and the fun's declination, be both north or both fouth, take their fum ; but if one be north and the other jfouth, their difference is the fun's meridian altitude. With the apparent time from noon, enter Table XXII-I. and from THE LUNAR OBSERVATIONS. 241 from the column of rifmg take out the logarithm corresponding to it. To this logarithm add the log. co-fine of the latitude, and the log. co-fine of the fun's declination. ^Their fum, rejecting 20 in the index, will be the logarithm of a natural number, which, being fubtra6ted from the natural fine of the fun's meridian altitude, will leave the natural fine of his true altitude at the given time. EXAMPLE I. Required the true altitude of the fun's centre, in latitude 49 57' N. when its declination is 19 26', at 6h. 56111. 305. in the morning ? H. M, S. 12 O O App. tirce 6 56 30 Time from noon 5 3 30 Its log. in coL of rifing 4,87850 Latitude 4957 N - Its log. co-fine 9>8o852 Decl, at that time 19 26 N. Its log. co-fine 9>97453 Co-lat. 40 3 o R Mer. alt. 59 29 o Nat. fine 86148 Nat. fine true alt. 40276 = 23* 45'. EXAMPLE II. What will be the true altitude of the fun's centre at London, when its declination is 20 49' S. at 3)1. 21 m, 305. apparent time in the afternoon ? K. M. s. App. time from N. 3 21 30 Its log. in col. of rifing 4>5590O Latitude 5i32'N. Log, co-fine 9^793^3 Decl. at that time 20 49 S. Log. co-line 9,97068 Co-lat. 38 28 N. Nat. num. 21062 log. 4, 3235^ Mer. alt. 17 39 Nat. fine 30320 Nat. fine true alt. 5 19 Nat. fine 09258 H h CASE 242 THE LUNAR OBSERVATIONS. CASE IT. foe Apparent Time, the Latitude and Longitude given, iofiml the Al- titude of any of the known fixed Stars. RULE. Turn the longitude into time, and add it to or fubtract it from the time at the fhip, according as it is eaft or weft, the fum or dif- ference will be the time at Greenwich. Take the fun's right afcenfion from the Nautical Almanack, proportion it to the time at Greenwich, and add it to the apparent time at the {hip, which will give the light afcenfion of the meri- dian, or mid-heaven. Find the ftar's right afcenfion and declination in Table Xli. and take the difference between its right afcenfion and the right afcen- fion of the meridian, which will be the diftance of the liar from the meridian. Having the {tar's diftance from the meridian, with its declina- tion and the (hip's latitude, the true altitude is found in the fame manner as has been {hewn in the laft examples of finding the true altitude of the fun. EXAMPLE. What will be the true altitude of Aldebaran, April IF, 1806, at 5h. 56m. 20 s, P.M. apparent time, in latitude 55 58' N,. and long. 3 6' W. ? H. M. s. App. time at {hip - * 5 56 20 Long, 3 6' W. in time - o 12 24. Time at Greenwich 6 8 44. Sun's right afcen. Apr. u,at n. by N. A. I 17 14 Prop, part, for 6h. 8m. 445. o o 56 Sun's right afc. at time of ofef. i 18 10 App. time at {hip - 5 56 20 Right afc. of the meridian 7 14 38 Star's right afcenfion 4 24 48 Star's dift, from meridian 2 49 42 Log. col. of rif 4,41803 Lat. - 55 58' o" N. L. co-fine 9,74794 Star's dec. 16 . 6 35 N. L. co-fine 9,98260 Co-iat. 34 2 o i '. Nat. n. 14079 Log, - 4>H-57 Mer, alt. 50 8 35 N, fine 76773 alt. 38 49 o N. fine 62694 CASE THE LUNAR OBSERVATIONS: 243 CASE in. The apparent Time, the Latitude and Longitude of the Ship being given, to find the true Altitude of the Moon's Centre. RULE. Turn the longitude into time, and if it be weft add it to, but if it be eaft fubtraft it from, the apparent time at the ftiip, and it will give the time at Greenwich. Take the fun'o right afcen. out of the N. A. and proportion it to Greenwich. time, which, being added to the time at the fhip, the fum will be the right afcenfion of the meridian or mid-heaven. Takeout of the N. A. the moon's right afcenfion and declina- tion, and proportion them to the time at Greenwich. Turn the moon's right afcenfion into time, and take the difference between it and the right afcenfion of the mid-heaven, which will be the diftance in time of the moon from the meridian. Having the (hip's lat. together with the moon's deelin. and dift. from the meridian, the true altitude is found, in the fame manner as has been fhewn in finding the true altitude of the fun andilar. EXAMPLE. What will be the moon's true altitude April 28, 1809, at 6h. 2om. P. M. in lat. 42 34' S. and long. 84 30' weft of Green- wich by account ? H. M. , App. time at fhip 6 20 Moon's dec. at noon 7 54 S. Long. 84 30' in ti. -f 5 38 2 io f x by, 9973 gives-f- 2 9 Red time u 58 Moon's dec, at red. ti. 10 3 H. M. s. G's ri. afc. 28 ap. 2 21 31 3>'s ri. afc. at noon 194 37 3' 45'' x,4986gtves + i 52 7 10' x, 9973, gives +79 Ri. afc. at red. time 2 23 23 20; 46 App. time at fhip. + 6 20 In time s: 6h. 4:7 OK 45. AR of the meridian 8 43 23 3> 's right afcenfion 6 47 4 D*s dift frommsr. Sip's latitude 5''sdec. Comp. lat Mer. alt. i 56 19 Log. in col. of rifing Log, co- fine Log. co-fine Nat* num. 57 29 Nat. fine 3 93960 986717 999328 _ 3 80005 True altitude 51 16 N. fine 78014 ^ In the laft example, proportional parts are taken in finding th right afcenfion, declination and log. rifln^. H h a Bv 244 E LUNAR OBSERVATIONS. By the three laft cafes the true altitudes of the obje&s are found, therefore if the apparent altitudes be wanted, the difference,, be- tween the fun's parallax and refraction mult be added to the fun's true altitude, the refraction muft be added to the true altitude of a ftar, and the difference between the moon's refraction and pa- rallax in altitude muft be fubtra&ed from the true altitude of the moon thus found , to obtain the refpeclive apparent altitudes of their centres. To find the Longitude ly the Edipfes of Jupiter's Satellites. On the day preceding the evening on which it is propofed to ob- ferve an eclipfe, look for the time when it will happen at Green- wich, in page 3d of the month in the Ephemeris. Find the diff. of longitude either by a good map, fea chart, or dead reckoning. Let the watch be regulated by the fun with all poflible exadnefs to the apparent time. Turn the difference of longitude into time, and add it to, or fubtra& it from, the apparent time, according as it is eaft or well of Greenwich, the furn or difference will be nearly the time when the eclipfe is to be looked for in that place. But as the longitude is uncertain, it will be proper to begin 20 or 30 mi- nutes before. Obferve the hour?, minutes and feconds of the beginning of the eclipfe, called immerlion, that is, the very inftant that the fatel- lite appears 'to enter into the fhaciow of Jupiter; or the ernerfion, that is, when it appears to come out of the fame. The difference of time between the obferved imrnerfion, or ernerfion, and that fet down in the Nautical Almanack, being turned into degrees, will give the difference of longitude between Greenwich and the place of obfervation. Thefe observations made on the firft fatellite, or that which moves neardi: to the body of Jupiter, is the moft proper for deter- mining the longitude ; and here it may be obferved, that its emer- {ions are not vifible from the time of Jupiter's conjunction with the fun to the time of his oppofition to the fun, and that its immer- fions are not vifible from the time of the planet's oppofition to the fun, to the time of its conjunction. The configurations, or the pofitions in which Jupiter's fatellites appear at Greenwich, are laid down every night when vifible, in page the 1 2th of the month in the Ephemeris. EXAMPLE. Suppofe on Jan. 8, 1809, in long. 18 23'E. by account, an emeriion of Jupiter's firfl fatellite was obferved at iih. 3m. appa- rent time, required the longitude I H. M. s. At Greenwich that day the ernerfion began at 9 50 26 Obferved cniej lion at {hip n 30 Diff, in time i 12 34 turned THE LUNAR OBSERVATIONS. 245 turned into longitude gives 1 8 8' 3c/'j,.becaufe the time at Green- wich is lefs than at the place of obfervation, the error in the lon- gitude is 5 miles and 49 fecants. As thefe eclipfes happen aimoft daily, they afford the moft ready means of determining the longitude of place on land, and then the longitudes of fea-coafts might be better afcertained than they are at prefent ; they might alfo be applied at fea, could they be ob- ferved'with fufEcient accuracy in a {hip under fail, which can hardly be done, fince the leaft motion of a telefcope that magni- fies fuificiently to make thefe obfervations, would throw the'ob- je&s out of the field of view. The eclipfes of Jupiter's fatellites may be well ohferved by one of Dolland's new achromatic telefcopes of three feet in length, or by a reflecting telefcope of 18 or 20 inches focal length. To find the Longitude by the Eclipfes of the Moon. This is performed by comparing the times of the beginning or ending, as alfo the times when any number of digits are eclipfed, or when the earth's fhadow begins to touch or leave any re- markable fpot on the moon's face. Then will the difference of time between the like obfervations made at different places, turned into degrees, be their difference of longitude, But thefe eclipfes happen too feldom to be of any general ufe at fea. To find the Longitude by a Chronometer or Time-keeper. Whea it is intended to make ufe of a time keeper^ it is requl- fite to examine its rate of going before you leave the land, and adjuft it to the meridian of the place from which you reckon your longitude. To do this, you muft afcertain the apparent time by the fun's altitude (or by fome other method) and apply to it the equation of time, taken from page 2, of the -Nautical Almanack, according to its title of add or fubtraft ; the fum or difference will give the mean time ofobfervation : this, compared with the watch, will fhew how much it is too fail or too flow, aad by obferving this difference for feveral days fucceili vely, you will afcertain its rate of going: if you find it gain or lofe a few feconds per day, you muft make that allowance on all future obfervations at fea. Infteadof comparing the time (hewn by the chronometer, to the mean time at the place ofobfervation found as above, you may compare it with that mean time reduced to Greenwich-time, by adding to that mean time the difference of longitude between Greenwich, and the place of obfervation, when it is to the weft- ward of Greenwich, but fubtradting it when to the eaftward ; an regulated your time-keeper, the loBgitude at fea is readily found by ic, as will evidently appear by the following examples ; EXAMPLE EXAMPLE I. Suppofe that on March 25, 1809, the apparent time was found by an altitude of the fun to be ih. 5m. 95. P. M. when, by a time- keeper well regulated to mean Greenwich time, it was 4-h. grn. 6s. P. M. Required the longitude? H. M. s, Apparent time - - 159 * Equation of time -{- o 612 Mean time I n 21 Time per watch 4 3 6 2 51 45 equal to 42 56' 15" of weft longitude, becaufe the time at Greenwich is greater than the time at {hip. EXAMPLE II. Suppofe that on Sept, 12, 1809, tne apparent time was found by an altitude of the fun to be4h. ^m. 6s. P. M. when the time per chronometer is 2h. P. M. the watch being too flow for mean Greenwich time i im. 9$. Required the longitude ? H. M. s. H. M. s. Apparent time 4 3 6 P. M. Time per watch 200 Equat. of time o 3 46 Watch error -J-o II 9 Meantime 3 59 20 P. M. Time at Greenw.2 n 9 P. M. Ti. at Greenw. 2 1 1 9 Diff. of time I 48 u equal to 27 2' 45" eaft longitude. OBLIQUE TRIGONOMETRY. AXIOM II. N all plane triangles the fides are in dire& proportion to the fines of their oppo lite angles. To find d Side. As the fine of an angle Is to its oppofite fide, So is the fine of either of the other angles in the &me triangle To the fide oppofite thereto. Tojind an Angle. As any fide ^given Is to the fine of its oppofite angle, So is either of the other fides in the fame triangle To the fine of its oppofite angle. CASE I. Two angles and one fide Z.EDC 100 oo' ^ven, to find cither of the /.DCS 54 oo *l'he angle BDCmoo and angle DCBrr 54- And the le^. BD~ zao* are given to find the fides. OBLIQUE TRIGONOMETRY. 247 CONSTRUCTION. Draw an indefinite line GF., add the two angles D and C together, and fi inor thurfum from 180 leaves the remaining angle B z(>'-\ on the line GE ; point as at B, Jefcribe the angle B 26, and on BH let oiTBD 2ac. On D mat <* The angle BDC 100, then DC will intericd: the line GE in the point C, which com- pletes the triangle, and BC will meafure on the fame fcale from which BD was laid down 268 nearly, and DC 119 alfo on the fame fcale. any To find CB. To find DC. 0,09204 9,64184 2,07633 Asthefiae of the ang.C 54" co. ar. 0,^9*041 As fine ang. C 54" co.ar. Js to the fiJe BD 220 3,342.41-1* to the fuk BD 220 So is fupt. fi. of ang. BDC 80 9,99335 ! So is fine ang. B 26' 1 | To the fide BC 267.8 3,43781 JTo fide DC 119.2 By Gunter. ift. The extent from 80 to 54, on the line of fines, will reach from 220 to 267 OB the line of number s for BC. 2d. The extent from 54 to 26, on the line of fines, will reach from 220 to no on the line of numbers for the lide DC. CASE II. and III. Two fide* and an angle oppofite to one of them being given, to find the other op- poiict ar: 3,80618 ;&o is. fi.,mg.B,or;csfuppl. 76 14' 9,98734 AC 3;>M. So is the iide AB 640 To fine angle C 50 14' Angle A add 26 o Subtract from Angle B 103 46 wiU bTIcu^TT t V )bf ?' Ve '. that if ', he & 1 an S Ie be H*fci the an ,*L- ***** WiU be acute ; hut when the given angle is acure, and opp.olite a ^ivcn lefier f iU fupplemcnt to 180 mult be By Gunter. oritsfup. 77 305 To fide AB 149-3 W417 By Guntcr. ift. The extent from 190 to 30, on the line of numbers, will reach from 38 43' to 7 13' on the line of tangents for half difference. 2d. The extent from 77 30', which is the fupplemcnt of 102 30', to 31 32 on the line of fines, will reach from 80 to 149 3', on the line of numbers, for the fide AH required. The Learner may be at a lofs how to know to which angles the above fusn and dif- ference belong, but let him remember the greatefl angle is oppofite to the greateft fide, and the contrary, which will determine it. AXIOM IV. In any plane triangle, it will be As the greateillide Is to the fum of the other two fides, c o is the difference of thofe fides To the difference of the fegments of the bafe made by a perpendicular, let fall from the angle oppofite the bafe. And half the difference of the fegments added to half their fum will give the greater fegment, but if fubtradied from their half fum will leave the leffer fegment, the triangle being thus cut becomes two right angled triangles, the hypothenufes and bafesof which arc given, to find the angles by Axiom I. in right angled Trigo* liomctry, page 34. CASE OBLIGUE SAILING. CASE VI. The three fides of a plane triangle given, to find the angle* The fide BA 88, BC 54. AC 108, given to find the angles ABC, 3BCA. BAG, CONSTRUCTION. Draw the indefinite right line FG, on which, from any point therein, as at A,fet off AC 108, then, 88 in your compafles, and one foot on the point A, fweep an arch alfo with the diftance 54 in your compaffes, and one point on C, fweep another arch interfering the former arch in the point B, and it is done ; BA, BC, AC, will mea fure 88, 54> 108 refpe&ively on the fame fcalc. The proportion by Axiom IV. AB 88 To find AE~ AD DC the diff. of ferments, BC 54 142 Sam of fliortcft fide* 34 Diff. ditto Halfbafe 54 Half diff. fcgm. 2^-3 As the fide AC ir>8 co. ar. 7,96658 Is to th^ fum of fides A B and BC 142 2,1977.9 So is diff. tides AB and BC 34 i ,53 148 To AE the diff. of feg. of bafe 44, 7 1,6503.? AD - 76,35 Great fegm. DC 31*65 Leaft fegm. Half **, OJ Having divided the triangle into two right-angled triangles, the hypothenufe and bafes of which are given, to find the angles by Axiom I. as follows : To find the angle DAB. As the hypothtnufeAB 88 co. ar. 8.05552 Is to radius 90 zo.ocoo 15 LV Ai**--*w s So is fide AD the great feg. 76.35 1.88281 To fine ang. CBD 60* n> 90 Thecom.isang.A=z*9 49 To' find the angle DBC. As hypoth. BC 54 co. ar. 8.26761 Is to radius 90 lo.eooo So is DC 3 1. 65 1-50037 To fi. ang. CBD 35 53' 90 976798 Its com. ang.Crr 54 07 -fang. A. 29 49'rr 83 56 and 18083 5'.i ; ang. B 96 4' OBLIQUE SAILING. 'E come next to the doctrine of oblique triangles applied to problems of fail- ing: and though it may be applied to the meaiuring of inacceflible objects, yet we Ihall confine it to thofe problems which are more immediately neeeffary in navigation, and is chiefly 'ufed in taking the maps of harbours, fea^coafts, &.c. as follow*. Oblique Sailing exemplified by proper Example CASE I. The bearing and diftance of two places from c'ach other, as alfo the bearing of each of them from a third place, being given, to find the diflance from the faid third place to each of the other two places. EXAMPLE. Coafting a ^ on g ftore, I faw a.cape of land which bore from me N. N. E- I flood, away W. N.^' ao mi 'l es 9 an ^ the fame cape bore from me N. E. by E. the dUl ancc ^ t ^ ie ^*P at ^ ot ^ ft^tions from tl>c cape ? I i I would OBLIQUE SAILING. CONSTRUCTION. Having drawn the cempafs N. E. S. W. let A reprefent the place of the fhip at her firfl ftation, from whence, through the N.N.E. point, draw the indefinite right line CA, alfo through the W. N. W. point, draw another indefinite right line, BA, and fet off thereon 20 miles from a fcale of equal parts from A to B ; through the centre of the compafs alfo draw the N. E. by E. and S. W by W. points, and parallel thereto from the point B, draw the line BC meeting the N- N. E. in the point C, and it is done ; now from the N. eaft- \vard, 2 points, and from the N. weftward 6 points, together make 8 points for tbc . BAC, alfo the difference between the N E. by E. and N. N. E. points are 3, onr:33 45'~/_BCA, and the difference between W N.W. ardS.W.byW. points is 5 or 56* 15'^ ABC, then the /_ACB-r-Z.ABCzr 90, therefore the other is a right angle, cr 90. To find the diftance AC. As fine ang. ACB 33 45' co. ar. 0.25526 .. AB aonai, 1.30103 : : Sine ang. ABC 56 15 9-9*9^5 ; AC dift. from her i ft? ftation 29 : 93 mjles. J To find the diftance BC. As fine ang ACB 33 15 co.ar. 0.25526 : AB 20 mi. 1.30103 : : S. ang BACn 90 oo 10.00000 1*47614 EXAMPLE II. -.dift.BC = 36 mi. 1.55629 Being at fea, I faw two headlands, whofe bearing from one another I found by the chart to be W. by N. and E. by S . diftance 15 miles, the northernmoft bore from me S . S. W . and the fouthernmoft S . E. by E . I demand my diftance from each of th iaid headlands ? CONSTRUCTION. N Having drawn the com- pafs, fet off AB the S. S. W. bearing and AC the S. E. by E. bearing, draw through the centre the dot- ted line reprefenting the bearings of the two places from one another, andW from A towards D, on this line, fet off from any fcale of equal parts, 15 miles from A to D, and draw AB; draw DC jurallel to BA until it cuts AC at the point C, through C draw BC parallel to AD, and it is done. Calculation q/ the Angks Between N. N. E. and E. by S. is 7 points, or 7 8* 45'=: A ABC, between S. S. W. and ', E. by E. is 7 points, or 78 45'nthe angle BAC, and between W. by N. and N. W. by W. is two points, or 22 3C/, the angle ACB. Calculation of the Sides. As fine 78" 45 ; co. ar. 0.00843 II being an ifofceles triangle. Is to BC~i5 mile* 1.17609 AC~BC 15 miles. 5oisfine/LC22 30 9.58284 '^St, To ABirj. 85 miles, 0.7673$ This OBLIQUE SAILING 2 S t \E. 1 6 miles, the other lemand the diftance be- Tbis example, and the firft, are ufed for finding the diftance of a fhip from any headland, &c. when the fhip is about to take her departure from the land. CASE II. The bearings and diftance of two places from each other, and the diftaace of one of thofe places and the bearing of the other from a third place being given, to find the bearing of the firft, and the diftance of the fecond from the third place. EXAMPLE I. Admit two {hips fail from the fame road, one fails N. E. fails 23 miles, and then finds the firft to bear N. N. W. I tween the two fhips? CONSTRUCTION. I ft. Having drawn the cora- pafs. let A be the place the Ihips departed from, and draw the N. E. i E. line AB equal 16 miles. ad. From B draw the right line BC parallel to N. N. W. then with 20 miles between"' the compafles, fetting one foot in A, with the other interfeft the line BC as in C, and join AC, then, is the ABAC the courfe which the fecond fhip fteered, reckoned from the N. E. % E. foutherly. Calculation of the Angles. The bearing from B to C is S. S. E. the oppofite point to N. N. W. which is two points, alfo A bears from the fame point B, S. W. ^ W. the oppofite point to N. E. - E. which is 4 V points and two from the S. eafterly, make 6i points for the 33 45'- In A ACB, cvvo iiues equAi, vii. tnc uaes oppoute tnoic angles, that is, the fide AB ~ the fide BD As fine /. ACB~ 33* 45' co.ar. 0,25526 ZTio miles; and the ^ ABD is an ifocles A : fine AB ~ 10 i,ooo~o 1 80 ;: fine Z.CAB 11:56 15 9,91985 22 JO BC 14,97 1,175" 2)l57 3 or 15 miles nearly. 78 45 Laftly, In the A CBD is given the fidelAs fine ABCD zz 43 o, 5.564 CBi4,96 ; the fide BDiomiles, and Z.CBD. : to BD 10 o 1,00000 For betwixt the N. by E. and N. E. by N. : : fine Z.CBD 22 30 9,58284 is 2 points, or the *iCBD : 22 30'. , - -- As fum of fides BC & BD~24,97 8.60258 : C D the diftance of both 68,9 1,8388 : diff. fides BC & BD 4,97 0.69636 Again, : : tang, i fum opp.^srr 78 45' 10,70134 From L. B C D 33 43 - Subtract N. byE. n 15 Ung. i difference 45 2 10,00028 - - - - Z. CDB 123 43 22 28 that is D bears from C. S. 22 28 E. or S. S. E. and C the /. BCD 334? contrary from D. THE MANNER OF SURVEYING COASTS AND HARBOURS. To take the Draft of a Coafl in Sailing along It. HAVING brought the {hip to the moft convenient place from whence the principal points of the Coaft or Bay may be feen, either caft anchor, if it is convenient, or lie as fteady as poffible ; or, if the coaft is tocr fhoal, Jet the obfervations and meafures be done in a boat ; then, while the veflel is in a ftationary fituation, take with the azimuth compafs, or fextant, the bearings in degrees, &c. of fuch points of the coaft as form the moft material proje&ions or hollows ; write down thefe bearings, and make a rough fketch of the coaft, obferying carefully to mark the points whofe bearings were taken with letters, for the fake of reference. Then let the (hip or boat run in a direcl: line along, which muft be carefully meafured by the log, or otherwife, one, two, or three miles, more or lefs, until (he comes to a fituation from whence the fame points before obferved can be feen again : there let the veflel lie as in the foregoing ftation, and again obferve the refpe&ivc bearings and leading- marks where twop >iats or beariqgs, as moun- tains, churches, trees, and houfes, any two remarkable objec-T.* in one, in degrees, &c. of the fame not^d points, which are alfo to be wrote down, and a rough fketch of the coaft (hould be alfo taken from COASTS AND HARBOURS. from this ftation, for which purpofe prepare an obfervation table* in which write diftint)y and regularly the feveral celeftial obferva- tions, bearings, diftances, meafured by the log line, the rocks, fhoals, foundings, overfalls, races of tide , and other remarks that may be made along- the coaft ; the table may confift of 7 or 8 co- lumns difpofed in the following order: N;,TE. The fextant will be found the readieft and moft correct inftrtiment to take the angles, by being held in an horizontal pofltion, by which means any two objects, not exceeding 120, may be brought into contact ; it will not be amifs to take material points by the compafs, and intermediate ones by the fextant or quadrant. Obftrvaiions In navigating the Cocift from Cape to Point , being MiUs^ meajured by the Log y the Cou. jrom Sta- tion i to 2, being S. | W, Year, Month and Pay. Sun's Mer. Alt. Bearings at ftation. Time and diftance failed from ftation. I Bearings and dif- tances taken at thefc diftances. Bearings of rocks, fhoals, and their efti- mated diilance when on a line with a point or heads of the coaft. Remark, ontojetides, nature, and djmenfion* of rocks, fiioals, and anchorage. D.M. H.M. Miles Path. 22 Points and heads. M. i. 2 7 H.45 I 5 A.N;5W. B.W.ao'S. This rock dries and lecmediod yds.N.&S. a leading- marktoitis While the veflel is running the bafe line from ftation to ftation, an accurate appearance of the coaft fhould be made, to do which, let four expert perfons be appointed, one to take the bearing exactly with an azimuth compafs ; one to overfee the running out oi the log-iine, and to keep an account of the (hip's way, fo as to be rea- dily able to tell the diftance run when required , the third to attend the heaving of the lead, to write down the foundings and bearings of one or two head points, or remarkable points of the coaft, taken jit each depth ; the fourth a draftfman, to draw out the neceffary bearings and diftances, and delineate the figures and windings of the coaft at each ftation, and to correct their forms and dimenfions when the ihip is failing along the land. Then let the feveral bear- ings be corrected by the variation to reduce them to their true po- fitions ; then, in fome convenient part of a meet of paper, defcribe a circle, the larger the better, on which lay off the feveral bear- ings taken from the firft ftation, and let them be numbered i, 2, 3, &c. on the outfide of the circle ; alfo lay down the feveral bear- ings taken at the 2d ftation, let thefe be numbered with tlie fame feures on the mfide of the circle. Draw THE MANNER OF SURVEYING Draw a line to exprefs the fhip's run, both in length and courfe, and from the end of the line, expreffing the firft ftatlon, draw lines parallel to the refpe&ive bearings taken at that end, and note it in the circle j mark the interfeclions of each pair of lines, directed to the fame point, with the numbers annexed to their bearings j and, through the interfe&ions fo marked, draw by hand a curved line ; obferve to wave the line in and out as near as can be like the bend- ing of the coaft itfelf. Againft each part draw the appearance of the elevated, or low ground, in the fketches, diftinguifhing rocks, cliffs, or high lands, low lands, fnd hills, &c. If there are any currents or eddies, ex- prefs them in their proper places, by darts or- arrows, the point? being turned that way the currents fet ; put in the feveral found- ings at low water, in fmall figures, diftinguifhing whether fathoms or feet ; fhew the time of high water on the full and change days, by Roman figures, and tell the rife in feet, put in a compafs with a fcale of miles or leagues, fuch as the veiTels run was laid down by; add the name of the place, the coaft, and the latitude and longitude, as true as can be obtained. If there is a fhoal or fand on the coaft, let it be taken by a boat failing round it, and keeping an account of the courfes, diftances, and foundings, to be put in the draft; the boat mu ft, from fome part of the faid fand or fhoal, take the bearings of two points of the coaft, where bearhigs have been taken from the fhip, or the bear- ing of the boat, or fome part of the fheal, or fome beacon in that place muft be taken by the fhip, at the ftations where fhe takes the bearings of the fhore; for, by either of thefe means one point of the fand being obtained, the reft of it can be laid down from the boat's account. If the coaft to be drawn is a bay or harbour, winding in fuch a inanner that all its parts cannot be feen at two ftations ; let as many bafes or lines be drawn, and exactly meafured, as may be found neceflary, obferving that the fev, ral diftances run fhould join to one another, in the nature of a traverfe; that each new fet of p! \je6ts or points obferved fhould be taken from two ftations at the end of a known diftance, and that the objects whofe bearings are taken do not fo much extend beyond the limits of the bafe, as to make angles with it lefs than about f or |- of a point, but rather re- ferve fuch objects for the next meafured bafe line; for when lines lie very obliquely to one another, their interfe&ions are not eafily afceitained. Thus may a coaft of any extent be furveyed, by carefully mea^ Turing of ftationary bafe lines, and from their ends drawing angles to each other. If any particular parts of the harbour cannot be conveniently feen from either ftation, take the boat into thofe places, and, having well examined them, make fketches thereof, eftimating the length and breadth of the feveral inle'ts, either by the rowing or failing of the boat; take as many bearings, foundings, and other notes, as, may COASTS AND HARBOURS. 257 may be thought necefTary ; then annex thefe particular views in their proper places in the general draft. If there are any dangerous fands or rocks, befides inferring them in their proper places, there fhould be a double line drawn through that point, on one or more objects a{hore; and for this purpofe choofe a church, mill, houfe, noted tree, a clift, or any remark- able thing that can be diftin&ly feen at fea, and which can be brought to bear in the fame right line with the point to be avoided ; but if that point is under water, there muft be two land-marks brought ' to bear with the danger, either in a right line, when it can be, or in two lines, and thofe two lines, and thofe land marks may be put down in their proper places, by their interfeclion of two obje&s in one bearing, and two objects in another bearing ; which will give the ftation of the fhip, and the diftance and the bearing of the dan- ger from that ftation, noted when near or on it ; but i two fuch interfetions cannot be obtained, it muft be put down from the two points on fhore, in one with the computed diftance therefrom, or from the interfering bearings of two fmgle points on {hore. It fhould be remarked in the draft, what places, if any, are unfit for anchorage, and what are fit, by writing rocky ground, foul anchorage, good anchorage ; and in the latter to draw the figure of an anchor. Alfo, if there is any particular channel more conve- nient to fail through than another, it is to be pointed out by lines drawn to its entrance, from two or more noted marks on fhore. The foregoing method of furveyine a coaft, fuppofes in general, that it is taken by a fnip in her paflage along, nut having an oppor- tunity of going afhore. But when circumftances will permit the meafures and obfervations to be made on land, the furvey can be more accurately taken than on the water. To Survey an Harbeur ly Obfervation ajbore. MAKE an eye-draft of the place to be furveyed ; and, in going round its coaft, fix in the moft remarkable points and bend3 of the fhore ftation ftaves or ftrait poles, tall enough to be feea at a considerable diftance; but if at any of thofe places there is a noted tree, houfe, or any other remarkable thing, that object may ferve inftead of a ftation ftafF; and it will be convenient to black the ftave*, and tie a piece of white bunting to the jop of each ; then, in the eye-draft, put letters at the noted points, or mark , for dif- t in cl ion- fake. Choofe the moft level fpot of ground, wherein a bafe line may be meafured, of one or more half miles in length, or a length of not lefs than a tenth part of the diftance of the two extreme object marked for obferving-, and let the di reel ion of the meafured bsfie line be fo laid out, that from both ends of it as many of the ftation ftaves before planted, or the objects before remarked, may-be feen ; the bearing or pofition of this bafe muft be determined by degrees K k and THE MANNER OF SURVEYING and minutes, and alfo its length muft be accurately meafured to feel and parts, either by a meafuring chain, or by a piece of log-line of 100 feet long, properly marked at the end of every 10 feet. From one end of the bafe obferve, with any inftrument proper to take bearings, the pofifcoii or bearing in degrees and minutes of ail the ftaves or .objects within view, and write them down orderly 5 do the fame from the other end of the bafe, and let all the bearings t>e corrected by the variation of the compafs. Then thefe meafures and corrected hearings being plotted or laid down, will -^ive the moft confpicuous points on fhore. the inter- mediate fpaces are to be filled up' from the fketches of them made en the fpot. But if any fuch obje^s ftiould fpread on either hand, fo far from beyond the limits of the bafe, that at either end thereof, the other end and thofe objects or ftaves fhould appear nearly in the fame di- rection, or to make the plan fit for all nautical purpofes, and may be embclliihed with proper co- lours, if necefla y. Sea-drawings, taken according to the foregoing precepts, befides the real ufe they are of, cannot fail to recommend the young ma- riner who furveys and conftruds them, to the notice of h4 fupe- riors. To reduce a Draft to afmaller Scale. WITH a black lead pencil draw the draft to be reduced all over with crofs-lines, forming exad J 4 ;,uies, draw the clean paper for the copy all over with he fame number of fquares, but their fides larger or fmaller in proportion to the in tended fize of the fcale, fuch as |, ^,&c. length of the other, diftinguiih by a ftronger mark, with a figure eve- y fifth or fixth row of fquares in both, fo that the feveral correfponding fquares may be readily perceived; then, in each of tne fquares of the draft, draw, by the eye, a curve on the paper, limilar to that in the fquare of your copying draft, till the whole is copied; make the black lines with India or other ink, and when drawn, the black-lead lines may be rubbed out with bread or India rubber. I here give two Examples, as an elucidation of what has laft been fa id. EXAMPLE I. AB is the bafe line, equal to^ Mile. BG=N. with Bearings. BH=S. BF=S. Thefe inftruments give the points GC DE HF in ordertfrom each ftation; that is, BG and AG interfed, as alfo BC and AC, &c. Obferve, the laft letter muft be the fame in both bearings, and it will be the beft to follow the bearings one way all round the com- pafs from the firft ftation; as alfo when arrived at the fecond fta- tion, begin with your firit objea feen at firft ftation, and follow the letters round belonging to each objea, by which the laft letter in each bearing will fucceffively follow in order. 'This is an example when on board (hip. Kk2 260 THE MANNE*. OF SURVEYING EXAMPLE II. This harbour was furveyed by bafe lines taken on fhore, which, when it can be done, is far preferable. The bafe line AG 812 fathoms, was taken, as by directions, on the moft even fpot on fhore ; now v beginning from the point A : AB-W. byS. \ S.\ GB=S.S.W. AC~W. by N. J Bearings GC=sW. by S. * S* AD-W.N.W.|N. \ from Sta- AE N.N.W.AW. /tioH A. AF~N.byW.fVV. GD=W. JN. f Bearings from GE = W.N.W.N. f Station G. GFzzN.W.byN.^N. AGN.N. E. J8ia fath. After having made thefe obfervations, it will be necefljry to proceed to the northern part of the coaft. In all cafes whcie a coaft is furveyed in feveral parts, it is moft advifable to meafure a new fundamental, bafe for each part, when it can be conveniently done. A line meafured from the {ration F, towards K, is well adapted to our purpofe. Let FK, therefore, be the fecond bafe line ; its length, by admeafuremenr, is found to be 778 fathoms; and its bearing, by compafs, N. E. \ E. Take bearings from each end of this bafe as before. "I Bear- fKF-S.W.-from fromSta- FK=N.E4E.778fath. | Sta- | KL=N.byW. tionK. J tionF lKN=N.iE4W.J It is plain, that the connexion between the two parts of this furvey is preferved by the fecond fundamental bafe being drawn from the point F, v/hofe fituation was before determined by ob- fervations from the firft bafe line. If this particular pofition of the firft bafe line had not been convenient, and it had been taken at a diftance from every point determined in fituation from the firft bafe line, the connection would have required an obfervation of the bearing of one of the faid points from each end of the fecond bafe. Thus, fuppofe the line IK to be the fecond bafe jine, inftead of FK, the pofition of IK, with refpecl to the given point F, may be known by taking the bearing of F from I and K. The end of the fhoal, marked M, lies with D, bearing; N. and E. N. by E. f E. All the obfervations which are required to be made on ihore being completed, through the interfedtions of the bearings draw the configuration of the coaft, as before directed, and finifh the drawing by the inftructions there given; which, if well attended to 3 no difficulty can well occur. To find the Height and Dijlancss of Qbjefts at Sea. WHEN the object is perpendicular, and thediftance to it can be meafured, find the angle of altitude with a quaclrant, and meaiure the diitance to it as exa& as poilible, and then you have the COASTS AND HARBOURS. 26* the angles and bafe, to find the perpendicular; or, if you eo back- ward or forward until the angle of altitude be 45, the diftance be- tween you and the object will be the perpendicular height. EXAMPLE I. Being 69 fathoms from the bottom of a tower, I find its alti- tude, after allowing for the height of my eye, above the water 15 lo*. Required the height I ....._... , ,.. + . Draw ABjn96, upon B eredl: the perpendicular BC, and draw AC, making an angle with AB=i5 10' till it cuts BC in C, then will BC be the height of the tower. Or, As radius 10.00000 As co-fi.ang.Aco.ar, Is to the bafe 96 1.98227 : Bafe 96 So is tang. ang. A. 15 10' 9.43308 : : S. ang. A. To the height BC 26.2 1.41535 itheperpen. EXAMPLE II. Being at fea, I obferved the altitude of a mountain, and found it 20 g , and then failing from it in a direct line four miles, I found the altitude of the mountain to be 14, dip and refraction allowed for. I require the perpendicular height? D A CONSTRUCTION. Draw the horizontal line DC. On anypointAmake the ZLBAC ao, from A fet off four miles to D, on D make the ^LBDC 14, and from where the line DB cuts the line AB as at B, let fall the perpendicular BC on the bafe DC, and BC meafured will be the perpendicular height required. 180 o The angle BAG ** ao c The ang. BAD The ang. ADB rhs angle ADB s 160 o 14 o 174 o 180 o >!< <> O As fine ^DBA=6* o' ADrr 4 miles : : Sine Z.BDA 14* co, ar. 098077 9.38368 0.96651 Then A ABC given AB~9-i53 and A find BC. Radius 10.00000 : AB 9.258 0.96651 : : Sine Z, ao 9.5 3 405 : BC~3,i66 0.5005$ 262 CURVATURE OF THE EARTH So that the height of the mountain is 3 miles T ^-|| = I 13 poles, &c. NOTE. In finding the > DAB fee Prob. 5th in Geometry* Of the Curvature of the Earth. MOST perfons know that if they are raifcd above t*he furface of the adjacent land or water, they can not <;nly fee different objects that lie on that furface better, but alfo fee thofe more and more remote as they advance higher* The irregularity of the fur- face of the land will not be fubjedled to any one rule that will give the diflance to which objects may be feen at dMerent elevations 3 but at fea, where there is generally an uniform curvature of the water, upon the fuppofition of the fpherical form of the earth, thofe diftances may be eaiily computed. RULE. To the earth's femi diameter add the height of the eye, multiply the fum by the height, then the fquare root of the product is the diftance at which an objeifr. on the furface of the water can be feen by an eye fo elevated ; and by this rule wa<- Table XXI. computed, the diameter of the earth being taken at 4.798117 feet, according to Sir Ifaac Newton's meafures. This Table may be uiefully ap- plied to eftimate the diftance of an object at fea, the elevation of that objel above its horizon being known. EXAMPLE I. Sailing towards a headland, on which is a light houfe elevated 600 feet above the furface of the water, we faw the lights at night juft appear in the horizon ; how far were we at that time diftant from that light houfe ? Look in^Table XXIII. for 600 feet in the column marked height in feet, and right againft it, in the column marked diftance in miles, is 29.994. So that the diftance may be reckoned about ^O miles. EXAMPLE II. Being in company with fome merchants walking on a fandy fhore, on the look out for a veflel which was expelled, whofe top- gallant maft was 140 feet above the furface, allowance being made for her immerfion in the water, we obferved through the telefcope a (hip's vane juft appearing in the horizon. How far oft is that (hip, fuppofing it the veffel expected? Anfwer, againft 140 feet, the height, ftands 14.488, that is her diftance ; here is no allowance made for the height of the eye above the horizon ; but it is obvious, that the higher the eye, the farther it can fee: now as objects are feen in a ftrait line, and that line is a tangent to the earth's fur- face, therefore it follows, that to find the diftance of two elevated CURRENT SAILING. 263 bjets, when the right line joining them touches the fur face of the earth, between thofe objects look for the diftance anfwering each height, and their fum is the diftance required. Thus, in the fecond example, fuppofe the eye raifed fix feet above the water's edge, it can fee an object on the furface 2,999, or three miles off". This diftance added to 14 \ miles, make the diftance of the fhip to be 17 miles. EXAMPLE III. A man being on the main-top gallant maft of a man of war, 200 feet above the waier, fees a 100 gun ihip fhe had engaged the day before huli-to ; how fur were thofe fhips diftant from one another ? A (hip of 100 guns, or a firft-rate man of war, is above 60 feet from the keel to the rails, from which deduct about 2o, leaves 40 for the height of her quarter above water. Now a fhip is feea jbull-to when her upper works juft appear. Then 200 feet high gives 17.316 miles. And againft 40 ftands 7-744 25.060 miles is her diftance. CURRENT SAILING. are certain fettings of the ftreams, by means of _ which all bodies moving therein are compelled to alter their courfe and fubmit to the motion imprefied upon them by it: whence, if a current fets with the courfe of a fhip, it augments her motion J>y as much as the drift or rate of driving it. Thus, if a fhip faiis N". N. E. 20 miles, in a current that fets N. N. E. 8 miles, in the fame time her true courfe will be N. N, E. 28 miles in that time ; but if a current fets againft a {hip, it kf- fens her velocity by juft as-much as the current's drift is. So that if the (hip fails N. E. 49 miles, in a current that fets S. W. 10 miles in that time, then her true courfe will' be N. E. 39 miles; and if in the fame time that the fhip fails N. E. 49 miles in a current that fets S. W. 59 miles, then the {hip will fall a-fteni, and her true courCe will be S. W. 10 miles ; but if the (hip thwarts the current, it not only lefiens or augments her velocity, but gives her 2. new motion, compounded of that of the fhip and current ; If a body be agitated A H by two motions at the fame time, the one with a certain velocity that will carry it according to the direction of the line AB, the length AB in a Certain fpaceotime 3 the 164. CURRENT SAILING. other according fo the direction of the line AD, with a velocity that will carry it to the diftance AD in the fame time, then the body will defcribe the diagonal AC, and at the end of that time will be found in the point C. The fetting and drifts of the moft remarkable tides and currents arepretty well known, but if in unknown currents, the ufual way to find the fetting and drift is thus: Let three or four men take a boat a little way from the (hip, and, by a rope fattened to the boat's ftem, let down an heavy iron pot, or loaded kettle, into the fea, to the depth of So or 100 fathoms when it can be, whereby the boat will ride almoft as fteady as at anchor, then heave the log, and the number of knots run out in half a minute will give the miles which the current runs per hour, and the bearing of the log {hews the fetting of the current. EXAMPLE I. If a (hip fails E. N. E. 98 miles in a current that fets S. W. 17 miles in the fame time, what is her true courfe and diftance ? 1)157 30 } Sumofreq. fail down to the cheftree. About. The fituation of a fhip as foon as fhe has tacked* About flip! The order to prepare for tacking. Abreoft- The fituation of two or more ihips lying with their fides pa- rallel, and their heads equally advanced ; in which cafe they are abreuft of each other. ABKEA&T OF ANY PLACE meansoifor directly opposite 10 it. EXPLANATION OF SEA TERMS. 267 Adnft. The ftate of a fliip broken from her moorings, and driving; about without controul. Afloat. Buoyed up by the water from the ground. Afcre. All ihat part of a lliip which lies forward, or near the ftem, Italfo fignifies farther frwurd\ as, the manger Hands AFORE the fore- maft ; that is, nearer to the ftem. Aft. Behind or near the fternof the fhip. After. Aphrafe applied to any object in the hinder part of the (hip, as the after hatchway, the after- fails, &c. A-^mund. The (ituation of a fhip when her bottom, or any part of it, re(ts on the ground. A-head Any thing which is fituated on that point of the compafs to which a (hip's ftem is directed is fa id to be a head of her. -hull. The fituation of a (hip when all her fails are furled, and her helm to the lee-fide ; by which (he lies with her head being fomewhat inclined to the direction of the wind. A-lee. The pofition of the helm when it is puflied down to the lee- fide. All in the wind. The ftate of a (hip's fails when they are parallel to the direction of the wind, foas to fhake, or quiver. All hands hcny ! The call by which all the ihip's company are fum- moned upon deck. Aloft. As the maft-heads, or any where about the higher rigging. Along-fide. Side-by-fide, or joined to a fhip, wharf, &c. Along-jhore. Along the coaft; a coaft which is in the fight of the fhore, and nearly parallel to it. Aloof. Is diftance. Keep aloof, that is, keep at a diftance. Amain. At once, fuddenly: as, LET GO AMAIN! Amid/kips. The middle of a (hip, either with regard to her length or breadth. To anchor. To let the anchor fall into the ground, for the (hip to ride thereby. Anchorage. Ground fit to hold a (hip by her anchor. he anchor is a cock-bill. The fituation of the anchor when it hangs by the ftopper at the cathead- At anchor. The fituation of a (hip riding at her anchor. An-erd. The pofition of any maft, &:c. when erected perpendicularly. The top mails are faid to be AN-END when they are hoifted up to their ufual ftations. Apeek. Perpendicular to the anchor, the cable having been drawn fo tight as to bring the ihip directly over it. The anchor is then faid to be APEEK. Arm the lead. Apply a pully to the lower end. Afiare. On the ihore. It alfo means A- GROUND. sijiern. Any diftanc. behind a (hip, as oppofed to A-HEAD. Athwart. Acrofs the line of a (hip's courle or keel. Athwart rloewfe. The fituation of a (hip when driven by accident acrofs the fore-part of another, whether they touch or are at a fmall diftance from each other, the tranfverfe pofition of the former are prin- cipally underftood. Athwart ihe fore foot. When any object crofles the line of a (hip's courfe, but a-head of her, it is faid to be ATHWART HER FORK FOOT. L 1 i Athwart* 268 EXPLANATION OF SEA TERMS. Atbpivg'. Cleaning the upper part of a ihip's bottom, or that part which lies immediately under the furface of the water; and paying it over with tallow, or with a mixture of tallow, falphur, relin, &c. Both fleets aft. The fituation of a fhip failing right before the wine*. Bow-grace. A frame of old rope or junk, laid out at tiie bows, Items, and fides of Ihips, to prevent them from bdng* injured by flukes of ice. Bow -line bridla. Lines made faft to the cringles in the fides of the fails, and to which the bow-line is fattened. Lines made fait to the bridles, to haul -them forward EXPLANATION OF SEA TERMS, when npori a wind, which being hauled tort, enables the (hip to fail nearer to the wind. To pull upon any body with a tackle, in order to remove . ,A" large piece of timber which (lands out from the bows of a (hip. . A particular method of veering a (hip, when the fwell of the fea renders tacking impracticable. B&n*g. It ig performed -by laying the head-fails aback, to pay ofF the fliip's head when got in the Wind, in order to return the fhip's head into the line of her courfe. lo b,a:e tht yards. To move the yards, by means of the braces. To b> ace about. To brace the yards round for the contrary tack. To bract /harp. To brace the yards to a pofition, in v.-hich they will make the fmalleft poflible angle with the keel, for the fliip to have head -way. To brace. to. To eafe cff the lee-braces, and round in the weather- braces, to afiifl the motion of the fnip's head in tacking. To brail up. To haul up a fail by means of the brails. Brtnls. A name to certain ropes belonging to the mizen, ufed to trufs it up to the maft But it is likewife applied to all the ro\ es which are eim-loyed in hauling up the after corners of the ftay-fails. Tobreakbulk. The aft of beginning to unload a Ihip. 71? break fieer. When a thip at anchor is forced, by the wind or current, from that petition in which fhe keeps her anchor moll free of herfelf and mod firm in the ground, fo as to endanger the tripping or fouling her anchor. Breaming. Burning off the filth from a fhip's bottom. Breaft-fajl. A rope employed to confine a (hip tideways to a wharf, or to fome other Ihip. To bring by t::e 1st. See TO BRO ACH TO. To bring to. To check the coarfe of a (hip when fbe is advancing, by arranging the fails in fuch a manner as that th?y (hall counteract each other, and prevent her from either retreating or advancing. To broach to. To incline fuddenly to windward of the (hip's courfe againft the helm, fo as to p re lent her fide to the wind, and endanger her lofing her marts. The difference between BROACHING TO, and BRINGING BY THE LEE, may be thus defined : fuppofe a fliip under great fail is fleering fouth, having the wind at N. N. W. then wefl is the weather-fide, and call the lee-fide. If, by any accident, her head turn round to the weiiward, fo as that her Jails are all taken a-back on the weather-fide, (he is faid to BROACH TO. If, on the contrary, her head declines fo far eaftward as to lay her fails a-back on that fide which was the lee-fide, it is called BRINGING BY THE LEE. Eroadfide. A diiciiarge of all the guns on one tide of a (hip both above and below. Broken- backiti* or kogd. The nate of a fhip which is fo loofcned in her frame as to drop at each end. Bulkhead. A partition. Buoy. A floating conical cafk, moored upon fhoals, to (hew where the danger is j alfo ufed to anchors to (hew where they lie. inei* Lines that come down from the top of the maft to the foot EXPLANATION OF SEA TERMS. 2J I foot rope before the fail, and by which the bunt or belly of the fail is hauled up outwards. Jj_y the b'-'fird Over the iliip's fide. By the bead. The Hate of a ihip when fhe is fo unequally loaded as to draw more wilier forward than fhe cii^ht. j.y the -ivind. The course of a thip as nearly as pofiible to the direction ' 'of the wind, which is generally within fix points of it. Cap. A piece of wood fixed on the head of the matt, through which the next matt goes. Capft&n. An inurnment by which the anchor is weighed oat of the ground, it being a great mechanical power and is ufed f.r fetting up the fhrouds, and other work where great purchafes are required. To careen. To incline a ihip on one tide io low down, by the app! cation of a ftrong purchafe to her mafts, as that hei bottom on the other fide may be cleanfed by breaming, and examined. Cafting. The motion of falling off, fo as to bring the dreclion of the wind on either fide of the (hip, after it has blown fome time right a-head, Itis particularly applied toa fhip about to weigh anchor. To cat the anchor. Is to hook the cat- block to the ring of the anchor, and haul it up clofe to the cat-head, Cat's Paw. A light air of wind perceived in a calm, fweeping the furface of the lea very lightly. A hitch taken on the lanyard of a Ihroud, in which the tackle is hooked in letting up the rigging, and for other purpofes- Cat-harping. Short pieces of rope which connect the lower Ihroudg together where the futtock ihrouds are fattened Caulking. Filling the feams of a Ihip with oakum. Centre. This word is applied to that fquadron of a fleet, in line of battle, which occupies the middle of the line; and to that column (in the order of failing) which is between the weather and lee co- lumns. Chains, or Channels, A place built on the fides of the (hip, projecting out, notched to receive the chain-plates, for the purpoie of giving them a greater angle. Chain-plates. Are plates of iron fattened to the fhip's fides under the chains, and to thefe plates the dead eyes are fattened by ir n ilrops. Chapelling, or building a Chapel, is when a veffel on a wind, in litde wind, is caught a-back, and turns round on her keel to the fame tack without Itarting either tack or Iheet. Chafing. When two things rub and injure each other. Chaj'e. A vejflel purfued by fome other, Chafer. The veflel purfuing. Chcrrly. A phrafe implying heartily, quickly, cheerly. To daw off. The a6t of turning to windward from a lee-more. Clrar is variously applied. The weather is (aid to be CLEAR, when it is fair and open; the fea-coaft is CLEAR, when the navigation is not interrupted by rocks, &c. It is applied to cordage, cables, &c. when they are difentangled, fo as to be ready .for immediate fervicc. In all thefe fenfes it is oppofed to FOUL. To clear tht anchor. Is to get the cable off the flukes, or ttock ; and to difencutijber it of ropes ready for dropping. CLar EXPLANATION OF SEA TERMS. Char kawfe. When the cables are direded to their anchors without tying a thwart each other. To citar ike hawfe. Is to take out either a crofs, an elbow, or a round turn. Made faft, as the cable is to the ring of the anchor. /. To haul the yards down by the clew-lines. Clew-fines. Are ropes which come down from the yards to the lower /(Corners of the fails, and "by which the corners or clews of the fails are ii.au led up. To clew up. To haul up the clews of a fail to its yard by means of thf clew-lines. Ci-fe hauled. That trim of the (hip's fails, when (he endeavours t make a progrefs in the neareft direct!' n pofiible towards that point of the com pafs from which the wind blows. To club haul. A method of tacking a fhip when it is expected flic will mils tiays on a lee fhore. Coaftmg. The act of making a progrefs along the fea-coaft of any country. Cockbitt. See the nnchor is Ti cdl the cable. To lay :t round in a ring, one turn infide another. Ctmmandrr. A large wooden mallet to drive the fid into the cable when in the act of fplicing. To (ome horns. The anchor is faid to come hcme w hen it loofens from the ground by the effort of the c ble, and appioaches the place where the fhip floated at the length of her moorings. Coming to. Denotes the approach of a (hips head to the direction of the wind. Courj'e. The point of a compafs to which the fhip fteers. Crank.. The quality of a ihip, which, for want of a fufficient bal- 1 ft, is rendered incapable of carrying fail without being expofed to danger. Crteper. A fmall iron grapnel ufed to drag in the bottom of rivers, Src. f?r any thing loft. C> ingle. A ftrand of fmall rope introduced feveral times through the bolt rope of a fail, and twitted, t which ropes are fattened. To rr&tvtfjail. 1*0 carry more fail than ordinary. Cfovu-fiot. Is a number of fmall lines fpred from t v e fore parts of the tops, by means of the piece of wood through which they pafs, and being hauled taut upon the flays, they prevent the foot of the topfails catching under the top rim 5 they are aifo ufed to futpend i he awn- ings. Cunning. The art of directing the helmfman to guide the ihip in her proper courfe. To cut and run. To cut the cable and make fail inftantly, without waiting to weigh anchor. liawit. A long beam of timber ufed to fifli the anchor. See FISH THE AX CHOP,. Dtad water. The eddy water, which appears like whirlpools, doling in with the fhip's ftern, as (he fails on. Dead lights. A kind of window-ihutter for the windows in the ftern of a {hip, ufed in very bad weather. Dead 'wind. The wind right againft tie fliip, or blowing from the very point to which (he wants to go. bend *jts. Blocks of.wood through which tie lanyards of the (hrouds are reeved, < EXPLANATION OF SEA TERMS. 273 To 'deaden a Jbifis way. To impede her progrefs through the water. Difmafled. The ftate of a ihip that has loft her mafts. Deg-f the (hip's head from the direction of the wind. It is ufed in oppofition to COMING TO. Fall ot off! The comm md to the fleerfman to keep the fhip near the wind. Fathom. A meafure of fix feet. To fetch Mvy> To be (ha ken or agitated from one fide to another fo as to locfen any thing which was before tixed. Fid. A fquare bar of wood or iron, with moulders at one end j it is ufed to fup ort he weight of the topmaft, when ercdted at tne head of a lower mart. 'frufiwrfpticinf A large piece of wood, of a conical figure^ ufed to extend the (hands and layers of cables in fplicing. To fill. To brace the fails fo as to receive the wind in them, and advance ihe (hip in her courfe, after they had been either Ihivering or brace.d a- back. F'jh A Inrge piece of wood. Fifii the maft, apply a large piece cf wood to it to ftrengthen it. t Jb- o'.k A large hook by which the anchor is received from under the ci!t'lu-ad,and brought to thefi.leor gunwale : and the tackle which is uff-d for this purpofe is called the fiih tackle. To fyh the anchor. To draw up the flukes of -the anchor towards the top of the bow, in order to flow it, after having been catted, by means of the davit. Flag. A general name for colours worn and ufed by fhips of war. Flat-aft, 'ihe lunation of the fails when-their iurfaces are prefled aft againft the maA by the force of the wind. To EXPLANATION OF SEA TERMS. . 275 To fiat in. To draw in the aftermoft lower corner or clue of a fail towards the middle of the flap, to give the fail a greater power to turn the vefiel. To flat in forward. To draw in the fore, (beet, jibb-ilieet, and fere- flayfail-fheet, towards the middle of the fliip. flaw. A fudden breeze or gnft of wind. Fleet. Above five fail of the line. Floating. The flate of being buoyed up by the water from the ground. Flood-tide. The flate of a tide when it. flows or rifes. Flowing-fleets. 'The pofition of the meets of the principal fails when they are loofened to the wind, foas t > receive it into their cavities more nearly perpendicular than when clofe hauled, but more obliquely than when the fhip fails before the wind. A fhip going two or three points large has FLOWING" SHEETS. Fore, ihat part of a iliip's frame and machinery that lies near the ftem. Fore-and-aft. Throughout the whole (hip's length. Lengthways of the (hip. To fore-reach upon. To gain ground of fome other (hip. Forecajlle. The upper deck in the fore part of a (hip. To forge over. To force a (hip violently over a (hoal by a great quantity of fail. Forward. Towards the fore part of a fhip, Foul, As FOUL WEATHER, FOUL BOTTOM, FOUL GROUND, FOUL ANCHOR, FOUL HAWSE. As Oppofed tOFAIR, we fay FOUL WIND. To founder. To fink at fea by filling with water. Foxes. Two or more yarns'twifted together by hand. To free. Pumping is laid to FREE the fhip when it difcharges more water than leaks into her. To f re/ben. When a gale encreafes it is faid to freflien. Tofrejhen the hawfe. Veering out or heaving in a little cable to let another part of it endure the chafing in the hawfe-holes- It isalfo applied to the act of renewing the fervice round the cable at the hawfe- holes. Freft>-ut a capftern, or other machine of the like kind, by means of bars, hnndfpikes, &c. To heave a-bcad. To advance the fliip by heaviue-in the caMe or other ropi f.:ftcned to an ancil r at fome diftance before her. ~1 o heave a peek. To heave. in the cable, till the anchor is a-peek. To h a--ve a- ft cm. To move a {hip backwards by an operation {iml.'ar tO thit of HEAVING A-HEAD. To htaw dvwn. TO CAREEN. 'l r j heave in the cabl?. To draw the cable into the {hip, by turning the capilern or windlafs. To heave-in flays. To bring a {hip's head to the wind, by a manage- ment of the fails and rudder, in order to get on the other tack. To-beavtout* To unfurl or loofe a fail j more particularly applied to the ftayfaiJs: thus we fay, loofe the topfails and HEAVE OUT the ilayfails. Tohsa-jejhort. To draw fo much of the cab'e into the {hip, as that flie will be almoft perpendicularly over her anchor. To hea-ve tigh- or taught. To turn the cjptlern round, till the rope or cabl" becomes ftraitened. EXPLANATION CF SEA TERMS. To heave ike capflern. To turn it round with t!:e bars, Tobtavf the lead. To throw the lead overboard, in order to find the pepth of water. To brave the log. To throw the log overboard, in order to calculate the velocity of the fhip's way. To heave too. To ftop the veffel from going forward. Heave handfomely . Heave gently or leifurely. Heave heartily. Heave ftrong and quick. Heave ofthefea. Is the power that the fwell of the Tea has upon a (hip in driving her out, or fafter on, in her courfe, and for which allowance is made in the day's work. To heel. To floop or incline to one fide; thus they fay TO HEEL TO PORT; that is, to heel to the larboard fide. Helm. The inftrurnent by which the iliip is fleered, aud includes both the xvheel and the tiller, as one general term. Helm a-lee ! A direction to put the tiller over to the lee-fide. Helm a-weatber / An order to put the helm over to the windward fide. High-and-dry. The fituation of a Ihip when fo far run a-ground as to be feen dry upon the ftrand. Hitch. To make faft. Toholft. To draw up any body by the afliflance of one or more tackles. Pulling by means of a fingle block is never termed HOIST- JNG, except only the drawing of the fails upwards along the mails or Hays. Hild. Is the fpace between the lower deck and the bottom of a fhip, and where her ftores, &c. lie. To flow the hold, is to place the things in it. Tohold'fts rwn. Is applied to the relative fituation of two {hips when neither advances upon the other; each is then faid TO HOLD ITS OWN. It is like wife faid of a (hip which, by means of contrary winds, cannot make a progrefs towards her deftined port, but which, however, keeps nearly the diftance fhe had already run. To held on. To pull back or retain any quantity of rope acquired by the effort of a capflern, windlafs, tackle, block, &c. Home. Implies the proper fituation of any object ; as, to haul HOM5 the top. fail meets is to extend the bottom of the top-fail to the lower yard, by means of the meets. In flowing a hold, a calk, &c. is faid to fee HOME, when it lies clofe to fome other object. Horfe. A rope under the yards to put the feet on. Hoy. A particular kind of veffel. Hull of the fliip. The body of it. Hull- down. Is when a {hip is fo far off, that you can only fee her mafts. Hull-to. The fituation of a ftiip when (he lies with all her fails furled; as in TRYING. To hull ajL-ip. To fire cannon-balls into her hull. Hulk. A iliip without malls or rigging j.aHb a veffel to remove mafls into or out of ihips by means of fheers, from whence they are called (Leer hulks. Jack. The union flag. yarning. Particular method of taking a turn with .a rape, &c. The blocks through which jeers are drove. EXPLANATION OF SEA TERMS. >crs.- The ropes by which the lower yards are fnfpended. "fibb. Theforemolt tail of a ihip, ftt upon a boom which runs out fro:n thebowfprit. Jib-boom. A ("par that runs out from the bowfprit. J'lly boat. S malleft boat on board. Junk. Old cable, or old rope. Jurymajt. Any (par that is fet up, when the proper mall is carried a w a v . K..d!cd. Any part of a cable, covered over with old ropes, to pre- vent its furfacefrom rubbing againft the (hip's bow or fore foot. Ktdge A fmall ;uu:hor. Kf-tL Tb"- principal piece of timber on which the vcflel is built. Keel. hard. To drag a per fon backwards and forwards under a ihip's keel, for certain offences. To ki\'p a\'.aj. To alter the (hip's courfe to one rather more large. To keep full. To keep the fails diftended by the wind. ^o keep bold of the land. To (leer near to ,or in light of the land. To keep off. To fail off, or keep at a diftance from the Oiore. To ktep the land aboard. The Aims as TO KEEP HOLD or THE LAND. Tokxpjour luff. To continue dofe to the wind. To keep the wind. The lame as TO KEEP YOUR LUFF. Kentledge. What is put in the bottom of the veifel to keep the ground tier from getting wet. Kink. Is when a rope has too much twill. Knee**. Are pieces of timber which confine the ends of the beams to the veflel's fide. Knippfin. A large kind of plated rope, which, being twilled round th Hiefienger and cable in weighing, bind them together. Knot Adivifion of the log-line, anfwering, in the calculation of the (hip's velocity, .to one mile. Knot. r \ here are many forts; fuch as overhar.d knot, wall knot, diamond knot, &c To labour. To roll or pitch heavily in a turbulent fea. Laden in bulk. Freighted with a cargo not packed, but lying loofc, as corn, fait, &c. Laid- a p. The fituation of a (hip when moored in a harbour, for want of employ. Lancb-ho Signifies to let go the top rope, when a top-malt, or top. gallant-mad, is fidJrd. Land. fall. The fir it land difcovcred after a fea voyage. Thus a GOOD r.AND-FALL implies the land expected or deii red; a BAD LAND. PALL the reverfe. Land-locked. The fituation of a Ihip furrounded with L-nd, fo as to exclude the profpeft of the fea, unlels over fome intervening land. Laniards of the ihrouds, are the fmall ropes at the ends ot them, by which they are hove taught, or tight. Larboard. The left fide of a (hip, looking towards the head. Larboard tack. The fituation of a (hip when failing with tiie wind blowing upon her larboard fide. Lnjb. To bind. Laying the land. A (hip which increafes her diftance from the coalt, fo as to make it appear lower and fmaller, is faid to LAY THE LANTD. Lead in p* EXPLANATION OF SEA TERMS. A fair wind for a (Lip's courfe. **?' A chink or breach in the ildcs or bottom of a fhip, through which the water enters into the hull. To leak. To admit water into the hull through chinks or breaches in the fides or bottom. Lee. That part of the bemifphere to which the wind is directed, to diflinguifh it from the other part which is called to windward. Laches. Are the fides of the fails. Leecbliaes. Are lines which haul np the leeches to the yard. Ler, or no near. An order to the helmfman not to keep the fliip fo clofe to the wind. Noththfrvf. A term ufed by the man at the cun to the fteerfman, directing him not to go fiom the wind. Nun-buoy. The kind of buoys ufed by fbips of war. Oakum. Old pope untwilted and pulled open a Oars. What boats are rowed with. N n Qn. EXPLANATION OF SEA TERMS. Offing. To feaward from the land. A Ihip is in the offing, that is, fhe is to fea ward, at adiftance frpm theland. She tfands for the offing, that is, towards the Tea. tjf-and-on. When a {hip is beating to windward, fo that by one board (he approaches towards the more, and by the other ftands out to fea, {he is faid to ftand OFF-AND-ON fhore. Offward. From the ihore ; as when a fliip lies a- ground, and l$ans towards the fea, {he is faid to heel offward. On board. Within the {hip; as, he is come on board. On the beam. Any diftance from the ihip on aline with the beams, or at right angles with the keel. On the bow. An arch of the horizon, comprehending about four points of the compafs on each fide of that point to which the fhip's head is directed. Thus they fay, the fhip in fight bears three points ON THE STARBOARD-BOW; that is, three points towards the right- hand, from that part of ttie horizon which is right a-head. On the quarter. An arch of the horizon, comprehending about four points of the compafs, on each fide of that point to which the fhip's ilern is directed. Open. The fituation of a place expofed to the wind and fea. It is alfo exprefled of any diftant object to which the light or paflage is not intercepted. Open hawfe. When the cables of a fnip at her moorings lead ftrait to their refpective anchors, without eroding, me is faid to ride with an OPEN HAWSE. Orlop. The deck on which the cables are flowed. Over-board. Out of the {hip ; as, he fell over-board, meaning, he fell out of, or from the {hip. Overhaul. To clear away and difentangle any rope j alfo to come; tip with the chafe; as, we overhaul her, that is, we ^ain ground of her. Over-fet. A fbip is OVER-SET when her keel turns upwards. Out-of-trim. The ftate of a fhip when Hie is not properly balanced for the purpofes of navigation. Out-rigger. A fpar projecting from the vefiel to extend fome fail, or to make a greater angle fcr a {biftingback-ltay, &c. Palm. A piece of fteel when mounted acts as a thimble for fe wing canvafs. Parcel a rope. Is to put a quantity of old canvafs round it before the fervice is put on. Parcel a fcam. Is to lay a narrow piece of canvafs over it after it is caulked, before it is payed. Parliament -heel. The fituation of a {hip when {he is made to ftcop a little to one fide, fo as to clean the upper part of her bottom on the other fide. f-aning. Being driven from the anchors by the breaking of the cable. To [awl the capftent. To fix the pawls, fo as to prevent the capftern from recoiling, during any paufe of heaving. To pay. To daub, or pover, the furface of any body with pitch, tar, &;c. in order to prevent it from the injuries of the weather. To pay away or pay out. To flacken a cable or other rope, fo as to let It run out for fome particular purpofe. ^ EXPLANATION OF SEA TERMS.' 283 To pay off. To move a (hip's head to leeward. Peek. A ftay-peek, is when the cable and the fore-ftay form a line. A fhort peek, is when the cable is fo much in as to deftroy the line formed by the (lay-peek. To ride with the yards a-peek, is to have them topped up by contrary lifts, fo as to reprefent a St. Andrew's crofs. They are then faid to be a Portland. Pendant. The long narrow flag worn at the maft head by all mips of the royal navy. Brace pendants are thofe ropes which iecure the brace-blocks to the yard-arms. Pendant broad. A broad pendant hoifted by a commodore. Pierced. A term for gun ports. Pitching. The movement of a ihip, by which (he plunges her head and after-part alternately into the hollow of the fea. To ply to windward. To endeavour to make a progrefs againft the direction of the wind, Point-blank. The direction of a gun when levelled horizontally. Points, A number of plated ropes made laft to the fails for the pur- pofe of reefing. Poop. The deck next above the quarter deck. Pooping. The (hock of a high and heavy fea upon the (lern or quar- ter of a Ihip, when (he feuds before the wind in a tempeft. Portland yards. Are the lower yards lowered half way down and toped an end. Fortoife. The fame as PORT LAST; TO RIDE A PORTOISE is to rifle with a yard ftruck down to the deck. fort. Ufed for larboard, or the left fide; alfo a harbour or haven. Port. A name given on fome occafions to the larboard fide of the (hip -, as, the (hip heels to port, top the yards to port, &c. Port the helm! The order to put the helm over to the larboard fide, Port-loft. The gunwale. Ports. The holes in the (hip's fides from which the guns are fired. Prefs of fail. All the fail a (hip can fet or carry. Preventer. An extra rope, to affift another. Prizing. The application of a lever to move any weighty body. Purchafe. Any fort of mechanical power employed in railing or re- moving heavy bodies. Purchafe. To purchafe the anchor, is to loofen it out of the ground. Pudding and dolphin. A large. and leiler pad made of ropes, and put round the malts under the lower yards. Barters. The feveral ftations of a (hip's crew in time of action. Quartering. When a (hip under fail has the wind blowing on her quarter. Quoit. Is a rope or cable laid up round, one fake over another. Raft. A parcel of fpars la (lied together. Raft-pert. A port in a veflel's bow or ftern to take in fpars or timber, To raife. To elevate any diftant object at fea by approaching it! thus, TO RAISE THE LAND is llfcd IR Oppofition tO LAY THE LAND. To rake. To cannonade a (hip at the flern or head, fo that the balls fcour the whole length of the decks. Range of cable. A fufficient length of cable, drawn upon deck before the anchor is caft loofe, to admit of its finking to th bottom without any check. , - N n 2 Rat lives , 284 EXPLANATION OF SEA TERMS. Ratlines. The fraall ropes faflened to the fhrouds, by which the men go aloft. R.each. The diftance between any two points on the banks of a river, wherein the current flows in an uninterrupted courfe. Ready about ! A command of the boatfwain to the crew, and im- plies that all the hands are to be attentive, and at their itations for tacking. Rear. The laft divifion of a fquadron, or the laft fquadron of a fleet. It is applied likewife to the laft fliip of a line, fquadron, or di- vifion. Reef. Part of a fail from one row of eyelet-holes to another. It is applied likewife to a chain of rocks lying near the furface of the water. Reefing. The operation of reducing a fail by taking in one or more of the reefs. Reef-bandi. Pieces of canvafs, about fix inches wide, fewed on the fore part of fails, where the points are fixed for reefing the fail. Reeve. To reeve a rope, is to pot it through a block, and to unreeve it, is to take it oat of the block. Ribs of ajhip. That is, the frame. Rendering, The giving way or yielding to the efforts of fome me- chanical power. It is ufed in oppofition to jambing or liicking. Ride at anchor. Is when a thip is held by her anchors, and is not driven by wind or tide. To ride athwart, is to ride with the (hip's fide to the tide. To ride hawie-falien, is when the water breaks into the hawfe in a rough fea. Riding. W hen expreiTed of a fhip, is the flate of being retained in a particular ftation by an anchor and cable. Thus the is laid to RIDE EASY or TO RIDE HARD, in proportion to the ftrain upon her cable. She is likewife laid to RIDE LEEWARD TIDE if anchored in a place at a time when the tide fets to leeward, and to RIDE WINDWARD TIDE if the tide lets to windward: to RIDE BETWEEN wi NIT AND TIDE, when * the wind and tide are in direct oppofition, caufing her to ride without any ftraiu upon her cables. To rig. To put the ropes in their proper places. Rigging, 'ihe ropes to rig with. Rigging out a boom. The running out a pole at the end of a yard to extend the foot of a fail. To rig the capfmrn. To fix the bars in their refpeclive holes. Righting. Keftoring a (hip to an upright pofition, either after ihe lias been laid on a careen, or after the has been prelTed down on her fide by the wind. To right the helm. Is to bring it into midlbips, after it has been pufhed either to {larboard or larboard. Ring-ropes. Several turns round the cable and through the ring to fecure the cable. Road. A place near the land where ftiips may anchor, but which is not flickered. Robins. Small plaited yarns with eyes to fafren the fails to the yards with. Rolling. The motion by which a (hip rocks from fide to fide like a C'ad'.e. Is what the cordage and cables are made with. EXPLANATION OF SEA TERMS. 285 ^ A nr.me applied to any maft, yard, or boon, placed in merchant-fhips, or a rail or fence above tke veffel's fide, from the quar- ter-deck to the forecaftle. Round-hoitfe. A houte built upon deck. Rounding. Ropes ufed to put round the cable in the wake of th* hawfe, or ilem of the mip, to keep it from rubbing or chafing the cable. Ronndwg-in. The pulling upon any rope which paflVs through one or more blocks in a direction nearly horizontal; as, ROUND-IN the tveather braces. Round-turn. The fituation of the two cables of a (hip when moored, aftei they have been feveral times crolTed by the Twinging of the mip. Rounding-up. Similar to ROUNDING- IN, except that it is applied to ropes and bl cks which act in a perpendicular direction. To row. To move: a boat with oars. Ronvfing. Pulling upon a cable or rope without the afliftance of tackles. Rudder. The machine by which the fhip is fleered. .Rullock. The nitch in a boat's fide, in which the oars are ufed. Run. The after part of the veilel under water. Runner- pennani. The firit that is put over the lower mafts with a block in each end. To runout a warp. To carry the end of a rope out from a mip in a boat, and fattening it to fome diltant object, Ib that by it the Ihip may- be removed by pulling on.it. 7 ofa^ to It2~<-varst. To make confiderable lee woy. Sailing trimf Is expreffed of a fhip when in the beft ftate for fail- ing. Sallyport. A large port in the quarters of a fire-fhip where the cap- tain comes out at, when he fets her on lire. Salvage. A part of the v, ; lne of a fhip and cargo paid to the falvors. Scanting. The variation of the wind, by which it becomes unfavour- able to a Ihip's making great progrefs, as it deviates from being large, and obliges the 'veiTel to iieer clofe-hauled, or nearly to. Scraper. A ftcel inftrument to fcrape with. Scudd. To po right before the wind; and going in this direction without any fail fcl is called ipooning. Scuttle. A fmall cover to cover a fmall hole in the deck. Scuttling. Cutting large holes through the bottom or fides of a (hip, either to link or .to unlnde her expedition fly when ftrandcd. Sea. A large wave is fo called. Thus they fay, A HEAVY SEA. It implies likewife the agitation of the ocean, as ^ GREAT SE\. It expreilV.s the 4'n'^ction of the waves, as A HEAD SEA. A LONG SKA means an uniform and fteady motion of long and extenfive waves; a SHORT SEA, on ,the contrary, is when they run irregularly, broken, and interrupted. Sea-boat. A veiTel that bears the fea firmly, without draining her mafts, &c. Sra-dothfi, Jackets, trowfers, c. Sea-mark. A point or object on more, confpicuoully feen at fen. Seams. The joints between the planks. A fufficLnt diftance from the cojft or any dangerous rocks. 286 EXPLANATION OF SLA TERMS, rocks, &c. fo that a {hip may perform all nautical operations withcnit danger of fhipwreck. Scazc. To bind or make fa ft. Stazeing The fpun.yarn, marline, &c. to feize with. Sending. The a6t cf pitching precipitately into the hollow between two waves. Sfrvr. To wind fomething about a rope to prevent it from charing or fretting. The fervicc is the thing fo wound about the rope. Setting. The aft of obferving the fituation of any diftant object by the compafs. Tofetfail. To unfurl and expand the fails to the wind, in order to give motion to the (hip. Tofet up. To increafe the tenfion of the ihrouds, back-flays, &c. by tackles, laniards, &c. Stttb. To lower j as, SETTLE THE TOP-SAIL HALYARDS, lowr them. Shank of an anchor. The part between the ring and the flewks. Shank- fainter. The rope by which the fhank of the anchor is held up to the fliip's fide j isalfomade fail to a piece of iron chain, in which the (hank of the Anchor lodges. Tajhape a courft-. To diredl or appoint the track of a fhip, in order to profecute a voyage. Sheer. The fheer of the (hip ie'the curve that is between the head and the (tern, upon her fide. The fhip fheers about, that is, fhe goes in and out. Sbtfrs, are fpars lafted together, and raifed up, for the purpofe of getting out or in a maft. Sheering. The veflel is faid to fheer when the cable and anchor is cot right a-head. ''Sheer-bulk. A veffel to takeout and put in the lower mails and bowfprit. Tojbeer off. To remove to a greater diftance. Sheet. Ropes fixed to the lower corners of fquare fails, &c. Tojheet home. To haul the fheets of a fail home to the block on the yard arm. Tojhift the helm. To alter its petition from right to left, or from left to right. Tojhip. To take any pcrfon, goods, or thing, on board. It alfo implies to fix any thing in its proper place; as, to SHIP THE OARS, to fix them in their rowlocks. Ship-Jhatik. A double bight taken in a rope with a hitch at each end. Ship Jhape Doing any thing in a iailor-like manner. Skivering. The ftate of a fail when fluttering in the wind. Shcal. Shallow, not deep. Shoe. A piece of wood in the fbape of a ihoe, ufed in nfh'ng the janchor, to prevent the bill from rubbing the planks, or catching the bends. Tojhoot a-head. To advance forward. Shore. A general name for the fea-coail of any country. 1"njhorten fail. Ufed in oppofition to MAKE SAIL. Shrouds. Large ropes iixed on each fide of mads. Sinnctt. A imall platted rope, made from rope-yarns. Skidds. Pieces of wood to put over the fide, to hinder any thing from rubbing the fides. EXPLANATION OF SEA TERMS. Slack-water. The interval between the flux and reflux of the tide, when no motion is perceptible in the water. To flip the cable. To let it run quite out when there is not time to weigh the anchor. To flue. To turn any cylindrical piece of timber about its axis without removing it. Thus, to SLUE A MAST or BOOM, is to turn it in its cap or boom iron. Sound. To try the depth of water ; alfo a deep bay. Spars. , Pieces of trees as they are cut in the wood. Spanijh burton-ivindlafe- A particular way of fetting up the topmaft rigging in merchant veilels. Spear of the pump. The handle of an hand-pump. To f pill the mizen. To let go the iheet, and brail it up. Tofpill. To difcharge the wind out of the cavity or belly of a fail, when it is drawn up in the brails, in order to furl or reef it. Spilling-lines . Are ropes contrived to keep the faifs from beinj blown away, when they are clewed up, in blowing weather. Splice. To make two ends of ropes Lft together by um wilting them, and then putting the ftrands of one piece with the ftrands of the other. Split. The (late of a fail rent by the violence of the wind. Spoon-drift. The diftance flic runs when fcudding without any' fail. Spray. The fprinkling of a fea, driven occasionally from the top of a wave. Spring. A fpring upon the cable, is a hawfer bent to the cable, out- fide the hawfe, taken in at the moft convenient pait of the Ihip aft, for the purpofe of calling her. Spring-flays. Are rather fmaller than the Hays, placed above them, and intended to anfwer the purpofe of the Hay, if it fliould be ihot away, &c. Spring-tide*. Are the tides at new and full moon, which flow higheft and ebb loweft. To fpring a mafl,yard, &c. To crack a maft, yard, &c. by means of (training in blowing weather, fo that it is rendered unfit for ufe. To fpring a leak. When a leak firft commences, a Ihip is faid to SPRING A LEAK, To fpring the luff. A fliip Is faid to SPRING HER LUFF when (he yields to the effort of the helm, by failing nearer to ihe wind tha% before. Spun-yarn. Two, three, or four rope-yarn twitted together. Spur-Jbores. Are large pieces of timber which come abaft the pump. well. Spurling-line. Is a line that goes round a fmall barrel, abnft the bar- rel of the wheel, Jtnd coming to the front beam of the poop-deck, moves the tell-tale with the turni-ng of the wheel, and keeps it always in fucU pofition as to fhew the polition of the tiller. Squadron. Five fail of the line. Squall. A fudden violent blaft of wind. Square. This term is applied to yards that are very long, as TAUNT is to high malls, the yards \ To brace th^ yards, fo as to hang at right angles TQ 288 EXPLANATION OF SEA TERMS. To continue advancing. Tojiand in. To advance towards the fhore. Tufiundnff. To recede from the fhore. Starboard. The right-hand fide of the fhip, when looking forward. Starboard-tock. A fhip is faid to be on the STARBOARD-TACK, when failing with the wind blowing upon her flarboard fide. Starboard the helm! An order to pufh the helm to the larboard fide. ' To ftay a fiif>. To arrange the fails, and move the ru.'der fo as to bring the fhip's head to the direction of the wind, in order to get her on the other tack. Stay-peak. \Vhen the cable makes the fame angle as the flay doth. Stays. Large ropes coming from the matt heads down before the mnfts, to prevent them from fpringing, when the ihip is fending deep. Sieady / The order to the helmfman to keep the Ihip in the direc- tion fhe is going at that inftant. Steadj. In failing, is when fhe is going her "right courfe off the wind. Steady ilejhip. That is by running a rope or towling out on either fide when at anchor. Steering. The art of directing the fhip's way by the movement of the helm. Steerage-way. Such degree of progreffive motion of a fhip as will give effect to the motion cf the helm. Stee^e. Turning up. The bowfprit fteeves too much, that is, it is too upright. To ftem ike tide. When a fhip is failing again-ft the tide at fuch a rate as enables her to overcome its power, fhe is faid to STEM THE TIDE. Stem. The fore part of the vefTel. Stern. The after part of the veffel. Siernfaji. A rope confining a ihip by her flern to any other fhip or wharf. The fanned a-flern, oppofed to HEADMOST. The motion by which a fhip falls back with her ftern foremoft. Stiff. The condition of a fhip when fhe will carry a great quan- "ty of fail without hazard of overfetting. It is u(ed in oppofition to RANK. Stirrup. A piece of rope j one end nailed to the yard, in the other a thimble for the horfe to reave in. Stoppers. Large kind of ropes, which being fattened to the cable in a fferent places abaft the bitts, are an additional fecurity to the fhip at pchdr. Tofioiu. To arrange and difpofe a fhip's cargo. Strand. One third part of a three -ftrand rope. Stranded. When a veffel is got aground on fome rocks, and filled with water. To ^ cam the buoy. To let it fall from the fhip's fide into the water, previoufly to cafting anchor. the Stretch-ci-t. A term ufeci to the men in a boat, \vhen y fliould pull ftrong. / EXPLANATION OF SEA TE&MS* 289 ToftriJte. To lower or let down any thing. Ufed emphatically to denote the lowering of colours in token of furrender to a victorious enemy. To Jlrikt foundings. To touch ground with the lead> when endeavour- ing to find the depth of water. Strops. Eitner rope or iron, which are fixed to blocks or dead eyes to attach them to any thing. Sued 01 Sewfd. When a {nip is on (hore, and the Water leaves her, (he is faid to be fued ; if the water leaves her two feet, fhe fues, or is fued two feet. Surf. The fwell of the lea that breaks upon the (hore, or on any rock* Tofurge the capftern. To flacken the rope heaved round upon it. Sway. The feme as Hoift. Sway away. Hoift, ufed in getting up mafts or yards. Swabb. A kind of large mop made of junk to clean a (hip's deck with. Swell. The fluctuating motion of the fea either daring or after a ftorm. Sweeping. The at of dragging the bight or loofe part of a rope along the furface of the ground, in a harbour or road, in order to drag up ibmething loft. Swift the capftern bars. Is to confine the outward end of the bars one to another, with a rope. Swinging The at of a {hip's turning round her anchor at the change of wind or tide. To tack. To turn a ihip about from one tack to another, by bringing her head to the wind. Taking-in. The a of furling the fails. Ufed in oppofition to SET- TING. Taken a-back. See A-back. Tarpaulin. A cloth of canvas covered with tar and faw-duft, or fome other cornpofition, fo as to naakeit water proof. Taught. Improperly, though very generally, ufed for TIGHT* Taunt. High or tall. Particularly applied to mafts of extraordi- nary length. Tell-tale. An inftrument which traverfes upon an index in the front of the poop deck, to (hew the pofition of the tiller. Tending. The turning, or fwinging, of a Ihip round her anchor in a tide- way at the beginning of ebb and flood. Thwart. See A- THWART. Thwart Jhips. See A-THWART SHIPS. Thus ! An order to the helmfman to keep the (hip in her pfefcnt fituation, when failing with a fcant wind. Tide. way. That part of a river in which the tide ebbs and flows ftrongly. Tier' A row; ascable-tier, atierof guns,caflcs, or a tier of (hips, c, Tide -gate. A place where the tide runs ftrong. : Tide it up. To go with the tide againft the wind. Timbers. What the frame is compofed of. Tiller. A large piece of wood, or beam, put into the head rudder, ana 1 by means of which the rudder is moved. TompioHs, or Tomkins. The bung, or piece of wood, by which mouth of the cannon is filled to keep out wet. O o 29<> EXPLANATION OF SEA TERMS. Topping. Pulling one of the ends of a yard higher than the other, To tow. To draw a (hip in the water by a rope fixed to a boat or other ihip which is rowing or failing on. Toueft T TOW do you find the golden number ? J~J A. I add one fo the given year, and divide the fum by 19, the remainder will be the golden number. <%. How do you find the epaft for any year ? A. By dividing the given year by *o,, and multiplying the remainder by 1 1, the produft will be the epaft, if it does not exceed 30 ; hut ir it doe*. I fubtraft 30 from it as often as I can, and the remainder will be theepaft. Q How do you find the moon's age? A. To the epact I add the day of the month, and the number of the month ; their fum will be the moon's age, if it does not excetd 30 ; but if it doesj I fubtracl 30 from it as often as J can, and the remainder will be her age. Q. How do you find the moon's fouthing, or the time of her coming to the meridian ? A. I multiply the moon's age by 48, and divide the produd by 60 ; the quotient will be the hours, and the remainder the minutes when (he is on the meridian part noon ; Or, I may multiply the moon's age by 4, and divide the product by 5, the quotient will be the hours, and the re- mainder, multiplied by 12, will be the minutes when fhefouths, or is on the meridian, in the afternoon : But if this time (hould exceed 12, I fub- traft 12. from it, and the remainder will be the time of her fouthing in the morning. ^. How do you find the time of high water at any place ? A. To the moon's fouthing on the given day, I add the time of high water, full and change, at the given place, and the fum will be the time of high water there in the afternoon ; but if this time fhould exceed iz, I fubtraft 12 from it, and the remainder will be the time of high water in the morning 5 and if it exceeds 24, I fubtraft 24 from it, and the remain- der will be the time of high water in the afternoon *. ^ Suppofe that you go into an harbour, and find by your watch that it is high water at any hour of the day ; by what means do.you find the times when it is high water on full and change days in that place ? A. I find the time of the moon's fouthing on that day, and fubtracl it from the time of high water at the given place, if I can, and that will be the time of high water. If I cannot, I add 1 2 to it, and then fubtracl the above time; the remainder will be the time of high water at the given place, on full and change days. * The time of high water is found more corrcd by the Tables, fee p*c X28, i-o > How 294- IX AM I RATION OF A ^ Hoxv do you find the zc.nrh difhnce of any object? A. By correcting the altitude f'-r tin- dip, r-rfrnchon and femidiameter, and then fubrr.-.ctin;; : .t iromgo , the remainder will be ihez-nith d ftancc, which will he. either north or Couth, according; as the object bears of me. Q. Suppofe the zenith difbmce 10 north", and the declination 20 north, what latitude are you in, and of what name ? A. Ten degrees north. ^ 1 he fun is in your zenith, what latitude are you in ? A. The fame os the declination is, wither north or fouth. ^ Your zenith diftan^e is 20 north, anc} your declination is 20 north, what latitude are ycu in ? A. Upon the equator, and consequently in no latitude. Q. Suppofe th:-.t your zenith dilhnce is 50 fouth, and the declination 10 north, what latitude are you in ? -4. Sixty degrees north. Sj. Suppofe y<-ur zenith diftance be 45 north, and the declination 15? fouth, what latitude are you in? A. Sixty degrees ibuth. Q. Suppofe your z-ffith diftance is 45 north, and the declination 15 north, what latitude are you in ? A. Thirty degrees fourh. ^. What do you mean by the wcH amplitude? A. The true amplitude is the number of decrees that the fun, moon, or jftirs, ri ! 'e and fct, to th ; e northward or Couthward of the true eaft or weft. The magnet ; c amplitude is the number of degrees they rife or fet to the northward or fouth ward of the eaft or wt ft point of the compafs. ^ How do you find the true amplit-jd ? A. As the co-fine of the latitude : is to the radius : : Co is the fine of the fun or ibir's declination: to the fine of the true amplitude. Or if the (ecant of the latitude be added to the fine of the fun or tier's declination, the fum (rnecliri^ 10 in w the index) will J?e tin- log, fine of the true amplitude. Q. Bu r foppbfrng t l e evening r m m'.p.g proves cloud v, and you cannot fee the. fnn or (tar, how will you find the variation of the corap.ifs 5 A. By nn azimuth. ^ Vv hit do you mean by an azimuth ? Tb-- true azimmh is tlie diiiiiic of the fun or (lar from thetrue north (>\- fouth at every d'-gree aiu! minute of altitude. Thf magnetic azimuth is th ir diitance, at each degree and minute of altitude from thr nnrth or f ATth point of the compafs. ^. H'w do you find the true aziniuih ? A By adding the complement of the latitude, the complement of the altitude, and the fun or liar's polar diLbnce into one fum ; from half this fum I fubtraft the polar diftance,' noting the half fum and the re- niainder : Then to the arithmetical complement of the co-fine of the latitude, I add the arithmetical complement of the co-fine of the alti- tude , the log. fines of the half fum and the remainder ; half the fum of thefe four logarithms will give the co-fine of half the true azimuth, which being doubled is the true azimuth, reckoned from the north in north latitude, and from the fouth in fouth latitude. Or, it may be found thus : To the log. co fecanls of the co-latitude and altitude, add the log. fines of the half fum and the remainder; half the fum of thefe four logarithms (rejecting 20 in the index) will be the log. co-fine of half the true azimuth, as before. ^ You YOUNG SEA OFFICER. 4J. You have given the true amplitude or azimuth by calculation, and the magnetic amplitude or azimuth by obfervation; how do you find the variation ? A. Fy placing both the amplitudes or azimuth before me; then, if the true amplitude or azimuth be to the right hand of the magnetic, or obferved, the variation is eaft, but if H be to the left hand, it is weft. Q. You have the latitude and longitude the thip is in, confeqiumtljr her place, how do you fhape her courfe, or in other words, find her courfe and diftance to any other place, whofe latitude and longitude is known ? A. It may be found briefly by the tables of difference of latitude and departure, bnt by logarithms I will fay, As the meridional difference of latitude : is to radius : fo is the dif- ference of longitude : to the tangent of the courfe. And A. As the co fine of the courfe : is to the proper difference of lati- tude : : fo is radius . to the diftanoe. ^J. You have the difference of latitude and departure made good in the 24 hours, how do you find the courfe and diftance, and the (hip's .place, by logarithms? A, As the difference of latitude : is to radius : : fo is the departure : to the tangent of the courfe. And, As the co fine of the courfe : is t n the difference of latitude : : fo is radius : to the diftance made good in the 24 hours. .Having the latitude and longitude left, and the difference of latitude, I find the latitude in, and the meridional difference of latitude; I then fay, As the co-fine of the courfe: is to the meridional difference of latitude, : : fo is the fine of the courfe : to the difference of longitude. Or, as the proper difference of latitude : is to the departure : : fo is the meridional difference of latitude : to the difference of longitude. Having Phe lon- gitude left, and the dir^rence, the longitude in is fouru} by addition or fubtra&ion, as the cafe requires. 4J. You have now the (hip's place by calculation, how do you find it on a Mercator's Chart? A. By laying a ruler acrofs the Chart on the fhip's latitude, and taking her longitude in ray compaifrs, and fetting one point, on the meridian, by the fide of the ruler, I turn the other eaft or weft, according as the longitude is, (by the fide of the ruler) and it will point out the ihip's place. !$. You have now the fhip's place, how do you find her bearing and diftance to any other known place? A. By laying a ruler over the point where the fliip is, and the given place, and with the companies I take the nea reft difta/ice between the ruler and the centre of fome co'.rp-.'s on the Chart $ and Hide the coin- pa fles along the ruler (keeping both points ^erptndicu'Iar :o it: the fart licit point from the ruler will Ihew the courfe, or beanr the (hip and p .un, I take the diftance between the (hip and place in the cornpaffe.s, and th^n lay one point on the meridian as much below the ilr the other is above the given phic'- : that diftance, reckoned lesgiirs or miles on the meridian, according as it is divided, will be the diftanca ' J^. You are ordered to a ihip, (he is lying in dock; prepare to take Jier out of dock, A. -I 296 EXAMINATION OF A A. \ would fake on board what kentledge was neceflary, ftream an- chor and cable, kedge anchor, hawfer and towline, with fome fpare ropes for guys, to keep her fair for the dock gates} buoy and buoy ropes, for liream andkedge. 1^. When your Ihip is out of dock, what is firft to be done? A. I would fccure her, then take on board the remainder of the kentledge and level the hold; by laying the kentledge from the fore part of the fore hatchway to the after-part of the after hatchway. ^ If you are taking in bales, how would you dunnage, and which part of the fliip mod ? A. I would dunnage fix inches, and moflly about the pump well, main hatchway, the wake of the chains and floor timber heads. 4J. Suppofe you have one and a half foot water in your hold, and your ihip heels four ftreaks; what dunnage ought you to have to pre- fev ve the cargo ? A. Three feet. Q How would you moor your mip at Gravefend ? A. I would come to with my fraall bower, veer the fervice into the hawfe, and then hang my bed bower anchor to the long boat, and with the tide drop her a ftern: when the cable is taut, let go the anchor, firft letting go the ih?.nk rope, to keep the cable more taut. ^. How would you hang the anchor to the long boat ? st. Take the buoy-rope over the roller (which is in the middle of the ftern of the long boat), bring the bight round the main thwart, cockbill the anchor, hook the cat to the anchor, and lower away, until the flukes of the anchor are clear of the boat's bottom, then make faft the buoy- rope, have a fhank-rope through the ring, (which is at the boat's ftern- poft) pafs it round the lhank of the anchor, make it faft to the after thwart, lower away and unhook the cat, then veer away the cable j be careful to heave the buoy over board and fpare buoy rope before you iet go the anchor. ^. How do you moor in the Downs ? A. With my beft bower to the S. W. I would veer away with the laft quarter ftreara-tide, and moor with the fmall bower to the N. E. jg. Where is the beft anchoring in the Downs ? A. Upper Deal church and caftle in one, in eight or nine fathoms water. . How would you unmoor in the Downs with the wind at North ? A. 1 would fplice my ftream cable to my fmall bower, and veer away at NOTE. All cables ought to be 120 fathoms in length, and are in proportion to each other as the cubes of their diameters. The number of threads of which a cable is compofed being always proportioned to the length and thicknefs, and the weight and value of it is determined by this number. The number of threads and weight cf cablesof different circumferences may be feen i the following Table: YOUNG SEA OFFICER. 297 at half ebb, that I might have tirne to ftow my belt bower, and ihorten in my fmall bower cable, before the fhip tends to windward. Q. Proceed to unmoor (hip as it is done in the navy. A. I would fend for the matter to fee the hawfe is clear, turn all hands up to unmoor ihip.. lay the capftan bars for Ihipping, call the mate to fee the meffenger palled for the beft bovver, rig the davit our, hecaufe I will take it up the firft quarter flood, get the cat and fifh to pafs for the beft bower, ftretch along the fiih-tackle; quarter-matters clown in the tier, and ftand by to veer away the fmall bower cable ; (hip the caplian bars, pin and fwift them ; clap on the ftoppers before the bitts, and bring to the meffenger. At the fame time unbit the beft bower, rowfe aft the flack cable; heave taut, take off the ftoppers, hold on the mef- fenger, and heave away; veer away the fmall bovver cable; clap on ihe nippers. Thick and dry for weighing, heave cheaply; the anchor's -\ way, keep faft the fmall bower cable; quarter matter take hold of the helm; look out for the anchor; the anchor is in fight; heave and pauI (he oapftan ; hook the cat ; haul taut, and take a turn ; (urge the meffenger round the capftan ; take off the nippers ; out cable ; cable enough ; haul cat ; belay the catfall ; pafs the ftopper ; hook the fillij try tifli by hand; haul with the fifh, belay the filli-tackle fall; pals the lhank painter 5 bowfe too the ftock with the tackle ; belay the (hank-painter; make faft the ftopper and ftcck ladling ; come up cat and fifh ; unhook both ; haul the buoy and buoy rope in; then thift the meifruger for the fmall bower and bring too, ciap on the ftoppers before thr oitis and unbit the cable; rowfe aft the Hack cable; man ihe apftan ; hold on the mefienger; forocaftle-men rig out the davit for the fmall bower; when the anchor is a ftay peek, fend the top men to loofe the fails ; man the yards; ftretch along the topfatl iheets; let fall the topfails; overhaul reef tackles, bunt-lines and clue-lines: foot the fails out of the top j haul home the topfail-fheet ; ftretch along the topfail-halyards and man them; quarter mafter and boatfwain's mates attend to the braces j hoift away the topfails; topfails atrip; belay the halyards; trim the fails; heave up the anchor; ftow it as before, and haul the buoy and buoy rope in. ^. liow would you unmoor with the wind S. K. or S. ? A. Veer on the beft bower cable, and take the fmall bower-anchor up firft; and proceed as before-, then heave in to the ihort fervice on the beft bower, &c. If the anchor has gre.t hold and afraid of Hand- ing the meffenger, clear away the main capftan and lafli a block, or purchafe blqcks, on the cable, and one to the main-malt, 01 one to the two ports abreaft of the main, malt ; reeve a hawier through them, and heave on both capftans together. ^ Suppofe you are clofe upon a wind, in moderate weather, with all your fails fet, ho-.v will you tack the Ihip? A. I would ftretch along the lee bow-lines, and weather- braces, ths weather- fheets and lee-tacks; then put the helm a-lee, let go the fore fheet, lee fore-top fail, brace and fore.top bow-line; jib and ftay-fail fheets. Wfien the fore topfull touches, b ace too and help-her; when aback, brace up and help her; when the wind is out of the after fails, raife tacks and meets: ihift the fiay-G-.il tacks, and haul over the ftay- fail fheets; when the wind is rather a point on the bow, if lure of coming about, haul the main fail. :V .B. One watch of the top-men QII the quarter-deck^ and fore-caftle to fet up the weather-breaft biick- P p flays. 29$ EXAMINATION OF A flays. If {he has ftern way, fhift the helm and top the fprit-fail yard ; haul n board the main tack and aft the main (hee'. Brace np the main yard when the afler fails are full ; haul off all ; and haul on board the fore tack ; keep in the weather braces forward, and let her come to, then brace up ; haul aft the fore- flieet, jib and flay fail fheets 5 (fet up the back flays when the fhip is head to wind) and haul the bow-lines; then haul tnut the weather-braces, lee tacks, and weather- iheets ; have the b'aces let go at once ; when the word is given to haul rnainfail, (all the hands on the braces fhould keep hauling taut in for the run) the yards will fwing of themfelves. 4J. How \*ould you tack a fhip under her three top-fails ? A. I would put the helm a-lee, eafe otfthe fore-top fail brace, keep fan 1 the fore top bowline : when the fore top-fail touches, brace to and help lier ; when the wind is a-head, haul the main top- fail and fliift the helm : then brace up the main yard, and haul the main-top bowline; when the after- fails are full, let go and haul; keep in the weather- brices forward, and when fhe comes to brace fharp up, haul the main and fore top bowlines, haul taut the weather braces, and top the fprit- fail yard. ^- How do you veer, or wear a (hip with a 1 ! her fails fet ? A. I would haul the mizen up, and the mizen flay fail down, or brail it up, hard a weather ihe he'm, fhiver the mizen top fail, let go the main and main- top bowlines, eafe oft the main (beet, the lee main brace, and round in the weather brace. When the wind is abaft the beam, raife the main t-ckj wh^n the wind is aft fquare 'he he:er the cahjes to be bent ; thus get their ends up, reeve, liaufe, and ring ropes to haul them out, the forecaitle men to clinch them, and quarter- mailer to clap the bends on, reeve the runners and tackles, unftow the anchors, bend the buoys and bony- ropes, fingle the ftoppers and (hank, painters, hit the bower.cables with a long range, have the dog (toppers to pafs, fee the tiers clear, have hand leads and lines in the chains, fend down the top.ro; es, reeve the top* tackle-falls unfling the lower yards, when the cables are bent, &c, clap the hawfe bucklers on. *. Yon are off the Eddy (lone, the wind at S. W. in a hard gale, under a reef fore-fail, and you rnuft anchor in Plymouth Sound, how will you bring up for the fafety of the ihip, -and with what anchor ? A., To give myfelf time for anchoring, I will haul my forefiwl up, get tbe fhect anchor over the fide, and bit the cabie to the after-bits with a range, get down too-gallant mall, and fprit- fail yard, in foie and aft, unfki the lop-ma^s and ftretcfi along the jeers, clap the wing (topper on the feeond YOUNG SEA OFFICER. 001 fecond cable of the beft bo-,ver; being all clear, I'll fe roy forefail and (leer in for the Sound, and when I am near the place I intend to anchor in, I'll man the fore clue garnets, and ftand by to lower the yards and top-mafts, being ready, lower away, haul the fore-fail clofe up. and furl k a Portland, clap rolling tackles on the lower yards, and heel mpcs ou ihe top-mafts ; having the marks on to anchor, ftream the beft bovver buoy, and fee that it goes clear of the fhip, and when I intend to fating up, put the helm down, and haul the mizen out, then let go the anchor and veer away at leaft one arid a hajf cable before I check her ; fhould the (hip drive with two cables our, en the beft bower, ftream the imall bower- buov and 'let go the anchor, which will allow me to veer a cable on the final! bower; this will bring her up if ir blows ever fo hard, an,i I have Itill the Ihect anchor to Hand by ; when I have brought up, and double- bitred and ftopcred the cables, I'll get the top- fail yards fore and aft in th tops, and make the (hip as fnug as poffible ; as foon as the gale is over, get the anchors up and moor properly. 'Ihe beft method is to unbend the fmall bower buoy rope from the anchor, it being liable to get foul of the beft bower cable, by the bucy going over and over again of the faid cable,, which has been ortcn the cafe. N. B. In coming from the vveftward with a hard gale of wind, and bound inro the Downs, take the fame method. 4J. Suppofeyou are on a lee fhore, and had neither room to veer or ft ay, nor any anchoring ground, how would you put the fnip's head round the "other way. A. I would put my helm hard a-lee ; when (he comes head to wind, raife the fore and main tacks dire&ly,. make a run with my weather bracts and lay all aback at once, then haul forward my lee-tacks and bow-lines as-far as I can, that the (hip may fall round on her heel, and when the main-fail begins to fhiver, 1 would haul it up, fill my head fails, and fhift the helm hard a-vveather ; when the wind comes on the other quarter, haul on board the main tack, and bring her clofe to the wind. ^ Suppofe it blows hard, you cannot carry your courfes, night coming on, and it is likely to blow harder, what will you do ? A. I will haul the fore fail up and furl it, balance the mizen, haul it out to keep her to, then haul up the weather main clue-garnc t and bunt-line, then the lee-clue-garnet-bunt-lines and leach-lines, fquare the yards, and get ftrops round the maft above the booms to hook the yard tackles to for rolling tackles, then reef the fail; when reefed, h ml on board ihe tack, get aft the iheet handfomely, tend the braces, bowfe up the bow-line, and haul up the mizen. i?. You are juft abreaft of Portland, coming up Channel, the wind has taken you back; you have all fails fet, and you have no time to take them in, for you will be on (hore or in the Race prefemly, how will you pro- ceed ? A. If Ihe has head-way, I will put the hdm-a-port, let go the fore ihert and larboard braces ; as foon as the after-fails fhiver, haul down all the ding-fails ; if it blows freih take in top.gailaht fails, brace up the after* yards; '.vhen full, brace up forward and haul on board the fore-tick, uiu: all (harp, aud haul the bow-lines, and then haul taut tbe weather-braces, ^ Suppofeyou are turning over the Fluts with your top-fails and fore 1 - fail, you endeavour to put about, but the will not ft ay, there is a fand a-h?ad, within a caMe's length of you, what will you do? A. \ wilh heave all ?. ! >ack, when foe has paid we'll off, (hi ft the helm ; r-r^ce about the. henl-laii* and Chivcr the aflci-laiis ; then (Le will veer round asy.) ibnd off. You EXAMINATION OF A <. You arc in a gale of wind, and fplit your fore-courfe, what will yoUf do? A. I'll man the weather fore clue-garnet, hunt-lines and leach-!ines# cafe off the fort-tack, and when clued up, man the lee-clue-garnet and haul it clofe up; let go the lee-brace j when I let go the fheet and fquarethe yard, haul taut the lifts and braces, fend hamis to unbend the /ail; when another is hent and I want to fet it, I will haul on board the fore-tack, and haul aft the fore- fheet, brace (he yard up and haul the bow-line. 4J. It blows hard, and ycu want to reef your courfes^ how would you proceed ? A. I will let go the top-fail fheets and lifts, man the down-haul fackles, lower away the jeers, let go the bow-lines and clue the fails up> round in the weather-braces, haul taut the lifts, braces, and rolling tackles ; then fend hands up to reef the fails ; when I want to- fet them, I will pro ceed with the fails as before. <. Suppofe it blows hard at S. W. and you are drove from your anchors in the Downs, what would you do ? A. I would fteer for the Gull firearn, which I (hall know by having the opper Light on the South Foreland to bear S. W. by S. then fteer away between the N. E. and N.E. by N. which will carry me between the Brake and the Goodwin Sands, keeping to the Goodwin in nine or ten fathom* and to the Brake in feven or fix. i^. Ycu are (landing on a wind with all your fails fet; your enemy is in fight, ftanding towards you, how do you clear your (hip for aclion ? A. I will call all hands to quarters, up hammock?, the quarter- makers to (low them in the netting, and on the gang- way ; get the top-men'ar hammocks up in the top ; down all chefts in the hold ; quarter-matters ftovr them ; take in all the fmall fails; fling the lower yard with top-chains, get the puddings and dolphins up j then fling the top-fail yards half mau: or clofe op; ftopper the top-fail fheets, ftoppers on the jeers, or elferack them ; gun- ners get the match tubs between every two guns, matches, powder horns* crows, and handfpikes, fufficient for every gun ; all hands to quarters, keep filence and mind the word of command, fire not a gun until the word of command is given ; min i you do not fire a (hot in vain. Now I have all the three mafts in one, Fire ! ^ Suppofe you are in chafe of an enemy's (hip of war, upon a wind, with all your fails fet; (he is right a-head, on which fide will you engage her? A. I will engage her to leeward, by reafon (he cannot put away before the wind, and if there is any thing of a fea, Che may not be able to fight her lower tier of guns. If light breezes and hot weather it would be better to engage to windward, to let them receive the fmoak and heat of the fire, ^ You are chafing from the wind, and carry away your main- top- maft, how will you proceed ? A. I would haul up the mam-fail, and fend hands up into the top with a rope or hawfer, to clap on thar part of the mail that hangs dowu, then cut the lanyards of the main top-mad (hrouds, and lower way, caft off the hawfer, reeve it to fend the itump down, .clear away the rigging, unfling the main-yard, get the foretackle on it and bo wze forward the yard, then lower the flump upon deck, and get the fpare top-maft ready for the crofv trees; clap the hawfer on, and fway it up high enough for the rigging. 4*; You are lyi' g to in a hard gale of v ind under your main courfe, you carry away ycur main-ma'.}, how wiii you proceed to clear the wreck ? A. I will clap my helm a-wca?her, brace my fore and fore-top fail yard) full, then call all hands to get p>l<-axes, &c. to clear away the rigging, -^ Why will you put the ihip before the wind I A. Because YOUNG SEA OFFICER. 30J A. Becaufe the mall will go a-ftern clear of the rudder, and prevent its damaging the fhip. <. You are going large and fee a (hip in the wind's eye, how will yoa proceed to chafe her ? A. I will turn all hands up, get my tacks on board, brace up my yards and haul aft the meets ; haul the bow-lines, fet the jib and ftay fails, keep her full, and by making Ihort boards and turn directly to windward, whicia will prevent her putting away large. -s. Suppofeyou were to carry away yoor bowfprit, what would you do ? A. I would immediately veer (hip, and keep her before the wind; and then, for the fecurity of the fore-mail, 1 would carry forward the fore-run^ ners and tackles, and bowze them well taut, till I can get a hawferor faf- ficient rope, and clinch it round the malt-head, and fecure it to the bits of the fore-caftle or the cat-heads; then take the beft fpar I have and make a jury bowfprit of it. Q Having a fair wind, how will you fet your fore-top-maft ftudding fail on the larboard fide? A, Firft haul taut the trufs tackles, and bowze the fore-yard clofe to; then haul raut the larboard fore-lift, and ftarboard fore-top-fail clue-line; on board his Majrfty's fhips the top burtons are on the top-fail yards to keej> them fquare when ftudding-fails are fet, {rhe top-fails, lifts, and clue-lines not thought of) the fore-top men down on the fore-yard, and rig out the larboard itudding-fail boom, firft fending down the ftudding-iail tack and outer halyards, up to the fore-top-fail larboard yard-arm ; and reeve the hal- yards, fend them down and bend them ; the tack being bent and all ready, man the halyards and hoift away, haul out the tack, &c. If the wind is oa the beam or quartering, fet it abaft the top-fail ; if right aft, before the topfail, (which is don^ by a man ftanding on the fore yard-arm, with the Jeach of the ftudding-failin his hands.) ^ Suppofe you are in an engagement, and your main-top-maft ftay is {hot away, how will you fecure your maft ? A. I will fend my fhifting back ftay forward by the main-top-maft ftay- fail halyards, and reeve it through a block abaft the lore-mall head, bowfe it taut, and that will fecure the^maft. Q. Your fhip comes to againft her helm, what will you do ? A. I will haul my mize^n up, and miver the after-fails. ^ She comes to yet, it (he flays (he wili be on board fome other fhip? A. I'll 1st go the lee-fore and lore-top-fail braces, raifc the fore tack aniS let go the bow-lines, haul in the weather braces, and box her off. ^ How do you fplice your cables ? A. I will put ihe whole (hands of the beft or fmall bower cables twlr each way, and point each flrand with a tail of three fathoms each ; then feize them with quarter and end feizing to make them lie fnug, which is the readieft way for clearing the hawze. They being foon fplicedand n- fpHccd Irn pointed. ^ How would you mark the lead-line? A. Black leather at 2 and 3 fathoms, white at f, red at 7, black at 10* white at 13, (fome feamen ufe black at joand 13) white at 15; as at 5, red 2t 17 as at 7, two knots at 20 fathoms, and fo on, an additional knot at every 10 fathoms, with a fingle knot between each IQ fathoms to mark the line at every 5 fathoms. ^ You are fent down in the dark for a top-iil, how do you know a il from a fore-fail, or a main-top-fail from a fore-top fail ? - '.t has thiec bow-line cringles it is a rnaia-fail ; if it has but two, it EXAMINATION OF A it is a fore-fail : if it is marled abaft the foot rope, it is a main-fail, if I fore it is a fore-fail : if a main- top-fail, it has four bow-line cringles, i: ifbe- ifa fore top-fail but three : all top-fails are marled to the rope, becaufe the foot rope is ferved. ^. The Cheers are along fide, how do you get them in ? A. Par-buckle them in with their heads aft on the poop, and get the fore and main runners on them for guys ; lafh on two four- fold blocks, reeve the irtafting-falls, get girt lines on ihehead of the (hears tofteady the mad-head, put heel lafhings on the (hears, with good oak plonks under them, to tranfport them forward on ; lafh one of the four-fold blocks forward to the flerr, and brir.g the fall to the capftan ; heave the (heers hij-h enough : when done, I'll take forward two runners and tackles to affift the fh.-ers, take the mizen.maft firft in, then raife the fheerseretf, take in the main- mail, bowfe the heels of the fheers forward, and keep them uprighr to take in the forc- maft. 4J. How do you rig a lower rr.aft ? A. I will lath on the girt-line-blocks, put on the bolters parcel and tar them, put over the runner and tackle-pendants, then rhe : 'einoft of the ftarboard-fbrouds, then the larboard, and fo on ; then the (lay and fpring ftay, fcize in the -dead eyes for the (hrouds,and th? harts for the {by, reeve the lanyards, fet up the ringing, get the top over head, and boh it, rattle down the fhrowds, and frize on the cat-harpin-legs, hoo!; the fuftock (hrouds and bitch them, feize do'.vn the ends, lafh the hanging jeer blocks under the top, with the ftrops under tht (iays, lead up and lafh to the mait- Jiead, get the cap into the top for the head of the top-malt, and la(h the blocks on for the main lifts. 4J. How do you get a top and cap over? A. Make faft a girt line block, on each fi-^e of the maft-bead, reeve the girt-lir.es, and pafs them under the fop, and make them faft to the after- pan of the top, ftop them to the bolt holes in the middle and fore-part of the top, then Avay away : when high enough, cut the upper (lops, having a guy on the after part of the top-brim, and the top will fall over the- mad- head, then lower away, and put it in its birth, haul upon the guy and bolt it, lay the cap fteady over the truflel trees for the top-maft kead, to receive it; when the top-maft-head is through it, laih the cap to the top-malt till high enough, then place the cap on the maft-head, and drive it down. How do you rig a main- top-malt ? A. I will tar the mail head, get the crofs-trecs over, fix the holders and parcel them, put over burton-pendan's, then the fhrou-Js, and back-days, proper and fpring-day, and cap, fway up the mall and fid it, feize in the dvad eyes, ftay the mad, fet up the (hrovvds, rattle them down, lafti the bullock-blocks to the maft-head. l' ; ^. How do you rig a top-gallant mad ? A'. I will fend down the top- rope, reeve it through the (heave hole, and make it faft round the hounds of the mad, and ftanding part of the rope, leaving enough end to make faft to the cap for doubling, put on a feizing about half way up, which done, fway away ; when the head is through the cap, make faft the fpare end or (landing part of the top-rope to the cap, cut the feizing, clap on the gromtnet, then tlie fhrouds, back (lays and flay, fway up the mail, fid it, and fet the rigging up. ^V How do you rig a bowfprit ? A. I will laih the collar for foreftay,-the bob-ftays and bowfprit ihrouds, then the collar for the fpring-ftays, then the block for the lop-ma ft flay, fix the man-rope, gamracm the bowfprit, and fet bob. flays and fhrouds up, ^ How YOUNG SEA OFFICER. 3Q 5 >. How do you rig a jib boom ? A. I will put over the traveller, horfes, and guys, the top gallant (lay- block, and lafti on the blocks tor the top gallant-bow hne, and jib- down-haul-block to the traveller. $*. How do . ou rig a lower yard ? A. I will getth? yard athwart the gunwale, hfh the jeers, clue.-garnrts, bunt-lines, leach-lines, and flab-line blocks, then put over the yar.i-y.nri" horfes brace pendants, trv* yard tackle pendants, tlun the top fail : and lift blocks, reeve the jot-re, braces, lifts, anil yard-tackle f.-lls, tiufs parels, fway the yard up, haul all taut, and belay. Jg. How do you rig a fore top fail .yard ? A. 1 will reeve a hawfer for a top-rope, through the bullock block, rmrt fend it down, and having put over the horfes, make the top rope bil to the middle of the vard, (lopping it to the yard.ann, fa-ay it up above the top, put over the brace, pendants and lift blocks, reeve the lifts and briers,' cut the yard-arm feizing, and crofs the yard, 1 (h the tvej bunt-iiuo, -,r. ' .' line blocks, reeve the tye and halyards, fway it up above the cap, anci' it, reeve {he clue-line.-,, : un'-lines, and reef-tackles. J^J. How do you r g a tup-g.'Hant yard ? A. 1 vvill feize the clue. line- bh-cks on, pat the horfes over fhe ynr ' fway it up on the cap, and rig the yard arms, by putting on the brace- pendants and lifts, then crofs the yard and parti it. 4J. You have loft your rudder at fea, what method vvill you take to ilr<:i thefhip? A. I will take a large fpar, or part of a top-maft, and cut it flat in the form of a ftern-poft, bore holes at proper distances in tlvu part whuh U to be the fore part of the preventer, or additional ller;t-po{l, then take the thickeft piank I have on board, and make it as near as 1 can into the form of a rudder, bore holes at proper (iiltances in the tore part of it, and in the after part of the pievcntt-r ftern-poft to correfpond wiih rach oiiur; and reeve rope grommets through thoft- holes in the rudder and after part of the ftern-poft for the rudd r to play upon. Through the preventer ftern-poit reeve guys, a ad at tlv fore part of them fix tackles, and then put the machine over-board ; when I get it in proper pofirion or in a lin-- with the (hip's ftern-poft, lafh the upper part of the preventer poft to the upper part of the (hip's item poft, then hook tackles at or near the main chains, and bowfe .taut on the guys to confine it t. lower part or the ftern-poft; Having boKs b- red through the preventer and proper ftern-poft, I will run an iron bolt through both, taking care not to touch the rudder, which will prevent the ialfe ftern-poft from rifing up or falling down. By the guys on the arter part of the rudder, and tackles .fixed to them, I may fleer the ftiip. I muft take care to bowfe taut the tackles on the preventer ftern-poft to keep it clofe to the pr/per ftefli-poft. J^jJ. Your (hip is leaky, you cannot keep her free by the pumps, what will you do. A. J will take a fpare top-fail, or fome other fail, nnd fpread it upon the deck, cover it all over \vjth oakum, and bind n to he fail with a needle and twine in feveral places, to keep it faft to the fail, then take an hawftr.and cut it into proper lenpths to go under the (hip's bottom, and corne irvod, weigh at high water, and caft her in fhore. But to fail to 'he eaftward with the win i wefterly, I would begin to unnoor at half ebb, take up my beft bower, and weigh at low water. ^ The wind at N. E. in moderate weather you mean to turn up the Swin, at what time of the tide would you weigh ? A* At flack water, loofe the fails and up ?nchor. ^ What are the marks for running through the Gull Stream? A. To keep the unper light-houfe on lv South Foreland, in one with the weftf-rnmoft end of the fouthernmofr cliff in Old Stains B*y ; which is a fwamp that lies between the r^vu cliffs a large half-mile to the fouthward of Kingfdown upon the South Foreland. >. How do you know when you can weather the South Sand-head ? A. When Upper Deal Mill is open to the fouthward of Walmer Caftle, or when the light-hou&s are in one, and Foikftone Church is open with Hay-Clift, I am clear. >. Suppofe you were coming into the Downs with the wind at S. W, blowing hard, which way would vou lay your fhip's head to bring her up ? A. I would lay the fhip's head to the eaftward, and come to with my beft bower, but if with the fmall bower, I would have her head in fhore. >. For what reafon would you do fo ? A. I fhould then keep (he cable clear of the cutwater. ^ What is the courfe from the South Foreland to Dungenefs, and what are the dangers ? A. From the South Foreland to Dungenefs, the true Courfe is S. W. by W. \ W. diftance 23 miles, The YOUfcG SEA OFFICER. 307 The Ripraps HeN. E. an<< vS. W. about 5 leagues in length ; theN. E. end bears from Dover Caftle S. S. E. 4 leagues, from Folkftone S. E. by S. Calais fteeple bears from if S. E. and Calais Cliffs S. S. E. 3 leagues, the S. W. end bears ;rom Dungenefs E. S. E. 4 leagues, on the N. E. part there are about i $ or 1 6 feet at low water, on the S. W. end 4 or 5 fathoms; it is deep to n both fides, having 20 and 22 fathoms clofe M it. To the weftward of Folkftone, there is a ledge of rocks that runs a large mile off the (here, I would come no nearer in than 14 fathoms. About 4 miles E. by N. from Dungenefs, there is a fhoal with not moie than 12 feet on it, which I (hall avoid by keeping in 10 fathoms. J^. Where will you anchor, and in what depth or water under Dungenefs ? A. I would anchor with theNefs Point S. W. by W. the Hght4ioufc W. S. W. athwart Romney Town, in 8, 9, or 10 fathom water. There is a (hoal about two miles to the weftward of the Nefs, with only 1 8 feet on it ar low fpring tides, the Nefs light bears from it N. E. by . 1 2 fathoms clofe to. <%. What is the courfe from Dungenefs to Beachy-head, and what are the dangers? A. W. \ S. diftance about nine leagues. Off the highland of Farleigh there is a (hoal of rocky ground with 14 feet on it, and li s pretty clofe in. In the channel off Dungenefs, there is 24 fathoms, and off Beachy-head from 26 to 30 fathoms ; I will, in thick: weather, keep in i j or 20 fathoms, from the Nefs to Beachy-head. When J deepen my water, haul to the Northward, but if I fhoal it, haul to the Southward. In clear weather I may ftand in fhore until Beachy-head bears W. by N. and not have lei's than 10 fathoms of water, muft then tack to- avoid Pemfey Shoal, which lies about two miles off the fhore, with Pemfey Church bearing N. and Beachy-head W. by S. 14 feet on it. There is a (hoal with 14 feet on it, and lies with Beachy-head W. f N. 12 miles ; E. by S. 6 miles from Beachy-head is the Horfe of WiJlington, a fmall (hoal, having 16 feet on it at low water. ^. Being off Beachy-head, at the clofe of a winter's evening, in a gale of wind at N. E. bound to Spithead, what is beft to be done ? A 1 would lie to with my (hip's head to the N. N. W. till morning^ then (he will drive about a channel courfe at the rate o( two knots an hour, allowing that what fhe would lofe in the ebb, (he would gain in the flood, and be in a fair way in the morning; I would come no nearer to the Gwers than 18 or 20 fathoms. ^. What is the courfe and dangers between Beachy-head and Dunnofe ? A. The courfe is W. by N. J N. diftance about 20 leagues. The dangers are, Owers ; the mark to go clear cfftheeaft part of them, is the white way on Crow Hill in one with Chicheiter Church, a little to the caftward ot Pt-gham Church, and the mark to clear the weft end, i$ St. Rook's Hill in one with Chichefter Church, they bear from Culver (tlifF E. S. E. \ S. about 4 leagues ; there is a floating light juft to the Eaftivard of them \ in going down Channel, it i keep Dunnoie W. N. W. Northerly, will carry me without them, I will come no nearer to them in thick wea- ther than 1 8 or 10 fathoms. ^. You are coming from the Weftward and off Dunnofe, what would you do ? 308 EXAMINATION OF A Monkron Fort, and run into Spithead between the Buoy of the Dean and the Biv v of tre W;,!n?r. N. B. In poing for Spi r head from the eaftward, there are 5 black buoys lyig on the Dean and Horfe,thev muft be all left on theftarboard tide, the outer one is called the Eaft Buoy o* Dean, it-lies in 27 fee' warer, tV marks for it are rhe flagftaffof Pint, haul up and anchor againft the 1 Pier, in 9 or 10 fathoms, with the Bill bearing S. S. E. Portland Caftle S. S. W. and Weymouth Caf- tle N, W. In failing out of Portland Road, I muft keep Week Church opn of the Stone Pier, and that will carry mecleartothe eaftward of the Shambles. The tide flop's hard from the Road to the Bill E. S. E. 7 hours, and the flood fers right of the Bill 9 hours. N. R. In cafe I (hould be embayed to the weftward of Portland, and no podi'iility of getting out between Burton andCbifwell, where it ebbs g hours and flows only 3 hours, there is a fteep beach of pebbles, I would there run my fhipon ihore with as much fail as I co-ild carry, efpeciaJly at the begin- ning of an ebb, and-remain en board for three or rour,feas, when I may get on fhore with fafety. ^ What is the courfe from Portland to Torbay, and how do you anchor there ? A. Tha courfe is W. N. W. and di'rance about 14. leagues ; to anchor in the bay, I would bring the Berry Head to bear S. by E. or S. S. E. and Brixham Church on wirh the Pier Head : the heft anchoring for fmall fhip< is 1 1 from Brixham Pier Head; in 7 fathoms, or juft to the Eait'ward of Torpier. >. What is your courfe from the Berry Head to the Start A. S. W. about 6 leagues. ^. Is there any danger near the St^rt ? A. Yes, about two miles to the rait ward of the Start, there is a (hoal with not more than 9 feer on it, the Bolt Head being kept open of the Start Point, will'carry meclearof it. . Vv bat is your courfe from the Start to the EdJiftone ? A. W 4S. 7 leagues. ^. Whatis your courfe from the Start to Ramhead ? A. vV N. W. 7 leagues- i. What is to be obferved : n failing into Plymouth Sound ? A. If coming from the weftwnrd, and am 2:0! round the Ramhead, I muft give Penlee Point a good birth, by reafon of a ledge of rbcirs that lies * For a more particular account.fee theDj,ECTJONspubliilied byToiiN HAMJ^ , Price 2s. 6d. EXAMINATION OF A lies off from if, then hnul N. N.E. * E. for anchoring ; the leading mark in is Plymouth Church, on with the middle Obeliik on the Uoa In going into the Sound I may anchor in Cawfand Bay. in 20 fa- thoms, with Penlee Point S. W. and the town of Cawfand W.N W. The leading mark to cany me in between the Knap and Shovel, is Plymouth oid church, on with a white , atch on the Hoa. I may go into the Sound on the eaft fide, between the Tinker and Shag-done, by keeping Mount Batton a f il's brradth open of Staden Point, and keep in that direction unti) Maker's church hears N. W. and Withy Fdge open, then haul over to the ea ft ward and anchor. &. How do you fail into Hamoaze r A. I \vosld keep King'and open of Redding Point until the large Houfe at Stoke touches the Eaft fide of Mill Bay j fleer in until the Obeliik comes on with Block Houfe Point; keep in that direction, till the eafternmoft fummer houfe on Mount Edgecomb Side comes open with the Point within which it ftands ; then fleer for it, until the eaft point of Mount Wife comes open with Block- Houfe Point ; then (leer mid-channel for Stone- houfe Pool till Drake's Ifland is (hut within BIock-Houfe-Point : I muft not open it till South Down comes open with the Obelilk, then fteer up the harbour with the fide of Drake's Ifland, juft touching Paffage Point,\vhich will lead me to the fouthward of the Harbour (heal, on the outer part of which 'here is a rock, with only fixteen feet on it, but on any other part, there is a 3^ fathoms. N. B. The marks to know the Sound when I am coming from fea in the day time, are, Ram Church, which ftands to the northwprd of the Ram-head, and a fquare tower ftanding on the higheft part of the land. J^J. You are bound intoFalmouth, how would you proceed ? A. In going to Falmouth, there is a rock, called the Block Rock, wiih'a pole on it, Mid mews itfelf at half tide; it lies heareft 10 the well Ihore ; I may fail in on either fide of it, but the eaft ride is the beft. If J would fail into Canick Road, I muft keep in the fair way, and my lead going, as there is a narrow deep channel all the way, of 16 or 18 fathoms. 1 may borrow on St, Maw's fide in 5 or 6 fathom. The bell anchoring in Carrick Road, is St. Maw's Caflle E.S.E. and lay my eattermnoft anchor in 16 or 18 fathom*, and my wefternmoft anchor in 4 or 5 fathoms. Jult paft St. Maw's there is a (and that is fteep to, called St. Maw's Sand, and lies almoft half* channel over. N. B. Great ihips anchor, with Manacle Point, on with the point of Falmeuth, or a great houfe, that is to the weftv/ard of Penryn, juft open Trefufis Point in 18 fathoms. The Manacles lie from Falmouth about S.S.. Q. How do you know the Lizard when you rirft make it? A. It is the ibuthemmoft land on the coaft, and may be feen 7 or 8 leagues off, in 4* fathoms. ^. How does the Land's End appear \fhen you make it ? A. It appears in hummocks with a church on it, and may be feen or 8 leagues off, in 54 fathoms. .<. What are the dangers off the Land's End ? * A. Miiny : iii, Tl, Runnel-ftone lies about nine tenths of a mile S. S. E. from Tol-peden-penwiih. 2d, N. E. by N. 'mm the Runnel-ftone there is a rock, calkd the Leaw- mean, which appear: ar halt ebb, with a patfage between it and the feldorn ufeti by am bat !>y ccailers. YOUNG SE*\ OFFICER. Jll 30", The Wolf Rock; bears from Tol-peden-penwith W. S. W. dlf. tance 7 % miles; it is fmall and may be feen at half tide ; the largeft of the Brefam Rocks, kept open of the outermoft of the Long Ships (on which there is a I'rgbt-houfe ere fled) will lead me clear to the wdhvard of the Wolf. 4th, The Long Ships lie N. W. by N. about 3 miles from th* S. W. pomt of the Land's End, and i mile W. N. VV. from the wefternmoft point ; thejr are high, and may be feen 4 or 5 leagues off. The K-ttle-hottom, is a fhoal with only fj fret on it, and lies about half-way, between the northernmoit part of the Long Ships, and the point of the Land's End. 6th, The Brelam rocks lie about 3 miles N.E.by N. | E. from the Long Ships. yth, The Seven Stones are a row of rock -that come not above water, but the lea always breaks over them; they lie from Cornwall W. \ S, dili. 5 leagues; and from St. Martin's Head, Scilly, N.E. dift. 3 leagues. <5\ If you are forced into Mount's Bay, where would be the fafeft an- choring ground ? A. Mount's Bay lies between the Lizird and tlie Land's End; there is a hi,h ifl ;nd i.r. :he eatt fide, and a Cattle on the weft fide of it, called St. Michael's ;vloum ; from the eaft iide of it lies a ledge of roc'-s, near a league into the Vi ; the Coaft s full of rocks, and not fafe to ancnor in. To (ail into t!-f Bay I muft 'ring St. Paul's fteeple W. and keep over to the weft ftiorr, an i make St. Clement's Ifland, which is before the town of iVla.nfe- hol- , having the caflle on the ftarb >ard fide ; I mall then fee a large fandf bay, and, when within the Ifland, there is a good anchoring in 7 or 8 fa- thoms. ^ If you are bound, or forced to go into Scilly, what would y^u da ? A. I would fteer for St. Mary's Sound, and run in for the fouthermnolt Point of St. Mary's Ifland, called Penninis Point, minding to keep the lead goini, and approach no nearer than 5 fathoms witer; about N. W. of Pen.iinis Point, a little more than halt a mile, is the Woolpack, tbe fhoailiei near to the fhore ; 1 mull coniinue to run in <; or 6 fathoms, keeping prettjr clofeto St. Mary's Uland, to avoid theSpanifh Ledge, which lies about half a mile W. by S. from Penninis Point ; fome part of this (hoal may be feen at low water, and part of the Woolpack (hews itftlf before low water; when I have got abreaftof the Wo"lpack, to which I mud give a good binh, about a cable's length, and iteer for the Stevcl Rock vyhich is bold to; when I am abreaft of the Stevel, muft fteer N. W. by VV. until Little Crow Iflaad con>es on with Bantfcarrcn Point; then fteer N. N. E. until Crow Ifland comes open a (hip's length of Bantfcarren Point, or bring the caft'e, which is on Sr, Mary's Ifland, to bear S. S, E. and anchor in 6 r 5 fathoms THE THE METHOD OF EXERCISING MERCHANT SHIPS COMPANIES FOR WAR. T is not prefumed, in the following pages, to offer any hints to the officers in the Royal Navy, who may be faid to be trained up in the fchool of war : we only attempt the humbler fafk of fuggefting a few obfervations to the commanders of merchant {hips, who, occupied in commercial purfuits in the time of peace, are fometime* deficient in the method of defending themfelves when attacked in timt of war. We would firft recommend to ftation their crews according to their rank and capacities, by forming a quaner bill, and to extrcife them in their refpe&ive nations. As merchant fhips are f varionfly fitted out with guns ancl mer it is impoflible to form a quarter bill to fuit all We have., however, given two quarter bills, one fora trading fhip of four- teen fix-pounders* and fifty men, and the other fora privateer of twenty nine-pounders, and 160 men, which may be varied as circumftances and the difference of guns, carriages, and men may require. A Quarter Bill for a Trading Ship of Fourteen Six-pounders and Fifty Men. The captain to command in chief, on the quarter deck, if it be fortified to afford commcn fhelter from fmall arms ............... I The chief mate to command the fix foremoft guns, and work the fliip forward ..... . ......................................................... The fecond mate to command the eight aftermoft guns ............ The boatfwain to pafs the word, and get the captain's orders ex- ecuted fore and aft, as occafion may require ........................ The carpenter to attend the pumps, foot-plugs', &:c ...... ............ The gunner to deliver the powder to the boys, as carriers ......... The doctor in the loweft, fafeft, and molt c< nvenient place the fhip affords .............................. . ...................................... A good man at the helm ................................................ Four men to each gun and its oppofae, and si boy to fetch pow- der ........................................................................... 35 Seven men at fmall arms and occasional duty ........................ 7 .5 A Quarter Bill for a Privateer of Twenty Guns, Nine-pounders, and Four Three-pounders on the Quarter-Beck and Fore- caftle. The captain to command the whole ....... The rnafter to aflift and work the ihip according to orders . A midflupman lo pafs the word of command fore and aft .. A THE METHOD OF EXERCISING, &C. 313 A quarter matter at the cun, and another at the helm ... * The firft marine officer with 24 muiketeers ....... 25 Three men for the two three-pounders, and a boy to fetch pow- der 4 On the Main Deck. The firft lieutenant to command the ten foremoft guns ... i The fecond lieutenant to command the ten aftermoil guns . . i The gunner to affift and attend all the great guns fore and aft . . I The two matters mates to attend the fore-top-fail braces, and work the {hip forward according to orders 1 The boatfwain's mate, with two feamen, to attift in working the (hip, and to repair the main rigging 3 The carpenter and his crew to attend the pump, and 'the wings about the water's edge, fore and aft, with ihot-plugs, &c. . . 4 Six men to each of the ten guns on a fide, and its oppofite, and a boy to fetch powder 70 On the Forecaftle. The boatfwain to command, with two feamen to work the fhip and repair the fore rigging 3 Three men, and a boy to fetch powder, for the two three-poun- ders 4 The fecond marine officer, with nine mufketeers 10 In the barge upon the booms, the third marine officer with eight muiketeers 9 In the main top, five men with a midfliipman at fmall arms, and to obferve the conduct and condition of the enemy .... % In the fore top, five men at fmall arms and to repair the rig- ging . - 5 In the mizen top, three men at fmall arms and to repair the rig- ging 3 In the powder room, the gunner's mate with an affiftant to fill and hand powder to the boys, carriers ^ In the cock-pit, the doftor and Jus mate 2 1 60 Here it may not be amifs to remark, that the people fhould be quar- tered to fight nearett to where they are ftationed to work the Ihip ; that is, the after guard on the quarter deck, the waifters in the waift, forecaftle men that are necefiary in the forecaftle, &c. The q ^ru* bill and difcipline of the crew flvould be kept from diforder as long as poflible; and when occafional duty requires the people to be let s;o from their quarters, it Ihould not be done at random, but with judg- ment, fuch as will fuit the occafion, from the muiketeers, or a man from, each great gun, &c. where they can be bett fpared. On Preparing forExercifeor Aftion. When all handi are called to quarters, every man fhould bring his Jtt r hanimpck 314 THE METHOD OF EXERCISING hammock well lafhed up, and flow it to the grearefl advantage to give flicker from fmall arms neareft to his own quarters, or give it to fome of his meirmates where they are mod wanted, that they may know readily where to find them when exercife or a6tion is over. > When the hammocks are properly flowed, the officers, according to their ftations and duties, are to fee the ihip effectually cleared of all incumbrances, and every thing prepared, fo that nothing may be want- ing that is neceflary for exercife or action. The lieutenants or mates, with the gunner on the gun deck, are to get all the hatches laid, except that where the powder is to be handed up j a match tub half filled with water, and four matches in the not- ches, placed as near midfhip as poffible to ferve two guns and their oppofites5 alfo fwabs to wet the decks, to prevent the fatal confe- quences that may attend the fcattered and blown powder from the priming of the guns making a train fore and aft, which has, in many inftances, taken fire from the firing of the guns, and done great da- mage. It is further the duty of the lieutenants to fee that the captain of each gun has his men, powder-horn, rope-fponge, rammer, crows, handfpikes, and train fackles, all ready in their proper places. The boatfwain mutt get the yards flung, the topfail fheets flopper- ed, and marline (pikes ready to repair the flanding or running rigging . that may be damaged. The carpenters are to get the pumps rigged, and (hot plugs, with all that is necciFary, ready in their proper places, to flop leaks and repair damages. The gunner, when preparing for action, is to fee that the charges in the guns are dry, and that there is a fufficient quantity of wads, and fhot of all forts, and cartridges ready filled. The marine officers are to fee all the mulketeers at their quar- ters, with their arms and ammunition in good order for exercife or action. Exercife of the Great Guns. 1 Silence 2 Call loofe your guns 3 Level your guns 4 Take out your tompions 5 Run out your guns 6 Prime 7 Point your guns 8 Fire 9 Spunge your guns 10 Load with cartridge i i Shot your guns 12 Put in your tompions 13 Houfe your guns 14 Secure your guns. I. Silence. At this word every one h to obfcrve a filent attention to the officers. 2. Cafl loofe your Guns. '.nuzzle lafljingVs to be taken off from the guns, and, being coil- ed up in a fmall compafs, is to be made fafl to the eye-bolt above the port, the lathing-tackles at the fame time to be caft loofe. and the mid- dle of the breaching feized to the thimble of the pomillion. The ipunge to be taken down, and with the crow, handfpike, &c. laid upon ;K by the gun. o. When prepared lor engaging an enemy, the feizing within the MERCHANT SHIPS COMPANIES FOR WAR. 315 the clinch of the breaching is to be cut, that the gun may come fuffi- ciently within board for loading, and that the force of the recoil may- be more fpent before it a6ts upon the breeching. 3. Level your Guns. The breech of your metal is to be raifed, fo as to admit the foot of the beds being placed upon the axle-tree of the carriage, with the quoin upon the bed, both their ends being even one with the other. N. B, When levelled for firing, the bed is to be lamed to the bolt which fupports the inner end of it, that it may not be thrown out of its place by the violence of the gun's motion, when hot with frequent difcharges. 4. Take out your Tompions. The tompion is to be taken out of the gun's mouth, and left hang- ing by its laniard. 5. Run out your Guns. With the tackles hooked to the upper bolts of the carnage, the gun is to be bowfed out as clofe as poflible, without the a ill dance of crows or handfpikes; taking care at the fame time to keep the breeching clear of the trufcks, by hauling it through the rings ; it is then to be bent fo as to run clear when the gun is fired. When the gun is out, the tackle-falls are to be laid along-fide the carriages in neat fakes, that when the gun, by recoiling, overhauls them, they may not be fub- ject to get foul, as they would if in a common coil. 6. Prime. Take off the apron and unftop the touch-hole, that the cartridge may be pierced with the priming-wire, and the touch-hole filled with pow- der, the pan alfo is to be filled ; and the flat fpace, having a fcore through it at the end of the pan, is to be covered, and this part of the priming is to be bruifed with the round part of the horn.. The apron is to be laid over, and the horn put up out of danger from the flaih of the priming. 7. Point the Guns. At this command the gun is, in the firft place, to be elevated to the height of the object, by means of the fide fights; and then the perfon pointing is to direct his fire by the upper fight, having a crow on one fide, and a handfpike on the other, to heave the gun by his dire&ion till he catches the objed. N. B- The men who heave the gun for pointing are to ftand be- tween the (hip's fide and their crows or handfpikes, to efcape the in- jury they might otherwife receive from their being ftruck againft t hertz or fplintered by a ihot; and the man who attends the captain with r< R r 2 match 316 THE METHOD OF EXERCISING match is to bring it at the word, " Point your guns ;" and, kneeling upon one knee oppolite the train truck of the carriage, and at fuch a diftance as to be able to touch the priming, is to turn his head from the gun, and keep blowing gently upon the lighted match to keep it clear from afhes. And as the miffing of an enemy in action, by neglect or want of coolnefs, is.moft inexcufable, it is particularly recommended to hare the people thoroughly inftructed in pointing well, and taught to know the inconveniences of not taking proper means to hit their mark ; therefore they ihould be made to elevate their guns to the ut- moft nicety, and then to point with the fame exaclneis, having caught the object through the upper fight. At the word, 8. Fire, The match is inftantly to be put to the bruifed part of the priming ; and when the gun is difcharged, the touch-hole is to be flopped, in order to fmother any fpark of fire that may remain in the chamber of the gun ; and the man who fpunges is immediately to place himfelf by the muzzle of the gun in readinefs, when at the next word, 9. Spunge your Guns, The fpunge is to be rammed down to the bottom of the chamber, and then twifted round, to extinguifh effectually any remains of fire ; and when drawn out to be flruck againft the outfide of the muzzle, to ihake off any fparks or fcraps of the cartridge that may have come out with it, and next its end is to be ihifted ready for loading; and while this is doing the man appointed to provide a cartridge is to go to the box, and by the time the fpunge is out of the gun, he is to have it ready; and at the word, 10. Load with Cartridge, The cartridge (with the bottom end firft, feam downwards, and a wad after it) is to be put into the gun, and thruft a little way within the mouth, when the rammer is to be entered ; the cartridge is then to be forcibly rammed down, and the captain at the fame time is to unftop the touch-hole, and keep his priming-wire in the touch-hole,and, feeling the cartridge, is to give the word home, when the rammer is to be drawn, and not before. While this is doing, the man appointed to put in a fhot is to provide one, or two, according to the order at that time, ready at the muzzle, with a wad likewife, and when the rammer is drawn, at the word, ii. Shot your Guns, The fhot and the wa4 upon it are to be put into the gun, andthruft a little way down, when the rammer is to be entered as before. The fhot and wad are to be rammed down to the cartridge, and there have a couple of forcible ftrokes, when the rammer is to be drawn, and laid out of the way of. the guns and tackles, if the exercife or action is con- tinuing, but, if it is over, the fpunge is to be fecured in the place it is at all times kept in, the ftopper put in the touch-hole, and the apron put on. 12, Put MERCHANT SHIPS COMPANIES FOR WAR. 317 12. Put in your Tompions. The tampions to be put into the muzzle of the cannon. 13. Houfe your Guns. The feizing is to be put on again upon the clinched end of the breeching, leaving it no flacker thaw to admit of the guns being houfed with eaie. The quoin is to be taken from under the breech of the gun, and the bed, Hill reftingupon the bolt, within the carriage, thruil under, till the foot qf it falls off the axletree, leaving it to reft upon the end which projects out from the foot. The metal is to be let down upon this. The gun is to be placed exactly fquare, and the muzzle is to be clofe to the wood, in its proper place tor palling the rauzzle-lafhings. 14. Secure your Guns. The muzzle-lafhings muft be firft made fecure, and then with one tackle (having all its parts equally taut with the breeching) the gun is to be laihed. The other tackle is to be bowfed taut, and by itfelf made faft, that it may be ready to carl off for lathing a ftcond breeching. N. B. Care mull be taken to hook the fir ft tackle to the upper bolt of the carriage, that it may not otherwise obftrucl: the reeving of the iecond breeching, and to give the greater length to the end part of the fall. No pains muft be fpared in bowtiftg the lathing very taut, that the guns may have the leaft play that is poffible, as their being loofe may be productive of very dangerous conlequences. The quoin, cro\v, and handfpike, are to be put under the gun, the powder horn hung up. in its place, &c. Being engaged at any time when there is a large f \vell, n rough fea, in fqually weather, &c. as the mip may be liable to be fuddenly much heeled, the port tackle-fall is to be kept clear, and (whenever the working O f the gun will admit of it) the man charged with that office is to keep it in his hand; at the fame time the muzzle lathing is to be kept faft to the ring of the port, and being hauled taut, is to be fafien- cd to the eye-bolt, over the port-hole, fo as to be out of the guns \vay in firing, in order to haul it in any time of danger. This precaution is not to be omitted, when engaging to windward, anymore than when to leeward, thofe fituations being very fubjel to alter at too ihort a warning. A train-tackle is always to be made ufe of with the lee-guns, and the men llatloned to attend it are to be very careful in preventing the guns running out at an improper time. THE METHOD OF ATTACKING OR DEFEND. ING A SHIP. AS foon as the {hip lias got to fea, I would recommend to take the firft favourable opportunity to have all hands called to quarters, the officers in their -itations to have every thing made properly ready and 3l8 THE METHOD OF ATTACKING, &C.' and fit for aftioh ; to have a general exercife not only of the great guns and fmall arms, but the method of working and managing the (hip, to take advantage of the openings which often occur in attack- ing or being attacked by another fingle fhip, which fhould be ftudied by every commander, and the defigned manoeuvres fliould be taught the people in their general exercife, that they may know how to act and move regularly from one place and fide to the other as occafion may require, without confufion, which is always the cafe, when the intended manoeuvres are not made known to the people. For thefe reafons, as foon as poflible, it fliould be made known to them, that if a fhip of nearly equal force mould bring too with a de- lign to fight, it was intended not to run directly along fide, and lie too like a log and depend upon mere battering with one fide only, or upon the flern chafe guns. Begin the attack upon the weather quarter, fhooting the {hip up in the wind, with the helm a-lee, till the after lee gun, with which you mould begin, can be brought to bear upon the enemy's Hern, then fire the lee broadfide. Immediately boxhaul the fhip round on her heel, fo as to bring the wind fo far aft, that the ihip may be fleered clofe under the enemy's ftern, giving particular orders to begin with the foremoft gun to rake them right fore and aft, as they pafs in that line of direction, all aiming and firing to break the neck and cheeks of the rudder's head, the tiller ropes, blocks, &c. fo as if poflible to deflroy the fleering tackle, which de- fign, if it proves fuccefsful, takes the management of their fhip from them, fo that fhe muft lie helplefs for a time in fpite of their endea- vours. When t N he aftermoft gun is fired, put the helm hard a weather to bring the fhip to the wind on the other tack, to keep clear of their lee broadfide, and act according to their motions, and the experience of the effect your attack has had upon them. If they continue t lie too, either renew the attack again in the fame manner as foon as the fhip will fetch the weather quarter again, or make fail off to efcape, if it is found that the great inequality of their fuperior force admits of no poifible chance of conquering them. And although this manoeuvre may not have given this advantage (which in my opinion ought al- ways to be attempted, and not to fubmit tamely although a Ihip is. doubly the force) yet the power of their broadfides may be chiefly avoided by it. But when the inequality of force is not fo great but there is a pof- (ibility of conquering, and if the fuccefs of the firft attack is perceived to oblige the enemy to continue lying too in order to repair the damage done their rudder or tiller, c. then the blow fhould be followed, by renewing the attack again with all poffible expedition, in the fame manner, which gives the opening not only to fire the whole round of great guns to advantage, but allb to the marines and topmen to fire their fmall arms at the fame time to great advantage, fo as to do the moft execution poflible, by firing and raking them fore and aft through their moft open and tender part, the item, with the leait rifk poflible from the enemy's guns, and therefore gives the greater! poflible chance to make an eafy conqueft, efpecially if fo lucky as to deftroy and pre- vent the recovery of their fleering. A (hip of much fuperior force may be brought to fuch a diftrefted condition, as to be obliged to make a lubmifliou for want of the helm to command her, therefore when an opportunity offers in fighting this fhould be always aimed at. ON SHIPS IN DISTRESS. 319 But fuppofe the enemy laid too as above mentioned, find themfelves not much hurt by this manoeuvre, and that you have not fucceeded in destroying their fleering, and therefore ) ou may expect that they will immediately tack or wear fhip, and ftand after you, depending upon their Superior failing and force, mall run up along your lee fide, ex- peeling, by making a general difcharge of their fmall arms and great guns on your deck, which Iks open to them by the (hip's heeling to deftroy your people, and to make you fubmit : when this is likely ta be their defign, orders mould be given to your people, to keep them- felves as dole under fhelter as poflible from their fmall fhot until their general difcharge is over; then if the Ihip is found not fo difabled, but that the toplails can be thrown aback, make a general difcharge from the lee lid of the great guns, loaded with round mot only, point- ed to the weather fide of the enemy's bottom amidfhips, to one point at the water edge, and boxhaul the Hup to run clofe under their ftern, aiming at raking and defiroying their fleering with the other broad- lide; then fbmd off on the other tack, and act according to circum- ftances and the condition you rind yourfelf in compared with the ap- pearance of the enemy and their motions, who maybe obliged to con- tinue on the other tack to repair damages. But when the enemy's mip of force makes only a running fight, and you have the advantage of failing fatter, the molt fure and likely me- thod to make an eafy conqueft, is to run clofe up, and (hoot or fneer your mip acrofe their ftern each way, making a general diicharge of all your force, aiming with the great guns at the rudder he.td and Peer- ing tackling; and you will have this advantage, that if the ihot mifs the rudder head by raking the (hip fore and aft through the (torn, they may do the greateft execution poMible to diitrefs the enemy, fo as to make a fubmiffion. On this occasion, when it blows frefh, and you are obliged to carry a preffing fail large or before the wind, to make the great guns as ready as polfible, and prevent their being fired too low, all their breeches fhould be laid quite down in the carriage, and if your mip is crank the yards fhould be braced fo as to fhiver the fails at the time each broadfide is fired. In all thefe manoeuvres, where the whole round of great guns are defigned to be fired, two or more men ought always to be left to load each gun again when fiied on one fide, whilil the others move over again to fire the oppolite, that neither fide may be left unguarded. . Thefe or any other manoeuvres may be taught the people, by heav- ing a tight empty beef calk over-board, and making it the object of attack. Nor would I advife to fpare a little powder on thefe occaiions, as a little expended in exercife may fave a great deal fired to no pur- pofe in action. Two mips failing in company afford an excellent op- portunity of exercifing manoeuvres. Note. At the end of this work are given two Tables; one mewing the proportion of powder for fea guns, the other the number of ihct contained in different fized grapes. ON SHIPS IN DISTRESS. QUDDEN diftrefs ^f (hips has often ftruck their crews with fivh ^ panics, as to occafion them, in many iuftances, to take the worft iniiead ef the belt means or methods for their falety or relief. It will 32O ON SHIPS IN DISTRESS* not, therefore, I truft, be unacceptable to endeavour to point out every thing that m:iy be of fervice on thefe melancholy occafions, as far as circumftances and fituations can be conceived to happen. When a Chip proves weak and works the oakum out, fo as to make dangerous leaks between wind and water, it has been frequently prac- lifed to nail meet lead upon the feams, which is fubjeft to break by the ihip's working. Leather or canvafs nailed on flack, with oakum under, will anfwer the purpofe much better. In cafes where mips have worked their frames loofe, it has been frequently pracYifed with fuccefs, to take feveral turns of a hawfer or cable round them, and to heave thefe turns well taut, to pi event foundering. Should a dangerous leak fuddehly break out, as foon as the pumps are manned and fet to work, the utmoft endeavours fhould be imme- diately ufed, and all poilible means tried, to rind out and flop the leak, before the people become exhaufted by continual pumping ; \vben difcovered, I would recommend fothering ; for a deicription of which fee page 305 of this work. To recover ana get a Skip upright from being o*verfet or laid on her Side at Sea. This is certainly a tafk that deferves the utmoft attention. If ground is to be reached by any means, the lee anchor or anchors Should be immediately let go, in order to bring the wind upon that bow that is laid down ; that the wind may ac\ upon the mails and fails, which may be fet fo as to bring the {hip-upright again. But in deep water, where anchors can be ot no fervice, it is recommended, if a towline, hawfer, or cable end can be readily come at, and if the driver boom, hencoops, or any other bulky things can be {lung by the middle with ropes, and made faft to it, that they be veered away with a long fcope over the lee-quarter, to make fuch great flop-waters as to make the mip wear, and bring the wind on the quarter that is down, that the mip may be brought to, on the other tack, and the fails trimmed, fo as to get her upright again without cutting away the mafls, which nothing can juftify but the utmoft neceflity, to fave a fhip from foundering, becaufe of the great diflrefs it brings her under for want of her mafts, efpecially her lower mafts, when fhe has a long run to her defigned poit, or to a place where me can get this g eat damage repaired. To make a Ship 'wear and fleer that has loft her Foremaft. THIS may be done by veering a hawfer or cable end over the lee quarter, but without any flop waters, only the nun buoy or any fparc fpars lamed along it to buoy it from taking the ground, in cafe of coming into flioal water with little wind. This will a6t with great power with the helm, to make the {hip wear and fleer at pleafure. And a fpare yard or boom may be rigged out abaft the mizen ihrouds to guy the cable to leeward in proportion to the iliip's griping j and when failing before the wind to fecure it over the middle of the ftern, will prevent the mip broaching too a gain ft the helm both ways. On Steering a Ship that hat loft her Rudder. I would propofe on this occafion a bawfer^Dr cable end with the -nun buoys, fpare fpars, &c. lafhed along it, to buoy it up, in cafe of coming ON SHIPS IN DISTRESS. 32! coming into ilioal water, and a boom rigged out on each fide, clofe aft athwart the ftern, w:th a block on each at equal diftances, as far as they can be fupported from the ftern, and' a block on the rail or gunnel exactly onpofite the middle of the wheel barrel, where the fleering rope, marked with a rope yarn in themiddie, is to be taken with three or five turns round the wheel, when the mjdfhip fpoke and the mark on the rope are right up ; then the two ends to be patted acrofs from the under part of the wheel, and reeved through the blocks on each fide, and made faft to the hawfer or cable that is towed a-ftem exactly amidrtiips, and as tight as it can well be to go clear of the flern ; and then veer and heave freely from fide to fide, as the fleering of the (hip, with the trimming of the fails on this occafion, may re- quire. [See the Plate and defcription of Captain Peckenham's Makeshift Rudder, publifbed in the 7th volume of the Tnnfactions of the So- ciety of Arts, Manufactures and Commerce, which is earneftly recom- mended to the attention of all Commanders ] On preferring Boats from foundering *when Skips founder. SUNG any maft, yard, or fpar, the longer the better, by each end, the bight of the fpan to-be twice the length of the boom ; bend the boat rope exactly in the middle of the bight of the fpan, which need not be above 10 ifathom long: let your boat drive end on under the lee of this boom, which will break off the violence of the fea from her. On ajhip being near a dangerous Lee-Jhore. TO keep a {hip off a dangerous lee-lhore, every effort of mind and body fhould be exerted, as being the only chance to fave the lives of the crew ancl property on board. Carrying fuch fail as will give her good way through the water upon a wind, as long as me will carry it, is certainly the beft method to effect thispurpofe; it is alfo advifablc to reduce all tophamper that holds wind as much as poffible; for if the ihore proves fo deep, or the bottom fo rocky, as not to afford fafe an- chorage, their fafety may depend entirely on carrying fail. Suppofe in this fituation it is found that the (hip will not clear the Chore on either tack, anJ after the utmoft endeavours (lie is per. ceived to loie ground; but as there is no anchorage, there is no other means but to continue turning to the laft, as the wind may abate, or may vary or change in your favour, even when you think it is the laft tack you can poffibly make before you muft inevitably go on fliore. But when it happens that there is clear anchoring ground at a good diftance from the more, and failing proves ineffectual to keep clear of it, then the chief dependence muft be upon the ground tackle applied to the beft advantage, Suppofe then the fhip to be properly prepared, and to have let go a kedge anchor and tow-line bent like a buoy-rope ro the crown of the flream-anchor, and the inner end of the ftream-cable bent to the crown. of the beft bower or iheet-anchor, with a long fcope of cable to make the {hip ride fafe and eafy : where it is known, or found by founding \vith the lead armed with tallow, that the ground is foul, then no more cable fbould be veered out than neceflny requires to bring the fhip up, to ride with as mort a fcope as pofnble, becaufe the cable is liable to be cut or chafed j if that happens there is then the more room S s afteru, 322 ON SHIPS IN DISTRESS. aftern, and a better chance for a fecond or third anchor, trying to the laft moment all poflible means to keep the lliip from the fhore. V/here the water is fo deep that the anchoring ground lies but a Kttle more than a cable's length from the Ihore, then all the anchors fliould be let go to the bell advantage. To put this difficult perform- ance in practice, I would recommend to get the fquare fails handed \V|ith all poflible difpatch, but to keep the fore topmaft, main, and mizen ftay-lails fet, the yards braced full, and the helm put hard a wea- ther to keep headway upon the {hip, ihootirg her along the (bore as much as poflible till all the anchors are let go, beginning with the wea- thermoft anchor, or that which has the cable in the weathermoft haufe hole, and fo on with the next weathermoft anchor, paying out the ca- bles as faft as poflible, that the (hip may keep fhooting a head till all the anchors are let go. And when the neceflity of the fituation re- quires it, no hefitation iliould be made, immediately to cut away all the malts, except the foremaft and the bowfprit fthe fore topmaft ftay-fail being made to hoiil to the fore mafthead) which will not only make the {hip ride with lefs ftrain upon the anchors and cables; but if they give way {he will be the better prepared, when neceflity requires it to be done,, as the laft refuge, to run and lay the fliip on more to the bed advantage, in order to fave all the lives and property that is poflible to be faved, rather than let the {hip founder, or ftrike the ground at an anchor by the tide falling, &c. which affords no chance of faying either Jives or property. On Ships being forced on a dangerous Lee Shore* SITUATIONS, circumftances, times and places are fo different and various, that to give advice on tHs dreadful occafion is difficult. The foeft management on a gradual riling ftiore, in a tidsfway, is to ufe all poflible means to keep the lliip from going on fhore till-after high wa- ter, and the main and mizen-maft being firft cut away, then to run right before the wind and waves with all the canvafs that poflibly can be fet, end on upon the fliore, to make the {hip free herfelf the more, and to run the higher and fafter upon the ground, fo that by the advantage of the tide falling, flie may foon be fet fo faft as to be out of the power of the waves to hurt her much. By this management, in my opinion, not c nly ail the lives, but the {hip and cargo may be often faved, which would be all loft by letting her goat random with a flowing tide. For it muft be confidered, that a (hip going on fliore in a tidefway upon a flood will continue beating as long as the tide flows rind until it falls ; and if (he lies broadfide to the waves, they will have about three times more power on her than when they laid end on to them; and a Ihip will bear but little beating on her broadfide, in pro- portion to what flie will bear upon her bottom. otwithffcruUng a {hip may be thus fuccefsfully run and fet faft upon a (here, with little damage to her hull, and no danger to be apprehended till towards high water next title, if the ftorm continue fo long, yet peo- jple'too often let their frars overcome their reafon, and, being in too great hurry to quit the {hip, and attempting to get on (h ore through the waves, may often lofe their lives; when if they wait till low water they might get on fliore wish little or no rifque; and where the rife and fall of the tide is great the {hip may come quite dry^at low water: therefore, the people Ihoukl be retrained from going on ihore with ;hs boats 'till towards low water; aud when got f ^ o {hore, SAVING LIVES FROM A SHIP. 3 2 3 fhore, it may bg abfolutely neceffary, in order to preferve the boats, to haul them above high water mark, where they may be turned boitom up, and made a place of ihelter when there is no other to be had, and be ftill ready to go to thefhip,if the weather permits and occafion requires. Different mores require different management on this dreadful occa- fion. And where the ihore is nothing but hard rocks deep to, and under water, and high cliffs above water, which are impoilible to be climbed up, in this filiation no fail can be of any ft-.rvice, therefore all the mailr mould be cut away, and fafety then depends entirely on the ground tackle being ufed to the beft advantage ; and if the Ihip drives till ihe comes near the high cliffs, it is well known tfcey make both th-3 wind and waves rebound from them to fome diftance, where if the ground tackle happen to hold, it may give the (hip a chance to ride. On faving Lives from a Ship loft on a Lee Shore. ' I ^O aid and affift in faving the lives of people f;om mips that are -* forced on a dangerous lee more, mutt be allowed to be one of the greater! a6ts of humanity. Time, circiimftances, and fituations arelb various, that it is very difficult to write what may be to the purpofe on this melancholy occafion. Succefs in many fituations may 4epend greatly on affiftance from people on more j but as that is uncertain and cannot be expected in the night, or in defert places, or where a cur- rent or tide runs fo ftrong between the tide and the (lioreas to prevent booms, mafts, yards, &c. with ropes made fait to them from being veer- ed on ihore, in this cafe the utmoft endeavours mould be ufed on board, and every method tried to convey the people on Ihore. Let the expe- riment of a flying Storm Kite be made, that may by the force of the wind carry an iron creeper or grapling made fait to the end of a rope from the wreck to the more, by which accefs may be got to the ihore when prevented by the tide, current, or returning waves. I would propofe thefe kites to be fuch as may be eafily and readily made on board any wrecked veffel, and to confift only of two (lips of thin deal board, about three inches broad, the long piece to be 7, 8, or 9 feet locg, according to the weight of the creeper, grapling, or boat's anchor, and the rope defigned to be fent on more and the crofs piece about half the length of the long piece, to be nailed about a third from the top that forms the kite, to be fpanned with log or lead line from the four ends of the boards, and covered with a piece of light fail, and flung from the four ends of the boards, and ftrengthened with a ipan in the middle to the lower part of the crofs board, where the kite rope is to be feized, and at the lower end of the kite a rope ^ ) 3, or 4 fa- thoms long is to be bent to the grapling, creeper, or boat's anchor, to anfwer the purpofe of the kite's tail. Then it may be alked, how the kite may be made to fall fo low that the anchor, &c. may take hold of the ground, if necefficy requires this immediately to be done? Let the Kite rope run loofe for a time, and the weight of the anchor, rope, &c. will immediately make it fall upon the ground ; and to xhe kite line a larger rope may be hauled on (hore -by the inhabitants, and fixed fo that not only lives but property may be faved by it. But in order to get a graphng on ihore another experiment might he made, viz. to moot it with a rope bent to it lathed along the outer end of a handfpike ; made round juft to fit the bore of a great gun, and long S s z 3^4- ON SAVING LIVES FROM A SHIP. enough to reach from the ring of the grapling to the wad next the powder ; the gun elevnted to its higheft range. Let it now be fuppofed lh;U a rope is got from the wreck to the fliore, and fecured'as well as poflible, till fomebody can be got on fliore by it tofecure ir better. Make a bowling knot in the tail of the ftrap of a fingle block j then reeve the fhore rope through the block, and to that part of the wreck where it may lead and be hauled taut to the greater! advantage to fupport the block, travelling upon it from the wreck to the ihore in the fureft and bed manner poffible ; and if the wreck have any lower mafts ftanding, the fhore rope leading over the main-niaft head would molt likely anfwer the purpofe beft, and the top afford a convenient place to get fixed in, and go from, in the machine to the Ihore. But the facility or difficulty attending the execution of thefe means, are in proportion to the height and diftance of the Ihore from the wreck ; if the fliore be low and near the wreck, the fliore rope may be made to lead the machine upon it, with an eafy afcent from the wreck to the fliore, wirh a man or two in it, without much ftrain either to the rope, or grapling on fliore ; when this is likely to be the cafe, a line fliould be made fall to the machine to haul it to the wreck again ; by which means it may happen that a fliipwrecked crew may foon get on fhore with eafe and fafety. But when the fliore happens to be at a great diftance and higher inn ;.ny part of the wreck, this experiment will of courfe be attended i more difficulty. In order, therefore, to eafe the ftrain on the ihore rope and gn-pling, fix a fninll fail to the machine, fuch as a ham- mock or two, &:c this, fet as a fail upon the machine that is to run light befbre the wind in a florm, will certainly help greatly to lift and leiien the ftrain of the machine on the fliore rope, anti force it forward with great power towards the fliore. A man or two got on fliore by thefe means may greatly contribute, by making things fecure on fliore, to the faving the whole crew, before the fhip goes to pieces. But fuppofingthe fhip to be wrecked where there is neither tide nor current to prevent any thing that will float being drove on fliore by the waves ; in this cafe a towline, or any fuitable rope with a hauling line, may be made faft about the middle of a fpar, and veered away on ihore as far as it will go j and if it happens to be an uneven rocky fhore, it may chance to fix itfelf -faft amonglt the rocks. But if it be a fandy or gravelly fhore, then no fuch chance can be expected j it will then require fome people on fliore to haul it up, and put it under the fand or gravel, with its broadfide to the wreck, to make it bear the ftrain that is neceflary for the rope to be tight enough for the machine to travel upon from the wreck to the fliore. Before concluding this article we {hall give a defcription of the MA- RINE SPENCER, pr'efented to the Royal Humane Society of London by jVIr. KNIGHT SPENCER, and communicated to me, together with the Refufcitative Procefs, by Dr. Hawes, Treafurer to the above Society, conceiving they may be of infinite ufe in many inftances. - The Marine Spencer is a girdle of a diameter to fit the body, fix inches broad, ccmpofed ot about 800 old tavern corks fining upon, a ilrong twine, well laflied together, covered with canyafs and painted in oil, fo as to make it water-proof. Two tapes or cords, about two feet V?ng, mufi bb fattened to the back of the girdle, with loops.at the ends. Another DIRECTIONS FOR RESTORING DROWNED PERSONS., &C. 325 Another tape or cord, about three feet long, in the middle of which a few corks an: ftrung covered with canvafs, and painted as above, muft alfo be fattened to the back of the girdle. Two pins of hard wood, three inches long and half an inch diameter, mutt be fattened to the front of the girdle, one to the upper, the other to the lower part. When the Marine Spencer is to be ufed, Hide it from the feet clofe up under the arms ; bring the two tapes or cords one over each moulder, and fatten them by the loops to the pin on the upper part of the front of the girdle ; bring the other tape or cord between the legs, and faften it to the other pin. A perfon thus equipped, though unacquainted with fwimming, may fafely trull himielf to the waves ; for he will float head and moulders above the water in any ftorm, and by paddling with his hands may eafily gain the ihore. A Marine Spencer conftrnfted as above, and covered with ftrong canvafs unpaintedj will have nearly the fame buoyancy, though more liable to damage from the effe6ts of fea water.* We further add the Refufcitative Procefs, wiihing to contribute all in our power to the benefit of our fea faring brethren. * There is now in vogue a Leather Girdle, which, when filled with air, they have given the name ol" Life Preferver. Directions for the Reftoration of the Drowned, thofe fuP pended by the Cord, intenie Cold, or tremendous Lightning, I. /CONVEY carefully the body, with the head raifed, and fend to \^j the nearer!, medical affiftant. 2. Strip, dry the body, clean the mouth and noftrils. 3. Young children to be put between two perfons in a warm bed. 4. An adult -Lay the unfortunate perfpn on a bed, and in cold wea- ther near the fire. In fummer expole the body to the rays of the fun, and air fhould be freely admitted. 5. The body to be gently rubbed with flannel fprinkled with fpirite, flour of muftard, &c. fait never to be employed ; alfo a heated warm- ing pan, properly covered,, may be lightly moved over the back and fpine. 6. To reftore Breathing. Introduce the pip? of a bellows (when no apparatus is at hand) into one novtril j the other and the mouth being 1 clofed, itfflatg toe lungs, till the bread be a little railed ; the mouth and noftrils muft then be let free. This procefs to be repeated till the re- turn of life. 7. The breaft to be fomented with hot fpirits ; warm bricks or tiles Covered, &c. to be applied to the ibles of the feet and palms of the hands. 8. Tobacco fmoke is to be, thrown gently into the fundament with a proper intlrument, or the bowl of a pipe covered, fo as to defend the mouth of the afliftant. 9- Elcclricity to be early employed, either by the medical afiiftants, or other judicious practitioners. It is much to be lamented that the moO approved methods of afTift- 4fig (hips in Uiih'cfs are not rccoramended or described in prints, tor the pur pole 326 REMARKS TO ASSIST COMMANDERS, pnrpofe of being diflributed amongft our fhips, and amongft the inha- bitants along our fea coaft ; and rewards fhould be held out to the poor people along fliore for every human life faved by them from veffels in diftrefs ; which reward might alfo be the means of faving their own lives from tbejuft laws of their country, by preventing them from plun- dering, and might encourage them to" join heartily in whatever method they perceive people on board the wreck take to preferve themfelves, and to help them in it, by fecuringthe fhore rope, or ufing the hauling line to haul the machine on more, if it-is high above the wreck, &c. The difficulty we now meet with in manning both ihips of war and merchant ihips, mould teach us to ufe every poffible method to preferve the lives of our brave feamen, thofe fupporters of our glory, power, wealth, and confequence as a nation. How pleating rnuft the reflec- tion be to all who contribute to help them ! Remarks calculated to aflift Commanders when coming into the Britifh Channel. AS Mariners know that their reckonings are always uncertain, in proportion to the length of their feveral paffages from the times of their laft departure, it is natural to fuppofe that they muft, when approaching to any difficult and dangerous navigation, experience great anxiety of mind for the iifrie. As the Britifh Channel has proved fatal to many, it may fairly be ranked among thofe places which are deemed dangerous to ihips, in their approach after long paffages; and, there- fore, all thofe whoareentrufted with the conducting of (hips through it, ought to acquire fuch knowledge as may enable them to perform the duties of their important office. Channel- coafters, by the frequency of their paffing and repairing through it, -acquire fuch knowledge as thofe who are employed in foreign voyages cannot pretend to : hence It becomes neceffary to furnifh the latter with fome ufeful information j more efpecially, as it is next to impofiible for the human mind, when engcged in various purftiits, to remember every neceflary article, fuch ss the courfe and diftance irom one place to another ; the precife folia- tion of rocks and fhoals ; and the direction and ftrengtb of the tide in the x^arious places. Commanders of {hips, when coming from abroad, and about to enter the Britifti Channel, mull be exceedingly anxious to accomplish the ultimate de&gn of their voyage, by bringing their refpecYive Ihip falely into port. To the affifiance of fuch, the follow- ing obfervations are intended to contribute : they are founded on ex- perience, and will, if properly obferved, prove highly ferviceable, efpecially when lon^ nights, or thick weather, augment tho-fe dangers wfoicb attend the Channel navigation. Ships, in approaching the Channel from a longpaflage, thould not only try for foundings in time, but run, if poilible, in the latitude of 49 25' North. Having, in that parallel, got foundings in 82 fathoms, line white fand, with black and yellow fpecks, you may be fare that you are near the. outer edge of the bank; and about 50 leagues to the weft ward of Scilly. Ey running 16 or 17 leagues further to the eaft- vard, in t e fame parallel of latitude, you will have 90 fathoms, fine white land : and continuing to run four leagues more to the eaftward, you will (lioai your water to 82 fathoms. Soon afterwards, you will have 72 and 75 fathoms, fine white fand, with fometimes a mixture f REMARKS TO ASSIST COMMANDERS. of green; and in proceeding 1.6 or 17 leagues further to the ea ft ward in this latitude, you will have 72, 75, 77, and 80 fathoms. The foundings will be, for the moft part, fine land, but different in colour; fomeof them will be white fand, mixed with yellow fpecks ; and others fine green fand, with fome mud. In the latitude of 48 23' North, and 61 leagues to the weftward of Ufhant, lies the Nymph Bank. It ftretches about S. S. E. and N. N. W. 12 leagues in length and four ia breadth and has 64 fathoms on it, fine grey fand. The following are the Soundings in the Parallels of 48 2O f , and and 48 30', with their federal depths of Water and Diftancesfrom the I/land of USHANT. QUALITY OF THE SOUNDINGS. Leagues. 5 2 49 46- 43 40 37 3$ 32 29 24 21 18 14 ii 9 ~ 8 6 A. 1TT-M 2 Fine grey fand, mixed with black C Fine grey fand, mixed with small (hells and ) I broken bits ... j Grey fand, mixed with bits of brown (hells f Grey fand, mixed with bits of (hells and 1 $ brown fand . . j Grey fand, mixed with bits of (hells and gravel Grey fand, mixed with (hells and gravel Grey fand, mixed with fmall cornet (hells Sand, mixed with gravel, (hells, and fmall cornets Whitifh grey fand and flat ftor.es Light grey sand, with bits of (hells Coarfe fand, with bits of cockle (hells f Light grey fand, with bits of brown and yel- 1 low (hells, and fmall (tones Light grey fand, mixed with barley-beards Whitifh grey fand, bits of (hells and fine cornets J Light grey fand, mixed with barley-beards 1 I and fmall (hells . . . j Fine grey fand, with^bits of (hells ( Grey fand, fpotted with red, and mixed with ~) I bits of (hells j Whitifli coarfe mining fand, with fine (hells \ Whuith coarfe mining fand, mixed with bar- ) ley beards and coral t . . . Whitifli coarfe fand Fren. Ft.. 62: 106 no 117 104 I 10 1 08 108 100 98 90 84 80 79 75- 75 7 G 65 64 99 97 1 06 94 59 97 97 90 88 Si 76 /i /i 63 68 59 58 When running for the channel in latitude 49' 25', which is the bed latitude, and you have run fo (ar to the eattward as to fhoalen your vvater to 65 or 67 fathoms, and the foundings are (hells ard fmall yellow ft >ries or red fand, you may thence conclude that you are abreaft of Scilly ; or if you have 68 fathoms, white fand with grey fpecks, and f^me times (hells and (tones, Scilly will then bear about N. E. from you, diftancc 10 leagues. Your foundings will always inform you whether you are to the northward. or fouthwanl of Scilly. In the latitude of Scilly you will have oazy ground, in 60, 65, 75, or 80 fathoms. \V, N, W. 10 leagues from Scilh', lies 31& REMARKS TO ASSIST COMMANDERS. lies JonesVBank, on which you will have but 30, 3$, and 40 fathoms 5 and, a little to the fouthward of ir, you will have 72 and 75 fathoms. In running for the channel, in the latitude of 49 30', you will have the fol- lowing depths of water and foundings, when you are abreaft Scilly ; name- ly, 60 fathoms, oaze and broken Shells ; 64 fathoms, white fand with grey fpecks ; 6$ fathoms, (hells and ftoncs ; and C fathoms, fine grey fand. The foundings near Scilly are very different from all others in this latitude: pieces of rotten rock, as broad as a fmall bean, and of a ftone colour, will come up with the lead, which will not be the cafe any where elfe in the fame parallel. More to the foutbward you will have deeper water, with fine land, interfperfed with black fpecks like ground pep- per. Jn the night, or in foggy weather, you fhould come no nearer to Scilly than 60 fathoms ; for, in that depth, you will not be more than iix or fcven leagues from it. Abreaft of Scilly, in the latitude of 49 20', you will have 70 fathoms, cranny, or yellow and white fand; and, to the eaftward of Scilly, in the latitude of 49 8 ; , you will have 56 or 58 fathoms, coarfe fand. You ihould then fteer more to the northward, and endeavour to make the land about the Lizard j your inay fafely make it in the night, as well as in the day, if the weather be clear ; for the light-houfes ftand fo high, and the coaft is fo clear, that you may, without danger, come within half a mile of the point. If the weather/ prove fo thick that you cannot fafely make the land, come no nearer to the Lizard than 45 fathoms j for, in that depth, you will not be more than three leagues off the point : your foundings there will be pebble jflones and fcallop (hells. Ships, when coming into the Channel, ought always, if poflible, to make the land about the Lizard; and ihould they afterwards meet with thick weather, they will not only know how to fteer, but alfo how they advance up the Channel, which will become more and more neceflary in proportion to the contraction of its boun- daries. Some have, contrary to their expectations, got on the fouth iide of the Channel. This error is greatly owing to the iirong in- draught between the iilands of Guernfey and Jerfey, and. the coaft of Brittany, which, ought always to be guarded againft, efpecially in thick weather. It frequently happens that mips, coming into the Channel, have not had an observation for fome days back, which, together with the operation of leant and contrary winds, and the fet- tingof the tides, tend to perplex and bewilder the inoft experienced mariner, when thick weather prevents him from getting a fight of the land. The variation of the compafs in the entrance of the Chan- nel, is nearly 29 W. ; but as the variation is continually increaling at the rate of about a degree in every five years and a half, it will be neceflary to add eleven minutes for every year, fubfequent to the year 1806, which will give you the true variation at any time pretty exa. TABLE TABLE I. Difference of Latitude and Departure for Point. i DI Lat. IXpJDift Lat Dtp Dift Lat. JDep Dift i Lat. Dep' ! Difl Lar.- Dep ! 01 O oo.c > 61 60. 03.0 1 12 [ 120.9^5. .80.? ,05.9 . 241 240.7 u .8 02.0 00. 1 62 6r. ^3.0 2 1 I2I.9io6. 8 : iSi.S oS. 9 42241.7)11 9 j3-u 00. 1 63 62. OJ. I 23 122.9)06. ] 182. i 09.0 43 242.7 11.9 04 . o CO . . 64 63- 03. ] 2 123. 9 06. M3.i 09.0 4-1 2 43-7 12. 05.0 00.2 65 64 03.2 2 124.8 06. 8 ; 184.8 09.1 45 244.7 12.0 36.0 oo. 3 I 66 65. 03.2 2 125.806. 8 > 185.? 09. i 4^ 245.7 (2. I :>7.0 0.3) 6 7, 66. 03.3 2 126.8 06. 8 - r86.fc 09.2 47 246.7 f2. I 08.0 oo. 4 i 67. 03.3 2 T27 .S'O6. V 39. 06.9 2OC f99.8 09. 60 '59-7 f2.8 2 21.0 OI .C Si 80. 4- c | 141 140.8 06.9 201 2QG.S 09.9 261 260.7 12.8 2 22.0 01. I 8 - Si. 04 . c\ 42 141.8 37.0 02 201. 'S 09.9 6: 261.- 12.9 2 23.0 OI . I 8 3i 82. 04. i 4^ 142.8 07.0 03 20X.S ro.o 6? 262.7 w-9 2 24.0 01 .2 84: 83. c 04. i 44 143.8 07.1 04 203-8 IO.O 64 26s. 7 '3o 2 25.0 Of. 2 So 84.9 04.2 45 144.8 07.1 O^ 204. 8 IO. 6j '-64.7 13.0 I 2 26.0 01.3 86 85 v g 04.2 4" '45- S 07.2 06 20>-.8 10. 66 26^.7 IM 2 27-0 01.3 7 86.9 04.3 47 146.8 07.2 07 206. S ro.2 6' '.66.7 .3-1 1 * 28.0, 01.4 88| 87.9 04.3 4$ 147.8 7-3 08 -07.7 10.2 68 -6?.7 13.* 2 29.0 01.4 89] 88.9 04.4 40 148.8407.3 09 208.7 ro.3 69 168.7 13-2 3 }0.0 01. 5 90 ! 9-9 04.4 rr) 49- S 07-4 1C 209.7 10.3 70 269.7 '3-2 i 3 31.0 o-S 911 90.9 H-5 1 ^ I '5o.8 07.4 211 410.7 10.4 271 270.7 '3-3 i 3 32.0 ,i.6 92 91.9 4- 5 52 i 5 r . v 07.5' 12 211.7 10.4 7^ 271.7 'so 3 33-0 01.6 9? 92. c 04.0 5? i-Ss.J 07. t; 13 212.7 10. ; 7^ *72- 7 3.4 1 3 H.O or .7 94 93.9 04.6 54 -3-:- 07 6 14 213-7 10.5 74 -73-7 3-4 3 35.0JOJ.7 9< 94 9 4-7 55 154-8 07.6 i ij 214.7 10. ^ 7> 274-7 '3-5 3'> 46.0JOI.8 9 6i 9 '-9 04-7 56 155.8 07.7 16 215.7 to. 6 76 - 7 5 7 n-s 3 }7.o!or.g| 97 96.9 ?4- <7 156.8 07.7 I" 216.7 10.6 77 2 7 6. 7 3.6 3* 3.0 01 . 9 | 98 97-9 4.'^ 58 157-8 >7.8 I- 217.7 to. 7 78 -77-7 '3.6 39 9.001.9' 99 98.9 4-9 59 38.* 57.8 $ 218.7 10.7 79 -7S-7 ^3.7 4 C 0.0 O2.o|f 100 99-9 4-9 60 59j 07. 9 2C 219.7 0.8 go -79.7 1.7 4 1 I -0 02. oil 101 ice. 9 5-c 161 60. 8 07.9 221 220.7 o.S 281 80.7 irs | 4 7 1.9,02.1 02 101 .9 5-c 62 (Si'.P DS.o 2i .121.7 0.9 82 S'l.f H.8 | 43 2.902., 03 IO2 .9 5-' 63 62.8 08.0 2 1 222.7 0.9 8j 32.7 13-9 I 44 3-9.02.2 04 103.9 5- 1 6 4 63.8 D8.I 24 223.7 i .0 84 2^.7 13.9 4^ 4'' 4.902.2 05104.9 5.902.3] o6|io^.9 5-2 66 64.8 65,? 08. 1 08 I I; 26 >4-7 J2'i.7 J.O 1. 1 85 86 284.7 '85.- 4-0 4.0 [1 47 6.9,02.;! 07 106.9 5-3 6; 66.Mio8. 2 27 226.7 if .1 87 >Wv7 4' 1 fl 4' 7.9:02 4 08 107.9 5-3 6S 6 7 .SioS.2 28 227.7 I I .' 2 88 g 7 -7 J.I 49 8.902.4 09, 108.9 5.4 69(168. 8(08.3 29 228.7 II. 2 80 288.7 ' a 5c _9_9jo2.c 10 109. o, 5 4 7cjr69.8|o8.3 3 229.7 "3 90 :8q. 7 *V| 51 0.9 02.5 1 1 1 1 10.9 5-4 17' rc.^ 08.4 231 130.7 ri.3 291 290.7 14-3 1 5 - 1.9102.6 12 r 1 1 . 9 5' 5 I*- 171.8 38.4 32 w-i 11.4 92 191.6 14.1 s " 2.9:02.6 '3 112.9 J..5 73 172-^08.5 33 .32.7 n. 4 93 2Q2.6 4-4 I 54 3-9.02. 7! | 14 't3-9 5- 6 74 f73-^ : ' ,8.5 34 -33.7 i. ; 94 -"93-6 K-4 1 53 4-9 o 2. 7 i: 114.9 5'6{j 7S 7.4.J c ^x.6 35 -34.7 r.'s 9^ i94.6 t4.5 56 .-.9 o 2 -7 115.9 5-7 7t [75. Xc )8.6 36 JS.7 1.6 96 195.6 '4-5 I ;- 58 >. 9 02. XI 7-9102.8 j 17,116.9 i'l ^ 76. 8c 77- 8c '^ 8.7 37 38 -36.7 37-7 i. -6 i. -7 97 98 196,6 '97-6 4.6 1 4.6 if 59 .9 o 2 -9 J 9, rib. 9 5-8 1 79 78. 8c 8.8 39 38.7 1-7 9Q 98.6 14.7 1 6c .9 o 2.9 20 '9-9 9 8o 79. kc 8.8 40 39-7 1/8 300 .99.6 14.7 I Dfft ep I at, * Dift J Dep. at.ljbift Dep. 'Lat. \ Dift )ep. .at.! Dift Dcp. Lat. 1 ^a tor 7 --J Points. JJ TABLE I. Difference of Latitude and Departure for | Point, Dift Lat. DepjJDift Lat. Dep Dift Lat. Dep Dift Lat. Dep Dift i ii Lat. Dep i 01. 00. I 61 60.7 ->6.o 121 120.4 11.9 181 180.1 7-7 241 239-8 13-6 2 02. O 00.2 62 61.7 36.il 22 121.4 12.0 82 iXl.l 7-8 42 240.8 13.7 : 03-OJ00.3 63 62.7 06.2 2 3 122.4 12. I 83 182.1 7-9 43 241-8 3-8 - 283.6 27-9 46 45.8 04.; o6Jio5. 5 (10.4 66 165.2 16.3 26 224.9 -2.2 86 284.6 28.0 4" ^6.8 04.6 07 106.5 :o.5 67 166. 2 16.4 2" J25.9 22.3 87 ?.8". 6 28., 4 X 47.8 04.7 oS 107. s ro.6 6S 167.2 16. 5 2 V 226.9 22-3 88 286.6 28.2 49 48.8 04. S 09 108.5 10.7 6ciji68.2 j6.6 2q 227.9 tz>4 89 187.6 8. 3 50 19.3 04.9 icjiog. ; to. S 701169.2 16.7 30 Z25.9 12.5 90 aSS.6 28.4 51 ,-o.8 2|.0 ir lino. 5 10. 9 171 170.2 16.8 231 229.9 22.6 291 28,,. 6 28. S P SI.-7 05.1 12 111.5 ri.o 721171.2 16,. 230.9 12.y 92 290.6 28.6 51 52-7 05.2 13 112.5 r i. r 73 .72.217.0: 33 231.9 t8 93 291-6 28.7 54 53-7 05-3 4 1 1 3 5 11.2 74 '73.2 17-1 34 232.9 22 . f 54 292.6 28.8 5< 54-7 QS-4 15 114.4 11.3 7* 174.2 17.2 35 *33-V 23.0 95 193.6 ,8.9 Sfy - r 7 Q: : "(- 36 2;4. Q 27 . I q6 24. 6 ''O .O 57 ;6. t 5 .6 17 116.4 tf.S 77 2 I 7 6. H7- 3 17 235.9 23.2 97 195.6 29-1 . 58 S7-7 05.7 18 ri7-4 ii. 6 78 177. 17.4 tf 236.9 23-3 98,296.6 19.2 59 .8.7 S.8 19 118,4 11.7 79178. 17- S 39 237.9 23-4 9Q 297-6129.3 60 -9.7 05.C 2C 119.4 ' i 8 ^c t79- 17.6 4 c 238.8 23.5 300 2 9 8.6'J2 9 . 4 SHF Dep Lat. Dift Dep. Lat. Dili Dep. Lat. Dift Dep. Lat. Difl Dep, Lat, 7 | Points, TABLE I. Difference of Latitude and Departure for Point. Dift Laf. Dep Dift Lat. Dep Dift Lat. Dep JDift Lat. Dep Dift Lat, Dep : i 01. 00. I 61 60.3* 09.0 121 119.7 17.8 181 179.0 26.5 *4i 238.4 35.4 i 2 02. O 00.3 62 61.^ 09.1 22 120.7 17-8 82 180.0 26.7 42 239.4 35-5 3 03.0 00.4 63 62.3 09.2 23 121.7 18.0 83 181 o 26.8 43 240.4 35 7 ; 4 04.0 oo.C 64 63.3 09.4 24 122-7 18.2 84 182.6 27-0 44 241.3 15-8 5 04.9 00.7 6S <>4-3 09.5 25 123.6 18.3 >5 183.0 27.1 45 242.3 35-9 ! 6 01.9 00.9 66 6s.^ 09.7 26 124.6 18.5 86 184.0 27-3 46 243-3 35-i i r~ 06.9 01. 67 66.3 09.8 27 125.6 18.6 8 7 185.0 27.4 47 244.3 36.2 ! 8 07.9 01.2 68 67.3 IO.O 2"? 126.6 18.8 88 186.0 27.6 48 *45-3 16.4 ! 9 08.9 01-3 69 68.3 10. I 2 9 127.6 18.9 89 187.0 27.7 49 246.3 36.5 ; 10 09.9 or. 5 70 69.2 10.3 30 128.6 10. I 90 1*7-9 27.9 5 247.3 36.7 ] ii 10.9 01.6 7i 70.2 10.4 ijl 129.6 19.2 191 188.9 28.0 251 248.3 36- S 11 11.9 01.8 7* 71.2 10.6 3* 130.6 19.4 9 2 189.9 28.2 52 *49-3 37-0 *3 12.9 01.9 7.3 72.2 10.7 33 I3I.6 19.5 93 190.9 18.3 53 250.3 37-1 14 13.8 02.1 74 73.2 10.9 34 '32-5 19.7 94 191.9 28.5 54 251.3 37-3 15 14.8 03.2 75 74- II. 35 133-5 19. 8 95 192.9 28.6 5.5 252.2 37-4 16 M.8 02.3 76 75- ri.2 36 r 34-S 20.0 96 193.9 28.7 *6 253.2 ?7-6 17 16.8 02. 5 77 76. "3 17 '35-5 2O. I 97 194-9 28.9 57 254.2 37-7 18 17.8 02.6 78 77- 11.4 38 136.5 2O. 2 98 195.9 29.0 5 255.2 37-9 19 18,8 02. 8 70 78. ii. 6 39 '37^5 Z0.4 99 196.8 29.2 59 256.2 38.0 20 19.8 02.9 80 79- ir. 7 40 138.5 20.5 200 197.8 29.3 60 257-z $*-i 21 zo.8 03.1 81 80. n. 9 141 '39-5 20.7 201 198.8 9-5 261 2<3.3 3*1 2 1. 21.8 03.2 82 81. 12.0 42 140.5 20.8 02 199.8 29.6 62 25 9 .2 38.4 23 22.8 03-4 83 Sz. I*. 2 43 141.5 21.0 o-> 200.8 29.8 63 26o.2 38.6 24 23-7 03.5 8 4 *3. I2. 3 44 142.4 21. I 04 201.8 29.9 64 26I.I 3*- 7 2^ *47 03.7 85 *4. 12. S 45 '43-4 21.3 O<; 202.8 30.1 65 262.1 38.9 16 25-7 03.8 86 85. 12.6 46 144.4 21-4 06 203.8 30.2 66 263.1 39o 27 '6.7 04.0 87 86. 12. S 47 <45-4 2 .6 07 204.8 30.4 67 264.1 39-2 2& -7-7 04.1 88 87.0 12.9 48 T46-4 21.7 08 205.7 30. s 68 itf-J 39-3 29 28.7 04.3 .89 88.0 13.0 49 r 47-4 21. 9 09 206.7 30.7 69 266.1 39.- 5 30 29.7 34.4 90 89.0 I 3 .2 50 148.4 22. O 10 207.7 30.8 7o 267 , i 39 6 31 30.7 04.5 9i 90.0 13.4 151 149.4 22.2 21 I 208.7 31.0 271 268.1 39.8 3 2 }*? 04.7 92 91 .0 r 3-5 52 150.4 22.3 12 209.7 ji.i 72 ^69. I 39-9 33 32.6 04.8 93 92.0 13.6 53 i5i-3 22.4 13 210.7 31.2 73 270.0 40.1 34 53-6 05.0 94 93.0 13.8 54 152.3 22.6 14 211.7 31.4 74 271.0 40.2 35 54.6 05.1 95 94.0 '3-9 55 153-3 22.7 IS 212.7 3.1-5 75 272.O 40.4 3* J56 05.3 96 95.0 14.1 56 '54*3 22. 9 16 213.7 31-7 76 2/3-0, 40.5 37 l6.6 05.4 97 95-9 14.2 57 155.3 23.0 1,7 214.7 31-8 77 274.0 40.6 3 37.6 05.6 9* 96.9 14.4 58 156.3 2.3.2 18 2is.6 32.0 78 275.0 40.8 39 18.605.7 99 97-9 H-5 59 157.3 233 19 216.6 32.1 79 276.0 40.9 40 39.6-05.9 100 98.9 14.7 60 158.3 23-5 2C 217.6 32-3 80 2/7-0 4r.i 41 40.6 06-0 101 99-9 14.8 161 159-3 23.6 211 218.6 3L4 2 $7 278.0 41.2 42)41.5 06.2 02 100.9 M.o 62 l6o. 2 23.8 21 ^19.6 32.6 82 2 7 8. 9 41.4 434*.-5 06.3 03 101.9 15.1 63 161.2 2}. 9 23 -20.6 32-7 83 279.9 41.6 44U3.5 06.5 04 102.9 r 5-3 64 162.2 24.! 24 221.6 32.9 84 280.9 41.7 45 44-5 06.6 05 103.9 15.4 65 163.2 24.2 aS 222.6 |3.o 85 281.9 41.8 46 45-5 06.7 06 104.9 15.6 66 164'. 24.4 26 123.6 33-2 86 282.9 42.0 47 46.5 06.9 07 105.8 M-7 67 l6 5 . 24-5 27 224. q 13-3 87 a8j. 9 42.1 48 47-5 07.0 oS ro6.8 15.8 68 166. 24.7 28 **55 >3-5 88 284.9 4 2 -3 49 4*-5 07. 2 09 107.8 16.0 69 167. 24.8 2q 226. s ,3.6 89 2^.9 42-4 i 5 49-5 07-3 IO roS.S 16.1 70 1 68. 24.9 30 227.5 33-7 90 286.9 42.6 51 so. 4 07.5 III 109.8 16.3 171 169. 25.1 231 22S.S 3 y 9 291 287.9 42-7' j 52 5 1 4 7 .6 12 no. 8 ,6.4 72 170. 25.2 .32 -29-5 34.0 92 288.8 42.8 ! 53 =52.4 07.8 13 rn.8 16.6 73 171. 25.4 33 230.5 34-2 93 289.8 43-o ' 54 53-4 07.9 H U2.8 16.7 74 172. ^5-5 34 131. S 34-3 94 290.8 43.1 55 54-4 08. 1 15 113.8 16.9 75 173- 25.7 35 232.5 34-5 95 291.8 43-3 56 55-4 08.2 16 114.7 17.0 76 174- 25.8 36 '-3.3.4 34.6 96 292.8 43-4- 57 56.4 08.4 17 115.7 17.2 77 '75- 26.0 37 234.4 1 4 .8 97 293.8 43.6 5 57-4 08..5 18 116.7 17.3 78 176. 26.1 38 235-4 34-9 98 204.8 43-7 55 56.4 ob. 7 19 117.7 17.5 79 *77- 26.3 39 236.4 35i 99 295.8 439 6c 59-3 08.8 20 118.7 17.6 80 1/8- 26.4 40 237-4 35.2 300 296.8 44.0 Dili Uep Lat. Dift Dep. Lat. Dill iDep. Lat. Dill Dep. Dit. Dili Dep. Laf. A a 2 for 7 Points. TABLE I. Difference of Latitude :iml Departure for 1 Point. Dirt Lat. Dep Dift Lat Dep Did Lat. Dep Dift Lar. Dej Difl Lar. Dep j 01. C 00.2 61! 59.8 11.9 12 n8. 7 e^.6 181 177. s 5^ 24 236., }47.o ] 2 02. c 00.4 62 60.8 12 . 119.6 23-8 82 .78.; 35- 42 237. i 47-2 ' 02.9 00.6 63 61.8 F2. T20.6 24.0 83 179- 5 4 238. 47-4 i I 03.9 OO.8 64J 02.- 12 . 121 .6 84 !8o.c; >5- 44 47.6 c 04 . 9 01. 63 63.8 1 I . 1 22 .6 -4-4 8s 181.4 45 240. 47-8 j 05.9 01.2 66 64.- 12.9 123.6 86 182.4 36. 4' M 1 -: 48.0 ' 7 cb .9 01.4 67 1 3 . 124.6 24. -> 87 183.4 36. 4; 48. 2 8 07.8 01.6 68 66.7 13. 2S f2S. S 88 184.4 }6. 4'- 243 .- 4i.4 r 08.8 01.8 69 67-7 13.5 25 126.5 25.2 89 185.4 36. c 4S N 09-8 02.0 70 6S.7 13-7 3 '270 90 186.3 37- 50 245.2 f 8 . S 11 lo.S 02. 1 71 69.0 13-9 131 r 2 3 ; 2S.6 ! I9 1 187-3 37-3 251 246.2 49.0 12 II.* 02. 3 1\ 70.0 14.0 3 2 129. S 13.8 92 188.3 37-5 52 247.2 19 . 2 11 12.8 02 . :; 73 71.6 14.2 33 130.4 25.9 93 .89.3 37-7 53 248., 19-4 I.' 13-7 02.7 74 72.6 .4.4 34 131.4 26. i 94 190.3 37-8 54 249.1 49.6 j ; 14.7 02 . 9 7 5 14. f 3 5 132 .4 26.3 95 191.3 38.0 <; ; 250- 1 49-7 I' 15-7 03.1 76 74-5 [4.8 36 '33-4 26. ; 96 I92.Z 38.2 5 2ST.I 49-9 I 7 16.7 03 . " 77 75- c 15.0 .37 f 34-4 26 - 97 r '-) 3 2 ^8 .4 57 252.1 50. i 1 8 17. ; 33. i; 1* 76.5 15.2 3S 135-3 26.9 | 98 194.2 38.6 58 -0.3 J>i 18.6 03.7 r( )l 77.5 I 5-3 2(; 28.4 05.7 89 ^7' 3 17-4 49 r 4 6.r 2 ). I 09 205.0 40.8 69 26-3.8 52-5 30 29.4 05.9 90 88. 3 17.6 47.1 29-3 10 206.0 41.0 7 v - / 264.8 -,2.7 3i 3^-4 06.0 9 1 89.3 7.8 151 48.1 29.5 21 i 206.9 41.2! 271 26s. S 52. 9 32 31.4 06.2 92 90.2 7-9 52 49.1 29.7 12 207.9 41.4 72 266.8 53-1 3 ? 32.4 06.4 93 91.2 8.1 50.1 29.8 J3 208.9 41.6 7? 207.X 53-3 33-3 06.6 94 92.2 8.3 54 51.0 5O.O 14 209.9 4'-7 74 268.7 53-5 35 34-3 06.8 95 93-2 8. 5 55 52-0 30.2 I S 210.9 41.9 7 5 269.7 3.6 36 35-3 07.0 96 94.2 8.? S6 53-o 30.4 16 211. 8 42.1 76 270.7 3.8 37 36.3 07.2 97 95. T 8.9 54 .0 30.6 I? >12.% 42.3 77 271.7 4-o 38 37-3 07.4 98 96. I 9-1 55 155.0 30. 8 18 213.8 42. ; . ^ ,6.8 52 -1 .0^0.1 roo . ** I..9 72 168.7 3.6 3? '.27. - 15-3; 9- >7.o 5^ S2.C ro.-< M t ro. v 2 C - j r ^9 7 33.8 3.3 128.5 15-5 93 287., >7 . 2 S3-o ro. c; J4; r i i . i 2. : 7-i 170.7 ',3-9 j4 229. s ^5-7' 04 288.4 57.4 5; 53-9 ro.- 2.4 7 ; 3 5 230.5 289.; S7-6 5" 54-9 10.9 i6|ii3.S 2.61 if f 72.6 ^4. ? 36 131-5 |6.o 96 290.3 57-7 57 55 9 rr . i I7JH4.8 2.8 77 <73-6 54-5 37 132.4 *6'.2 97 291.3 7-9 s8 56.9 ii.; 181115.7 3-0 78 f 74-6 H-7 3 i33-4 |6. 4 98 292.3 58.1 59 57. 9 ii. S 191116.7 3-2 79 175.6 34 <> 39 ^34-4 (.6. 6 293.3 5^ 3 60 58.8 n. 7 20 1 117-7 3.4 So 176.5 35-i 40 135.4 |6.8 70C -94.2 58-5 Dili Dep, Lat. ! Dili Dep. Lat. Dift Dep. Lat. Did Dep. Lat.! Di(t Dep. Lat. for 7 Points TABLE I. Difference of Latitude and Departure for 1 J Points. iDift Lat. Dep Dift Lat. Dep Dift Lat. Dep Dift Lat. Dp> Dift Lat. Dep ; i 01. OO.2 6 59-2 .4.8 121 "7-4 29.4 181 175.6,44.0 24 233.8 58.6 2 01.9 00.5 62 60. i 15.1 22118.3 29.6 82 176.5 H- 2 . 42 234-7 58.8 2 02.9 00." 63 61.1 23 119.3 29. c 83 177-5 44-5 43 59.0 j 4 03.9 01. 6 4 62.1 15. ( 24 120.3 30.1 *^ 178^5 44-7 44 236.7 59-3 c 04.9 or. 2 6- 6.3-1 15. 8 2s 121.3 30.4 8 ; J 7aks 4 : 237-7 59-5. 6 05.8 01.5 66 64. e i6.c 26 122.2 30.6 86 186^ 4^ 38. t 59.8 06.8 01 .7 67 65.0 16.3 27 123.2 3-', 8; 181.4 " 4; 239 . 6 bo.o ! 07.8 01 .9 6^ 66.0 16.^ 28 124.2 31.1 88 182.4 45-7 "4^ 240.6 60.3 9 08.7 02.2 6 9 66.9 16.8 29 125.1 ? T - 8c. i -8 3 . 3 1 4. 5 . Q 49 241. ^ 60.5 10 09.7 02-4 7 C 67.9 17.0 3 126. I 3 I . (: 90 184.3 46.2 50 242 . 5 60.7 ii IO-7 U 2 . 7' 68.9 17.3 IV I27.I 11.? 191 18^.3 46.4 IJi H3- 5 61.0 12 ii. 6 02 .9 7 2 69.8 17.5 32 128.0 3?. . J 02 ;86 . 2 46 . i 244.4 61.2 13 12.6 0^.2 70.8 17 - t 35 129.0 32.; 93 |t8 7 .2 46.9 55 245.4 61.5 ! 14 13.6 03.4 74 71.8 18.0 34 130.O 32. ( 47-1 54 246.4 61.7 j 15 14.6 0^.6 7S 72.8 18.2 35 IjlO 32. S 9^189.2 47-4 c ; 247.4 62 .0 16 15-5 73-7 18.5 36 131.9 33- c 96 190. i 47.6 5^ 248.3 62.2 17 16.5 04. 77 74-7 18.7 37 132.9 33-3 97 191.1 47-9 57 24 ) 3 62.4 , 18 J 7-5 04.4 ,.< 75-7 19.0 3.8 J33-9 3J-5 98 T92. J 48.1 5- 250.3 62.7 19 18.4 04.6 79 76.6 19.2 39 r 34. ^ 33- 99 193. c 48.4 5 6: 39 4 22 215-3 53-9 82 273-; 8.5 ; 43 4 t. 7 10.4 03 99.9 -5- c 6? 158.1 39.6 2? 216.? 54.2 8j 274. ,- 8 .8 44 42.7 0.7 CJ. oo. 9 5 3 ' 64)159.1 39-8 2 4 -17.3 54*4 84 !75-5 9.0 : 45 43-7 O. y o ^ 101.9 -5- 6- 160. i 40.] 2C 218.3 54-7 8; *7.5 9-2 ; 46 44.6 I .2 06 102.8 2, ; ' 6f 161.0 40. ; 2( -19.2 54- ( ! 86 277-4 9-5 l 47 45-6 I. 4 o:iio3.8 6.c 6- 162.0 40.6 ~"i -20.2 87 278.4 0.7 48 46.6 1.7 1 04 . X 26.2 6b 163 .0 40. y 28 -21.2 55-4 88 2.79.4 0.0 49 47-5 1.9 09 io;. : 26.; 6c 163.9 41.1 2 9 -22 . 1 55.6 89 280.3 0.2 50 48.5 2. I 1 106.7 7C 164.9 41.3 22^.1 90 281.3 0.5 5* 49-5 2.4 in 107.7 27 C 1711165.9341.5 231 224.1 36. \ '' 291 J* 2. 3 7 7 52 50 4 2.6 roS.6 27.2 7*1 166.8 4' * 32 22>.0 56-4! 02 283.2 71.0 [ 53 2.9 I : 109.6 27. 5 7 < 167. 8 4> o 33 - 2fi c 91 284.2 71.2 i 54 52.4 3. I 14 1 10. 6 2 7-7 74 1 68. 8 14*. 3 34227.0 56.9 94 285.2 71-4 : 55 53-4 3-4! I ' 1 1 1 .6 2 7 . -, ! 169.8 35 128.0 57-i| 9; 286.2 71.7 , ?6 54-3 3-6 : id 1 12. c; [jS.2 170.7 42.8 36 228.9 57-31 9 287.1 57 55-3 1.8 17 U3.5 28.4 7 7 171.7 43- c 37 229.9 57-6 97 288. T "2.2 58 4-1 1 8 114.5 28.7 172.7 1-3-3 38 23.-). 9 289 . J 72.4 : 59 57-2 4'3 19 115.4 28.9 7 r 173.6 $$ 5 39 58.1 09 290.0 72.7 ! 60 18.2 4 .6j 20 I o 4. Z9-2 80 174.6 ^3-7| 40 232.8 5^-3! 300 291.0 72 -.9 j Dift Dep. .at. 1 Jift Dep. La^. Dift Dep. Ut, Difti Deo. Lat. Dift Dep. La*. for 6' -| Points. j TABLE I.. Difference of Latitude and Departure for 1 t Points. Dift. Lat. )e 1 Dift. Lat. 3ep. Dift. Lat. Dep.| Dift. Lat. |Dep. Dift. Lat. 3ep i 01 .0 K>3 b* 5^-4 7-7 121 15.8 35-ij 181 173.2 52. 5 241 130.6 to. o 2 01.9 30. 6< 62 59 3 8.0 22 16.7 35.4! o2> 174.2 52.8 42 131 .6 0.2 3 02.9 )O9j 63 60.3 8.3 23 17.7 J5-7 8^ 175.1 53 J 43 -32.5 70.5 4 03. S 31 . 2 64 61.2 3.6 24 18.7 36.0 84 176. i 53-4 44 133- S 70.8 04.8 31 . 5 65 62.2 8.9 2$ 19.6 36-3 8S 177.0 S3-7 45 134. S 71. 1 6 05.7 >i-7 66 6*?. 2 9.2 26 20. 6 36 . t> 86 178.0 46 13 S -4 7L4 7 06.7 D2.G *|6; 64.1 9-4 27 21.5 36.91 87 179 .0 54.3 47 136.4 71-7 1 07. 7 02.3 DJ 65.1 9-7 2 s 22.5 37- 2 88 179.9 54.6 48 M7. 3 72.0 ! 9 08 .6 02.6 69 66.0 o.cj 29 123.4 57-4 89 180.9 54-9 49 72-3 10 09.6 02. Cy 70 67.0 o . : 30 124.4 37-7 90 181.8 139.2' 72.6 1 i 10. ; 0^.2J i 67.9 zo.t 131 125.4 38.0 191 182.8 55-4 251 240.2 72.9 12 li .' 68.9 126.1 38.3 02 181.7 r - r- 52 241 . i 73.2 13 iz. 4 03.8 3 . y 69.9 33 127.3 93 184.7 5 6.c 53 242. ) 73-4 14 13.4 04.1 4 70.8 i i . ; 34 128.2 } 8! 9 94185.6 56.3 S4 243.1 73.7 15 14.4 04.4 S 71.8 21. S' 3 ; 129.2 39. Sj 95 186.6 56.6 $5 244.0 74-0 16 15.3 04.6 70 72.7 22.1 130. i 39-5) 9 6 187.6 56.9 5< 245.0 74.3 17 16.3 04.9 77 73-7 22.4 37 131.1 39. b 97 188.5 57.2 S7 245. 9 74.6 18 17.2 OS. 2 74-6 22.6 132.1 40.0 98 189.5 57.5 5 246.9 74-9 lq 18-2 05.5 79 7S-6 22.9 39 i33.o 40.3 90 190.4 S7-8 S9 247.8 75-2 20 19.1 o 5 -> 80 76.6 23.2 4 134 o 40.6 200 191.4 58.! 60 248.8 75-5 21 20. r 06.1 81 77-5 23.5 141 r 34-9 40.9 201 192.3 58.3 261 249.8 75-8 22 2I.I 06.4 82 78. s 23.8 135-9 41.2. O2 193.3 58.6 62 250.7 76.1 23 22.0 06.7 83 794 24.1 43 136.8 4 f s 03 194.3 58-9 63251.7 76.3 2 4 23.0 07.0 84 80.4 24.4 44 137.8 41.8 04 195.2 59.2 64 252.6 76.6 5 23.9 07.3 8; 81.3 24.7 138.8 47. i 05 196.1 59- > -53- 6 76.9 26 24.9 07.5 86 82 3 46 139-7 42.4 06 197.1 S 9 .S 66 ^34-5 77-2 27 25.9 07. J 8- 83.3 2S.2 47 140.7 4*-' 07 198.1 60.1 67 255 . f 77-5 28 26.8 o3.i 83 84.2 48 141.6 43 -c ok 199.0 60 4 256.5 77-8 ZQ 2 7 .S 08.4 89 8s-z 25.8 49 142.6 43-3 09 200 .O 60.7 69 257-4 78.! 30 zS.7 08.7 90 86.1 26.1 SO i43o 43-5 1C iOI .O 61.0 70 258.4 78.4 3 ' 29.7 09.0 9* 87.1 26. 4 15 144-5 43-8 211 201.9 61.2 271 259.3 78.7 32 30.6 09. ? 92 88.0 '4S-5 44.1 12 202.9 61 . c 72 260.3 78. 9 33 31.6 09.6 89.0 27.0 SI 146.4 44-4 13 203. S 61.8 73 261.2 79.2 34 3 i -5 09.9 94 90.0 7.3 S4 147.4 44-7 204.8 62.1 74 262.2 79-5 35 33-5 IO.2 90.9 2 7 .6 5 148.3 45- s 205.7 62.4 75 263.2 79-8 36 34-5 10.4 96 91.9 27.8 H9-3 45-3 16 206.7 62.' 76 264. i 80. i 37 35-4 1O.7 97 92. S 28.2 S" 150.2 45.6 17 207.7 63-0 7" z65- i 80.4 3$ 36-4 II .0 98 93-8 28.4 58 151.2 4S-9 18 208.6 63. 78 266.0 80.7 39 37-3 II.3 99 94-7 28.7 59 152.2 46.2 19 209.6 63.6 79 267.0 So. 9 40 33.3 i r .6 100 95-7 29.0 ISO 46.4 20 210.5 63-9 80 267.9 81.3 4 1 39.2 U.i 101 90.7 i 9 . 3 16 154.1 46.7 Z2IJ2II.5 64. j 281 208.9 81.6 42 40. 2 12. 2 02 '97-6 29.6 62 155.0 47.0 2 212.4 64.4 82 269. 9 81.9 i 43 4I.I 12. 03 98.6 29.9 6 156.0 47-3 23 213.4 6 4- 83 270. fc H2.2 44 42.1 ii.i 4 99.5 30.2 64 156.9 1 214.4 r ^. 84 271 .8 $2.4 45 43-1 13 . 05 lox 5 30.5 6 157-9 47-9 2; 215.3 65,31 85 -2.7 82.7 i 46 44.0 n- 06 101 .4 30.8 6 48.2 26 216.3 65.6) 86 -73-7 83.0 47 45.0 13.6 07 102.4 31 I 6 159.8 48- S 2" 217.2 65.9 87 174 k S3 . i , 4? 45-9 13-9 08 103.3 3L4 6 160.8 48.8 28 2IS.2 66.2 88 2-5-6 83.6 46- 9 14.2 o<. 104.3 5i.fi 6 161.7 49-o 29 ZI9. I 66.4 89 276.6 3-9 5 C 47.8 14.5 1C 105.3 70 162.7 49-3 30;220. i 66. v 90 277.5 84.2 : 5' 48.8 14.8 II I 106. 2 72.2 ij 163.6 49.6 2311221 . i 67.1] 291 2 7 S. f 84.5 j 5 : 49.8 50.7 15.1 15.4 12 n 107^2 3i8 7 7 164.6 49-9 SO. 2 32 33 J222.0 223.0 67-3 67. C 1 92 279-4 280.4 84.8 1 85.0 51.7 15-7 M 109 . 1 33- 1 7 166.5 .34 223.9 67 . r 94 281.3 85-3 5. 52.6 16.0 ICll 10. 33-4 7 167.5 So.S 3< 224.9 68.2 282.3 85.6 se 53.6 16.3 tC III.O 33-8 7 168.4 Ji.l 36 >25-9 68. s 9 C 283.3 85.9 I 5- 54-5 16.5 i* U2.0 7 169.4 C I .'A 37 226.8 68.8 97 28 4 . 2 86.2- tf 55-5 16.8 i* II2-9 34-3 7 170.3 Si-7 227.8 169. 1 9* 285.2 86.5 Sr 56., 17-1 J f 113.9 34- S 7 171.3 S2.0 39 228.7 69.4 9S 286.1 86. S 6c 57-4 17-4 2C 1 14.8 8 172.3 40 229.7 p " 1 3 c 287.1 S 7 .i Dift Dep. Lat. Dirt . Dep. JLat. Dift Dep. Lat. )!Dift. Dep. lLat. Dift. Dep. L-it. 1 for -^ Points. TABLE I. Difference of Latitude and Departure for If Points. Dift at. 1 Dift Lat. I Depj Dift Lat. I Dep Dift Lat. Dep Dift Lat/" Dep. f i 00.9 c >o-3j 61 57-43 .0.51 121 13-95 p. 8 rfi [70.4161.0 241 226.9 Si. 2. i 2 01. 9 c >o.7 62 58.4: 0.9; 2 14.04 (.i.i 82 [71.4:61.3 42 227.9 81.5 3 4 02. 8 C 03. 8 c >I.O >i.3 63 64 59.321.2! 60.3 21.6 23 24 15.8^ u6.8< M-4 M- 83(772.3(61.7 84 I73.2j02.OI 43 44 228.8 229.7 81.9 82.2 5 04.701.7} 6; 61.2 11.9 2? [17.7, *2. il 85174.2162.3 230.7 82.5 6 05.6102.0 66 62.1 Z2.[ 26 118.6, ^2.4 86 175.1 32.7 46 231.6 82 o 7 06.6 02.4] 67 63. J 22.6 1 27 119.6142.8 ^7 176.1 47 232.6 83-i 8 07.5 02. 7 68 64.0 22.9 28 20. 5:43.1 8 X 177.0 63.3 48 23"" r 83-5 9 oS-sh.oj 69 65.0 3-* 29 121.543.5 89 177.9 53.7 4^ 234.4 ^3-9 10 09.4,03.4 70 OS-9 3.6 3 122.4 4.3.8 9 178.9 54.0 5 235-4 04 .2 u 10.4 3-7 7i 66.8 3-91 131 123.3 44.1 191 179.8 H-3! 2^1 ~r ^4.6. 12 "3 4.0 72 67.8 4-3 32 124.3 44-5 92 180.8 64. 7 | 52 2 37-3 84.9 13 12.2 4-4 73 6S.7 4.6 33 125.2144.8! 93 181.7 65.0! 53 238.2 *s>* X 4 13.2 4-7i 74 69.7 4-9, 34 126.2)45.1 94 182.7. 65.4 54 239.2 85.6 15 I4.I 5- * 75 70.6 5-3' 35 127. i 45. 5 183.6 65.7 55 240.1 85.9 1 6 15.1 5-4 76 71.6 5.6! 30 128.045.8 96 184.5 66.0 56 241 .0 86.2 17 i6.c 5-7 77 72. ; 5-9 37 129.0146.2 97 1*5. S 66.4 57 242.0 86.6 18 17.0 6.1 7^ 73-4 26.3 3* 129.9146.5 98 186.4 66. 7| 53 242.9 86. 9 19 20 17.9 18.8 6.4 6.7 79 80 74-4 75-3 7.0 39 40 130.946.8 131.847.2 200 187.4 188.3 67.0 67.4 59 60. 243.9 244-8 87.2 87.6 21 19.8 07.1 81 76.3 7-3 141 132.847.5 201 189.3 67-7 261(245.7 87.9 22 20.7 07.4 82 77.2 27.6; 42 133.747.8 O2 190. 2 '63. j 62(246.7 88.3 23 21 .7 22.6 oSil 83 84 78.1 79.1 8.0'; 43 44 .34.648.2 '35-6:48.5 03 04 191. i 192. i 68.4 68.7 63 64 24,7.6 248.6 88.6 88. 9 25 2 35 08.4 8j 80.0 -8.6 45 136.5*8.8 OS 193.0 69.1 6s 249.5 89-3 26 24.5 oS.8 8b 3i.o -9.0 46 I37.549.2 06 194.0 69.4 66 250.5 9.6 27 -5-4 09.1 87 81.9 -0-3 47 138.449.5 07 194.9 69.7 67 251.4 8^-9 28 26.4 09.4 8S 82.9 29.6 4* 139. 3149.9 08 195.8 70.1 6S 252-3 29 27.3 09.8 89 83. 8 50.0 49 140.3 50.2 09 196.8 70.4 69 90.6 1 30 28.2 IO. I 90 84.7 30-3 50 141.2 50.5 10 197.7 70.7! 70 254.2 90.9 31 29.2 0.4 9 J 85.7 30.7 IS 1 142.2 50.9 211 19*. 7 71.1 271 * 5 5 * 91.3 32 30. i 10.8 92 86.6 31.0 5* 143.1 51.2 12 199.6 71.5 256. i 91.6 33 3 * - * n. i 93 b 7 .b 31.3 53 144.1 51-5 13 200. 5 7 1 7 73 257.0 92.0 34 32.0 11.5 94 88. c 3i.7 54 145.0 14 zoi.5 72. 1 '74 2<;8.0 92.3 35 33.0 1 1.8 95 89.4 ) Z . O 55 145 . 9 S2.2 15 202.4 72.4 7 ^ 258.9 92.6 36 33 9 12. I 96 90.^ 32. i 56(146.9 52.6 16 203.4 72.8 76 259.9 93.0 3" 34.8 T2. 5 9' 91.3 32.7 57H7.8 52 .9 1 7 204.3 7V 1 77 260.8 93-3 3^ 35-8 12.8 9* 92.3 33.0 58 148.8 53.2 18 205.2 73-4 "8 261 .7 93-7 39 36-7 I3.I 99 93-2 33-4 59 I49-7J53- 6 9 206.2 7V* 7Q 262. 7 94.0 j 40 37-7 '3.5 IOC 94.2 33-7 60 150.6 53.9 20 207. i 74-1 80 263.6 94-3 i 4 38.6 13.8 10 95- 34.0 161 151.6 54-2 221 208.1 74-5 28 1 264. 6 94-7 ! 4* 39-5 14. o 96. c 34-4 62 152-5 54.6 22 209.0 74.8 82 265.5 95.0 4 40. 14. o 97. c 34-7 63 153-5 54-9 *3 210.0 75-1 83 266.5 95-3 j 44 41.4 14. o* 97-9 35.0 64 154-4 S5'-2 75- *> 84 267.4 95-7 4 42.4 '5- 98.9 35 4 65 '55 4 55.6 25 211. 8 7^.8 268.3 96-0 I 4 4J-3 '5- 99.8 35-7 66 r 56. 3:55.9 26212.8 76 i 86 269.3 96-4 4 44- 15.8 o 100. 56.0 6- 157-2^6.2 27 213.7 76,5 87 270.2 96.- 4 45.2 16.2 c roii 36.4 6^ 158.2 56.6 28 214.7 76.8 88 271.2 97.0 4 46. 16.5 IC2. 36.- 69 159. i ;6. 9 2C 215.6 77-1 89 2/2.1 97-4 5 47- i6.5< I 103. 37-1 7^ 160. i 57-3 3c 216.6 77-5 90 273.0 97 *" r 48.0 T7.2 II 104. 37-4 171 161 .c S7-6 23] 217.5 77 ' 291 2-4.0 98.0 5 49-0 17.5 12 I0 5 . 37-7 72 161 .r 57-9 32 2l8. 4 78.2 92 274-9 98.4 5 49.9 17.9 ] 106.4 38. 7-3 162. f 58. 33kr9.4!79.5 93 275.9 98.7 5 50. ^ 1 8. 2 K 107. }8. 4 7^ 163. S 5^.6 W 22O. 3 78.8 94 276.8 99.0 5 51.8 .8.5 I 108. 58." 7, 164. i 59- c li 221-3 79-2 9- 277.8 99 4 5 52.~ 18.9 iC 109. 39- 7< 165.1 59-3 V 122.2 79-5 96 278.7 99-7 5 53- 19.2 no. }9-4 / / 1 66.: 59- 3 " 223.1 79.8 97 279.6 100. I 5 54- 19-5 I> in. 39-8 75 167. < > 60. c l\ } 224. I 8O.2 >} 98 280.6 100.4 J_ 56* 19.9 iO.2 If 2C 40. 40.4 7< 8< 168.. 169." j6o. 560. K : 4 C ) 225.0180. 5 >226.o|8o.8 300 282. s 100.7 IOI . I Dift Dep. Lat. Dirt Dep Lnt Dift Dep. Lat Dili Dep. Xat. Dift Dtp. Lat. / for 6 | Points, TABLE I. Difference of Latitude and Departure for 2 Points, Diit.' L:.t. Dep. Dirt.' Lat. Dcp Dift. Lat. Dep.hDift Lat. Dep Dift Lat. Dep. i oo.g 00.4 61 56.4 23 121 III. 8 46-3 131 167.2 69-3 j 241 22Z-7 9 Z,2 a u; . sjoo.8 62 57-3 2}-7 22 112.7 4^-7 82 168.1 69.- 223-6 92 .6 3 o*.8!oi.i 63 24.1 23 U3.6 47.1 8- 109. i 70.0 43 224.5 93-o 4 0^.7 lor. 5 64 24. > 2i 114.6 475 84 170.0 70.4 44 225-4 93-4 <; 04. 6 JO i .9 6. 60. i 24. i 25 115.5 47.8 8> 170.9 70.8 45 226.4 93-8 6 o - > - 02 . 3 ft 61.0 26 116.4 48.2 86 71-9 71.2 46 227.3 94 -i OK <;|o2-7 6- 6L 9 45. 6 27 117.3 48.6 ^7 72.8 71.6 47 2Z8.2 94-5 07.4:0;.! 6. 62.8 26.0 2? 1/8.3 49-o 8b 73-7 71.9 48 229.1 94.9 9 OJ-.J 03 4 O'j 63 . 7 i6 .*, 20 119.2 49*i 89 74 6 72.3 49 230. I 95-3 10 09. 2 03 . 8 7 C 64-7 26 S 3 C 120. I 49 -7 90 755 72.7 .50 231.0 95-7 __ IO.2 64.2 7 65.6 tj.2 *3' 121. JO,J 191 170.5 73- * 251 231.9 96.1 t .. 1 1. 1 14.6 66.5 *7< 3~ 122.0 50. t. 9- 177.4 73- 52 i^z.3 96.4 13 12.0 05.0 7^ 67.4 27. c 3.3 122.9 50.9 1/8.3 3-9 53 -33.7 96.8 14 iz 9 05.4 68.4 34 123-u 51.; 94 179.2 /-!- 54 234-7 97.2 I c 05.7 7- 69.3 18*7 35 124.; 31-7 95 180.2 74.6 5-5 135-6 97-6 16 14.8 36.1 76 70.2 29.1 3< 54. G 9* 181.1 75.0 56 236.5 98.0 15. 7 -6. * 7 1- I 29.; 37 126.6 52 'i 97 182.0 75-4 57 237-4 98. 3 iS 16.6 ,6 9 72.1 29.8 127.5 52.1 9^ 182.9 75.8 5B 238.4 98.7 19 17 6 07.; 79 39 ,3-2 99 183.9 76.2 59 239-3 99.1 | 2C -7.7 8.C 73-9 30 r 129.; 53-6 20,. 184. i 76.5 60 240.2 99 5 19.4 XV. C Si 74 31.0 141 '.30.3 H- 23! 185.7 "6.9 161 241.1 999 "2. "" 20.3 08.4 82 75-8 31.4 4 : 131.1 54 r 3 01 186.6 77-3 62 ^42.1 100.3 27 21 .2 oS.S 8* 76.7 43 132. 1 54-7 03 1^7.5 77-7 63 243.0 100.6 I 24 *2.2 09.2 84 77-6 $*.i 44 133.0 55- J 0^ 188.5 78.1 64 243.9 IOI.O j o>.6 8 ' 78. s 4 : 134.0 55-5 05 189.4 78.5 6s 244.8 101.4 ft 6 24.0 IO.O 86 79-5 32.9 46 134-9 55-9 06 190.3 78.8 66 * 45 .8 101.8 ro. 3 87 80.4 33*3 47 135.8 56.3 O7 191.2 79.2 67 246.7 102.2 ! 28 2 S.O 10.7 $S 81.3 48 136.7 0.6 08 192.2 79-6 68 247.6 ro2.6 29 1 1 . i 89 82.2 34.1 49 137.7 57-0 09 193.1 60.0 69 >48-S 102.9 30J 2,7-7 11.5 90 83.1 34-4 5 138.6 57-4 10 194.0 80.4 70 249.4 103.3 3' 28.6 11.9 9 i 84.1 54. i xji '39-5 57.8 *ii 194.9 50.7 271 250.4 '03-7 ;, 29.6 92 85.0 3 52 51 140.4 58.2 12 '95-9 if.l 72 1 5 I 3 104. i j , ; ;o > r .: . 6 93 Sv9 35.6 53 141.4 5^ .6 13 196.8 $1.5 73 152.2 104.5 34 31.4 13.0 86.8 36.0 54 142.3 58.9 M 197.7 Si. 9 74 253 i 104.9 31 32.3 33-3 15.4 95 96 87.8 88.7 16.4 55 143.2 144.1 59-3 S9-7 : c 16 198.6 3 *. 3 75 76 254.1 255-0 (05.2 105,6 , 37 J* 39 40 34- 35-' 36.0 37-c 14.2 14.5 14.9 '5-3 97 98 99 I0o 8 9 .6 90.5 9^5 9-- -4 37-' 37-5 37-9 57 58 6c 146.0 146.9 147.8 60. i Go. c 60.8 6 r . : i 18 19 20 200.5 201.4 202.3 203.3 &? 11 79 80 255-9 156.8 257-8 258.7 106.0 i 106.4 [06.8; 4 ' 7^ . 9 IC.J 101 93-3 38 . 7 161 148.7 ) i . 6 2*1 204.2 ^4. 6 i8j|55>.6 IO 7 5 42 i 44 39-7 4 6 16. i i6.'s o: 03 04 94-2 95.2 96. i 39- 39-4 62 63 64 149.7 150.6 62.0 62.4 62. S 22 24 205.1 :o6.c 106.9 ^5 3 85.7 8*1*60.5 83261.5 84(262.4 107.9 108.3 108. 7j 46 41 . < 42. s 17-2 5 06 97.0 97-9 40.2 40.6 6; 66 '52-4 63-1 63.5 25 *6 207.9 208.8 *6. i 86. ; c 263.3 86(264.2 109.1 09.4 i 47 I 4 s p 49 43-4 44-3 45-3 40.2! rS.o 18.4 18.8 f 9 .i 07 09 10 98.9 99.8 [00.7 ioi.6 4-9 41-3' M-7 67 68 69 yo 155-2 156.1 167 i b 3 . 9 64.7 65.1 2 9 30 209.7 zio.6 in. 6 ita, 5 ^6.9 87.6 8S.o 8Si266ii 89)267.0 90267.9 09.5 10.2 10.6 no 5 1 53 54 47.1 48.0) 49. c 49-9 3i.f'i5-4 96 86.8:41 .0 56; 141.0 66.7 r6 195-31 92-4 76 249 5 118.0 37 33-4- i vS 97 87.7 41-5 S7 141.9 67.1 17 196. r 92.8 77 250.4 u8Hj 33 34-4 16.2 98 88.6 41.9 S8 142.8^ 67.6 18 197.1 93-2 78 25'-3 118.9 39 35-3 16.7 99 89. S 42.3 S9 143-7 68.0 19 198.0 93-6 79 152.2 119.3 40 }6. 2 17.1 100, 90.4 42.8 60 144.6 68.4 20 198.9 94.1 8c 253.1 n 9 . 7 | ! 4 1 ' J7-J To 101 91.3 43.2 61 J 45-5 68.8 221 199.8 94o 281 254.0 120. I f 4 2 }S.o 18.0 Oi 92.2 4?- 6 62 146.4 69-3 22 zoo. 7 94-9 82 254.9 I2O. 6 | I 43 38.9 18.4 03 93-1 H.O 63 147.4 69- 7| 2; 201.6 95-3 83 255.8 121 - 44 $9.Sii8.8 04 94.0 44- S 64 I48-3 70. i J 4 2O2. 5 95-8 84 256.7 121. 4; 1 45 40.7 19.2 05 94-9 44-9 6s 149.2 70-51 2S 203.4 96.2 8s 257.6 121 .9 ! 46 41.6 19.7 06 95-8 45-3 66 150.0 71.0 26 204.3 96.6 86 258.5 122.3; 47 4^-5 20.1 07 96.7 4S-7 67 151 .0 71-4 27 20S.2 97.1 8? 2S9-4 122.7 i 4* 43-4 10.5 oS 97.6 +6.2 68 151.9 7i.S 28 206. I 97.5 88 260.3 123. 1 49 44-3 21.0 09 98.5 46.6 69 152.8 7i-3| 2 9 207.0 97-9 89 261.3 1*3.6 50 4.5-* n 4 10 99.4 47.0 70 1 53 '7 72-7 30 207.9 98.3 90 262.2 124.0 5' 46., zt.b 1 1 1 00.3 4-7-5 17 j r 54.0 73 23 I 208.8 98.8 291 263. i 124.4 $2 47.0 22.2 j 12 IOI.2 47-9 72 M5-5 73-5 32 209.7 99.2 92 264.0 124.8 i "^ 47-9 22.7 f3 102.2 48.3 7?; r s6. 4 74-oJ 33 2IO.6 99.6 9.3 264.9 125.3 54 4*.S 23-1 4 104. 1(48.7 74 57 3 74-4J 34 211.5 IOO. 1 94 265.8 125.7 5 53.3 2N. 2 19 10/.6 CO. 9 j ' 7Q 161 8 76.5' 39 216. i 102. 2 99 2/0 3 127.8 (o >4.2 *57 20 108.5 51.3 * 162. 7 77.0' 4 :. 1 7 . o ro2-6 300 271.2 128.3 )ift Dtp. Lut. Dill Dop. -Lat. bif} Dep. Lat. : Difti Dpp. Lat. Dift Dep. Lat. Bb tor 5 'A Points. TABLE I. Difference of Latitude and Departure for 2 f Points. Lat. Dep. | 159.6 8v3 160.5 161.4 86-3 162.3 86.7 163.2 87.2 164.0 87.7 164.9 88.2 165.8 88.6 166.7 89.1 167.6 89.6 16^4 90.0 169.3 90.5 170.2 91.0 171.1 91-41 172.0 91.9 172.9 92.4 173.7 92.9 174.6 93-3 175-5 93.8 176. i 94-3 177-3 94 .8 178.1 95.2 179.0 95-7 - 179-9 96.2 180.8 96.6 > 181.- 97.1 7 182.6 97-6 > 183.4 * j Q A ^ 98.0 3 185.2 99.0 i 186. 99-5 i 187. 99-9 3 187. 100.4 j. 188. 100.9 5 189. f\ T f\r\ 101.4 Tr>T .S Lat. 251 I 5 * 53 54 66 72 12.5 221.4 224.9 230.2 231 233 238.1 18.3 239.0 191.4 102.3 02.8 03.2 193 194-0 103.7 194. 104.2 104.7! 105. 1 105.6 106. i 106.5 107.0 107. 5 107.9 108.4 10$. 9 109.4 109.8 110.3 no. 8 III. 2 in. 7 112. 2 112.7 7. I 1 9 6, I 97 . 198. 199. 20O, 201 , 202 204, ZOf. 206 207 205 74 79 246.1 46. c 211 Dep Lat. 5 r, 4 259 96 99, - -| , 300 1264.61141 Biftl Dep. i Lat 263. 2-7-3 29.6 30.1 30.6 31.0 31-5 32.0 33.9 136.2 for 5 i- Toints. TAB LE I. Difference of Latitude and Departure for 2 Points. Dift Lat. Dep. Dift Lat. Dep. Dift Lat. Dep. Dift Lat. Dep. Dift Lat. Dep. i 00.9 00.5 61 52.3 31.4 121 103.8 62.2 181 155.2 93.] 241 206.7 123.9 2 01.7 01. 62 53-2 3 I -9 22 104.6 62.7 82 156.1 93-e 42 207.6 124.4 3 02.6 01.5 63 54.0 32.4 2 3 105.5 63.2 83 157.0 94.1 43 208.4 124,9 4 03.4 02. i 64 54-9 32.9 24 106.4 63.7 84 157.8 94. t 44 209.3 125.4 5 04.3 02.6 65 55.8 33-4 25 107.2 64-3 85 158.7 95.1 45 210. I 126.0 i 6 05.1 03.1 66 ' 56.6 33-9 26 108.1 64.8 86 159-5 95.6 46 211. 126.5 2 06.0 03.6 67 575 34-4 27 108.9 65-3 87 160.4 96.1 47 2II. 9 127.0 8 06.9 04.1 68 5*. 3 35.0 28 109.8 65.8 88 161.3 96.7 48 212.7 127.5 9 07.7 04.6 69 59.2 35-5 29 no. 6 66.3 89 162. i 97.2 49 213.6 128.0 10 08.6 S-' 70 60.0 3-6.0 JO "i-5 66.8 9 163.0 97.7 5 2H-4 128.5 ii 09.4 05.7 7* 60.9 36.5 131 112.4 6T1 191 163.8 98.2 251 215-3 129.0 1 lz 10.3 06.2 72 61.8 37.o 3* 113.2 67.9 92 164.7 98.7 52 216.1 129.6 13 II. 2 06.7 73 62.6 37-5 33 114.1 68.4 93 165.5 99.2 53 217.0 1.30.1 H 12. 07.2 74 63o 38.1 34 114.9 68.9 94 166.4 99-7 54 217.9 130.6 15 I2. 9 07.7 75 64.3 38.6 35 115.8 69.4 95 167.3 |00.2 55 218.7 131.1 16 13-7 08.2 76 65.2 39- 1 36 116.7 69.9 96 168.1 loo.S 56 219.6 131.6 ' 17 14.6 08.7 77 66.0 39.6 3? 117.5 70.4 97 169.0 101.3 57 220.4 132.1 18 15.4 09.3 78 66.9 40.1 38 118.4 70.9 98 169.8 roi.g 58 221.3 132.6 19 I6. 3 09.8 79 67.8 40.6 39 H9 .2 71.5 99 170.7 102.3 59 222.2 I 332 20 17.2 10.3 80 68.6 41.1 40 120. I 72.0 200 171.5 102.8 60 223.0 133:7 XI 18.0 10.8 8r 69.5 41.6 141 120-9 72.5- 2OI 172.4 I0 3-3 261 223. 9 134.2 22 18.9 11.3 82 70.3 42.2 42 121. 8 73-0 02 173.3 103. b 62 224.7 '34-7 ^ 23 19.7 n. 8 *3 71.2 42.7 43 122.7 7J. 5 03 174-1 104.4 63 225.6 135-2 24 20.6 12.3 8 4 72.0 43.2 44 123.5 74-o 04 175.0 104.9 64 226.4 135.7 ^5 21.4 12.9 85 72.9 43-7 45 124.4 74-5 5 175-8 I0 54 65 Z27.3 136.2 26 22.3 13.4 86 73-8 44-2 46 125.2 75-J 06 176.7 105.5 66 228.2 136.7 27 23.2 J 3-9 87 74.6 44-7 47 126.1 75-6 07 177-5 106.4 67 229.0 137-3 2& 24.0 14.4 83 75-5 45-2 48 126.9 76.1 08 178-4 106.9 68 229.9 i37-8| 29 24.9 14.9 89 76.3 45-3 49 127.8 76.6 09 179-3 107.4 69 230. 7 138.3 i 30 25.7 15.4 90 77-2 46.3 50 128.7 77-1 10 rSo.i 108. c 7o 231.6 138.8 31 26.6 15.9 9i 78.1 46.8 I5 1 129.5 77-6 211 181.0 108.5 271 232.4 I 39-3 3 2 27.4 16.5 92 78.9 47-3 52 130.4 78., 12 181.8 109.0 72 233-3 139.8 33 28.3 17.0 93 79.8 47.8 53 131.2 78.7 13 182.7 109.5 73 234-2 140.3 34 29.2 r7-5 94 80.6 48.3 54 132.1 79-8 *4 183.6 TIO.C 74 235-0 140.9 35 30.0 18.0 95 81.5 48.8 55 132.9 79-7 *i 184.4 i ic. j, 75 235-9 141.4 36 30-9 18.5 96 82.3 49-4 56 133.8 80.2 16 185.3 rn .c 76 236. 7 141.9 37 ]i.7 19.0 97 ?3-2 49-9 57 134-7 80.7 17 186. i rii. 6 77 237. 6 142.4 38 32.6 19.5 98 84.1 50.4 is *35-5 8!. 2 18 187.0 112. I 78 238-4 142.9 39 33-5 20. o 99 84.9 50.9 59 136.4 8l. 7 *9 187.8 112. ( 79 239.3 H3.4 40 34.3 20.6 100 85.8 51.4 60 137-2 82.3 20 188.7 n 3 .i 80 240.2 14.3.9 4 35-2 21. I 101 86.6 51.9 161 138.1 82.8 221 189.6 113.6 2bl 241.0 144.5 42 36.0 21.6 02 87.5 52.4 62 139-0 83.3 22 190.4 114.1 82 241.9- 145.0 43 36 9 22.1 03 88.3 52.8 *3 139.8 83.8 23 191.3 114.6 83 242.7 M-S-S 44 37-7 22.6 04 89.2 53-5 64 140.7 84.3 24 192. i fI5 2 8 4 243.6 146.0 I 45 58.6 23'.! 05 90. i 54.0 65 r 4i5 84.8 25 193.0 ri 5-: 85 ^44-5 146.5 46 39-5 2 3 .6 06 90.9 54-5 66 142.4 85.3 26 193.8 116.2 86 245-3 147 . o 47 40.3 24.2 7 91.8 55.0 67 143.2 85.9 27 194.7 116.7 8~ 246.2 147-5 48 41.2 24.7 08 92.6 55-5 68 144.1 86.4 28 195.6 117.2 88 H7^o 148. i 49 42.0 25.2 09 93-5 56.0 6'j 145.0 86.9 2 9 196.4 117.7 89 247.9 148.6 50 42.9 25.7 ro 94.4 56.6 70 145.8 87.4 30 197-3 118.2 90 248.7 149*1 Si 43-7 26.2 in 95-2 57-1 171 146.7 47.9 2 3 I 198.1 118.7 291 249 . 6 149.6 52 44.6 26.7 12 96.1 S7-6 72 T 47-5 88.4 32 199.0 119.2 92 250.5 150. t 53 45-5 27.2 13 96.9 58.1 73 148.4 88.9 33 199.9 1 1 9 . S 93 25 r -3 150.6 54 46.3 2 7 .8 14 97-8 58.6 74 149.2 $9.5 34 200.7 120.3 94 2s2. 2 151.1 55 47.2 28.3 15 98.6 59.1 7S 150. i 89.8 3S 201.6 120.8 95 253.0 151.7 56 48.0 28.8 16 99-5 59.6 76 151.0 90.5 36 202.4 121. 7 96 253.9 152.2 57 48.9 29.3 17 100.4 60. i 77 151.8 91.0 37 203.3 121. 8 97 254.7 152.7! 5 49-7 29.8 18 IOI.2 60.7 78 152.7 91-5 38 204.1 122-4 98 255.6 'S3- 2 59 50.6 30.3 19 102. 1 61.2 79 153-5 92.0 39 205 .0 i2a.t, 99 256.5 !53'7 60 5*5 30.8 20 102-9 61.7 80 154.4 92- s 40 205.9 123.4 300 257.3 154.2 Dift Dep. Lat, Dift Dep. Lat. Dift Dep. Lat. Dift Dep. Lat. Dif Dep. Lat. b b 2 for 5 'Points. TABT.E I. Difference, of Latitude and Departure for 3 Points, Dif t Lat . Dep. iDift Lat. Dep. i Dif> Lat. Dep. 'Dift Lat. Dep. |Difi Lat. Dep. i oo. i t 00.6 i 61 sO.7 33-9 121 100.6 67.2 iSi 150.5 100. 5 241 200.4 133.9 2 01.' 01. I 62 51.6 34-4 22 101 .4 67-8 82 151.3 IOI. I 4 2 201.2 '34-4 3 02. 01.7 63 52.4 15.0 23 102.3 68.3 8} I 52. 1 101.7 43 Z02.0 4 3'- 02.2 64 53-2 35-6 2 4 103. 1 68.9 84 153.0 1O2. 2 44 202.9 135-5 ! 5 04. . 02.8 65 .54.0136.1 25 103.9 69.4 85 153.8 102. b' 4S 203.7 6 05. c 03.3 66 54-9 36.7 26 1 04 ..8 70.0 S6 154.7 103.3 46 204.5 136.7 i 7 os.-' 63 9 67 55-7 37-2 27 105.6 70.5 87 155.5 103.9 47 205.3 '37.2 8 06.: 04.4 68 56.5 37-8 28 106.4 71.1 88 156.3 104.4 48 206.2 9 j 07 . ? 05 .0 69 $7-4 38-3 29 107.3 71-7 89 157.1 105.0 49 2O7.0 138.3 i JO o*.3 05.6 70 58.2 3^-9 108.1 72.2 90 158.0 105.5 207.9 138.9 1 1 09.1 06. i 71 59.0 39,4 131 108.9 72.8 191 158.8 106.1 251 208.7 f 39-4 12 ro.c 06.7 72 595 40.0 .32 109.8 73.3 92 159.6 106.7 209.5 140.0 13 j 10.8 07.2 73 60 7 40.6 3,3 110.6 73-9 93 1*0.5 roy. 2 53 210-4 140. 5 ! 1 4 f 1 1 . f> 07.* 74 61.5 41.1 34 111.4 74-4 94 161.31x07.8 54 211. 2 141.1 I s 12. s oi.3 75 6z. 4141.7 35 1J2.2 75-0 162. i 1 108. 3 212.0 141.7 j [ 1 6(11.3 o*.9 76 63,?. '42.2 II3.I 75-5 96 163.0! 108.9 S6 212 9 142.2 i 7 14.; 09.4 77 64.0 42.8 37 113.0 97 163.8! 109.4 57 zi3. 7 142.8 i ' I>.0 ro.o 78 64.0 ! 43. 3 Jfc II4.7 76-7 98 164.6 r 10.6 58 214.5 *43. 3 i ! 9 15.8 10.6 79 65.7J43-9 39 115.6 77.? 99 165.5 110.5 S9 215.4 M3-9 4O 16.6 n. i 80 66.5J44-4 40 Il6.4 77-8 200 166.3 in. i 60 216.2 144-4 2T I7c 11.7 81 67-3 45.0 141 II7.2 78.3 201 167. i 111.7 261 217.0 145.0 22 18.3 12.2 82 68.2 45.6 118.1 78.9 O2 168.0 112. 2 62 217.8 Z 3 19.1 12.8 83 69.0 46.1 43 118.9 79-4 o? 168.8 112. 8 63 218.7 146. > 24 20.0 13.3 84 69.8 46.7 44 119.7 80.0 04 169.6 U3.3 64 219.5 146.7 25 20. 8 13.'.) 8s' 70.7 47- 120. b 80.5 05 170.5 1*3-9 65 220.3 147.* z6 Zl .') 14.4 86 71.5 47-8 46 121.4 81.1 06 I7I.3 114.4 66 221.2 147.8 27 22.4 15.0 87 72.:; 48.3 47 122.2 81.7 07 172.1 115.0 67 222-0 M8.3 28 88 73-2 48.9 C23 . I 82.2 08 172.9 1 1 . 5 68 222.8 148.9 29 24.1 16.1 So 74. c 49-4 40 123.9 82.8 09 17.3.8 116.1 69 223.7 149.4 30 24. Q 16.7 90 74.8 50.0 5 124.7 83-3 10 174.6 116.7 70 224.5 150.0 31 25.8 17.2 91 75-7 50.6 t5i 125.6 ^3-9 II I I/5-4 117.2 1/1 225.3 150.5 32 26.6 17.8 92 76. s 51.1 s.2 126.4 84.4 12 176.3 117.8 72 226. 2 151.1 33 27.4 18.3 93 77.3 5*-7 ^ 127. a 85.0 13 Il8. 3 7.3 227.0 151.7 34 18.9 94 78.2 52.2 54 128.0 85-5 H 177.9 118.9 74 227.8 152.2 S ' 29. I 19.4 95 79. 0152. 8j 5? 128.9 86 i 15 178.8 119.4 7s" ^2"5.7 !s2.8 36:2 9 .o 20.0 96 56 129.7 86.7 16 '79 -6 120.0 76 229.5 1 5 ? 3 .>7 ! 3o.s; 20.6 97 80.7-. 53.9! 57 130. ; 87.2 17 180.4 120. <; 77 230.5 153- 9 38,31.6 21.1 98 81,5*5-4.4: 131.4 87.8 18 1*1.3 I 2 I . J 78 231.1 154-4 39 32.4 21.7 99 82.3 55 -o 59 132.2 88.3 '9 182.1 (21.7 79 232.0 155.0 40 22.2 ICO 83.1 5 5 . 6 6c 133.0 88.9 20 182.9 122.2 - o 232.8 55-5 4J H" * 22.8 101 84.0 56.1 li-i 133.9 89.4 i2I 1*3.8 122.8 281 233.6 156.1 42 34-9 23.3 02 84.8 56.7 62 134.7 90.0 22 184.6 II3.3 82 234-5 156.7 43 35-8 23.9 01 8s-. 6 s 7 .2 6} ni'S 90. c; 2 1 185.4 12 ^ . Q 83 235-3 157.2 44 36.6 24.4 04 86. 5 57-8 64 136.4 91 . 1 24 186.* 124.4 84 236. i 157.8 45 >7 "4 25-0 Os 87.3 58.3 137-2 91.7 2v 187. i J25.O. 237.0 158.3 46 ;8.2 06 88-1 58.9 66 138.0 92.2 26 187.9 i2<;. 5 86 237. S 15?. 9 47 i6. I O? 89.0 59-4 67 138 9 92.8 27 ,88.7 126. i 87 238.6 rs" 9 .4 48 39-9 2/>, 7 48 89.8 60,0 6: 139-7 93-3 28 189.6 126. 7 88 239. 5 r6o.o 49 40.7 IT-.! 09 : 90. 6 60 6 69 '40.5 9-.' 9 29 190.4 127. au 8 9 240.3 r6o. c 50 4I-f n.% 10 9i.5J6i.i j 4*-3 94-4 30 191.2 127.8 90 2JfI. J r 6 1 , i V- 42.4 43-2 Wl ii i 9*-3 93.1 61.7 j i 7 i 143.0 95.0} 131 95. 5; 3:. I 9 S.I 192.9 128.3 128.9 92 242.0 242.8 161.7 162.2 ' 53 44-i *9-4 M 94-o 62. SJ; 73 1.43 .'8 frk\ 33 '93-7 129,411 93 243.6 162.8 54 44-9 30.0 14 94.8 63,3 74 144.7 96.7 34 194.6 130.0 94 2 44-5 163.3 55 56 45-7 46.6 30.6 16 (96.5 63-9 6 4-4i 7s 76 145.5 '4"6.3 97.2 35| T 95-4 36 196.2 130. 5 131.1 95 96 245-3 246.1 163.9 164.4 <;-r 47.4 j 1.7 /; 97- 3 f> 5 . c 77 147. 2 98.3 ; 57(197.1 131.7 97 246.9 rb^.o 58 48.2 32.2 18198.1 6 . x : 78 148.0 98.9 38 197-9 132 . 2 98 247 .8 J65.5 59 49. J 19 98.9 66.1 '9 r 4 8.8 99.4 39 198.7 132.8 99 248.6 166. i 60 49-9 33-3 20 99.8 66.7 : xc 140.7 100. c| 40 199.6 133-3 300 249.4 166. 7 'Dift' Dep. Lat. Dift |Dep M Lat. jX>ift Dep. Lat. [ Dift; Dep. Lat. Dift Dep. Lat, for 5 Points. TABLE I. Difference of Latitude and Departure for, 3 J Points', Dif Lat. 1 Dep. Dift Lat. ! Dep. Dift Lat. Dep. Dift Lat. Dep. Dif Lat. Dep. , oc.8 00.6 61 49.0 36.3 121 97.2 72.1 181 145.4 107. 6 241 193.6 143.6 j 2 01.6 01.2 62 49.8 36-9 22 98.0 72 . 7 82 146.2 108.4 42 194.4 144-2 3 02.4 01.8 6} 50.6 37-5 23 98.8 73-3 83 147.0 109.0 43 195.2 144.8 j A 03.2 02.4 64 51-4 58.1 24 99.6 73-9 84 147.8 109.6 44 196.0 H5-4 ! 5 04.0 03.0 6s 52.2 38.7 2; 100.4 74-5 *5 148,6 110.2 45 196. i '45-9 i 6 04.8 o,.6 66 53-o 39-3 26 IOI.2 75-J 8c> 149.4 no. 8 46 197. < ^S ' 7 05.6 04.2 67 53.8 39-9 27 IO2.0 75-7 7 150.2 in. 4 47 198.4 47-1 i 8 06.4 04.8 63 54 - 6 4-5 28 102.8 76.2! 88 1 51.0 112.0 48 199.2 'H7.7 | 9 07.2(05.4 69 5v4 41.1 29 103.6 76.8 89 151.8 112. 6 49 200. C 148.3 ' 1 10 o8.ojo6.o 70 56.2 41.7 3 104.4 77-4 90 152 .6 113.2 5 200. S 148.9 1 1 oS. 8 oo. 6 7i 57.0 42.3 [31 105.2 78.0 r 9 i 153-4 H3-* !*5I 2OI .(, J 49-5 ! 12 09.6 07. i 72 57.8 42.9 32 106.0 78. 6i| 92 154.2 114.4 S2 202.4 150.1 ; '3 jo. 4 07.7 73 58.6 43> < 3* 106.8 79-l 93 155.0 115.0 53 203.2 I 5Q-7 i 14! 11.2 08. s 7 Q7 77.0 57.8 C^ 126. I Q3 ? I "" 120. 3 222 . s i6> .0 s 3C.5 22.6 98 7*. 7 58.4 58 126.9 94-1 18 175.1 129.9! 78 223.3 165.6 ! ! 39 3*-3 23.2 99 79-5 59-0 59 127.7 94-7 J 9 175-9 r 3o.5j 79 224. J 166.2 : 40 32.1 23.8 IOO 80.3 59.6 60 128.5 95-3 20 176.7 131.1 So 224.9 166.8 1 4' 3*-9 24.4 ICJ ii.i 60.2 161 "9.3 95-9 42.1 1/7.5 131.6 281 223.7 107.4 42, 33 7 25.0 02 81.9 60.8 62 13^-1 96. < 22 T73.; 132-2! 82 226. (; f68.o 43 34-5 2 5 .6 93 82.7 61.4 6} 130.9 97-1 23 I79*i 132.8 83 227.3 168.6 1 44 35-3 26.2 04 83.5 62.0 64 T 3'-7 97-7 24 179.9 '33-41! 84 1Z*.1 r69.2 ! 45 36.1 26.8 05 84-3 62 -5| 65 132.5 98.3 2<; 180.7(134.0 85 228.9 169.8 j ; 46 3 6 -9 2 7.4, 06 85.1 *3.| 66 133-3 OS.Q 26 iSl.C 134.6 86 229.7 '70.4 i i 47 37-8 :8.o; 07 8 5 . 9 6 V7 67 134-1 99-5 27 ft.3 135-2 87 2?0.r 171.0 ' 4 38.6 28.6 G$ S6. 7 64. ^ 68 134-9 ICO. I 28 183.1 135-8 88 23 J -3 171.6 ; 49 39-4 29.2 9 87. s 64,9 69 '35-7 ^00.7 29 *8j-. 9 136.4 89 232.1 172.2 5 40.2 20.8 10 88.4 65-5) 70 136.5 101.3 3 iv: 4 . 7 137-0 90 -32.9 172.8 5 41.0 30.4 III 89.2 66.1 171 137-3 101.9 -V 185.5 137.6 191 ^33-7 r /3-3 j 52 41.8 3J-OJ 12 90.0 66.7! 72 138.2 102.5 3 a 186.3 138.2 92 134.5 '73.9 i 53 42.6 31-6 13 90.8 67-3 73 139.0 103.1 33 187.1 138.8 93 2 35-3 '74-5 54 43-4 32.2 H 91.6 67.9 74! T 39- 8 103.7 14 188.0 159-4 94 23.0. j '75-1 , 55 44.2 3*.i 5 9 2 .4 68.5 7S i r40.6|iO4.2 3S 188.8 140.0 95 ^36. c 17-7 ( 56 45- 33-4! 16 93.2 69.1 76 141.4 194,8 36 189.6 140.6 9* *37-7 r /6-3 ': 57 45.8 34 o 17 94.0 69.7 77 142.2,105.4 37 190.4 i4i.2|j 97 238.6 176.9 : $8 46.6 34-'6 rS 94.8 70.3 78 I43.o|io6.o 3* 191.2 141.8 98 2^9. < 177.5 : 59 47-4 3S- 19 95.6 70.9! 79 143.81106.6 19 192.0 142.4 99 240.: .78.1 ' 60 48.2 35 7 20 96.4 7*. 5 80 144.6 107.2 40 192.8 143.0 300 241 .c 178 7 | Difr Dep. Lat. Dift Dep. Lat. Dift Dep. j Lat. Dift 1 Dep. Lat. [Dlft Dep. Lat. lor 4, 1 Points! TABLE I. Difference of Latitude and Departure for 4 -*~ Point. Dift Lat. Dep. |pift| Lat. Dep. Dift Lat. Dep. Dift Lat. Dep. Diftl Lat. Dep. i i 00.8 00.6 61 47.1 38.7 121 93.5 70.8 81 !39*9 114.8 241 186.3 152.9 ': 2- 01.5 01.3 62 47-9 39-3 22 94-3 77-4 82 140.7 1*5-5 42 187.1 I 53- 5 3 02.3 01.9 63 48-7 40.0 23 95.1 7 S.o 83. 141.5 1 1 6 . i 43 187.8 154.2 4 03.1 o.5 64 49-5 40.6 24 95-9 78.7 84 142.2 116.7 44 188.6 154.8 5 03-9 03.2 6S 50.2 41.2 *5. 96.6 79-3 8S 143.0 117.4 4S 189.4 155-4 6 04.6 03.8 66 51.0 41.9 26 97-4 79-9 86 143.8 118,0 46 190.2 156. i 7 05.4 04.4, 67 Si. 8 4 2 -S 27 9 S.z 80.6 87 144.6 118.6 47 190.9 156.7 8 Ob. 2 os. i 68 .5*. 6 43-J 28 98.9] 81.2 88 145-3 U9-3 48 191.7 157.3 9 07.0 05.7 69 53-3 43.8 29 99-7 81.8! 89 146.1 119.9 49 192-5 158.0 ro 07.7 06.3 70 54.1 44 4 30 loo. 5 82.5 90 146.9 120.5 5o 193-3 158.6 ! II 08.5 07.0 7i 54-9 4S.o Hi 101 .2 Sj.i 191 147.6 121 .2 *5* 194.0 159.2 12 09-3 07.6 7^ 55-7 45-7 32 IO2.O 83-7 92 148.4 121. 8 52 194-8 159.9 13 ro.o OS.2 73 56.4 46.3 33 IO2.8 84.4 93 149.2 122.4 n 195.6 160. s -'4 10.8 03. 9 74 57-z 46.9 34 103.6 85.0 94 150.0 I23.I 54 196.3 161.1 r< n. 6 09. s 7< 58.0 47.6 3S 104.4 8S- 6 95 150-7 123.7 55 197.1 161.8 16 12.4 IO. I 76 S8. 7 48.2 36 10$. I 86.3 96 I5i'5 124.3 56 197.9 162.4 i" 13.1 10.8 77' "59-5 48.8 37 105.9 86.9 97 152-3 125.0 57 198.7 163,0 18 13.9 11.4, 7^ 60.3 49' S 38 106.7 87. s 9 153-1 125.6 58 199.4 163.7 19 14.7 12. I 79 6 1. 1 50. i 1 39 10;;. 4 88.2 99 1S3-8 J26.2 59 200.2 164.3 20 'V 12. 7 80 61.8 50.8 40 !CiJ,2 83.8 200 154-6 126.9 60 2OI.O 164.9 i 2I 16.2 15.3 ' 81 62.6 51.4 141 109.0 89.4 201 155-4 127.5 261 201.8 165.6 17.0 14,0 82 63.4 52. o 42 109.8 90. i 02 156.1 128.1 62 202.5 166.2 *3 17.8 14,6 83 64.2 52.6 43 110.5 90.7 03 156.9 izS.8 63 203.3 166.8 -4 18.6 5.3 84 64.9 53-3 44 111.3 91.4 04 M7-7 129.4 64 204. I 167.5 2=; L9-3 15.9 85 6S- 7 53*9 4S 112. 1 92.0 5 158*5 130. i 65 20 4 .8 168. i 16 20. I ttfS 86 66. S S4-6 46 II2-9 92 .6 06 159.2 130.7 66 205.6 168.7 2.7 20.9 17.1 7 67,3 SS-2 47 H3. 6 93-3 07 1 60.0 131-3 67 206.4 169.4 ! 28 21.6 17.8 88 68.0 55.8 48 114.4 93-9 08 160.8 132.0 68 2O7.2 170.0 i 29 22.4 18.4 89 68.8 S 6.-s 49 115.2 94-5 09 161.6 132.6 69 207.9 170.7 30 23.2 19.0 90 69.6 57-i 5 116.0 95.2 to 162.3 133-2 70 208.7 I7I-3 31 24.0 19.7 91 70.3 S7-7 151 116.7 9S.8 211 163.1 133-9 Z7i 209.5 171.9 i * 2 24.7 20. 2 2 71.1 58.4 S2 117.5 96.4 12 163.9 !34-5 72 210.3 172.6 33 25.5 2O.9 93 71.9 59 - 53 118.3 97-1 13 164-7 i35-i 73 211. 173-2 34 **V3 21.6 94 72.7 59-6 1 S4 119.0 97-7 14 165.4 135-8 74 211.8 173.8 35 27-1 22.2 9^ 73 4 60.3 S*" 119.8 98.3 '5 166.2 136.4 75 212.6 *74-5 56 27.8 22.8 96 74.2 60.9 S6 120.6 99.0 16 167.0 i37.o 76 213-4 175- 1 37 28.6 *3-5 97 75. 61.5 i <;7 121.4 99.6 17 167.7 137.7 77 214. I 175-7 | 3* 19-4 24.1 98 7S-8 62.1 58 122. I IOO.2 18 168.5 138-3 78 214.9 176.4 39 30.1 24.7 59 76. ; 62.8 S9 122.9 100.9 *9 169.3 135.9 79 215.7 177.0 : 1 4~ 30.9 25-4 roo 77-3 63.41! 60 123-7 IOI.5 20 170. i 139.6 80 216.4 177.6 4 1 3i-7 26.0 roi 7 8.l 64.1 161 124.5 IO2. I 221 170.8 140.2 281 217.2 178.3 ; 42. 3 - ' 26.6 02 78.8 64.7 62 125.2 101.8 22 171.6 140.8 82 218.0 178.9 ! 43133-2 27-3 03 79.6 65,31 63 I26.O 103.4 23 172.4 141.5 83 218.8 179.6 44 34- 27.9 04 80.4 66.0 j 64 126.8 104.0 24 173.2 142. i 4 219-5 180.2 i 45 34.8 28.5 05 81.2 66.6! 65 127-5 104.7 25 r 73-9 142.7 85 220.3 180.8 ; 46 3S-6 29.2 06 81.9 67.2 66 128.3 'OS'S 26 174-7 J 43-4 86 22 I. I 181.4 ' 4" 3*. 3 29.8 07 M 67.9 67 129. I 105.9 27 175-5 144.0 87 2*4.9 182.1 M 37-i 30.5 08 SJ-S 63. 5 6* 129.9 106.6 2* 176.2 144.6 88 22*1.6 182.7 I 49 37*> 3ii 09 84-3 69.1(1 69 13O.6 107.2 29 177.0 M5.3 89 223.4 183.3 i ^o 3^-7 3 r -7 10 85,0 69- 8 70 131.4 107 8 3 177.8 145-9 90 224.2 184,0 i <;i 39-4 32-4 II I 3 5 . S 70.4 171 132.2 108.5 231 178.6 146.5 291 224.9 184.6 i S- 40. a 33- 71.1 72 133-0 109. i 32 !79-3 147.2 Q2 225.7 185.2 1 53 41.0 33.6 13 87.4 7i-7 73 133-7 109.7 33 180.1 147.8 93 226.5 185.9 i <4 41.7 34- 3 J4J88.I 72-1 74 134-5 ifo.4 34 180.9 148.4 94 227.3 186.5 42.5 34-9 i ; 83.9 7V 7S 135.3 ui.o 35 181.7 149.1 95 228.0 187.1 1 56J43.3 35'5 16 89.7 73-6 76 136.0 iii. 7 36 182.4' 149.7 96 228.8 187.8 i f 57M4-I 36.2 17 90.4 74.2 77 136.8 112.3 37 183.2! 150.3 97 229.6 188.4 1 < 8 44.8 36.8 18 91.2 74-9 78 137.6 112.9 3 184.0] 151.0 98 230.4 189.0 59 4=;. 6 37-4 19 92.0 75-5 79 138,4 113.6 ! 39 184.7 151.6 99 231.1 189.6 60 46.-; 38.1 20 92.8 7 6. T 80 i39-i 114.2 ! 40 185.5 152.3 300 231.9 190.3 |bift Dep Lat. jDif Dep. Lat. Dif Pep. Lat. Dif Dep. Lat. Dift Dep. Lat. j for 4 \ Points. TABLE I. Difference of Latitude and Departure for 3 Points, Dift Lat. Dep. Dift Lat. Dep. ift Lat. Dep. Dift 1 Lat. i Dep. jJDift Lat. ! Cc p. j i 0.7 0.7 61 45.2 I.O 21 89.7 81.3 181 34.1 21.6: [41 178.6 i6i.X 2 01.5 1.3 62 45-9 1.6 22 90.4 81.9 82 34-9 22. 2 ! 42 79-3 ibz. <; I 2. 2 2.0 63 46.7 2-3 23 91.1 82.6 83 35.6 2 2 . V 1 4; r 80. i 163 .2 4 3.0 2.7 64 47.4 3-0 24 91.9 *3-3 84 36-3 23 .6J 44 180.8 163.9 5 3.7 3-4 65 48.2 3-7 25 92.6 83.9 85' 37-1 2 4- - i 45 181.5 164.5 6 4.4 4.0 66 48.9 4-3 26 93-4 84.6 80 37-8 24. 9 46 152.3 7 5.2 47 67 49-6 5-o 27 94.1 85.3 87 38.6 47 183.0 165. 9J< 8 05.9 5-4 68 50.4 .5-7 28 94.. 8 86.0 88 39-3 26. 31 48 183.8 9 06. 7 6.0 69 51.1 46.3 29 95.6 86.6 89 40.0 26.9 49 184.5 167.2 10 07.4 6.7 70 51.9 47.0 $0 96-3 87.3 90 40.7 27.6' 5 185.2 167.9 ii 08.2 07.4 71 52.6 47-7 }I 97-1 88.0 191 41.5 28.3! 151 186.0 168.6 12 08. 9 08. i 72 53-3 48.4 32 88.6! 92 4* -3 28 -9j 186.7 169.2 13 09-6 08.7 73 54.1 .9.0 33 98.5 89.3 93 43.0 29. 61 53 187.5 169.9! 14 10.4 09.4 74 54.8 .9.7 34 99-3 90.0 94 43-7 30-3 54 188.2 170.6 j 15 II. I 0. 1 75 55-6 50.4 35 IOO.O 90.7 95 44-5 188.9 171.2 16 II-9 10.7 76 56.3 51.0 36 100.8 9 r 3 96 45.2 31.6 56 189.7 171.9 17 12.6 11.4 77 5/.i 51 .7 37 101.5 92.0 97 46.0 3*3 57 190.4 172.6 18 13-3 12. I 78 S7.8 52.4 3* 102 . 3 92.7 98 46-7 33-0 58 191.2 73-3 19 I4.I 12.8 79 5^-5 53- 1 39 103 .-o 93.3', 99 47-4 33-6 59 191.9 20 14-8 13.4 Xo 59-3 53-7 40 103.7 94.0 -00 48.2 34-^ 60 192.6 174.6 21 I 5 .6 14.1 81 60.0 54-4 141 104.5 94-7 -01 4 3. 9 135.0 261 I 93-4] 75-3 22 I6. 3 14.8 82 60.8 55- ] 4- 105.2 95-4 02 49-7 35-7 62 194.1 " r 9 23 17-0 5 .^ 83 61.5 55-7 106.0 96.0 03 50.4 136.3 63 94-9 24 17-8 16.1 84 62.2 56 4 44 106.7 96.7 04 151.2 I3/.0 64 195.6 --. ? 2 5 18.5 16.8 85 63.0 57 * * 45 107.4 97-4 OS 51.9 r 37- 7 6s 196.4 7o.o 26 19-3 17-5 86 63.7 07 .8 46 108.1 98.0 06 IS2.6 I3S.3 66 197.1 78. 6J! 27 20.0 18.1 87 64. S *$>.< 47 108.9 9^.7 07 53-4 139.0 67 197.S 79*3J 28 zo.7 18.8 88 65.2 59.1 48 109.8 99-4 08 '54- 1 139.7 68 198.6 29 21.5 19.5 89 65.9 59.8 49 110.4 00. I 09 154.9 140.4 69 199.3 iSo.f; 30 22.2 20.1 90 66.7 60.4 5P III. I 00.7 10 155.6 141 .0 200. i 181.3 31 23.0 20.8 91 67.4 61. i 15* 111.9 01.4 2 1 15^.3 141.7 i-i 200. 8 IS2.0 j 32 23-7 21.5 92 68.2 61.8 12 112. 6 IO2. I 2 I57-I 142.4 7 2 201.5 182.7 j 33 24-4 22.2 93 68.9 62. 5 53 113.4 102.7 | 157.8 143.0 73 202.3 183.5 ! 34 25.2 22.8 94 69.6 63.1 54 114.1 [03.4 4 153.6 143-7 74 203.0 184.0 i 35 25.9 2 3-5 95 70.4 63. fc 55 114.8 104.1 1 159-3 144.4 75 203.8 184.7 1 36 26.7 24.2 96 71. i 64.5 56 115.6 104.8 6 1 60.0 '45 -i 76 204.5 185.4 37 27.4 24.8 97 71.9 65. i 57 116.3 105.4 - t6o.8 H5-7 205.2 186.0 ; 3 28.2 25-5 98 72.6 65.8 117.1 106. i j 161.5 146.4 78 206.0 186. -i 39 28.9 26.2 99 73-4 66.5 59 117.8 106.8 c 162.3 70 206.7 187. 4J 40 2 9 .6 26.9 IOO 74.1 67.2 60 118.6 107.4 o 163.0 H7-7 80 207.5 41 30.4 27. 101 74.8 67. i 161 119.3 108.1 221 163.8 148.4 281 208.2 188.7 42 43 31-9 28. 02 03 75-6 76.3 68. 69. 62 63 I2O.O 120.8 108.8 109.5 2. 164. 165. 149.8 82 83 208.9 209.7 185.4 I90.I 44 32.6 29. 04)77. 69. 64 121.5 IIO. I 24 166.0 150.4 84 210.4 190.7 45 33'3 3. 05 77.8 70. 65 122.3 110.8 2 166. 151.1 85 211 .2 I til. 4. 46 34'I 30. 06)78. 7 r - 66 123.0 111.5 2.f 167. 151.8 86 2H.y 192. I I 47 34-8 3 1 * 07 79- 7 1 - 67 123 ." 112. 2 ^ 1 68. 152.4 87 ?. ! 2 . 7 1^.7! 4'3 356 $ 2 ' 08 80.0 72. 68 124.5 I 12. 8 2 168. '53 - 1 8^ 213.4 49 363 3- 09 80. .' 3 6s 125.2 1 1 3 * 5 2 169. 89 214. 1 IQ4.I 50 37-o 33- 10 31. 73- 70 126. c 114.2 3 170.^ 154-5 90 214.9 104.8 1 5 37.8 34- 2 in 82. 74* 171 126. 114.8' 23 171. 155.1 191 zj 5 .6 I'.;;. 4! 5 2 38. j, 34-9 12 83. 75- 72 127-4 115. 5 i| 3 171. 155-8 196.1 5 39.3 3-5 <> \1 83. 75. 73 128 1 16. z t ^ 172. 156.,- 93 217*1 196.8 ji 54 40.0 36.3 14 84.5 76. 74 128. U6-9 3 '73- 157.1 94 -17.8 197-4! 5 40.8 36. 9 it; ^5.2 77- 75 129. "7. Si 3 174. 157.8 95 218.6 198. 1 i 5' 4I-. 37.6 16 86.0 77- 76 130. 1 3 174. 158.5 96 210.3 198.8 ! 57 42. 38.3 17 86.7 78:. 77 131. 118.9 I 3- 159.2 97 220. i '99-5 j 58 43-0 39-o iH 87.4 79- 78 131- 119.5 3 176. 159.8 98 220.9 200. I j 59 43- 39.6 irj 88.2 79- 79 132. 12O. 2 3 177. 160.5 2.: i. 5 ;oo. 8 ' 6c 44- 40-3 2C 88.9 80. Sc 133- 120.9 161.2 300 221.3 201.5 Dii t Dep -Lat. Dif t Dep -Lat Dii Dep Lat. |JDi Dep Lat. Difti Dep. i Lat. tor 4- ^ Points TABLE I. Dinerence of Latitude and Departure for 4 Points. Dift --T Lat. Dep. Dift i Lat. Dep 'Dift Lat. Dep. Dift Lat. Dep. JDiftj Lat. Dep. i 00.7 00.7 61 43.1 43i 121 85.6 85.6 181 128.0 128.0 241 170.4 170.4 2 01.4 01.4 62 45.8 43.8 ! 22 86.3 86.3 82 128.7 128.7 171.1 171.1 3 02. I 02.1 63 44-5 44v r 23 87.0 87.0 8} 129.4 129.4 43 171.8 171.8 4 02.8 02.8 45-3 45*3 24 87.7 87.7 84 130. i 130. i 44 J72.5 172.5 c 03.5103.5 6s 46.0 46.0 25 88.4 88.4 130.8 130.8 45 173.2 173-2 6 04.2 04.2 66 j.6 . 7 46.7 26 89.1 89.1 86 i3t-5 I S I . S 46 1/3-9 173-9 04.9 04.9 67 47-4 27 89.8 89.8 87 132.1 132.2 47 174.7 174-7 8 05.7 05.7 . 68 48. i 48.1 i 28 90.5 90.5 88 132.9 132.9 48 175-4 f 75-4 9 06.4 06.4 69 48.8 48.8 1 29 91.2 91.2 89 133.6 133-6 49 176.1 176.1 10(07.1 07.1 70 49 ' 49-5 3 91.9 91.9 90 134-4 134.4 50 176. b 176.8 i nl 07- 8 07.8 71 SO. 2 SO. 2 (31 92.0 92.6 191 135.1 135.1 251 r 775 177-5 12 08.5 08.5 72 50.9 50.9 93-3 93-3 92 I 35-8' 135.8 5* 178.2 178.2 13 09.2 09.2 73 51.6 51.6 33 94-o 94.0 93 136.5 136.5 53 i 7 S. 9 178.9 14 09.9 09.9 74 52.3 52-3 34 94.8 94.8 94 137.2 137.2 54 179.6 179-6 10.6 10.6 75 53.0 53.0 ,35 95-5 95 5 95 137*9 137.9 55 180- 3 180.3 16 ii*3 11.3 76 53-7 53-7 36 96.2 96.2 96 138.6 138.6 56 181.0 181.0 17 12.0 12.0 77 54-4 54-4 37 96.9 96.9 97 139.3 139-3 57 181.7 181.7 I? 12. 7 12.7 7S 55.2 55.2 38 97-6 97.6 95 140.0 140.0 5 '5 132.4 182.4 19 13.4 13 4 79 55-9 55.9 39 98.3 98. 3 99 140.7 140.7 59 183.1 183.1 20 14.1 So 56.6 56.6 40 99.0 99.0 200 141.4 141.4 60 183.8 .83.8 IS I4.S r 4 .8 8 1 57-3 57-3 141 99-7 99-7 201 142.1 142.1 261 184.6 184.6 '22 TS-6 IS- 6 82 S 8.eUS.o 100.4 100.4 02 142.8 142. b 62)185.3 185-3 23 16.3 16.3 8} 58.7 58.7 4-3 101. I IOI.1 03 H3.5 H3.5 63 186.0 186.0 24 17.0 17-0 84 59.4: 59,4 44 loi.S lOI.fc 04 144.2 144.2 64 186.7 186.7 r 77 8s 60.1 60. i 45 102.5 102.5 05 145.0 145.0 65 187.4 187.4 26 18.4 86 60.8 60.8 46 103.2 103.2 06 i45'7 H5.7 66 188.1 i83.i 27 19. i 19- 1 6l. S 61.5 47 103.9 103.9 c? 146.4 146-4 67 188.8 188.8 28 19.8 19.8 88 62.2 6j.2 48 104-7 104.7 08 147-1 147.1 68 189-5 189.5 29 20.5 20.5 80 62.9 62.9 105.4 105.4 09 H7.8 147.8 69 190.2 190.2 70 2.1 .2 21.2 90 63.6 63.6 5 106.1 106.1 10 148 . s 148.5 70 190.9 190.9 3 1 21.9 21.9 91 64.3 64.3 151 106.8 106.8 211 149 . : 149.2 171 191.6 191 .6 22.6 22.6 92 65 I 6s. i 107.5 107.5 12 H9-9 149.9 72 192.3 192-3 33 23-3 -3'3 93 65.8 6s. 8 5? IOS.2 108.2 !3 150.6 150.61-73 193.0 I93.o| 34 24.0 24.0 94 66. s 66. s 108.9 108.9 14 151.3 151.3 74 r 93-7 193.7) 1 35 2 4-7 24.7 9S 67.2 67.2 55 109. 6 109.6 IS 152.0 152.0 75 94-5 194.5 i 15.5 96 67.9 67.9 56 110.3 110.3 16 152.7 152.7 76 195.2 195.2 [ _ 26.?, 26.2 97 6S.6 63.6 57 III .0 III.O 17 153.4 153.4 7 195.9 195.9 1 IS 26.9 26.9 92 69-3 6 9-3 58 111.7 in. 7 18 154.1 154.1 78 196.6 196. 6 ' 39 27.6 27-6 99 70.0 70.0 59 112.4 112.4 19 154.9 154*9 79 197.3 197.3 40 28.3 roo 70.7 70.7 60 113. T 113-1 20 155-6 155.6 80 198.0 198.0: 4 1 29.0 29.0 101 71.4 71.4 161 113.8 113-8 221 i5 -3 156.3 281 198.7 198.7 42 29.7 29.7 02 72 .-i 72.1 62 II4.6 114.6 22 157.0 157.0 82 199.4 199.4 43 30, 4 31.1. 3-4 31.1 03 04 72.8 73-5 72.8 73-5 63 64 H5'3 116.0 115-3 1 1 6 . o 23 2 4 157.7 158.4 157.7 158.4 84 200. i 200.8 200. I 200. S ^ 4' 31.8 31.8 74-2 74.2 116.7 116.7 -25 159.1 159.1 8s 201.5 201-5 46 32. 5 32.5 06 75.0 75. c 66 117.4 117.4 26 159.8 I59-* 86 202.2 202. 2 47 33.2 33.2 07 75.7 75-7 67 118.1 ii8.il 27 160.5 160.5 8? 2O2.9 202.9 > 33-9 33.9 08 76.4 76.4 68 118.8 118.8 2$ 161.2 161 .2 88 2O3.6 203.6 49 34.6 35-4 34-6 35-4 09 10 77.1 77. ^ 7 7 ; 69 70 119.5 120.2 119.5 120.2! 30 161.9 162.6 161.9 162.6 89 90 204 4 205.1 204.4J 205.1 i CI 36. i in /TT? o T?r T2O.9 120.9 2^1 163-3 163.3 291 205. S 205.8 ! 5 2 36.8 12 79.2 79.2 72 121. 6 121.6 32 164.0 164.0 92 206. 5 206.5 375 37-5 13 79-9 79-9 73 122.3 122.3! 33 164.8 164.8 93 207.2 207.2 ! 54 38.2 38.2 14 80.6 80.6 74 123.0 123.0 34 165-5 165.5 94 207.9 207.9 ! 55 }8-9 38.9 1 S Si. 3 81.3 75 "3-7 123.7 35 166.2 166.2 95 208.6 2O. 40.3 39-6 4. 3 16 82.0 17 ^2.7 32.0 82.7 76 ^ -, 124-5 124.5 125-2 36 37 166.9 167.6 166.9 167.6 i 9^ 209.3 2IO.O 209.3 2IO.O ! 58 41.0 41.0 18 83.483-4 7^ 125.9 125.9 38 168.3 168.3 95 21O-7 210.7 I 59 4i-7 19 84.1 84.1 79 126.6 126.6 39 169.0 169.0 99 211.4 2II.4 60 42.4 42.4 20 84.9 84.9 80 127-3 127.3 40 169.7 169.7 ;3 212. I 212 . 1 Dift Dep. Lat. 1 Diit Dep. Lat. Dift; Dep. Lat. Dift Dep. Lat. 'Dift Dep. Lat. for 4 Points. TAKLE II. Difference of Latitude and Departure for 1 Decree. Difl Lat. Dep. Dif i Lat. Dep. Diftl Lat. -Dt-p. ;'Dia ! Lat. Dep. ; Dift| Lat. Dep. OI .O OO.O 61 61 .0 OI . in 121.0 o:.i iai] iSi.o| 03. 2 ^41 ^41 .c 04.2 | 02. < 5 00.0 62 62.0 or . 22 122.0'Oi. I Si i 182. o| 03.2 42! 242.0 04. z 03. < > oo. j 63 63.0 01 . 23 123.0 02 . I ' s 1183.0 03.2: 43:243.0 04.2 04. c ) CO. I 64 64.0 01 . 24 1:4.0 o:.2 184.0 OJ.i] 44! 244 04.3 05. c ) 00. I 65.0 01 . 2.5 J2C.C-- 01.2 . 1X5.0; 03. a. 4; 24;. o| 04 3 o:').c ) 03. I 66 C6.o 01 2 26 126 .0 Oi.2 ,' 86 ! i86 o 03.2 ,6 246.0 04.3 0".C 00. I 67 67.0 01 .1 27 ^27 0(02.2 i i 8 - j 1 8 7 . r 03 . ? ; 47 24" .c 04.3 oS.c OO. I 68 68.0 OI .2 28 128 .O Q2 . 2 1 88|,88.c 03.3 ' 4^; 2." r s.o 09 c CO. 2 69 69.0 01.2 2 9 129.0 02.2 ! *' 9 . O 03.3,; 49 249.0 04.3 10 ro.c 00.2 70 70.0 OI . 2 ;o 130.0 02.3 '; ^ r f ;:o.O 03.3 ;o 250,0] 04.4 j , I J .0 00.2 7i 71 o 01.2 1 31 1 U.O 02.3 I9J 191.0 03.3 .'.51 251.0 04.4 12. C OO.2 72 72.0 01.3 .32 I32.C 02.3 192 .0 03-4 5* J 5*.<3 4 4 I3.C 00.2 73 73'0 ; or. 3 ! 33.o 02.3 193.0 3-4 53 253-oj 04.4 ! 4 14.0 30.2 74 74.0 01.3 3^5 '34-o 02. 3| ; 9, '94- 03. 4 i 54]^54*o 04.4 15- c CO. 3 75 75-0 i-3 5 ^ '35-0 02.3:1 9^ 195.0 3-4j 55i 2 55-o 04.5 \ r6.o oo. 3 76 76.0 01.3 36 136.O 02 .4 of. 196.0 03.4; 56 2 -,6.0 04.5 j .7.0 00.3 -7.0 01.3 37 37-0 02.4 9 7 197.0 oj-4 2 5 7 o 04-1 j 15. C 00.3 78 78.0101.4 5 V '3^.0 02.4 98 198.0 03.5 58 2>8.0 04.5 19.0 00.3 7') 79.0 1.4 >0 139.0 02.4 99 199.0 03 - 5 59 2 ; 9 . o 04.5 .0 20.0 00.3 80.0 J i. 4 40 .40.0 200 '00.0 03-5 6c 260.0; 04.5 21 21 .0 00.4 81 fc i .o!oi .4 141 41.0 3 2 . ; 201 201 .0 03-5 261 261.0 04. d i 22 22.0 -0.4 82 82.0 01.4 142.0 02 .5 C2 1C2.0 03.5 62 .".6 i.o 04.6 23 23.0 ,00.4 83 83.0 43 '43 - 02. 5 0.3 203.O 03. 5 63 .'63.0! 04.6 24 24.0 (00.4 84 S 4 .o >i. 5 44 144.0 02.5 04 ^04.0 05-6 64 264.0 04.6! I 2 5 2 s.O 00.4 *5 8<.o 01.5 4? 145.0 02.5 05 .'OC.O 03.6 6 5 265.0 04.6 26 26.0 00.5 86 46 146.0 02.5 06 106.0 03.6 66 266.0 04.6 27 27.0 co. 5 87 87*0101.5 47 T 47o .2.6 07 207.0 03.6 67 267.0 04-7 28 28.0 00.5 88 8.0 oi.< 48 148 o 02.6 08 108.0 03.6 08 268.0 4-7 29 -9.0 00.5 8q 89 o oi . 6 49 149.0 02.6 09 209.0 03.6 69 269.0 4-7 i 0.0 00.5 i.O co.c 01.6 5O ! N .O .-> , 1C 2'O.O 03-7 70 270,0 4*7 , 3I 1.0 00.5 qj tyl .0 01.6 ffl 1 _> 1 . 02.6! 2 ii, iij.o 03.7 271 271.0 04.7 ! 32 2.O 00.6 92 92.0 01.6 1 ^2.0 02. 7 i! 2 M2.0] 03.7 72 272.0 04 7 33 3-o 00.6 95 93.0 oi .6 531 '53-0 C2. 7 i 3 213.0 03.7 7 ; 273.0 04.8 34 4.0 oo. 6 04 94.0 bi.fi 54 r 54.0 C2 7 214.0 23.7! 74 274.0 04.8 5.0 .0.6 95 95.0 01.7 55: 155.0 '--- '5 215.0 03 -8 275-0 04.8 36 6.0 00.6 96 96.0 oi. 7 5 ft i c 6 . o ' o . v 216.0 03.^ 76; 276.0 04.8 ! 37 7.0 00.6 97 97.0 01.7 S7 [ ; 7 c o.: . 7 17 217.0 03.8 77 277.0 04.8 S.o oo. 7 98 98.0 31 -7 5Sj 158.0 02.8; 18 218 o 03-S 7i| 278.0 04.9 39 9.0 00.7 09.0 DI . 7 59 i59.o!oi.S|l 19 210.0 03. 1 79 ' 279.0 04 9 40 0.0 00.7 100 00 . O Dr. 7 60 j i6o.Ojo:.Rj 20 120.0 03.8 Sc 280.0 04.9 1 4 1 I .0 co. 7 101 iOI .O D1.8 16 1 i 6 i.o I 02.8'' -21 221 li Q O3.9jl2 > >l 231. O 04.9 I 42 2.0. 00.71 02 102.0 3f. 62 162.0 02.81; 22 222.0 05 . 9 Ij 82! 282 .0 04.9 : 43 3 . o oo. 8j 03 '03.0 01.8 63 163.0 r-2.3. 2? 223.0 o j . Q T S ; : 2 ? ,' . o 04.9 i 44 4 . o 00.8 04 TOf.o bi.S 64)164.0 2.9 224.0 03.9 ji ^4: 2,84 o 05.0 45 5.0 00.8 05 ! o ; . o o i . S 6 ; 1 1 6 5 . o 02 .0 -5 225.0' 03.9! b^i 1,^5 .0 05.0 ! 46 46.0 00.8 c6 o6.O'Oi.S ; f-6 '66.0 02. 1 .0 if 115,0.02.0 75i i/5-o o* . o | : - 23; .01 o.-} . ' <.;< 195.C 05.1 56 > 6 , o 01 16 1 16.0 02. cj 76 76.0 03. i , 36; -3< 1 -o 04. i 96*296.0 05.2 s" ' ^7.0 01 17 u 7,0 02.0 77 7-.0 o^.X , '.7! * 37-o 04. j 07 297.0 O'.i 58.0 01 .0 18 ;S .0 02. i 7? i -S.o 03.1 i -S.o 04.2 9 S | : 9 S . O ; 05.?. ! 59 59.0 .1.0 19 19.0 02. i 79 17 / c 03.1 ^9 259.0 04.2 99 209.0! 0> .2 ; o.o or . i 20 2O.O'02. I ^o i:-o.o o;.i 4 2-iC.O 04-2 3 - 300-0: 05.2 Dili Dep. L:-.t. ! l)ilV Drp. Lat, .Dill! Dep. i Lat. Dift Dop. Lit. !)( Dep. ' Lnt. i c: c for Sy Decrees. TABLE II. Difference of Latitude and Departure for 2 Degree?" Dift Lat. Dcp.'l Dift' Lat. Dep.!?it Lat. Dep. Dift Lat. Dep. Dift Lat. Dep. ! 01 .0 DC . 1 01 61.0 . "* 20. 9 34.2 rSi 80.9 06.3 4* 240.9 05.4 2 o^.o 03.1 62 62.0 . 22 21.9 34-3 82 81 9 06 .4 42 241.9 08.4 3 03.0 JO. I 6 >. 63 .0 .z! *3 22.9 M-3 8; H2. q 06.4 43 242.9 08.5 4 04.0 00. I 64 64.0 23.9 4-3 84 83.9 06.4 44 243.9 08.5 , o; .0 OO. 2 i 65 6s- o M i -- 24.9 4.4 85 84.9 06. 5 45 244.9 08.6 6 06.0 OO.2I 66 66.0 f,3 20 25.9 04-4 86 85.9 06.; 46 1-5-9 08.6 - 07.0 00. 2 : 6 7 67.0 2-3 -7 26.9 04.4 8? 86.9 06.5 47 |6.8 08.6 8 08.0 00.31 68 68.0 2.4 28 27.9 04-^ 88 87:9 06.6 4 b 47*8 08.7 9 09.0 00.3 69 69.0 2-4 2 9 28.9 04.5 89 88.9 06.6 49 48.8 08.7 10 10. 00.3 70 70.0 ^2.4 3 29.9 04.5 90 89.9 06.6 5 49.8 08.7 i j 11 .0 00.4 7* 71.0 2.5 131 30.9 04.6 IQI 90.9 06.7 .51 50.8 08.8! 12 12.0 00.4 7* 72.0 02.5 3 3i-9 04. 6 92 91.9 06.7 52 Si.g 08.8 ; 11* i;.o oo. 5 73 73-o 2.5 3^ 3^-9 04.6 93 92.9 06. 7 53 SS .8 08. 8 ! 14 14.0 oo. 5 74 74.0 02.6 34 33-9 04.7 94 93-9 06. J? 54 53.3 08.9! I c 15. p 00. S 75 75 .0 02.6 35 34-9 04.7 9< 194.9 06.^ 55 54.8 08.9 1 6 16.0 OO.b 76 76.0 02.7 3<> 35-9 04.8 96 195.9 06.8 56 55-8 08.9 i 17 17.0 00.6 77 77.0 02.7 37 36-9 04.8 97 96.9 06 . <; S7 S 6.8 09.0 iS 18.0 00.6 78 78.0 02.7 3^ 37-9 *.8 98 197.9 06. c 5 57-8 09.0 ' J 9 19-0 00.7 7P 79.0 02.8 39 38.9 04. c. 99 198.9 06. c 59 58.8 09.0 20 iO.O 00.7 b'o 80.0 02.8 40 39-9 04.9 200 199.9 07. c 60 59.8 09. i 21 21. O 00.7 ft! ( 1.0 02. & 141 40.9 04.9 2O I 200.9 07.0 261 60.8 09. i 22 ZZ .0 co. 8 82 8z.o 02.9 42 41.9 o;.o 02 201.9 07. c 62 6i.g 09. i : 23 23.0 oo.S 8 3 8*.9 02.9 43 42.9 o^.c 03 202.9 07.] 63 62.8 09.2 i 24 24.0 bo.S 8* 83.9 02.9 44 43-9 05.0 4 103.9 07.1 64 63.8 09.2 ' 25 25.0 00.9 85 84.9 03.0 45 144.9 05.1 05 204.9 07.2 65 64.8 09.2 ! 26 26.0 00.9 .86 85--) 03.0 4& 145.9 05.1 06 205.9 07.2 66 65.8 09.3 ! 7 27.0 00.9 87 86.9 03.0 47 146.9 05.1. 07 206.9 07.2 67 66.8 09.3 j 28 28.0 01 .0 88 87.9 03.1 4- H7-9 05.2 08 207.9 07.5 68 67. S 09.4 a 9 29.0 01 .p 89 88.9 03.1 49 148.9 05.2 09 208.9 07-3 69 -68.8 09.4 30 30.0 01. 90 89.9 03.1 50 149.9 05.2 rc 209.9 07.3 7o .69.8 09.4 3 31.0 01. I 9i 90.9 03.2 '5 1 150 9 05-3 211 210.9 07.4 :-7i .70.8 09.5 1 32 32.0 01. I 92 91.9 03.2 5 2 151.9 05-3 J2 211 .9 7-4 72 271.8 09.5 j 33 33.0 01.2 93 92.9 03.2 53 152.9 05-3 ; 13 a-12-9 07. /i 73 272.8 09.5 34 34 o 01.2 94 93-9 03.3 54 I 53-9 05.. 14 213-9 07. 7* 273.8 09.5 35 55*o or. 2 9 s ; 94.9 03-3 55 154.9 05.4 15 214.9 07. 75 274-^109.6 i *6 36.0 01.3 9 6 S-9 03.4 5< 155-9 o.S-4 1 16 215.9 07. 76 275-* 09.6 37 3.7.0(01.3 97 96.9 03.4 57 136.9 os*. 17 216.9 07. 77 276.8 09.7 i ^ ;8,o 01.3 98 97-9 03-4 5^ 157.9 05. li 217.9 07. : 7^ 277-8 09.7 i 39 39- 01.4 99 98.9 03.58 f 158.9 05. 19 218.9 07. 7 ( 278.8 09.7 | 40 ..0.0 01.4 too 99.9 3 . 5 :,_6_p 159-j 05.6 20 219.9 07. : 80 279.8 09.8 j 4 ' 41.0 01.4 101 100. 9 03-5 16 160. 9 05. 22 22O.9 07. !2b zSo.8 09.8 i 4- 42 .0 o*; 5 02 101 .9 03.6 62 161.9 05- 22 221 .9 07. 8. 281.8 9 .8 43 43.0 CI . < 03 JI02-9 03.6 1 6^ 162. 9 05.7 i 2' 222-9 07- : H 282.8 09.9 | 14-0 oi.. 5 041103.9 03.6 64 163.9 05.7 : 2 4 223-9 07. i ^4 283.8 09.9 | 45 45.0 O I . 6 05 104.9 .V7 5 164.9 05.8 i 2 224.9 07. ! 8 284.8 09.9 46 46.0 oi .6 06 105.9 -'3 7 6 165.9 3 .8 2 225.9 07. ! 8 28.;. 8 JO.O 47 47 -c 01.6 07 106-. 9 03.7 6 166.9 05.8 ; 2 226.9 07. i 8 286.8 10. O 48 48.0 QJ . 7 081107.9 03.8 6 167.9 05.9 2 227.9 08. 1 3 287.8 10. I 49 49*5 01.7 O9'io3.9 03.8 6 168.9 05.9 ^ 228.9 08. i 8 268,8 10. I co ! ;o,o 01.7 10 ICQ . 9 03.8 7 169.9 05-9 i 3C 229.9 68. i 9 289.8 10. I 5* 51.0 oi. X ,.-i 110,9 03.9 17 170.9 06.0 *JJ 230.9 08. ! 2 9 2,90.8 10.2 M -.2.0 or. 8 12111.9 03.9 7 171.9 O6.0 i 32 231.9 c8. 9 291.8 ro.2 53 S3-Q 01.8 13 riz. 9 03-9 7 172.0 06.0 33 232.9 08. 9 291.8 1O.2 ! <4 '54 o or. 9 J-'J. "3-9 04.0 7< 173.9 06. I , 34 2 33-9 08. 9 293.8 10.3 5^ ; o . o or .9 02. o i 15 "4-9 16 115.9 04.0 04.0 7 7 174-9 175-9 06. I 06. I -34-9 J-35-9 o . : 08.. i 9 i 9 294.8 295.? 10-3 10-3 ^7 ! C7.o 02 .c 17 ri6,9 04. j 7 176.9 06.2 37;23f>-9 oS. < ! 9 296.8 10.4 j c3 s*. o 02.0 i i8 117.9 04.1 7 177.9 O6.2 38 ^37-9 c-. ] 9 297.8 10.4 59) 59. ctoz.i 19 115.9 04.2 19 178.9 06.2 39 23^-9 08. (, 298.8 10.41 60 5o.o 02. i 1C 119.9 04.2 8 179.9 06.3 4 C > 239-9 08.. - 30 299.$ > 10-4 JDiftlDep. Lat. Dift Dep. Lat. ;;D; Dep. Lat. Dli t J)ep. Lat. D Dep. Lat. for SB Degrees. TABLE II. Difference, of Latitude and Departure for 3 Degrees, Dift Lat. 1 Dep. [ Dift Lat. Dep. Dif Lat. Dep. jJDif Lat. Dep. Dift Lat. Dep. ijoi.o co.i jj 61 60.9 03.2 121 120.8 06.3 181 180.7 09.5 241 240.7 12.6 2 Oi.O 00. I 02 br .9 03.2 22 121. 8 06.4 82 181.7 09.5 42 241. 12.7 3 03.0 00.2 63 62.0 3-3 23 122.8 06.4 87 182.7 c 9 .6 43 242. 12.7 4 04.0 00.2 6 4 63-9 03-3 2 4 123.8 06. 5 84 183-7 09.6 44 243. 12.8 5 05.0 00.3 65 64.9 ov 4 *5 124.8 06.5 85 184.7 09.7 45 244. 12.8 6 06.0 00.3 66 65.9 03-5 26 125.8 06.6 86 189.7 09.7 46 245. 12.9 7 07,0 00.4 67 66.9 OVS 27 126.8 06.6 87 186.7 c 9 .8 47 246. 12.9 S 08.0 OO.4 68 67.9 03.6 28 127.8 06.7 88 187.7 09.8 48 247. 13.0 9 09.0 co.s 69 68.9 03.6 29 128.8 06.8 89 188.7 09.9 49 248. 13.0 10 IO.O 00.5 70 69.9 03 7 30 129.8 06.8 90 189.7 09.9 5o i.49- 13.1 ii II. 00.6 7 1 70.9 03.7 131 130.8 06.9 191 190.7 IO.O MI 2 SO. 7 13.1 12 12.0 00.6 7^ 71.9 03.8 32 131.8 06.9 92 191.7 IO.O 52 251.7 13-2 13 I'S.O 00.7 73 72.9 03.8 33 132.8 07.0 93 192-7 IO. 1 53 252.7 13.2 H 14.0 00.7 74 73-9 03.9 34 133.8 07.0 94 J93-7 10.2 54 253-7 '3*3 is I5.O 00.8 7S 74-9 03.9 35 134.* 7 .! 95 194.7 10.2 55 254-7 '3-3 16 r6.o 00.8 ?6 75-9 04.0 36 135.8 07.1 96 195.7 10. 3 5 6 255.6 13.4 i? 17.0 00.9 77 76.9 04.0 37 136.8 O 7 t 2 97 196.7 10.3 57 256.6 13-5 18 18.0 00.9 78 77-9 04.1 38 137.8 07.2 98 197.7 10.4 58 357.6 13-5 19 19.0 01. 79 78.9 04.1 39 138.8 07.3 99 198-7 10.4 59 258.6 13.6 20 20. o 01. O 80 79-9 04.2 40 139.8 07.3 -00 199.7 10.5 60 259.6 13.6 zr 21.0 01. 1 Si 80.9 04.2 141 140.8 07.4 2OI 200.7 10.5 261 260.6 13-7 22 22 OI . I 82 81.9 04.3 42 141.8 07.4 02 201.7 10.6 62 261.6 13.7 23 23.0 01.2 83 82.9 04.3 43 142.8 07.5 03 202.7 10.6 63 262.6 13-8 2 4 24.0 01.3 84 83.9 04,4 44 143.8 0-7.5 04 203.7 10.7 64 263.6 13.8 2S 25.0 01.3 8s 8 4 . q 04.4 45 144.8 o 7 .6 05 204.7 10.7 6f 264.6 13.9 26 26. c or. 4 86 SS.Q 04.5 46 145.8 07.6 06 205.7 10.8 65 265.6 13.9 27 27-0 01.4 87 86.0 04.6 47 146.8 07.7 07 206.7 10.8 67 266.6 14 o 28 28.0 01.5 88 87.9 04. 6 48 147.8 07.7 08 207.7 10.9 68 267.6 14.0 20 29.0 01.5 89 88.9 04.7 49 148.8 07.8 09 2c8.7 10.9 69 268.6 14.1 30 30.0 01.6 90 89.9 04.7 5 149.8 07.9 TO 209.7 1 1.0 70 269.6 14.1 31 31.0 01.6 9i 90.9 04.8 151 150.8 07.9 211 210.7 ii .0 27* 270.6 14.2 32 32-0 01.7 92 91.9 04.8 52 151.8 08.0 12 2II.7 ii. i 72 271.6 14.2 33 33-o 01,7 93 92.9 04.9 53 K2.8 08.0 13 212.7 ii. i 73 272.6 14-3 34 34-0 01.8 94 93-9 04.9 54 153.8 .8. i 4 213-7 i r. 2 74 273.6 '4-3 35 55-0, 01.8 95 94-9 05.0 ss 154.8 08.1 is 214. 7 11.3 75 274.6 14.4 36 6.o 01.9 96 95-9 o^.o -'6 iSS-8 08.2 16 219.7 it. -3 76 275.6 14-4 37 36. 9 01.9 97 q6. 9 05.1 S7 156.8 08.2 T 7 216.7 11.4 77 276.0 '4-5 3 J7-9 02.0 98 97-9 OC. I S8 157.8 t*. 3 18 217.7 n. 4 78 277.6 i4o 39 3*-9 02 .O 99 95.9 0-.2 S9 158.8 08.3 19 8.7 ir. 5 39 278.6 14.6 i 40 39-9 02. I IOC 99-9 05.2 60 159.8 08.4 20 219.7 ii. i *o 279.6 14.7 4i 40.9 01. I JIOI 100.9 OS.3 10 I 160.8 0.^4 :2I 220.7 u. 6 -8 1 280.6 14.7 42 41.9 02. 2 ; 02 roi .9 05.3 fi2 161.8 08. < 22 22-1.7 11.6 82 281.6 H-* 43 42.9 02.3 03 rc2. s 05.4 63 162. S 08.5 23 222.7 11.7 83 282.6 14.8 j 44 43-9 07.3 04 103.9 OS- 4 64 163.8 08.6 2 4 223.7 II. 7 84 283.6 14.9 45 44-9 02.4 S 104.9 05.5 65 164.8 08.6 25 224.7 II. 5 8; 284.6 14.9 46 45-9 O2 .4 06 105.9 OS-S 66 165.8 08.7 26 22- .7 ! I . S 86 z3<;.6 15.0 47 4.6.9 02. S 07 106.9 os. 6 67. 166.8 08.7 27 226. 7 11.9 87 2S6.6 15.0 48 47-9 02. S 08 'C7.9 05.7 68 167.8 oS.8 28 227.7 I i . 9 88 287.6 15.1 49 48.9 02 6 09 108.8 OS- 7 69 168.8 68.8 2 9 228.7 12.0 89 288.6 15.1 50 49-9 o>.6 10 109.8 05.8 70 169.8 08.9 3 229.7 12.0 qo 289.6 15.2 51 50.9 02.7 III 110.8 os. 8 171 170.8 08.9 231 230.7 12. 1 91 290.6 15.2 ^2 51.9 02.7 12 tii.8 05.9 7-2 171.8 09-. o 32 231.7 12. I 92 291.6 15-3 53 5^.9 02.8 13 112. 8 05.9 73 172.8 09.1 33 *3*-7 12.2 93 292.6 15-3 54 53-9 02.8 *4 113.8 06.0 74 173-8 09.1 34 233.7 12.2 94 293.6 15-4 55 54-9 02.9 r ^ 114 8 06.0 7S 174-8 09.2 35 234-7 12.3 95 294.6 15.4 5<> 55-9 02.9 16 115.8 06. ii 76 175-8 09.2 36 235-7 I2. 4 96 295.6 '5-5 5? 56.9 03.0 17 116.8 06. i 77 176.8 09.3 37 236.7 12.4 97 2<,6.6 15-5 , 5 57-9 03.0 18 117.8 06:2' 78 177.8 09-3 38 237.7 12-5 98 297.6 15.6 j 59 58.9 03.1 '9 irf.8 06. a! 79 178.8 09.4 39 238.7 I2. 5 99 29.8.6 15.6 i 60 59-9 0?. I 20 ri9.8 06.3; 80 179-8 09.4 40 239.7 12.6 CO 299.6 IS -7 Dift Dep. 1 at. 'IDifti Dep. Lat.! Dift Dep. Lat. Dift Dep. Lac. Dift Dep. Lat. C c 2 for 87 Degrees. TABJ.K II. Diiterenee wf Latitude and Departure for 4 Dcgrce5, j ' ' ' ' Dili Lat. Dtp.. piTt| Lat. Dep. 'JDift Eat Dep. Dift Lat. Dep. Dift f.ar. Dep. i 01 .0 oo . r 61 ( o. 9 04.3 12 1 110.7 08.4 181 180.6 12.6 1241 240.4 16.8 2 ">2 .O 00.. I 62 61 .S 04.3 2Z 121.7 oS..; S^ 181.6 12.7 : 42 241.4 16.9 3 o: .0 OO. 2 63 62. S 04.4 122.7 08.6 83 rji.6 12.8 43 242.4 17.0 4 04.0 JO. ? 64 63.8 04.5 :.j 123.7 oS.6 84 i'> 3 .6 li.S i 44 3 43-4 17.0 s 015.0 o, .3 6, 04. S; 04. s 25 124.7 08.7 85 184.6 12.9 4c 244.4 17.1 6 06.0 oo . 4 65. S 04.6 26 125.7 08.8 86 i8s. 5 13.0 46 -45 4 1.7.2 7 07. c 00.5 6; 66. S 04.7 >7 126.7 08.9 87 186.5 13. c 47 246.4 17.2 8 08.0 00.6 68 67.8 04.7 28 127.7 08.9 88 187. S 13-' 4 S 247.4 '7-3 9 09. c .0.6 69 63.8 04. S 29 128.7 09.0 89 188.5 13.2 49 243.4 17-4 10 o 00.7 70 69.8 04.9 >o 129.7 Of), t 90 1*9- s r 3-3 50 149.4 17.4 ii I I .0 co.x ; 71 70.8 Ds.Q 131 130.7 09. i icy I 190.5 '3-3 251 250.4 '7-5 12 12.0 oo.S 7* 71- S 05.0 32 1.3 1-7 09.2 92 191.5 13-4 52 151.4 17,6 I 5 13-0 -0.9 ! 73 j 72. S 05.1 5 3 r 32. 7 9-31 93 192 , 5 '3-5 53 252.4 17.6 14 I 4 .0 01 .0 74J 73- ^ 0^.2 34 I 33-" 9-3,! 9-J '93'5 13.5 54 253-4 r/.7 15.0,01.0 75 74 8 J--.2 3> 134.7 09.4! 95 194.5 13.6 55 254.4 17.8 ' 16 16.0 01 . I 1 7^ 7s .S o> .3 36 ! T 3 5 - 7 09 -5 If 96 195-5 13 .7 5* 255-4 17.9 17 r 7 .o I . 2 77 76. i > os. 4 37 i 1 36. 7 09 .6 'j 9" ' 196.5 13.7 57 256.4 17.9 18 fg.Q 01.3 77-^ 05.4 1 3^ '37.7 09.6 98 197. s 13.8 257.4 18.0 19 19 .0 oj.3 79 ;8.8 o-. - ; ! 39 138.7 09.7 1 Q(J 198.5 13-9 59 258.4 18.1 20 20.0 01.4 So 7-9. 9 05.6 j 40 V39.7 09.8 l'':o 1-99.5 14.0 60 259.4 18. i , r 20.:, 01. s Si 80.* 05.- 1141 140 7 ! 09 . S ilioj 200.5 14.0 261 260.4 18.2 22 21.9 01. s 82 Si.S 05-7 ' 42 141.7 09.9, a 201 . 5 14.1 62 261.4 18.3 23 22.9 01.6 83 82.8 Os-.S 43 142.7 10. oj 03 20t . <; 14.2 63 262.4 18.3 24 23.9 i 01.7 84 83. 8(05.9 44 '43-6 IO.O 04 203.5 14.1 64 263.4 18.4 *5 24.9 01.7 8' ^4.*? 05.9 4 s " 144.6 10. I 05 204.5 J 4-3 65 264.4 18.5 26 01. S S6 85. S' 06.0 46 145.6 IO.2 06 205. s 14.4 66 265.4 18.6 27 26.9 01 .0 S7j 86.8 06. i 47 146.6 10 3 07 206.5 14.4 67 266.3 18.6 28! 27.9 ! 02.0 88 S 7 .8 06. i 48 147-6 10.3 oS 207. <; 14.5 68 267.3 18.7 29 zi. 9 02. o So 88.8 06.2 49 148 6 10-4 09 208.5 14.6 69 268.3 18.8 30: 19.9:02. 1 89 .8 06.3 sO 149 - 6 TO. 5 10 209. 5 14.6 70 269.3 1 8. 8 31 i 30.9 : 02. 2 91 ; 90. t 06.; id i5X).6 10.5 211 210.5 14-7 271 270.3 18.9 32; ? i . o 02. 2 92 i 91.8 c6_4 52. 151.6 10.6 12 111.5 14.8 72 271-3 19.0 33 32.9 02.3 93J 92-8 06. C; 53 152.6 10.7 1J 212.5 14.9 73 072.3 19.0 34 33-9 02-4 94j 93-8 06.6 54|is3.6 10.7 14.9 74 273-3 19.1 35 34-9 02. 4 06.6 55 1 154.6; 10.8 15 21.1.5 15.0 fS 274-3 19.2 ? 5 9 02. S 96; 95-S 06.7 ;6 155-6 10.9 r,6 215.5 15.1 76 275-3 19.2 37 36.9 02.6 97 9 6 . S 06.8 56 6 11 .0 17 216. <; 15.1 77 276.3 J 9-3 38 ; ; - . '; 02. 7 qS, 97.8 06.8 sS 157.6 I I . C 15 217.5 15.2 78 277-3 19.4 39 V-i-9 02.7 99! 98.8 06. 9 si;'; 1^8.6 II. I 19 218.5 15-3 79 278.3 19.5 40 '9-9 02.8 too 99.8)07.0 6 o ' i ^ 9 6 II .2 20 219.5 15-3 279-3 19.5 4 r 40.9 02.9 ror 103.8 Thl > 160.6 II. 2 221 210.5 15.4 281 280.3 19.6 '$ 41.9 42.9 02. 9 03.0 oijiot.8 03 102.7 62 j 16-1.6} 11.3 ;') ; 162.6 11.4 22 2 3 221.5 222. ' i5v5 82 S3 281.3 282.3 19.7 19.7 44 43-9 03 ..I 04 103.7 07-3 6 4 J<>3 6 II-4 24 *23"5 15.6 84 283.? [9.8 4< 44*9 03.1 05 104.7 07-5 6i 164.6 11. s - s 224.5 J 5 -7 5 184.3 '9-9 ! 46 47 4 46.0 03.2 03.3 06^05.7 07-4 07 106.7 >07. 5 165.6 r66.6 ii. 6 11.6 26(225.4 271226.4 15.8 15-8 86 87 185.3 286.3 2C .0 . 2O. 03.3 c8 MO~ 7 Jo? s 167.6 1 1 7 2 227-4 15-9 88 2^7.3 20. 1 49148.9 03.4 09 i rc8. 7 4-9 03-8 15 114.7 oS.o 75 i74 6 32.2 35 234-4 16.4 95 294-3 20 . 6 ; ;6 >5'9 ?9 1 6 u s . 7 08 .j, 76 1 7s'. 6 12.3 36 235-4 16.5 96 295.3 20.6 i 57 ;6.<> 04.0 17 116.7 08-2 77 176.6 12-3 37 236. 4 1 6 . ^ 97 290.3 2-Q.7 s S - - f) 04 . o 59 ;i.'V04.i r8, 19 117.7 OS,2 08.3 7P *- ^ 178'. 6 12.4 11. 5 J8U37-4 39^23^.4 1 6 . 6 16.7 99 297.3 298.3 20.8 20.9 >o:^ 9,04.2 30 119.7 08.4 So 179.6 11.6 40 239.4 16.7 j^oo 299-3 20.9 D : i"t' -p. ! Lui. I-Hft. IJcp. Lat. ! Dift: Dep. Lat. 1 Dift 1 Dep. j Lr.t. |-Dift Dep. .Lat. tor SO Decrees. It. Difference of Latitude and Departure for: 5 Degrees. Dif Lat. Dep. Dift Lat. Dep. Dift Lat. Dep. Dift Lat. Dep. Dift Lat. Dep. i CI.O OC. I 61 60.8 05.3 121 120. 5 . 10.5 181 180.3 15.8 241 240. 21 .0 ! 2 02. o OO.2 62 61.8 '05.4 22 121.5 10.6 82 181.3 15.9 42 241. 21 . I ' 3 03.0 00-3 63 62.8 OS'S 23 122.5 jo. 7 $3 182.3 15.9 43 242. 21.2 ! 4 04.0 00.3 64 63.8 05.6 24 123.5 10.8 4 183-3 16.0 i 44 243- 21. 3 i 5 05.0 O0.4 6s 64.8 OS-7 5 124.5 10.9 5 184.3 16.1 45 244. 21.4 ! 6 06.0 oo. 5 66 6-5. 7 os. 8 26 125-5 II. 86 1*5-3 16.2- 40 245. 21.4 ! 7 07.0 OO. 6 67 6*5.7 01.8 27 126.5 ii. i *7 186.3 16.3 47 246. 21.5 8 08. o 00.7 68 67.7 os- 9 28 127.5 I I. 2 OO 1*7-3 16.4 48 247. 21.6 I 9 09.0 00.8 69 6-8.7 06.0 29 128.5 1 1. a 89 188.3 16.5 49 248. 21.7 j JO 10. 00.9 70 69.7 06. i 3C 129.5 IT. 3 90 189. S 16.6 i 5 249. 21.8 j 1 1 11. 01, O ! 71 70.7 06.2 131 130.5 11.4 191 190.3 16.6 251 250.0 21.9 1 12 12. O 01 ,0 i 72 71.7 06.3 32 131.5 11.5 92 i9'-3 16.7 52 251.0 21.0 J 3 13.0 OI. I 73 72.7 06.4 33 132-5 11.6 93 192.3 16.8 1 53 252.0 22.1 J 4 13.9 01.2 74 73-7 06.4 .34 133.5 11.7 94 193-3 16.9 54 253.0 --.2.1 15 14.9 01.3 7S 74-7 06. S 35 '34-5 ii. 8 95 '94-3 17- 0| 55 254.0 22.2 i 16 15.9 01.4 76 75-7 06.6 3<3 135-5 11.9 96 J 95-3 17. ill 56 255.0 22.3 7 16.9 oi. s 77 76.7 06.7 37;J36.5 11.9 97 196.3 i7-*J 57 256.0 22. 4 - 18 17.9 01.6 78 77-7 06. S' 38 '37-5 12.0 S>8 197'? 17.3 5S 257 o - 2 -5 i 18. 9 01.7 79 78.7 06.9 30 138-5 12. I 99 198.2 *7 3i 59 258.0 22.6 j 20 19.9 01.7 80 79-7 07.0 40 M9-5 12.2 200 199.2 17.4 ^o 259.0 22-7 ; 21 20.9 01.8 81 80.7 07.1 141 140.5 12.3 SOI 200.2 17-5 261 260.0 22.7 22 21.9 oi .9 82 81.7 07. 1 42 141.5 12.4 C2 201. 2 j 17.6 62 261 .0 22. S i 23 22.9 02.0 83 8;. 7 07.2 4^ 142.5 12 . <; 03 2Ci.2i 17-7 63 262.0 22. 9 | . 2 4 23-9 02. I 84 83.7 07.3 44 143-5 12.6 04 203 . 2 17. S 64 263.0 23-Oj ! 25 24.9 02.2 8-6 08.4' 56 155-4 13.6 r6 215.2 18.8 76 274.9 24.1 37 3M 03.2 97 96.6 c8.< 57 156.4 13.7 17 J2I6.2 i8. 9 j] 77 -75-9 24.1 1 38 37-9 03-3 98 97.6 08.51 58 '57-4 13.8 IS 217.2 19.0 7* 276.9 24-2 I 39 3*. 9 03-4 99 98.6 08. 6 = 59 158.4 13.9 '9 218.2 19.1 79 277-9 24.3 1 40 39-* 03-5 ICO 99.6 08.7 6c 159.4 13.9 20 219.2 19.2 8c 2/S.( ( 24.4 i 41 40.8 03.6 101 100. 6 08.8' 161 160.4 14 c 221 220.2 '9-3 2>>I "9-9 24.3 1 42 41.8 03.7 G2 101.6 08. qi 62 161 .4 14.1 22 221.2 19-3 82 280.9 24.6 1 43 42.8 03-7 0, 102.6 09.0 6} 162.4 14.2 23 222.2 19.4 ^3 281.9 24.7 i 44 43.8(03.8 4, 103.6 09. I 64 163.4 14.3 24 223.1 19.5 84 282.9 24.8 i ^ 44.8 03-9 OS 104.6 09.2 6S 164.4 14.4 25 224.1 19.6 85 283.9 24.8 46 45.8 O4.O 06 105.6 9 .2 66 165.4 14.5 26 2^5-1 19.7 sS 284.9 24.9 47 46.8 04.1 &7 106.6 09-3 67 166.4 14.6 27 226.1 19.8 87 285.9 25.0 4 47.8 04 2 08 107.6 09.4 68 167.4 14.6 28 227. I 19.9 &8 286.9 25.1 49 48.8 C4-3 09 108.6 09.5 69 168.4 14.7 29 2^8.1 20.0 89 2*7-9 25-2 i 50 49.8 04.4 10 109 . 6 09.6 70 169.4 14.8 30 229.1 20. C 9o 288.9 *5J 1 5i 50.8 04.4 in 1 1 0.6 09-7 i/i 170.3 14.9 231 230. I '20.1 291 289.9 25-4J 5* 51.8 04.5 12 i II. 6 09.8 75 171.3 15.0 3* 231.1 20.2 [j 92 ^90.9 25.4 53 52.8 04.6 3 112. 6 09 "S 73 172.3 15.1 33 232.1 29-3 I 93 291.9 25-5 i 54 53-* 04.7 14 "3.6 09-9 74 *73-3 \5-Z 34 233.1 20.4 1 94 292.9 25.6 55 54.8 04.8 IS 114.6 IO.O 7S J74-3 J 5'3 35 234- 1 20. 5 !J 95 293.9 25.7 56 55-* 4-9 16 n<.6 IO. 1 76 175.3 15-3 36 235-1 20.6 96 294.9 25.8' 57 56.8 05.0 17 116.6 10.2 77 176.3 J5-4 37 236.1 20.7 97 295.9 2 5-9 ; 5 57-8 05.1 18 117-6 10.3 73 177-3 *5-5 38 237.1 0'.7 9 8 296.9 26.0 59 58.8 05.1 19 n8.s 10.4 79 178.3 IS. 6 39 23*. i ^0.8 99 297.9 26.1 60 59.8 05.2 | 20 119.5 I0. 5 80 179-3 15.7 40 239.1 20.9 300 298.9 26.1 Dift Dep. Lat. - Dift Dep. Lat. (ipift Dep. Lat. Dift! Dep. Lat. Dift Dep." Lat. for 85 Degrees. TABLE IL Difference of Latitude and Departure for 6 Degrees. Dift Lat. Dep. Dift Lat. Dep. Dift Lat. Dep. Dift Lat. Dep. Dift Lat. Dep.; i 2 3 4 c 6 8 9 10 OI.O 02. o 03.0 04.0 05.0 06.0 07.0 08.0 09.0 09.9 00. I 00.2 oo. 3 co. 4 oo. j; 00.6 00.7 00.8 00.9 01 .0 61 62 63 64 65 66 67 68 69 70 60.7 61.7 62.7 63.6 64.6 65 6 66.6 67.6 63.6 69.6 06.4 06.5 06.6 06.7 c6.8 06.9 07 .0 07. t 07.2 07.3 121 22 23 24 25 26 27 28 29 30 120.3 121.3 122.3 123 . 3 '24-3 125.3 126.3 1*7.3 128.3 129.3 12.6 12.8 12.9 13-0 13.1 13.2 13-3 13-4 '3-5 13-6 151 32 83 84 ii 87 88 89 90 181.0 182.0 183.0 184.0 185.0 186.0 187.0 188.0 189.0 18.9 19.3 19.1 19.2 19.4 19.5 19.7 19.8 19.9 241 42 43 44 45 46 48 49 So 239.7 240.7 241.7 242.7 243.7 244.7 245.6 246.6 247.6 248.6 25.2 25.3 25.4 25-5 25.6 25.7 25.8 25.9 26.0 26.1 1 1 10.9 01. I 7 : 70.6 07.4 '3* 130-3 13.7 191 190.0 20.0 251 249.6 26.2 12 11.9 01.3 7- 71.6 07.5 32 131.3 13.8 92 190.9 2O. I 250.6 26.3 'i 13.9 01.4 73 74 72.6 73-6 07 .6 07.7 33 34 132.3 '33-3 13.9 14.0 93 94 191.9 192.9 20.2 20.3 53 54 251.6 252.6 26.4 26.6 1 5 14.9 75 74.6 07.8 35 134-3 14.1 95 93-9 20.4 253.6 26.7 16 17 20 15.9 16.9 17.9 19.9 81.7 01.8 01 , 9 02. o 02. i 77 7S 79 80 75-6 76.6 77.6 78.6 79-6 07.9 08.0 OS.2 08.3 08.4 3* 38 39 40 135-3 136.2 137- a 138.2 139.2 14.2 '4-3 14.4 '4-5 14.0 96 97 98 99 200 194.9 195.9 196.9 197.9 I9 8. 9 20.5 20.6 20.7 20.8 20.9 5/ 53 59 60 254.6 255-6 256.6 257.6 258.6 26.8 26.9 27.0 27.1 27.2 22 20.9 21.9 02.2 02.3 82 80.6 81.6 oS. 5 oS.6 14; 42 140.2 141.2 14.7 2OI 02 199.9 200.9 21.0 21. I 261 259.6 260.6 27-3 27.4 23 22.9 02.4 *3 82. c 08.7 43 142.2 14.9 0} 201.9 21 .2 63 261.6 27. s 24 23.9 02.5 84 83.5 08.8 44 143.2 15.0 04 202.9 21.3 262.6 27.6 25 26 27 24.9 25.9 26.9 27.8 02. 6 02.7 02.8 02.9 86 87 88 84.5 85.5 86. s 87.5 08.9 09.0 09.1 09.2 45 46 47 48 144.2 145.2 146.2 147.2 15.1 I5.3 15-5 05 06 C7 08 203.9 204.9 205.9 206.9 21. 4 21.5 21.6 21.7 65 66 67 68 263.5 264.5 265.5 266.5 27.7 27.9 28.0 29 28.8 03.0 89 88.5 09.3 49 148.2 IS- 6 09 207.9 21.8 69 267.5 28.1 30 29.8 03.1 90 89.5 09.4 5 149.2 15-7 10 208.8 22.0 70 268.5 28.2 31 30.8 03.2 9 1 90.5 09.5 151 150.2 15.8 211 209.8 22. I 271 269.5 28.3 3 2 31. b 03.3 92 91.5 0. 2 6> 66 67 263.0 264.0 265 .0 3^.3 32-4 28 27.8 03.4 88 g'S 10.7 4*5 146.9 18.0 08 206.4 25.3 68 266.0" 31.7 29 20.8 03-5 89 88.3 10.8 49 147.9 18.2 09 207.4 25.5 69 167 .0 ;2.8 ] 30 29.8 03.7 .90 89.3 II .0 5 148.9 18.3 10 108.4 70 168.0 31 30.8 03.8 9* 9-3 n. i 149.9 18.4 109.4 2 5-7 171 169.0 32.0 ; 3 4 31.8 03-9 92 9 J -3 11.2 51 150.9 18.5 2 210.4 iS-8 7~ 270.0 33 34 32.8 33-7 04.0 04.1 93 94 92.3 93-3 3 If. 5 53 '5i. 9 54:152.9 18 6 18.8 3 4 211.4 212.4 16.0 2 ' . I 73 7-4 271.0 1"2.O 33-3 ; 35 34-7 04.3 95 94-3 1 1. 6 c c ; 153.8 18.9 ?. 1 3 . 4 16.2 75 2 ? ; 36 35-7 04.4 96 95-3 ii. 7 154.8 19.0 6 214.4 16 ^ 76 173.9 3/ 30.7 04-5 97 96-3 ii. 8 57 155.8 19.1 iy 215.4 26.4 274.9 3?.8 ' 38 39 37-7 38.7 04.6 04.8 99 97-3 98.3 11.9 12. 1 55 59 156.8 157-8 19-3 19.4 IS 116.4 217.4 26 6 26.7 7 8 79 275-9 33*9 | *4 O 40 39.7 04.9 100 90-3 12 . 2 60 158.8 19-5 20 26 8 Z"7. 9 34- i 41)40.7 05.0 fOI 100.2 I2. 3 161 159.5 19.6 221 219.4 26.9 178.9 34.1 i- 42 41.7 05.1 02 IOI.2 12-4 62 160.8 19.7 22 210.3 27. i X? ^4 4 43 42.7 05.2 03 102,2 [2.6 6j j 6 1 . 8 19.9 23 121 .3 27.2 83 1 8o o 34-5 i 44 44-7 05.4 04 103.2 12. 7 6} 161.8 20.0 24 i2*. 3 -7-3 84 i3i .i) 45 46 44-7 45-7 05.5 05.6 05 06 104.2 105.2 it.* 12.9 6; 66 163,8 164.8 20. I 20.1 -5 26 M3-3 224.3 27.4 27. q 85 86 282.^ 47 48 49 46.6 47-6 48.6 05.7 05.8 06.0 07 08 09 106.2 107.2 108.2 13.0 13.2 67 68 69 165.8 166.7 167.7 20.4 20.5 20. .6 28 29 215.3 116.3 227.3 27.7 17-8 17.9 87 69 284.9 285.9 286.8 35 o j 3 5 ~ ! i 50 49.6 06 . 1 10 109.2 13.4 70 168.7 20.7 30 "8.3 28.0 90 287.8 ,^3 I 5i 5* 50.6 51.6 06. 2 06.3 1 1 1 12 I IO.2 III. 2 1 3 5 13-6 171 72. 169.7 170.7 20. S 21 .0 -3' S 2 - 129.3 *S/3 Ql 280.8 35 5 ij 35-6 J 53 54 55 53-6 54-6 06. 5 06.0 06.7 *3 15 1 12. 2 U3-2 114.1 13-6 .3.9 14. o 73 74 5 171.7 172.7 173-7 21. I 21.2 21.3 33 34 31 13-1.3 28.4 28.5 93 95 190.8 291.8 191.8 55-7 35. j :6.o : J 59 60 55.6 56.6 57.6 59-6 06.8 06.9 07.1 07.2 07.3 16 17 18 20 115.1 116. i 117-1 118.1 119.1 14.1 14.3 14.4 *4-5 14.6 b 8 9 gc 174-7 175-7 176.7 177-7 178.7 21.4 2J.6 21 . 7 21.8 37 38 39 40 -34-2 235.1 236.2 2.37. - 28.8 ? -8. 9 29 .0 29.1 2.). 2 96 97 99 JOO 193.8 194.8 105.8 296.8 297.8 36.1 36.2 1 36.3 ij Dift Dep. Lat. Dift Dep. Lat. Dift Dep. Lat. f>iu Dep. - Dift tor S3 Decrees TABLE II. Difference of Latitude and Departure for S Degrees. Uift Lat. Dep. Dift Lat. Dep. Dift Lat. Dep. Dift Lat. Dep. 'Dift Ut. Dep. i Ol.O 00.1 6l 60.4 08.5 121 119.8 16.8 iSi 1 79 2 25.2 241 238.7 33-5 2 02. O 00.3 6* 61.4 o3.6 Z2 120.8 17.0 82 180.2 25-3 4' 239.7 33-7 3 01.0 00.4 63 62.4 o3 .8 2 3 121. 8 17.1 83 jtfti.a 43 240.6 33-S 4 104.0 00.6 64 08.9 24 122.8 17.3 84 182.2 25.6 44 241.6 34-o 5 j5- oo. 7 65 64,4 09.0 123 .8 17-4 85 183.2 *5 7 45 242.6 34-' 6 ! o 5 . y 00.8 66 09.2 26 124.8 17-5 86 184.2 25.9 46 243.6 34-2 8 06.9 07.9 01. 01. I 67 68 66.3 67.3 09.3 09-5 28 1-15.8 126.8 ll'.l 88 186.2 26.0 26.2 48 244.6 245.6 34-4 34-5 9 0^.9 01.3 60 68.3 09.6 29 127-7 iS.o 89' 187.2 26.3 49 246.6 34-7 10 09.9 01.4 70 69.3 09.7 30 18.1 90 188.2 16.4 50 247.6 34-8 i j 10.9 01.5 71 70*3 09.9 131 129.7 18.2' 191 189. 26.6 251 248.6 34-9 12 11.9 01.7 72 7*3 10. O 3 2 1.8.4 92 190. 2b. 7 S 2 249-5 35- * 13 12.9 01.8 73 72.3 10.2 33 131.7 18. ;, 93 191. 26.9 53 250.5 35.2 14 1 5,9 01.9 74 73-3 10.3 34 132.7 18.6 94 192. 27.0 54 251.5 35-3 I ; 14.9 oa. i 75 74-3 10-4 133.7 18.8 95 i93- 27.1 55 252.5 35-5 16 15.8 02. 2 76 7S-3 10.6 36 134-7 18.9 96 194. 27.3 56 253-5 35-6 TT 16.8 02.4 77 76.3 10.7 37 135.7 19. ij 97 195. 27.4 57 254.5 35. 18 T7.8 02. 5 78 77-* 10.9 136.7 196. 27.6 5* Z 55'5 35-9 19 20 r8.S 19.8 02.6 02.8 79 So 78.2 79.2 11 .0 n. i 39 137.7 138.6 19.3 99 200 197- I9 8. 27.7 27.8 59 60 256.5 257. 5 36.0 1 36.2! 2 1 20.8 OJ.9 61 80.2 i*3 141 139.6 19.6 '.01 199.0 28.0 261 258.5 36.3 12 21.8 03.1 82 81.2 11.4 42 140.6 19.8 o: 200.0 28.1 62 259.5 36.5 23 22.8 03.2 $3 82.2 n. 6 43 141 . 6 19-9! 03 2OI.O 28.3 63 260.4 36.6 24 23.2 03.3 84 83.2 ii. 7 44 142.6 20. 0| 04 202.0 28.4 64 261.4 36.7 25 26 24.8 03.5 03.0 85 86 84.2 ir. 8 12.0 45 46 143.6 144.6 2O. 2 20.3' 05 06 203.0 2O4.0 28.7 65 66 262.4 263.4 36.9 37.0 2." 26.7 03.8 87 86.2 12. I 47 145.6 20.5: 07 205.0 28.8 <>7 264.4 37-2 27.7 03.9 88 87.1 12.2 146.6 20.6: 08 206.. o 28.9 68 265.4 5.7-3 " 9 3 28.7 29.7 04.0 04.2 89 90 SS.i 89.1 2.4 49 50 147*5 10.7 20.9 09 10 207.0 208.0 29.1 29.2 69 70 266.4 267-4 37-4 37.6 [ 31 30.7 04.3 91 90. i 2.7 I5t 149.5 21.0 in 208 . 9 29.4 27' 268.4 37-7 32 Jt-7 04-5 92 91. i 28 52 150. 5 21.2 12 209.9 29.5 72 269.4 37-9 1 33 04.6 93 92.1 2 . 9 151.5 13 210.9 29. 6 73 270.3 38.0 1 34 .7 04.7 94 9 3 . j 13-1 54 152.5 21.4 H 211.9 29 8 74 271.3 38.1 35 H7 04.9 95 91- i 13-- 55 '53-5 21.6 '5 212.9 29.9 75 272.3 3^*3 3<.6 0^.0 96 95.1 '6 154- 5 21 .7 16 213.9 30. i 76 273-3 38.4 37 ' 3* 36.6 05.2 05-3 9? 96.1 97.0 1^6 jj ^55-5 156.5 21.9 22,0 17 18 214.9 215-9 30.2 30.. 3 77 78 274-3 27v3 jM 39 38.6 <54 99 98,0 13.8 59 22. I 19 216.9) 30-5 79 76.3 35. s 40 39.6 05. 6 IOO 99.0 13-0 6c 158.4 22.3 20 2I-.QJ 30.6 40 / / 3 _ _L_ j 41 40.6 05.7 101 IOO.OJ 14. I 161 159-4 22.4; 121 ttS.tf 30.8 281 278.3 39-' 02 roi .0 14.1 62 160.4 22. 5 22 219.8 30.9 82 279.3 39.2 i 43^.6 44 43-6 06.0 06. i 03 04 ro2.o 103 .0 H-3 *4-5 63 64 Tfil .4 162.4 22.7 22.8 23 24 zio 8 221.8 31-2 84 280. 2 28l.2 39-4 39-5 4? 4.4:6 06-3 104.0 14.6 163.4 23.0 Z~ 222.8 31-3 !j 282.2 39-7 46 45.6 06.4 06 105.0 66 164.4 2j.I 26 223.8 3 r 5 86 2 *32 ,39 -^ 47 48 46.5 47 '5 06. s 06.7 07 08 ro6.o 107.0 14.9 15.0 67 165.4 166.4 2J.~ 27 28 224.8 225.8 31.6 87 88 284.2 285.2 39-9 40. i ! 49 ;o 4*<5 49-5 07.0 09 107.9 TO '108.9. 15-2 15- * 69 70 167.4 168.3 23-5 2 V 7 2 9 30 226.8 227. S 32.0 90 286. 2 287.2 10.2 40.4 S 1 50.5107,1 Ill [109.9 i il; jo. 9 15.4 15.6 72 169.3 I7O.3 23-9 l \l 228.8 229.7 32.1 .32.3 -9 1 92 286.2 40.5 40.6 53 52. s; 07.4 13 111.9 73 i/r-3 24. I 31 230.7 32.4 93 290. 4O.8 54 53.51 07 5 I4iu2.9 15-9 74 1 7*. 3 24.2 34 23 T - 7 32.6 94(291. 40.9 ! 55 ! 56 54-5 > c ' 5 07.7 07.8 15 r6 113.9 114.9 16.0 z5.i /6 173.3 174-3 24-4; 35 24-5' 36 232.7 233-7 32.7 32. S 95 96 293- 4I.I 4L2 56,4 ;;.4 07-9 08. T 18 115.9 16.3 I I 6 . I l6.A 77 78 175.3 24.6 37 176.3 24.7 ! 5S 234-7 235-7 33-o 33-1 97 98 294- 41-3 295- S1-1-5 | ? 08.2 19 ! 17. 8j 16.6 79 '77-3 2 1.9 39 .256.7 .33-3 99 296. 41. b ; 6 |59-4 oS. 4 20 ;is.8|i6.7 80 25.1 | 40 237." 33-4 300 297. 41.8 1 D ift i Dep. Lat. [(Dift I Dep. 1 Lat. Difr Dep. Lat. -Dift Dep. Lat. j'Dift Dep. I/at. for 82 Degrees. TABLE II. Difference of Latitude and Departure fof f) Degrees. DiftlLat. Dep. Did Lat. Dep. Dift Lat. Dep. Dift Laf. Dep. Dift Lat. Dcp. i 01. O OO.2 6r 60.2 09.5 121 "9-5 18.9 181 178.8 zM -4 1 238.c 3 / i 2 02. 00.3 62 61.2 09.7 22 120.5 19.1 82 179-8 28. S 4 2 239. o 37-9 3 03.0 00.5 63 62.2 ?-9 23 121.5 19.2 83 180.7 28.6 4^ 240.0 33.0 4 O4.0 00.6 64 63-2 IO.O 24 122.5 19.4 84 181.7 28.8 44 241.0 38-2 5 04.9 oo.g 6s 64.2 10.2 2<5 I2 3-5 19.6 8s 182.7 28.0 45 242.0 38.3 6 05.9 03.9 66 65.2 10 3 26 124.4 19.7 86 183.7 29.1 46 243.0 38.5 7 06.9 01. I 67 66.2 10.5 27 125.4 19.9 87 184.7 *93 47 244.0 38.6 8 07.9 01.3 68 67.2 10.6 28 126.4 20.0 88 185.7 29.4 4? 244.9 3^-8 9 O3.9 01.4 69 68. 10.8 2 9 127.4 20.2 89 186,7 29.6 49 245.9 39-o 10 09.9 01.6 70 69. II. C 30 128.4 20.3 90 187.7 29.7 50 246.9 39-i ii IO-9 01.7 7i 70. II. I 131 129.4 20.5 191 188.6 29.9 2C1 247.9 39-3 12 11*9 01.9 72 71. 'i-3 3* 130.4 20.6 92 189.6 30.0 52 248.9 39 4 3 iz.8 02.0 7> 72. 11.4 33 131.4 20.8 93 190.6 30.2 S3 249.9 39*6 M 13- * 02. 2 74 73- 11. 6 34 132-4 21. 94 191.6 30.3 S4 250.9 39-7 15 14.8 02.3 75 74- 11.7 35 133.3 21. I 95 192.6 30.5 55 251.9 39-9 1 l6 15.8 02. 5 76 75- 11.9 36 J 34.3 21.3 96 193.6 30.7 56 252.8 40.0 i/ 16.8 02.7 77 76. 12.0 37 135-3 21. 4 97 194.6 30.8 57 253.8 40.2 18 17. 8 02.8 78 77.0 12.2 38 136.3 21.6 98 195.6 31.0 58 254.8 40.4 r 9 18.8 03.0 7Q 78-0 12.4 39 137.3 21.7 99 196.5 31. 1 S9 255.8 40.5 ! 20 19.8 03.1 80 79.0 12.5 40 138.3 21.9 200 r 975 31.3 6c 256.8 40.7 21 20.7 03.3 81 80.0 12.7 141 139-3 22. I 201 198.5 31.4 261 257.8 40.8 22 21.7 03.4 82 &I.O 12.8 42 140.3 22.2 02 199.5 31.6 62 2 S 8.8 41.0 1 * 3 22.7 03.6 83 82.0 13.0 43 141.2 22. 4 03 200.5 31.8 6? 2.9.8 4.1.1 24 23-7 03.8 84 83.0 13.1 44 142.2 22. ; 04 201.5 31-9 64 260.7 41.3 1 4 5 24.7 03.9 8s 84.0 13-3 45 143.2 22. 7 s 202.5 32.1 6s 261,7 41-5 16 25-7 04.1 86 84.9 n-s 46 144.2 22.8 06 203.5 -32.2 66 262.7 41.6 17 26.7 04.2 87 85.9 13.6 47 145.2 23.0 07 204.5 32.4 67 263.7 41.8 28 27.7 04.4 88 86.9 13.8 4* 146.2 23.2 08 205.4 32-5 68 264.7 41.9 29 28.6 04.5 89 87.9 13-9 49 147. 2-3 .31 09 200.4 32.7 69 26 S . 7 42.1 30 29.6 04.7 90 88.9 14.1 50 148. 23-5 re 207.4 32.9 70 266.7 42.2 31 30.6 04.8 91 89.9 14.2 '51 149. 23.6 211 208.4 33-0 271 267.7 42.4 i 32 31.6 05.0 92 90,9 14.4 52 150. 23.8 12 209.4 33-2 72 268.7 42.6 33 32.6 05.2 93 91.9 14.5 53 151. 23.9! J 3 210.4 33-3 73 269.6 42.7 34 33.6 5-3 94 9 2.8 14.7 54 152. 24.1 *4 211.4 33-5 74 270,6 42.9 1 35 H-6 5-5 95 93-8 i 4 . 9 55 '53 24-2 15 212.4 33-6 75 271.6 43.o ! 30 35.6 05.6 96 94.8 r 5 .o 56 154- 24.4 16 213-3 33-8 76 272-6 43.2 37 36. s 05.8 97 95.8 15.2 57 155- 24.6 *7 214.3 33-9 77 273.6" 43 '3 3* 37.5 05.9 98 96.8 l 5-3 58 156. 24-7 18 115.3 34-i 78 274-6 43-5 39 3*- 5 06. i 99 97.8 *S-5 59 157-0 24.9 19 216.3 34-3 79 275-6 43-6 1 4 ?9-5 06.3 ICO 9** 15.6 60 158.0 25-0! 20 217.^ 34 4 8c 276.6 43,8 4 1 40.5 06.4 roi 99.8)15.8 161 159.0 25.2 i2I 218.3 3'4-6 2^r 277.5 44.0 I 4 2 41.; 06.6 02 ioo.7 16.0 62 160.0 25-3 22 219.3 34-7 82 2/8-5 44.1 43 + 2 -5 06.7 03 roi .7 16.1 63 ifn o 25.5 23 220.3 34'9 83 279-5 44-3 44 *3-5 06-9 04 102.7 16.3 64 162.0 25.7 24 221 2 35-0 84 280. s 44-4 I 45 44.4 07.0 S 103.7 16.4 65 163.0 2S.S 25 222.2 35-2 8; 281. S 44-6 46 45-4 07.2 06 104.7 16.6 66 164.0 26.0 26 223.2 35-4 86 282. s 44-7 4" 46.4 07.4 07 105.7 16.7 67 164.9 26.1 27 224.2 35-5 87 283- S 44-9 4^ 47-4 07.5 08 106.7 16.9 68 165.9 26.3 28 225.2 35-7 88 284.-; 45.1 49 4^.4 07.7 09 107.7 17. i 69 166.9 26.4 29 226.2 3S. 8 89 285.4 45-2 So 49-4 07.8 10 ro8.6 17.2 TO 167.9 26.6 30 227.2 36.0 90 286.4 45.4 5 1 .0.4 c8.o til 109.6 17.4 171 168.9 26.8 2?I 228.2 36. i 291 287.4 45*5 52 51.4 08. i 12 IT0.6 17-5 72 169.9 26.9 32 229.1 36.3 92 288.4 45 -7 53152-3 j 54 53.3 08.3 084 13 H 111.6117.7 tI2.6'l7.8 73 74 170. 9 171.9 27.1 27-2 33 34 230. I 23L1 36.4 36.6 93 94 289.4 290.4 45.81 46.0 55 54-3 08.6 1.5 113.6 ! iS.o 172.8 27-4 3S 232.1 9> 291.4 46 . i 56 55-3 08.8 16 114.6)18. I 76 173-8 27.S 36 23^.1 36.9 96 292.4 46-3 57 ?6.3 08.9 17 115.6 18.3 77 174-8 ~1-1 37 234-1 37-' ->7 293.3 46.5 5* <7-3 09. i 18 116.5 I*- ' 17S- 8 27-.S 38 -35-1 37.2 1 c,8 294-3 46 . 6 1 59 158 -3 09. 2 19 117 . s; j 18.6 79 176.8 28.0 39 2^6.1 37-4 99 295.3 46.8 ! *o|59.3 Oy 4 : 20 fj'3.5 18.8 o 177.8 28.2 40 2^7.0 37-5 |p C 296.3 46.9 Diil Dep. Lat. Dift Dcp. .Lat. Did Dep. Lat. Dif Dep. Lat. Dif Dep. Lat. 1 -_ 13 87.6 15-5 49 146.7 25-9 09 205.8 36.3 69 64.9 46.7 ^!0 05.2 90 88.6 is. 6 50 H7-7 26.0 10 206.8 36-5 70 265.9 46.9 -,0.5 05.4 91 89.6 1 5 48 Hrji 148.7 26.2 211 207.8 ,6.t 71 266.9 47-1 1 51.5 05.6 92; 90.6 16. oil 52 149.7126.4 12 208.8 36.^ 72 267.9 47-2 33 32. 5 93' 9 1 - 6 16. i ji 51 150.7 U6.6 13 i 209.8 37-^ 7; 268.9 47-4 34 05.9 16.3 54 I5I-7 26." *4 210.7 37-2 74 269.8147.6 3 06.1 95 93.6 16.5 .55 152.6 26.9 ! 15 211.7 37-3 75 270.8 47.8 06.3 96 94* 5 16.7 56 153-6 27. 1 16 212.7 37-5 76 271.8 47-9 37 36.4 06.4 97 95-5 i6.S ?7 154.6 27- i '7 213.7 37-7 i 77 272.8 48.1 | 3* 37.4 06.6 98 96. s 17.0 58 27.4 18 214.7 37*9 j 78 273-8 48.3 | -8.4 06.8 99 97-5 17.2 S9 156.6 27. 19 215.7 3 8.c 79 274-8 48.4 40 39-4 06.9 100 98.5 ! 60 157-6 27. 20 216.7 3^. 80 275-7 48 . 6 4' 40.4 07.1 101 199.5 17.4 !c6i 158.6 28. 1221 217.6 38.4 28 276.7 48.8 42 41.4 07.3 02 100.5 j 62 159-5 28. 22 218.6 38. 8 277-7 49.0 j 43 42-3 07.5 03 101.4 17.9 63 160.5 28. 23 219.6 38. 8 278.7 49-1 ' 44 43-3 44-3 07.6 07.8 041102. t 05 103.4 18.1 iS.a 6"4 65 161.5 162.5 28. 28. 24 2*0.6 221.6 38. 39-0 84 8 279-7 280.7 49-3 | 49-5 i 46 08.0 06 104.4 18.4 66 163.5 28. 26 222.6 39- I 8 281.7 49-7 ; 47 46.3 0^.2 07(105.4 18.6 67 164.5 29. 27 223.6 39' 8 282.6 49.8 | 48 47 -3 08.3 08 106.4 18.8 68 165.4 29. 28 224.3 39- 8 283.6 50.0 49 48.3 08.5 09 107.3 18.9 69 166,4 29. 2 9 225.5 39- 8 284.6 50.2 j 10 49-2 0^.7 10 108. 19. t 70 167.4 ZQ 3O 226. 5 39- 9 285.6 5 : 4 j 51 50.2 o879 III 109. 3 19.3 171 168.4 29. 231 227.5 40. 29 286.6 50-5 \ 5' 51.1 09.0 12 I 10. 19.4 72 169.4 29. 32 228.5 40. 1 9 287.6 50-7 'I 53 52.2 09.2 n in. 19.6 73 170.4 3- 33 229.5 40. 9 2^8.5 50.9 54 53-2 09.4 112. 19.8 74 171.4 30. 34 230.4 40. 9 289.5 51.1 54-i 09.6 15 j 113. 20.0 75 172.3 30. 35 231.4 40. 9 290.5 51.2 ^ 09.7 16 114. 20 . i 76 173.3 30. 36 232.4 4 r. 9 291.5 5 r 4 56. I 09.9 17 11 5.2 20.3 77 174-3 3. 3V 233-4! 4' 9 292.5 51.6 tf 57- * JO. I 18 116. 10.5 78 175-3 30. 3^ 234 4 4i- 9 293.5 51-7 5<3 38.1 10.2 19 117. 20.7 79 i %6 . 3 31. 39 z-3 5 4 41. 9 294.5 ir-9 6c ^9 > i 10.4 20 118. 20.8 80 177-3 3i- 4 C 236 4 i 41. 30 295-^ ^ 52-1 Dif Dep. Lat Dif t Dep Lat. Dif t Dep. Lat DJf Dt^p. Lat Di Dep. Lat. for 80 Degrees. 1 TABLE II. Difference of Latitude and Departure for II Degrees. Dift' Lat. Dep. JDif Lat. Dep Dif Lat. Dip. fcif t Lat. Dep. Dift Lat. Dep. . i Joi.o a !o4.o O0.2 00.4 61 62 59-9 60.9 ii. 6 ii. b iz 2. u8.8 119.8 181 82 177-7 178.7 34-; 3*.; 241 256,6146.0 i <}4 ?. 3 ~ . ( ' 46 . 2 3 102.9 03 . 9 00.6 00.8 63 64 61.8 64.8 12.0 24 120.7 121.7 23-5 23-7 83 j 84 179.6 r8o.6 3S-* 4^ 2 3 S. : 44 ; 23-9. < 46.4 | 46.6 6 c 04.9 05.9 01. O 01. I 65 66 63.8 64 S I t2 "' 2 26 122.7 123.7 23.9 44.0 1 85 86 181.6 182.6 35 3 45 35.5 4^ 440.5 46.7 j 241.5(46.9 j 7 06.9 ! or. 3 6" 65.8 12.8 27 124.7 24.2 87 I r8'-.6 35-7 47 242.5 47 - * 8 y 07.9 oi . <; 68 66.8 13.0 48 125.6 24.4 88 184-5 35.9! 48 243.4 47-3 oS.8 01.7 69 67.7 17.2 29 126.6 44.6 89 1*5-5 36.1 49 244.4 47.5 10 09.8 01.9 70 68.7 j 13 4 30 I47.6J24.8 00 186.5 36-3 >o 24-4 47-7 1 1 10.8 02. I 71 69.7 13-5 13* 128. 6(25.0 191 187.5 36.4 2 5* 246,4 47-9 12 02.3 "7 70.7 13 7 3- 129.6 25.2 94 188.5 36.6 52 247.4 4^. i 13 12.8 02.5 73 71.7 13.9 33 130.6 25.^ 93 189.5 36.8 53 248.4 48.3 13.7 02.7 74 72.6 14.1 34 131.5 V5 6 94 190.4 37.0 54 2 49-3 4^.5 15 14.7 02.9 73 6 '4-3 35 132.5 25.8 9> 191.4 37-2 55 25.0-3 48.7 Tfi 03. 1 76 74.6 14.5 36 133-5 26.0 96 192.4 37-4 56 251.3 48.8 17 16.7 03.4 75-6 14-7 37 134.5 26 i 97 193.4 37.6 5" ' 252-: 49.0 18 17.7 03.4 76.6 14.9 38 135. 5 26.3 98 194.4 37.8 55 253.3 49.2 r 9 18.7 03.6 79 77-5 15-* 39 136.4 26.5 99 1 9 S 3 38.0 59 254.4 49.4 20 19.6 03.8 80 78.5 x 5-3 40 137.4 26. 7 .:oo 196. :; 38.2 t'O 255-2 4V- 6 21 20.6 04.0 8l 79-5 M.5 141 138.4 26 .9 201 97.3 38.4 2bi 256.2 49- S 22 21.6 04.2 82 80.5 15.6 42 139.4 -7.1 02 '98- 3 38.5 bz 257.2. 50.0 : 23 22.6 04.4 ^3 81.5 15.8 140.4 27.3 03 I 99-3 38.7 63 258.2 50. i 24 23.6 04.6 84 2.5.16.0 44 141.4 27- 5 04 200.3 38-9 64 459.1 50-4 : 24.5 04.8 85 83.4(16.4 45 142.3 27.7 5 201.2 39.1 ''5 460. i 50 . 6 ; 26 25. 5 05.0 86 84.4)16.4 46 143.3 27.9 06 2O2.2 39-3 66 261. i ^o. 8 27 48 26.5 27-5 05.2 53 87 88 85.4 86.4 16.6 16.8 47 48 r 44-3 28.0 28.2 07 08 203 . 2 2O4.2 39-5 39-7 67 68 462. i 263. i 50.9 L 51.1 49 28.5 05. 5 89 87-4 17.0 49 146.3 48.4 09 405.2 39-9 69 264.1 5i-3 i 30 29.4 05.7 90 88.3 17.4 5 147-2 28.6 10 206. T 40.1 70 265.0 5i-5 3 1 30.4 05. 9 91 89.3 17.4 151 148.2 28.8 211 207. I 40.3 -1 l 266.0 5i-7 32 31.4 06. i 90-3 17.6 52 149.2 29.0 12 20? . I 40.4 "2 267.0 51.9 33 06. 3 93 91.3 5} 150. ^ 49.2 13 209 . I 40.5 73 268.0 52. i .1 34 33-4 06.5 94 17-9 54 151.2 29.4 4 210. I 40.8 74 269*0 52-3 1 35 34-4 06.7 95 93-3 iS.z 55 152.2 29.6 15 41 I. O 41.0 75 269.9 52.5 J 3 6 35-3 06. 9 96 5 & 153.1 29.8 16 212. O 41.4 76 270.9 ^2 7 37 56.3 07.1 97 95.2! r8. 5 57 154.1 30.0 '7 213.0 41.4 77 271.9 52-9 37-3 07.3 98 96.2 18.7 58 155-1 30. i 18. -I4.O 41.6 7 s 472.9 53 o ! 39 07.4} 99 97.?. 18.9 59 156.1 3-3 '9 2I5.C 41.8 A 9 473-9 53-2 j 40 39-3 07.6 roo 19, i 60 I57-I 30.5 ?.o 216.0 41.0 So 274.8 S3-4 I 4 1 40.2 07-81 tor 99.1 19.31 If; I 158.0 30.7 241 216.9 44.2 281 275.8 5>>6 j 42 41.2 04 oo. i 19.5 62 159.0 30.9 22 217-9 42.4 82 476.8 ^3.8 ! 43 42.?. 08.2! 0} oi. i 19.7 63 160.0 3*i 23 218.9 4 .for 12 Degrees, Dift Lot, Dep r ibift Lat. Dep. Dift Lat. Dep. i Dift Lat. Dep. [Di ft ' Lat. .. -? Dep. i u.o 00.2 61 59-7 12.7! 1.21 118.4 25.2 181 177.0 37.6 24} 235-7 50.1 2 " 2 . O OO . 4 62 60.6 12.91 22 JI 9-3 25-4 82 178.0 37-3 42 2:56.7 50.3 ! 3 02.9 00.0 63 61.6 13 . i 23 120.3 25-6 83 179-0 38.0 43 237.7 5- 5 4 03.9 oo.a 64 62.6 13.3 24 121.3 25.8 84 1 8 o.o 38.3 44 50.7 5 04-9 OI .0 65 63.6 T 3 5 25 122.3 26.0 181.0 ^8.5 45 239-6 50.9 6 05.9 01.2 66 64.6 13.7 26 123.2 26.2} 86 181.9 38-7 46 240.6 51.1 7 06.8 01.5 67 65.5 13-9 27 124.2 26.4 87 182.9 47 241.6 51.4 8 07.8 01.7 63 66.5 14.1 28 125.2 26.6 83 183.9 39- * 48 242.6 51.6 9 08 . 8 01 .9 69 67-5 r 4-3 29 126.2 26.8 89 184.9 39-3 49 243.6 51. S 10 09.8 02.1 70 68.5 r.|.6 30 127.2 27.0 oo 185.8 39 -5 244-5 52.0 ii 10. 02-3 7* 69.4 14.* i:i 128.1 27. 2 I 191 186. 8 39-7 - x 245-5 52.2 12 1 1. 7 02 5 72 70.4 15.0 32 129. i 27.4J 187.8 39-9 52 246.5 52.4 13 12.7 02.7 73 ~i-4 15.2 33 130.1 27.7 93 188.8 40.1 53 247.5 52.6 J 4 13-7 02. 9 74 7^.4 r 5-4l 34(131-1 27.9 94 189.8 4-3 54 248.4 52.8 15 14.7 03.1 75 73'4 15.6 J5{.*S*Q 28.1 95 190.7 4-5 55 249 4' 53- 16 15-7 03-3 76 74 3 15.8 36 133-0 28. 3 96 1,91.7 40.8 56 250.4 53-2 17 16.6 03-5 77 75-3 16.0 37 134.0 28.5. 97 192.7 41,0 251-4 53-4 18 17.6 03 7 7^ 76.3 16.2 3? 135.0 193.7 41.2 S^ 252-4 53-6 19 18.6 04 . o 79 77-3 16.4 39 136.0 28.9 99 194.7 41.4 59 253-3 53-8 20 19.6 0-1.2 80 78.3 1 6. 6 40 1 3-6 9. 29.1 200 195.6 41.6 60 254-3 54.1 21 20.5 04.4 81 79.2 1-6:8 141 137-9 -') -3 201 196.6 41 .8 261 255-3 54-3 22 21.5 04.6 82 80.2 17.0 42 138.9 29.5 O2 197.6 42.0 62 256.3 54-5 23 22.5 04.8 83 81.2 17-3 43 139-9 29.7 03 198.6 42.2 63 257.2 54-7 24 23-5 O5.0 84 82.2 r 7> 5 44 140.9 29.9 04 '99-5 42.4 64 258.2 54-9 *5 24-5 05.2 8; 53-1 J 77 45 141. .8 30.1 oq 200,. 5 42.6 259.2 55-i 26 25.4 05.5 ^6 3 4 .i 17.9 46 142.8 30-4 06 201.5 42. 8 66 260.2 55-3 27 26.4 05.6 87 85.1 iS.i 47 143.8 30.6 07 202.5 43-0 67 26l .2 55-5 28 27-4 05. ft 33 86.1 r8.3 48 144.8 30.8 o3 203.5 43-2 68 262.1 55-7 29 23.4 O6.O 89 -57.0 18.5 49 14 v 7 31-0 09 204.4 43-5 69 263. I 55-9 30 29.3 06.2 ,90 38.o 18.7 <;o 146.7 31:2 10 205.4 43-7 70 264.1 56.1 31 30.3) 06.4 91 89.0 i3. 9 '5i I47.7 31.4 211 206.4 43-9 271 265. \ 56.3 32 31.3 06. 7 92 90.0 19.1 52 148.7 31.6 12 207.4 44.1 72 266.1 56.6 33 3 a 3 06.9 93 91.0 19-3 53 H9-7 31.8 13 208.3 44-3 73 267.0 56.8 34 33-3 07.1 94 91.9 19.5 54 150.6 32.0 H 209.3 44-5 74 268.0 57-o 35 34.2 07.3 95 92.9 19.8 55 151.6 32.2 210.3 44-7 7-5 269.0 57.2 36 35-2 07-5 96 93-9 20. 56 152.6 32-4 J ,211.3 44.9 76 270.O 57-4 37 36.2 07.7 97 94.9 20.2 57 153.6 32.6 T 7 212.3 45-i 77 270.9 57-6 3 37-2 07.9 98 95-9 '.0.4 58 154-5 32-9 18 213.2 45-3 7-8 271.9 57-8 39 3$. 'i 05.1 99 96.* ic.6 59 -55-5 33-i 19 214.2 45-5 79 272.9 ^8.0 40 39.1 08.3 too 17.8 20. . 60 156 5 31-3 20 215.2 45-7 80 273-9 58.2 i 4I 40.1 08.5 101 98.8 21 .O 161 157.5 33-5 221 216.2 45-9 281 274-9 58.4 42 41.1 08.7 02 99.8 11.2 62 158. 5 33-7 22 217. 46.2 82 275-8 58.6 43 42. i 0^.9 Oj io>. 7 21-4 63 159.4 33-9 2l3. 46.4 83 2-6.8 58-8 44 43.0 Gl) . T 4 101 . 7 21.6 64 162-4 24 219. 46.6 84 277,8 ^9.0 45 44' 09.4 -5 TO2 . 7 21.8 6; 161.4 '34-3 i q 220. 46.8 S5 2-3.8 59-3 j 46 i i o 09 . 6 o>, '03-7 22. O 66 162.4 34.5;; 26 221. 47-o 86 279.?: 59-5 47 46 . o 09.8 7 104.7 22.2 67 163.4 34.78 27 222. O 47-2 '87 280.7 59-7 4* 47-o 10. G c.8 105.6 22 . 'j 63 164. 3 34-9 2S 223.0 47-4 88 | 2*1. 7 59-9 49 47-9 10.2 09 106.6 -'-2. 7 .69 165. : 35-i | 29 224.0 47.6 89 [282.7 60. i 5 .-,8.9 JO. 4 JO IO7.6 22.''. 70 166.3 35-3 225.0 47.8 90 23;. 7 60.3 51 !> ) 10.6 in ro$.6 23.1 t 7 i 167.9 35-6 231 226.0 48.0 291 284'. 6 60.5 52 50.9 ro.3 12 109.6 2.3.3 72 168.2 358 32 226:9 48.2 92 285.6 60.7 53 Si. 8 II. O 13 no. 5 23.5 169.2 36.0 33 227-9 48.4 93 286.6 60.9 54 II. 2 14 111.5 23.7 74 170.2 36-2 34 228.9 48.7 94 287.6 <9I.I 1 5 s. 53.8 II.4 M 112.5 23-9 171.2 35 229.9 48.9 95 288.6 6l.3 5-6 54-S ii. 6 16 II3-5 24.1 76 172,2 36.6 36 23O.8 49- J 96 289.5 61.5 i 57 55,- II..) 17 114.4 77 I73-I 36/8 37 23 1. S 49-3 97 290.5 61.7 58 56.7 12. I 18 115.4 24. <; 78 I74.I 37.0 38 232.8 49 o 291.5 2.O 5? 57-7 12.3 19 116.4 24.7 79 175 . i 37-2 I .39 233.8 49.- 99 292.5 62.2 6p 58.7 12.5 20 117.4 24.9 80 I 7 6.I 37-4 40 234,8 49.9 300 293-4 62. 4 { Dift Dep ? Lat. Dift Dep. Lat. Dift Dep. Lat. Dift Dep. Lat. Dif Dep. Lat. i for 78 Degrees. TABLE II. Difference of Latitude and Departure for 13 Degrees. Dift Lat. ! Dep. Dift Lat. Dep. 35ft Lat. Dep. ! Dift Lat. Dep. Dift Lat. Dep. 1 i 01. OC.2 61 59-4 13.7 [21 17.9 27.2 1*1 176.4 40.7 241 34-* 54-* ! 2 01.9 00-4 62 60.4 13.9 22 18.9 27.41 82 177-3 40.9 42 *3$.8 54-4 \ 3 02.9 00.7 63 61.4 14.2 23 19.8 27 .7 i 83 '78.3 41.2 43 2^6.8 54-7 : 4 3-9 00.9 64 62.4 14.4 24 20.8 27.9'; 84 J79-3 41.4 44 54-9 i 5 04.9 01. I 65 03-3 14.6 25 21.8 2 S . I 85 rSo. 3 41.6 45 _^S . 7 6 05.8 01.3 66 64.3 14.8 26 122.8 28.3 ^0 lSl.2 41.8 46 239. 7 - - _ j 7 06.8 01.6 67 65.3 5-"i 27 23-7 28.6 87 182.2 42.1! 47 240.7 8 07.8 01.8 68 66.3 1 5 3 28 124.7 28.8 88 183.2 4-- 3 j 4 8 9 08.8 02. o 69 67.2 15-5 29 125.7 29.0J 89 184.2 42.5 49 242,6 56.0 ( 10 09.7 02.2 70 6S.2 r 5 . 7 3 126.7 2 9 . J 90 I85.I 42.7- 5 243 . 6 ii 10.7 02.5 71 69.2 16.0 f3I 127.6 29.5 191 186.1 43 -Q 251 244.6 5^-5 ! 12 11.7 02.7 72 70.2 16.2 32 128.6 29.7 92 ffy.i 43-2) S2 245.5 13 12.7 02.9 73 71.1 16.4 33 129.6 29.9 93 I'iS.i 43-4 S3 246.5 56.9 H 13-6 03.1 74 72.1 16.6 34 130.6 30.1 94 189.0 43-6 H7-5 57.1 : 15 14.6 03.4 75 73- 1 - 16.9 35 131.5 30.4 95 190.0 43-9 55 248.5 ' *6 15.6 O 3 .b 76 74.1 17. I 36 1 3 2 5 30.6 96 191.0 44.1 5" 249-4 57-6 1 17 16.6 03.& 77 75-o *7- 3 37 i33o 30. S 97 192.0 44-3 57 250.4 J7-8 : 18 17-5 04.0 78 76.0 17-5 38 *34-5 31.0 98 192.0 44-5 & 251.4 SS,o 1 V 18.5 04 3 79 .77-0 17.8 39 '35-4 3'- 3 99 193-9 44.8 S9 252.4 20 19.5 C4-5 80 78.0 18.0 40' 136.4 31-5 200 194-9 45-o 60 253.3 58 5 21 20.5 04.7 81 78.9 18.2 141 r 37-4 3 ' 7 201 195.8 45.2 261 2 54-3 5S/" I 22 21.4 04.9 82 79-9 18.4 4 2 138.4 3^-9 02 196.8 45.4 62 58.9 23 22.4 05.2 83 80.9 18.7 43 r 39-3 32.2 03 197.8. 45-7 63 256.3 59 *-j 24 23-4 05.4 84 81.8 18.9 44 140.3 32.4 04 198.8 45-9 64 257.2 25 24.4 05.6 ^5 82.8 19.1 45 141-3 32-6 0.5 199.7 46.1 258. -2 ^9.6 26 25-3 05.5 Kb 83.8 79.3 46 142.3 .32.8 06 200.7 46.3 66 259.2 59.8 27 26.3 06. i 7 84.8 19.6 47 143.2 33 * 07 201.7 46.6 67 260.2 60. i 28 27.3 0*6.3 88 85-7 19.8 48 144.2 33-3 08 202.7 46.8' 68 26l.I 60.3 29 28.3 06.5 8<] 86.7 20. o 49 145.2 33-5 09 203.6 47.0 69 262. I 60.5 30 29.2 06.7 1 90 87.7 20 .1 5 146.2 33-7 10 204.6 47-2 70 263.1 60.7 31 30.2 07.0 9i 88.7 20.5 151 147.1 34.0 211 205.6 47.5 27 1 264.1 6 1 . o | 32 31.2 07.2 92 89.6 20.7 52 148.1 34 - : - 12 206.6 72 265.0 61 a ! 33 32.2 07-4 93 90.6 20.9 53 149.1 34-4 13 207.5 47 '; 73 266.0 61.4 34 33-i 07.6 94 91.6 21. I 54 150. i 34.6 H 200.5 4 S.i 74 267.0 61.6 33 34- l 07.9 95 92.6 21.4 55 151 .0 34-9 I 5 209.5 48.4 75 268.0 61.9 3^ 35-i 08. i 9 b 93-5 21.6 =>6 152.0 10 210.5 48 . 6 1 268.9 37 36-1 08.3 97 94-5 21.8 57 153.0 35-3 17 211.4 48.8 17 269.9 6a . 3 i 3* 39 37-o 38.0 08. 5 08.8 98 99 9S-5 96-5 22.0 22.3 5* 1 54 . o '54-9 35-5 35.* 18 19 212.4 213.4 49.0 49 3 270.9 27T.O : 1 40 39.0 09.0 100 97-4 22.5 60 '55>9 36.0 20 214.4 49- S So 272.8 63.0 ; i 4 1 39-9 09.2 IOJ 98.4 22.7 161 156.1; 36.2 Z2I 215.3 49-7 281 2 73. * 6?-'2 ! 42 4 -9 09 ,t 02 99-4 22.9 62 157.8 36.4 22 216.3 49-9 82 274.8 - 43 41.9 09.7 1 O' 100.4 23.2 6? 158.8 36.7 23 217.3 50 . 2 83 27^.7 6j.7 144 42.9 09.9 4 101.3 23.4 64 '159.8 36-9 24 218.3 50.4 84 -76.7 67.9 , 45 43-8 IO.I 05 102.3 2 3 . h 6; 160.5 37-i 2S 219.2 50. ( 85 -77-7 46 44 > IO. '. 06 103.3 23 .8 66 161.7 37-3 26 22O. 2 50.8 86 178,7 47 45. bJ 10.6 07 104.3 24.1 67 162.7 27 221.2 51.1 S7 279.6 64.6 48 46. * 10.8 08 105.2 24.3 6J 163-7 37-8 28 222.2 51 . 5 280.6 64 ? 49 47-7 II. 09 106.2 69 164.7 38.0 29 223.1 89 281.6 65.0 j 5o 48.-^ II. 2 10 107.2 24.7 70 165.6 38.2 33 224.1 51.7 | 90 282.6 : 5 J 49-7 II-5 III 108.2 25.0 171 166.6 3S-5 231 2/5-1 S2.0 [291 283.5 ( '5-5 i 53 54 50.7 51.6 52.6 II-7 II-9 12. I 12 Ij I/ 109. i IIO. I III. I 25.2 25.4 25.6 72 73 74 167.6 168.6 38. 7 38.9 39-1 32 33 34 J226. I 227.0 220 .O 52.2 52.4 52.6 92 93 284.5 285.5 286.5 65.7i 65.9 I 66.1 5. 53 '* 12.4 15 112. I 25.9 / > 170.5 39-4 35 22Q.O 52.9 9S 287.4 66.4 ' 56 54.6 12.6 16 II3.0 26.1 76 171.5 39 - 6 36'; 270.0 66.6 57 58 55-5 56.5 iz. 8 13-0 17 1 8 JI4.0 115.0 *6.*5 77 172.5 173.4 40.0 37 230.9 3*-9 53 3 53 -f 97 98 2?9-4 290.4 66.8 67.0 1 59 60 gj T 3-3 19 20 II6.0 116.9 26.8 27.0 79 80 174.4 40.3 40.5 39,232.9 40 233.8 54-o 99 300 291.3 292.3 67-3^ 67.5; |Dif Dep. Lat. ;Dif Dep. Lat. Dif Dep. Lat. Dift Dep. Lat. 'DM Dep. Lat. : y for 77 Degrees. TABLE II. Dinerence of Latitude and Departure for 14- Degrees, Dift Lat. Dep. Dif Lat. Dep. Dif Lat. Dep. Di Lat. Dcp. Dif t Lat. Dep. i OI.O 00.2 61 59.2 H.S 121 117.4 29.3 181 175.6 43.8 241 231-& ;sT?! 2 01.9 00. S 62 60.2 15.0 22 118.4 *9-5 82 176.6 44.0 42 234.8 58.5 3 02.9 00.7 63 61.1 15.2 23 1/9.3 29.8 8- 177.6 44-3 43 235- s 58.8 4 3-9 01 .O 64 62.1 '5-5 2 4 ^20.3 30.0 g^ 178.5 445 441*36-8 59.0 c 04.9 ,01.2 6S 63.1 IS-; 2S T2I.3 30.2 *S 179- 44. b 45 237.7 59.3 6 05.8 i-5 66 64.0 I&.O 26 I2i-3 30.S 86 i So- 45*0 46 a*8.7 59.5 7 06,8 01.7 67 65 o 16.2 i 27 123.2 30.7 "8? 181.4 45- * 4" 239-7 59-8 8 it k / . 01.9 68 66.0 16.5 28 124.2 31.0 88 182.4 45-5 48 240.6 60.0 9 OH. 7 02.2 69 67.0 16.7 29 125.2 31.2 89 i3.4 45'7 49 241.6 60.2 10 C9.7 02.4 70 67.9 16.9 30 126. t 31-4 90 184.4 46.0 j 50 242 6 60.5 ii 10. ; 02.7 7i 68.9 17.2 rv I27.I 3L7 191 185.? 46.2 2^1 243.5 60.7 12 u. 6 02.9 72 69.9 17.4 3* I2S.I 3 '-9 92 186.3 46.4 5* 244,5 61.0 i 13 12.6 03.1 73 TO. 8 17-7 33 129.0 32.2 9T 187.3 46.7 53 2 45-5 61.2 i 14 13-6 3-4 74 71.8 17.9 34 130,0 3Z-4 94 i88.z 46.9 54 246.5 61.4 15 14.6 03.6 75 72.8 18.1 35 131 o 32-7 95 189.2 47-2 SS 247.4 6i. 7 | 16 15-5 03.9 76 73-7 18.4 36 132.0 3*. 9 96 190.2 47-4 S6 248.4 6r.9J 17 16.5 04.1 77 74-7 18.6 37 132.9 33-i 97 191.1 47-7 57 249.4 62. 21 18 17-5 04.4 78 75-7 18.9 38 133-9 33-4 98 192. i 47.9 58 250.3 62-4! 19 it.4 04. 6 79 76.7 19.1 39 U4-9 33-6 99 193.1 4 3.i 59 251-3 62.7J 20 19.4 04.8 80 77-6 19-4 40 135.8 33-9 200 194.1 48.4 60 25^-3 62. 9 | 21 20.4 Of. I 81 3TT6 19.6 141 136.8 34>* 2OI 195.0 48.6 261 53' 63-1 ! 22 21. 1 Of. 3 82 79.6 19. 42 137.3 344 02 196.0 48.9 62 254.2 63.4' 2.1 22-3 05.6 83 80.5 20.1 43 138.8 34-6 03 197.0 49.1 63 255-* 63.6 *4 23.3 o S . 8 84 81.5(20.3 44 139-7 34-8 04 197.9 49-4 64 256.2 63.9 *5 24-3 06.0 8s 82.5120.6 45 140.7 35-1 OS 198.9 49.6 65 257.1 64.1 26 25.2 06.3 86 i*.* 20. 8 46 141.7 35-3 06 199.9 49.8 66 258.1 64.4 27 26.2 06.; 8? 84.4 21.0 47 142.6 35.6 C7 200.9 50.1 67 259.1 64.6 ! 28 2~. 2 06.8 88 8s. 4 21-3 48 143.6 3S.8 08 20 1. 8 50.3 63 260.0 64.8 29 2S.J 07-0 89 86.4 21. S 49 144.6 36.0 09 202.8 50.6 69 261 .0 6 5 . i j 30 2q.J 07.3 00 87.3 21.8 5o 145-5 36.3 10 203.8 50.8 70 262.0 65-3 ! 3' 30.1 07.5 9 1 88.} 22.0 '5i f 4 6. 5 36. S 211 204.7 51.0 271 263.0 6s- 6 { 3* 31.0 07.7 92 29-3 22.3 52 r 47-5 36.8 12 205.7 51-3 72 263.9 6|.8 j 33 32.0 08.0 93 90.2 22.5 53 148.; 37-0 13 206.7 5LS 73 264.9 66.0; 34 33-0 08.2 94 91.2 22.7 54 149.4 37-3 H 20T.6 51.8 74 265.9 66.3! 35 34- 08.5 95 92.2 23.0 55 i SO. 4 37. 5j IS 208.6 52.0 75 266.8 66.5! 36 34-9 08.7 96 93-i 2^.2 56 151-4 37-7' 16 20.9 . 6 52.3 76 267.8 66.8: 37 35-9 09.0 97 94.1 23-5 57 i5*-3 38.0! 17 210.6 52-5 77 268.8 67.0! 38 36.9 09.2 98 95.1 23.7 58 '53-3 38.J 18 211,5 5*-7 7<> 269.7 67-3! 39 37.8 09.4 99 96,1 24.0 59 154.3 38. s 19 212.5 53-0 79 270.7 7o 40 S3.9 09.7 IOO 97.0 24.2 60 155-2 3t7 20 213.5 53- i 80 271-7 67.7 41 JM 09.9 101 98.0 24.4 161 156.2 3*. 9 221 -14-4 53-5 281 272.7 62 .0 42 40.8 IO.2 O2 99.0 24.7 62 I57-* 39.2 22 215.4 53.7 82 273-6 8.2 43 41.7 10-4 03 99.9 24.9 63 158.2 39-4. 23 216.4 53-9 8? 274.6 8-5 44 L2 7 10.6 04 00.9 2S-2 64 159.1 39'7 24 217.3 54-21 84 275-6 8.7: 45 43-7 10.9 os 01.9 iS -4 6S 160. i 39-9 *S 218.3 54-4 8s 276.5 63. 9 : 46 44.6 ii. i 06 02.9 2S-6 66 161. i 40,2 26 219.3 54-7 86 277-5 69.2 ; 47 45.6 11.4 07 03.8 25.9 67 162.0 40.4; 27 20.3 54-9 8? J78.S 69.4 48 46.6 ii. 6 08 04.8 26.1 68 163.0 40.6! 28 21.2 55.2 88 279-4 6 9 7 . 49 47- <; 11.9 09 os. 8 26.4 6 9 164.0 40.9 2 9 22>2 55-4 89 z8o. 4 69.9 ; 50 48.5 12. I 10 06.7 26.6 70 164.9 41. ij 30 23.2 55.6 90 281.4 70.2 i 5i 49- 5 12-3 in 07.7 26.9 171 165.9 4.1.4 231 24.1 55.9 291 282.4 70.4, 52 $0.5 12.6 12 08.7 27.1 72 166.9 41.6 32 225.1 Si.i 92 a*3-3 70.6 53 54 12.8 13 09.6 27-3 73 167.9 41.9 J3 26.1 56.4 93 2*4-3 70.9 54 52.4 13.1 H 10.6 27.6 74 16.8.8 42.1 34 27.0 56.6 94 2*5-3 71.1 55 53-4 '3.1 l| ii. 6 27.8 75 169.8 42-3 35 28.0 56.9 95 286.2 71.4 56 54-3 '3-5 16 12.6 zS.i 76 170.8 42-6 36 29.0 57.1 96 287.2 71-6 57 $$3 M.8 17 '3-5 28.3 77 171.7 42.8 37 23O,0 57.3 97 288.2 7 r. 9 58 58.3 14.0 iS 14.5 28.5 78 I72. 7 43-i 38 30.9 57-6 98 289.1 72-1 59 57.2 '4-3 '9 '5-5 28.8 79 173-7 4V3 39 31-9 57-8 99 290.1 72-3 60 58.2 14. < 20 16.4 29.0 80 *74-7 43-5 4 32. 9 58.1 3o 291 . i 72.6 Dif> !>ep, Lat. Dift' Dcp. Lat.) Dift |Dcp. Lat. Dift! Dep. Lat. Dift Dep- Lat. for 76 Degrees, Dift: Lat. Dep. fcift Lat. Dep. Dift Lat. Dep; Dift Lat. Dep. Djf J-at. Dep. I OI .O 00.3 61 58.9 15.8 in 116.9 31.3 181 174.8 46.8 241 232.8 62.4 2101.9 00.5 62 59-9 16.0 22 117-8 ji.2 82 175. S 47.1 4* *33-8 62.6 3JOJ.9 00.8 63 60.6 t6. 3 23 118.8 31.8 83 176,8 47-4 43 234-7 62.9 4 03-9 01. 64 61.8 16.6 24 119.8 32.1 84 177-7 47-6 44 35-7 63.2 5 04-8 01.3 65 62.8 16.8 25 120.7 32 '4 85 17*. 7 47.9 45 236,7 63.4 6 05.8 01.6 66 63.8 17.1 7.6 121.7 32.6 86 179-7 48.1 46 237.6 63.7 7 06.8 01.8 67 64.7 J 7.? 27 T2Z.7 3 Z '9 87 180.6 48.4 47 238.6 63-9 b 07-7 02.1 68 6S- 7 17.6 28 I2J.6 3 J-i 88 r8i.6 4*-7 48 239.5 64. 2 9 oS. 7 02.3 69 66.6 17.9 29 124.6 33-4 89 182.6 4*-9 49 240.5 64.4 10 09.7 02.6 70 67.6 18.1 30 125. ( 33-6 9 3-5 49.2 50 241.5 64.7 ; 1 1 10.6 J02.S 1 7I 68.6 18.4 131 1*6.5 339 191 184.5 49-4 251 242.4 65.0 12 it. 6 03.1 72 69.5 iS.6 3 2 127.5 34-i 92 iS 5 . 5 49-7 5* *43-4 65-* 13 12.6 03.4 73 70.5 18.9 33 128.5 344 93 186.4 50.0 53 244.4 6 5 -5 *4 13-5 03.6 74 71-5 19.2 34 129.4 34-7 94 187.4 50.2 54 2 45'3 65-7 15 14.5 03.9 75 7*. 4 19.4 35 130.4 34-9 95 188.4 50.5 55 246.3 66.0 16 15.5 04.1 76 73-4 I 9 .7 36 131.4 35.2 96 189.3 50.7 5 247.3 66.3 17 16.4 04.4 77 74-4 19.9 37 132.3 355 97 190.3 51.0 57 448.2 56. 5 18 17.4 04.7 ?3 75 3 20.2 38 133-3 35-7 9* 191.3 51-2 '58 249.2 66. 8 1 *9 18.4 04.9 79 76. 3 20.4 39 134-3 36.0 95 192.2 5L5 59 250.2 67.0 2-O 19-3 05.2 80 77-3 20.7 40 r.35-2 36.2 200 193.2 51.8 60 251.1 67-3 I 21 20.3 05.4 81 7*. 2 21.0 141 136.2 36.5 20 t 194.2 52. 261 252.1 67.6 22 21.2 05.7 82 79.2 21.2 42 137-2 .36.8 O2 195-1 52.3 62 253-1 67.8 23 22.2 06.0 83 80.2 21.5 43 138.1 37-0 3 196. i $*'"$ 63 254.0 68.1 1 24 23.2 06.2 84 81.1 21.7 44!i39.i 37.3 04 197.0 S2.8 64 255.0 68.3 1 25 S4.I 06.5 *5 82.1 22. O 4< 140, r 37-5 o^ 198.0 53.1 65 256.0 68. 6j 26 Z5.I 06. 7 86 8.3.1 22.3 46 141.0 37-8 06 199.0 5.3-3 66 256.9 68.8 27 -6.1 07.0 fe 84.0 22. 5 47 142.0 ,8.0 07 199.9 53 6 67 257.9 69. i 28 27-0 07.2 88 85.0 22.8 48 143.0 38^3 08 200.9 53-8 68 258.9 69.4 29 *8.o 07.5 8 9 86.0 23.0 49 H3.9 38.6 09 20 r . 9 54.1 69 2^9.8 69.6 30 29.0 07.8 90 86.9 23-3 5o 144.9 38.8 I O 202.8 54-4 70 260-8 69.9 3* 29.9 08.0 9i 87.9 23-6 >1 r 45'9 39.1 21 1 203.8 54-6 -~i 261.8 70.1 : 3* 30.9 08.3 92 88.9 2 3 .* S 2 146.8 39 3 12 204.8 54-9 72 262.7 70.4 33 31.9 oS.s 93 89. 3 Z4.1 53 147.8 39- 6 13 >5' 7 55i 73 263-7 70.7 34 32.8 08.8 94 90.8 24.3 54 148.8 39-9 M 206. 7 55-4 74 264.7 70.9 35 33.8 09.1 95 91.8 24.6 55 149.7 40. i is 207.7 55-6 75 265.6 71.2 j ! 36 34-8 09.3 96 92.7 2 4 .* 56 150.7 40.4 16 208.6 55-9 76 266.0 71.4! 37 35-7 09.6 97 93-7 aS'i 57 151.7 40.6 I? 209.6 56.2 77 -67.6 7L7 j J 36.7 o;.8 98 94' 7 2.5.4 S 8 152.6 40.9 18 210. 6 56.4 78 268.5 72.01 J9 37-7 10. I 99 95.6 2,'. 6 59 153-6 41.2 19 211.5 56.7 79 269.5 72.2 40 38.6 10.4 100 96.6 21-9 60 I54J 41.4 20 7.12.5 56.9 80 270.5 72. 5| 4i 39-6 10.6 roi 97-6 26.J 161 55.5 41.7 221 213.5 57.2 81 271.4 72.7 41 40.6 10.9 02 93- 5 26.4 62 r 56-5 41.9 22 214.4 57-5 82 272.4 73.0 43 41.5 n.i 03 99-5 26.7 63 *57.4 42.2 *3 215.4 57.7 81 -73.4 73-2 44 42.5 11.4 04 100.5 26.9 64 158.4 42.4 24 216.4 S3.o 84 274-3 73-5 45 43-5 ri. 6 05 101.4 27.2 6* 159.4 42.7 25 217.3 58.2 8s 275.3 73-3 4-b 44.4 11.9 06 1 IO2 .4 27.4 66 160.3 43.0 26 218.3 ^ 5 86 276.3 74-o 47 45 4 12.2 07 103.4 27-7 6; 161.3 43.: 27 219.3 S8.8 8? 277.2 74-3 45 46.4 11.4 08 104.3 28.0! 68 162.3 43-5 :8 220.2 59-Oi 8i 278.2 74-5 49 47-3 12.7' 09 105.3 28.2 69 163. 2 43.7 29 221 .2 593 89 279.2 74-8 50 4M 12-9 10 106 . 3 28.5 70 164.2 44-s 30 22?. - 2 59- 5, 90 280.1 7 ;.i! 5i 49 -i 13.2 11 1 107.2 28.7 7i 165.2 44-3 1' 22 3 I 59.6 291 281.1 75-3 ! 52 50.2 35l 12 ro8.2 29.0 72 166. i 44. ; it 224.1 60. c ' 9 2 282.1 75.6 53 Sr.a 13-7 13 ; rog. i 29.2 73 167. i 44-8 33 22 S. I 60.3 93|2?3.o 75-8 54 52.2 14. o{ 14; i 10. i 29.5 74 i 63 . i 4S-o 34 226.O 60.6 94 284.0 76.! 55 53-1 14.4 Is i III. I 29.8 75 169.0 45-3 35 227.0 60.8! 95 284.9 76.4 5 6 54.1 '4*5 l6 112.0 30.01 76 170.0 45 .6 36 228.0 61.1 . 96 285.9 76. 6 57 55-i r 4 .i| I7jii3.o 30-3 77 171.0 45- S 37 228.9 61.3 97 286.9 7 6 -9 : { .Sa 56.0 15.0 i| M 4 .o 30.5! 7* 171.9 46.1 38 229.9 6 1 . 6 ' 9* 287.8 77.1 59 57-o| rS-3 191 114-9 30.8 79 172-9 46.} 39 l^O.g 61.9 9Q 288.8 77.4 60 | ^X .0 15-5! 2oj 115. q 31.1 g c 173-9 46.6 40 231. S fctVT loo 289-8 77-6 BiftJDep.i jLat. i Dift' Dep. LatT Diftl be p. UtT Dift Dep. Lat. flDift Dep. l.at. tor 75 Degrees TA BLE II. Difference of Latitude and Departure for 16 Degrees. 'Dift La,.' Dep. Dift Lat. Dcp. jjoift Lat. Dep. Dift Lat. Dep. Dirt Lat. Dep. * 01. 00.3 61 s*. 6 1 6 . S 121 116.3 33-4 181 174.0 49.9 241 231-7 66 .4 2 01.9 00.6 62 59 -6 17.1 22 117-3 33-6 82 174.9 50.2 42 232.6 66.7 3 02.9 00.8 b 3 60.6 17.4 2 3 IlS.2 33-9 83 !/5-9 5-4 43 233.6 67.0 4 03.* or. i 04 61.5 17. b 24 II9.2 34- 2j 84 176.9 50.7 44 234-5 67.3 5 04.8 01.4 $5 6z. 5 17.9 25 120.2 34-5 8s 177.8 51.0 4S 235-5 67.5 6 05.8 01 .7 66 63.4 15.2 26 I 2 I . I 34-7 86 178.8 5 T -3 46 2^6. s 67.8 7 06.7 01.9 67 64.4 18.5 27 122. I 35-o 8 ? 179.8 5i-5 4? 237.4 68. r S 07.7 03.2 6b 65.4 I8. 7 28 123.0 35.3 88 180.7 Si. 8 48 232.4 68.4 ; 9 o8..1 02-5 69 66.3 ig.O 29 124.0 35-6 89 181.7 52.1 49 239-4 63.6 ! 10 09.6 02.8 70 67-3 19-3 30 125.0 35.8 9 182.6 52.4 5 240.3 68.9 1 " 10.6 OJ.O 7 1 68.2 19.6 131 ^5.9 36.1 191 183.6 S2.6 151 241.? 69.2 12 ii. 5 03.3 72 69. 2 19.8 32 126.9 3<>-4 92 184.6 52-9 52 242:2 69.5 13 IZ.5 03 6 73 70.2 20.1 33 127.8 36.7 93 i85'5 53-2 S3 243.2 69*7 *4 H 5 03.9 74 71*1 20.4 34 128.8 36.9 94 r 6 6 . z, 53-5 54 244.2 70.0 15 14.4 oi.i 7 C , 72.1 20.7 35 129.8 37.2 95 187.4 53-7 55 2415.1 7. 3 16 15.4 04.4 76 73-i 20.9 36 130.7 37-5 96 188.4 54- 56 246.1 70.6 ! i 17 i..3 04.7 7" 74.0 21.2 37 1 >*-1 97 i$9-4 54-J 57 247.0 70.8 : i'- *73 O'.O 78 .75-0 2!. 5 3^ 132.7 3^-0 98 190.3 54- 6 58 248.0 71. r 1 I9 18.3 05.2 79 75-9 *I.S 39 133.6 38.3 99 W'l 54-9 59 249.0 71.4 , 20 19.2 05.5 So 76.9 22. I 40 134.6 38.0 200 192.3 55-i 60 249.9 71.7 2.) 20. a 05.8 81 77-9 a*.3 H- r 35--: 3^-9 20 1 193.2 55*4 261 250.9 71.9 i *2 21. I 00. 1 82 78.8 22.6 42 136.5 39- 1 02 194.2 55-7 62 251.9 72.2 23 22.1 06. 3 H3 79-8 J2.9 43 137.5 39-4 03 I95- 1 56.0 63 252.8 72.5 14 2.?.0 06.6 84 So. 7 23.2 44 138.4 39-7 04 196.1 56.2 64 253-8 72.8 *5 24-0 06.9 85 81.7 23.4 f? T 39-4 40.0 OS I97.I 56.S 6s 254.7 73.0 26 Z5.O 07.2 86 S2. 7 23-7 46 140.3 40.2 06 198.0 56.8 66 255-7 73-3 -7 2(5.0 07.4 87 83.6 M t 47 Hi-3 40.5] 0? 199.0 57.i 67 256.7 73.6 28 26.9 07.7 ss 84.6 24>3 4^ 142-3 40.8] 08 199.9 57-3 68 257.6 73-9 2 9 27.9 08.0 8 9 8,. 6 24.5 49 143.2 41.1) Oq 200.9 57.6 69 258.6 74.1 30 28.8 05.3 90 fcb-5 24.8 5 144.2 4i-3 10 201.9 57-9 70 259.5 74-4! 3i 29. S 08.5 91 87. < 25.1 145.2 41.6! 211 202.8 58.2 2/1 260.5 747 32 30. S 08.8 92 bS. 4 25.4 146.1 41.9 12 203.8 S-4 72 261. s 75-0 33 3'. 7 09. 1 93 89.4 S .6 ^47.T 42.2 13 204.7 58.7 73 262.4 75-2 34 S*-7 09 4 94 90.4 25.9 54 148.0 42.4 H 205.7 59o 74 263.4 75-5' 3> IV* 09.6 95 91.3 26.2 55 149 . o 42.7 IS 206. 7 59-3 7S 264.3 75.8 36 54.6 09.9 9 o 9*o 26. c 56 150.0 43.0 16 207.6 59o 76 265.3 76.1 37 35-6 10 2 97 93-2 26.7 57 250.9 43 3 17 208.6 S9-8 77 266.3 76.4 3? 36.5 10. 5 95 94.2 27.6 5* 151.9 43.6 18 209.6 60. i 78 267.2 76.6 39 37-5 10.7 99 95.2 27.3 59 ISZ.8 43.8 19 210.5 60.4 79 268.2 76.9 -4- .|8j II. 100 96. i 27.6 6c 153.8 44.1 20 211.5 60.6 ^0 269. 2 77-2 4i 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 ir. 6 02 98.0 28.1 62 155-7 44-7 22 *i3-4 61.2 82 27I.I 77-7 43!4i-3 11.9 03 99.0 28. 4 63 156.7 44-9 23 214.4 6r.s 83 272.O 78.0 44,42.3 I 2- I 04 IOO.O 28.7 64 157.6 45.2 24 215-3 61.7 84 273.0 78.3 -45' 45- 3 i 12 -4 05 100.9 28.9 6^ 158.6 455 25 216-3 62.0 85 274.0 78.6 46 44 .' *a7 Ob ioi .9 29.2 66 159.6 45.8 26 217.2 62.3 86 274-9 78.8 47145'* 48(46.1 13.0 13.2 07 08 102.9 rc 3 .8 *9-5 29.8 67 68 160.5 161 .5 46.0 46.3 27 28 218.2 219.2 62.6 62.8 87 88 275-9 276.8 79-1 79-4 49 47-1 *3'S 09 104.8 30.0 69 1 6.2 . 5 4-6.6 29 220 i 63.1 89 277.8 797 >o 48.1 13.8 10 105.7 30.3 70 163.4 46.9 30 221 .1 63-4 90 278.8 70-9 5i 4.9.0 i4.Ji|in 106.7 30.6 171 164.4 47.1 ^3* 222 . I 63-7 > 9 i 279.7 80.2 5 2 sO.O J 4 . 3 ! 12 107.7 30.9 72 165.; 47-4 32 223.0 63.0 92 280.7 80. s 53 50-91 J4 6 13 108.6 31.1 73 166.3 47-7 33 224.0 64.2 93 281.6 80.8 ! 54 51.9114.9 14 109.6 31.4 74 167-3 48.0 34 224.0 64.. 94 282.6 Si.o 1 ^5 52. q 15.2 15 no. 5 }'? 75 168.2 4 $.2 35 225.9 64.8 95 283.6 81.3 i 56 53-8 IS.-.4 16 ni. 5 32.0 76 169.2 48.5 36 226.9 6;. i 96- 284.5 *i.6 57 54-8 15*7 7 HZ. s 32.2 77 I/O. I 48.8 M 2.2 7 .8 6S- 3 97 285.5 81.9 i ^ & J5.8 16.0 18 "3-4 32-5 7 171.1 49.1 38 228.8 65.6 98 286.5 82.1 ! ^ Q -6.7 16.3 '9 114.4 32-8 79 172.1 49.3 39 229.7 6-5.9 99 287.4 82.4 60 57-7 16.5 10 115.4 33- 1 Ho 173-0 49.6 , 40 230.7 66.2 300 288.4 82.7 {Dift Dtp.' Lat. Dift Dep. Lat. llDiff Dep. Lat. .Dift Dep. Lat. Dift Dep. Lat. for 7-i- Degrees. TABLE II. Difference of Latitude and Departure for 17 Degrees. DJft'Lat. Dep. Dift Lat. DepJDift Lat. Dep. Dift| Lat. D=p. Dift L.it. Dep. i 01 .0 00.3 61 58.3 17.8 121 115.7 >54 10 I 73.1 52.9| 241 230. c 70.5 2 01.9 00.6 62 59 3 18.1 21 116.7 3 S 7 , 82 74.0 53-- 4 2 231.4 70.7 3 02.9 oo . 9 6* 60.2 18.4 23 117.6 36.0 ' 83 75 o 43 232.4 71.0 i 4 03.8 01.2 64 61.2 18.7 24 1/8.6 36-3 76 o ?.? 44 23? 3 7i.3 S 04.8 oi. 5 65 62.2 19.0 25 119.5 ?6. s 8; 76. 9 54.1 4 : 234.5 71.6 6 05.7 or - 66 63.1 19.3 26 120. 5 36.8 86 77-9 54-4 4'> 235-3 71.9 7 06.7 oz.c 67 64.1 19.6 27 121.5 37,1 8- 78.9 54-7 47 236 2 7*. 2 I 8 07 . 7 02.3 68 65.0 19.9 28 122.4 37-4 88 79.8 55.0 237.2 9 08.6 02. t 69 66. c 20.2 29 123.4 37-7 89 lie. 7 55-3 49 I33.I 72. 7 10 09.6 02.9 70 66.9 20.5 ;o 124.3 38.0 QO 181.7 55^ 73.o i j 10. s 03.2 7 1 67.9 20.8 i}i 125.3 3* 3 191 182.7 555 251 240.0 73-3 12 11.5 03. s, 68.9 20.9 3 a 126.2 3-! 6 9- 183.6 56. i 52 241.0 73-6 13 rz 4 03. s 73 69.8 21.3 33 127.2 38.9 93 184.6 56.4 53 I4I.9 74.0 14 13-4 04.1, 74 70. S 21.6 34 128.1 39.2 94 185.5 56-7 54 74.1 r 5 14-3 04.4 75 71.7 21.9 35 129. 1 59- 95 ,86.5 57.0 55 243.9 74-4 I l6 15-3 04.7 76 72.7 22.2 36 130. 1 39 ^ 96 187.4 57-3 56 244.8 74-7 16.3 05.0 77 73-6 22. 5 37 IJI. 40.1 97 188.4 57-6 57 245.8 1 J ^ 17.2 05.3 78 74-6 22.8 3* 132.0 40-3 98 189.3 57-9 58 246.7 75-3 19 8.2 05.6 79 75-5 23. I 39 131.9 p.t 99 190.3 58.2 59 247.7 75 6 I 20 I9.I 05. h So 7 ft. 5 23.4 40 f 3 ) 9 4-0-9 200 f9 1 '3 5^-5 6- 248.6 75-9 21 20.1 06. 1 Si 77.5 23.7 141 134.^ i-' - 201 192.2 58.8 26] 249.6 76.2 22 21 .0 06.4 82 78.4 24.0 42 155-8 4.1.5 O2 193:2 59.1 62 250.6 76.6 22. C 06.7 83 79-4 4-3 43 136.8 41.8 o; 194.1 63 251.5 7i.8 24 22.9 07.0 84 80.3 24.6 44 137-7 42.1 04 195.1 59-6 64 252.5 77-1 ; . 2" 23.4 07-? 8s 8, .3 24.9 45 138.7 42.4 5 196.0 59 9 77.4! 26 24.9 07.6 86 82.2 25.1 46 139.0 -I 2 : 06 197.0 60. z 66 254.4 77-7 27 07.9 87 83.2 25.4 47 140.6 07 198.0 60. s 67 255-3 78.1 1 z8 26.8 88 84.2 25-7 48 141.5 43 3 08 198.9 60.8 68 256.3 78.4 27.7 08.; 8 s. i j 26.0 49 142.5 09 '99-9. 61.1 69 257.2 78.6 3o 28.7 o-!.S 90 86.1 26.3 5 143.4 4-3 .Q IG 200. 1 61.4 70 2S8.2 78.9 1 3i 29 6 09.1 91 87.0 26.6 fSi r 44-4 H.I 2 I 2OI.4 5i .-, 271 Z>9-2 79.2 i 32 30.6 09.4 92 88.0 26.9 52 145.4 14.4 12 202.7 62.0 7 ^ 260. I 79o 33 31.6 09.6 93 88.9 27.2 53 146.3 44-7 13 203.7 62.3 7' 261 i 79-7- i 34 32-S 09.9 94 89.9 27. s 54 H7.3 4S-o 1^ 204.6 62.6 74 262.0 80.0 ! ! 35 33-5 IO. 2 95 90. S 27.8 55 148.2 45.? IS 205.6 62.9 75 263.0 80.1 ; 36 34-4 ia.5 96 91.8 56 149.2 45.6 16 106.6 63.2 76 263.0 80.6 : 37 35-4 ro.V 97 92.8 2*. 4 57 150. i *5-9 17 207.5 63.4 77 264. - 81.0 j : 3* n. i 98 93.7 28.7 58 151.1 18 208.^ 63.7 78 265.9 3l . 2 1 ! 39 37.3 11.4 94-7 28.9 59 152.1 46. s rq 209.4 64.0 79 266.8 Si. 5 ! 40 38.3 ir. 7 100 95.6 29.2 60 I 53v 46 . ' 20 210.4 64.: 80 267.8 81.7 ; 4 1 ^9.2 12.0 101 96.6 29.5 161 154.0 47- l iZI 211.3 64.6 281 268 7 82.0' 42 40.2 12.3 Oi 97-5 29-8 62 154.9 47-4 22 212.3 64.9 82 269.7 82. * 43 41.1 12. 6 ov 98*5 30.1 63 155.9 47-7 2? 213.3 65.2 83 270 6 Si. 6 44 42.1 12,9 04 99-5 30.4 64 i;6.8 47-9 24 214.2 6S-5 84 2 71 .6 82.9 45 43.0 13.2 00.4 30.7 6S 157-8 48.2 2" 215.2 65.8 8s 271.5 83 .2 46 44.0 13.4 06 roi. 4 66 158-7 48.; 26 216. i 66.1 86 73.5 83.5 47 44-9 13.7 07 102.3(31.3 67 159-7 48. S 27 217. i 66.4 ^7 274-5 83.9 ' 48 45-9 14.0 08 103.3 31.6 68 160.7 49-i 28 218 .0 66.7 88 275-4 S 4 . I 49 46.9 H-3 09 104.2 31-9 69 161.6 49-4 29 219.0 67.0 89 276.4 84.4 1 5 47-8 14.6 10 O^,2 32.2 70 162.6 49-7 30 220 67.2 90 277-3 ? 4-7 5' 48.5 14.9 III 106. i 32. S i 7J 163.5 50.0 271* 220.9 67-5 2QI 278.3 85.0 52 49-7 15.2 12 107 . l 132 7 71 164.5 50.3 32 221.8 67.8 279.2 85.4; 53 50.7 15.; n 108.IJ33-P 73 165.4 50.6 33 222.8 6g.i 93 280.2 S-7 54 51.6 r 5 .8 109.0 33-3 74 166.4 34 22 3 .8 6S. 4 94 2*1. 86.0 55 S2.6 16.1 jr no.o 3V6 75 167.4 51.2 35 224.7 68.7 95 282.1 86-1 56 53-.fi 16.4 16 110.9 33-9 76 168.3 5 r -5 225.7 69 ,o 96 283. 1 86.4 5- 54-5 16.7 17 111.9 34-2 77 169.3 51-7 J7 226.6 69.3 97 284 o 86.8 58 5S.5 17-0 18 tIZ.g 34-5 78 170.2 52. o 38 227.6 60.6 98 2^5-0 87.0 59 56.4 17- i 19 in. 8 34-8 79 171.2 52-3 39 228.6 69.9 99 285.9 87.3 60 >7-4 37 5 20 114.8 So f 72. r S2.6 40 229 5 70.2 300 186.9 87-7 Dift Dep. Lat. Dift Dep. Lat. Dift Dep. Lat. Dift Dep. Lat. Dift Dep. Lat. K e for 73 Degrees. TABLE II. Difference of Latitude and Departure for 18 Degrees, --^.M Dift I. ..-. Lat. Dep. Dift Lat. Dep. Dift Lat. Dep. Dift Lat. Dep.l Dift Lat. Dep. i i 01 .0 00.3 61 58.0 18.9 21 115.1 37- V 181 172.1 55-9 241 229 i 74-5 2 01.9 00.6 62 59- 19.2 22 116.0 37-7 82 173.1 56.2 42 230 2 74.8 3 02.9 00.9 63 59-9 19-5 a 3 117.0 35.0 83 174.0 s6.6 43 23I.I 75.1 4 03-8 01.2 64 60. 9 f\ T R 19.8 24 117.9 3-3 ~0 /: 84 8- 175.0 56.9 44 232.1 75-4 5 6 04.8 05.7 01.5 01.9 66 62.8 20.4 25 26 119.8 35.!) 38.9 86 1 7 5 9 176.9 57- 46 234.O 76.0 06.7 02.2 67 63.7 20.7 27 120.8 39.2 7 177-8 57.8 47 234.9 76.3 8 0^.6 02. < 68 64.7 21. O 28 121.7 39-6 88 178.8 58.! 48 235-9 76.6 9 08.6 02.8 69 65.6 21.3 29 122.7 39-9 89 179-7 58.4' 49 236.8 76.9 10 09.5 03. I 66.6 21.6 30 123.6 40.2 90 180.7 58.7 50 237-8 77-3 ii 10. s 03.4 7i 67-5 21. 9 131 124.6 40.5 191 181.7 59.0 251 238.7 77-6 12 11.4 37 72 68.5 22.2 32 125.5 40.8 92 182-. 6 59-3 52 2.39-7 77-9 1.3 12.4 04.0 7,3 69.4 22.6 33 126.5 41.1 93 183.6 59.6 53 240.6 78.2 14 74 70.4 22.9 34 127.4 41.4 94 184. c 59-9 54 241.6 78.5 15 14.3 04.6 75 23.2 35 128.4 41.7 95 185.5 60.3 55 242.5 78.8 16 15.2 04.9 76 72.3 23-5 36 129.3 42.0 96 186.4 60.6 56 243.5 17 16.2 os. 3 77 73-2 37 130.3 42.3 97 187.4 60.9 3 / 244-4 79-4 18 17.1 os. 6 78 74-2 24.1 38 131.2 42 . 6 98 188.3 61.2 58 145.4 79-7 Ty 18.1 os. 9 79 75-1 24.4 39 132.2 43.0 99 189.3 61 . 5! 59 246.3 80.0 to 19.0 06.2 80 76.1 -4- 7 4 133.1 43-3 200 190.2 6i.8j 60 247. 3 80. 3 21 20. o 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. X 82 78.0 42 43-9 02 192. 1 62.41 62 249.2 Si.o 23 21.9 07. i 8" 78.9 2S-6 43 136.0 44-2 03,193.1 62.7! 63 2SP-I 81 . 3 ' 22.8 07.4 84 79-9 26-0 44 137.0 44-5 04(194.0 63-0 64 25I.I 81.6 25 23.8 07.7 80.8 26.3 45 r 37-9 Os 195.0 63-3 65 252.0 81.9 ! 26' 24.7 08.0 86 81.8 26.6 46 138.9 45- * 06 195.9 63.7 66 253.0 82.: 27 25.7 08.1 87 82.7 26.9 47 139.8 45-4 07 196.9 64.0 67 253.9 82.5 26.6 08.7 83 8j-7 27.2 48 140.8 4S-7 08 197.8 64-3, 63 254-9 82.8 29 27.6 09.0 89 84.6 27-5 49 141.7 46.0 09 198.8 64.6, 69 255-8 83-1 30 28.5 09-3 90 85.6 27.8 50 142.7 46.4 10 199.7 64 . 91 7o 256.8 83.4 31 29.5 oj.6 91 86.5 28.1 151 143.6 46.7 211 200. ~ 65.2J -7 1 257-7 83.7 S 2 30.4 09.0 92 87.5 28.4 52 144.6 47.0 12 2O1.6 6 5 . 5 72 258.7 *4-' 33 10.2 93 88.4 28.7 53 H5-5 47-3 13 2O2.6 65.8 73 259. 6 84.4 1 34 32-3 to. 5 94 89.4 29.0 .54 146.5 47.6 14 203.5 66.1 74 20O-. 6 8 4 . 7 35 33-3 10.8 95 90.4 29.4 55 147.4 47-9 15 204.5 66.4 75 261.5*85.0 36 34*2 ii. i 96 ^9-7 , 56 148-4 48.2 16 205.4 66.7 76 2') 2\ 5 85-3 37 35-* 11.4 97 92,3 30.0 57 149-3 48.5 17 206.4 67.1 77 263.4 85.6 36.1 11.7 98 93.2 3-3 58 150.3 48.8 18)207.3! 67.4 78 264.4 85.9 39 37.1 12. I 99 94.2 30.6 59 151.2 49,1 19 208. 3 j 67.7 79 265.3 86.2 40 38.0 12.4 100 95 - 1 30.9 60 152.2 49-4 20 209.2! 68. o 80 266.3 86-5 : 41 39.0 12.7 101 96.1 31-2 161 153. i 49-8 221 2IO.2 6S. 3 Si 267. 2' 86.8 t 42 39-9 13.0 02 97-o 3i-5 62 154.1 50.1 z^ in. i 68.6 82 268. 2 ^7.1 ! 43 40.9 13-3 03 98.0 31.8 6.3 155-0 50.4 23 212.1 68.9 83 269. 1 87 -4 : 44 41.8 rj.6 04 98.9 .32.1 64 1,6.0 50.7 24 213.0 69.2 84 270. J 57.8 42.8 13.9 999 32.4 6s 156.9 51.0 25 2I4.O 69.5 85 27LI 88.1 46 43-7 14.2 06 100.8 32. ? 66 157.9 51.3 26 214.9 69.8 86 172.0 88.4 i 47 44 7 T 45 07 '101 .8 67 158.8 Si. 6 27 215.9 70.1 87 273.0 88.7 48 45-7 14.8 oS 102.7 33/4 68 159-8 Si- 9 1 28 116.8 70.5 88 273- 1 , 89.0 49 46.6 I5-I 09 103.7 33-7 69 160.7 52.2 2.Q .217.8 70-8 89 274.9 89-3 47-6 15-5 ro 104.6 70 161.7 52.5 \ 30 2T8.7 71 .1 90 275'^ 89.6 Si 48. s IS. 8 in 1105.6 34-3 171 162.6 52.8 231 219.7 71.4 -9 1 276.6 89.9 52 49- S r6.i 12 Uo6. 5 34-6 72 163.6 53-2 32 j 220. 6 71.7 92 277-7 90.2 i 53 50.4 16.4 131*07.5 34-9 73 164.5 53-5 33 221.6 72.0 93 278.7 90.5 i 54 51.4 16.7 14 108.4 35.2 74 165.5 53-8 34 222.5 72.3 94 279-6 90.9 55 52.3 17-0 109.4 35-5 75 166.4 54* i 35 223-5 72.6 95 280.6 91.2 56 53-3 I/.3 16 110.3 35-8 76 167.4 54-4 36 224.4 jz.fi 96 28l.S 91.5 57 54.2 S S ' - 17.6 17.9 17 18 111.3 1X2. 2 36.2 78 168.3 169.3 54-7 37 225.4 38(226.4 73.2 73- 5 97 282.5 98 83.4 91.8 92.1 59 56.1 ,8.2 19 II3-2 36.8 79 170.2 55-3 39 227-3 73-9 99 2H-4 92.4 60 57.1 18.5 20 114. I 37-i 80 171.2 55-6 40 '228.3 74.2 500 2??. 3 92.7 Dift Dep, iTaT Hi ft Dep. Lat. Dif Dep. Lat. Difti Dep, Lat. Dift Dep. Lat. j for 72 Degrees, TABLE II. ftijcrfnc'c of Latitude and Departure for lp Degrees. Dift Lat. Dep. Di Lat. Dep Di Lat Dep Di Lat Dep Dif Lat Dep. j 00. C 00.3 6 57-' 19. 12 114. 39- 18 171. 58. 241 227. 78.5 2 01.9 00.7 6 58.6 20. 2 115. 39- 8 172. 59- 42 228. 78.8 02.8 01. 6 59.6 20. 2 116. 40. 8 X 73- 59 43 229. 79*1 * (. 03.8 01.3 64 60.5 20. Zt 117. 40. 8 '74- 59- 44 230. 79-4 i 04.7 Ol.h 6 61.. 21. 2 118. 40. 8 174- 60. 45 231. 79-8 ( 05.7 O2. O 66 62.4 21. 2 119. 41. 8 '75- 60. 46 232. So. i 1 06.6 02.^ 6- 63-3 21. 2 120. 41. 8 176. 60. 47 233- 80.41 8 07,6 O2. 6 68 64.3 22. 2 121. 41. 8 177. 61. 48 234. 80.7 9 08. s 02.9 69 65.2 22. 2 |22. 42. 8 178. 61. 49 235. 81.1 10 09.5 03.3 70 66.2 22.8 30 122. 42 . 9 179. 61. 50 236. 8i-4| ii 10.4 03.6 7J 67.1 23- n I2 3 . 42.0 19 180. 62. 251 237. 81.7 12 n. 03.9 j 72 68.1 23.4 32 124. 43-0 92 181. 62. 52 82.0 ; 13 12. 04.2 73 69.0 2 3 .8 3 I2 5 . 43-3 9 !82. 62. 53 239- 82.4 j 13. 04.6 70.0 24.1 34 126. 43.6 94 183.4 63. 54 240.2 82.7 15 14.2 04.9 7 70.9 24.4 3 127- 44.0 9 184.4 63- 55 241- 83.0 16 I5-I 05.2 71-9 H-7 36 128. 44-3 96 63- 56 242. 83-3 17 16.1 05. 7 / 72.8 25.1 37 129. 44.6 97 186. 64. 57 243.0 83.71 18 17-0 05. 7 73-8 25.4 38 130. 44-9 98 I8 7 .2 64. 58 243-9 84-0 i '9 18.0 06. 79 74-7 2 5-7 39 I3I.4 45-3 99 188. ? 64.8 59 244-9 84-3 20 18.9 06. 80 75.6 26.0 40 132.4 45-6 200 189. 65.1 60 245-8 -4.6 2 t 19.9 06. 81 76.6 26.4 141 133-3 45-9 20 190.0 55.4 261 246.8 85-0 22 20.8 07.2 82 77-5 26.7 42 134-3 46.2 02 191.0 62 247.7 85-3 23 21.7 07. 83 27.0 43 135.2 46.6 03 191.9 66. 63 248.7 85.6 24 22, 7 07.8 84 79-4 27.4 44 '36.4 46.9 04 192.9 66.4 64 249.6 25 23.6 08. 85 80.4 27-7 45 i37.I 47-2 05 193.8 66.7 65 250.6 86.3 26 2 4 .6 08. 86 81.3 28.0 46 138.0 47. . 06 194.8 67.! 66 251.5 86.6 27 25. 5 08.8 8? 82. 3 28.3 47 139.0 47-9 07 195.7 67.4 67 252.5 86.9 28 26.5 09.1 3S 83.2 28.7 48 139.9 48.2 o'8 196.7 67.7 63 253.4 87.3 29 27.4 09.4 89 84.2 29.0 49 140.9 48.5 9 197.6 68.0 69 2 54-3 87.6 30 28.4 09.8 90 85.! 29-3 5 48.8 TO 198.6 68.4 70 87.9 31 29.3 IO. I 9 i 86.0 29.6 151 142.8 49-2 ill 199.5 68.7 7i 2 S 6.1 -8.2 32 30.3 10.4 92 87.0 30.0 52 143.- 49-5 12 200.4 69.0 72 -57-2 88 . 6 33 31-2 10.7 93 87.9 30-3 53 H4-7 49-8 13 201.4 69.3 73 258.1 ^8.9 | 34 32. i ii. I 94 88.9 30.6 54 50. i 14 .02.3 60.7 74 259-1 89.2 35 3 3 J 11.4 89.8 30.9 55 146.6 50.5 15 -Q3-3 70.0 75 260.0 89-5 36 34.0 11.7 96 90.8 31-3 56 H7-5 50.8 16 204 . 2 70.3 76 261 .0 89.9 , 37 35-0 12.0 97 91.7 3^.6 57 48.4 51. i 17 205.2 70.6 77 261.9 90.2 i 38 35-9 I2. 4 98 92.7 31-9 58 49.4 -1.4 IS 06. I 71.0 78 262.9 90.5 39 36.9 12.7 99 93-6 32.2 59 50/3 1.8 19 07.1 71.3 79 263.8 o.S 40 37.8 13.0 100 94-6 32.6 60 5i.3 2. I 20 08.0 71.6 80 264.7 I .2 4 1 33.8 13.3 101 9^5 32.9 161 52.2 2.4 21 O9.0 72.0 81 265.7 1.5 42 39-7 02 96.4 33-2 62 53-2 2.7 22 09.9 72.3 82 266.6 1.8 I 43 40.7 14.0 03 97-4 33-5 63 54.1 3 r 23 IO-9 72.6 83 267.6 2. I 44 41.6 14.3 04 33-9 64 3-4 24 ii. 8 72.9 84 268.5 2-5 45 42.5 14.7 05 99-3 34-2 65 56.0 3-7 25 12.7 73-3 85 269. <; 2.8 46 43-5 15.0 06 OO. 2 34-5 66 57-0 4.0 26 '3-7 73-6 86 270.4 3 r 47*44-4 '5-3 07 01.2 34.8 67 57-9 4*4 27 14.6 73-9 $7 271.4 3-4 48 45-4 5-6 08 02. I 3v2 68 58.8 4-7 28 15.6 74.2 88 272.3 3.8 j 49 46.3 i6.oj 9 03.1 35.5 69 59-8 29 16.5 74.6 89 273.3 4.1 | 50 47-3 6-3 IOJI04.0 35-8 70 60.7 5.3 3 17.5 74-9 9 274-2 4.- 4 51 48.2 6.6 II ro^.c 36.1 71 61.7 5-7 31 18.4 "5.2 275-r 4-7 ! 52 49-2 6.9 12 105.9 36.5 72 62.6 6.0 [2 19.4 "5-5 92 53 50.1 7-3 13 06. S 36.8 73 63. 6 6-3 13 20.3 75.9 93 277.0 5-4 54 51.1 7.6 14 07.8 37- T 74 64-5 6.6 34 21 .2 76.2 94 178.0 5-7 55 52.0 7.9 I c 08.7 37-4 75 6-5 7.0 35 22.2 76.5 ,78.9 6.0 56 52.9 8.2 16 09.7 37-8 76 66.4 7-3 36 23.1 76.8 96 179.9 96.4 : ^7 53-9 8.6 17 10.6 38.1 77 67.4 7.6 37 24.1 77.2 97 180.8 >6-7 58 54-8 8.9 18 11.6 38.4 78 68.3 8.0 38 25.0 77-5 98 181.8 ;/.o 59 55-8 9.2 19 i 12.5 58.7 79 69.2 8-3 39 26.0 7-8 99 37.3 * 60 56.7 9-5 20 j 13-5 39.1 80 70.2* 8.6 o 26.9 78.1 OO 183.6 97-7 Dift Dtp. Lat. ift! Dep. Lat. ift Dep. Lat.l ift Dep. ^at. ift Dep. Lat. E e 2 for 7 1 Degrees. TABLE II. Difference of Latitude and Departure for 20 Degrees. Dift Lat. Dep. Dift Lat. Dc-p. Dift Lat. Dep. Dift Lat. Dep.! Dift Lat. Dcp. ; i 00.9 00.3 61 57-3 20 9 tii 113.7 4* -4[ Si 170. i 61.9 241 226. 5 82.4 2 01.9 00.7 62 58 . 3 2.1. 2 22 114.6 41.7 82 171.0 62 2 42 227.4 82 8 3 02.8 01 ,C 63 59.2 21.5 23 115.6 42. i 8? 172.0 6-2.6 43 228 3 83-1 4 03.8 01.4 64 60. i 21-9 2 4 116.5 42.4 *4 172.9 62.9 44 22:;. 3 83-5 5 04.7 01.7 6S 6.1. i 22.2 2S 117. - 42.8 173-8 63 . 3 230.2 83.8 6 05.6 02. 1 !,6. 62.0 22.6 26 1*8.4 43.1 86 174-8 63.6 46 231.2 84.1 7 06.6 02-4 67 6^.0 22.C) 27 H9-3 43*4 87 175-7 64.0 47 23*. i 8 07.5 02./ 6S 63.9 23.3 2S 120.3 43. 88 176.7 64.3 48 84. S 9 oX. 5 03.1 69 64.8 23.6 2 9 121 .2 44.1 89 177.6 64.6 49 234 85.2 ! IO. 09-1 03.4 70 65 * 23 9 30 121 2 44- 5 90 178-5 6s -o m-9 85.5 I I ( 10. , 0}.b 7' 66.7 24-3 ''3 1 I23.I 4471 191 179.5 6s. 3 251 235-9 85.8 Ii n-3 04.1 7 67.7 2 4 .b 32 124.0 45.1 92 180-4 6s-7 236- S 86.2 i '3 12 .2 04.4 "3 6&. < 2^.0 33 I2i5.0 45-5 93 1*1.4 66-c c^ 237-7 86.5 i *4 I3-- 04. b 74 69.5 15-3 54 125.0 45. &. 94 Ba.-j 66.4 54 238.7 86.9 i-s 14.1 05.1 75 70.; 25-7 35 120-9 46.2 9> 183.2 66.7 239.6 87.2! 5 1 6 I 5.0 05.5 76 71.4 26.0 3ft 127. >s 46.5 96 ,84.2 67.0 56 240.6 87.6 . i 16.0 05.8 77 72.4 *6,3 37 128.7 46.9 97 185.1 67.4 S7 241.5 87.9! i 16 9 06. 2 78 73-3 26.7 3- 129.7 47 - 98 186.1 67.7 58 242.4 88.2 : 19 17.9 06. 5 79 74.2 27.0 39 I }O.6^ 47- s 99 187.0 68.1 S8.6! ! 20 18.8 06. j 8c 7^.2 27.4 40 m 6 47.9 200 187.9 6S. 4 60 244-3 88.91 i 21 19.7 07-2 Si 70.1 'i/.7 141 132. 5 4 8 2 2OI 188.9 68.7 261 4 45-3 89". 3 1 23 co. 7 2.1.6 07.5 07.9 8? 77.1 : 78.0 28.0 28.4 4 2 4? V33-4 134-4 48.6 48.9 02 03 189.8 190.8 69.1 69.4 63 246 .2 247.1 89.6 90.0 1 24 25 1 26 22.6 21-5 24.4 08.2 oS 6 08.9 '4 8s 86 78.9 79-9 80. S 29.4 44 45 46 135-3 136.3 137.2 49-3 49.6 49.9 04 06 191.7 192.6 193.6 69.8 70.1 70.5 64 66 248.1 249.0 250.0 90-3 90.6 QI.O ! 27 25.4 09.2 87 8i.S 29.8 47 138.1 5-3 C7 194.5 70.8 67 2^0.9 28 26.3 09.6 S8 82.7 30.1 48 139. > 50.6 08 71. i 6S 9L7 29 27.3 9.9 8-9 83.6 30-4 49 140.0 51.0 09 196.4 71-5 69 2S2.8 92.O ; 30 28.2 10. 3 90 84.6 30.8 5 141.0 5 r -3 TO 71.8 70 2 S3 -7 ; 31 29 I 10.6 9> 8s. s 3*. i 1! fi 141.9 51.6 211 198.3 32 30.1 10.9 92 86. s 5 2 142.8 52.0 12 199.2 72.5 72 2SS-6 93.O 33 31.0 "3 93 87.4 31.8 53 H3.8 52.3 13 2OO. 2 73 256.5 93-4 I 34 < i . 9 II. 6 94 88.3 32.1 54 144.7 52.7 *4 2OI. I 73-2 74 257.5 93.7 35 36 32.9 33. 12.0 . 3 95 96 90.2 32.5 56 45-7 53-4 15 16 202. O 2O3.O 73-5 73-9 751*58.4 76 259.4 94.1 94-4 ! 37 34-8 12.7 97 91.2 33 .2 5? '47-5 53-7 17 203.9 74-2 7" 260.3 94*7 ! 3 S 35-7 13.0 98 92. i 33-5 58 148.5 54.0 18 204.9 74.6 78 26l .2 95.1 *9 36.6 3- 3 99 93-o 33-9 59 149.4 54-4 19 205.8 .74-9 79 262.2 95-4! 40 37-6 13.7 100 94.0 34-2 bo 1 50 . 4 54.7 20 206.7 75.2- 80 263.1 95 .8| 4 1 38-5 14.0 101 94.9 34-5 .161 151.3 55-i 221 207.7 75-6 281 264.1 96. i 42 39-5 H-4 02 95.8 34-9 62 152.2 55-4 22 208.6 7S-9 82 265.0 96.4 43 40.4 *4 7 03 96.8 J5-2 6j ) 153 . 2 55-7 23 209.6 76.3 83 265.9 96. 8i 44 41.3 15.0 04 97-7 35-6 ^4 154. i 56.1 2 4 210.5 76 6 84 266.9 97-1 1 45 42.3 15.4 OJ 98.7 35-9 65 SS- S6-4 *5 211.4 77.0 8s 267.8 97- S 46 43.2 15.7 06 99.6 36.3 66ji 5 6.o 56.8 26 212-4 77-3 i 86 268.8 97-8 47 44-2 16.1 O7 100. 5 36.6 67 156.9 57.1 27 213.3 77-6 87 269.7 98.2! 48 45.1 16.4 08 101.5 6 9 68 57-5 28 214.2 78.0 88 2/0.6 49 46.0 16.8 09JIO2.4 37-3 69 158.8 57.8 29 215.2 89 2-71.6- 98.81 50 47.0 17.1 10 103.4 17.6 70 159.7 58.1 30 216. i Q - 90 272. 5 99.2 ' 5 1 47-9 17.4 III 104.3 38.0 171 160.7 58.5 231 217. 1 -79-0 J2 9 I 173- 5 99-5 : 52 4* 9 17.8 12 105.2 38. 3 71 161.6 58 .Si 32 218.0 79-3 i 92 274.4 99.9 5-3 49.8 iS.i 13 106.2 38. b 73 162.6 59.2 13 2 19.0 79-7 275*3 100. I 54 50.7 18.5 H 1 07. i 39.0 74 163.5 59-5 14 219.9 80.0 94 276.3 t 100. 5 55 5 1 ' 7 18.8 is ro8. i 39-3 7S 164.4 59-9 35 220.8 80.4 9S 277-2 100.9 5^ 52.6 19.2 16 109.0 39.7 76 165.4 60.2 36 221.8 *0. 7 1 96 278.1 IOI.2 57 53-6 19.5 17 109. 40.0 7 7 166.3 60.5 37 222.7 97 279. i 101.6 58 54-5 19.8 18 110.9 40.4 78 167.3 60,9 38 223.6 81.4 i 98 28^0.0 TOI .9 i ^9 55-4 20.2 19 iri.S 40.7 79 l6$.2 61.2 39 224.6 81.7 99 281,0 ioz. 3 i 60 56.4 2.0.5 20 112. 8 41.0 80 l6 09. 2 10 09-3 03.6 70 6S-4 ?.$.! 30 121.4 46.6 90 177.4 68.1 233-4 89.6 II 10.3 03.9 71 66.3 25.4 131 122.3 46.9 191 178.3 68.4 151 234.3 90.0 12 II. 2 04.3 72 67.2 2^.8 y 123.2 47-3 92 179.2 68.8 S* 90.3 *3 12. 1 04.7 73 68.2 26.2 33 124.2 47-7 93 180.2 69.2 53 236.2 9O.7 '4 I3.I 05.0 74 69.1 26.5 34 125.1 48.0 94 181.1 69. S 9I.O *5 14-0 05.4 75 70.0 26.9 35 120. O 48.4 9S 182.0 69.9 SS 238.1 91.4 16 14-9 05.7 76 70.9 27.2 36 I2/.0 48.7 96 183.0 70.2 S6 239.0 91.7' 1 is 15.9 16.8 06. I !o6. 5 / / 71.9 72.8 27.6 28.0 38 127.9 128.8 49.1 49-5 97 98 183-9 184.8 70.6 71.0 57 S8 239.9 240.9 92.1 92.5 19 20 17.7 .8.7 c6.S 07.2 80 73-8 74-7 28.3 28.7 39 40 129.8 130.7 49.8 50.2 99 200 185.8 186.7 7L3 71-7 59 60 241.8 242.7 91.8 9.3-2 21 19.6 07.5 br 75-6 29.0 141 131.6 50.5 201 187.6 72.0 2t>I 2 437 93. s 23 24 20.5 21.5 22.4 07.9 08.2 08.6 82 83 ?4 76.6 77-5 78.4 29.4 29-: JO. I 4 2 43 44 132.6 133-5 '34-4 50.9 51.2 51.6 O2 03 04 188.6 189.5 190.5 72.4 72.7 62 63 6 4 244.6 246.5 93.9 94-3 94.6 27 28 2 9 23.3 24-3 26.1 27.1 iS.o 09.0 09-3 09.7 10. 10.4 10.8 85 86 87 88 89 90 79-4 80.3 81.2 82.2 83.1 84.0 3-5 30.8 31.2 31.5 31.9 32.3 45 46 47 48 49 r 35-4 136.3 137.2 138.2 '39-.' 140.0 52.0 53-0 53-4 53.8 07 OCJ 1C 191.4 192.3 193.3 194.2 73-5 73.8 74.2 74-5 74.9 75.3 65 66 67 68 69 247.4 248.3 -49-3 250.2 251.1 252.1 95.0 953 95-7 96.0 96.4 96.8 31 28.9 ii.i 9 1 85.0 3i .6 151 141.0 54.1 211 197.0 7 S 6 2-1 2^3.0 07. i 3* 29.9 11.5 92 85-9 33Q 5 2 141.9 54-5 12 197.9 ,6.0 72 253.9 97.5 33 30.8 11. 93 86.8 33-3 53 142.8 54-8 13 198.9 76.3 73 254.9 97.8 34 3 1 *7 12.2 94 87.8 33-7 54 143.8 55-2 '4 199-8 76.7 74 98.2 35 36 32.7 33-6 12.5 12.9 95 96 *4. 7 89.6 34-4 55 56 144.7 145.6 55-5 55-9 15 16 200.7 201.7 77-0 77-4 76 256.7 -577 98.6- 98.9 3*8 39 34^ 35-5 36.4 13-3 13.6 14.0 97 98 99 90.6 91.5 92.4 34-8 35-5 58 59 146.6 147-5 148.4 56-3 56.6 57.0 7 18 19 202.6 203.5 204.5 77.8 78.1 78. s 77 79 258.6 259.5 260. S 99-3 99.6 1 1OO.O i 40 37-3 H.J tco 93-4 35J- 60 149.4 57-3 20 205.4 78.8 261.4 'co. 3 j 4 1 38.3 14.7 101 94' 3 36.2 1611150.3 57*7 221 206.3 79.2 28 r 262.3 =] i oo . 7 1 4* 39.2 15.1 02 95- * 36.6 62 151.2 58. i 22 207.3 263.3 IOI . I ! 43 44 40.1 41.1 15.4 15. & 03 4 96.2 97.1 36.9 37-3 63 64 .1 U,2 '53-1 58.4 S8.8 23 24 208.2 209. I 79-9 80.3 8 4 3 264.2 26^. i 101 .4 101 .8 4i 42.0 16. i 05 98.0 37.6 65 154-0 59.1 2S 210. I 80.6 s 266.1 IC2. I 46 42.9 .6.5 06 99.0 38.0 66 59-5 26 2H.O 81.0 267.0 47 48 43-9 44-8 17.2 07 08 99-9 loc. 8 JSI* 67 68 156.8 60.2 28 211.9 87 88 267.9 268.9 102.9 49 50 45-7 46.7 17.6 17.9 9 1C 101.8 102.7 39-4 69 70 157-8 I 5 8.7 60.6 60. t) 70 217. 8 214.7 82. i 82.4 89 90 269 8. 260.7 103.6 IO"? .9 5i 52 47-6 48.5 18.3 18.6 1 1 1 12 103 .6 104.6 39-8 40. i L Vz 159.6 160.6 61.3 61.6 ^ 215-7 216.6 8%'r 291 92 271.7 172.6 1 04 . 6 53 54 49-5 50.4 19.0 19.4 13 105.5 106.4 40.5 40.9 73 74 161.5 162.4 62 .0 62.4 33 2I7. 5 218.5 sf j 83.9 93 04 27.3-5 274. ; 105.0 105.4 55 % 52.3 19.7 20-1 15 j 107.4 16 i 108. 3 41.2 41.6 75 76 163.4 164.3 62.7 63.1 3: 36 219.4 2.2C . V 84.4 84.6 95 96 2/5 4 7-76. 3 105.7 1 06* i hi 59 60 54 * 55- r S6.o 20.4 20.8 21. I 17 i* 19 ^o 109.2 IIO. 2 III. I 1 12.0 41.9 42.3 42^ 77 78 79 So 165.2 166.2 167.1 168.0 63.4 63.8 64. i 64.5 37 38 39 40 221-3 222.2 223.1 224.1 84-9 85-3 85-6 86. o 97 98 99 277-3 j 106.4 270.2. ic6.8 279. i ! 107.2 280. 1 1 107. 5 iDift, uep. Lat. Dik Dep. Lat. Dift Dep. Lat. Difr Dep. Lat. Dift Dcp. Lat. tor -69 Degrees TABLE II. ftiifcrcnce of Latitude and Departure for 22 Degrees, I hit Lat. Dep Dift Lat. Dep. Dif Lat. Dep. Dif Lat. Dep Dif Lat. Dep. i oo. 9 oo.^ 6 1 56.6 22.9 121 112. 2 45-3 181 167.8 67.8 241 423.5 90.3 2. 01.9 00.7 62 57-5 23.2 22 113.1 45.7 82 168.7 68.2 42 224.4 90.7 3 02. 01. I 63 58.4 23.6 2' II4.0 46.1 83 169. " 68.6 43 225.3 91.0 4 03.7 01.5 64 59-: 24.0 24 115.0 46. 84 170.6 68.9 44 226.2 91.4 5 04.6 01.9 65 60.3 243 25 115.9 46.8 85 171.5 69-3 4S 227.2 91.8 6 05.6 Oi.2 66 61.2 24.7 26 II6.8 47-2 86 1 7?- . 5 69." 46 228.1 92.2 7 (06.5! 02. 6 67 62.1 25.1 27 II7.8 47-6 87 '734 70.1 47 229.0 92.5 8 07.4 OJ.O 68 63.0 25-5 28 n8;7 479 88 174-3 70.4 48 229.9 92.9 9 08.5 03-4 69 64.0 2S-S 29 119.6 48.3 89 175-2 70.8 1 49 230.9 93-3 10 9-3 o?-7 70 64.9 26.2 30 I2O O 4-7 90 176.2 71.2 50 231.8 93-7 1 JI 10.2 04.1 71 6 S .8 26.6 131 121. s; 49.1 191 177. 7'S [251 232.7 94.0 f it II. I 4v5 72 66.8 27.0 3* 122.4 49.4 9* 178.0 71.9 52 233.7 94.4 i ij 12. I 04.9 73 67.7 27. : 33 1*3-3 49.8 93 178.9 72.3 53 234-6 94.8 i i4 I 3 .0 0^.2 74 68.6 27.7 34 124.2 50.2 94 179-9 72.7 54 235.5 95.2 15 13-9 5 .6 75 69.5 28.1 33 12;;. 2 50.6 9< 180.8 73-0 55 236.4 95-5 1 16 I 4 .8 O6.0 76 70.5 28. ; 36 126.1 50.9 96 iSi." 73.4 56 237.4 95-9! 1 1? 15.8 06. 4 77 71.4 28.8 37 127.0 5^3 97 182.7 73.8 S7 238.3 96.3 | \ is I6. 7 06.7 78 72 j 29.2 3* 123. e 5 r -7 98 183.6 74.* 58 239.2 96.61 [ L9!i7-6 07.1 79 73-2 29.6 39 128.9 52.1 99 184.5 74. 59 240.1 97-0 I* } 20 i8. S 07.5 80 74.2 30.0 40 129.8 52.4 200 185.4 749 60 241.1 97.4' 1 2.J 19-5 07.9 Si 75-1 30.3 141 130.7 52.8 201 186.4 75-3 261 242.0 97.8 i 22 20.4 OS.2 82 76.0 SO. 7 I 42 *Sf-7 53-2 O2 187.3 75-7 62 242.9 98.1 2 3 21.} o'i.6 3 77.0 31.1 43 132.6 S3- 6 03 188.2 76.0 63 243-8 9 S. 5 i * 4 ?**J 09.0 84 77-9 3^-5 44 133-5 53-9 04 189.1 76.4 64 244.8 98.9 1 * 5 23.2 09.4 85 7 8.8 3J.S 4S I 344 54-3 o<5 190. 1 76.8 65 2 45'7 99-3 26 2 4 .I 09.7 86 79-7 32.2 46 J 35-4 54' 7 06 191.0 77 2 66 246.6 99.6 27 2^.0 IO. I *7 80.7 32.6 47 136.3 55i 07 191.9 77-5 67 247.6 IOO.O 1 28 26.0 10. < 88 81.6 33-0 48 137-2 55-4 08 192.9 77-9 68 248.5 100.4 *9 26. 9 10.9 89 8s. <; 33-3 49 138.2 55-8 09 193.8 78.3 69 249-4 100.8 30 2 7 .* II. 2 90 *3-4 33-7 5 i39- r 56.2 10 194.7 78.7 70 250.3 IOI.I 31 28.7 ii. 6 9i 84.4 34-1 ill 140.0 S 6.6 2ir 195.6 79.0 -7i 251.3 101.5 32 29.7 12.0 92 8,-. 3 34-5 52 140.9 56.9 12 196.6 79-4 72 252.2 101.9 33 30.6 r2. 4 93. 86.2 34*8 53 141.9 57-3 13 197.5 79.8 73 *53-' 102.3 34 31-5 12.7 94 87.2 35.2 S4 142.8 57.7 r 4 198.4 80.2 74 254.1 102.6 35 32.5 13.1 95 88.1 3^.6 55 143-7 58.1 S J 99-3 80.5 75 255.0 103.0 36 33-4 '3- 5 9 6 89.0 36.0 <6 144.6 |8. 4 16 200.3 Jo. 9 76 255.9 103.4 37 34-3 13-9 97 89.9 J6.3 57 145.6 58.8 n 201.2 Si- 3 77 256.8 103.8 3* 1 35-2 14.2 98 90.9 36.7 5 146.5 59.2 18 202. I 81.7 78 257.8 104.1 39 36.2 14.6 99 91.8 37-1 59 147-4 59.6 r 9 203.1 82.0 79 25.7 104.5 40 37 - 1 15.0 ICO 92.7 37v5 60 148.3 59-9 20 2O4.0 82.4 80 259.6 04.9 4i 38.0 15. 4 101 93.6 37.8 61 '49-3 60.3 221 204.9 2.8 281 260.5 05-3 42 38,9 15-7 02 94.6 38.2 62 150.2 60.7 22 20^.8 3.2 82 261.5 105.6 43 39-9 i6.-i 03 95 o 38.6 63 151.1 61.1 23 206.8 3.5 83 262.4 106.0 44 40.8 16.5 04 96.4 39.0! 64 152.! 6!. 4 2 4 207.7 3.9 84 263.3 106.4 45 41.7 16.9 05 97-4 39.3| 65 153.0 61.8 25 -08.6 4-3 85 264.2 106.8 46 42 .7 17.1 06 98.3 20.7 66 I 5 > Q 62.2 "6 -OO . s 4.7 86 265.2 107. i 47 43-6 17.6 07 99.2 40.1 67 .1 .> V 154-8 62.6 27 2t0. 5 5.0| 87 266.1 107.5 48 44 5 18.0 08 IOC . I 40.5 68 155.8 62.9 28 n.4 5.4! 88 267.0 107.9 49 45-4 tS.4 09 101. I 40.8 69 156.7 63.3 29 12.3 5-8 1 89 .68.0 108.3 50 46.4 18.7 ID IO2 .O 41.2 70 157.6 63.7 30 '3-3 6.2 90 268.9 108.6 i 5I 47-3 19.1 II 1O2.9 41.6 ?r 158- S 64. i 3i 14.2 6.5 9 1 .69.8 109.0 52 48.2 19.5 12 103.8 42.0 72 J59-5 64.4 32 15. i 6.9 92 -70.7 109.4 53 49.1 19.9 13 104.8 42.3 73 160.4 64.8) 33 16-0 7-3 93 71-7 109.8 54 so.r 2O. 2 H 105.7 42.7 74 161.3 65-2J 34 17-0 7.7 94 72-6 110. I 55 51 ,o{ 20. 6 [ 15 106.6 43-1 7^ 162.3 65.6 35 17.9 8.0 95 735 110.5 56 51.9 21 .0 16 107.6 435 76 r6 3 .jt 65.9! *6 18.8 8.4 96 74-4 110.9 57 52.8 21.4 17 108.5 43-3 -~ 164. i 66.3! 37 19.7 8.8 97 75-4 111.3 -.58 53- 8 21.7 18 109.4 44-2 7^ 165 .0 66.7 >S 20 .7 9-2 98 76.3 in. 6 1 5V 54-7 22. I *9 no. 3 44^| 79 166.0 67.1 30 21.6 39.5 99 77.2 112. 60 55.4 22. 5 20 111.3 45, oil ^ 166.9 67.4! 40 22.5 39.9 00 78.2 II2-4 Dift Dep. Lat. Dift Dep. Lat. j|Dift Dep. Lat. Dift Dep. Lat. jfDift Dep. Lat. tor 68 Degrees, TABLE II. Difference of Latitude and Departure for 23 Dift Lat. Dep Dif Lat. Dep. Dif Lat. Dep. Dif - Lat. Dep. !Dif Lat. Dep. j 00.9 00.4 61 S6.2 23.8 121 111.4 47-3 151 166.6 70.7 M.I 221.8 94-2 2 01.8 oo. S 62 57-i 24.2 22 112.3 47-7 82 167.5 71. i i 4^ 222.8 94-5 3 02.8 OI.2 63 S8.o 24.6 2-, 113.2 4 S.i *3 168.5 71.5 ! 4S 243-7 94-9 4 03-7 01.6 64 58-9 25.0 24 114.1 4*-S 84 169. i 71.9 ! 44 224.6 95-3 c 04.6 02.0 6s 59.8 25.4 2-j 115.1 48.8 85 170.3 72-3 45 2^5-5 95-7 6 Q$.5 02. 3 66 60.8 25.8 26 116.0 49.2 86 171.2 72.7 ! 46 22.6.4 96.1 7 06.4 02. 7 67 61.7 26.2 27 116.9 49.6 87 1/2. i 73.-I 47 227-4 96.5 07.4 03.1 68 62.6 26.6 z8 117.8 50.0 88 173-1 73- S 48 228.3 96.9 j 9 08.3 03- 5 69 63.5 27.0 29 118.7 50.4 89 174.0 73.8 49 229.2 97-3 10 09.1 03.9 70 64.4 27.4 30 119.7 50.8 90 174.9 74.2 5 230.1 97-7'j ii 10. I 04-3 7i 6s- 4 27.7 131 120.6 51-2 191 175-8 74-6 251 231. c 98.1 12 II. O 04.7 72 66.3 28.1 32 121.5 51.6 92 176.7 75-o 52 232.0 98.5 13 12. 05.1 73 67.2 ftS.j 33 122.4 52.0 93 177-7 75-4 53 232.9 98.9 14 iz.9 05.5 74 68.1 28.9 3* 123.3 52.4 94 178.6 75-* 54 233-8 99.2 T5 13-8 05.9 7S 69.0 290 3S 124.3 52.7 9S *79-5 76.2 55 234-7 99.6! 16 14.7 06.3 76 70.0 29.7 36 125.2 53-1 96 180.4 76.6 5' 1 235- ^ 100. O 17 IS. 6 06.6 77 70 '.9 30.1 37 126.1 53-5 97 181.3 77.0 57 2^6.6 100.4 18 16.6 07.0 78 71.8 30.5 38 I2".O 53-9 98 182.3 77-4 58 237o 100.8 19 17-s 07.4 79 72.7 30.9 39 128.0 54-3 991183.2 77-8, 59 238-4 tpl.2 20 18.4 07.8 80 75.6 3_M 40 128.9 54-7il2oo|i84.i 78. r| 60 2^.1 ioi. 6 21 19-3 OS.2 81 74.0 31.6 141 129.8 55-* 201 185.0 78.5! 261 240.3 IO2 .O i 22 20. -5 08.6 8z 75-5 32.0 42 130.7 55-5 O2 185.9 78.9 62 241.2 I02. 4 2 3 21.2 09.0 8j 76.4 32.4 43 131.6 55-9 o; 186.9 79-3 63 242.1 102.8 24 22. I 09.4 84 77-3 32.8 44 132.6 56.3 04 187.8 79-7 64 243.0 03.2 5 23.0 09.8 s. 78.2 33.2 4S 133-5 56-7f 05 188.7 80.1 6S 245.9 3-5 26 Z3-9 10. 1 86 79.2 33-6 46 I34. 4 S7-o| 06 189.6 80.5 66 244.9 " 27 H-9 10.5 8; 80.1 34- 47 '35-3 57.4L 07 190.5 80.0 67 245.8 04.? 28 10.9 88 81.0 34-4 4* 136.2 57.8 oS 191.5 81.3 68 246.7 04.7 29 26.7 1 1. 3 89 81.9 34-* 49 '37-2 5.2 09 192.4 81.7 69 247 . 6 0*5.1 30 27.6 11.7 90 82.8 35-i 5 : 138.1 58.6 10 '93 -3 8.2. I 7O 4jJo 05-5. 31 28. S 12. I 9i 83.8 35-6 151 139.0 59.0 211 194 2 82.4 271 *>9-5 05,9 32 29. s 12-5 92 4-7 35-9 5* 139-9 59-4 12 I95.I Sa.S 72 250.4 06.3 3} 30.4 12.9 93 8 S . 6 36.3 S3 140.8 59-8 13 I96.I 83.2 73 25 T - 3 oo. 7 34 31.3 13-3 94 86.5 36.7 54 141.8 bo. 2 '4 197.0 83.6 74 252.2 07.1 35 32.2 13-7 95 87-4 37.1 55 142.7 60.6 M 197.9 '4.0 7S 253-1 0/.5 36 33.1 I4.I 96 88.4 37-5 56 143.6 <)I.O 16 198.8 S4'41 76 254.1 07. 8 37 34.1 14.5 97 V3 37-9 57 144 . 5 61.3 J 7 199.7 84.8 77 255.0 08.2 38 3S.o I 4 .8 98 90.2 3*-3 55 145.4 61.7 18 200,7 "> ; . ; 78 2v5-9 oS..6 39 ^.0 15.2 99 91.1 38.7 59 146.4 62. i 19 201 .6 3s. 6 79 2 ;6.8 09.0 40 36.2 15.6 100 2.1 39-i 60 147-3 62.5 20 202 . 5 6.0 So 257.7 OQ-4 4 1 ^7.7 16.0 IOI 93.0 39-5 61 148.2 62. c, 221 203.4 6. 4 281 258.7 09.8 ' 42 3?- 7 16 .4 02 93-9 39^9 62 149.1 63.3 22 204.4 6.7 82 259.6 10.2 1 43 39.6 16.8 0} 94.8 40. 2 1 6> i 50.0 63-7 23 20 s. 3 7-i 8? 260.5 10.6 ; 44 40.5 17.2 04 95-7 40.6 64 151.0 64.1 24 206.2 7-5 ^4 26114 i I 1 .0 45 41.4 17.6 S 96.7 41 .O 6j 151.9 H>5 2S 207-. i 7-9 85 262.3 tir. 4i 46 42.3 18.0 06 97-6 41.4' 66 IS2.8 64.9 26 208.0 8.3 86 263.3 MI. 7 , 47 43-3 18.4 07 9*.. 4 1.8! 67 153-7 65.3 2 7 j 2 09 . 8.7] 87 26 4.^ I 12 . I ; 48 44*2 18.8 08 99-4 42.21 68 154-6 65.6 2S 209 . 9 9- 1 88 26 5 .I 1 1 2 . s ! 49 45-1 19-1 09 10x3 4 a.6j 69 155-6 66. o 2 9 210.8 9-5 ( 8 9 266.0 U2.9 So 46.0 19. < 10 IOI.3 4?.o 70 156 5 66 4 30 211^.7 9 . o 90 266. 9 1 T 3 3 : si 46.9 19.9 III 102.2 43-4J 7' 157-4 66.8 2.31 212.6 0.3] 491 267.9 '13-7 52 47-9 20.3 12 I03.I 43. S 72 iS*,3 67.2 3* 213.6 o.6f 92 268.8 114.1 j 53 48.8 20.7 13 104.0 44.2 73 159-2 67.6 33 2I 4 . S I.O 93 269.7 lI 4-5 ; 54 49-7 21. I H I04. 9 44-5 74 60.2 68.0 34 215.4 1.4 94 270.6 114.9 55 50.6 21.5 5 105.9 44-9! 75 161.1 68.4) 35 216-3 1.8 9S 271.5 1*5-3 ; 56 <>i' s . 21.9 16 106.8 45-3 76 62.0 68. 8J 36 217.2 f .2 96 272.5 IJ 5-7; i 57 S2.<; 22.3 17 107.7 4>7 77 62.9 69.2 37 218.2 2.6 97 273-4 116.0 ; 58 53-4 22.7 18 108.6 46.1 78 63.8 <> 9 .6 J* 2I9.I 3-o 98 274-3 i r 6 . 4 59 54-3 23-1 19 109.5 46.5! 79 164.8 69.9 39 22O.O 3-4 99 275.2 riG.S , 60 55-2 23.4 20 no 5 46.9 801-165.7 70.3 40 22O. Q 3.8 300 276.2 117.2 . Dift Dep. Lat. 1 Dift Dep. Lat. 1 Dift! Dep. Lat. DifJ Dep. _,at. Dift Dep. Lat. tor 67 Decrees. TABLE II. Difference of Latitude and Departure for 24- Degrees. Dift Lat. Dep. Dift 1 Lat. DepJ Dift Lat. Dep. Dift Lat. Dep. Dift Lat. Dep. i 00.9 oc.4 ?! 55-7 24.8 J 121 110.5 49.2 181 165.4 73.6 241 220.2 98.0 i 2 01.8 oo.S 62 ;6.6 25.2 22 111.5 49.6 82 166.3 74-0 42 221. I 98.4 i 3 02.7 01.2 63 57-6 25.6 23 112.4 50.0 83 167.2 74-4 43 222.0 98. 8 i 4 03.7 oi . 6 64 58.5 26.0 24 "3-3 50.4 84 168.1 44 222.9 99.2 5 04.6 02.0 6; 59-4 26.4 as 114.2 50.8 169.0 75-2 4S 223.8 99-7 6 OS-S 02 . 4 66 60. 3 26.8, 26 115.1 51.2 86 169.9 75-7 46 224.7 IOO. 1 j 7 06.4 02.8 67 61.2 27.3 27 116.0 51-7 87 170.8 76 i 47 100.5 ! 8 07-3 3.3 68 62.1 27-7 28 116.9 52.1 88 171.7 48 226.6 100.9 9 08.2 03.7 69 63.0 28.1 29 117.8 52.5 89 172.7 76.9 49 227-5 101 .3 09. i 04.1 70 6 3-9 28.5 30 118.8 52.9 90 173.6 77.3 50 228.4 101.7 H 10. 04-5 71 64.9 28.9 131 119.7 53-3 191 1/4-5 77-7 2SI 229.3 102.1 12 11 .0 04.9 72 65.8 29-3 32 120.6 53-7 92 '75-4 78.1 230.2 101-5 *3 11.9 c,S-3 73 66.7 29.7 33 121.5 54.1 93 176.3 78.5 S3 23I.I 102-9 12.8 OS-7 4 67.6 30.1 34 122.4 54-5 94 177.2 78.9 232.0 i3.3 !^ 13.7 06. i 7S 68.5 30.5 }5 123.3 54-9 95 178.1 79-3 SS 233.0 103-7 16 14.6 ,6. <; "6 69.4 30.9 30 124.2 55-3 ,6 179 i 79-7 104. i j ; . r 06.0 - j 70.3 31.3 77 125. 2 180.0 oO. 1 ' 1 234.8 IO4, C 18 16.4 07- S ?8 7i-3 31.7 '* 126. J 56.1 98 180.9 S8 104.9 | ! ' 17.4 07 . v 79 72.2 32.1 39 I27.O 56.5 99 181.8 So. 9 59 236.6 105.3 j 1 20 18.3 08. ; 73 ' 32.5 40 127.9 56.9 200 182.7 81.3 60 ^37-5 105.8 1 21 I 9 .2 o5. 5 j SJ 74.0 32.9 141 12*. 8 57-3 201 183.6 Si. 8 261 238.4 106.2 22 20. I 08.9 1 82 74-9 33-4 42 129.7 ?7.8 O2 184.5 82. 2 62 239-3 106.6 = 3 11. O 09.4 ! 8? 75-8 33-8 43 130.6 58.2 03 185.4 ^2 6 63 240.3 107.0 ! 24 21.9 00.8 84 76.7 34-2 44 131.6 58.6 04 186.4 83.0 64 241.2 107.4 2S' 22.8 IO. 2 8 "5 77-7 34.6 45 132.5 59.0 OS 187.3 S 3 -4 6s 242.1 107.8 20 23.8 10.6 1 S6 78.6 35.0 46 133.4 59-4 06 188.2 S 3 .8 66 243.0 108.2 ' 27 24.7 11 .0 87 79-5 35-4 47 59-8 07 189.1 84.2 67 247.9 108.6 ! 28 2 S .6 11.4 88 80.4 48 135.2 60.2 08 190.0 8d.6 68 2 4 ;.fc 109.0 29 26.? ii. 8 | 89 81.3 36.2 49 136. 1 60.6 09 190.9 85.0 69 245 7 109.4 30 27.4 12.2 90 Sf.2 36.6 5 137.0 61.0 10 191.8 85.4 70 246.7 109.8 31 28.3 12,6 91 83.1 37-0 IS* 137.9 61.4 211 192. S 85.8 *7i 247.6 I IO.2 32 29.2 13-0 92 37-4 S2 138.9 61.8 12 193.7 S6.2 72 248.5 no. 6 i 3? j J J 30.1 13-4 93 85-0 37-8 139.8 62.2 J 3 194.6 S6.6 73 249.4 IIl.O . 34 3I.I 13.8 94 85.9 38.2 54 r 4 o. 7 62.6 14 '95-5 87.0 74 250. s 111.4 35 32.0 14.2 86.8 38.6 SS 141.6 63.0 IS 196.4 87.4 7*5 251.2 in .9 36 3^.9 14.6 96 87.7 39-0 S6 142.5 6 V5 16 197-3 87.9 76 252.1 112.3 3 7 33-8 15.0 97 88.6 39-5 S7 143.4 63-9 17 198.2 88.? 77 253-1 112. 7 38 34-7 15-5 98 89.5 39-9 58 64.3 18 199.2 88.7 78 254.0 113.1 39 3S-6 it;. 9 99 90.4 40-3 59 145-3 64.7 19 200. i 89 i 79 2 54 *9 113.5 40 36.5 .6.3 too 91.4 40.7 60 146.2 65.1 20 2O1 .0 89.5 80 255.8 113.9 41 37-5 16.7 101 92.3 41.1 101 147.1 6;. 5 221 201.9 s 9-9 281 256.7 JI 4-3 | ' 42 17. J 02 93.2 62 148.0 65.9 22 202.8 90.3 82 257.6 114.7 ! 43 39-3 17-5 03 94.1 47.9 63 148.9 66.3 23 203.7 90.7 83 * 5* * ^ 115-1 ' 44 40.2 17.9 04 95.0 64 149.81 66.7 24 204.6 91.1 84 259.4 us -5 ! : 45 4i.i 18.3 05 95-9 42.7 150.7 67.1 205.5 91-5 85 260.4 11^.9 I 46 42.0 18.7 06 96.8 43.1 66 151.6 67-5 26 206. 5 91.9 86 261 . ^ 116.3 i 47 42.9 10. i 07 97-7 43-5 67 152.6 67.9 27 ^207.4 92-3 87 262.2 116.7 i 4? 43-9 19.5 08 98.7 43-9 68 153.5 68.3 28 208.3 92-7 88 263^ j 117.1 49 44-8 19.9 Of) 99.6 44-3 69 68.7 2 9 209.2 93-1 89 264.0 117.5 SO 45-7 20.3 10 100. 5 44-7 70 '55^ M^.i 30 210. I 93-5 90 264.9 118.0 S ; 51 46.6 20.7 1 1 J 101.4 4<;.i 171 Is6.2 69.6 2V 211. 94. c 291 265.8 118.4 ; -z 47 -S 21.2 12 102.3 45.6 72 157.1 70.0 32 21 1.9 94-4 92 266.8 118.8 ! . 53 48.4 21.6 M 103 .2 46.0 73 158.0 70.4 .33 212-9 94.8 93 ^67.7 119.2 54 49-3 22.0 M 104.1 46.4 74 159.0 70.8 34 213.8 95.2 94 268.6 119.6 ss SO. 2 22.4 IS I05.I 46.8 7 S 159.9 71.2 3S 214.7 95-6 95 269.5 I2O.O S6 51.2 22.8 16 106.0 47-2 76 160.8 71.6 215.6 96.0 96 270.4 120-4 57 5*. I 23.2 17 106.9 47-6 77 161.7 72.0 37 216.5 96.4 97 271.3 120.8 i 58 2-3-6 18 107.8 48.0 78 162.6 72.4 33 217.4 96.8 98 272.2 121. 2 \ 59 53-9 24.0 19 108.7 48-4 79 163-5 72.8 39 2l8.3 97.2 99 273.2 121.6 ! 60 54-8 24.4 20 109.6 48.8 80 164.4 73.2 40 219.3 97.6 300 274.1 122. O Dift Dep. Lat. Dift Dep. tatf-J Dift Dep. Lat. 'ibift Dep. Lat. Dift Dep. Lat. for 60 Degrees. TABLE II. fliffVrence of Latitude and Departure for 25 Degrees. F Dif Lat. Dep. Dift Lat. Dep. II3.-5 52. 85 167.7 7^.2 4 222. 103-5 J 6 05.4 02.5 66 59.8 27-9 26 114.2 53. 86 168.6 78.6 i 4 223. 104.0 ,1 06.3 03.0 1 6 ' 60.7 tS.J 27 115.1 53- 7 ^9-5 79. c 4 223. 10 4-4 1 } 07.3 03.4 6* 61.6 28.7 28 it 6 . o ^4- 8S 170.4 79-5 i 4 224. 104.8 1 9 08. 3. oj.S 6-o 3>> 125. 58.3 9 179 4 83.7 5* 233. * lOg.O | 9 17.2 08.0 7 71.6 n-4 3 126.0 58.7 99 180.4 84.1 59 234-" I093 I 2C 18.1 03.S 80 72- S 33-* 4 126.9 59.2 200 181. 84. 60 235.6 I0 9 . q I 21 19.0 08.9 8 73-4 34. i r 4 127.5 59.0 iOI 182.2 84.9 261 236. "0-3 i 22 19.9 09.3 1 82 74-3 34-7 4 2 128.7 60.0 02 r8 3 .r 5-4 6z *37.j 110.7 I 23 20. 8 09.7 83 75-2 ^- J 43 129.6 60.4 03 184.0 85.8 63 238.4 III. I i *4 21.8 10. I 84 76 . 1 355 44 130.5 60.9 04 184.9 86.2 64 239.3 in. 6 1 25 22 . 7 to. 6 S., 77.0 3S-9 4S 131.4 61. 3 05 185.8 86.6 <>5 240.2 1 1 2 . |J 26 23.6 n.o 1 86 77-9 36.3 46 132.3 61 .7 06 1*0.7 87.1 I 66 241.1 II2. 4 1 27 24.; 1 1.4 87 78. 8 36.8 47 i|}.a 6i. T 07 1*7.6 87- s 67 242.0 112. 8 1 28 25.4 n. 8 88 79-3 37-2 48 134.1 62. s 08 188.5 87.9 63 242.9 "3-3 I 29 26.3 12. 1 89 80.7 37-6 49 135.0 63.0 09 1*9.4 88.3 69 243.8 II5-7 I 30 27.2 12.7 90 ?i.6 38.0 5 H5- 9 63.4 IO 1 90 . 3 S8./ 70 244-7 II 4 .I II 3i aS.i 13. 91 82.5 38.S IS* 136.9 63.5 211 191.2 89.2 2/1 245.4, "4-5 I 32 29.0 13.5 92 81.* 38-91 5 IJ7-8 64.2 12 192.1 89.6 72 246.5 115.0 I I 33 29.9.13.9 93 84! 3 39-3- 53 i3-7 64.7 13 193-0 90.0 73 247.4 "5-4l: 34 30. S 14.4 94 85.2 39-7. S4 139.6 65.1 H *93-9 90.4 74 24^.3, i 5 .i| 35 3i-7 14. S 95 86.1 4^.1: 53 140.5 65.5 15 194.9 90.9 75 249.2 116.2 1 36 S.6|r$.a 96 87.0 40.6; 56 141.4 6<. 9 16 195.8 9'- 3 76 ^50.1 16.6 1 37 n-s 15.6 97 87.9 41. oj S7 142.3 66.4 17, 196.7 91.7 77 -51.0 I7.J 'I 38 34-4 16.1 98 88.8 4i-4 53 145 ^ 66.8 18 197.6 92.1 7* 252.0 I7 *5 1 39 35-3 i6.<; 99 89.7 41- 8. 59 r44.i 67.2 19 19*. 5 92.6 79 -52.9 17.91 1 4 36.3 16.9 100 90.6 4-3. 60 145.0 67.6J 20 199.4 93.o 80 53-8 18.3 1 1 4I 7.2 17.3 IOI 91.5 42.7 161 145.9 j8.o 21 200. 3 93'4 281 54-7 18.8 1 42 8.1 17.7 02 92.4 4?. I: 62 146.8 68.5 21 201.2 3.1 82 55.6 ig.z 1 43 9.0 18.2 03 93-3 43. s! 63 147-7 8-9 2 3 202. I 94-2 83 56.5 19.6 I 44 9-9 18.6 04 94-3 44. o| 64 148.6 9-3 4 2O3.O SH-7 84 57 4 20. o 1 45 0.8 It). 01 05 95-2 44-4| 6s 149.5 9-1 25 103, 9 95.1 *S 5..3 20.4 I 46 4*. 7 19.41 06 96.! 44-8 66 150.4 0.2 26I204.S 95-5 86 59.2 ao. 9 I 47 42.6 r 9-9 07 97.0 45.2; 67 151.4 0.6 2?r 205.7 95-9 7 60. i 21.3 1 4* 43-5 2Q. ^ j 08 97-9 45-6 6S 152.3 I.O 28 206.6 96.4 88 61.0 21.7 1 49 44.4 20. 7 j 09 98.8 46.1 69 153-2 1.4 29 107.5 96.8! 89 61.9 22. I 1 50 45-? 21.1 10 99-7 46.5 70 154.1* 1.8 30 208 . 5 97-2 90 62.8 22.6 I 5i 46.2 21.0 II 00.6 46.9 171 55 o 2.3 V 109.4 97.6 9 1 63-7 23.0 52 47 -i 22.0 12 01.5 47-3 72 55-9 2.7 3 2 110.3 98.0 92 64.6 23-4 1 53 4.8.0 2i. 4 13 02.4 47.8 73 S 6.8 3-ij 33 2It -2 9*-S 93 65-5 aj.8 1 54 4^-9 22.8 14 03.3I43-2 74 57-7 3-5 34 212. i 98.9 94 66.5 24.2 55 49-* 23.2 15 04.2 tf.6l 75 58.6 4.0; 35 '*3-c 99-3 9S 67.4 24.7 1 56 50.8 13.7 16 05.1 4.9.0" 76 59-5 4 4 36 213.9 99-7 96 68.3 25.1 57 5^-7 H.I 17 06.0 49. 4 1 ' 77 60.474.8 r 214.8 OO.2 97 69.2 25.5 1 58 52.6 *4-5 iS 06.9 w-v|i 72 6i.;: 75 r ?8 215-7 20.6 98 70.1 25.9 59J53-5 :4-9 '9 07.9 5-3j; 7<; 62.2,75.61 ^9 216.6 01. O 99 71.0 26.4 60)54.4 5.4 20 08.8 50.7 80 63.1 76.1 40; -17- ^ or. 4 00 71.9 26.8 1 >if Dep. Ut. Dift Dep. Laf. 1 Difr Dep. 'f-at. 1 iff Den. I>.t. Dift Den. r.at. 1 F f for 65 Degrees. 1 TABLE II. Difference of Latitude and Departure for 26 Degrees. ift ut. e P . Dift Lat. Dep.' ift Lat. )ep.' Dift Lat. Dp. ift Lat. 1 Dep. 1 0.9 0.4 61 54.8 16.7 21 08.3 3.6 81 162.7 79-3 41 16.6 05.6 2 1.8 0.9 62 55-7 27.2 22 09.7 >3-5 82 163.6 79.8 42 17. s 06. i 3 2.7 '! 63 56.6 27.6 23 10 6 53-9 83 164.5 80.2 43 18.4 06.5 4 j. 6 1.8 64 57-5 28.1 24 11.5 54-4 84 165.4 9o. 7 44 19*3 07.0 5 4-5 ^.^ 65 58.4 28.5 25 12.3 54.8 166.3 fti.i 45 22O. 2 07.4 6 5.4 2.6 66 59 3 28.9 26 13-- 55 .2 86 167.2 81.5 46 221 . I 07.8 7 6.3 3-J 67 60.2 29.4 27 14.1 S5-7 87 168.1 82.0 47 222.0 08.3 8 7. 2 3-5 6S 61.1 29. J> ft 3 115.0 ,6.1 88 169.0 82.4 48 222-9 08.7 9 8.1 3 9 69 62.0 30.2 29 115.9 56.5 89 169.9 82.9 49 223-8 9 . 10 9.0 4-4 70 62.9 30-7 30 16.8 57.0 90 170.8 83.3 5o 224.7 9 .6 11 9.9 4.8 7i 63.8 31.1 31 II7-7 57-4 191 171.7 83-7 Si 225-6 IO.O ! T2 0.8 5-3 72 64.7 31.6 32 118.6 57.9 92 172.6 84-2 S* 226. s 10. SJ 13 1-7 5-7 73 65.6 32.0 33 "9-5 58.3 173-5 84.6 227.4 10.9 14 2.6 6.1 74 66.5 32-4 34 120.4 58.7 94 174.4 8s. o 54 228.3 11.3 15 3-5 6.6 75 67.4 32.9 35 121.3 59 - 175-3 85- s 5S 229.2 11,8 1C 4.4 07. 76 68.3 33-3 36 122.2 59-6 96 176. 2 *5-9 S6 230.1 12. 2 I? 5-3 07. s 77 69.2 33-8 37 123 . I 60. i 97 177-1 86.4 S7 231.0 12.7 18 6.2 ^7.9 78 70.1 34.2 38 124.0 60.5 98(178.0 86.8 58 231.9 1. 7I 08 . 3 79 71.0 34.6 39 124.9 0.9 99 I7.9 87.2 59 232.8 x 3-5 20 8.0 08.8 1 80 71.9 3S-i 40 125.8 1.4 200 179.8 87.7 60 233.7 14.0 21 8.9 o 9 .*f Si f.ti 35-5 141 126.7 t.8 2OI 180.7 88.1 61 234.6 14.4 zt 9.8 09. 6H 82 73-7 35-9 42 127.6 2.2 O2 181.6 88.6 62 235-5 14.9 23 0.7 10. i| 83 74.6 36.4 43 128.<; 2.7 03 182.5 89.0 63 236.4 24 1.6 10. 5 i 84 75-5 36.8 44 129.4 3-1 04 183.4 89.4 64 237-3 15-7 25 2. 5 If 'S !l 76.4 37.3 45 130.3 3.6 OS 184.3 89.9 6S 238.2 16.2 26 3-4 11.4 86 77-3 37-7 46 131.2 4.0 06 185.2 9. 3 66 239.1 16.6 27 4-3 ii. 8 87 78.2 38. r 47 4.4 07 186. i 90.7 67 240.0 17.0 28, 25.2 12.3 88 79.1 38.6 48 133-0 4.9 oS 186.9 91.2 68 240.9 29 26.1 12-7 8 9 80.0 39.0 49 133-9 5-3 09 187.8 91.6 69 241.8 17.9 30 27.0 13- 2|| 90 80.9 3JK5 5^> 134.8 5-8 10 188.7 92.1 70 242.7 18.4 3 27.9 13.6 1 9I 81.8 39-9 I5 1 135.7 66.2 211 189.6 92.5 271 243.6 18.8 32 28.8 14.0 92 82,7 40,3 52 136.6 66.6 12 190.5 92-9 72 244.5 19.2 3 29-7 14.5 93 83.6 40.8 53 137-5 67.1 13 191.4 93-4 71 245.4 19.7 34 30.6 14.9 94 84-5 41 2 54 138.4 67-5 H 192.3 93-8 74 246.3 20. I 3 31. 1 5-3 95 85.4 41.6 5S 139-3 67.9 15 193.2 94.2 75 247.2 20.6 3 32.4 15.8 96 86.3 42.1 5* 140.2 68.4 16 194.1 94-7 76 248.1 21. O 3 33. i6.2|| 97 87.2 57 I4I.I 68.8 17 195.0 95- 1 77 449.0 21-4 3 34* 16.7 98 88.1 43.0 58 142.0 69.3 18 195.9 9S-6 78 249 . 9 121.9 3 17-1 99 89.0 41-4 59 142.9 69.7 19 196,8 96.0 79 250.8 122.3 4 36. 17.5 100 89.9 43.8 60 143 8 70.1 20 197.7 96.4 80 251.7 122-7 4 36. 18.0 ioi 90.8 44. 16 144.7 70.6 221 198.6 96.9 281 252. b 123.2 4 37- 18.4 02 91.7 44-" 62 145.6 71.0 22 199.5 97 3 82 123.6 4 18.8 03 92.6 4S- 6 146.5 71- S 23 200.4 97. b 83 254.4 124.1 4 39- 19-3 4 9V5 45.6 64 147-4 71.9 24 201 .3 98. 84 25v3 124.5 4 40. 19-7 05 94.4 46. 6 148.3 72-3 2S 202.2 98. 8 256-2 124.9 4 41. 20.2 06 95-3 46. 6 149.2 72.8 26 203 . I 99- 86 257.1 T25.4 4 4-- 20.6 07 90.2 46. 6 150. i 73.2 27 204.0 99- 87 258.0 12;. 8! 4 43. 21. O8 97. i 47- 6 151.0 28 204.9 99. 88 126.3 ' 4 44. 21.5 9 98.0 47- 6 1151.9 74.1 29 I20S-8 100.4 89 259.x 126.7 i 5 44. 21.9 10 98.9 48. 7 IS2.S 74-5 30 '206 . 7 100. 90 260. 127.1 i 45 22.4 III 99.8 48. J7 153-7 75 -o 231 207.6 IOI . 29 261. 127.6 I 46. 22.8 12 103.7 49. 7 1S4- 6 75-4 32 20J. -' 101 . 92 262.4 128.0 47- 23-2 13 101.6 49- 7 1 5 5 r 75 .8 33 209.4 IO2. 9 263. 12*. 4 ' 48. 23-7 14 IO2. q 50. 7 156 4 76.3 34 210.3 IO2. 94 128.9 ; 49- -4-M T 5 103.4 50. 7 157.3 6.7 35 211.2 103. 95 2^ . 129.3 - 50. 24.5 16 104.3 7 158.2 77.2 36 212.1 103. 96 266. 1*9.8 $? 25-0 17 105.2 Si- 7 159 T 77-' 37 213 .olio} . 97 266. 1^0.2 i "52- 25.4 18 106.1 51 . 7 l63.G ?X.c ! r 213.9 104. 98 267- 130.6 | 53 -5-9 *9 107.0 52. 7 160.4 78*5 39 214. 5: 104. 99 263. f -j I , I 6 53- Z6.J 20 107.9 5 2 - 8 161.8 78-0 40 215.' IO5 . 300 269. D Dep Lat. ('foil Dep. Lat Dift Dep. Lat. JJDift Dep. Lat Dif t Dep Lat. for 64- Degrees. TABLE II. Difference of Latitude and Departure for 2? Degrees* ; Dift!Lat. Dep. ift Lat. Dep. PjDift Lat. ep. ; ift Lat. Dep. ift Lat. Dep. i 00.9 oo. s 61 54-4 7-7 121 07.4 4-9J Si 61.3 82.2 41 14.7 109.4 2 01.8 00.9 62 55.2 8.1 22 08.7 5-4 52 62.2 82.6 42 15.6 109.9 3 02.7 01.4} 63 56.1 8.6 M 09.6 5.8 83 63.1 83-1 U 16.5 110.3 4 03.6 01. 8j 64 57.0 9.1 24 10. ; 6-3 84 63.9 83.5 44 17.4 no 8 | 5 04.5 03.3! 65 57-9 9-5 *5 111.4 6.7 *5 64.8 84.0 45 i-3 [II. 2 6 05-3 02.7 66 58.8 0.0 2t> 12.3 7- 2 86 65.7 84.4 46 19:2 111.7 7 06.2 03.2 67 59-7 0.4 *? 13.2 7 7 8? 66.6 84.0 47 20. i [12. I 8 07. i 03.6 68 60.6 0.9 28 14.0 8.1 88 67.5 85.4 48 21.0 iz.6 9 08. c 04. i 69 61.5 1*3 29 14.9 8.6 89 68.4 85.8 49 21.9 13.0 10 08.9 04.5 70 62.4 i.S 3^ 115.8 9.0 9 69.3 86.3 5 22.8 T 3-5 ii 09.8 05.0 71 63.3 2.2 HI 16.7 9'5 91 70.2 86.7 51 23.6 14.0 12 10.7 05-4 72 64.2 2.7 3* 17.6 9-9 92 71.1 87.2 5i 24.5 14.4 13 ii. 6 05.9 73 65.0 3 i 33 15.5 0.4! 93 72.0 87.6 53 25.4 14.9 r 4 12. -, 06.4 74 65-9 3.6 34 19.4 0.8 94 72.9 88.1 54 26.3 r 5-3 15 IS -4 06. S 7. 66.8 4.0 35 20.3 i-3 95 73-7 88. s 55 27. 2 15.8 16 14.3 07-. 3 76 67-7 4-5 36 121. 2 T ' 7 i 96 74-6 89.0 5 6 28.1 16.2 17 15.1 07.7 77 68.6 5.0 37 122. 1 2.2 97 75-5 89.4 57 29.0 16.7 1 18 16.0 03.2 73 690 5-4 3* 123.0 2.7 93 76.4 89.9 5* 29.9 17.1 *9 iC) . 9 08.6 79 70.4 5-9 V) 1*3.8 3-1! 99 77-3 90.3 59 30.8 17.6 20 17-8 09. i So 7^3 6.; 40 124.7 3.6! 00 78.2 oo .8 60 3*.7 18.0 21 18.7 09 . 5 Si 72.2 6.b ! 141 12,-. 6 4.0} 01 79.1 91.3 61 32.6 18.5 22 19.6 10 O 82 73-i 7.2 4 1 126.5 4-5 oi So'.o 91.7 62 33-4 18.9 *3 20.5 10.4 *3 74.0 7-7 43 127.4 4-9, 03 80.9 92.2 63 34-3 19.4 i * 4 zi.,4 10.91 84 74 * 8.1 M 128.3 5-4 04 Si. 8 92.-:, 64 35-2 19.9 S- a.-3 "3 8; 75-7 38.6 45 129.2 5-3' OS 82.7 93-i 65 36.1 20.3 j 26 2.1 -1 ii. 8 86 76.6 9.0 4 6 130.1 06 S 3 .5 93'. 5| 66 37. c 20.8 -7 24.1 12.3 1? 77-5 39-5 47 131.0 6.7 07 84.4 94.0 67 r--< 21.2 28 24.9 12.7 88 78.4 40.0 4^> 131.9 7.2! 08 8-4 90; 12 88.9 96.2 72 .42.4 23-5 ! 33 29.4 15.0 93 82.9 L2. 2 53 136. 3 9-5 13 89.8 96.7 73 243 . : 23.9 i 34 30.3 15-4 94 83.8 42. 7 54 137-2 9-9 H 90.7 97.2 74 244. 24.4 35 31.2 15.9 95 i?4. 6 43-i 5S 138.1 0.4 IS 91.6 97-6 1 r -45- 2 4 .8 3<> }2. I 16.3 96 85.5 43.6 ;6 139.0 0.8 16 9*-5 98.1 7 6 -45 125-3 3 7 33.0 16.8 97 86.4 44.0 57 139.9 1.3 17 93-3 9*. 5 77 246.8 1*5-8 3* 33-9 F7-3 95 87.3 44-5 5* r 4 o * 1-7 18 194.2 99.0 78 247.', !26.2 39 J4'7 n-7 99 88.2 44 9 50 141.7 2.2 19 195.1 99.4 79 248..' I26. 7 40 35,6 I*. 2 100 89.1 4>-4 60 142.6 72.6 20 196.0 99.9 ^0 249.5 I2 7 .I 4 1 <6. 5 18.6 101 90.0 45-9 161 143-5 73-1 221 196,9 IOO. ' 281 250.4 I2 7 .6 42 ?7-4 19.1 02 90.9 46.3 62 H4-3 73-5 22 197-8 loo. b 82 251-5 128.0 43 3*- 3 19.5 03 91.8 46.8 6 145-2 74.0 23 19^-7 101.2 83 252.2 I28. 5 44 39.2 20.0 04 92.7 47.2 64 146 .) 74-5 li 199.6 IOI.7 84 253.0 123.9 45 40.1 2O. i 5 93.6 47-7 65 r 47 .o 749 25 200 . 5 IO2. I 8 253-9 129.4 4 6 41-0 26.9 06 94-4 48.1 66 -47-9 75-4 26 201.4 IO2.6 86 254.8 129.8 47 41.9 21.3 07 95-3 4*. 6 6; 148-8 75-8 27 202.3 I03.I 8~ 255-7 130.3 48 42.8 21.8 08 96.2 49.0 6 149.7 7M 2' 203-1 103-5 8b 256. 130.7 49 43-7 22.2 09 97.1 49-5 61 150.6 74.7 2 9 204.0 104.0 8 257. I3I.2| 5 44-6 22.7 10 98.0 49-9 70 151- 77.2 30 204.9 104.4 90 258.4 I3I-7 51 45-4 23.2 III 98.9 50.4 i 17 152.4 77.6 i3 205. b 104.9 -9 259. 132,1 52 40-. 3 23 .6 12 99.8 S o. 8 7 153- 78.1 32 206.7 105.3 9 260. T32.6 53 47.1 24. 1 13 100.7 M3 7 IS*- 78. 3 207.6 105.8 9 261. fSJ.o 54 48.1 24. H 101 .6 Si. 8 7 155.0 79.0 3' 208.5 106 . 9 262. 133.5 55 49.0 25.0 15 roz. 52.2 T5 r 55- 7Q-4 3 209.4 ro6. 9 262. 133.9 5<> 49-9 25.4 It r 3-4 5-- 7 76 156. 799 3 2IO. ' 107. 9 263. 154*4 57 50.8 -5- 17 104. 53-1 77 157- 80.4 3 211 .2 107. 9 26a. f34-^ $8 5 1 7 26. 18 105. 53 <" 7:5 158. 80. 3 212.1 108. 9 265. 135-3 59 52.6 26. 1 9 106. 54-o 79 59- Si. 3 2I3.C > 108. 9 265 135-7 4 53-5 27. 20 106. 54-.^ *c I 6 3 . i 81. 4 *I3* > 109. 30 267. 136.2 Dif Dep |Lat Dif Dep Lat. Dif t Dep Lat Di Dep Lat D Dep Lat. F f 2 for 63 Degrees. TABLE II. , Difference of Latitude and Departure for L V 8 Decrees. Dift Lat, Dep. 'Dift Lat. Dep. Dift Lat. Dep.lJDift Lat. Dep. Dift| Lat. Dep. i 00.9 00.5 61 53-9 2H.6 i i i 106.8 56.8 IM M9- 85.0 241 212.8 113.1 i oi.S 00.9 62 54-7 29.1 12 107.7 57-3 2 160.7 85.4 42 213.7 115.6 3 01.6 01 .4 63 5J-6 29.6 *3 108.6 57-7 83 161.6 8>. 9 43(214-6 114. i 4 03- 5 01 .9 64 56-5 30.0 2 4 109.5 58.2 84 161.5 86.4 44 215.4 114 6 e 04.4 04-3 6s 57-4 jo.5 25 110.4 5^.. 7 8; 163.3 86.9 45 216.3 r 15.0 6 05.3 02.8 66 5*. 3 31.0 26 111.3 59.2 86 164,2 87.3 46 217.2 i'5-S 7 06.2 03.3 67 59.2 }!< 27 ill. j. 59-6 8? 1*5.1 87.8 47 218.1 116.0 8 07.1 63.8 68 60.0 31.9 18 113.0 60. i 88 166.0 88.3 48 219.0 116.4 9 07.9 04.2 69 60.9 32-4 9 "3-9 60.6 89 166.9 88.7 49 219.9 1 16.9 10 oS.S 04.7 70 61.8 32.9 30 114.8 61.0 90 167.8 89.2 So 220.7 117.4! n 09.7 DS. * 7* 62.7 33-3 r 3 r *f5-7 6<. S 191 168.6 89.7 251 221.6 117.8 12, 10.6 05.6 7^ 63.6 33-* 3* 116.5 62.0 92 169.5 90. i W 222.5 118.3 13 it. 5 06. 1 73 64-5 34-3 33 117.4 62.4 93 170.4. 90.6 & 223.4 n8.8 I J 4 12.4 06.6 74 65 3 347 34 118.3 62 . 9 94 1/1.3 91.1 54 2^4-3 119.2 i 15 13.2 07.0 7S 66. i 35- 35 119.2 63.4 95 172.2 91.5 55 225.2 119.7 , i r 6 14- r 07-5 76 67. r 3<;-7 36 f20. I 63.8 96 I73.I 92 .0 56 226.O 120.2 ' ' 1 7 15.0 08.0 77 68.0 36.1 37 121 .0 64-3 97 173-9 92.5 57 226.9 120.7 1 T ^ 15.9 08.5 7 68.9 36.6 3* 121. S 64.8 98 174.8 93.0 58 217.8 I2J. I i I9 r6 8 08.9 79 69.8 37.J 39 IZ2-7 65.3 99 175-7 93-4 59 228.7 121.6 i 20 17-7 09.4 So 70.6 37.6 40 123.6 65.7 200 J76.6 93-9 60 229.6 122. J ! II .So 09.9 Si 71.5 38.0 141 124.5 66.2 2OI '77-.S 94-4 261 230.4 122-5 i , 22 19.4 10.3 82 72.4 #5 42 125.4 66.7 02 1/8-4 94.8 62 *3i-3 123.0 | *3 2Q-3 10.8 3 73-3 39-0 43 116.3 67.1 03 r/9- 95-3 6? 232.2 123.5 *4 21.3 n3 4 74 - 39-4 441117.1 67. 6 H 04 i 80- i ! 9^.8 64 233.1 123.9 i 2; 22.1 11.7 & s 7 '.i 399 4^" 128.0 68.1 05 181.0] 96.2 65! 234 "4-4 ! 26 23-0 12. i 86 75-9 40.4 46 128.9 63.. 06 181.9! 96.7 66J234-9 i24. 9; 27 1*8 I*. 7 8- 7M 40.8 47 129 .8 [69.0 C7 182.8 97,2 67 235.7 125.3 28 24-7 13.1 S8 77-7 4L1 48 130.7 69.5 08 1*3.7 97 7 6S 236.6 !2 5 .8 29 25,6 H.6 89 78.6 41.8 49 131.6 70.0 09 '*4.5 98.1 69 237-5 126.3 1 3 a6. S 14.1 90 79-5 4*3 5 132.4 70.4 10 i5.4 98.6 70 238.4 26.8j | V 27.4 14 6 9' 80.3 41-7 '5i '33-3 70.9 211 tS6.3 99.1 271 239-3 127.2 : r- iS.j 1-5. o 9^ 81.2 43-2 <5* I34-* 71-4 12 tS 7 .2 99-5 72 240- 2 127.7 I 3? -9 * f 5 5 93 8*-i 43." 53 135.1 (71. 8 13 !X.l 100. 73 24 r . o 128.2 ; 1 34 $0.0 16.0 . 94 85.0 44.1 >4 136.0 72.3 14 189.0 100. <; 74 241.9 128.6 : 35 50.9 16.4 9; 83.9^44-6 S5 136.9 T2.S IJ 189.8 100.9 75 242.8 129.1 i 3 .6 r?3 98 86 < 46.0 58 i39o 74 18 192.5 102.3 "8 *45.5 '30-5' 39 *4-4 i3.; 99 S 7 . 4 46. < 59 140.4 74- 6 19 193.4 102. X 79 246.3 3-9' 1 40 15-3 18.8 100 88.3J46. 9 60 141.3 75-i 10 I 9 4.2 103 3 80 247.2 nr.5 4* 3<>.2 19.2 101 89.2147.4 161 142.2 75.6 221 195. I 103.8 281 248.1 131.9; 42 UI i9.7 OS 90.1 47-9 62 143.0 76. i 22 196.0 104.2 82 249.0 132.4 43 38.0 20.2 03 90.9 43.4 63 143.9 7^-5 23 196.9 104.7 8] 249.9 132.9 44 33. 3 20.7 04 91.8(48.8 64 144.8 77-0 2 4 197.8 105.2 V 4 vo.8 '33-3: 4< J9-7 21. r ON 9 2 -~J49-3 65 *45-7 77. 5 ! 2; 198.7 ro>.6 8; i< J..i. 6 I33* 46 40. 6 21.6 06 93.6149.8 66 /46.6|77-9i 26 199.5 106. i 86 2S2-.> : 34-S, 4" 4 r -5 22. 1 O7 94- 5 1 5>- 67 r47.5 78.4 27 200.41106.6 7 253.4 134-7 48 42.4 21.5 08 9^-4 ^0.7 68 148.3 78,9 28 201.3 r O7.o 88 254.3 ^35 -> 49 43-3 23.0 09 96.2 cr.2 69 149.2 79.3 2 9 202.2 107.5 89 255.2 135.7 50 44.1 23. 5 10 j 97.1151.6 70 150. i 7 9 .8 30 203 . I 108.0 90 256.1 '3^- ' i 5 ' 15.0 23.9 III j 98.01 52. I 171! 151. o 80.3 1231 204. o 108.4 291 256.9 136-6, 52 45-9 24.4 12! 98.9)52.6 72 15^.9 ^0.7 32 204.8 108.9 92 257*8 137.1 53 45.8 24.9 13 99.'^ 153-1 73 'Sa.-7 * 33 205.7 109.4 93 58.^ 137-6 54 47-7 2<.4 14 roo.7J;3-5 74 i<;3-6 8'7 34 206.6 109.9 94 25^9.6 138.0 5! 48.6 15.8 rs ior.> ^4.0 7S 154.5 Si.iiJ 35 207.5 110.3 9> 260. - 38 5, 0)49.4 26.} 16 101.4^4.5 76 155-4 82.6 S^ 208.4 no. 8 96 261 .4 39-o 57! 50. 'j! 26. 8 171103.3 54*9 i 77 156-3 83.1 37 209 . 3 "i-3 j 97 262.2 r 39-4 <8s<;i..;!27.2 181104. 2 ^-.4 7* 157.2183.6 3 y 210. I 111.71; 98 263,. i. '39,- 9: ciffft.rfa?.? 19 j 105. i yv9 79 I5?;0!*4.0 39 ari.o II2.2! 99 264.0 140.4 6o| ^.o|z^.2 ao 106.0 56. 3 8oi T58.9 4 .^ 40 211.9 II2.7J1300 ^64. 9 140.8 Difj Dcjp J Lac. 'Wft Dep. Lat. Difi Dep. Lit. Dift Dep. Lat. ItDift Dep,' Rat. for 62 Dcgreos. I TABLE II. Difference of Latitude and Departure for 29 Degree*. Diftl Lat Dep Dif . Lat. Dep. bi Lat. Dep Dif Lat. Dep Dif t Lat. Dep. I OO. CO. 01 53 -4 29.6 12 105.8 58. I5'i 158. 87. Z 4 1 210. 5 1J6. or. 01 . 62 54- 30.1 2 106.7 59- 82 159-2 88. 4 2 211.' 7 "7-3 02. 01. 63 55* 30 o i z 107 .6 59- 8^ *'6o. 88. 4^ 212. 117.8 o^. 01. 64 56. c 31. c Zi 108.5 60. 84 160.0 89. 4H 213. i ,118.3 04.4 02. 65 56. S 31-5 2 109.3 60. 85 161.8 89. 45 214.; 118.8 os. 2 02. 66 S7-7 32.0 2 IIO. 2 61. 86 162.7 90. 46 215.2 r i9-3 06. 03. 67 S8. 32-5 27 III.l 61. 87 163.6 90. 47 2I6.C 5119.7 07.0 03. 68 S9- 33-c 28 112. 62. 88 164.^ 91. 48 2I6.C 120.2 07.9 04. 69 60. 33- S 2 9 112. 8 62. 89 165.3 91- 49 217- i 120.7 i o5.; 04. 70 61.2 33-9 30 113.7 63- i 90 166.2 92 . 5 218.; '21. 2 09.6 05. 7* 62. 34-4 1 r 3 114.6 63. 191 167.1 92- 251 219.= 121.7 xo. 5 05. 72 63. c H-9 32 115.4 64. 92 167.9 93- 52 220.4 122.2 ii .4 06. 73 6 V 8 35-4 33 116.3 64. 1 93 i68.b 93- S3 221.3 122.7 12.2 06.8 74 6 4-~ 35-9 34 117.2 65- ! 94 169,7 94. 54 222. 2 ^2J.| I3-I 07.3 75 6 5.6 36. 4 35 iiS.i 65. ! 95 170.6 94- 5 223. r 123.6 14 o 07.8 76 66,^ 36.8 36 118.9 65'. i 96 171.4 95- 56 22V Q 124. I 14.9 08.2 77 67-3 37-3 37 119.8 66. ' 7 172-3 95- 5' 224.^ 124.6 iS-7 08.7 | 78 68. a 37-8 38 120.7 66. ; 98 173.2 96.0 5 225.- I2 5 . r 16.6 09.2 70 69.1 38.3 i 39 121. 6 67.4 99 174-0 96. 59 226. 125.6 20 17.5 09.- 80 70.0 3 S.8 1 40 122.4 67.9 200 174.9 97.o 6c 227.4 126. I 21 18.4 10.2 81 70-8 39-3 1141 123-3 68.4 iOI 175. b 97-4 261 228.3 126.5 22 19.2 IO.7 82 71.7 39-8 1 42 124.2 68.8 O2 176.7 97-9 62 229.2 127-0 j 2} 20. I IT. 2 9s 72.6 40.2 43 125.1 6 9-3 03 177-5 98.4 63 230.0 127.5 Zi 21. O II .6 8 4 73- S 40.7 44 125.9 69.8 04 178.4 98.0 64 230. c 128.0 ' 25 2I.Q 12. I 85 74-3 41.2 45 126.8 70. 3 "5 179-3 99.4 65 231.8 128.5 j 26 22.7 12. 6 86 75-* 41.7 46 127.7 7?.t 06 180.2 99 9 66 232.6 129.0 ; 2 7 a) ft 13.1 87 76.1 42.2 47 128.6 71.3 07 181 o 100.4 67 233.5 129.4 1 z8 24-5 13.6 88 77-c 4*. 7, 4* 129.4 71 .h 08 181.9 00.8 68 234-4 I2 9 . 9 Z 9 *54 14.1 89 77-8 43- if 49 130.3 72 . 2 09 182.8 or. 3 69 2 35-3 130.4 j 30 6.* 14.5 90 78.7 43. 6* 50 131.2 72.7 10 183.7 01.8 /o 2 3 6 .1 130.9 3i 27.1 15.0 9* 79.6 44.1 151 132.1 73--- 211 184- S 02.3 271 237.0 I3I.4 32 28.0 J 5-5 92 80.5 44.6 52 132.9 73-7 12 185.4 02.8 72 237-9 131.9 33 8.$ 6.0 93 81.3 45-1 53 H3- 8 |74- 2 IJ 186.3 03.3 73 ajg.fc 132.4- 34 9-7 6.s 94 82.2 4S-6 5* 134-7 74 7 H 187.2 03.7 74 239. t (32. s 35 0.6 7-0 95 83-1 46.1 SS 135.6 75.i IJ i83.o 04.2! 75 240.; 33.3 36 1-5 7-5 96 84-0 6. 5 56 136.4 - ; . ( 16 188.9 04.7, 76 241.4 133.8 37 2.4 7>9 97 84.8 47.0 57 137.3 76.1 *7 189.8 05.2; 77 242.3 '34-3 3 3-2 8.4 9: 85.7 4-7-5 58 138.2 7 6 6 ! -s 190.7 05.7 7? 243.1 r 34 .8 39 4.1 8-9 99! 86.6 48.0 59 I39- 1 77-J '9 191.5 06.2! 79 -44 -c ^5-3 40 5.0 9.4 oo j 87,5 8.5 60 139.9 77-6 20 191.4 06.7 80 -44-9 35-7 41 5-9 9.9 01 88.3 49 o 161 140.8 78.1 21 J 93-3 07.1 s i 145.^ 36-2 4* 6.7 0.4 02 89.2 49-5 62 141.7 78.5 22 194.2 07.6! 82 146.6 36-7 43 7-6 0.8 03 90.1 49.9 63 42.6 79.0 3 195.0 08. 1 83 *47 37.2 44 8.5 M 04 91.0 0.4 6-4 H3-4 79-5 24 195.9 08. 6j 84 48.4 37-7 45 9-4 1.8 05 91. 8 0.9 6s 44-3 80.0 2.C 196.8 09.1 8s M-9-3 }8.2 46 0.2 M,3 06; 92.7 51.4 66 145 2 80. S 26 ^97-7 09.6 86 50. j 38.7 47 I. I 21.8 7 93.6 51.9 67 146.1 Si.c 27 198.5 IO. 1 87 151. c 39- 1 48 ,2,0 23-3- 1 08 94.5 52.4 68 46.9 81.4 28 199.4 ro. c 8x 51. c 39-6 49 2.9 23- 8j 09 95.3 52.8 6? 47-8 81.9 29 200.3 II. C 8-9 >2.^. 40.1 50 3-7 24. e| to 96.2 53-3 70 48.7 82.4 3 2O I. 2 II.: 9 C t$6 4.0.6 5J 4.6 24.7 ii 97-1 53.8 171 49.6 *a. 9 35 2O2.0 12. C 9i 545 41-1 5* 5-5 5.2 12 98.0 543 72 50 4 83.4 32 202.9 I2 -5 92 55.4)141.6 53 6.4 25.7 13 9 K*8 54.8 73 5i-3 83.9 33 203-S 13.0 93 5 6. 3 |] 4 2.0 54 7. a 26.2! J 4i 99-7 55 3 74 52.2 84.4 ^4 204.7 13.4 94 57-1 142.5 55 8.1 26.7 15 100.6 55.8 75 53-1 84.8 35 205.5 i3- r 9> ;8.c 143.0 5 9.0 27-1 16 jioi.c 56. 2 76 53-9 5.3 36 206.4 14. -c 96 5S-9 '43-5 57 9-9 27.6 17 I 02.3 56.7 77 54.8 8^.8 37 207.3 r 4- ( . 97 9.8 144.0 58 0.7 28.1 18 i 03-2 57.2 78 55-7 86.3 38 208.2 15.4 98 6^.6 M45 59 1.6 28.6 19 i 04.1 57-7 79 56.6 86.^ 39 20 ? .0[I15. 9 99 6hj 145.0 60 *'5 29.1 20 I 05.0 5*.2 1 80 57-4 87.3 40' 209.9 [Il6.^ 300 1.2 4 r45. .4 JDiftlbcp. Lat. ift Dep. Lat. | Dift Dep Lat ift D?p. 1 Lat. ' Difti Dep. Lar. ' for 61 Degrees. T.YBLE II. Difference of Latitude and Departure for 30 Degrees. iDiitfLat. Dep.hDift Lat. Dep. 1 Diftl Lat. Jcp.'Diftj Lat. 3e P .(|r )ift Lat. Dep. i 0.9 < 30.5 61 5.8. 50.5 121 104.8 o.5|i*i i 56.8 90.51 a 4 r 08.7 20.5 | 3. 1.0 62 53-7 !"oj 22 |I05.7 i.o'j 82 i 57.6 91 .o| 42 09.6 21.0 I 3 2.6 1.5; 63 54,6 **-sl 23 106.5 i.S ?3 . sM 9 l 5|i 43 10.4 21.5 1 4 3- 5 2.0 : 64 55-4 52.0 24 1 07.4 2.0 84 59-3 9 2 . o|: 44 ir-3 22. t 5 4-3 2.S | 6S 56.3 j*.5i 2S 08. 3 2-5 85 60. 2 92.5!' 45 12.2 22.5 1 6 5-2 3.0 | & 57-2 'l 7.6 09. i 3.0 86 t6r.i 93-^j 46 13-0 23-0 I j 6. i 3-> i 67 58.0 3VS 27 no.o 3.5 7 [61.9 93-5| 47 '3 9 2 3-5 1 8 6.9 4-0 ! 68 58.9 34-0 28 10,9 4.0 88 62. S 94- r j 48 ! 4 .* 24.0 I 9 7-8 4^ i 69 59.8 34- S 2 9 en. 7 4-5J 89 63-7 94-5 49 15.6 24o 1 to M 5.0 i 70 60.6 35-B 3 LI2.6 5.0 90 64.5 95.0 5 16.5 25.0 11 9o 55 7i 61.5 35-5U MI H3.4 -S-S) 191 65.4 95-5 -Si I7. 4 25-5 I 12 0.4 6.0 72 62.4 36.oU 3- II4-3 6.0 92 66.3 9 6.o\\ S* 18.2 26*0 1 13 1-3 6.5 73 63.2 J6*5l 33 II5.2 6 -5i 93 67.1 96.5 53 19.1 26.5 I 14 2. 1 7.0 74l 64.1 37- o| 34 r 1 6 . o <-; 94 6-5.0 97-j 54 20.0 27.0 1 is 3.0 7-5 75 6s- o 37- S 3^ 116.9 7-5 95 68.9 97-Sfl 55 20.8 27-5 1 16 3-9 8.0 76 6s- 8 ,8.0 36 117.8 >8.o 96 69.7 98.0 56 21 .7 28.0 1 15 4-7 i;5 77 66.7 p!s <7 1 1 3 . 6 18.51 97 70.6 9So 57 22.6 28.5 I iS s.6 q.O 76 67.5 39.0 38 119.5 ^9.0 98 71.5 99.0 58 ^3-4 29.0 1 9 6.s 9'5 79 68.4 39-5 39 120.4 59 SB 99 7- 3 99-5 59 224.3 29.5 I 2C *"* ? Q.O 80 69.3 40.0 40 121 . 2 70.0! ioo 73-2 lOO.OJj 60 225.2 130.0 1 21 ITa 0-5 81 70.1 1 40.51 141 T22. I 70.5 1201 74.1 100.5 Ui 226.0 !3o.5 1 a 9.1 uo 82 71.0 41.0 42 123.0 /r.o] 02 74-9 IOI .OU 62 226.9 131.0 1 23 9-9 11.5 3 71.9 4i-5 43 123.8 7i -SB 03 75.8 IOI.5H 6 3 227. b *3i5 1 *4 10.8 12.0 84 72.7 42.0 44 124.7 72-0 o^ 76.7 IO2.0 6^ 228.6 132,0 I 2. c 21.7 12.5 8s 73.6 4*.5 4S 125.6 72 ' 5 ! ^ 77-5 102. S 1 65 229.5 132-5 1 26 *i. ; 13.01* 86 74-5 43.0) 46 126. < 7-J .M Ou 7^-4 103.0 66 230.4 133-0 1 2-7 *3-4 13. s *7 75-3 43- S i 4: 127.3 73-5| o 79-3 103.5 67 231.2 r 33-5 28 14.2 14.0 88 76.2 44.0 4^ 128.2 74.08 o 180.1 104.0 68 232.1 134.0 29 25.1 14. s ^9 77-1 44-5 49 I29.O 74-5J o iSr.c I04.5fl 6 9 233.0 I 34-5 30 26.0 15-0 90 77-9 45.0 50 129. 75-o'J i 181.9 105-0 | 70 233. i i35.o 1 3 26.5 ! S-5 9i 78.8 4S-; l$* 130.8 75'5j2i 182.7 105.5 27 234. 135-5 | 3 27 .7 16.0 92, 79-7 46.0 s^ I3I.6 7 6 . o i 183.6 106.0 7 235. 136.0 I 3 2 : S.6 I6.S 93J 80.5 46.5 ^ *.5 76.5J i 184.5 106.5 7 236. 136.5 1 34 .29.4 17 o 94} 81.4 47.0 S4 f 33-4 77-oJ i 185-3 107.0 7 237. i37.o 1 3 30-0 x 7-5 951 *i-3 47 5 SS i34- 2 77.5 i 186.2 107- 5 7 238. 137-5 1 3 3F.2 18.0 96 i 8 3 ,i 48.0 S6 135.1 78.0; i 187.1 loS.oj 7 239. c 138.0 1 3 32.0 iS.s 97 84.0 4^.> " 136.0 78.5' r 187.9 108.5 7 239.9 138.5 1 3 i*.9 19 o 98 84.9 49.0 ^ 136.8 79' 0; I 188.8 i9-y 7 240. b 139.0 I 3 33-S 19.5 <><> 8s. 7 49-5 137-7 "9-5 i 189.7 109.5.] 7 241 .6 139-5 1 4 34- 2O 100 86.6 50.0 I 60 138.6 o.o 2 190 S uo.oi 8 242.5 140.0 1 4 35- 20.5 101 87. s 50.5 161 139.4 ^0.5 12 191.4 iio.5p 243-4 HO. 5 1 4 36.4 21.0 02 83.i 51.0 62 MOo I.O 2 192.3 III .0 j 244.: 141. Ojl 4 37- 21.5 0^ 89.2 5 r -5 6 3 141.2 ^1.5 i [93.1 111.5 ! 245.1 141.5 1 4 38. 22.0 04 90.1 52.0 1 64 142 . q 82.0 2^ 194. c I 12.0 8 246. c 142.0 1 4 39.0 22.5 OS 90.9 5*. 5 6s 142. Q 2. S 2 = 194.9 II1.5 5 246.5 H2-5 1 4 39- 23.0 06 91. S 53.0 1 66 143.8 S3.0 2( T 95-7 II3-0 8t *471 143-0 4 40. ^3-5 07 92.7 53-5 1 6 " 144.6 *3.5 2 ' 196. (j II3-5 87 -4* - H3-5 4 41. 24.0 08 93-5 54.0 68 H5-5 84.0 2^ i97.f 114.0 8*1*49-4 144" ! 4 42. 24,5 oc, 94-4 54-5 69 146.4 84.51 2^ 198.3 II4.5 89 250.. i '44-51 t 43- *5.o 1C 95-3 55.0 S 70 147.2 85.0! 3^ > 199.2 H5.0 9 C > 251- 145.0 5 44. 25.5 I II 96. i 55-S [171 I48.I 5-5 23 200, i 115.5 ^91 252. ( >i45.5 5 4v 26.0 12 97. c > 56.0 72 149. c 86.0 32 200.5 116.0 9 2 . 252. ) 146-0 j ^ 45- 26. s 13 97- f 5.f H r? 149-? ^6.5 3. 5 201 . 116.5 93-1^3- 7146.5 r^ 46. 27.0 M 98.' S7-o 1 74 150.7 57. c 3 }. 202. ( > 117.0 ! 94| 2 54. S 147.0 5 r 47- 48. 27- s 28. c T: "iC 99. (. 1OO. .57-5 S8.o 75 8 rf 151.6 152.4 *7.5| 3 88. o| 3 5 203.. 5 204.^ ; 117-5 j. ii8.c 9 i 9< 5.255. > 256. 5147.5 3 148.0 ~ 49. 28. s 1 17 ioi.: 5S.< i 77 153-: 88. r i } ; 205.2 '. 118.5 9 7 257. 2 148.5 c 50. 29.0 j iS ro2.; - 59-ofl 7^ I 54- a 89.0 3 3 206. r 119. c 9 i 2s8. i 149.0 5 5 1 - 29. s 1C 103. 59-5 n 7^ 155. c > 89.5 3 9 207. < 3 II9.f 9 1 5 -58. 9 149'5 6 52. ?o.c 2C ) 103. < ) 6ooJ 8c 1 5 5 . < ) 9- c 4 o 207 ? I2O.C i 30 D 259. S 150.0 ;Dii Dep Lat. Dift Dep. Lat. J !fDif t Dep. Lat. iDi ft Dep Lat. Di ft Dep. Lat. tor 00 Degrees TABLE II. Difference of Latitude and Departure for 31 Degrees. Dift Lat. Dep. Dift Lat. Dep. Dif Lat. Dep. 1 Dift Lat. Dep. Dift Lat. - Dep. i i a 3 4 6 7 9 10 00.9 01.7 02.6 03.4 04.3 05.1 06.0 06.9 07,7 08.6 00.5 01. 01.5 02. I 02. 6 03.1 03.6 04.1 04.6 05.2 61 62 63 64 65 66 67 68 69 70 52.3 53-1 54-o 54-9 55-7 56.6 57-4 58.3 59.1 60.0 31-4 31.9 32.4 33-c 33o 34-0 34-5 35-o 35-5 36.1 121 22 23 25 26 27 28 2 9 30 103.7 104.6 105.4 106.3 107.1 108.0 108.9 109. 7 1 10.6 111.4 62.3 62.8 63.3 64.4 64.9 65.4 65.9 66.4 67.0 181 82 83 84 85 86 87 88 89 { 90 l^'.o 156.9 157.7 158.6 159.4 160.3 161. 7 162. c 762. c, 93-2 93.7 94-3 94.8 95-3 95.8 96.3 96. S 97-3 97-9 241 42 43 44 45 46 48 49 50 206.6 207.4 209. i 2JO.O 210-9 271-7 212.6 213-4 -74.3 124.1 124.6] 72 5 . 2i 725.7 126.2 1 I26.7i I2 7 . t\ 127.7; 128.2 : ii 12 13 I 4 '5 16 i 7 09.4 10.3 II. I 12.0 12.9 14^6 0-5.7 06.2 06.7 07.2 07.7 08.2 08.8 71 72 73 74 76 77 60.9 61.7 62.6 63-4 64-3 65-1 66.0 36.6 37-1 37-6 {S.i 38.6 39.1 39-7 32 33 34 35 36 37 112.3 713.1 114.0 114.9 115.7 116.6 117.4 67-5 68.0 68 . 5 69.0 69.5 70.0 70.6 191 92 93 94 95 96 763.7 164.6 165.4 166.7 167/1 i6S.c 168.9 98.4 9 8. v 99-4 9 9- .9 100.4 ico . 9 2 5J 53 54 56 215. I 216.0 2l6-9 217.7 218.6 27 9 . 4 2 'O . '29.3: 129. 8 ( i^o.S 18 19 20 is. 4 16.3 17.1 9-3 09.8 10.3 7^ 79 80 66.9 67.7 68.6 40.2 40.7 41.2 3^ 39 40 118.3 119.1 '120.0 71.1 71.6 72.1 99 200 169.7 170.6 171-4 IO2.C 102.5 103.0 58 59 60 221. I 222.0 222. 9 132.9. '33-4 21 22 18.0 18.9 10.8 81 82 69.4 7Q-3 41.7 42.2 141 42 I2O-9 I2I.7 72.6 73-1 201 02 173 *'J 103.5 104.0 261 6^ 223.7 224.6 '34-4, 24 26 19.7 20.6 21.4 22.3 ii. 8 12.4 12.9 13-4 84 Ii 71.1 72.0 72.9 73-7 42.7 43-3 43-8 443 43 44 45 46 122.6 123.4 125.1 73-7 74-2 74- 7 75-2 03 04 05 06 174-9 1-6*6 104.6 I05.J 105.6 106. i 63 64 65 6b 225.4 226.. 227.1 ^28.0 135*5 736.0 '3 6 -5: 27 28 2 9 23.1 24.0 24.9 13.9 14.4 14.9 &7 88 89 74.6 75-4 76.3 44-8 45-3 45-8 47 48 49 726.O 126.9 127.7 757 76.2 76. 7 7 08 OQ 177.4 178.3 106.6 70". 7 707.6 68 60 2 2 9-7 1 :o 6 13?^' 738.0! 7lS c f 30 25.7 i5-5 90 77-1 46.4 5 728.6 77-3 10 180.0 108.2 70 231.4 1 3- *5 139.1 32 33 34 35 36 37 38 26.6 27.4 28.3 29.1 30.0 30.9 31.7 32.6 16.0 16.5 17.0 T 5 18.0 19.1 19.6 91 92 93 94 95 96 97 98 78.0 78.9 79-7 80.6 81.4 82 3 83.1 84.0 46.9 47-4 47.9 48.4 48.9 49.4 50.0 55 52 53 54 55 56 57 58 129.4 I30-3 132.O 132.9 133-7 134.6 135.4 77-8 78.3 78.8 79-3 79.8 80.3. 80.9 Si .4 ill 12 13 M 76 1 7 18 780.0 181.7 ^4 185".! 186.0 186.0 70S. 7 log. 2 109 7 no. 2 I 7O. 7 III. 2 in. 8 112.3 *{ 73 74 75 76 77 78 232.- 233-1 234 234-9 235 -1 236.6 -37-4 '39 6 740. i 140.6 741.1 741.6 142-2 142.7 39 40 33-4 34-3 20. i 20.6 99 700 84.9 85-7 51.0 59 60 136.3 137.1 81.9 82.4 '9 20 187.7 188.6 112. 8 113.3 79 80 239-1 240.0 144.2 4 1 42 43 44 45 46 47 4? 49 jo 35- 1 36.0 36.9 37-7 38.6 39-4 4-3 41.1 42.0 21. I 21.6 22. 1 22.7 2 3 .2 23-7 24-2 24.7 25.2 25.. 8 101 02 03 04 05 06 07 08 09 10 86.6 87.4 88.3 89.1 90.0 90.9 91.7 92.6 93-4 94-3 52.0 52.5 53-0 53-6 54.1 54.6 55.6 ,-6., 56.7 161 62 63 64 65 66 67 69 70 138.0 138.9 139-7 740.6 141.4 142.3 I43.I 144.0 144.9 145-7 82.9 83.4 84.0 84.5 85.0 86.0 86.5 87.0 87.6 221 ^^ 23 24 25 26 27 28 2 9 30 189.4 190.3 191.7 192.0 192.9 193-7 194.6 195-4 196.3 113.8 "4-3 114.9 715.4 - r i 5 - 9 .16.4 1 16 9 7 1 8 . : 281 82 83 84 8; 86 87 88 89 oo 240.9 241.7 242.6 243-4 244-3 246.0 246.9 247.7 248.6 145.2 745-8 146. 3 14". 8 47.3 147-8 148.3 148.8 149.4 5i 52 53 54 55 -5? 43-7 44.6 45-4 46.3 48 fo 48.9 26.3 26.8 2^8 28.3 28.8 29.4 III 12 13 14 i; .6 77 95. i 96.0 96.9 97-7 98.6 99-4 oo. 3 57.2 57-7 58.2 58.7 59.2 ! 59-7 60.3 7* 73 74 75 76 77 146.6 147-4 148.3 149.1 150.0 750.9 151.7 88.1 88.6 89.1 89.6 90. i 90.6 9 1. -2 7 33 34 35 36 198.0 198.9 '99 - : 20j. 6 201.4 203. ] Iig.O ll. 9 .s 120.5 121 .0 I2I-5 722. J 93 94 91 96 9" 249.4 * 3 V ' 3 2 C 1 . 2 252.0 253." 1*4.6 149.9 750.4 150.9 751.4 5 i . 9 49-7 29.9 18 01 . I 60.8 78 152.6 91.7 ""8 204 . c. 122.6 59 60 Dift 50.6 5i-4 Dep. jo. 4 3_o_-9 Lat. 19 20 7O2.0 102-9 67.3 61.8 79 So 153-4 I 54 .? 92.2 Q2.7 39 40 204.9 205.7 Dep. I2 3 ., i8 3 .6 Lat. 99 300 " 257. ' i 54.0 7^4.5 Lat. , ->iit Dep. Lat. | T>ifr Dep. Dift Dift Dep. I or 59 Decrees. SBMWWSK **""' " i - n i 11rffr ,, ll frjjjiij-ja TABLE II. Difference of Latitude and Departure for 32 Degrees, 'Dift Lat. ! Dep. Dift Lat. JDep. Dift Lat. Dep Dif] Lat. Dep. Did Lat. Dep. oo. a GO. 5 61 5'-7 32.3 I2J 102. 6 64. 181 153.5 95-9 241 204.4 127.7 2 01.7 01 . 1 62 52.6 32.9 i 22 103.5 64.- ; 82 96.4 42 205.2 [28 . 2 1 4 02.5 03.4 01. t 02 ._! 6S 64 53-4 54-3 33-4 24 104.3 65.2 65-7 1 83 1 *4 155.2 156.0 97-0 97.5 43 206. i 206.9 128.3 129.3 5 04.2 O2-.6 6s 55-J 34 4 i 2 5 106.0 66.2 85 156.9 98.0 4 207.8 f 29.8 6 OS- I 03.2 66 ?6.o 35.0 26 106.9 66.8 86 157.7 98.6 46 208.6 130.4 - os. 9 67 S6.* 35-5 27 107.7 67-3 87 158.6 99.1 47 209.5 130.9 8 06.8 04. i 68 36.0 28 108.6 67. b 88 159.4 99 .6 48 210.3 I3L4 9 07.6 04.^ 69 58. s 36.6 2Q 109.4 6^.4 89 160.3 1 00*2 49 211. 2 I3L9 10 oi-5 os 3 70 59 4 37.i i 30 I1O. 2 68.9 90 161 i 100.7 50 212.0 132.5 ii 09.3 05. s 7I 60.2 37-6 j ' 3 i MI . I 09.4 191 162.0 101 . 2 251 212.8 '33- 12 10.2 06.4 72 61 ^1 3* in. 9 69.9 92 162.8 IOI.7 52 213.7 133-5 13 II .O 06. Q 6 1 ..9 38 . 7 ^ 112. 8 70- 93 163.7 IO2-3 53 214.6 '34- x I I .9 07-4 74 62.8 39.2 1J 113.6 71.0 94 164.5 102.8 54 215.4 134.6 15 12.7 07-9 75 63.6 59.8 35 114.5 7i-5 95 165.4 103.3 55 216.3 135* i ! i6 it.6 08. s 76 64-5 4^-3 | 36 115.3 72. i 96 l66;2 103.9 56 2I7.I 135.7 17 14-4 09.0 77 65-1 40.8 37 116.2 72.6 97 l6 7 .I 104.4 57 217-9 136.2 09. s 78 66.1 41.3 38 117.0 73-1 98 167-9 104.9 i 58 >- 1 8 . S 136.7 1 '9 16.1 ro. i 79 67.0 41.9 35 117.9 7^-7 99 168.8 10 s. 5 59 219,6 '37-2 i 20 17.0 13.6 80 67.8 40 trS. 8 74.2 200 169. 6 106.0 60 220. 5 137.8 i 2I 17.8 ;i. i Si 68.7 42.9 141 119.6 74-7 201 1-0.5 106. s 261 221.3 138.3 22 18.7 11.7 82 69. s 43'.5 4- 120.4 75- 2 O2 171. 3 107.0 62 222.2 138.8 : 33 19.5 12.2 83 70.4 43 121.3 75- 03 T72.2 107.6 63 223.0 '39-4 -4 io-4 12 .7 "1.2 44-5 44 122. I 70.3 04 173.0 108.1 6-j 223.9 i399 i 25 21 .2 *3' ' 8s 72.1 45 123.0 76.8 5 173.8 168.6 6 5 224.7 140.4 | 26 22.0 13.8 86 72.9 45-6 46 123.8 77-4 06 174-7 109.2 66 225.6 141.0 1 27 22-9 r 4'3 87 73.8 46.1 47 124.7 77-9 07 175-5 109.7 67 226*4 141.5 ! 28 23-7 88 74-6 46.6 48 78.4 OS 176.4 IIO. 2 68 227.3 142.0 ! 29 2 4 .6 15.4 89 75-5 47-2 49 126.4 79-o 09. 177.2 no. 8 69 228.1 42.5 i 30 25.4 15.9 90 76.3 47-7 50 127.2 79.5 ro I78.I 111.3 70 229.O 43-1 j 31 26.3 16.4 91 77.2 48.2 151 123. I 80.0 2U r/8. 9 111.8 271 229.8 43-6 j i 32 27.1 17.0 92 78.0 48.8 5* 128.9 ^0.5 12 179.8 112.3 72 230.7 44- T : 33 17. s 91 78.9 49' 3 129.8 81 . i 13 180.6 12.9 7 i 23I.S 44.7 ! 34 2S.8 rS.c 94 79-7 49.0 54 I3O.6 81.6 M iSi.S 113.4 74 232.4 45.2 | 29.7 18. 9S 80.6 50.3 $5 I3I.4 S2. I IS 182.31113.9 75 233.2 45-7 ! ' 36 19. i 96 81.4 SO. 9 5 132.3 82.7 16 183.2 114.5 76 234-J 46.3 I 3 ~ 31.4 19.6 97 82.3 51.4 57! 133. r 83.2 1 7 184.0 115.0 77 234-9 46.8 32.2 20.1 98 51.9 58 134.0 83-7! 18 184.9 115.5 78 235-8 47-3 __ 33 * 20. 7 99 84.0 5 I34.S 19 116. i 79 236.6 47-8 ; 40 ZI- 2 100 84.8 53-0 60 135-7 54.8 20 186.6 ti6.6 80 237.5 48.4! j 4 1 34-8 21-7 101 *5-7 53'5 i6r t36. 5 [5.3 221 187.4 117.1 28. 238-3 48.9! $5.6 22.3 02 86.5 54. i 62 '37-4 22 188.3 117.6 82 239.1 49-4 ; 43 36.5 22.8 03 87.3 54-6 63 138.2 >6.4 23 189.1 118.2 83 240.0 50.0 ' 44 37-3 23-3 04 88.2 55 ' 64 139. S6.J 24 190.0 118.7 84 240.8 50.5 45 23. H 89 p ?*6 6s 139.9 ^7-4 15 190.8 119.^ 8s 241.7 51.0 ^9.0 : 4-4 06 89.9 $.2 66 140.8 S8.c 26 191.6 r 1 9 . S 86 242,5 51.6 47^ 39-9 24.9 07 90.7 56.7 67 T4I.6 38.fr 27 1 9 i . 5 120.3 S? 243.4 52.1 4 s 40;.' 7 2.5,4 oS 91.6 57-2 6^ 142.5 59.0 28 193.4 izo.8 SS 244.2 52.6 49 41.6 26.0 09 91.4 <7-8 69 143.3 89.6 29 194.2 121.4 89 245.1 53- J J.2.4 >6. 5 10 93-3 5S.3 70 144.2 )O 1 30 195.1 121. q yo 245.9 JLLZ L rj 4. 1 . 3 27.0 III 94-1 s8.8 171 f 45' )0.6; ~?l' 195.9 122.4 291 246.8 54-2 ^ 2 1-4.4. t 27.6 12 9S-c 59-4 7; 145-9 91.1] 32 196.7 122.9 9- 247.6 54-7 53 44-9 z'i. i J3 SQ-9 7? 146-7 7 1 7 33 197.6 123-5 93 248.5 55-3 I 54 25.6 T 4 96.7'' 60. 4 74 147.6 r>2. i! 34 198.4 124.0 94 249.3 55.8 46.6 -9- * Is 97.5 60.9 7.5 148 4 y2.8j ^N 199-3 124.5 9 ; 250.2 56.3 56 47 -S -9- 7 Itt 98.4 6r . ? 76 149.3 93-3J 36 200. 1 125.1 96 251.0 56-9 57 4^.3 17 62.0 77 450. i )") 8j 37 201.0 125.6 97 *5l 9 57-4 ' tf 40-2 ift Dep. .Lat. 3ift| Dep. Lat. Dift Dep. Lat. Dift Dep. L?r. G g for 5? Degrees. TABLE II. Difference of Latitude and Departure for 34 Degrees. Dift! Lat. Dep. irat Lat. DepJ;Dift Lat. Dep. Difti Lat. Dep. Dift Lat. Dep. | i oo S'GO.'; 6l 50.6 34.1 121 co. 3 07.; 150. I ICl .2, 241 199.8 34-* 2 01.7 01 .1 62 Si-4 34-7 22 101 . I 68.2 82 150.9 [101 .8 , 42 200. 6 353 3 02.5 01.7 63 S2.2 35-2 23 102. o 6S.8 83 151.7 102.3 201. 5 35.9 4 03.3 02.2 64 J5-.8 24 io2.8 69. 3 84 1.52-5 102.9; 44 2O2i3 36.4 5 04. I |o2.?- 53-9 36.3 25 103.6 69.9 8s ^53-4 103.5! 203.1 37-0 6 OJ.O 03.4 66 >47 36.9 26 104.5 70. 5 86 154.2 104.0 46 203.9 37.6 " t 05.8 03.9 67 *o 5 37.5 27 I0 5-3 71.0 87 155.0 104.6 47 204.8 38.1 8 0').6 04. <; 68 ci.4 38.0 28 106.1 71.6 88 r55-9 105.1 48 205.6 38.7 9 07.^ 05 o 69 jS.6 29 106.9 72. r 89 156.7 105.7 49 206.4 139.2 10 08.3 05.6 70 i8.oJ3o.i 30 107.8 72.7 90 1.57-5 106.2} 50 207.3 139.8 ii OQ.I OO . 2 TI 5^-9! >9- 7 ni io3.6 73-3 ICJI 153.3 ro6.8i 251 208.1 140.4 12 09.9 06.7 72 39 7 4 -"3 ?2 109.4 73- S 92 159.2 107.4! 52 208.9 140 9 13 10. S 7*3. 73 00.5 40.8 33 1 10.3 744 93 160.0 107.9] S3 209.7 141.5 ! 4 ti.6 07- & 74 61.3 41.4 34 fir. i 74-9 94 160.8 108.5 54 210.6 142.0 15 I 2. A 08.4 62.2 41.9 35 in. 9 75-5 95 161.7 109.0 55 2II.4 142.6 16 n> 3 p-9 -6 63.0 42 . 5 36 II2.7 76.1 96 162.5 109.6 56 212.2 143.2 (!" 14.1 09.5 77 63.8 37 II3.6 76.6 97 '63.3 IIO. 2 57 2I3-I 143-7 l8 14.9 10. 1 78 64.7 43.6 38 U4.4 77-2 98 164. i 110.7 58 213.9 J 9 15.6 10.6 79 65.5 44.2 39 II5.2 77-7 99 165.0 111.3 59 214.7 144-8 20 16.6 IT. 2 44-7 40 J16.T 78 ./ 200 165.8 in. 8 60 215.5 145.4 21 i-.4 11.7 *i 4S-3 141 1 16.0 78.8 201 166.6 112.4 261 216.4 145.9 22 15.2 12.3 82 6S.c 4^-9 42 117.7 79-4 C2 167.5 113.0 62 217.2 146.5 i 2 3 I). I I2. 9 83 68.8 46.4 43 uS.6 80.0 03 168.3 "3-5 63 218.0 147.1 24 19.9 13-4 84 69.6 47-o 44 119.4 ^'o. s 04 169.1 64 218.9 147.6 20.7 14.0 8s 70.5 47-5 45 120.2 81.1 5 170. o 14.6 65 219.7 148.2 26 21.6 14.5 86 /"i 3 48.1 46 121 .C 81.6 06 170.8 115.2 66 220.5 148.7 27 22.4 IS- J 87 72.1 48.6 47 !21. 9 82.2 c-7 171. 6 115.8 67 221.4 149.3 ! 28 25.2 is. 7 73-o 49.2 48 122.7 82.8 08 172.4 116.3 t<8 222.2 149.9 24.0 16.2 89 73. 49.8 49 123. s 33 C 9 r /3-3 116.9 69 223.0 150.4 [ o 24.9 16.8 90 -4 . b so 124.4 8^.9 10 174.1 H7-4 70 22 3 .8 151.0 j i 5..7 17.3 91 75-4 ;o. , ! U T2.5. 2 .H-4 211 174.-) Ilb.O 271 "4-7- 51.5 I 2 16,5 [7.9 92 / ' ; j j i . 4 52 126.0 85,0 12 175.? 1 1 8 ^5 72 225.5 152.1 ' 33 a 7. 4 18.5 93 77. I S3 126.8 8 .2 19.0 94 779 52.0 54 I2 7 .7 86. T 14 '77.4 ; i ') . 7 74 227.2 153-2 35 29.0 19.6 95 78*8 53- l 55 128. 5 S6. 7 15 178.2 I2J. 2 75 228.0 153.8 3<> 29.8 20. 1 96 79-6 53-7 56 129.3 87.2 16 17*9.1 120. S 76 228.8 T 54-3 37 30.7 2O.7 97 30.4 54.2 57 130.2 87.8 . 17 179.9 I2I.J. 77 229.6 154-9 ! 3* 31.5 21.2 98 3l.2 131.0 88.4 1 8 1^0.7 2U9 78 230. 5 155-5 i 39 32.3 21,8 99 82.1 5^-4 59 131.8 88. c 19 181.6 22.5 79 231.3 156.0 , 40 3:. 2 22.4 IOO 32. 9 60 132.6 89.5 20 182.4 12^ .0 80 232.1 156.6 ; 4' 34-o 22. 9 101 53.7 5b.5 161 T33.5 90.0 .'.21 183.2 123. & 281 235.0 157.1 ! 42 02 ^4. 6 57.0 62 134, 3 90.6 22 184.0 (24. i >2 233.8 r 57-7 43 3-. 6 24.0. pj $5.4 57.6 63 135.1 91.1 23 184.9 124 7 83 234-6 158.3 36. q 24.6 04 36.2 64 136.0 91.7 2 4 185.7112^.3 84 235.4 158.8 : 1 J 5 37-3 25.2 07.0 58.7 6s 136.8 25 186.5 125.8 85 236.3 159-4 i ! 46 2 5-7 c6 ^7.9 59-3 66 137,6 92.8 26 187.4 I26. 4 237-1 *59-9 f 47 jq .C 26.: 07 88.7 59.8 67 13^.4 .93.4 2? 188,2 12^.9 ^7 237-9 I 60. 5 ; 39.8 26.0 08 ^9-5 60,4 68 '39-3 93*9 aS 189.0 127.5 88 138.8 161.0 : | 49 40.6 27.4 09 ,0.4 6i.c 6 9 140.1 94-5 29 189.8 f tS . i "9 239.6 161.6 1 I 5 28.0 TO ;f .2 61.5 70 140.9 95.1 30 no. 7 iz3.6 90 240.4 162.2 ' 5 1 12 f 3 28. < Ml ?2.0 62.1 141.8- 95.6 2Jl' 191.5 129.2 2C.I 241.2 162.7 N2 43-1 29.1 12 92.9 62.6 7? 142.6 96. 2 32 192.3 [29.7 92 242.1 1 63-3 ! 53 29.6 13 ')3-7 63.2 73 143.4 96.7 33 193.2 130.3 93 242.9 163.8 54 44-* 30.2 H.S 6^.7 74 144-3 97^3 34 194.0 130.9 94 H3-7 164.4. 55 45.6 30.3 15 95-3 75 145.1 97-9 35 194. X 131-4 95 244.6 165,0 46.4 3 r -3 16 96.2 64.9 76 145.9 98.4 36 195.7 132 .0 96 245.4 165.6 57 473 31.9 *7 97.0(65.4 7.7 146-7 99.0 37 196.5 1.32.5 97 246. 2 166.1 ! 5^ <*.! 32.4 18 97.8 66.0 78 147.6 995 38 197-3 133.1 98 247.1 166,6 48.9 19 98.7 66.5 79 148.4 ICQ. I 39 198.1 133-6 99 247.9 167.2 T j e'o 40-7 33-6 20 99-5 67.1 80 149.2 100.7 40 199.0 134.2 300 248.7 167.8 Dift Dep. Lat. Dift Dep. Lat. l Difl Dep. Lat. Dif Dep. Lat. Difl Dep. Lat. for .'36 Degrees. TABLE II. Difference of Latitude and Departure for 35 Degrees. Dift Lat. Dep. Dift Lat. iDep. flDift Lat. Step. Dift Lat. Dep. Difr Lat. Dep. i 00.8 00.6 6l 50.0 35.0 121 99.1 6 9-^ ; 5! 48.3 1103.5 4' 97-4 38.2 2 01.6 01 .1 62 50.8 35-6 22 7 o.o 82 49.1 104.4 4 2 138.8 3 02.5 01.7 63 51.6 36.1 23 103.8 70.5 ) 8} 49-9 105.0 $3 99.1 139.4 4 03.3 64 52.4 36.7 24 101.6 71. ii 84 53-7 105.5 44 99 -y 140.0 5 04.1 02- 9 6y - -, i2 37.3 25 102.4 7U7 8s 1 06. i 4i Oj-7 140.5 6 04.9 03.4 66 54. i 37-9 20 103.2 72.3 86 52.4 106. 7 46 01 . q 141.1 7 QS-7 04.0 67 54-9 3M 2? 104.0 8? 532 107.3 47 02.3 141-7 ' 8 06.6 04.6 68 55-7 39.0 28 104.9 73.4! 54.0 107.8 48 03.1 142.2 9 07-4 05.2 69 56.5139.6 29 105.7 74.0! 89 108.4 49 04.0 142.8 JO 08.2 05.7 70 57-3 40.21 30 106.5 74-6 90 55-6 109.0 50 04 . 8 143-4 11 09.0 05.3 71 5-S.2 40.7! f3 167.3 75* 1 91 50.5 109. 5 Si 05. b 144.0 12 09.8 oo. 9 72 59.0 32 108.1 75* 7 92 57-3 no. r 52 06.4 I44-5! 13 10.6 07-5 73 59-8 41.9 33 108.9 76.3 93 S : 5.i 110.7 53 07.2 145.1 M "5 oS.o 74^0.6 42.4 34 109.8 76.9 94 S*.9 111.3 54 08.1 14". ? 1.5 12.3 o> . 6 7; 61.4 43-o 3S no. 6 77-4 QS 59-7 in. 8 ss 08.5 146.3 16113,1 09.2 76 '62.2(43.6 36 111.4 78.0 96 60.6 112.4 5- 09.7 146.8 17 13.9 09.8 77 GJ.J 44- - 37 112 .2 7 3.6! 97 61 .4 113.0! 5 " IO. C 147.4 18 14.7 10 .3 78 63-9I44-7 II3.0 79. a! 98 62.2 113.6 11.3 148.0 19 115. 6 10.9 79 H.7145.3 39 79-7 99 03.0 114. i 59 12.2 148.5 20 j 16.4 ir. S 114.7 80.3 00 63-8 114.7 60 1 >'' 149 i 21 I 7 .2 12-0 81:66,4 115.5 8o. 9 ! 01 64.0 IIS-: 61 13-8 149.7 smio.o 12.6 82 67.2 47.0: 4 2 81.4' 02 ;;-. 62 14. 6 150.3 2 3 : r s . 8 15.2 83 64.o 47-6 43 II7.I 82. oj 03 166. ^ 116.4 6; I ;. 4 150.9 24 i,. i $.8 84 68.8 4^.2 44 n*. o 82. 6 j 04 67-1 II7.0 64 151-4 25 ao.5 14.3 8s 6.). 6 4 ^.S 45 118.8 83.' ' OS 67-9 II7.6 65 17. ! 152.0 26 21.3 14.9 86 70.4 46 119.6 83.7! 06 6^.7 IlS.2! 66 17.9 i S 2 . 6 27 22 . I 7 * 3 439 47 120.4 84.3 07 163,1 Il8. 7 | 67 187 153 . i 28 22.Q 16.1 88 72 . i 50. 5 121. 2 oS 170.4 II9.3! 68 219.5 153-7 29 23.8 16.6 89 7*. 9 Si.o 49 122. I 85~5 09 171.2 II9. 9 69 20 4 154-3 : 30 2 4 .6 17.2 90 73-7 51.6 5 122. <) 86.0! 72-. o 120. S 70 2t .: 154-9 i 31 25-4 17.8 9 r 71-S 52. z IS 1 123.7 86. oj II 172.8 121 .O'| 71 221 .0 1 5 S 4 32 26.2 92 75-4 52.3 S2 124.5 87.2! 12 173-7 121. 6 j 7- -22.S 156.0 33 27.0 18.9 93 76.2 S3-3 125.3 87.8 n J74- S 122.2 | 71 223.C 156.6 i 34 27.9 19.5 94 77.0 53-9 5f 126. I 88.3 M 1/5-3 74 ,24.^ 35 28 .7 20. I 95 77-8 54 -5 55 127.0 88.9 15 176.1 123.3 - z S ': i S7 . 7 ! 36 29. s 20. 6 96 78.6 S6 127.8 89-5 16 176.9 123.9 76 158.3 37 3 3 21 . 2 97 79-5 SS-6 57 |g..6 90.1 17 177.8 24. S 77 226.9 38 31.1 2T.8 80.3 129.4 9"o.6 18 178.6 I2s.O 7?, --7-7 159. 5 39 31.9 22.4 99 81 . i 56.8 59 130.2 91.2 19 179-4 l S .6 79 22$. S 1 6 o . o 40 32.8 4X.q IOO Jlv> 00.6 01 49.4 35-9 121 97-9 71.1; 181 146.4 106.4 241 195.0 141.7 1 2. 01.6 OI.2 62 50.2 36.4 22 98.7 82 147. 2 107.0 42 195.0 142.2 3 02.4 01.8 63 51.0 37.0 23 99-5 72.3 83 148,1 107.6 43 196,6 141. 4 OJ.I 02.4 -r 51.8 37-6 24 105.3 72. 9 84 148.9 108.2 4.1 197.4 143.4 5 04.. o 02.9 55 52.6 25 ID I. ' 73-5 8s 149.7 103.7 45 198.2 144.0 6 04.9 03.5 66 53-4 38.8 26 IOI.9 74-i 86 150.5 109.3 46 199.0 144.6 7 o s 7 04 I 67 54.2 39-4 27 102.7 74.6 87 15 1 -.3 109 . 9 199.8 145.2 8 06.^ 04.7 68 55-o 40.0 25 103.6 75-2 88 152.1 no. s 48 200.0 145.8 9 07.3 05.3 69 55.8 40.6 29 104.4 75-8 89 152.9 n i . i 49 2O I .4 146.4 10 O^.I 05.', 70 56.6 41 i 30 105.2 7-6-4 90 153-7 in. 7 5 202 . 3 146. 9 FT? 05, 9 06.5 71 S7-4 41.7 HI 103.0 77-0 191 154-5 112.3 251 203.1 H7-5 12 09.7 07.1 72 58.2 43 3" 106.8 77.6 92 155.3 IT2-9 20 3 . 9 ,48.1 13 10-5 07.6 73 59 i 42.9 33 107 . 6 78.2 93 156 i 113.4 S3 204. 148.7 14 II.3 0^.2 74 59-9 45.5 3 1 108.4 7^8 94 156.9 ri 4 .0 205. 149-3 T5 12.1 0^.8 7S 60.7 44-i 109.2 79-4 95 157.8 114.6 ss 206. 149.9 16 12.9 09.4 76 6i.s 44-7 36 IIO.O 79-9 96 158.6 115.2 207. 150.5 17 13.8 io.o 77 62.3 45-3 37 no. 8 80.5 97 159-4 115.8 57 2O7. 151.1 18 14.6 10 6 7 63.1 45.* 3 "* 1 1 1 . 6 81.1 98 160.2 116.4 208 . 151.6 i is- 4 II. 2 79 63 9 46-4 39 IT2-5 81.7 99 161.0 117.0 59 209. 152.2 -0 n. 8 80 64.7 47.0 40 113. 3 82 < 200 161 8 117-6 60 210. 152.8 21 17.0 12.3 81 65.5 47.6 141 114.1 82.9 201 162.0 n8.i 261 211 . 153.4 22 17-8 12.9 82 66.3 48.2 42 114.0 83.5. O2 163.4 118.7 62 212. O 154.0 23 18.6 13 5 83 67. i 48.8 43 II5-7 84.. 0} 164.2 '19-3 63 212.8 154.6 24 19.4 84 68.0 49'4 44 116.5 84.6 04 165.0 119.9 64 213.6 r 55-2 20.2 14.7 8s 63.8 117.3 85.2 165.8 120.5 6s 214.4 155-8 26 21.0 86 69.6 ;o 5 4^ 118.1 85.8 06 166.7 121. I 66 215.2 156.4 27 *i.3 15.9 87 70.4 51.1 47 118.9 86.4 07 167.5 I2I.7 67 216.0 156.9 28 22.7 16.5 88 71.2 51-7 119.7 87.0 o-; 168.3 122.3 6S 2 I 6 .' ^ 157.5 29 23- s 17.0 89 72.0 S*:3 49 120. 5 87.6 09 169. j 1*4.8 69 2,7.6 158.1 30 24.3 17.6 90 72 8 52.9 5" J 121.4 88.2 10 169.9 123-4 70 218.4 isS.7 31 *5~7i i8.z 91 736 53.^ iSi 122.2 88. a 211 170.7 124.0 271 11.9.'; 159-3 32. 2S-9 18.8 74 4 S4 i 52 123.0 89-3 12 171.5 124.6 72 220. . 159-9 n 26.7 19.4 93 75-2 53 123.8 89-9 13 172.3 125.2 73 22O '9 160.5 34 27. s 20.0 94 76.0 .5.5 3 54 124.6 90.5 173-1 12-5.8 74 221.7 161 . i 35 98-. 3 20.6 76.9 SS-8 5 ^ 125.4 91.1 IS 173.9 126.4 7S 222 .5 161.6 S 6 29.1 21.2 96 77-7 56-4 56 126.2 91.7 16 .174-: 127.0 76 22 3 3 162.2 37 2) 9 21-7 97 78- S S7 . O 57 127.0 92.3 '7 175.6 127-5 77 224.1 162.8 38 30.7 22.3 98 79-3 57 " b I2-.S 92.9 rS 176.4 IZ5 . I 7$> 2:4.9 163.4 39 .31.6 22.9 99 80. i 58.2 59 128.6 93-5 19 177-2 12^. 7 79 164.0 40 32-4 IOO 80.9 58.8 60 129.4 94.0 20 178.0 129.3 80 226.5 164 6 4 ' r 13-2 24.1 101 81.7 59-4 161 r33-3 94.6 221 178. d 129.9 281 227.3 r6 5 .2 34.0 24.7 02 82. < 60.0 62 I3I.I 95.2 22 179.6 130.^ 82 2:8.1 165.8 43 34-8 25-3 03 83-3 60. 5 63 I3I.9 95-8 23 180.4 131.1 83 229.0 166.3 44 2C.9 04 84.1 61. i 64 96.4 24 l3l.2 131.7 84 229.8 166.9 45 36.4 26.5 05 84-9 61 7 6S 133.5 97.0 182.0 85 230.6 167.5 46 37-2 27-0 O6 62.3 66 J 34-3 97-6 4 5 l82.8 132.8 86 231.4 i6S.i 47 38.0 2 7 .6 07 86.6 67 98.2 27 183.6 133,4 87 232.2 i63.7 48 38.8 23.2 .OS 87.4 63- s 63 135-9 98 .7 28 184.5 134.0 88 233.0 169.3 49 39.6 2?.8 09 88.2 64.1 69 13^.7 99.3 2') 185.3 134.6 89 233*- 8 109.9 40.; -9-4 10 89.0 64-7 70 137-=; 99. q 3 186. i 1 3 5 2 90 234-6 170.5 "i 41.3 30.0 III 89. 5 65.2 171 138-3 100.5 231 1 86. >> * 3 5 - 291 235.4 171.0 ; 5 2 42.1 30.6 12 90.6 65.8 7 2 139-2 IOC . I 32 107.7 136.4 92 236.2 171 .6 53 42.9 31.2 13 91.4 66.4 73 140.0 ioi ,7 33 188.5 137.0 93 237.0 172.2 S4 43.7 31.7 14 92.2 67.0 74 140.8 ro_ . 3 34 189.3 137-5 94 237.9 172.8 55 44' S 32-3 M 67.6 .75 .141 .6 101.9 35 190. i ,38.1 95 238-7 r/3-4 56 45-3 32-9 16 93-8 68.2 76 141.4 1^3-5 36 190. 9 138.7 96 239-5 174.0 1 57 46. i 33-5 17 94-7 '68.8 77 143 ^ 104.0 37 191.7 139 3 97 240.3 174-6 1 5 * 46. 9 34- r 18 9S-S 69-4 78 144.0 104.6 3 ^ 192-5 139.9 241.) ,75-2 47-7 34-7 19 96-3 69 9 79 H4- 8 105 2 3 / I93.4 140.5 99 241 . 9 175-7' 60 35-" 20 97. f 7*>- : 80 14^.6 io;-8 4"^ 194 2 141.1 300 241.7 17^-3 | D-n. Lat. Difr Den. Lat. Diit Dep. Lat. Dili Dep. Lat. JDii't Dep. Lat. I tor j-i Degrees. TABLE II. Difference of Latitude and Departure for 37 Degrees., Dif .Lat. Dep Difl Lat Dep Dif Lat. Dep jDif Lat. Dep Dift! Lat. Dep. 00.8 00.6 61 Us.- 36. X2 96. o 7- li 144.6 108. 24 191,4 J 45 o 2 01.6 01. 2 62 49-5 37- 22 974 73-4 82 145-4 10.) . 4 193 .3 I-1-5-6 02.4 ox.8 63 50-3 37- 23 98.. 74. c 8 146.2 110. 4 IQ4- l 146.2 ' 4 03.2 02.: 64 5i. 38. 24 99.0 74 84 146 . 9 110. 44 194.5 ,146.8 i 04.0 03.0 65 51.9 39- 2 3 99 .8 75-2 8 147 . 7 Ill . 4 '9S-7 147.4 ! 04.8 03.0 66 52. 39- 26 100.6 75-* 86 1480 III. 40 196.5 148.0 j 0=5.6 4.2 67 53' 40. 27 101.4 76.., 87 149.3 112. 47 197.5 1^8.6 g 06.4 04.8 68 54-3 40.9 2, 102.2 77. c 88 150 i 113 . 4 198.1 H9-3 c 07.2 69 55- 1 41. 29 IO s . O 77-6 8< 150.9 113.; 4*7 198.9 149.9 | 10 o3.o 06.0 70 55-9 42. 30 loj.i 7*. 2 90 151.- 114. 5- 199.7 150.5 j II o8ib 06. 6 7' 56.7 42.7 131 104.6 76. h 191 15*. e 114. ( 25 200.5 151.1 j 12 09.0 07.2 72 57- . 43-3 32 105.4 79-4 92 '53,3 115. S 2 201.3 151.7 ' 13 10.4 07.8 58. 3 43-9 106.2 80.. 93 154.1 116.2 5 202. I I 5 2 3 1 14 XI .2 8.4 74 59.1 44o 34 107.0 80.6 94 154.9 116. 54 202. 9 152.9 ! I c; 12.0 09.0 75 59-9 45. i 3S 107.8 8 1 . _ 95 155-7 IJ7-. 5 -, 203 7 16 12.8 09. 6 '76 60.7 45-7 36 108.6 Sx.t 96 156-5 118.0 56 20^.5 154.1 i j- 13.6 10.2 77 61.5 4<>.3 37 109.4 82 . 97 '57-3 118.* S*/ 205-2 T 54-7 iS 14 4 to. 8 78 62.^ 4 6,t 38 IIO. 2 83.1 158.1 119.2 58 206.0 155.3 19 15.2 11.4 70 63.1 47-5 3< III.O 83.- 99 158.9 1x9. b 59 206.8 '55-9 ' 2-O iS.c 12. O 80 63.'; 48.1 in. 8 84.3 200 159-7 120.4 60 207.6 1^6.5 ! 21 16.0 12. 6 81 64-7 48.7 141 112.0 84. c; 201 160. 5 121.0 i(ji 208.4 157.1 i 22 J7.6 13-2 82 65.5 49-3 42 II3.4 02 161.3 121.6 t)2 20 9 .2 157.7 23 18.4 13 .8 g 60., 50.0 43 II4.2 86.1 03 162. i 122.2 6j 210. C ; 50 .3 24 19.2 f4.4 84 67.1 50.6 44 11 ^O 86.7 04 162.9 1*2.15 64 210.8 158.9 25 20.0 15.0 85 67-9 51 .2 45 115.8 87-3 ON 163.7 123.4 65 211.6 J 59-5 [' 26 20.8 15.6 86 68.7 51.8 46 116.6. 87.9 06 164.5 124.0 66 212.4 160.1 j 27 21. 6 16.2 87 69. 5 52.4 47 117.4 38.; 07 165.3 124. 6 67 160.7 ' 28 22.4 16.9 S3 70.3 53.0 118.2 89. j oS 166.1 12^.2 6b -14.0 161.3 ' 29 23.2 !7.5 89 71.1 .3.0 ,49 119.0 89.7 09 166.9 125. s 69 214.8 16149 30 14.0 18.1 90 71.9 54.2 5 llg.b 90.3 10 167.7 126.4 70 15.6 162.5 31 24. S 1 5.6 18.7 9' 72.7 54-8 '5 ' 120. fc 90.9 21 1 168.5 127,0 i'~ 6 7' 16.4 163.1 3 2 33 26.4 19.9 93 74-3 5 2 53 122.2 9' -5 92.1 169.3 I/O. I 128.2 73 18.0 164.3 34 27.2 >.. 5 94 56.6 54 123.0 9*-7 I^ 170.9 128.8 74 18.6 164.9 35 a8.o 21. I 75-9 7-2 55 123-8 93-5 15 171.7 129.4 75 19.6 165.5 i i 36 28.8 21.7 96 76.7 57-8 56 124.6 93-9 16 172-5 130.0 76 20.4 166.1 j 37 29.5 22.3 97 77-<5 8.4 57 25.4 94-5 17 173-3 130.6 77 21.2 166.7 ! 30-3 22-9 98 78., 9.0 58 126.2 95.1 r8 74. r 31.2 76 22. O ^7-3 j 39 31. i 23-5 99 9.6 127-0 95-7 1 9 174. 9 131.% 79 Z2.l 107 .Q 40 31.9 24. I 100 79-9 O.2 ' 60 2 7 .8 96.3 20 132.4' 23- t 168.5 ; 4i 3--7 24.7 01 ! 80. 7 o. -S 61 z-j.6 96.9 221 76.5 133.0 bi 24.4 169.1 42 33-5 *5-3 02 81. s 14 62 29.4 97- 5J 22 177-3 33-6! 82 25.2. 160.7 43 34-5 25.9 03 82.3 2.0 63 JO. 2 98.1! 2 3 178.1 34- 2 : 83 26.0 170.3 44 35 - 1 26.5 04 83-1 2.6 64 31.0 98.7! 24 78.9 34-8, -4 26.8 170.9 ; 45 35-9 27.1 05 83.9 3-2 65 3J.8 99-3' 25 79-7 135.4 8 -" 2 7 . (-.. 171-5 46 36.7 27.7 06 84.7 3-5, 6fc 32.6 2b 60.5 36.0 V. 2 ',-.4! 172. 1 47 37-5 28.3 07 85.5 4.4 67 33-4 oo* ; 27 81.3 56.6' 87 29.21 I7 2 .7 j 4? 8. 3 28.9 oS 86.3 5-0 68 34-- or . i 28 82.1 37** 88 50 d 173.3 49 9.1 29.5 o 9 J8 7 .i 5.6! 6.) 35-0 01.7 29 82.9 37-8, 8, jO.S; 173.9 50 ] ? - 9 30. i 10)87.8 6.2' 35.8 02.3 30 33.7 38.4 90 3 1 . 6: i 74 5 51 40.7 30.7 nJ88.o 6.8 -i 36.6 02., , ,, 84-5 39 -! 01 32.4; i 7 ;.i 52 41.5 3 I 3 12189.4 7-4 72 37 4 03.5 32 85.3 9- 3'3- ?- : 175-7 53 .2.3 31.9 13 90.4 jJ'.o 73 38.2 04.1 33 86.1 40.2 l >3 <4 o i 76.3 54 3- l 32-5 1 4 j 9 1 - o 8,6 74 39- 04.7 34 86.9 40.. \ 9-r .?4- 176.9 55 43-9 33-1 15 91.8 9.2 75 39.8 05. t 35 87.7 41,41 95 J5-6 J77-5 56 44 '7 337 i6j 9 z.6 9*8 76 40.6 05.9 .36 88.5 42.0: 9 6 36 4 178. i ^7 45-5 34-3 17 93-4 0.4 77 41.4 Oft. ; 37 89. 3 42. n 97 37-21178.7 5 46.3 34-9 18 94.2 i .0 78 42.2. 07. i 38 90. 1 45 -A 9^ 38. d 179.3 59 7 i 5- 5 19 95,0 1.6 7Q 43.x. 07.7 J9 90.9 43.5? 9^ : . - 1-9.9 60 7-9 6.1 20 95-8 2.2 80 43-8 08. < 40 91.7 44-- 00 ^9.61180. 5 Dift Dep. Lat. Dift Dep. Lat. Dift Dep Lat. Dift Dep. Lat. 1 Dift Dep. Lat for 53 Degrees. TABLE JI. Difference of Latitude ana Degrees. Dift Lat. Dep. J Dift Lat. Dep. Dift Lat. Dep. i|Dift Lat. ep. L,at. Dep. i 30.8 30.6 61 48.1 37.0 121 J53 74-5 Si 42.6 1.4 141 89.9 48-4 2 31.6 31.2 62 48 . 9 38.2 22 96.1 75-i 82 43-4 2. I 42 90.7 49.0 3 32.4 31 .8 63 49.0 j8.8 23 96.9 75-7 83 44.2 i . 7 43 49.6 4 33.2 32 . 5 j 64 50.4 39-4 97-7 84 45.0 3-3, 44 92-3 [50.2 5 ^3-9 03. I j 65 51.2 40 -.0 25 98.5 77-0 85 4.5-8 3-9 45 93.1 I5 o.8 6 34.7 93-7 66 52.0 40. 6 2.6 99-3 77-6 86 46.6 4-5 46 93-9 i 05.5 04-3 67 52.8 41.2 27 OD. i 78.2 87 47-4 15.1 47 94.6 152.1 8 00.3 04.9 68 53-6 41.9 28 00.9 73. SH 83 48.1 15-7 48 95-4 f52.7 9 07. i 05-5 69 54-4 42-5 Of .7 79.4) 89 48.9 10.4 49 96.2 153-3 10 O7 . 9 Cb.2 70 55-2 30 02.4 80. o| 90 49-7 17-0 50 97.0 153.9 1 ii os . ; 7i 55-9 43-7 03.2 80.7.1 19, 50-5 17.6! 51 97.8 154-5 12 09.5 07-4 72 56.7 44-3 32 04.0 *MI 51.3 18,1 S 2 ' 98.6 155.1 13 IO.2 08.0 73 57-5 44-9 33 04.8 81.9 93 52.1 18.8 53 99-4 155.8 H II. C5.6 74 ^.3 45 -0 34 05.6 94 32.9 19.4 54 00,2 156.4 15 u.8 09.2 75 59 - 1 46.2 35 06.4 95 53-7 20. I 55 00-9 157.0 1 6 2.6 09.9 76 59-9 46.8 36 07.2 if.'?! 96 54-5 20.7 56 201.7 157-6 17 3-4 io 5 77 60.7 7-4 37 05.0 84. 3 f 97 55.2 21-3 57 2O2 .5 158.2 18 4.2 ii. i 7* 6 1 . c 8.0 3 08.7 8s- o 98 56.0 21.9 53 203.3 158.8 19 5.0 11.7 79 62.3 48.6 39 09.5 5-6 99 56.8 7 -2 5 59 204.1 159-5 20 5-8 12.3 80 63.0 9- 3 ; 40 10-3 86.2 200 57 6 23 I 60 204.9 160. i 21 16.5 12.9 bi 63.^ 9-9 i "4 1 II. I 86.81 201 5^4 23.7 61 205.7 160.7 22 17.3 3-5 : 82 64.6 o-5 42 II.9 87.4 02 59.2 24.4 62 206.5 161.3 23 .8 . i 4.2 :8 3 65.4 i . i 43 12. 7 88.0 o? 60.0 25.0 63 207.2 161.9 24 18.9 14.8 84' 66. 2 5i-7 44 113.5 88.7! O4 60.8 25.6 64 208.0 162.5 25 19.7 1.5-4 8=; 67.0 32.3 45 *4 3 89-3 OS 61.5 26-2 208.8 163.2 26 20.5 16.0 86 67-^ 52. j 46 15.0 89-9 06 62.3 26.8 66 209.6 163.8 27 21.3 r6.6 87 68.6 53-6 47 115.8 901.5.; 07 63.1 27.4 67 210.4 164.4 28 22. I 17.2 .88 69.3 54 2 48 ir6.6 91.1 08 63 9 28.1 68 211. Z 165.0 *9 22-9 17.9 89 70.1 54-8 49 117 4 91.7 9 64-7 28.7 69 212 .O 165.6 | 30 2 3 .6 18.5 'io 70.9 55-4 50 riS.a 92.3 10 65- . 129.3 70 212.8 166.2 j 31 24.4 19.1 91 71-7 56.0 -15* 119 o 93.0, 211 60.3 129.9 271 213,6 (66.8 j 32 25.2 19-7 92 72.5 56.6 5* 119.8 93-6 12 67. 130.5 72 214.3 167.5 | 33 26. C 20. 3 93 -,, , 57-3 53 I2O.6 94.21! 13 67. 131.1 73 2I5.I 168.1 34 26.8 20.9 94 74. j 57-9 54 12.1. i 94-8 if 68. 131.8 74 215.9 168.7 I 1 35 2 7 .6 21.5 95 74-9 58-5 " 122. 95-4 1 169.4 32.4 75 216.7 169.3 28.4 22 2 96 75-6 59.1 50 122-9 96.0 j l6 170.2 33. 76 217.5 169.9 37 29.2 22.8 97 76.4 59-7 .57 123. 96.7 1 171.0 133-6 77 21*. 3 170.5 1 38 29.9 23'4 98 77-2 60.3 5^ 124- 97-3 I 171. n4- 2 78 219.1 171.2 3'9 30.7 24.6) 99 7^.0 61.0 59 125.' 97-9 I 172. 134.8 79 219.9 171.8 40 31.5 24.6 too 78.8 61.6 1 60 126. 98. s \ 2 r~3- 135-5 80 220.6 172.4 4 1 32-3 25.2 ioi|7Q.6 6i. 2 16 126. 99. i 22 174. 136. 28 221 .4|I7?.0 42 33- 1 25-9 02 80.4 62. 8 6 127. 99-7 2 174. 136.7 82 222.2 173.6 43 33-9 26 5 03 [8i.a 63.4] 6 128 100.4 2 175- 137. 8 223.0 174-2 ! 44 34.7 27.1 04 62.0 64.0 6 129. 101 .O 2/ 176. 137-9 84 223-8 174.8 35-5 27.7 82.7 64.6 6 130. 101 .6 2 177. f 38. 8 224.6 '75- 5 ! 46 36.2 28.3 06 33*3 65-3 6 130. f02.2 I 2 178. 139- 8 225.4 176. i 1 47 37.0 28.9 07 H 3 6.S-9 6 f02.8 2 178. 8 226.2 176.7 | .48 37-8 29.6 08 85.1 66.511 6 132. 103.4 1 ~ 179- 140.4 8 226.9 177-3 49 38.6 ^0.2. 09 85.9 67.1 6 *33- 104.0 i * 2 180. 141.0 8 227.7 177-9 I 5 39-4 30.8 i io 86.7 67.711 7 134- 104.7 N 181. 141 9 228.5 178.5 | 5 40.2 5i-4 III 87.5 68.3 17 134- 105.3 E 182, 142. 29 229.3 179.2 ! 5 41-0 32.0 12 ' 83 . ' 69.0 7 '35- 105.9 3 1^2 . 142. 9 230. I 179.2 i 5 41.8 32.6; 13189. c 6 9 .6 : 136. 106.5 3 183. 143.4 93 230.9 180.4 5 5 42-6 43-3 33-2 3V9 14 89.8 i 15 j 9^ 70.2 7 70-8 137- 137- 107. 1 i7-7 184. l8 5 . 144. .-44. 94 95 231.7 232.5 181.0 181.6 5 44- l 34-5 16191.4 71-4 138- 108.4 3 186. 145. 96 233-3 182.2 44-9 3 5 l 17192.2 72.0] 139- 109.0 -3 186. 145. 97 234.C 182 .9 5 4v7 35-7 18 '93. c 72.6|| 140. 109.6 3 187. 146. 9* 234. i J 83-5 5 46.5 36.3 1C 93- 1 - 73- 141. 1 1 . 2 H ? 1 88. 147. 99 *35-< 184. i 6 47-3 36.QI 2X > 94. 73.911 8 141. 110.8)1 4 189 147. 300 236.^ M 8 4 . 7 Dift Dep. Lat. Dift Dep Lat. || Di Dep Lat. KS Dep Lat Dif t Dep. Lat. | ior 52 Degrees. TABLE II. Difference of Latitude aivl Departure for 39 Degrees. Dift Lat. Dep. Dift Lat. Dep. Dift Lat. Dep. j Dift Lat. Dep. Dift Lat. Dep. i 2 00.8 01.6 00.6 01.3 61 62 47-4 48.2 38.4! 39.0 121 22 94.0 94.8 76.1 76.8 82 140 141 ^ 113.9 JI 4-5 241 42 1*7-3 188.1 151.7 ^52.3 1 3 02 3 01.9 63 49.0 39.6 23 95.6 77-4 83 142 .2 115.2 43 188.8 152.0 4 03.1 02.5 64 49-7 40.3 24 96.4 78.0 84 .0 115.8 44 189.6 i 5 6 03.9 04.7 03.1 03-8 66 50-5 40.9 25 26 97-t 97-9 78.7 79-3 86 144 .8 S 116.4 117.1 45 46 190.4 191.2 '154.2 154.8 7 05.4 04.4 67 52 . i 42.2 27 98.7 79-9 7 *45 .3 117.7. 47 192.0 8 06.2 05.0 68 52.8 42.8 28 99-5 80.6 88 146 . i 118.3 48 192.7 156. i 9 07.0 05.7 69 53.6 43-4 29 100.3 ,81.2 89 146 . L 118,9 49 156.7 IO 07.8 ob. 3 70 54-4 44.1) 30. lor .0 81.8 90 .' 119.6 So 194.3 157-3 ' ii 08. S 06.9 71 55-2 44-7 131 ioi.8 82.4 191 148 A I 2O. 2 195. i 158.0 12 09.3 07.6 72 56.0 45-3 32 102.6 83.1 92 149.2 120.8 $2. iQS-8 158.61 13 IO. I 08.2 73 56.7 45-9 33 103.4 83-7 93 .0 121.5 51 196.6 159.2 '4 10.9 08.8 74 57-5 46.6 34 104. i 84.3 94 150 .8 122. I 197.4 15 II.7 09.4 75 5^-3 47-2 35 104.9 85.0 s 122.7 55 198.2 160.5 16 I2. 4 IO. I 76 59.1 47-8 36 105.7 85. 6 Q.O 152 : !23-3 S6 198.9 161.1 17 18 19 13.2 14.0 14.8 10.7 11.3 12.0 77 78 79 59.8 60.6 61.4 48.5 49.1 49-7 37 39 106.5 107.2 108.0 86.2 86.8 87.5 97 98 99 153 . i S 7 124.0 124.6 125.2 57 58 59 199.7 200 . 5 201.3 161.7 162.4 ! 163.0 20 J 5-5 12.6 80 62.2 50.3 40 io?. 8 88.1 zoo .4 125.9 60 202. 1 163.6 2 1 16.3 13.2- M 62.9 { 51.0 141 109.6 88.7 201 156 , 126. s 261 2O2. % 164. 7 22 17.1 13.8 8-2 63.7)51.6 42 110.4 89.4 02 1.55 .0 C27.i 62 203.6 164.0 23 17.9 r 4-5 83 64.5)52.2 43 HI. I 90,0 03 .S 127.8 63 204.4 165. 5 24 18.7 15-1 84 65.3:52.0 44 111.9 90.6 04 is8 . s 128.4 64 205.2 166.1 25 26 19.4 20.2 J; 4 86 66.1 53.5 66.81 54.1 45 46 112.7 1 13- 5 9L3 91.9 35 06 1 60 3 129.0 129.4 65 66 205.9 206.7 166.8 167.4 27 21.0 17.0 87 67.6 54,8 47 114.2 92.5 67 160 . ( . 130.3 67 207.5 168.0 28 21.8 i 7 .6 88 68.4 55-4 4* 115.0 93.1 o> 161 .6 130.9 68 208.3 168.7 29 30 22.5 23-3 iS.^ 89 90 ^9-9 56.0 56.6 49 5 115.8 116. 6 - 93-8 94-4 TO- 162 4 131.5 132.2 69 70 209. i 209.8 169.3 169.9 3* 24.1 ^9-5 9 1 70.7 57-3 I5 1 117.3 95.0 il I 164 .c 132.5 271 210.6 170.5 32 24.9 20. i 9 2 7 1 . 5 57-9 c,, 118. i 95.7 12 164 ,8 '33.4 72 211.4 171.2 33 25. 6 20. 8 93 72.3 58.5 53 118.9 96- 3 13 i6s . ; 134.0 73 212.2 171.8 34 26.4 21.4 94 73-1 59.2 54 119.7 96.9 '4 1 66 3 74 212-9 172.4 35 27.2 22.0 9S 73-8 59-8 'SS 120. 5 97-5 is 167 . T 1 3 - -, 2(3.7 173.1 37 28.0 28.8 2Z.-J 96 97 74.6 75-4 60.4 6r.o 56 121. 2 122. 98.2 98.8 167 168 9 135.9 136.6 76 77 -H-5 215-3 173.7 174.3 3^ 29* s 23.9 Q ^ 76.2 61.7 58 122.8 9). 4 18 169 4 J 37" 2 216.0 17 s. e> 39 30.3 24-5 99 76.9 62.3 59 123.6 100. I 19 bo. 2 I37--S 79 216.8 175.6 40 31.1 25.2 100 7 7 7 61.9 60 124.3 100.7 20 71 .0 .80 217 .6 176.2 4 1 31.9 25.8 [QI 78. r 63.6 161 I25.I 101.3 221 171 . 7 139.1 2'8 I 218.4 176.8 42 32.6 26.4 02 79-3 64.2 62 125.9 roi . 9 22 172 82 219.2 177. c 43 33-4 27. 1 03 5O.6 64.8 63 126.7 102.6 23 . 140.? 219.9 178.1 44 34.2 27.7 04 80.8 65.4 64 127. s 103. 2 24 '74 141.0 8.! 220.7 178.7 45 46 35.0 35-7 28.3 28.9 06 8 r . 6 82.4 66.! 66.7 65 66 128.2 129.0 103.8 104.5 25 26 17 S 141.6 142. 8s 221 . 5 222.3 179.4 180.0 47 48 36.5 49-6 07 08 B.3-9 07.3 68.0 6? 68 129.8 130.6 I05.I 105.7 2? 28 1 7 6 177 4 142.9 143. N 7 88 223.O 223.8 180.6 iSi.z 49 38.1 3^9 30.8 31-5 09 10 84.7 85.5 68.6 69. 2 69 70 131.3 132.1 106.4 107.0 2 9 3 178 .0 .7 144.: 89 224.6 QOJ225.4 181.9 182.5 51 39-6 32.1 III 56.? 69 . 9 171 132.9 107.6 1231 Mfi - I 45- il 291 226.1 183.1 52 53 54 55 56 40.4 41.2 42.0 42.7 43-5 32.7 33-4 34 o 34-6 35- a 12 13 M- i - 16 -57.0 S 7 .8 $8.6 *9-4 90.1 70. s 71.1 72.4 7* 73 74 75 133.7 134.4 135.2 136.0 136.8 IOS.2 108.9 109.5 1 10. 1 no. 8 32 33 34 35 36 l| ' 9 .6 4 146.0 146,6 147.3 '47-<, 92 93 94 95 Q6 226.9 229.3 230.0 183.8 184.4 185.0 185.6 186.3 57 58 44-3 45.1 35-9 36.5 18 90.9 91.7 73-6 74' 3 77 73 137.6 138.3 111.4 112. 37 lS r , 2. '49-1 149.8 97 98 230.8 231.6 186.9' 187."! 59 60 46.6 37-1 37-8 *9 20 91.5 93-3 749 75-5 79 80 139.1 13 j. 9 112. 6 II3-3 39 4Q is 18 -7 S 150.4 151. c 99- 300 232.4 233- t I83.2J 188.8 Dift Dep. Lat. bift Dep. Lat. Dift Dep. Lat. Dift D Lat. Dift Dep. Lat. ; for 5 I Degrees. TABLE IT. Difference of Latitude and Departure for 40 Degrees. ====== Dili ; Lat. Dep. Dift Lat. Dep Dif Lit. Dep. Dif Lat. Dep. Dif Lat. Dep. i 00.8 00.0 61 46.7 39 121 92.7 77- '- ibi 138.7 116.3 241 184.6 154.9 2 01.5 or. 3 I b2 47-5 39-9 22 93-5 7*-4 82 139.4 117.0 42 185.4 155-6 3 02.3 01.9 63 4-3 40, 23 94- a 79.1 *3 140.2 117.6 43 186. i 156.2 4 ?>' 02.6 64 49.0 41. 2 4 95.0 79.7 84 141.0 118.3 44 186.9 156.8 c '0.5.8 03.2 6f 49. 8 41.8 2S 95 7 80.3 ?5 141 7 118.9 45 187-7 r 57-5 6 04.6 3-9 66 50.6 41.4 26 96.5 81.0 ! 86 142.5 119.6 4 6 188.4 158.1 1 7 05.4 04. s 67 51-3 43- 1 27 97-3 81.6 8? H3-2 I2O.2 47 189.2 158.8 ! 8 06. i 95.1 6S 52.1 43" 28 98.1 82.3 88 144.0 120.8 48 190.0 J 59-4 9 06.9 05.8 ! 69 52.9 44-4 29 98.8 82.9 89 144.8 I2I.5 49 190.7 160.1 TO 07.7 06.4 70 53-6 45.0 30 99.6 83- c 90 H5.5 122. I 50 191.5 160.7 ri 08.4 07.1 1 ?I 54-4 45-6 [31 100.4 84.2 191 146.3 122.0 251 192.3 161 .3 rz 09.2 07.7 72 55' 1 40-3 3* ror . i 84.8 92 147.1 123.4 52 193.0 162.0 ! i } 10. 08.4 73 55-9 40.9 33 101.9 85.5 93 147.8 124.1 53 193.8 162.6 | H 10.7 09.0 74 56-7 47.5 34 ioz.6 86.1 94 148.6 124.7 54 194.6 l6 3-3 1 : i ; 11.5 09.6 75 5 7- '5 48. . 35 103.4 86. S 95 149.4 125-3 55 l 9S-3 l6 3 9 i 16 12.3 IO. 3 76 ,8.2 48.9 36 104. 2 87.4 96 150. i 126.0 56 196. i 164.6 ! f i 17 I3..0 10.9 f 77 59-0 4>- 37 104.0 SS.i 97 150.9 126.6 57 196.9 165.2 ' i 18 13.8 n. 6 7S 59 .x 50.1 38 105.7 88.7 98 151.7 127.3 5* 197.6 165.9 i | 19 14.6 12. 2 79 60. 5 50.8 39 106.5 89-3 99 152.4.1127.9 5 ; > 198.4 166.5 i 20 15.2 12.0 1 80 6i.< 5^-4 40 107. i 90.0 200 153.2 i 128.6 60 199-2 167. i i ? -i 16.1 '3-5 8l 62.0 52.1 14 108.0 90.6 :oi 154.0 129.2 161 197,9 167.8 i 22 16.) f 4-i 82 62.8 52.7 4 1 108.8 9i-3 02 '54-7 119.8 62 200.7 168.4 ' i -3 17.6 14.8 83 63.6 53-4 43 109. $ 91.9 03 155-5 I30.> 63 201. 5 169.1 \ 24 i*.4 r5-4 84 64.3 54-0 44 110.3 92.6 04 r 5 6 -3 I3I.I 64 202.2 169.7 f 2 5 19.2 16. i 85 OS i 54.6 ^.5 rii . i 93-2 05 157.0 I3I-I 65 2O3.O 170.3 26 19.9 16.7 86 65.9 55-i 46 in. 8 93-8 06 157-8 r 32-4 66 203.8 171.0 ! i? 20.7 17.4 8- 66.6 55-9 47 112. 6 94-5 C7 158.6 133.1 67 204,5 171.6 ' 28 21.4 18.0 88 '>7-4 56.6 48 "3-4 95.1 08 x 59-3 133-7 6S 205.3 172.3 i9 22 . 2 18.: 8q 6fc.a 57-2 49 114. i 95-8 09 160. i r 34-3 69 2O6. I 172.9 30 23.0 19-3 90 08.9 57-9 50 114.9 96.4 10 160.9 i35-o 70 206.8 173-6 3* 2V 7 19.9 91 69.7 58.5 *5i i'5-7 97. i 211 i6x.6 US- 6 271 207.6 174.2 11 32 24.5 20.6 92 70.,- 59-i 52 116.4 97 7 12 162.4 i3 6 -3 72 208.4 174-8 33 25.3 21. 2 93 71.2 59-8 .5.? 117- i 9*-3 13 163.2 136.9 73 209. I 175.5 34 26.0 21.9 91 72.O 60,4 54 nS.o 99.0 J 4 163.9 137-6 74 209. 9 176.1 1 35 26.8 22,. s 9" 72.8 6i.j 55 n$,7 99.6 15 164.7 13*. z 75 2IO.6 176.8 J* 27.6 23.1 96 73- S 61.7 56 1/9.5 100. 3 if. 165.5 "38.8 76 211.4 177.4 |7 28.3 2}.8 97 74-3 62.4 5? 120.3 100.9 17 i 65. 2 139.5 77 212.2 178.1 3* 2t).I 14.4 98 75-i 6-3-c ^ I2T.O 01.6 18 167.0 140. i 78 213-0 178.7 39 29-9 25.1 99 75-8 63.6 59 121. 8 102.2 19 167. S 140.8 79 213-7 J 79-3 40 J0.6 25.7 too 76.'-' 64.; 60 1 2 ?. . 6 102.8 20 168*5 141.4 80 214.5 180.0 4I 31-4 26.4 roj 77-4 64. . 6 1 "'3/3 3 5 ^ZI 169.3 142.1 281 215-3 io.6 4^ 32.2 J27.0 02 78.1 6; ')' 61 1 24. i 04. i 22 170.1 142.7 82 216.0 181.3 43 32.9 t7j 0} 78,9 6.6.J 6? 124 9 04.8 13 170.8 H3 3 83 216.8 181.9 44 3 3 7 jfl,3 04 "9-7 66. 64 12,'. 6 05-4 2 4 171.6 144-0 84 217.6 182.6 ; 45 H*5 28.9 oc 80.4 67.,- 65 126.4 06. i 2; 172.4 144.6 85 "8-3 183.2 45 55.2 29.6 06 ^1.2 S8.r 66 127.2 06.7 26 173.1 H5- 3 86 219.1 i8 3 .8 47 36.0 30:2 07 32 .O 6i..^ 67 12-7*9 07.3 27 *739 145.9 7 219. q 134.5 4 S 36.8 30.9 08 Sl.y 69.4 68 12.8.7 oS o 2S 174-7 146.6 88 220.6 185.1 : 49 37-5 31-5 OQ '3*5 70, j 69 129.5 08.6 2 9 175-4 147.?, 89 221.4 185.8 50 3*. 3 32. t 10 ^4-3 70 7 70 130.2 09. 3 30 176.2 147.8 90 222.2 186.4 ! 5 1 39.1 32.8 III 85. o 71-3 71 131 o 9-9i .31 177.0 148.5 291 222. 9 187.1 5- }9.8 33-4 12 8^.8 72.0 72 131.8 10.6 32 i77'7 149.1 92 223.7 187.7 i 53 4.0.6 34.1 13 86.6 72.6 73 132.5 II. 2 33 17^.5 149.8 93 224.4 188.3 54 41.4 34-7 I 4 *7-3 73-S 74 J33-3 n. 8 14 1/9.3 150.4 94 225.2 189.0 55 4.2.1 35-4 15 88. f 7J-y 75 ^34.1 12.5 35 180,0 151-1 95 226.O 189.6 56 42.9 36.0 16 88. 9 | 7^-6 76 134-8 13.1 36 180.8 151-7 96 226.7 190.3 57 43-7 3,6.6 17 89.6 7, .2 77 135-0 n.8 37 181.6 I52-3, 97 22-7-5 190.9 58 44-4 J? : 3 18 90.4 7;.- v 7? 136.4 14,4 13 182.3 153-0 ^ 93 Z28. 3 191.6 59 45.2 37-9 ^9 )l.Z 7i-S 79 137-1 15.11 39 itfj.'i i53- 6 99 22,9.0 192.2 60 4.6.0 38.6 20 91.9 7'-i 80 I379 115.7 40 183.8 2ti 300 229.8 192.8 Dift) Dep. Lat. Dift Dep. lat. Dift Dep. Lat. DifJ Dep. Lat. I Dift Dep. Lat. tor 50 Degrees. TABLE II". Difference of Latitude and Departure for 41 Decrees. Dift Lat. Dep. Dift Lat. Dep. Dift Lat. Dep. Dift Lat. Dep. { Dift Lat. Dep. i 00.8 00.7 61 46.0 40.0 121 91.3 79-4 81 136.6 118.7 141 181.9 158.1 2 01.5 01.3 62 46.8 40.7 22 92. j 80.0 82 137-4 119.4! 42 182.6 158.8' 3 02.3 02.0 63 47-5 4 r 3 23 9Z.8 80.7 83 138.1 T2O. 1 43 183.4^ 159.4 4 03:0 02.6 64 48.3 42.0 24 93.6 81.4 84 138.9 120.7 44 160.1 5 03.8 03.3 65 49.1 42.6 25 943 82.0 85 139.6 121.4 45 iHp.9 160.7 6 04.5 03.9 66 49.8 43-3 26 95.1 82.7 86 140.4 122. O 46 185.7 161.4 7 05.3 04.6 b7 50.6 44.0 27 95.8 83-3 87 141.1 122.7 47 186,4 162.0 8 06. i 05.2 68 51-3 44.6 28 96.6 84.0 88 141.9 48 187.2 162.7 9 06.8 05.9 69 52.1 45-3 29 97-4 84.6 89 142.6 124.0 49 187.9 163.4 10 07.5 06.6 70 52.8 45.9 30 98.1 85-3 90 143-4 124.7 188.7 164.0 ii 08.3 07.2 7i 53-6 46.6 131 98.9 85-9 191 144.1 125.3 251 189.4 164.6 12 09.1 07.9 72 54-3 47.2 3 2 99-6 86.6 92 144.9 126.0 5 2 190.2 165.3 13 09.8 08.5 73 55-; 47-9 33 100.4 87. 3 93 H5.7 126.6 53 190.9 166.0 M 10.6 09.2 74 55.8 48.5 34 IOI.I 87.9 94 146.4 127.3 54 191.7 166.6 15 H 3 09.8 75 56.6 49-2 35 101.9 88.6 95 147.2 I2 7 . 9 55' 192.5 167.3 16 12. 1 10.5 76 57-4 49.9 36 102.6 89.2 96 147.9 128.6 56 193-2 168.0 l l 12.8 II. 2 77 ^8. i 50.5 37 103.4 89.9 97 129.2 57 194-0 168.6 18 13- b ii. 8 78 5*. 9 51.2 38 104. 1 90.5 98 149-4 129.9 58 194.7 169.3 19 14-3 12.5 79 59.6 51.8 39 104.9 91.2 99 150.2 130.6 59 T 9"5-5 169.9 20 15.1 X 3't bo 60.4 52.5 40 105.7 91.8 200 150.9 131.2 60 196.2 170.5 21 15.8 13-8 81 61.1 53.1 141 106,4 92.5 201 151.7 131.9 261 197.0 171.2 22 16.6 14.4 b'2 61.9 53-8 42 107.2 93.2 O2 152.5 62 l 97-7 171.9 23 iv. 4 15. i 83 62.6 54-5 43 107,9 93-8 03 133-2 6.3 198.5 172.5 | 2 4 18.1 l S-7 84 63-4 55-1 44 108.7 94-5 04 154.0 133.8 64 199.2 '73-2 2 5 18.9 16.4 8'5 64.2 55-* 45 109.4 95-i OS ^34-5 6s 200,0 173-9 26 19. 6 17.1 86 64.9 cb. 4 46 II0.2 9.5.8 06 *55- 5 I35.I 66 200.8 *74 5 ! 27 20.4 17.7 S 7 65-7 57.1 47 110.9 96.4 07 156.2 135-8 67 201.5 175.2 j 28 21. I 18.4 88 66.4 S7-7 48 III.7 97.1 08 157.0 136.5 68 2O2. 3 175.8! 29 21-9 19.0 89 67.2 58.4 49 112.5 97-8 09 !57-7 I37.I 69 203.0 1/6.5 30 22.6 19.7 90 67.9 59-o 50 113.2 98.4 10 158.5 70 203.8 I77-I 31 23-4 20.3 9 1 68.7 59-7 151 114,0 99-i 21 I 159.2 138.4 271 204.5 177-8 32 24.2 21.0 92 69.4 60.4 52 114.7 99-7 12 160.0 I39-I 72 205.3 178.4 3J 24.9 ir.6 93 70.2 61.0 53 H5.5 100.4 13 160.8 139-7 73 206.O 179.1 34 25.7 22.3 94 70.9 61.7 54 116.2 IOI.O 14 161.5 74 206.8 179*8 1 35 26.4 23.0 95 71-7 62. 3 55 117.0 101.7 15 162.3 I4I.I 75 207.5 180.4 36 27.2 23. b 96 72.5 63.0 117.7 102.3 16 163.0 I4I.7 76 208.3 181.1 38 28.7 24.3 24.9 97 98 73-2 74.0 63.6 64.3 57 118.5 119.2 103.0 103.7 18 163.8 164.5 142.4 143.0 78 209I 209.8 i&.7 182.4 39 29.4 25.6 99 74-7 64 9 59 I2O.O 104.3 19 165-3 143-7 79 210.6 183.0 40 30-2 26.2 roo 75-5 65.6 60 120.8 105.0 20 166.0 144-3 80 211.3 183-7 4 1 30. 9 26.9 101 76.2 66.3 161 I2I-5 105.6 221 166.8 145'Oi z8i 212. I 184.4 42 3 1 - 7 27.6 02 77,0 66.9 62 122-3 106 . 3 22 167.5 145.6 82 7.12.8 185.0 43 31-5 28.2 03 77-7 67.6 63 123.0 10 t . 9 23 168.3 146.3 83 2^3.6 185.7 44 33-2 18.9 04 78,5 68.2 64 iz 3 .8 107.6 2 4 169. i 147.0 84 214.3 186.3 46 34.0 34-7 29.5 30.2 05 06 79-2 80.0 68.9 69 .5 66 124.5 ro8.2 108.9 25 26 169.8 170.6 147.6 148.3 85 86. 2I5.I 2J5.8 187.0 187.6 47 35-5 30.8 07 80.8 70. 2 67 126.0 109.6 27 171.3 148.9 8? 216.6 188.3 48 3 b.2 31-5 0* 81.5 70. 9 68 126.8 iro.2 28 172. i 149.6 88 217.4 i$8. 9 49 37.o 32.1 09 82.3 7*-5 69 127.5 110.9 29 172.8 89 2I8..I 189.6 5o 37-7 32.8 10 83.0 72.2 70 128 3 HI. 5 30 173.6 150.9 90 218.9 190.3 51 38.5 33-5 III 83-8 72.8 171 129.1 112. 2 231 174-3 I5I.5 291 219.6 I9O. Q 5 39 .2 34- 12 84-5 73-5 72 129.8 112. 8 32 175.1 152.2 92 220.4 I9I.6 1 53 54 40.0 40.8 34.8 354 13 14 ^5-3 86.0 74-1 73 74 130.6 114.2 33 34 175-8 176.6 152.9 153-5 93 94 221.1 221.9 192.2 192.9 55 41.5 36.1 I S 86.X 75-4 75 132.1 II4.8 35 177-4 154.2 95 222.6 !93-5 56 42.3 36.7 1 6 87-5 76.1 76 132.8 II5.5 178.1 154.8 96 223 4 194.2 j 57 58 43-0 43-8 37-4 38 i 17 18 88.3 89.1 76.8 77-4 77 78 133-6 134-3 116. i 116.8 37 38 178.9 179.6 155-5 I56.I 224,1 224.9 194.8 59 44-5 38.7 '9 89.8 7$. i 79 135.1 117.4 39 180.4 156.8 99 225.7 196.2 60 45 3 39-4 20 90.6 78.7 80 135.8 n8.i 40 181.1 157.5 300 196.8 Dift Dep. Lat. Dili Dep. Lat. Dif Dep. Lat. jDif Dep. Lat. Dif Dep. Lat. 11 n tor 49 Degrees TABLE II. Difference of Latitude and Departure for 42 Degrees. Dlft Lit. Dep. rDift Lat. Dep. [ipift Lat. Dep. jDiftj Lat. Dep. Dift Lat. Dep. i 00.7 00.7 61 45 3 40.8! 121 89.5 81.0! 181 134-5 121. I 4* 179-1 161.3 ^ 01 . ^ 01.3 62 46.1 41. 5 22 90.7 8i.6l 82 135.3 121. a 42 179.8 161.9 3 02.2 02.0 63 46.8 42.2 23 9i4 82.3; 83 136.0 122.5 43 r8o.6 162.6 4 03.0 02.7 64 47-6 42.8 24 92.1 83.0! 84 136.7 123.1 44 181.3 163,3 5 03.7 03-3 65 4M 4}-<; *| 92.9 83.6 8S 137.5 123.8 45 182.1 163.9 6 04-5 04.0 66 49.0 44.2 26 93-6 84.3 86 138.2 *M-5 46 182.8 164.6 7 05.2 04.7 67 49.8 44.8 47 94.4 Ij.p 87 1391-0 125.1 47 83.6. 165.3 8 05-7 05.4 68 50*5 45-5 28 95.1 85.6 88 r 39-7 I2 5 \8 48 84.3 165.9 9 06.7 06.0 69 Si-3 46.2 29 95-9 86 3 89 140.5 126. 5 49 185.1 166.6 10 07-4 06.7! 70 52.0 46.8 30 96.6 87.05 90 141.2 127. i 5o 185.8 167.3 ii Q8.2 07.4 7i 5*% 47*5 Mi 97-4 87.7 191 141.9 127. b! si 186. 5 168.0 12 08. 9 08.0 7* 53-;? 48.2 32 98.1 88.3 92 142.7 128. S S* 187.3 168.6 13- 09.7 08.7 73 54.2 48.8 33 9?. 8 89.0 93 143.4 129.1 53 8^.e 169.3 H 10.4 09.4 74 55.0 49- S 34 99.6 89.7 94 144-2 129.8 54 188.8 170.0 T5 ir. i 10. O 75 55-7 SO. 2 35 100.3 90-3) 9S 144.9 iSO-S 55 189.5 170.6 16 n. 9 is. 7 76 0.5 So.8 36 101 . 1 91.0 96 145-7 131.1 J6 190.2 r7i.3 i? 12.6 11.4 77 57-2 5 T 5 37 101.8 9^.7 97 146.4 131.8 57 191.0 172-0 18 13.4 ia.0 78 58.0 52.2 3* 102.6 92.3 Q8 147.1 132.5 5^ 191.7 172.6 19 14.1 12.7 79 q8.7 52.9 39 103.3 93.0: 99 147.9 133.2 59 ^92. 5 173-3 20 14.9 n.4 80 59*5 53-5 40 104.0 93.7 200' 148.6 133.8 60 f 93-2 174.0 - 21 15.6 14.1 8l 60.2 54. 2 141 104.8 94.3 iioi 149.4 '34-5 .61 194 o 174.6 21 16.3 14.7 82 60.9 54-9 42 105. c; 95.o[i 02 ^50.1 1354 62 x 94-7 '75-3 2 3 17.1 IS- 4 83 61.7 55- x 3 43 106. 3 95-7 o; 150.9 r 35-8 63 195,4 176.0 24 17.8 16.1 84 62.4 56.2 44 107.0 96.4 04 151.6 13(5-5 6a 196.2 176.7 *5 t*,6 16.7 85 63.2 5 6 -9 4S 107.8 97.0 o> 152.3 137-2 65 1 9 6 -', r 77-3 26 19-5 17.4 86 6 3-9 57-N 46 108.5 97-7 06 153.1 137.8 66 197.7 T7&.0 27 20. I 18. J 7 64.7 58.2 47 109.2 98.4 07 153- s 138.5 67 -9-4 73.7 28 20.8 18.7 88 65.4 58-9 48 i ro.o 99 o 08 154.6 z 39-2 68 199.2 179.3 29 21.6 19.4 89 66.1 59-6 49 110.7 99-7 09 '55-3 139.8 69 199.9 180.0 30 22.3 20. i 90 66.9 60.2 41.6 12 88. 82. i 132.4 123.4 24 176. r6 4 . 4 2 . OI. <; 01. 4 62 45 v 42.3 2 89. 83. S 124.1 4 177. ( 165.0 02. Z 02. o 63 46.1 43.0 2 90. 83- 8 133-3 124.8 4 177. 165. 7 i 02. 7 2 7! 64 46.8 43-6 2 90. 84. 8 134.6 125. _, 44 178. 166 .4 1 03. 03- 4 6s 47-5 44-3 2 91. 85. 8 135.3 126.2 4 179. ; 167.1 6 04. t 04. i 66 48.3 45.0 2 92. 85. 8 136.0 126.9 46 179. ( 167.8 7 05. 04. 8 67 49.0 45.7 2 86. 8 136.8 127.5 4- r36.i 168.5 8 05. c 05. 5 68 49.7 46.4 2l 93- 87. 8 '37-5 128.2 1 3 1 . ., 169.1 9 06. < 06. i 69 50.; 47.1 2 94- 88.0 8 138.2 128.9 49 182.1 169.8 10 07.- 06. 3 70 51.2 47-7 3 >5- 88.- 9 139.0 129.6 50 rBi.S 170.5 ii 08. c 07.51! 71 51.9 48.4 13 95- 39-3 *9 r 39-7 130.3 251 183. i 171.2 12 08. i 03.2 72 52.7 49.1 3 96. 90.0 9 140.4 130.9 5- 184., 171.9 13 09. oS. H 73 53-4 49-8 3 97- 90.7 9 141.2 131-6 53 185. t 172.5 i * 4 10.2 09. d 74 54-i 50.5 3 98. 91.4 9 141.9 132.3 54 185.8 173.2 15 II. C 10. 2 [I 75 54-9 5 i.i 3 98. 92.1 9 142.6 133.0 55 188.5 J73-9 1 6 ir. 7 10.9(1 76 .55.6 51.8 3 99- 02.8 9 143 .3 133.7 56 187.2 174-6 i? 12.4 ' 77 S6.3 52.5 3 100.2 93-4 9 144.1 134-4 V i88.c J 75-3 18 12. 78 57.0 -3.2 3 100.9 94i 98 144-8 135.0 5 188.7 176.0 19 13.9 13. oj| 79 57.8 53-9 39 101." 94.8 99 H5-5 135-7 59 189.4 176.6] 20 14.6 >||8o 5^5 54.6 40 102.4 95-5 200 146.3 136.4 60 190.2 '77.3 21 I*. 14.; 59-2 55-* f 4 103. 96.2 2OI 147.0 I37.i 261 190.9 78.0 22 16. I5.o{| 82 60.0 55-9 103.9 96.8 02 r 47-7 137-8 62 19! .6 178.7 23 16. 1 S ' ^ 60.7 56.6 i 4"? 104.6 97-5 O3 148.5 138.4 6} '9* -3 179-4 17. 16.4 \ 84 61.4 57- ^ 44 105-3 98.2 04 149.2 139-1 64 193. i 180.0 2C 18.3 17.0?! 85 62 . 2 58.0 4 106.0 98 .9 05 149.9 139-8 6s 193.8)180.7 26 19. < 17.7 ! 86 62.9 58-7 46 166.8 99.6 06 150.7 140.5 66 94.5,18!. 4 27 19-7 18.4 87 63.6 59.3 47 107.5 00.3 07 r 5' -4 141.2 67 95.3 182.1 28 20.5 19.1 88 64.41 60.0 48 108.2 00.9 08 152.1 41.9 68 96.0 182.8 2 9 21.2 I 9 .8 (I 89 65.1 -60.7 49 09.0 01.6 9 52.9 42.5 69 96-7)^3.5 30 21.9 20. S 90 65.8 6l.4 50 09.7 02.3 10 53-6 43-2 - 70 97 -5 184.1 31 22.7 21. 1 I 91 66.6|6z. i i5i 10.4 03,0 211 54-3 43-9 271 98.2 184.8) 32 23-4 21.8 11 9 2 67.3 62.7 52 II. 2 03.7 12 55-0 44.6 7* 98.9 185- Si 33 24.1 22.5 H 93 68.0 63-4 53 II.9 04-3 13 55-8 45-3 73 99-7 186.2^ 34 24.9 23.2 94 68.7 64.! 54 12.6 05.0 H 56.S 45.9 74 00^ 186.9 35 2S.6 23.9 9S 69.5 64.8 55 13-4 05.7 57-2 46.6 7S 01. I 187.51 36 26.3 2 4 . ': 96 70.2 65-5 14.1 06.4 16 58.0 47-3 76 01.9 188.2 37 27. I 25.2 97 70.9 66.2 57 14.8 O/.I i? r 5 8. 7 48. Q 7 7 02.6 188.9 38 27.8 25-9 7L7 66.8 58 15.6 18 59-4 48.7 78 03-3 189.6 1 39 28. S 26.6 1 " 7^-4 67. s 59 16.3 08.4 19' 60.3 149.4 79 04. c '90. '3 i. 40 29.3 27-3 ICO 73-1 68.2 60 17.0 09.1 20 60.9 150.0 04.8 191 .0 41 30.0 28.0 '10 I 73-9 68.9 161 17. 7 09.8 21 61.6 150.7 281 5-5 191.6 42 30.7 28.6 02 74 -6 6 ; . 6 62 18.5 10.5 22 62. A 151.4 82 06.2 192.3 ! 43 31.4 29. 3 03 75-3 "0. 2 63 19.2 ri.2 23 63.1 83 07.0 193.0 44 32.2 30.0 i 04- 76.1 70.9 64 19-9 n. S! 2 4 63.8 IS2.8 84 07.7 r 93-7 45 32.9 30.7 || o.s 76.8 71.6 20.7 I 2 . S 64.6 153.4 8s 08.4 194.4! j 46 33.6 31.4 06 77o 72.3 66 21.4 13.2] 26 154.1 86 09.2 195.1 i 47 34-4 32.1 j 07 7*-3 73"-o 67 22. I 13.9 27 66.0 154.8 ft" 7 9 -'9 48 32.7 08 73-7 6S 22. 9 I 4 .6 66.7 155-5 Sd 10.^196.4 49 31-8 33-4 09 79-7 74-3 6q 23-6 15-31 2q 67.5 1S6.2 j 89 n .4 1 1 3 45-3 43-* 23 88.5 85.4 83 131.6 127.1 43 174.8 168.8 ! 4 02.9 02.8 64 46.0 41-5 24 89.2 86.1' 84 132.4 127.8 44 J75-5 l6 9-5 i 5 03.6 03-5 65 46.8 45.2 as 89.9 86.8 8S I33.I 1.8. <; 4S 176.2 170.2 ' 6 04-3 04.2 bb 47-5 45.8 26 90.6 7.5 86 533-8 129.2 46 177.0 170.9 7 05.0 04.9 67 48.2 46.5 27 91.4 88.2 87 '34-5 129.9 4? 177-7 171. 6 ! 8 05.8 05.6 68 4*- 9 47-* 28 92.1 88.9 88 135.2 130.6 48 178.4 172.3 9 06.5 06.3 69 49.6 47-9 29 92.8 89.6 89 136.0 JS 1 ^ 49 179-1 173.0 10 07 a 06 9 70 50.4 48.6 3 93 -.5 90-3 90 136.7 132.0 5 179.8 1/3-7 ii 07.9 07.6 7J 51.1 49-3 131 94.2 91 .0 191 137-4 132-7 2SI 180.6 '74-4 J2 08.6 08. 3 72 51.8 50.0 32 95.0 9 i.7 92 138.1 J 33-4 52 '8?. T 175.1 J 3 09.4 09.0 73 5 2 -5 50.7 33 95-7 92.4 93 138.8 134-1 S3 182.0 175-7 H 10. I 09-7 74 53.2 51.4 34 96.4 93.1 94 139.6 134-8 ^4 182.7 176.4 15 10.8 10.4 75 54 -o 52.1 35 97.1 93-8 95 140.3 135.5 ss 183.4 177.1 16 11.5 ij. i 76 54-7 52.8 30 97.8 94-5 96 141 .0 136.2 S6 184.2 177.8 - J 7 12.2 1 1. 8 77 55-4 53-5 37 9*.S 95.2 97 141.7 136.8 S7 184.9 178-5 i 18 12. 9 12.5 7* 56.1 54.2 3* 99-3 95-9 98 142.4 i37o 53 185.6 179.2 : ij 13-7 13.2 79 56.8 54-9 & 100. 96.6 99 143.1 ! 3 *.a S9 186.3 179-9 ! 20 14.4 13.9 80 57-5 55.6 40 ico. 7 97-3 200 143.9 138.9 60 187.0 i So. 6 ! 21 I 5 .I 14.6 Si 58.3 56.3 141 101.4 97-9 :oi 144.6 139.6 :6i 187-7 181.3 j ! 22 15.8 15-3 82 59.0 57-0 42 IO2. I 98.6 02 H5- 3 140.3 62 i88.s 182.0 ! 23 16.5 16.0 83 59-7 57-7 43 102.9 99-3 03 146.0 141.0 63 189.2 182.7 24 17.3 16.7 84 60.4 58.4 44 103.6 IOO.O 04 146.7 141.7 64 189.9 183.4 *5 18.0 17.4 85 61. 1 59-o 4S ie4-3 100.7 OS H7- 5 142.4 6S 190.6 184.1 26 18.7 ifc.i 86 61.9 59-7 46 105.0 ioi .4 06 148.2 H3- 1 66 191.3 184.8 | 27 19.4 18.8 7 62.6 60.4 47 105.7 IO2.1 07 148,9 147.8 67 192. i 185.51 ! 28 20. I 19.5 88 63-3 61.1 48 106.5 102.3 08 149.6 *44o 68 192.8 186.2 29 20.9 20. i 89 64.0 61.8 49 107.2 103.5 09 150.3 145.2 69 193.5 186.6 jo zi.6 20.8 90 H-7 62.5 5 107.9 104.2- 10 151.1 145.9 70 194.2 187.6 1 31 12.3 21.5 9 1 65.5 63-2 15* 108.6 104.9 211 151.8 146.6 271 194.9 188.3.) ! 32 23.0 22.2 92 66.2 63.9 S2 109.3 105.6 12 152.5 H7.3 72 J 957 188.9 33 23.7 22. 9 93 66.9 64.6 S3 no. i 106.3 IJ 153.2 148.0 73 196.4 189.6 1 34 24.5 23- b 94 67.6 65-3 54 no. 8 fo/.o H 153-9 148.7 74 197.1 19. 3 1 1 35 25.2 24-3 95 68.3 66.0 5S 111.5 107.7 IS 154.7 H9-3 7S 197-8 191.0 i 3* 25.9 25.0 96 69-1 66.7 S6 112.2 108.4 16 '55-4 150.0 76 198- 31-0 07 77.0 74-3 67 120. I 116.0 27 163.3 157.7 87 200.5 199.4 ; 48 34-5 33-3 oS 77-7 7S.O 63 120.8 116.7 28 164.0 158.4 88 207.2 20O. I j 49 35.2 34>o 09 78.4 75-7 69 121. 6 117-4 29 164.7 159.1 8 9 207 . 9 200.8 5 36.0 -U- 7 10 79.1 76-4 70 121.3 ri8. i 3 165.4 159-* 90 208 . 6 201 .5 5i 36.7 35-4 III 79-3 77-1 171 123.0 118.8 -3 1 166.2 160.5 ZC)I 209.3 1O2. 1 , 52 37-4 36.! 12 80. e 77-8 72 123.7 119.5 32:166.9 161.2 91 2IO.O Z02.8 53 38.1 36.8 13 *i-3 78.5 73 124.4 120.2 33 167.6 161.8 93 210.8 23-5 ! 54 38.8 37-5 14 82.0 79.2 74 125.2 120-9 34 168.3 162.6 94 211.5 i04 . 2 39.6 38.2 15 82.7 79-9 7S 125.9 121. 6 35 169.0 J6;s2 9S 212.2 204.9 i b 4-3 38-9 16 3-4 80.6 76 126.6 122-3 36 169.8 163.9 )6 2 I 2 . ) 205.6 , 57 41.0 39- 6 i? 84.* 8.1.3 77 1*7.3 123-0 ?7 170.5 164.6 97 213-6 206.3 5 g 41.7 40.3 1 8 84-9 82.0 78 128.0 123.6 38 J 7 I.Z 165.3 98 214.4 zo/.o 5,9 4-4 41.0 *9 85.6 82.7 79 128.8 1-4-3 19 171.9 166.0 1 99 1I5.I 407.7 , 60 43-a 41.7 20 86.3 83.4 80 129.5 125.0 4 172.6 166.7 300 215-8 208.4 ' pift Dep. Lat. Dift Dep. Lat. Dift Dep. Lat. Dift! Dep. Lat. Dif De.p. Lat. f for 46 Degrees. TABLE II. Difference of Latitude and Departure for 45 Degrees, Dift 'Lat. Dep. Dift Lat. Dep. Dift Lat. Dep. Dift Lat. Dep. Dift Lat. Dep. ' i 00.7 00.7 61 43-i 43 i 121 85.6 85.6 1X1 128.0 128.0! 241 170.4 1 70 . 4 < 2 01.4 01.4 62 43.* 43-8 22 86.3 86,, 82 128.7 128.7 42 171. i 171.1 31 02.. I 02.1 63 44-5 445 23 87.0 87.0 Ss 129.4 129.4 43 171 .8 171.8 4 02.8 02.8 64 45'3 45-3 24 87.7 87.7 84 130. i 130, i 44 172.5 172.5 5 03-5 03.5 65 46.0 46.0 25 88.4 88.4 *S 130.8 130.8 4^ 173-2 173-2 6 04.2 04.2 66 46.7 46.7 26 89.1 89.1 86 I3I-5 I3I-5 46 173.9 173.9 7 04.9 04.9 67 47-4 47-4 27 89.8 89.8 8" 132.2 132.2 4" r /4./ '74-7 8 05.7 05.7 68 48.1 48.1 28 90.5 90.5 88 132.9 132.9 48 175-4 r 75-4 9 06. 4 06.4 69 48. V 48.8 29 91.2 91.2 89 J33-6 133-6 49 176. i 176. i 10 O 7 .l 07.1 7 49-5 49-5 30 91.9 91.9 90 134-4 r 34-4 5o 176.^ 176.8 ii 07.8 07.8 7i 50.2 50.2 [ 3 I 92.6 92.6 191 i35-i i35-i 251 177-5 177-5 12 08.5 08.5 72 50.9 50.9 3* 93-3 93-3 92 135.8 135-3 52 178.2 178.2 '3 09.2 09.2 73 51.6 51-6 33 94.0 94.0 93 136.5 136.5 53 178.9 178.9 ' 14 09.9 09.9 74 52-3 52.3 34 94.8 94.8 94 137-2 137-2 54 179.6 179.6 15 10.6 10.6 75 53-o 53-0 35 95-5 95-5 95 137.9 '37-9 5S i3o. 3 180.3 16 "3 11.3 76 53-7 53-7 36 96.2 96.2 96 138.6 138.6 56 181.0 iSl.O : 17 12.0 T2.O 77 54-4 54-4 37 96.9 96.9 97 139-3 J 39-3 57 181.7 181.7 18 12.7 12-7 78 5^.2 55-2 38 97-6 97.6 98 140.0 140.0 S8 r8 2 ... 182.4 19 13-4 13-4 79 55-9 55-9 39 9-3 98.3 99 140.7 140.7 59 183.1 .Sill 20 I4-I I4.I 80 56.6 56.6 40 99.0 99.0 200 141.4 141.4 60 i*M 183.81 21 14.8 I 4 .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 5 S.e 58.0 42 100.4 100.4 C2 142.8 142.8 62 r8s.^ '85.3] 23 16. 3 I6. 3 3 58.7 58.7 43 101. I ior . i 03 r 43-5 143-5 61 186.0 186.0 24 17.0 17.0 84 59-4 59-4 44 101.8 loi.S 04 144.2 144.2 64 186.7 186.7 25 17-7 *7-7 8s 60. i 60. i 45 102.5 102.5 OS 145.0 145.0 6 5 187.4 187.4. 26 I8. 4 18.4 86 60.8 60.8 46 T03. 2 103.2 06 14S.7 145-7 661188. i 188.1 27 I9.I 19. i 8 7 61.5 1.5 47 103.9 103.9 C7 146.4 146.4 6 7 ;i88.8 188.81 Z* 19-8 19.8 88 62.2 62.2 48 104.7 104,7 08 147.1 147.1 68 189. ? 189-5! 29 20.5 20. <; 89 62.9 62.9 49 105.4 105.4 09 147.8 147.8 $9 190.2 190.2 30 21.2 21.2 90 63.6 63.6 5 106. i ro6. i IO 148.5 i4 5 70 190.9 190.9 3^ 21.9 21. 9 91 6 4-3 64.3 151 106.8 i6.8 21 J 149.2 149.2 2 7 r 191.6 191.6 ] 32 22.6 22.6 92 65 i 65.1 5^ 107.5 107.5 12 149.9 149-9 72 192,3 192.3 | 33 23-3 23-3 93 65.8 65.8 53 108.2 108.2 13 150.6 150.6 73' 193.6- 193-0 , 34 24.0 24.0 94 66.5 66.; 54 108.9 108.9 H 15L3 151.3 74 i ( .)3-7 '93-7 { 35 24.7 *4-7 95 67.2 67.2 55 109.6 109.6 15 152*0 152.0 75''94-5 194.5 36 35-5 25. S 96 67.9 67.9 S6 110.3 110.3 1 6 [52.7 152.7 76 195.2 195.2 ; 37 26.2 26.2 97 68.6 68.6 57 III.O III.O 17 153-4 153-4 195*9 '95-9 ' 3* 26.9 26.9 98 69.3 69-3 5* 111.7 in. 7 18 i54.i i54-i /8 196.6 F96.6 j 39 27.6 27.6 99 70.0 70.0 59 112.4 112.4 19 154.9 154-9 79 r$7.3 107-3 ' 40 28.3 28.3 100 70.7 70.7 60 113.1 113.1 20 155.6 155.6 80 198.0 198;. 0| 4* 29 .0 29.0 ior 7 p. 4 71.4 161 113.8 113.8 221 i5 6 -3 156.3 281 198.7 iflS.Z- 42 29.7 29.7 02 72.! 72.1 62 114.6 114. 6 22 157.0 i57.o 82 199.4 199 -4 j 43 30.4 30.4 03 72.8 72. S 6} 115.3 115-3 *3 J57-7 157-7 8. 200. i 200. i i 44 31- 1 31.1 04 73-5 73-5 64 1 16.0 116.0 24 t5.4 i5M 84 200.8 200.8 ' 45 31.8 31.8 os 74-2 74.2 65 .16.7 116.7 aS 159.1 159-! 85 201.5 iot.5 ( 46 3*-5 3?- -5 06 75.0 75-0 66 117.4 117.4 26 159.8 159.8 86 202.2 202.2 ; 47 33-2 33.2 07 75-7 75-7 6? 118.1 iiS,i 27 160.5 160, s 87 2O2.0 202 .9 48 33-9 33-9 08 76.4 76. 4 68 118.8 118.8 28 161.2 161 .2 88 203.6 203.6 49. 34.6 34.6 09 77-i 77- T 69 119.5 119.5 2 9 161.9 161.9 89 204.4 ^4.4 ; 5 35-4 35-4 10 77.8 77- 8 70 1 2O. 2 120.2 30 162.6 162.6 90 205.1 20;. I 5 1 36.1 36.1 III 78.5 78..S 17 r 120-9 120-9 2^1 163-3 i6M 291 20^.b 2 "P j 5* 36.8 36.8 12 79.2 79-2 71 121 .6 T2I.6 3- 164.0 164.0 92 206.5 206. 5 j 53 37-5 37-5 13 79-9 79-9 73 122.3 122.3 33 164.8 164.8 91 207. 2 207;. 2 54 3-2 38.2 H 80.6 80.6 74 123.0 I23.C >;4 165. s 165-5 94 2P7-9 207.9 i 55 3*-9 38.9 i5 81.3 8r.3 7S 123.7 123.7 ^ 166.2 166.2 9S 208.6 zoS.6 ! 56 39-6 39-6 16 82.0 ^2:0 7* 124.5 124.5 36 166.9 166.9 96 209.; 209.3 57 4 -3 40-3 17 82.7 82.7;! 77- 125.2 125.2 3 7 167.6 167.6 97 210.0 210.0 58 41.0 41.0 l& 83.4i83.4 j 7"-$ 125.9 125.9 38 168.3 168.3 98 210.7 MO. 7 59 41-7 41.7 19 84.1184.1 i 7{J 126.6 I 126.6 39 169.0 169.0 99 2II.4 211.4 60 42.4 42.4 20 S 4 .9 84-9 ! 80 127.31127.3 43 169.7 169.7 3 212.1 212.. I Dift Dep. Lat. Dift Dep.j Lat. , iDift Dep. j Lat. Dift Dep. Lat. Dift Dep. Lat. for 45 Degrees, TABLR III. Of Logarithmic Sines, Tangents, and Secants, to every Point and Quarter- Point of the Compafs. oo & Sines. Co- fines. Tangents. O. OOOOO 3. 69132 8.99340 9,17125 Co-tang. Secant. 10. ooodo- 10. 00052 10. ocaic 10. 00473 Co-fecant Points. o -1 o i 0|- 0. COOOO 8, 69080 8-99130 9. 16652 !O. OOOOO 9- 99947 9- 99/^P 9. 9.9527 Infinite. 11.30868 ii. 00660 jo. 82875 Infinite. u. 309*1 11.00870 10. 83348 8 7 -} 7 * 7 1 2, ll J 1 I 1 1 1 1 1 . 9. 29024 9-3 8 S57 9.46282 9.52749 9.99157 9. 98679 9. 98088 9-973-84 9.^9866 9. 39878 9.48194 9-55365 10. 70124 10, 60122 10. 51806 10.44635 10.00843 10. 01321 10. 01912 10. 02616 10. 70976 10. 61443 10.53718 10.47251 1 z 1 2 J 2 i M 9.58284 9- 63099 9' 6 7339 9.71105 9. 96562 9. 95616 9- 94543 9-93335 9. 61722 9.67483 9 7279 6 9. 77770 10. 38278 10.32517 Jo. 27204 IO. 2Z23O 10. 17511 10. 12980 10.08583 10. 04271 10,03438 10. 04384 ic.0^457 10. 06665 10.41716 10. 36901 lo. 32661 10. 28895 6 51 5 1 5 1 13% lit ,9 9 9 9 . 74474 .77503 ,80236 . 82708 9.91985 9- 94 8 3 9. 88819 9. 86979 9. 82489 9. 87020 9.91417 9- 95729 o. 08015 10.09517 10. u 181 10. 13021 10. 25526 10. 22497 10. 19/64 10. 17292 }l 4 \. 4 -1 * 9. 84948 Co-fines. 9- 8 494 8 Sines. IO. OOOOO Co-tang. IO. OOOOO 10.15052 Co-feoant 10. 15052' Secant. 4 Tangents. TABLE IV. A Table of Logarithms from I to 10,000. No. i I 4 i 7 8 9 10 Log. No. Log. No. Log. No. ^og. No. Log. o .00000 30103 47712 60206 ' 69897 778i5 84510 90309 95424 I .OOOOO r- 21 22 23 M 25 26 27 28 29 30 1.32222 34242 36173 . 38021 39794 4H97 43*36 - 44716 46240 477-12 4 l 4? 43 44 45 46 47 48 49 5o 1.6127* - 623=5 63347 64345 6532.1 66276 67210 68124 69020 69897 61 62 63 64 65 66 67 68 69 70 1.73533 79239 79934 80618 81291 81954 82607 83251 83885 84510 81 82 83 84 85 86 87 88 89 90 9i 92 93 94 95 96. 97 98 99 IOO I. 90849 91381 91908 92428 92942 93450 9395* 94448 94939 95424 95904 96379 96848 97313 9777 2 98227 98677 99i 2 3 99564 OOOOO i 12 13 H 11 17 I? 19 29 1.04139 07918 "394 14613 17609 20412 *345 *552? 27875 30103 31 32 33 34 35 36 37 38 39 40 1.49136 50515 5x851 S&& ' 54407 55630 56820 5797* . 59106 60206 5r 52 53 54 55 56 P 5"9 60 1.70757 71600 72428 73^39 74 36 74^19 75587 /6343 77085 77815 7 1 7* -73 74 75 76 77 73 79 80 i .85126 85733 86332 86923 87506 88081 88649 89209 89/63 90309 I . TABLE IV. A Table of Logarithms from i to 10,000. N o I 2 3 4 5 6 7 8 9 495 16524 16 5S4 16 5 8 4 16613 16643 16673 16702 47 16732 16761 16791 16820 16850 16879 16909 16938 16967 16997 48 17026 17056 17085 17114 i7'4? I7I73 1720; 17231 17260 .17289, 49 17319 17348 1/377 17406 J 7435 I/4 6 4 17493 17522 7J5j i7-;8oj 150 ... 17609 2.17638 .17667 . 17.696 .17725 17754 .17782 . 17811 .17840 .17869, 5i 17898 17926 *7955 17984 r8o 1 3 18041 18670 18099 18127 18156 5^ 18184 18213 18241 18270 18298 18327 18355 18384 18412 18441 53 18469 18498 18526 18554 i8c* 3 l86ll 18639 1866-7 1*696 18724 54 18752 18780 18808 18837 18865 18893 18921 18949 18977 19005! 55 I933 19061 19089 19117 19145 I9I73 192Of 19229 19257 19285^ 5< 19312 I 934o 19368 19396 19424 I945I *9479 19507 J9535 19562 57 19590 19618 19645 i9 6 73 19700 19728 19756 19783 19811 19838 58 19866 19893 19921 19948 19976 2OOO-? 20030 20058 20085 2OI 12 i 59 20140 20167 20194 20222 20249 20276 20303 20330 20358 20385 TABEK !V. A Table of Logarithms from i to 10,000. N b 1 -i 3 1 4 s 6 7 8 9 160 2.20412 20439 .20466 2.2O493J2.2O520 .20548 20575 .20602 .20619 1.20656 6t 20633 20710 20737 20763 20790 20817 20844 ' 20871 10898 20925 62 20951 20978 21005 2IO32 21059 21085 2IIJ2 2H39 7 21165 21192 63 64 21219 21484 11245 21511 21272 21537 2I29 9 21564 21325 ,21590 21352 21617 21378 21643 21405 21669 21431 21696 214581 2^722] 6s 21748 2177; 21801 2l8l7 21854 21880 2I9O6 21932 21958 66 2.1OII 22037 22063 22O89 22115 22141 22167 22194 22220 22246' 67 22272 22298 22324 22350 22376 22401 22427 22453 22479 22505^ 68 22531 "557 22583 22608 22634 22660 22686 22/12 22737 22763, 69 22789 22814 22840 22866 22891 22917 22943 22968 22994 23019'; 170 2.23045 -.23070 -.23096 2.23I2I 2.23147 .23172' .23198 2.23223 .23249 2.23274' 71 23300 23325 23350 23376J 23401 23426 23452 23477 23502 23528 72 23553 23578 23601 236^9 23654 23679 23704 23729 23754 23779 73 23*5 23830 23855 23880 23905 23930 2 3955 23980 24005 24030 74 2405 s 24080 24105 24130 24155 24180 24204 24229 24254 24279! 7- 24304 24329 24353 243/8 24403 24428 24452 24477 24502 24527! 76 e 455' 24576 24601 24625 246^0 24674 24999 24724 24748 24773; "7 24797 24822 24846 24871 24895 24920 24944 24969 24993 25018'' 78 2504; 25066 25091 25H5 25139 25164 25188 25212 25237 25261 79 2528; 25310 25334 25358 25382 25406 2 =143 * 25455 25479 25503 1 80 2-25327 2- 25551 2.25575 2.25600 2.25624 2.25648 2.25672 2.25696 z. 25720 2.25744 S i *5/08 25792 25516 25840 25*64 25888 25912 25935 25959 25983 82 26007 26OJI 26055 26079 26102 26126 26150 26174 26198 26221 83 2624- 26269 26293 26316 26340 26364 ,26387 26411 26435 26458' 84 264^-2 26505 26529 26555 26576 26600 26623 26647 26670 266941 85 26717 26741 26764 26788 26811 26834 26858 2688l 26905 26928 86 26951 26975 26998 2^021 27045 27068 27091 27II4 27138 27161 87 27184 27207 27231 27254 27277 27300 27323 27346 27370 27393 88 27416 27439 27462 2/485 27508 2753 l 27754 27577 27600 27623) 89 2:646 27669 27692 27715 2773^ 27761 27574 27807 27830 27852 190 2.27875 1.27898 2.27921 2.27944 2.27967 2.27989 2.28.112 2.28C35 -.28058 2.28081 9* 2810; 28126 28149 28171 28194 28217 28240 2S262 28285 28307' 92 28330 28353 28375 28398 28421 28443 28466 28488 285II 28533 93 285156 2*601 28623 28646 28668 28691 28713 28735 28758 94 28780 28803 28825 28847 28870 28892 28914 28937 28959 28981 95 29003 29026 29048 29070 29092 29115 29137 , 29159 29181 -29203 96 2,j2l6 2 9-4 v 29270 29292 29314 29336 49358 29380 2940-3 29425 97 98 29667 29469 2,9688 29491 29710 295*3 29732 29535 29754 29557 29776 295^9 29fl 129601 29S.iO ,29623 29842 29645 29863 99 19885 29907 29929 29951 2997- 29994 30016 30038 30060 30081 200 '-30103 2.3012 a. 30146 2.30168 z. 30190 2.30211 -.30233 2.30255 2.30276 2.30298 . 01 30320 30341 30363 30384 30406 30428 30449 30471 30492 30514 02 30535 355/ 305/8 30600 30621 ,30643 3066; 3068=; 30707 30728 3 30750 3077 30792 30814 30835 30856 30878 30899 3O02O 30942 04 30963 3094 31006 31027 31048 31069 31091 3III2 3II33 3 1 1 54 o; 3i*75 . 3*218 3*239 31260 3128! 31302 3*323 3 T 345 31366 06 31387 3 I 4 C 3 *4 2 9 3*450 31471 3*492 3*534 3*555 31*76 07 3 * ^97 31618 3*639 31660 3168" 31702 3172; 31744 3*765 3*785 08 3 io6 31827 31848 51869 31890 31911 3*952 3*973 3*994 09 3201 f; 3203 32056 32077 3 :.o 9 8 32118 32130 32160 32181 32201 210 2.32222 2.3224. 2.32163 2.32284 2.3-30 2.3232;, 2.32346 3^32366 1.32387 2732408 II 32428 32449 32469 -32490 32510 32552 32572 32593 32613 J2 32634 32654 32675 32695 3271 32736 3275^ 32777 32797 32818 ?3 3283^ 32879 32899 329* 32940 32960 32980 33001 32021 H 334 33062 33082 33*02 53I-" 33143 33*83 33203 33224 j 5 33244 33264 33284 33304 3332 33345 3336 33385 33405 33425 |6 3344 3346 33486 33506 3352 33546 3356 33586 33606 33626 17 3364 3366 33686 33706 3372 33746 3376 337^6 338o6 33826 iS 3386 33885 33905 ' 3 ."$45 339 6 3398 345 34025 1$ 344 3406 3408^ 34104 2412. 34*6 3418 34203 34223 TAHLE IV. A Table of Logan than from i to 10,000. 3544 35*35 3543C 35S1 36003 3619,1 36530 36717 3690"! 3703 37273( 3745 7 o 39 ! 3/822 37144 3732S 375" 37694 37^7 377 . _ 37w_67 _379gj 38148 38256 3H35 50614 3*79* 38970 39146 39322 39498 38846 39023 39 r 99 39375 39550 397*4 39602 3^9 , 39950! 401231 4029 40466 40637! 40807 39749 39967 4014 403 4048 4065 408.^ 4099 4116 4' 33 . 39*40 40019 40192 40364 40535 4070; 408 41044 41212 40088 40261 40432 4060? 40773 40943 40037 40209 4038 40552 40722 40892 4106 41^29 4U97 .4! 647 41814 41970, 42144 423081 4166^ 4 1 S] 4199 41681 41847 42012 4189 42062 422x6 41390 4*553 41716 4*87* 43040 4204; 42210 42374 42537 42700 42862 430*4 43I.S: 4334 435^5 43664 47823 439'-i 4413^' 44*95 4445' 44607 4*341 42504 4266- *530 1.431172.43233, 43297 43457 43616 43775 43933 4409. 44248 4440-} 4456c 433^3 43473 43632 4379 1 43949 44107 44264 44420 45576" 440591 44^77 4437? 44 -; 4432 44483 44638' TABLE IV. A Table of Logarithms from i to 10,000. o O I ^ 3 4 3 6 1 8 9 1280 .44716 44731 2.44747 2.44762 4477* i-44793 2.44809 .44824 2.44840 .44855 ! 81 44871 44886 44902 44917 44932 44948 4496; 44979 44994 45010 81 45025 45040 45056 45071 45086 45102 45117 45*33 45148 451^3 83 45*79 45194 45209 45225 45240 45255 45271 45256 45301 45317 45332 45347 45362 45378 45.393 45408 45423 45439 45454 45469 85 45484 45500 45515 45530 45545 45561 45576 45591 45606 45621 86 45637 45652 45667 45682 456->7 457" 45728 45743 4575 s - 55773 87 4-5788 45^3 45818 45834 45^49 45864 45879 45894 4599 45924 88 45939 45954 45969 45984 46000 46015 46630 46045 46060 46075 89 46090 46105 46120 46135 46150 46165 46180 46195 46210 46225 290 .46240 .46255 2.462702.46285 .46300 2.46315 2.46330 .46345 2.46359 .46374 9 1 46389 46404 46419 46434 46449 46464 464/9 46494 46509 46523 92 46538 46553 46568 46583 46598 46613 46627 46642 46657 46672 93 46687 46702 46716 46731 46746 46761 46776 46790 46805 46820 94 95 46835 46982 46850 46997 46864 47012 46879 47026 46894 47041 46909 47056 46923 47070 4693:5 47085 46953 471*64 46967 47H4 96 47119 47144 47159 47173 47188 47202 47217 47232 47H6 47261 97 47276 47290 4/305 47319 47334 47349 47363 4737? 4739 2 4740/ 98 47422 47436 4745i 47465 47480 47494 47509 47524 4753S 47553 99 475*7 47582 47596 47611 47625 47640 47654 47669 47683 47698 300 .47712 .47727 2.47741 2.47756 .47770 2.47784 1.47799 .47813 2.47828 .47842 OI 47857 47871 47885 47900 47914 47929 47943 4795* 47972 47986 02 48001 48015 48029 48044 48058 48073 48087 48101 48116 48130 3 48144 48.173 48187 48202 48216 48230 48244 48259 48273 04 43487 48302 48316 48330 48344 48359 48373 48387 48401 48416 05 48430 48444 4*458 4 8 473 48487 48515 48530 48544 48558 06 48571 48586 48601 48615 48629 4864.1 48657 48671 48686 48700 07 48714 48718 48742 48756 48770 48785 48799 48813 48827 48841 08 4885.5 48869 48883 48897 48911 4M6 48940 48954 48968 48982) 09 4 99 6 49010 49024 49038 49052 49066 49080 49094 49108 49122 3*0 .49136 .49150 2.49164 2.49178 2.49192 2.49,266 2.49220 .49234 2 49248 2.49262 11 49276 49190 49304 49318 49332 4934^ 49360 49374 49388 49402 12 494 1 5 49429 49443 4945*7 4947J 49485 49499 49513 49527 49541 13 49554 49568 49582 49610 49624 49638 49651 49665 49679 14 49693 49707 49721 49734 49748 4976-2 49776 49790 49803 49817 i 49831 49845 49859 49872 49886 ,49900 499H 49927 49941 49955 16 49969 49982 49996 500 10 50024 50037 50051 50065 50079 50092 17 50101 50110 50133 5014- 50161 50174 50188 ^C2O2 5 215 50229 i 50243 5.6256 50270 50284 50297 53H 5-325 .50338 50352 50365 50379 50393 50406 50420 5043 1 5044- 1:046] 50474 504** 50501 32 2.5051 2. '^052912.50541 2'. 55 56 2.5o;6o"J2.505S3 2.50596 2.50610 2.5062^ 2.50637 2, 5065 50664 50678 5069 50705 50718 5732 50745 50759 50-72 2 5078 50795 50^13 50826 50853 50866 50880 50893 50907 2 5092 50934 50947 5096 50974 50987 51001 5101* 51028 51041 2; 5105 5I06S 51081 5109 :;iioV 51121 5 1 1 3 > 511415 51162 5H75 I 5 iiS 51202 51215; 5122 51242 5i-> 55 51268 51282 51295 5 r 3o^ 2 5133. 51348! 5136 51375 51388 5 H 5 * 51415 51428 51441 j 5*45 5H& ( 51481 5149 51508 51521 51534 51548 5156 51574 2 5160: 51614 5162 51640 51654 5166- 51680 5^93 51706 2 5172 5*73: i 51/461 5 r 75 51772 5i7( 5J79J 51812 5 l825 51838 33 2.5185 5198 i. 51865 2.5187812,51^91 51996 ' 52609 "52022 2.51904 5203 = 2-519 1 - 5204? 5206 2.5194^ 5207. 2.5l9r 52088 2.51970 5*101 2 5211 5212 i 52140 52153 52166 521/1 5219 5220 . 52218 52231 2 5224 5225 1 5227^ >! 522^ L 5229- 523^ 5232 523 >f 52349 52362 3 5238 \ 5240 t 524^-1 5H2; 5244: 5245 5246^ 52479 5249?. 3 5250 .5*51 7- 5 2 53< > 5254, 5*55* 52 ^6( 5 2 5 V ' 5259 5-6o 52621 ^ 5263 5264 7 5266, > 5267; 5168^ 5269 527' 52724 52737 5*750 3 5276 5277 52?8< ) 52^02 5281. 5.282- 51840 528; . 3 5289 5290 5 5291 7 $293c > . 5294. 5295< 5296 52982 5:99 53007 i 3 ' 2 5302 5303 'IIIMMII.II J 5304 3 5305* 5307 J 1 mi MI"" 1 5303. "iiti'ii ii 'ii a nil 5309 - si I Ljfmimmnjna 53" 53*35 -*~ TABLE IV. ^" ' ' '-' -' -' . , ,. 1 . A Table of Logarithms from j to 10.000. | .' ... ! N o 1 2 3 4 $ 6 - 7 8 _j?_ 1340 2.53148 2.53101 2.53173 2.53186 *-53i99 2.53212 2.53224 2-53237 2.53250 2.53263 4* 53-75 532SS 53301 533M 53326 53339 53352 53364 53377 5339 42 53403 53415 53428 5344i 53453 53466 53479 5349 1 53504 535 J 7 43 535 2 9 5354 2 53555 53567 5358o 53593 53605 536i8 53631 53643 44 53656 53668 53681 53694 53706 53719 53732 53744 53757 53769 45 53782 53794 53807 53820 53832 53845 53857 53870 53882 53895 46 53908 539^0 53933 53945 53958 53970 53983 53995 54008 54020 47 54033 5445 54058 54070 54083 54095 54108 54120 54133 48 54158 54170 54183 54195 54208 54220 54233 54M5 54258 5-.270 _49 54283 54295 54307 543- 5433 54345 54357 54370 54382 54394 is 50 2.54407 2.54419 2.54432 2 . 54444 2.54456 2 . 54469 2.54481 2.54494 2.54506 2 545 l8 5i 54531 54543 54555 54568 5458o 54593 54605 54617 5463 54642 5* 54 6 54 54667 54679 54691 54704 54716 54728 54741 54753 54765 53 54777 54790 54802 54814 54827 54839 54851 54864 ' 54876 54888 54 54900 549 * 3 54925 54937 54949 54962 54974 55986 5,4998 55011 55 55023 55035 55047 55060 55071 55084 55096 55108 55121 55133 56 55M5 55157 55169 55182 55194 55206 55^8 55230 55242 55255 57 55i 6 / 55^7y 55 2 9i 55303 553^5 55328 5534 55352 55364 553/6 58 55383 55400 55413 554 2 5 55437 55449 55461 55473 55485 55497 59 55509 _55522 55534 55546 55558 3557Q 55582 55594 55606 55618 360 2.55630 2.'55 6 42 2.55654 2.55666 2.55678 2.5569: 2'55703 1-55715 2.5=;7i7 2.55739 61 55751 5576? 55775 5573? 55799 558n 55823 55835 55847 55859 62 5#7? 5588s 55895 55907 559'9 55931 55943 55955 559 6 7 5=5979 65 5599i 56003 56or 5 56027 5603* 56050 56062 56074 56086 56098 64 56110 56122 56134 56146 56158 56170 56182 56194 56205 s62i 7 65 56229 56241 56253 56265 56277 56280 56301 56312 56324 56336 66 56348 56360 56372 56384 5 6 396 56407 56419 56431 5 6 443 56*455 6? 56467 56478 56490 56502 56$H 56526 56538 56549 56561 56573 68 56585 56597 56608 56620 56632 56644 56656 56667 56679 56691 69 5 6 703 56714 56726 56738 ^6750 56761 56773 56785 56797 56808 37^ t. 56820 2.56832 2.5684412 5655512.56867 2-56879 2.56891 2.56902 2.56914 2.56926 7* 56937 56949 56961 56972 56984 56996 57008 57019 57031 '57043 7* 57054 57066 57078 57089 57101 57U3 ' 57^4 57136 57148 57159 571?' 57i83 57194 57206 573 57229 5/14 1 57252 57264 57276 74 57*37 5 7 *99 573io 573" 57334 57345 57357 5,368 57380 57392 75 5743 574 * 5 57426 57438 57449 57461 57473 57484 57496 57507- 76 57519 57530 57542 57553 57565 57576 57588 57600 57611 5/6i3 77 57634 5?6}6 57657 5766 9 57680 57692 57703 57/15 57726 5/738 r 5/749 5776i - 57772 57784, 57795 57807 57?i8 5-830 57841 57852 79 __5^864 57875 57887 5/898 579^0 L/ll 1 _!I93J 57944 579-5 57967 380 z.57978 2.5799 2.58001 2.580:3 2.5^024 2.5803; 2. ^-047 z. 58058 2.58070 2.58081 81 58092 58104 58115 58127 58138 58149 58161 58172 58184 58195 82 58206 58218 58229 58240 58252 58263 58274 58286 58297 58309 8'3 58320 58331 5^343 58354 58365 58377 58388 58399 58410 58422 84 58433 5*444 58456 58467 58478 58490 58501 58512 585M 58535 85 58546 58S5; 58569 58580 5859J 58602 58614 58625 58636 5864.7! 86 58659 58670 58681 58692 58704 58715 58726 58737 5*749 58760' 87 58771 58782 5 8 794 58805 58'$ 1 6 58827 58838 ^8850 58861 58872 88 58883 58894 58906 58917 58928 58939 58950 58961 58973 58984 89 58995 ^9006 59Q r 7 59028 59040 590 ci 59062 59073 59084 59095 390 2.59106 2 . 59118 2.59129 2. 59 '40 2.^9151 2.59102 *-59'73 2.59184 2.59195 2.592071 9 1 59118 59229 59240 59251 59262 59273 59284 59295 59306 593i8 92 59329 59340 59351 59362 59373 59384 59395 59406 594 T 7 ' 594*8 93 59439 59450 59461 59472 59483 59494 59506 59517 59^28 59539) 94 5955<> 59561 59572 59583 59594 50605 59616 59 6 27 59638 59649 95 59660 59671 59682 59693 59704 59715 59716 59737 59748 59759 96 59770 59780 59791 59802 59813 59824 59835 59846 59857 59868 97 59879 59890 59901 599re 59923 59934 5994 : 59956 59966 59977 98 599 s8 59999 60010 60021 60032 60043 60054 60065 60076 60086 99 60097 6oio3 60119 60130 60141 60152 60161 60173 60184 60195 TAILS IV. A Table of Logarithms from i to lo.coo. N 1 3 J 4 $ 6 7 8 9 400|2.60206 2.60217 :,6022- 2 .60239 ,2.60249 *.6c26oJ2. 60171 2.60282 3.6*29; 2.60304 OI 60314 6032; 60331- 60347 60356 60,369 60379 60390 60401 60412 02 1 604?,3 6043? 60444 60455 60466 60477 60487 60498 6050*, 60520 3 60531 60541 60552 60563 60^74 60584 6059; 60606 60617 60627 04 6063? 60649 60660 60670 60681 60692] 60705 60713 60/24 60735 60746 60756 6076; 60778 60788 60799 60^ 10 60821 60831 60842 c6 60853 6086; 60874 .60885 608 y; 60906 60917 60927 609 3 > 60949), o~ 60959 60970 60981 6099! 61002 61013 61023 61034 6104-, 61055: v 61066 61077 61087 61098 61109 61119 61130 61140 '61x51 61162, 09 61172 61183 61194 6l2O^ 6121; 6i225j| 612.36 61247 61257 61268' 4 ic 2.6127-- 1.61289 2.61300 2.6i310 2.6132, 2. 6133* 2. 61342 2.61352 .61363 2.61774! n 61384 61395 6140% 61416 61426 61437 6144$ 61458 61469 61479 I 2 61490 6 1 500 61511 6152? 61532 61540] 61^53 61563 61574 61584, - I - 6159; 61606 61616 61627 61637 6 1 64l| 61658 6166*9 61679 61690 H 61700 6171 1 61721 61731 61742 6i75|l 61763 61773 61784 61-794! 61805 61*15 61826 6r836 61847 6i3?5|K 61868 6i87>> 61888 61899 16 61909 61920 61930 61941 61951 6i96 61972 61982 61993 62003' 17 62014 62^24 62034 62045 62055 62o6fflB 62076 62086 62097 62107 18 62118 62128 62138 62149 62159 62 176^.62180 62190 62201 62211 19 6222.1 62232 62242 62252 62263 62273 "62284 62294 62304 62315' 420 2.6232^ 2.623352.62346 2.62356 2.62366 2.62377 2.62387 2.62397 2.6240^ 2. 624?$ 21 614*? 624;*} 62449 624501 62469 62480 62490 61500 62;u 6257.1! 22 62542 62552 62562 62572 62^83 62503 626*3 62615 62624, 1 ' 62634 62644 62655 62665 6267s 62685 62696 62706 62716 02726 24 62737 62/47 6275-7 62767 62778 62788, 6279? 6z8ob 62818 6282 9) 2$ 62839 62849 62859 62870 62880 62890 65900 62910 61921 6293i; 26 62941 61951 62961 62972 62982 62992! 63002 63012 63022 63033 27 63043 63^53 63063 63073 63-083 63094 63104 63114. 63124 63I3-1 iS 63H4 63155 6316; 63 17 ; 63185 6 3 r 95 63205 6321^ 63225 63236; 29 63H6 63*56 63266 63276 63286 63296 63306 63317 633*7 43 2-6334- 1.633^7 2.63367 ^ 63377 2.63357 2.6339712.63407 -.63417 2.63,428 2.6343? 6344 s 6347? 63488) 6349! 635081 63518 635*8 63538 3- 1 6354S 63*;;;* 635*S 63579 63589! 6359., 65609 63619 63629 6 3 6 3v, 33 63649 6 ; o ^ 9 63669 6367$ 63680 63699 63709 63719 63729 63739] 34 63749 63859 63:69 63869 03779 13*79 63789 63799 638>9l 6389., 63^09 63909 63819 63919 63829 63929 63959 *( 6 3949 63959 63969 63979 63988 63998 64008 6401^. 64028 6403* 37 . 64048 6405* 640" ft 64088 64098 64108 641 1 ^ 64128 3 ? 64147 641 57 64167 6417- 64187 64197 64207 64217 64227 64237 jt, 64246 64*56 64266 6428'. 64296 64306 64316 64320 6 4335 44~ 2.6434; 2.643552.64365 *T6437; *S5 i - (J 4395 2.644042.64414 2 . 64424 1.64434! 1 1 64444 6*454 64464 - 473 "44\5 6449 ^ 64503 64513 64523 64532 4 1 64552 6456- 64-572 6459 64601 64611 64621 6463 r ' 64640 64659 64660 040% 6465c 6468 64699 64709 647IV 6472. ! 44 64-58 6474 6475! 64~6S 64:77 647?* H797 64507 64X10 64>2- 64836 64X46 64856 648 6s 64*7; 648 S 64895 64904 64914 649 2 H ! 4" 64933 64943 64963 64972 649'^ 64992 65002 65011 6502 ! 4" 65031 65040 65050 65060 65070 65079 6 sO&9 65099 6510^ 6511^ 65H7 65X57 65167 65176 65186 65191 6;20~ 6521 - 40 65225 65234 65244 65254 65*63 65273 65283 65292 6530; 6-312 45 2.65321 .6; 3 3i!i. 65341 2.65350 2.65360 2.65369 2.65379 ^ 653^9 2.653*;- 2 . 6^.408 { 6>4tS 654^7 6^437 (5544 654-6 6546 65475 65485 6 5 .j 9 c 65504 | 52 65514 6^523 65533 65 ; 4 ; 6?5 i ;2 65^6 65571 6l58i 65^9 > 656ot 53 65610 6;6 rg 6 ^629 65639 65648 6565 65667 05677 65686 65696 ! c 4 65706 657.15 65715 65734 65744 6575 65763 65772 6^782 6579^1 \ C.J 6 580 1 65811 65820 65839 6584 65858 65868 65^7, 65887 ^f 6 5 S 9 6 65906 65916 6592; 65935 6594 65954 65963 6597; 659*2 1 5' \ 65991 66001 6601 T 66020 66030 6(503 66049 66058 66068 66.; 7 J [ 6 $087 66096 66106 66115 66124 6613 66143 66153 66162 661/2} Cn! 6firV T 66191 66;ooj 66210 66219 6622 66238 66247 66257 66266) TABLS IV. A 1 able of Logarithms from i to 10,000. N 1 a 3 4 5 i 7 8 9 460 z 66276 2.66285 2.66295 2.66304 2.6631-! 2.6632.? 2. 66332'?.. 603.43 z.66;}S 2 .66361 6l 66370 66380 66389 66398 6640^: 66417 66427 6643* 6644 66455 62 66464 66474 66483 66492 66502 66511 6653^ 665.3 66549 63 66558 66567 66577 665^6 66 ^9< 66605 66614 . 666su 666^ 66642 64 66652 66661 66671 66680 6668^ 6669 6670* 6671 6672 66736 65 66745 66756 66764 66773 6678- 6679 66801 668 1 6682( 66829 66 66839 66848 66857 66b6~ 668/( 6688- 6689^ . 6690^ 6691 66922 67 66932 66941 66950 669^0 66961 6697 6698' 6699 6700* 6 7 OI5 68 67025 67034 67043 6705* 6706: 6707 67c8c > 6708 6709 6 7 1O8 -12 67117 67127 67136 67145 67 1 5/ 67164 ~ 7 111 6718 6719 672.01, 470 2.67210 2.67219 2.67228 2.67237 2.6724-; 2.6725 2.6726. 1X7.7^ rr6~72& IT67293 1 71 67302 . 673*1 67321 6/330 67330 6734 67357 6736 6737< 67385 7* 6 7394 67403 6741] '67422 6743^ 67440 6/44S 6745s 6746* 6/477| 73 67486 67495 ^7504 67514 6752" 6753 67541 6755 C 6 75 6c 6 7 > '*, 9 74 6757^ 6.7587 67596 676,05 6761^ 67624 67633 67^42 6765 67660 75 67769 67679 67088 6/697 67701 6771.5 677-^ 6/73: 6774: 6775*! 76 67661 677/0 67779 677815 67797 67806 67815 67^2? 6783^ 67843; 77 67852 67861 67870 67879 67888 6789- 67906 67911 6792 67934; 78 67943 67952 67961 67970 67979 67988 67997 .6Soc6 6801^ 6802^ _Z2 68034 68043 68052 68061 68070 68079 68097 6Sic( 68115;. 480 1.68124 176817] 2.68142 2.68151 7768l6c 2.68169 7768778 2768117 7.6819! i. 68205! fel 68215 68224 68233 68242 68*51 68460 68269 6^27^ 6828- 68296; 82 68305 68314 68323 68332 68341 68350 68359 6?36 68377 68^86! 83 68404 68413 68422 68431 68440 68449 68 4 sS 68467 68476 84 6845^ 68494 68502 68511 68 sac 68529 68538 68547 68556 68565 85 68574 68583 68592 6S6oi 68610 68619 68623 68637 68646 68655' 86 68664 68673 68681 68690 68699 68708 6S 7 i 7 68726 68735 6*744 87 68753 68762 68771 68750 68789 68797 68806 68815 68824 f 68842 68851 68860 68869 68878 688S6 68895 68004 68913 68922 68931 60940 68949 689^8 68966 68975 68984. 68993 69002 69011^ 490 2,69020 2 . 69028 *" f-937 ; . 69046 2.69055 2.69064 27^c73 7^9c72J777 9o7c 1.69099' ; 91 69108 69117 69126 69135 69152 69161 69170 69179 69188 i 9* 69197 6Q2Chj 69214 69223 69232 69241 69249! 69258 69267 69176 93 69285 69294 69304 69311 69:120 69329 69338 69346 69355 693H' 1 94 69373 69381 69390 69399 69408 69417 694-5! 6 9434 69443 6^52 ! 95 69461 69469 69478 69487 69496 69504 69513! 69522 6539>. i 96 69548 69557 69566 69574 69583 69592 69601 6960^ 69618 69627 j 97 69636 69644 69 6 53 6966: 69671 69679 6,688 69697 69705 69714 ! 9 69723 69732 69/40 69749 6975* x 69767 60775 69784 69793 69891 1 99 69810 69819 69836 69845 69254 6c,-86z 69^71 698^0 69888. [500 2.69^97 2 .69906 2.65914 2.69923 2.69032 .t. 69940 .69949 "769758 .69966 r. 6 9975 i or 69984 69992 70001 70010 70018 70027 70036 70044 70055 70062 j 02 70070 70-79 7008 'i 70096 70105 70114 70122 70131 70140 70I4&J ! 3 70157 70165 70174 70181 70191 70200 70209 702.17 70226 70234^ ! 04 70243 70252 70260 70269 76278 70286 70295 7^ 303 70312 7>_32i' i 5 70329 70338 7<>34 C 70355 70364 70372 70381 70389 7039? 7C4C6 1 I 06 70415 70424 70432 70441 70449 70458 70467 70475 70484 70492 i 07 70501 70509 70518 70526 / S 3 5 7QS44 70*52 70561 70561. 70^78; ! 08 70586 70595 70603 70612 70621 70629 7063* 70646 70655 70663 09 _ 70672 70680 706*9 70697 70706 70714 70723 70731 70740 70749 510 ^"0757 2770766 2.70774 -70783 r77C7$i i 7c8eo .70^08 1.70817 7770825 1.70834 ii 70842 708 5 1 708 >o 7 o86b 70876 7088; 70893 70902 70910 70919 12 70927 70935 70944 70952 70961 70569 70978 70986 70995 71003 13 71OI 2 71020 71029 71037 71046 71054 71063 7*071 71079 71088 14 71096 71105 run 711*2 71 130 7 1 1 39 71147 71*55 71164 71172 I 7Il8l 71189 71198 71206 71214 71223 71231 71240 7124* 71257 16 71265 7*273 71282 71290 71299 71307 7I3I5 71374 71332 7134* ;! 7*349 71357 71366 7*374 71383 71391 71399 71408 71416 7142": I 7*433 71441 7*450 71458 71466 7 '47 5 71492 7 '5oc 71508 19] 715*7 715*5 7*533 7*54^ 71550 71559 7*567 71575 71584 71591 TABXP, IV. A Table of Logarithms from i to 10,000. IN* O I Z 3 4 5 6 7 8 9 i sic i.7itoo -.71609 2.71617 2.71625 71634 .71642 2*71650 2.71659 .71667 .71675 1 21 71684 71692 71700 71709 7 r 7i7 717*5 71734 7174* 71750 71759 22 71767 7 : ?75 7*7*4 71792 71800 71809 71^17 71825 71834 71842 *3 7I S 5 o ?i*58 7l86 7 71875 7*883 71892 71900 71908 71917 71925 M 71933 71941 71950 7195^ 71966 71975 71983 71991 71999 72008 25 72016 72024 72032 72041 72049 72057 72066 72074 72082 72090 I 26 71099 72107 7ZII5 72123 72132 72140 72148 72156 72165 7*173 I 17 72181 72189 72I 9 8 72206 72214 72222 7*230 7*239 7*247 72255 ! ** 72263 72272 72280 72288 72296 7*304 72313 72341 7*3*9 7*337 29 7*14^ 72354 72362 72370 7*378 72387 7*395 7*403 72411 72419! .530 *.7M* S 2.72436 z.7^444 2.72452 .72460 2.72469 2.72477 2,7248; 2.72493 ".72501! 31 72509 7*5iS 72526 72534 72542 72550 72558 7*567 7*575 7*5 S 3 3 - 7^59' 7*599 72607 72616 72614 72632 72640 72648 72656 72665: 53 72673 72681 72689 72697 7*705 72713 72722 7*730 72738 7*746' 34 7-754 72762 7277- 727-9 72787 72795 72803 72811 72815 72827! TS 7*835 7*S43 72852 72860 72868 7*876 72884 72892 72900 72908' 36 72916 729 2 5 72933 72941 72949 7*957 72965 7297? 72981 72989 3; 72997 73006 730H 73022 73030 73038 73046 73054 73062 73070' 35 7307 730S6 73094 73102 73111 731*9 73127 73135 73H3 73'S 1 ' 39 7315') 73167 73175 73183 73*9' 73199 73*07 73215 73*23 7323IJ >S4C *-73*39 '-73*4: 2-73255 2.73263 -73*72 2. 7 3*8c 2.73288 *. 73*96 2 -73304 *-733*2| 4 1 733-c 7332* 73336 73344 73352 73360 73368 73376 73384 7339 2 i 4 2 734oo 73408 734i6 734*4 73432 7344 73448 73456 73464 73472| i 43 r 7348c 734** 73496 73504 735^2 735*o 735*8 73536 73544 73J5* 44 7356o 73 >6S 73576 73584 73592 73600 73608 73616 73624 73632; 45 73H 73648 73656 73664 73672 73679 73687 73695 73703 737UJ 46 75719 73727 73735 73743 73751 73759 73767 73775 73783 7379*1 47 73799 73807 73815 73823 ?3830 73838 73H 6 73854 73862 73870! 48 7387* 738S(< 73894 73902 739io 739 lS 739*6 73933 73941 73949 49 75957 739 6 5 73973 7398i 73989 7*997 74005 74013 74020 74028' 2.74036 1.74044 1.74052 2 . 74060 -.7406* 2.74076 2.74084 2.74092 2 74099 2.741071 74" 5 74'2? 74131 74139 74'47 74155 74162 74 ! 70 74178 74186) 74*94 74202 74210 74218 74225 74^33 74241 74249 74*57 74*65 j 74273 74280 74288 74296 74304 74312 743*c 743*7 74335 743431 54 7435J 743-^9 74367 74374 74382 7439" 74398 744 6 744 H 74421 55 744*9 74437 7444 > 7445-3 744 5) 74468 744^ 74484 74492 745001 745^7 7-f5 J 5 745*3 74>3' 74559 74547 74554 74562 74570 < 74578 74586 74 -"93 74601 74609 746 ' 7 74624 7463* 7464- 74648 74656 - 74663 74-671 7467V 74687 74695 74702 74-10 747>8 74726 74733i j S 7474' 74740 74757 74;64 747- 7478o 747*8 74796 74803 74811 . 40 I q :.74^> 2.74^34 1-74*42 2-74^5 2-74^ 2. 74*6 s 2.74873 2.74881 2.74889 74896 7494 74912 74920 T4927 74935 74943 7495 74958 74966 62 74974 749^' 74989 74997 7500s 75012 75020 75026 75035 75043 i 6^ 755 ' 75059 75066 7574 75081 75089 7597 75 ioc 75i'3 75120 i H 75:128 75136 75 I 4 : ! 7555J 75*59 75166 75^74 75182 75189 75 r 97 , ft 7; 20; 752*3 75220 75 2ZS' 75*36 75*43 75251 75259 75266 75274 t 66 7 S - "> 2 75289 7^297 75305 75312 75320 75328 75335 75343 7535 1 j-6v 7535* 753<>6 75374 75581 753% 75397 T544 75412 75420 754 a 7 ; 6^ 75435 75442 75450 7545- 75465 75473 7548i 75488 75496 75504 ; ^ 7 5 5 l J 735J9 75526 755^. 7 5 "42 75549 75557 75565 75572 755 So js;o 2.7<57 i.75595 2.7560; 2:75610 2.75618" 2.7562C 2.75633 2.75641 2.75648 2.75656 75'66-i 75^7' 756/9 75686 75694 75702 75709 75717 757*' 75732 7* 7574^ 75747 75755 7^762 75770 757^8 75785 75793 75800 75808 73 75815 75$a'3 7583' 75?38 7<5S 4 6 75S 5 : 75861 75868 7 5 8 7 C 75884 74 75891 75 W 759* 759 f 4 75921 75929 75937 '75944 75952 75959 7< 7S9 6 7 75974 7 '9^2 75989 75097 7600- 76012 76.020 76027 76035 7 f 76042 760^0 760,7 76065 76072 76080 76087 7609 76i_ 761 ro 77 76118 76125 76i33 76140 76148 7615" 76163 7 6r 7 c 76178 76185 76193 76100 '7620? 76215 76223 76230 76238 76*4 7625 76260 i 7S 76268 76275 76283 76290 7629"- 7630; 763*- 7632 7632 76335 IV. A Table of Logarithms from i to 10,000. N I 2 3 4 5 6 7 8 9 580 81 82 83 8 4 8 86* ll 2.76343 76418 76492 76567 76641 76716 76790 76864 76938 .76350 76425 76500 76574 76649 76723 76797 76871 76945 2.76358 76433 76507 76582 76656 76730 76805 76879 76953 2.76365 76440 76515 76589 76664 76738 76812 76886 76960 .76373 76448 76522 76597 76671 76819 76893 76967 2.76380 76455 76530 76604 76678 767.53 76827 76901 76975 2.76388 76462 76537 76612 76686 76760 76834 76908 76982 2.76395 76470 76545' 76619' 76693; 76768! 76842 76916 76989 2-76403 76477 76552 76626 76701 7-6775 76849 76923 76997 2. 76410 764^ ' 76559]; 76/08 76722 76856 76930 77004 89 77012 7701-9 77026 77034 77041 77048 77056 77063! 77070 77078 590 .77085 .77093 2.77100 2.77107 2.77115 2.77122 2.77129 2-77137 2.77144 9* 77159 77166 77173 77181 77188 7/195 772C3 77210 77217 7/22; 92 77232 77240 7724; 77254 77262 77269 77276 77*83 77291 7/298 93 77305 77313 77320 7/327 77335 77342 77349 77357 77364 7737 1 94 77379 77386 77393 77401 77408 774 I .-> 77422 77430 77437 77444 95 77452 77459 77466 77474 774^1 774^ 77495 7750; 77510 77517 96 7752 ^ 77532 77539 77546 77554 775 61 77583 77590 97 7^7597 77605 77619 77627 77634 77641 77648 776,6 77663 98 77670 77677 77685 77692 77699 77700 777H 77728 71735! 99 77743 77750 77757 77764 77772 77779 77786 77793 7/8oi 77808 600 -.77815 2.77822 2.7783- 2-77837 -.77844 2.77851 2.77859 2.77866 2.77873 2.77880 01 77887 77895 77902 77909 77916 77924 77931 7793* 77945 77952 02 77960 77967 77974 77981 77988 77996 78003 78010 78017 78025 03 78032 78039 78046 78053 78061 78o6> 78075 78082 78097 04 78104 78111 78118 78125 78132 78140 78147 78154 78161 78168 05 06 07 781/6 78247 78319 78183 782 H 78326 78190 78262 78333 78197 7^269 78204 78276 7^347 78183 78355 78219 78270 78362 78226 78297 73233 7^305 78240 70312 78383 08 09 78462 78398 78469 7840^ 78476 78412 78483 78419 78490 78426 78497 7*433 78504 785^2 7B447 78^9 78455 78526 610 2.78533 2 '.78 v*0 2.78547 2.78554 2. 7 S 5 6l 2.7X569 2.705-0 2.7858- 2.7*590 2 785^7 ri 12 78604 78675 786II 78618 78689 78625 78696 78633 78704 78040 78711 78647 78718 7?6 5 4 78725 78661 78732 78668 78739 13 78746 78753 78760 7876" 78.774 78781 78789 78796 78STO 4 IS 16 78817 78888 78958 78824 7889^ 78965 78831 78902 78972 78838 78909 77979 78845 7^916 78986 78852 78923 78993 78859 78930 79000 78866 78937 79007 78873 78944 78880 79021 17 79029 79036 79043 79050 79057 79064 79071 7-9078 79085 790t)2 18 79099 79106 79 1 T 3 79120 7912- 79 J 34 79H* 79148 791 -: 79162 19 79169 79176 79183 79190 79 J 97 79204 79211 79218 79225 79232 620 2.79239 2.79246 2.79253 2.79260 2.79167 2.79274 2.792-1 2.79aS> 2.. 79^9: 2.79302 1 21 79309 793*6 79323 79330 79337 79344 7 9 5 5 J 7935? 7936^ 22 79379 79386 79393 79400 79407 7<;4 I 4 794** 79435 7<;44- 1 2 3 7944< 79456 79463 79470 79477 79484 79491 79-19* 79505 79518 79525 7953- 79539 79546 79553 79 ;6o "9^6- 25 79588 79657 79595 7966^ 79602 79671 79609 796/8 796 if 79683 79623 79692 79630 79699 79f!7 79706 7964, 797 ' 5 71720 27 79/27 79734 7974* 79/48 79754 79761 79768 7977 s ; 79782 -0789 2^ 7979^ 79803 79810 79817 79^ 79831 79837 79^ 79 s 5 1 " 9 S;8 29 79865 79872 ^798/9 79^86 79803 7,9900 79906 799 'C 6 3 c 3 T -79934 80003 2.79941 80010 2.79948 80017 2.79955 80024 2.7996- 80030 2.79969 800:57 8004^ 2. 7.8o'>TS 2. 806?. 5 2.80632 2.80638 2.^004 z.Sc&?2. 2.8065 2.8066 2.80671 2.80679 41 4.2 80563 80760 . 80699 80767 80706 80774 807'! 80 ;8 80720 80737 8072 So 79 8073: 8c8oj 8080? 80747 80814 43 44 45 40 4- 8082 J 80885 80956 81023 3 ic M fv) r, 1 - VO -O 1 - OO C- OOOOOODOOCCWC/OOOOOOO VD 2.83251 83.315 8337S 83442 83506 -83569 83632 83696 83759 83822 2.^3257 83321 83385 83575 83639 83702 8376,' 83*28 2.83264 83327 339' 83455 835*8 83582 85645 8570.8 S3 3 & 2.83470 83334 8339* 83461 83588 83651 8371; 8377* 3841 2.83276 83340 83404 ,83467 83531 83594 83658 83721 83784 83847 ...83283 83347 83410 83474 83537 83664 83727 83790 8.3853 2.83289 8.3353 83417 83480 S 3544 83607 83670 83734 83797 8386^ .83296 ?3359 83423 834^7 83550 83613 83677 83740 83803 83866 2.83302 83366 83429 8.349: 83620 83^3 83746 83809 83872 2.83308!! 83372 1 83436 1 83499 I 83563 J 83626 1 83689 1 83753 1 83816 1 83879 1 6 9 c 9' r- ' 95 l> 8394* 84011 ' 407? 84136 8419* 84 '.6 1 2/83877 84017 84080 84142 84205 84267 z. 83*97 8396. 8402; 84086 84148 8421 ! 2.^3904 83967 84029 8409 2 j 841^ 84217 ' 4280} 2.83910 83973 84036 8 4 o 9 S 84161 84223 84286 .83916 83979 84042 84105 84167 842.30 84292 1.83923 83^8; 84048 8411 ) 84173 84236 84298 .83929 83992 84055 84117 8 4 i?o 84242 84305 1^3935 83998 84061 84123 84186 84248 84311 84004:! 84067 ! 84130 1 84192! 84255 I 84317 1 9* 99 84386 ^4448 8439* 84454 84356 84460J 5>4404 8434* 8 4354 84410! 84417 844? 3 j 84479 8442' 84485 8436; 84429 84491 8 4373 84435 84497 84442 I 84504! -Jl TABLE IV. A Table of Logarithms from 1 to io,coo. N o I 2 3 4 $ 6 7 8 9 700 2. 84510 2.8451 2.8452 2.8452 2.8453 2.8454 $8454 2.8455 2.M-55 2.84566 01 84572 845? 8458 8459 8459 8460 8460 8461 8462 84628 02 84634 8464 8464 8465 846; 8466 8467 8467 8468 84689 03 84696 8470 8470 8471 8472 8472 8473 8473 8474 84751 c -1 84757 8476 8477 8477 8478 8478 8479 8480 8480 84813 84810 8482 8483 8483 8484 8485 8485 8486 8486 84874 06 8488c 8488 8489 8489 8490 8491 84^1 -492 8493 4 93 6 07 84942 8494 8495 8496 8496 8497 8497 8498 8499 84997 eS 85003 8500 8501 8*502 8502 85034 S 5 o 4 8 50} 8505 85058 09 85065 8507 8507 8508 8508 8509 8510 8510 85114 85120 710 2.85126 2.8513 2.8513 2.8514 2.8515 2.8515 2.8516 2.8516 2.8517 2.85181 u 85187 8519 8519 8 >20 8521 8521 85224 85230 8523 85242 12 85248 85251 526 8526 85272 8527 8528 8529 8529 85303 1 2 85309 853i 8532 8532 8533 8533 8534 8535 8535S 85364 '4 85370 8537 853* 8538 85394 8=1400 8540 8541 85418 8-425 i ^ 85431 8543 8544 8544 8545 8546 8546 8547 85479 85485 16 85491 85497 8550 8550 85516 85522 85S28 85534 85540 85546 17 85552 8555 85564 85570 85576 855*2 85588 85594 8^600 85606 18 85612 85618 8562 8563 8563- 85643 8564, 85655 8566 85667 19 85673 85679 8568 8569 85697 85703 85709 8571, 8572 85727 720 2.85733 2.85739 2-8574 2.8575 2.85757 2.85763 2.85769 2-85775 2.b 57 8l 2.85788 21 85794 85800 8 S 80I 85811 85*18 85824 85830 85836 85842 85848 22 85854 85860 8 S 866 85872 85878 85884 85890 85896 8^902 85908 23 85914 85920 85926 85932 85938 85944 85950 85956 85962 85968 2 4 85974 8 59 8c 85986 85992 85998 86004 86010 86016 86022 86028 2 " 86034 86040 86046 86052 86058 86064 86070 86076 86082 86088 26 86094 86100 86106 86112 86118 86124 86130 86136 86141 86147 j^ 86153 86159 86i6s 86171 86177 86t83 86189 86195 86201 86207 23 86213 86219 86225 86231 86237 86243 86249 86255 86261 86267 2 9 86273 86279 86285 86291 86297 86303 86308 86314 86320 86326 730 -.86332 2-^6338 2.86344 2.86350 2.86356 2.86362 .86368 2.86374 .86380 .86386 3 1 86392 86398 86404 86410 86415 86421 86427 86433 86439 86445 32 86451 86457 86463 86469 86475 86481 86487 8649^ 86499 865041 33 86510 86516 86522 86528 86534 86540 86546 86552 86558 86564 34 86<7o 86576 86581 86587 86593 86599 8660; 86611 86617 86623 35 86629 866*5 86641 86646 86652 86658 86664 86670 86676 86682 36 86688 86694 86700 8670=; 86711 86717 86723 86729 86735 86741 37 86747 86753 86759 86764 86770 86776 86782 86788 86794 86800 3* 86806 86812 86817 86823 86829 86835' 86841 86847 868 ,'3 86859 39 86864 86870 86876 86882 86888 86894 86900 86906 86911 86917 740 2.86923 2.8692., .86935 .8694 I 86947 .86953 .a69s8 .8696^ .86970 2.86976 4 1 86982 86988 86994 86999 87005 87011 87017 87023 87029 87035 4 2 87040 87046 87052 87058 87064 87070 87075 87081 87087 87093 43 87099 87105 87111 87116 87122 87(28 87134 87140 87146 87151 44 87157 87163 87169 87175 87181 87186 7192 87198 87204 87210 45 87216 87221 87227 87235 87239 8724; 87251 87256 87262 87268 46 87274 8^280 87286 87.29, 87197 8730; 87309 87315 87320 873^-6 47 87332 87338 87344 87349 87355 87361 87367 87373 87379 87384 4- 49 87390 8744? 8739^ 87454 874* 87460 87408 87466 874*3 87471 87419 87477 87425 8748^ 8743* 87480 87437 _|7495 87442 87500 75 2.87506 2.87512 .87518 .87523 .87529 .87535 .87541 87547 S7>5 2 1.87558 Si 87564 8757C 87576 87581 87587 87593 87599 87604, S)6io 87616 S^ 87622 8762? 87633 87639 87645 87651 87656 87662 876^8 87674 53 87679 87685 87691 87697 87703 87708 877H 87720 87726 87731 54 87737 87;43 87749 87754 87760 87766 8/772 87777 87783 87789 5> 87795 8 7 8oc 87806 87812 87818 87823 87829 87835 8784. 87846 56 87^52 8785* 87864 87869 8787^ 87881 87887 87892 87898 87904 57 87910 8791; 87921 87927 87933 879*8 87944 8795 87*3.5 87961 58 87967 87973 8797? 87984 87990 87996 88001 88007 88013 SSoiS- 59 88024 88030 88036 88041 88047 88055 88058 88064 88070 8$07* K k IV. i A Table oi Logarithms from i to 10,000. N O I 2 3 4 SL 6 J 8 9 ' 700 7ssoi>;- .88003 ,8*09* ..88110 . 881 16 .88121 88127 88133 ', 6 1 88138 8S.44 88150 88156 8 S 1 6 1 88167 8^173 88178 88184 88190 i 62 8819; 88201 88207 88213 88218 88224 88230 88735 88241 88247 1 ^ 8825, 8825-: 88264 88270 8827^; $$281 88287 8*292 88298 88304 88309 8831^ 8^321 88326 88332 88338 88343 85349 88355 88360 ! 65 88372 883-7 88383 8*395 88400 88406 88412 88417 8^.42; 88434 88440 88446 88451 88457 88463 88468 88474 ' 67 884.80 88485 8*491 88497 88502 8850^ 88513 88519 8852^ 88530 68 88536 8854:. 88^47 88553 88559 88 ^64 88570 88576 88581 88587 : 6, 88J93 88598 88604 886ic 88615 88621 88627 88632 88638 88643 770 .88649 .88655 t S;66o 1.88666 .88672 1.88677 .88683 .88689 .88694 .88700 , 71 88705 88711 88717 88722 88728 88734 88739 88745 88750 88756 88762 88767 88773 88779 88784 88790 88795 88801 88807 88812 ' " 4 8 i3)8 88: : 4 88829 88835 88840 88846 888^2 8885^ 88863 88868 8887. g&*3 < 88891 88897 88902 88908 88913 88919 88925 i ?i> 8%i 88936 88941 88947 88953 88950 88964 88969 88975 88981 88986 88992 89003 89009 89014 89020 89025 89031 89037 -- 89042 89048 8 9 53 89059 89064 89070 89076 89081 89087 89092 I "' 8909^ 89104 89*09 8911^ 89120 89126 89131 8 9 , 37 89143 89148 7 y 89154 891 59 89165 89170 89176 89182 89187 89*93 89198 89204 780 gg 20 <; .89215 2.89221 1.89226 .89232 .89^37 -.89243 .89248 .89254 .89260 81 8 9 l6j 89271 89276 89282 89287 89293 89298 89304 89310 89315 82 89321 893:6 89332 89337 SQ343 89348 89354 89360 89365 89371 83 89376 89382 89(387 8939? 89398 89404 89409 89415 89421 89426 *') 894^2 8944.3 89448 89454 89459 89405 89470 8 947 c 89481 3s 89487 89492 89498 89504 89509 89515 89520 89526 8953* 89537 86 89542 89548 89553 89559 89564 89570 89575 89581 89586 89592 87 89^7 89605 89609 89614 89620 89625 89631 89636 89642 89647 | 83 89653 8^658 89664 89669 89675 89680 89686 89691 89697 89702 -9 89708 -^97*3 89719 89724 89730 8973. 89741 89746 8 9752 S 9757 790 .89768 a 8 9 774 13*9779 2.89785 .89790 2.89796 ..8^801 .89807 .89812 91 89Sl8 89823 $9829 89834 89840 8984, 89851 898 ,-C 89862 8986; 02 89873 89878 80883 89889 89894 89900 89905 8991 8991 89922 9" St^i? 89933 89938 89944 89949 8995 89960 8996 8 997 89977 94 8 99 8b 89993 851998 90504 90009 9001 90020 9002 90031 93 9003-> 9004 90048 9005 90059 9006: 90069 9007 9008 90086 96 9009 90097 90IO2 90108 90113 9011 9012, 9012 9013 90140 9" 90146 90157 9016 90168 9017 9017 9018^ 9018 90195 08 90200 90200 90211 9021 90222 9022 9023 9023 9024 90249 i 9 9025 90260 90266 9027 90276 9028 9028 9029 9029 90304 j 500 1 . 9030 a. 90314 2.90320 2.9032 2.9033 2 -903 3 ^ . Oft ^4. 2.9034 2.9035 2.90358 O 0^:6 90361 9374 9038 9038 90390 9039 9040 9040 904:2 I 02 1 9041 90423 90428 9043 904 3 c 90445 9045 9045 9046 90466 ! O 947 90477 90482 9048 9049. 9499 9050 9050 9051 90520 4 9052 90531 90536 9054 9054- 90553 9055 9056 9056 90574 O 90^S 90585 90590 9059 ; 9060 . 90607 9061 9061 9062 90628 o 9063 90639 90644 9065 90655 90660 9066 9067 9067 90682 o 9O68 90695 90696 9070 9070 90714 9072 9072 9073 97 3 k 1 Q074 90747 907^2 9075 0076 9076* 9077 9077 9078 90^89. o 9079 9o3or 90806 9081 90822 9082 9083 9083 90843 Si 2.9084 2.905.5,; 2- 90859(2.9086 2.9087 2.9087 2 . 9088 2.9088 2.9089, 2.90897 I 9090 90907 90913 9091 9092. 90925 9093 9094 909^ 909^0 1 90961 9096^ 9097 997 9098 9098 9099 9099 91004 i: 9ico 9101*, , 9I02C 9102 9103 9103) 9104 9 J0 4 9105 91057 1 A k 9*o6 9106? 9107.; 9107 9108 9io8< 9109 9110 9110 91110 i . 9111 91 121 9112^ 9113 9^3 9114 9114 9115 911-5 91164. i 9116 9II74 QIl8c > 91*8 9119 9119! 9120 9120 9121 91217 - 91 22 9I22& 9 r *3: t) I 2 1 9124 9124 9125 9125 9126 91270 ife QI27 9I28l . 91286 9 I2 9 9129 9130 9*30 913-1 9131 91323 ; ' 9 9132 .9*334 91335 9*34 9*35 - 9135 9136 9137 91376 TABLE IV. A 'I able of Logarithms from i to io,oco. N c o 1 2 3 4 5 6 7 8 9 ;820 .91381 9*3*7 2.91392 2.91397 .91403 .9140* 2.9141; 1.9141? z.9*4M .9*4-V i 21 9 r 434 91440 9'445 9H5 9*4:55 91461 91466 91471 9 X 477. 9148. 22 91487 91492 91498 91503 9I 5 08 91514 91519 9152. 9 i;-2v 9 J 53- I 2-2 91540 9i54? 91551 91556 9I 5 6l 91566 91572 91^7;] q i s > ; 915^ 24 91593 91598 91603 91609 9iM4 91619 91624 916 toj 9163; 9 i cV 2 ; - 91645 91651 91656 91661 91666 97672 91677 91682 9 i tJ ^ 7 9 l6 93i 26 91698 91703 91709 9I7H 9i7^9 91724 91730 9 T 73; 9 f 74 : i 27 91751 91756 91761 91766 917"* 9 1 ??/ 91782 9178; 9 T 79." 91795; 2b 91803 91808 91814 91-1 ^ 91824 91829 9 J -.H 9 iS4c 91*43 918501 I 29 9i85| 91861 9i86< 91871 91870 91882 9188; 9.89. 91807' 9,1903! 8 3 .91908 .91913 2. 91918 .91924 .9192;, 9 J 93^ 2.91939 9 V rH .9.950 ^^955 3 1 91960 91965 91971 91970 91981 9I9S6 91991 9 I ?v.i 92002 92007 32 92012 92018 92,02-, 920:10 92033 92038 9204^ 9*049 yzo5/; 9Z95ol 33; 92065 92070 92075 92080 92085 92091 91390 02 IO1 92'-' 921 i : , 34 92117 92122 92127 92132 92137 9214? 92148 92I5-: 9215-^ 92' 6 3i 35 92169 9217^ 92179 92184 92189 92195 92200 92205 92210 9221 v 36 92221 92226 92231 92236 92241 92247 92252 9 ;i 57 92262 92267 : 37 92273 92278 92283 9228b 92293 92298 92304 92300 92314 92319 3* J 92324 92330 92335 92340 92345 92350 92355 92361 92300 92371- 1 39 92376 923^1 9*337 9239 2 92397 92402 92407 V 2^I2 9-4' ?; 92423; |8 4 o .92428 .92433 .92438 92443 .9244^, 2.9245.; 2. yZ454 .9246^ .924.69 92474: i 41 92480 92485 92490 92495 92500 92505 92511 92516 92511 92526 I 4 2 92531 92536 92542 92547 92552 92557 92562 92567 9"o72 9*57*, i 43 92583 92588 9 2 593 92598 92603 9260^ 92614 92619 92624 92629 | 44 92634 92639 92645 92650 92655 92660 92665 92&/C 92675 92.681' 45 92686 92691 92696 92701 92706 92711 92716 92722 92727 92732; 46 92737 92742 92747 9-752 9275* 92763 92768 9*773 927-3 927^3' 47 92788 9 2 793 92799 92804 92809 92814 9244 934o: 860 2.93450 2 -'9345 ; 2.93460 a.93465 2.93470 2.9347;; 2.93480 K. 9 34 s 5 '-. 9 34-7- "934y5j 61 935oo 93505 9*510 93515 93520 935Z6 935?' 9353' 9354 ! 62 9355 1 93556 9356i 93566 9357' 93576 91 S^ 93'5c 935v^>: 6'-} 93601 93606 93611 93616 9 3 6 ? - 1 93626 936X1 y3"4' 64 93651 .93^6 93661 93666 93671 93676 9368- 93687 9?6o. 6; 93702 93707 93712 93717 93722 93/27 9373- 91737 9 5747 66 93752 93757 93762 9376/ 93772 93777 9379^ 93797 67 93802 93807 93812 93^7 93822 9382; 93' ; - - 0^8,2 447 62 9*852 93857 93862 9386- 9V872 93^77 93882 93892 93%.7 69 93902 93907 939 '^ 9391- 93922 939 2 7 93932 93942 93947. 870 2.93952 2.9395- 2.93962 2.9396- 2.93972 2.93977 2.93982 2.9398- 2-9399- 2- y.? 997 71 94002 94007 94012 9401- 94022 94027 9P3 94037 94042 94047 7* 94052 94057 94062 9406" 94072 940/7 940 '> 9408 6 9409 9.4^ 7] 9410 94:06 9411 9411 9412 c>4i?.6 94 3 9413^ 94 14 94146 74 94i5 94156 9416 94166 94 T 7 94176 94'^ 94186 9419 , 9,11 ,;' 7. 9420 94206 9421 94216 9422 94226 9423 942^ 9474 94245 "6 94250 9425 94260 9426 9427- 9427. 9428 94285 94 2< r 94295 7 94300 9430 943 ic 943i 94320 9432. 9433 943 3 : 9434 94345 .78 9434 94354 9435 r 94364 9436 9437^1 9437 9438^ 9438 94394 79 9439 9444 94405 944 M 9441 9442^ 9442 9443.' 9443 94443 Kk2 ~* TABLE IV, A Table of Logarithms from i to 10,000. N O I 2 3 4 5 6 7 8 9 880 .94448 -94453 1.94458 -.944 6 3 2.94468 2.94473 2.94478 2.944^3 2.94488 2.94493 8r 94498 9453 945^7 9451^ 94517 94522 94527 94532 94537 94542 82 94547 94552 94557 94562 94567 9457 1 94576 94581 94586 9459 1 8-3 94596 94001 94606 94611 94^16 94621 94626 94630 94635 946/10 84 94645 94650 94655 94660 94665 94670 94675 94680 94685 94689 85 94694 94699 94704 94709 947M 94719 94724 94729 94734 947^8 86 94/43 94748 94753 947$8 94763 94768 94773 94778 94783 94787 87 94792 94/97 94802 94807 94812 948,7 94822 94827 94832 94836 8> 94841 94846 94851 94856 94861 94866 94871 94876 94880 94885 89 94890 94 8 95 94900 94905 94910 94915 94910 94924 94929 94934 890 2 ' 949 o'o 2.94944 2.94949 ^ -94954 2.94959 2.94963 2.9496; 2 - 94973 2.94978 2.94983 9 1 94988 94993 94998 95002 95007 95012 95017 95022 95027 95032 92 95036 95 4 95046 95051 95056 95061 95066 95071 95075 95080 93 95085 95090 95095 95100 95^05 95109 95114 95119 95124 95129 94 95134 95139 95H3 95148 95153 95158 95163 95166 95 r 73 95177 9^ 95182 95*87 95192 95197 95202 95207 95211 95216 9^221 95226 96 9523,' 95236 95240 95*45 95250 95*55 95260 95265 95270 95274 97 ^95279 95*84 9528< 95*94 95299 95303 95308 95313 95318 95323 98 953 28 95332 95337 95342 95347 95352 9~535; 9536i 95366 95371 99 95S7f 953Si 953^1 95390 95395 9 54o 95405 95410 9 54 '5 0^419 900 2.95424 2.95429 -95434 *-95439 2-95444 2.95448 2-95453 2- -957 5 s 1.95463 1.9546,8 01 954/ 2 95477 9540- 954*7 95492 95497 95501 95506 955 11 95516 02 95521 955-5 95530 95535 95540 95545 95550 95554 95559 95564 03 95569 95574 95^/8 955*3 95588 95593 9559 s 9; 6.02 95607 95612 04 95617 95622 95626 95631 95636 9564' 95646 95650 95 6 55 95660! 95 6 65 95670 95674 956^9 95684 95689 95694 95698 95703 95708! 06 95713 9wiS 55722 957*7 95732 95737 95742 95746 9575' 95756! O7 95761 95766 9577- 95775 95780 957*5 957*9 95794 95799 95804 08 95809 95^13 95818 *3 95828 95832 95^37 95842 95847 95852! 09 95851 9586, 95866 95871 9587 95880 95^5 95890 95^9^ 95899; J9IO 2.95904 1.95909 2.95914 2.959182.95923 2.95928 2-95933 2.95938 1.9594, 2-95947 95952 9595" 95961 9^966 9597 95976 95980 959*5 95990 95995 95999 96004 96009 96014 96019 96023 96028 (,6033 9603* 96042 96047 96052 9605^ 96061 9606 9607 9607^ 96080 96085 96090 9609^ 96099 96104 96109 96114 96118 96123 96128 96135 96i37 96142 96147 961 52 96156 9616 96166 96171 96175 96180 96185 96190 96194 96199 96204 9620 96213 96218 96223 96227 96232 96237 96242 96246 96251 9625 9626 96265 96270 96275 961801 96284 96289 96294 96298 9630 96308 96313 96317 96322 96327 9 6 r>2 96336 9634 96346 9635 9635 96360 96365 96369 9 6 374 920 a.c,6;?c 2.96384 2.96388 2 -96393 2.9639 2.96402 2.96407 2.96412 2.964*7 2.96421 2 96426 9 6 43 J 9643 96440 9644 96450 96454 96459 9646-1 96468 2 9647. 96478 9648 96487 9649 96497 96501 96506 96511 9 6 5i5 2 9 652C 965*5 9 6 53c 96534 9653 96544 96548 96553 9655 s 9651)2 24 9656 96572 9 6 57 96^81 9658 9 6 59i 96595 96600 96605 96609 r a 96614 96619 96624 96628 9663 96638 96642 96647 96652 96656 9666 96666 96670 96675 9668 96685 96689 96694 96699 96703 2 9670^ 96713 96717 96722 9672 9 6 73 96736 96741 9 6 745 96750 i 2 9675 9 6 759 96764 96769 9677 96778 96783 96788 96792 96-97 !' 2 96802 96Sot> 9681 96816 9682 968^5 (56830 96834 96839 96^44 |9> '..96848 2.96853 2.96858 :. 96862 1.9686 2.96872 2.06876 2.96881 2.96886 2.96850 3 9689. 96900 96904 96909 9691 96918 96923 96928 96932 96937 |'3 9694- 96946 96951 96956 9696 96965 96970 96974 96979 96984 i 3 or>98b 96993 96997 97002 9700 970ir 97016 97021 97025 97030 | 3^ ' 9703 97039 97044 97049 9705 97058 97063 97067 ' 97 72 97077 3 9708 97086 97090 97095 97100 97104 97109 97114 97118 97123; 3 97128 97IJ2 97137 97142 97H 97T5I 97155 97160 97165 97169- 3 97174 97179 97'83 97188 9719 97197 97202 97206 97211 972i6j 3 97220 97225 97^30 97234 97239 9?243 97248 972,53 97257 972621 3 9726^ 97271 97276 97280 9728 97290 97294 97299 97304 97308 TABLE IV. ATable of Logarithms from i to 10,000. j N . 2 3 4 5 ,6 - 7 8 9 j 940 4 1 42 2.97313 97559 97405 97317 9/364 97410 .97322 97368 974*4 297327 S/373 97419 97377 97424 {..97336 97382 9-428 2.97340 9738.7 97433 97437 2P735 97396 9:442 2.97354 9 74 cc 97447 i 4 3 9745 1 97456 97460 974: 97470 9/474 97479 9-74*3 974"" 9'/4 l >3 44 45 46 47 97497 9/543 97589 97635 9/548 97594 97640 97506 9755 2 9759? 97644 975*' 97557 97603 97649 97516. 97562 97607 97653 97520 97566 97612 976 5 8 97525 97571 9^617 9764 97529 97575 97621 97667 97534 97626 97672 97539 975^5 97630 97676 | 4S , 49 97681 9772? 97685 97731 97690 9773 6 9/695 9774 97699 97745 97704 97749 97708 '97754 97759 97717 977f>3 97722 97768 .95 5 1 ! 52 ; 53 2.97772 97818 97864 97909 97777 97823 97868 97914 2.97782. 9/82; 97^73 97918 -.97780 97832 978/7 97923 2-9779-' 07836 97882 97928 2.97795 97841 97886 97932 1.97800 .9793' 97850 97896 97941 2.97809 9/855 97900 97946 2-97813 S7859 97905 9795 C 54 1 55 ; 5 6 p ! 59 97955 98000 98046 . 98091 98137 98182 97959 98005 98050 98096 98141 98186 97964 98009 98055 98100 98146 98191 97968 98014 9*059 98105 98x50 98195 97973 98019 98064 98109 97978 98023 98068 98114 98159 98204 97981 9802! 98118 98164 98209 97987 98032 98078 98123 9816* 98214 97991 98037 98082 98:27 98175 98218 98041 08087 98132 98177 '960 61 2.98227 98272 -.98232 98277 2.98236 98281 2.98241 98286 2.98245 98290, 2.98250 98295 2.98254 98299 2.98259 98304 2.98263 98308 "'9^313 62 63 : 4 ! 66 98318 98363 , 98408 98498 98322 98367 9*455 9 8f.02 98327 98417 98462 98507 9833.1 98376 98421 9851 j 9*336 98381 98426 98471 98516 98385 98430 98475 98520 98390 98435 *4'; 9 8 349 98439 98529 98354 98399 9^444 98489 98-534 96358 98403 98448 98493 98538 ! 67 68 ! 69 98543 98588 98547 98592 98637 98552 98597 98641 98556 98601 98646 98561 9860^ 98650 .98565 98610 0865; 98570 9*614 98659 98574 98619 98664 98623 98668 986525 9867; ;97 71 73 ! 74 -75 ?6 2.98677 98722 98767 98811 98856 98900 98945 1.98682 98726 9^77* 98816 98860 98905 98949 2.98686 98731 98/76 98820 98865 98909 98954 2.98691 98735 98780 9882; 98860 98914 98958 2.98695 98740 98784 98829 98874 98918 98963 2.98700 98744 98789 98834 98878 9892; 98967 2.9870. 98745 9879 9883* 9888 98972 9*753 98798 98843 98887 98976 2.98713 9875? 98802 9-8 847 98936 2.98717 98762 98807 * 98851 98896 98041 77 98989 99034 9899^ 99038 98998 9943 99003 99047 99007 99052 99012 99056 99016 99061 99021 99065 99069 99029 99^74 79 99078 99083 99087 99092 99096 99 _ioo 99 10 5 99109 . "1?4 L^iu? 980 2.99123 2-99*27 2.99131 2.9 9 i 3 f 2.99140 2-99*45 - -99 J 49 -. 99*54 1.90158 i . 9 9 ] 6 2 1 8l 99167 99171 99176 99180 99*85 99* 8 9 99 T 9 99198 99202 99207 82 99211 99216 99220 9922^ 99229 99?33 99*3* 99-4- 99'-47 99251 83 99260 99264 99269 992/3 9927: 9928 99286, 99291 99295 84 99300 99344 99304 99348 99308 9935 2 993*3 9935~ 993 1 / 9936; 99322 993 6 * 99 3 7/ 99330 99374 99335 99379 99339 99383 j 86 87 99388 99432 99392 99436 9939 6 99441 99401 9944- 99405 V99449 99410 99454 9941 99>5 99419 99463 99423 ; 99467 99427 99471 88 9947<" 99480 99484 99481 99493 ^994*9^ .,9950 99506 99511 ,995 '5 8c, 99520 99524 99^8 9953J 9953J 95|2J - X 9o54 99550 99 ; " 5 990 2.99564 2,99568 .99572 2-9957' ,1.9958; 1.99585 2-9*959 2.99594 2 <, 959v 9 1 9960- 99612 99616 9962 99625 99629 9963 . 99"3.^ 92 9965 99656 99660 9966^ 99669 996 j|] %9^7, ^ftp8; 9 9 6ot 99 ( '9 I 93 94 95 96 9969 9973 9978 9982 99691 9974. 99787 99830 99704 99747 99791 99835 99708 9975 2 9979 99839 99712 99?oo 99847 99717 9976^ 99804 99848 997 6.' 9980 9985 99769 99856 ' 9973-C 99774 9981-7 .9986) 9-9734 9977^ 99022 99S65 97 98 99 9987 9991 9995 99874 999 1 9996 99878 99922 99965 9988. 99926 99970 99*87 99930 99974 99891 99935 9989 9993 9998 09900 99944 99987 99904 99948 99991 990 C 9 99952 99996 TABLE V. Of ARTIFICIAL Sines, Tangents, and Secants, o Degs. Sine. 6.46373 oocoo ooooo ooooo ooooo ooooo ooooo ooooo ooooo ooooo ooooo 7.78594 80615 8*545 8 4393 86166 8780 96887 98223 995-Q .00779 02002 03191 435o 05478 06578 99999 99999 99999 99999 99999 99999 99999 99999 99999 9999 s 9.99998 99998 99998 99998 9999* 99998 99997 99997 99997 _99997 .99997 99997 99996 99996 99996 99996 9999 6 9999 r 9999< jCo-fine. 6 9999j_ 9.99995 99995 99995 V 99995 99994 99994 99994 99994 99994 9999j_ 6ine. angentl Co-tang. 3-oooco I Infinite. becant. . OOOOO o-lecant.l Infinite. 60 .46373 53627 o.ocooo .^3627 59 76476 235*4 ooooo 23524 58 94085 05915 coooo 059 1 5 57 .06579 .934*1 ooooo 2.93421 56 16270 83/30 ooooo 83730 I 55 24188 75812 ooooo 75^12 54 30882 69118 OOOQO 69118 5: 36682 63318 ooooo 63318 53 41797 58203 ooooo 58203 5 463^3 53627 ooooo 536*7! 5< ."50512 .49488 o . oocoo 2.49488 4< 54291 45709 ' ooooo 45709 4* 57767 42233 ooooo 42233 4' 60986 39 OI 4 O0900 39015 4 63982 36018 o:>ooo 36018 4 66785 33 2T 5 OOOOI 332i6 4 69418 3058^ OOOOI 3P583 4 71900 28100 OOOOI 28100 4 74248 25752 OOOOI 2575- 4 76476 2^524 OOOOI *35 2 5 4 7-78595 -.21405 O . OOCO I 12.21406 3 80615 19385 OOOOI 19385 82546 17454 OOOOI 17455 84394 15606 OOOOI 15607 86167 13833 OOOOI I3S34 87871 12129 OOOOI 12130 89510 10490 OOOOI 10491 9 ioS-9 08911 OOOOI 08912 92613 07387 COOOI 07388 94086 Q59 J 4 00002 05915 7 955*0 12.04490 10-00002 12.04492 96889 03111 O0002 03113 98225 oi775 OOOO2 oi777 99522 00478 OOOO2 00480 8.00781 11.99219 O0002 n .99221 02004 97996 O0002 97998 03194 96806 00003 96808 04353 95647 00003 95650 05481 945 ' 9 00003 94522 06581 934*9 00003 93422 8.07653 11.92347 10.00003 11.92350 08700 91300 00003 9 T 34 09722 90278 00004 90282 10720 89280 00004 89283 11696 88304 00004 88307 12651 87349 00004 87356 13585 86415 00004 86419 14500 85500 00004 85505 15395 84605 00004 84609 16273 83727 00005 83732 8.I7I33 11.82867 10.00005 11.82872 17976 82024 00005 82029 lS80; 81196 00005 81202 19616 80384 00005 80390 20413 79587 00006 79593 2119 78805 00006 78811 196* 78036 00006 78042 Z272O 77280 00006 77287 2346 76538 00006 76544 2419 75808 00007 1 75814 t.|Co-fecant.| Secant. 1 Co-tan Tangen 12 II 10 9 8 7 6 5 4 3 ^ M. 89 Degrees, TABLE V. Of ARTIFICIAL Sines, Tangents, and Secants, i Deg. M.t Sine. Co-fine. Tangent. Co-tang. Secant. (Co-fecant. 1 .24186 99993 .24192 1.75808 0.00007 1.75814 60 n I 24903 99993 24910 75090 00007 75097 2 25609 99993 25616 74384 00007 74591 ll 3 4 6 7 26304 26988 27661 28324 28977 99993 96663 99992 96992 99992 26312 26996 27669 28332 28986 73688 73004 72331 71668 71014 00007 00007 00008 00008 00008 / ~ J 7 73696 730^2 72339 71676' 7IO23 57 i 56 55 I 54 I 2 (1 8 29621 99992 29629 70371 00008 7O370 52 9 30255 99991 30263 69737 00009 / j / y 69745 51 10 8.30879 9.99991 9. 30888 11.69112 0.00009 i .69121 -d ii 3H95 99991 31505 68495 00009 68505 49 12 32103 99991 32112 67888 00009 67897 48 H 13 32702 99990 32711 67289 O9OIO 67298 47 H 33292 99990 33302 66698 OOOIO 66708 { Ii (\ II 15 33875 99990 33886 66114 OOOIO 661 25 ^ 11 4<; 1 16 34450 99989 3446i 65539 COO 1 1 65550 TJ [I 44 fl 17 35018 99989 35029 64971 COO 1 1 64982 M 4 ? r] 18 35578 99989 35590 64410 OOOII 64422 2 H 19 36132 99989 36143 63857 0001 I 63868 SI i 20 8.36678 9.99988 8.36689 11.63311 O.OOOI2 1.63322 ~r 21 37217 99988 3722 9 62771 00012 62783 39 i 22 37750 99988 37762 62238 OOOI2 62250 38 23 24 38276 38796 99987 99987 3^289 38809 61711 61191 00013 00013 61724 61204 37 25 39310 99987 39323 60677 00013 60690 ^- fl 26 39818 99986 39832 60168 00014 60182 j ^ || 54 j 27 28 40320 40816 99986 99986 40334 40830 59666 59170 00014 00014 59680 59184 M M-l 29 4 : 307 99985 41321 58679 00015 58693 III 30 8.41792 9.99985 8.41807 11.58193 10.00015 11.58208 3 r 3 1 42272 99985 42287 5.7713 cooi 5 57728 29 32 42746 99984 42762 5/238 coo 1 6 57254 o B 33 43216 99984 43232 56768 ocoi6 56784 '7 34 43680 99984 43696 56304 00016 56320 26 i 35 44 T 39 999^3 44156 55844 oco 1 7 5586*- 25 |, 36 44594 99983 4461 1 553^9 coo 1 7 - r 24 j 37 45044 454$ 9 99982 45061 45507 54939 54493 00017 coo 18 54956 54510 *T * 23 22 ! 39 45930 99982 45948 54052 00018 54070 21 40 8.46367 9-999*2 8.46385 11.53015 10.00018 n. 53633 20 4 1 46799 99981 46817 53183 coo 1 9 53201 19 42 47226 99981 .47245 5-755 00019 52774 18 43 $4 47650 48069 99981 99980 480.89 52331 51911 coo 19 OCOJ.O 52350 51931 17 16 i 45 48485 99980 4*505 5 J 495 coo 20 5 j 5 1 5 "! 46 48896 99979 48917 51083 OOO2 I 51104 4 47 49304 99979 49325 50675 00021 50696 * 48 49708 99979 49729 50271 COO 2 I 50292 12 ' 49 50108 99978 50130 49870 00022 49892 II 50 8. 50505 9.99978 8.50527. 11.49473 10. Of.. 11.4941,5 10 5* 50897 99977 50920 49080 C0023 Cy 52 51287 99977 51310 48690 00023 48713 8 53 51673 99977 51696 48304 00023 48327 54 52055 99976 52079 47921 00024 47945 ' 6 55 52434 99976 5M59 47541 00024 47566 5 56 52810 99975 52835 47J65 COG 2 5 47190 4 57 53183 99975 53208 46792 00025 46817 3 5$ 53552 99974 53578 46422 COO26 46448 2 59 539*9 99974 5394=: 46055 00026 4608 r I j 60 542^2 99974 ^4308 45692 000:6 45718 Co- fine Sine. Co-tang Tangent Co-fecant Secant. M~ 88 Dtgrees. TABLE V. Of ARTIFICIAL Sines, Tangents, and Secants. 2 Deg 5 56054 9997' 56083 439^7 00029 43946 55 6 56400 99971 56429 4^571 00029 43600 54 7 56743 99970 56773 43227 00030 43257 53 8 57084 99970 5/114 42886 00030 42916 52 it 9 5742 i 99969 5745* 42548 00031 4*579 5i 10 *-5?757 9.99969 8. -7788 11.42212 10.00031 11.42243 50 I/ 58089 9996^ ^8121 41879 00032 41911 49 in 5849 99968 58451 41549 00032 41581 48 13 58747 99968 5^779 4T22I 00032 41253 47 i! 1 4 5972 99967 59105 40895 .00033 40928 46 M 59395 99967 594 40572 00033 40605 45 r6 . 59715 -99953 S. 66816 r i. 33 184 10.00047 I -33*3i 20 41 C70J9 9993 2 67087 3*913 00048 32961 '9 42 6 73 cS 99952 67356 32644 00048 37.692 1 8 43 67-5 99951 67624 32376 00049 3M25 17 ! 44 67841 9995 1 67890 3-i ro 00049 3**59 16 ' 45 6 8 1 04 1)995-0 68154 31846 00050 31896 15 ! 46 68567 99949 68417 315^1 coo q i 31633 H : 47 68627 99949 68678 31322 o'oo 5 1 31373 13 l 4 3 68886 09948 68938 31062 OOO r 2 31114 12 ! 49 69144 99948 6 9 T q 6 30804 oc : 30856 II : ^o 5.69400 9-99947 8. 694^3 11.30547 10.00053 i . 30600 10 ' 5' 69654 99946 30292 000 r^ 30346 9 5* 69907 99946 6^96-2 30038 00054 30093 8 5? 70159 99945 70214 29786 00055 29841 7 1 54 70409 99944 , 70465 *9535 000^6 29591 6 : 55 70658 99944 70714 29286 00056 2934* 5 ; ^ 70905 99943 70962 29038 00057 29095 4 r- 7H5 T 9994Z 7I2c8 2^792 00058 28849 3 71305 99942 71453 28547 00058 28605 2 59 716^8 99941 71697 28303 00059 28362 I : 60 7:880. .9994P 71940 28060 ooos;t) 28120 Co- fine. Sine. Co-tang. Tangent. 'Co-fecant Secant. M. 87 Degrees, TAPLE V. Of ARTIFICIAL Sines, Tangents, and Secants. 3 Degs. IM Sine. Co-fine. Tangent. Co-tang., Secant. f Co-fecan t < . 7 1880 9-9994 8.71940 11.28060 10.00060 11.28120 "~6~oT i 72120 99940 72iSi 27819 00060 2~58o 59 72360 93939 72420 27580 00061 27640 58 3 7*597 9993^ 7*65* 27341 00062 27403 57 4 7*334 99938 72896 27104 00062 27166 56 5 73069 99937 73I3 2 26*68 00063 26931 55 6 73303 999^6 73366 26634 00064 26697 54 II 7 73535 99936 73600 26400 00064 26465 53 8 73767 99935 7383* 26168 00065 26233 5 2 9 73997 99934 74063 15937 00066 26003 5i 10 8.74226 9.99934 8.74292 11.25700 10.00060 11.25774 50 IX 74*54 99933 74521 25479 00067 25546 49 12 74680 9993^ 7474^ 25252 00068 25350 4* 13 74906 99932 74974 25026 00068 25094 47 '4 75130 9993J 75199 24801 00069 24870 46 15 75353 99930 75423 24577 . 00070 24647 45 16 755/5 99929 75645 4355 00071 24425 44 J 7 75796 99929 75867 24133 00071 24204 43 ! 18 76015 99928 76087 23913 00072 23985 42 19 76234 999*7 76306 23694 00073 23766 4i 20 4.76451 9.99927 3.76525 11.23475 10.00073 11.23549 40 21 76667 99926 76742 23258 00074 2 333* 39 22 76883 99925 76958 23042 00075 23117 38 23 77097 99924 77173 | 22827 00076 22903 37 H 773io 99924 773*7 22613 00076 22690 36 a 5 77522 99923 77600 22400 00077 22478 35 26 77733 99922 77811 22189 00078 22267 34 27 77943 99921 78022 21978 00079 22057 33 I 28 78152 99921 789.32 21768 00079 21848 32 29 78361 90920 78441 21559 oco8o 31639 3i 3o .78568 5,99919 H.7'<&49 [ti.i*35* ro.ooo&r ii 21432 30 3i 7*774 99^18 72855 21145 00082 21226 2 9 32 78979 99917 79061 20939 00083 2 102 I 28 33 79^3 99917 79266 ao 7 34 00083 20817 27 34 793^6 99916 79470 20530 01084 20614 26 35 79588 999 r 5 79673 20327 00085 20412 25 3^ 797^9 i>99'4 79^75 20125 00086 2021 I 24 37 79990 999 1 3 80076 19924 00087 20010 2 3 33 Sofia 939<3 80277 19723 00087 I98ll 22 3J 80388 99912 80476 19^24 [ cooSS 19612 21 40 80585 .99911 3.80*74 n. 19326 10.00089 11.19415 20 4 r 80782 99910 $08/2 19128 00090 1Q218 J 9 42 86978 99909 81068 - 18932 00091 I.)022 18 43 81173 99909 81264 ' 18736 00091 18827 17 44 81367 99908 81459 18541 00092 18633 16 45 81560 99907 81653 18347 I 00093 184^0 *5 46 81752 99906 81846 18154 00094 18248 J 4 47 81944 99905 82038 17962 00095 180^6 13 4* 8*i|4 99904 82230 17770 00096 17866 12 / -1L 82324 99904 82420 17580 00096 17676 II 5 1.82513 .99903 $ .82610 11.17390 10.00097 t I. 17487 10 5i 82701 99902 82799 17201 00098 17299 9 52 82888 99901 82987 17013 00099 I71I2 8 53 83073 99900 831/5 16825 C.OIOO I6 9 25 7 54 83261 99899 83361 16639 ooroi 16739 6 55 83446 99898 83547 16453 OOIO2 16554 5 56 83630 99898 83732 16268 OOIO2 16370 4 57 83^3 99897 83916 16084 00103 16187 3 53 83996 99896 84100 15900 00104 16004 * 59 84x77 99895 84282 15718 00105 &*3 1 1 60 84358 99894 84464 15536 00106 15642 /a- line. Sine. iCo-tang. " fangent. ICo-fecant SCcanf. M. Derees- T/v*Br,E V. Of ARTIFICIAL Sines, Tangents, and Secants. 4 Degs M. j Sine. . Co fine.. rangeut. Co-tang. Secant. "Jo-fecant. 5. .54* $3 ' >-S9 v >94 i . 84404 1.15536 1 0.00106 1.15642 60 I 84539 99893 84646 15354 00107 . 15461 59 2 84718 99892 84826 15174 00108 15182 58 3 84897 99891 85006 14994 00109 151-3 57 4 85075 99891 85185 14815 00109 14915 56 5 85152 99890 85363 OOI JO 14748 55 1 6 8 ,-429 99889 8^540 14460 OOI I I 1457 1 54 [ 99888 857*7 14283 OOI 12 1439,5 53 8 85780 99887 8,893- 14107 OOII3 14110 52 i 9 $955 99886 86069 T 393i 00114 14045 5 r 1 I0 i 3.86.28 9.99^35 ..86143 "'IS?!? IO.OOH5 1.13872 5 ii 80301 99-884 13583 OOIl6 13699 49 i 86474 99*3 86591 13409 OOII7 13526 48 j ! 13 86641; 9oSSi 86763 13237 00118 13355 47 ; 14 86Si6 99881 86935 1306$ 00119 13154 4f> i ' i^ 86987 99880 87106 ia?94 00120 13013 45 : i 87156 99879 87277* 11723 00121 12844 44 j : 16 87325 87447 12^53 OOI 21 12675 43 [ In 87494 99^/8 87616 1*384 00122 12506 41 | ' IK 87661 99^7 87785 12215 0012.3 IZ339 4i I ^7829 ' 5.87951 11.11047 10.00124 1.12171 4 21 879^5 9 9 "> " > 88120 11880 00125 11005 39 i *- 99874 88*87 11713 00126 11839 38 : 2 ? 88346* 9 ,873 88453 n 547 00127 11674 37 88490 99872 88618 11382 00128 11 sIO 36 I 2^ S86 54 9987I- 887*3 j 1117 00129 11346 35 I i 26 88817 99870 8^948 11052 00130 II 153 34 j 88980 99869 80111 10889 oo 1 3 1 I 1029 33 ! a3 89142 99868 89174 10726 00132 1 08 5 5 31 29 9304 09867 S 9 4<7 10563 00133 10(196 3i ' 20 8.89464 9.99866 '?. 89 598 n.*040i 10.00134 1 . 10 ',36 33 } i 89675 99865 89760 10240 oci35 10375 29 ; 89784 99-64 89520 I00i>0 oo i 3 6 10216 28 ; [ -i > 8994? 99863 90080 00910 00 i ,/ 1^057 27 i 34 90102 99862 90240 09760 00133 09898 16 1', 90260 9986 i 93399 09601 00139 09740 25 90417 ( t Q~6o 9C-5S7 09443 0014 j 09583 24 >- ( } c '74 r,07i5 09185 00:41 09416 2] 1 90872 00118 00142 09:70 12 v> 08971 00 i. 09 T 1 5 21 i , 40 s . . j i 1 8 5 p. 08815 10.00. 1 1 .08960 20 i 5*1 105 9985 5 9 i 340 08660 00145 08805 19 i ! 4.? 99 S S 4 9J495 08,505 00146 08651 18 1 9? 5ft* 91650 00147 08498 17 ' 44 91803 oSi97 ^0148 - 08345 16 ! 919? 7 08043 00149 8i93 15 o; COI CO 08041 '4 47 S'i rTo 99848 02261 , 07738 00152 07590 13 1 _* 92161 99847 91414 o7^8(k 00153 07730 11 i 07435 00154 9758j i I i \ 5 ii .07284 10.00155 11.07439 ' sf ^27:0 99844 92866 07134 00156 7 2 9 o 9 ! 02$ 59 99843 93016 06984 00157 07141 8 1 51 93007 99841 i 93165 06835- 00ic;8 06993 .7 ! 5 4 } 9?T54- i/y'^f 93>*3 p6| 00159 o(> ^46 6 -733 01 40 06538 00l6o 06699 5 , 9U4 S 99839 95609 06391 oo 1 6 1 o6;'Ki 4 ' 57 99*38 95756 06144 - 00162 06406 3 ; I? 99837 93903 .06097 oe 1 6 3 ^6260 2 1 59 99836 94049 ; 059 5 r 00164 06115 I : 968 H i94 J 95 . 05805 5 oo i (6 0^970 O r", Co-fine. Sine. Co-tang Co-fecant Co-iecan Secant. M.j 85 Degrees. TABLE V. Of ARTIFICIAL Sir.es, Tangents, an ! Sec rt* ; M. Sine. Co- line. Tangent- Co-t*njf. bc-cjint ,Co k'cant 3.94030 9.99834 8.94195 11.05805 10 . oc i 60 u.c58j;o oc i I 94^74 9?&33 94340 05660 001 07 05-26 J9 z 943 J 7 99832 944 ? 5 55 r 5 00168 05683 58 3 94461 99831 94630 05370 00169 "5^9 57 4 94603 99830 94773 05227 00170 OS397 56 5 94746 9 98 r 2 9 94917 05083 0017 1 05254 55 6 948-7 99828 95060 04940 00172 05113 54 7 95029 99527 95202 04798 00x73 04971 53 8 95170 99825 95344 04656 00175 04830 52 9 9531 99824 95486 04514 00176 046110 5i I'O 8.95450 9.99823 8.95627 11.04373 10.00177 11.04550 50 . ii 95589 99822 95767 04233 00178 04411 49 12 -95728 99821 9 5908 04092 00179 04272 48 3 ,95867 99820 96047 03953 00180 04133 47 14 96005 99819 96187 03813 00181 -03995 46 15 96143 99817 963-5 03675 00183 0.5^57 45 16 96280 99816 96464 03536 00184 03710 44 17 96417 99815 96602 03398 oo T 8 5 03583 43 18 9 6 553 99814 96739 03261 00186 03447 42 J 9 96689 99813 96877 03123 ooiSy 03311 4i 20 8.96825 9.99812 s. 9-013 11.02987 IO.COI8S 11.03175 4 21 96960 99810 97150 02850 00190 05040 39 22 97095 99809 97285 02715 00 1 '.) I 02905 3* 23 97229 99808 97421 02579 00192 02771 37 2 4 97363 99807 97556 02444 00193 02637 tf 25 9749 6 99806 97691 02309 00194 , 02504 35 26 97629 99804 97825 02175 00196 02371 34 27 97762 99803 97959 02041 00197 02238 33 zS 97894 99801 98092 01908 00198 02 ro6 32 . 29 98026 99801 98225 01775 00199 01974 3i 30 8.9X157 9.99800 8.98358 n .01642 1O. 00200 n .01843 3o 3i 98288 99798 98490 01510 OO2O2 01712 29 3 " 98419 99797 98622 01378 00203 015X1 28 I 33 98549 99796 9 3 753 01247 00204 01451 27 34 98679 99795 98884 on 16 00205 01321 26- 35 98808 99793 99015 00985 00207 01192. 25 36 989.37 99792 99H5 00855 OO2O8 01063 24 37 9<)o^6 9979 1 99 2 75 00725 OO2O9 00934 23 38 99194 99790 99405 00595 O02tO coS 06 22 39. 99321 99788 99534 00466 COM2 00678 ' 2I . 40 8.99450 9-99787 4.99662 i i .00335 i o . oo 213 1.00550 2O 4 r 99577 99786 99791 00209 00214 00423 J 9 1 42 99704 99785 99919 0008 1 002T5 CC2yO 1 8 43 993 99733 9.00046 10.99954 0021? CJ7O i/ 44 99956 99782 00174 99826 CC2I8 o,>:.'44 16 45 9.00082 9973i 00301 99699 00219 10-99918 J 5 46 00207 99780 00427 99573 OOI2O 99 "93 *4 47 oo3?i 997/8 00553 99447 00222 ^5668 13 48 00456 99777 00679 99321 00223 99 12 49 00581 90776 0^805 99195 00224 - 1-19 11 5 ;. 00704 9 '99775 9.00930 10.99070 I0.00i25 10.99296 10, 5i 00818 99773 01055 9 8 945 00227 99172 o ^ 52 00951 9977* 01179 9882 r C0228 99049 8.. 53 01074 99771 0:^03 98697 00229 9^926 7 54 01 196 99769 014*7 9 X 573 00231 98804 6 55 01318 99768 015-50 98450 WO2 32. 98602 5 5* 01440 99767 01673 98327 00233 98 560 4< 57 or i;6i 9Q765 01796 98204 ' 00235 9 8 439 3 5 * Oi6"82 99764 : o 1 9 T 8 ,98082 ' OOZ^O- 98318 z 59 01803 99763 '02040 979*60 "37 98197 i 60 01923 9976r 02162 9Jg 00239 95077 Co-fine. Sine. Co-tan^. Tangent. Co ilcaiit.) Decant M. LI 2 TABLE V. Of ARTIFICIAL Sines, Tangents, and Secants. 6 Begs. M Sine. Co-fine. Tangent. Co- tang Secant. ( Co-fecant 9 .oi 9 ~ 9-99761 9.02162 10.97838 10.00239 10.95077 OO I 03043 99?6o 02283 97717 00240 97957 59 2 0x163 99759 02404 9759'-> 00241 97*37 5 3 02283 99757 02525 97475 00.143 97717 57 4 02402 99756 02645 97355 00244 9759? 56 5 02520 99755 02766 97234 00245 97480 55 6 02639 99753 02885 97ri5 00247 973 6 i 54 7 02757 99752 03005 96995 00248 97243 53 8 02874 99751 03124 96876 00249 97126 52 _t 02992 99/49 03242 96758 00251 97008 51 10 9.03109 9,99748 9.03361 10.96639 10.00252 10.96891 5 IT 03226 99747 03479 9652! 00253 96774 49 12 03342 99745 3S97 96403 00*55 96658 48 13 03458 99744 03714 96286 00256 96542 47 14 03574 99742 03831 96168 00258 96426 46 M 03690 9974*t . 03948 96052 00259 96310 45 16 03805 99740 04065 95935 00260 96195 44 17 03920 9973S 04181 95819 00262 96080 43 II 04034 99737 04297 95703 00263 95966 42 19 04149 99736 04413 95587 00264 95851 4i 20 9.0426* 9-99734 9.04:28 10.95472 10.00266 10.95738 40 71 04376 99733 04643 95357 00267 95^*4 39 22 04490 99/31 04758 .95242 00169 955io 38 *3 04603 99730 04873 95W 002~0 95397 37 2 4 047. ' 5 997-8 04987 95013 00272 95285 36 25 04828 99727 05101 94"' 99 00273 95172 3^ 26 04940 99726 , 05214 94786 0^274 95060 34 27 05052 99724 05328 94672 00276 94948 33 28 05164 99723 05441 94-59 C0277 94836 32 J!L 05275 997^1 05553 94447 00279 94725 31 30 9.05386 9.99720 9.05666 10-94334 IO 002*0 to. 94614 30 gi 05497 99718 05/78 94222 00282 94503 29 32 05607 99717 05890 94110 00283 94393 28 33 05717 99716 06002 9399* 00284 94283 27 34 05827 99714 06113 93J87 . 00286 94173 26 35 05937 99713 06224 93*76 00287 94063 25 36 06046 9*7*1 06335 93665 00289 93954 24 37 06155 997fO 06445 93555 00290 93845 23 38 06264 99708 06556 93444 00292 93736 1 39 06372 99707 06666 933 34 00293 93628 21 40 9.06481 9.99705 9.06775 10.93225 10.0029:; 10.93519 20 4 1 06589 99/04 06885 93H5 00296 93411 J 9 42 06696 957 d2 06994 93006 0298 93304 18 43 06804 99701 07103 - 92897 00299 93^6 '7 44 0691 r 99699 07211 92789 00301 93089 16 45 0701$ 99698 07320 92680 00302 92982 15 46 07124 99696 07428 9 2 572 00304 92576 J 4 47 0723-1 99695 07536 92464 00305 92769 13 48 7337 99*93 07643 92357 00307 9- 6 63 12 .! 49 07442 99692 07751 92249 00308 92558 II 50 9.07548 9.99690 9.07858 10.92142 10.00310 10.92452 IO 5i 67653 99689 07964 92036 00311 92.347 9 5* 07758 99687 08071 91929 00313 92242 g 53 07863 99686 08177 91823 00314 92137 7 54 07968 99684 08283 91717 00316 92032 6 55 08072 99683 08389 91611 00317 91928 5 56 08176 99681 0849^ 9 r 505 00319 91824 4 57 08280 99680 08600 91400 00320 91720 3 5* 08383 99678 08705 91295 0032 i 91.617 2 59 08486 99 6 77 08810 91190 00323 91514 I 00 08589 99675 08914 91086 00325 91411 Co-fine. Sine. Co- tang. Tangent. Co-fecant. Secant. M, 8 3 Degree*, TABLE V. Of ARTIFICIAL Sines, Tangents, and Secants. 7 Degi. M. Sine. Co-fine. Tangent., Co-tang. Secant. Co-fecan 9.08589 9.995.75 p. 08914 10.91086 10.00325 10.91411 60 I 08692 99674 09019 90981 00326 91308 59 2 *795 99672 091*3 90877 00328 91205 58 3 08897 99670 09227 9773 C03SQ 91103 57 4 08999 99669 09330 90670 00331 91001 56 5 09101 99667 09434 90566 003, -3 90&99 55 6 09202 99666 09537 90463 00334 90798 54 7 09304 99664 09640 90360 00336 1/0696 53 8 9405 99662 09742 90258 00337- 90595 52 _9 09506 99661 09845 90155 00339 90494 5 JO 9.09606 9.99659 9.09947 10.90053 10.00341 io.i;o394 50 ii 09707 99658 10049 89951 00342 90293 49 12 09807 99656 10150 89850 00344 90193 48 ] 3 09907 99 6 55 10252 89748 00345 900^3 47 1 14 1 10006 99 6 53 IC353 89647 00347 ' 89994 46 I 15 IOI06 99651 10454 89546 00349 1^94 45 16 10205 99650 3E0555 S 9445 00350 %795 44 j- 7 j 1030.. 99648 10656 89344 00352 89696 43 18 10402 99647 10756 89244 00353 89598 4^ 1 '9 10501 99645 10856 89144 0035*; . ^9499 "8* io .,.10599 J-99 6 43 j.i 0956 10.89044 10.00357 io. 89.101 40 21 10697 99642 11056 88944 00358 89303 39 2.1 1^795 99640 11155 88*45 oo?r,o 87205 <8 23 10893 9^638 1 12 54 887^6 00362. %!0 7 37 24 10990 99 6 37 "353 8-:t47 00363 8t/oio 3* j. 2 5 11087 99 6 35 11452 88548 00-365 88 y i 3 35 26 i r 1 84 99 6 33 1155! ^449 00367 88810 34 27 11281 99632 11649 8*351 00368 88719 33 28 *'377 99630 11747 88253 03370 88023 ^ - O " 29 11474 99629 11845 88155 00371 88526 >* ; 30 9.11570 .9^627 -943 IC.S&OS7 0.00373 10.8^430 30 3t 11666 99625 1 2040 8; 9 6o 00375 88334 a y 32 n->6i 99624 12138 87862 00376 88239 2.1 33 11857 99622 12235 87/6S 00378 88,43 27 34 11952 99620 12332 8; 668 00380 88048 16 1 35 12047 9 <;6.S 12428 87572 00382 87953 25 36 12142 99617 12525 87475 00383 87*5$ 24 37 12236 99615 12621 87379 00385 87764 38 *3J3* 99 6l 3 12-17 87283 00387 87609 22 39 12425 99612 1281:5 87,87 00388 7575 21 40 3.125*9 .99610 . 12909 i o. 57091 i o . oo 5 ^ o io.b7^>Sf 2O 4 1 11612 99608 13004 86996 00392 87388 '9 42 12706 99607 13099 86901 00393 87294 ii 43 12799 99605 13194 * 86806 00395 <> 7^O I 17 44 13892 ^9603 13289 867 f r 00597 87108 16 ! 45 12985 99601 13384 S66i6 00399 8;ci - ^ 46 13078' 99600 134/8 86<22 00400 86922 '4 47 13171 99590 13573 86427 00402 ^6X29 13 48 13263 99596 13667 863S3 00404 **m i i 49 1 335 5 99595 l?7 lL_ 86239 00405 1 1 50 9.13447 99593 .13854 10.86140 10.00407 lo.go^Tr" io ; 5i 2 3539 99S9 1 13948 86052 00409 864.61 9 52 13630 99589 14041 8=;959 00411 86370 8 ; 53 13722 99588 14134 &'SS66 00412 862/8 7 54 I38i3 99586 14*7.7 S5773 004/4 86187 6 55 1 13904 99584 14320 8<;6So co4'.6 86096 5 56 13994 99582 144*2 8,588 00418 F:6:o6 4 57 13085 905i 14504 85496 00419 8^9^ 3 58 14175 99579 14597 85403 00421 85'25 2 59 14266 99577 14688 8^312 00423 *7S4 i 60 143-6 99575 14780 85220 00425 85644 O Co-fine. Sine. Co-tang. Tangent. 'Co-fecant becant. M. 8a Degrees. TABLE V. of ARTIFICIAL Sines, Tangents, and Secants. 8 Degs- ! M, Sine. Co- fine* Tangent. Co-tang, Secant. Co-fecant. ). 14356 99575 .147^0 IO.Ss2i:0 10.00425 10.65044 60 1 M445 99574 14872 85T24 00426 85,55 59 2 M535 99572 14963 85037 0.0428 85465 58 3 14024 .99570 15054 84946 C0430 85376 57 4 14714 99568 I5H5 84855 004-32 85286 56 , 5 14803 99566 15236 84764 00434 85197 55 6 14891 99565 !53 Z 7 84673 00435 85109 54 ; 7 14980 99563 154*7 00437 85020 53 8 .15069 99561 84492 00439 84931 9 15157 99559 15598 84402 00441 84843 51 10 9-15-45 9-99557 9.15688 10.84^12 10.00443 10.84755 50 ii 15333 99556 15777 84223 00444 84667 49 12 154*1 99554 15^67 84133 0044'') 845:9 48 U 15508 99552 15956 84044 00448 84492 47 H 15^96 ' 995> 16046 839.54 00450 844^-4 46 15 15183 99548 16135 83865 001-52 843:7 45 16 15770 99546 16224 83776 C0454 84230 44 1 7 15857 99545 16312 83688 oc'455 84143 43 18 i>944 99543 16401 835-99 00457 84056 42 19 160:0 9954 r 16489 83511 00459 839/0 4' 20 9. 161 16 9-99539 9^16577 10.834.^.3 10.00461 10. '83^4 40 21 16203 99537 16665' 83335 00463 83797 3 9 22 16289 99535 16753 83247 00465 83711 38 2 3 16374 99533 16841 004*^7 83626 37 24 16460 f * 99532 16928 83072 00468 83540 - 36 45 16545 99530 17016 82984 00470 83455 35 46 16631 99528 17103, 82897 00472 83369 34 *7 16716 99526 17190 8xi8io 00474 83284 33 28 16*01 99524 17277 82723 00476 83199 32 49 16886 995" 826157 00478 83114 3 ; - 9.16970 9.99520 9-17450 10.82550 10.66480 10.83030 3P 3>i 17055 99518 17536 824^4 00482 82945 29 32 17139 99517 17622 82378 00483 82861 28 33 .17223 99515 17708 82292 00485 82777 27 34 17307 99513 17794 82206 00487 82697 26 35 17391 995H 17880 82120 00489 82609 2^ 36 1/474 99509 17965 82035 0049 1 82526 2 4 37 .. 17558 99507 18051 8,949 00493 82442 23 , 3^ 17641 99505 I J 36 81864 00495 82359 22 39 17714 99503 18221 81779 00497 82276 21 40 9.17807 9.99501 ;.I?306 10.81694 16.00499 10.82193 20 4i j 7.890 99499 I 39 1 81609 00501 82110 19 4-2 T7973 99497 I $47 5 8'5 2 5 00503 82027 18 43 99495 IS 560 81440 00505 81945 17 44 1^-37 99491 1*644 81356 COsOO 81863 16 45 ,18220 99492 18728 81272 00508 8 [7X0 i 5 46 iHjOi i83i2 81188 005 ro 8-169$ M '47 i-JJ ^ 3 99488 18896 81104 0051 2 81617 13 4$ 18465 99486 18979 81021 00514 81535 12 49 1*547 99484 19063 . .8093.7 . 00516 8.1453 i r 50 9. 1^628 9.99482 9.19146 10.80854 ro. 00518 10.81372 10 5i 18709 99480 19229 '80771 00520 81291 9 5* 18790 99478 19312 80688 00522 81210 8 53 1*871 99476 19395 80605 00524 81129 7 54 15952 99474 19478 80522 00526 81048 6 55 19 33 99472 19561 80439 00528 80967 5 56 19113 99470 19643 82357 '00533 80887 4 57 i9 T 93 99468 197*5 80275 00532 80807 3 58 19273 99466 19807 80193 00534 80727 2 59 19353 99464 19889 Soni 00536 80647 1 60 194*3 t 99462 19971 80029 00538 80567 Co- fine. Sine. Co-tang. TangentJCo-fecant SecantT M> 81 Pegrees. TABLE V. Of ARTIFICIAL Sines, Tangents, and Secants. * 9 M. Sine. , Co fine.JTan:<-i t. Co-tang. Secant. ( TJo-iecant. 2-I9433 ? . 99462 19.19971 10*^0029 0.00538 [0.80567 oo i I95J3 99460 20053 79947 00540 80487 59 2" 19592 99 4-8 10134 79^66 00542 80408 f 3 19672 9945 6 ' 20216 797-4 00544 803 28 57 4 I975I 99454 20297 79703 00*146 80249 jtf 5 I 9 *3q 9945* 1*0378 79622 oc" S4 8 80170 c 5 6 19909 99450 20459 7954t 00550 80091 54 7 19988 99448 20540 79460 00552 SOG. (2 53 8 20067 99446 20621 79379 c554 7 9 '^3 52 9 2Oi 45 99444 20701 79299 005-56 79% 5 Si 10 9. 20223 9.99442 9.20782 10.79218 0.0^555 0.79 5 ii 40302 99440 20862 79'3# 00560 79 6 V 8 f" 12 20380 99438 20942 7958 00562 7962* 48 13 20458 994^6 2T022 78978 00564 79542 47 *4 ao53 r > 99434 2U02 7 88c>8 00566 7Wf5 46 , 15 20613 99432 2H82 78818 00568 79327 45 10 10691 99429 2I26l 73739 * 00571 79309 44 i/ 20768 99427 21341 78659 00573 ?9*S* 43 18 20845 99425 21420 78580 <>S75 79*55 42 J9 20922 99423 21499 78501 00577 79078 4 T 20 9.20999 9.99421 9.2157^ 10.78422 jo 00579 io- 79001 "40" 21 21076 99419 21657 7^343 00581 7^924 39 22 21153 99417 21736 78264 05583 78847 3* 23 21229 994*5 21814 .78186 00585 78771 37 24 21306 99413 21893 78107 00587 78694 36 25 21382 99411 21971 78029 00589 78618 35 26 t'458 99409 220 49 7795 1 00591 78542 34 27 2*534 9947 22127 77^73 00593 -8406 33 28 21610 99404 22205 77795 00596 r 8 39 o 32 29 21685 99402 22iS; ^ 77717 D0sq8 7S.3f5 3i ! 3 .) . 2i;()i 9,99400 ; 9.22361^ 10.77659 IO.Oo6oo 10.78239 tt~ 31 21*36 ()(} 3 9 8 22438 775 6 2 '00602 78 164 29 ?i 21912 99396 22516 774^4 00604 78088 28 33 21987 22-93 77407 oo6c6 78013 i? 34 22062 9939 2 226 ;o 77330 00608 7793$ 26 ' 1 3< 22137 99300 22747 77*53 00610 77S63 2 5 \ 2221 I 99388 za8a 4 77176 00612 777- ; ') 24 1 I 37 22901' 77099 00615 77/14 23 ! 3* 22361 99323 22977 77-23 00617 77639 ^ I 39 2Z4e-cant- M, 60 TASLF. V. Of ARTIFICIAL Sine*, Tangents, and Secants. 10 Deg, M.f Sine. L k ... Co- fine Tangent. C.*-iang. Decant. Co-fecant , O 9.43967 9-99335 9.24632 10/75368 10.00665 10.76033 60 J 24039 99333 24706 75294 00667 75961 59 2 24210 9*n* 24779 75221 00669 75^90 58 3 24181 99U3 24*53 75 J 47 00672 75819 57 4 t*jj| 99326 24926 7574 00674 75747 56 5 " 2|?24 993*4 25000 75000 00676 75676 55 6 24395 993-2 250/3 74927 00678 75605 54 7 24466 993^9 25146 74* ^4 00681 75534 53 8 24536 993X7 25219 74/3i 00683 75464 52 _ .4607 99315 25292 74708 00685 75393 5' 10 9.44677 -9- 99.? 1 3 9.25365 10.74635 10.00687 10.75323 5 1 1 24748 99310 25437 745 6 3 00690 75-5* 49 12 4*ll 99308 25510 74490 00692 75182 4 S M 99306 25582 744l8 00694 75112 47 '4 24958 99304 25655 7414J 00696 75t* 46 15 2^028 99301 25727 74273 00^99 74972 45 16 25098 99299 25799 74201 00701 74902 44 1 17 25168 99297 25871 74^9 00703 74^2 43 5*57 99294 25943 74057 00706 747^3 42 f 19 25307 99292 2601 5 739 8 5 00708 74693 4* 20 9-*5J7* 9.99290 9.26086 IO-739H IO. CO/10 10.74624 40 11 5445 99*9* 26158 73^42 00712 74555 39 22 25514 99285 26229 73771 00715 744*6 38 23 *5$M 99283 26301 73699 00717 744 7 37 1 24 25651 99281 26372 73628 007:9 74348 36 I 2 5 25721 99278 26443 73557 00722 74 2 ~9 35 ; 26 25790 99276 46514 73436 00724 74210 34 ! ! 27 15558 99274 26'^ 734 r 5 00726 74142 33 28 25927 99271 26655 73345 00729 74 7 3 32 : 29 t95 99269 26726 73274 00731 74005 -!L : 30 3.26063 9.99267 26797 0.73203 ro 00733 0-73937 3o 51 26131 99264 26867 73i>3 00736 , 7Jf 29 32 26199 99262 26937 75063 00738 73^01 28 33 26267 99260 27008 72992 00740 73733 2? 34 26335 99 2 57 2707$ 72292 00743 73665 26 35 26403 91^55 27148 72:452 00745 73597 2 5 36 .76470 99252 27218 727^2 00748 73530 24 37 4>5)S 99250 27288 72712 00750 73462 2 3 38 26605 99148 27357 72643 00-52 73395 22 39 26672 99245 27427 72573 00755 73328 21 40 9.26739 .99243 .27496 10.72504 0.00757 to. 73261 20 4 1 26806 99241 27566 72434 00759 73194 *9 42 26873 99238 27635 72365 00762 73127 18 4? 26940 99236 27704 72296 00764 73060 17 44 -27007 99*33 27773 72227 00767 72993 16 45 -7^73 99 2 3i 27841 72158 00769 72927 15 46 27140 99229 2~QTI r 72089 0077 r 72860 *4 47 27206 99226 27980 72020 00774 72794 J3 48 27273 99224 28049 71951 00776 72727 12 49 27339 9922T 281 17 71883 00779 73661 11 5 .27405 9.99219 2X186 to. 71814 0.00781 0.72595 10 51 2747 1 99217 28254 71746 0078? 72529 9 52 27537 99214 28323 71677 00786 72463 8 53 27602 99212 28391 71609 00788 72393 7 54 7$8 99209 28459 71^41 00791 72332 6 55 7734 99207 28527 7*473 00793 72266 5 5 6 27799 99204 2*595 7 > 4 "> 00796 72201 4 '7 27864 99202 28662 71338 00798 72136 3 58 27930 99200 28730 71270 00800 720 ;o 2 59 27995 99*91 28798. 71202 00803 72005 - I 60 28060 99*95 28865 7H35 00805 71940 I Co-fine. Siae. 'Co-tang. Tangeut. Co-fecant. 1 Secant. ' M. 79 TABLE V. Of ARTIFICIAL Sines, Tangents, and Secnnts. n M. bine. Co- line Tangent. Co- tang. Secant. (Co fecant *" o 9.28060 9.99195 9.28865 10.71135 10.00805 '10.71940 oc I 28125 99192 18933 71067 oo8o3 7i&?> 59 2 28190 99190 19000 71000 00810 71810 5* 3 28254 99187 29067 70933 008 r 3 71746 57 4 28319 99185 29134 70866 00815 71681 56 I 5 283*4 99182 29201 70799 ooSrS 71616 55 6 28448 99180 29268 70732 00820 7*552 54 7 28512 99*77 29335 70665 90823 71488 53 8 28577 99*75 29402 70598 00825 7H23 52 9 2864.1 99172 29468 70532 00828 7*3 59_ 5* 10 9.28705 9.99170 9~29535 10.70465 jo.coSjo 10.71295 5 j n 28769 99167 29601 70399 00833 7^31 49 ' 12 *38 3 3 99165 29668 70332 00835 71167 4 S i 13 28896 99162 2 9734 70266 00838 71 104 47 14 28960 90100 29800 7ozoo 00840 71040 46 15 29024 99*57 29866 70134 00843 - 70976 45 : 10 49087 99*55 2993* 70068 00845 79*3 44 17 29150 99152 29998 70002 00848 708 ^o 43 18 29214 99150 30064 69936 00850 70786 42 i *9 29277 99147 30130 69870 00853 . 70723 41 1 iO 9.29340 .,.99145 9.3'9S 10.6* 505 io.ooS5 10.70660 40 1 21 2940$ 99142 30161 69739 008 sS 7c794l 60930 68871 11 i 50 .31189 .90067 .32122 10.67878 10.00933 10.68811 IO ! 51 31250 99064 32185 67815 00936 68750 9 52 31310 99062 32248 677?* 00938 68690 8 53 31370 99059 32311 67689 00941 68630 7 54 3H30 99056 3*373 67627 00944 68570 4 55 3H90 .99054 32436 67564 00946 6^510 5 56 31549 99051 32498 67502 00940 68451 .4 57 31609 9904? 3*561 6/439 00952 68391 3 58 31669 99046 32623 6/377 009 c 4 68331 2 59 37*S 99043 32685 *1&4 009 < 7 68272 I 6 o 31788 99040 3*74^ 67253 00^60 68212 Confine. Sine. Co- tang. (Tangent. Co-fccant! Secant. M. M TABLE V. Of A RTI^ICIM, Siftes, Tangents, and Secants. 12 Degs, M. Sine, i Co- fine. 1 "anjrent. [Co-tang Secant. 2o-fecant. * .31788 .99040 "3*747 0.67253 0.00960 0.68212 "6o~ i 3 lS 47 99030 32^10 67190 00962 60153 59 2 31907 ' 99? 5 32872 67128. 00965 68093 58 3 31966 9*032 3?933 67067 00968 68034 57 4 32015 ' 99030 32995 67005 00970 67975 56 5 32004 90027 33057 66943 00973 67916 55 6 32143 99024 331*9 66i8i 00976 67857 54 7 32202 99022 33180 66830 00978 67798 53 8 32261 99019 33242 66758 00981 67739 52 9 32-319 99016 33.^3 66697 00984 67681 5 1 10 9-3237* 9.99013 }-333 6 5 10,66635 10,00987 0.6/622 5 u 32437 99 '.* 33426 66574 009^9 67593 49 12 3 2 495 99008 334S? 66513 00992 67505 48 1.3 32553 99005 33548 66452 00995 67447 47 H 32612 9yU2.2 33609 66391 00998 673^3 46 15 32670 99090 336/0 66330 OIOOO 6/330 45 16 32728 98997 33731 66269 01003 67272 44 i? 327*6 98994 33791 66208 01006 67214 43 !8 32844 '^8991 33853 . 66147 01069 67156 42 *9 32902 989*9 339 * 3 66087 . CIOII 67098 4 1 20 9.32960 9.98986 9-33974 10. 66026 10 01014 10.67040 40 zr 33018 98983 3434 65966 01017 66982 39 22 33075 98980 3495 65905 OI02O 66925 38 23 3|*33 98978 34'55 65S45 OI022 66867 37 24 33190 98975 34*U 65785 OI025 66810 36 25 33248 98972 34276 65724 01028 66752 35 | 26 33305 98969 34336 65664 01031 66695 34 Z7 333 6 2 98967 34396 65604 01033 66638 33 28 334*o 98964 34456 65544 01036 66>8o 32 29 33477 98961 345i6 65484 -01039 66523 3i .30 9-33534 9.98958 9-34576 10,65424 10.01042 10.66466 30 i 3* 33591 9 8 955 34 6 35 65365 01045 66409 29 i 3^ 33647 9 8 953 34695 65305 01047 66353 28 ; 33 33/4 98950 34755 6^245 01050 66296 *7 34 337^1 98947 34814 65186 01053 66239 26 35 33818 98944 34874 65126 01056 66182 25 36 33874 98941 34933 65067 01059 66126 -4 37 339-3 1 98938 3499 * 65008 cno6z 66069 -3 38 339 8 7 98936 35051 64949 olo64 66013 ^z ; 39 3443 98933 35111 64889 01067 65957 21 1 40 9.34100, 9.98930 9.35170 10.64830 10.01070 10.65900 :o ! 41 34156 98927 35229 64771 01073 65844 T 9 42 34212 98924 35288 64712 01076 657?3 18 43 34268 98921 35347 64653 01079 *S73* 17 44 343H 98919 35405 64595 01081 : 65676 16 45 3438o 98916 35464 64536 01084 65620 15 46 34436 98913 355*3 64477 01087 65564 '4' 47 3449 * 98910 3558i 64419 01090 65509 3 48 34547 98907 35640 64360 0-093 65453 12 49 34602 98904. 35698 64302 OTO()6 6539* II 5 9.3465? 9.98901 9-35757 10.64243 10.01009 10.65342. 10 5i 34" * 3 98898 355 64185 01 102 65287 9 52 347^9 98896 35873- . 64127 OII04 : 65231 8 53 34824 98893. 35931 64069 01 107 65176 7 54 34879 98890 3599 640 1 1 OHIO 65121 6 i 55 34934- ' 98887 36047 63953 01113 65066 5 56 - 349*9 98884 36105 63895 OHIO 65011 4 57 35044 9 SS8i 36163 63837 01119 64956 3 58 35099 98878 36221 63779 OII2Z 64901 a i 59 35154 98875 36279 63721 01125 64846 i L* 35209 08872 36336 63664 01128 64791 o Co fine 1 Sine. Co-tang,' Tangent. Co-fecant Secant, j M. TABLE V. Of ARTIFICIAL Sines, Tangents, and Secants 13 Degl M. Sine. Co- line. (Tangent.; Co-tang. Secant. Co-fecant i 2 3 4 5 9.35209 35^63 35318 35373 354'-7 35481 9.9^72 98869 98x67 9X864 .98861 98858 9.36336 36394 36452 36509 36566 36624 10.63664 63606 63548 03491 63434 63376 10.01128 01131 01133 01136 01139 '01142 10. 64791 64737 64682 64627 64573 645x9 6O 59 58 57 56 55 6 7 8 35536 3559 35644 98855 98852 98849 36681 36738 36795 6.33*9 63262 63205 01145 01 14^ 01151 64464 64410 64356 54 53 52 9 35698 98846 36852 63148 01154 64302 5 1 10 II 12 13 M 15 16 18 19 9-357^ 35806 35860' 359*4 35968 36022 36075 36129 36182 36236 9.98343 98840 98837 98834 98831 98828 98825 98822 98819 98816 9.36909 36966 37023 37080 37137 37^93 37250 37306 37363 374 r 9 10.63091 63034 62977 62920 62863 62807 62750 62604 62637 62581 10.01157 01160 01163- 01166 01169 011/2 01175 01178 01 iSi 01184 10.64248 64194 64140 64086 64032 63978 ' 63925 63871 63818 63764 5 49 48 47 46 45 44 43 42 20 9.36289 9.98813 9.37476 ro. 62524 lo.'oi i .'7 10.63711 40 2 I 22 23 3634* 36395 36449 98810 98807 98804 37532 37588 37644 62468 62412 62356 01190 01193 01196 636^8 63605 63551 39 38 37 24 36,02 98801 37700 62300 . 01199 63498 3 365^5 98798 3775 6 62244 OI2O2 63445 35 26 36608 98/95 3^8*2 62188 01205 63392 34 27 36660 98792 37868 62132 OI20'S 6334^ 33 28 36713 98789 37924 62076 OI2II 63257 3 2 29 36766 98786 37980 62020 OI2I4 63234 3' 30 31 32 33 9.36819 36871 36924 36976 9.98783 98780 98777 98774 9.35035 38091 38147 38202 10.61965 61853 61798 10.OI2I7 OI22O OT223 OI226 10.63181 63129 63076 63024 ' 3' 29 28 27 i (\ 34 37028 98771 38257 61743 OI229 62972 35 37081 98768 61687 OI232 6 2 Q i () 2 5 36 37 37133 37185 98765 98762 38368 .38423 61632 6i577 01235 0123 s * 628^7 62815 24 23 39 37237 37289 9 8 759 38479 61521 6r 4 66 OI24I 01244 62/63 62711 21 40 4 1 9-37341 37393 9.98733 98750 9.38589 38644 10.61411 61356 10.01247 OJ2 >O 10.62659 62607 2O 42 37445 98746 38699 61301 01254 62555 43 44 45 46. 47 37497 37549 376oo 3/652 37703 98743 98740 9S737 98734 98731 38754 38808 38863 38918 38972 61246 61192 61137 61082 61028 01257 OI26O OI263 01266 01269 62451 62400 62348 622Q7 16 15 13 4* 49 37755 378c6 98728 98725 39027 , 39082 60973 60918 01272 012/5 62245 62194 ii 50 5 1 53 .37909 37960 38011 9.987x2 98719 98715 90712 9.39136 39190 39245 39299 10.60864 6o3io 607-; 60701 1O.OI27& 01281 01285 01288 10.62142 62091 62O4O 61989 10 9 8 r 54 55 56 57 38062 38113 38164 38215 98709 98704 9870.3 98700 39353 3947 39461 39515 60647 60593 60539 60485 0129! 01294 01297, 02300 (11938 61887 61836 61785 5 4 3 58 38266 986,97 39569 60431 01303 61734. 59 3?^!7 98694 39623 60377 01306 ' 61683 60 38368 986.90 39^77 60323 OI3IO 61032 Co- fine. Sine. Co-tang.'Tangent. Co-fecant- Secant. . M m 2 76 Degree* V. Of ARTIFICIAL Sines, Tangents, and Secants. 14 Begs. M. Sine. Co- fine. Tangent- Co-tang. Secant. Co-fecant. o ,.38368 .98690 39677 0.60323 0.01310 to. 616^1 60 I 384*8 i 98687 39731 60269 01313 61582 3ft 2 38469 98684 39785 602 1 5 01316 6 1 S3 1 5* 3 38519 98681 39838 60162 01319 61481 57 4 38^70 98678 39892 60108 01322 61430 56 j 5 38620 98675 39945 60055 01325 61380 55 6 38670 98671 39999 . 60001 01329 61330 54 7 38721 98668 40052 59948 01332 61279 53 8 38771 98665 59 8 94 01 335 61229 52 9 38821 98662 40159 59841 01338 . 61179 10 9.38871 9. 986=59 ;. 40212 10.5978^ 0.01341 0.61129 50 ii 38921 98656 40-266 59734 01344 61079 49 12 38971 98652 40319 59681 01348 61029 48 13 39021 98649 40372 59628 01351 60979 47 14 39071 98646 40425 59575 01354 60929 46 15 39121 98643 40478 59522 01357 60879 45 16 39*70 98640 40^31 59469 01360 60830 44 : 7 59220 98636 40584 59416 01364 60780 43 18 39270 98633 40636 59364 01367 60710 42 '9 39319 98630 40689 593H 01370 60681 4^ 20 J9.39369 9.98627 9.40742 10.59258 10.01373 10.60631 40 21 39418 98623 4795 59205 01377 60582 39 22 39467 98620 40847 59 '53 01380 60533 38 23 39517 98617 40900 59100 ct?8 3 60483 37 39566 98614 40951 59048 01386 604H 36 25 396i5 98610 41005 5 8 995 01390 60385 35 26 39664 98607 41057 58043 oi393 60336 34 27 39713 98604 41109 58891 01396 60287 . 33 iS 39762 9860,1 41161 58839 01399 60238 32 29 398 r i 9*597 41214 58786 01403 60189 3* : 3 9.39860 9.98594 9.41226 10 58734 10.01406 10.60140 30 ! 3999 98^91 41318 58682 01409 60091 29 ! 32 39958 98588 41370 58630 01412 60042 28 j 33 40006 98584 41422 58578 01418 59994 27 : 34 40055 98581 4H74 58 -"2 6 01419 59945 26 35 40:03 415*6 58474 01422 59897 25 36 40152 98574 41^78 158422 01426 59848 24 3? 40100 98571 41629 58371 01429 59800 23 3* 4249 98^68 41681 58319 01432 597 5 r 22 J9_ 40297 ^565 4*733 58167 0^435 21 40 9^40346 9.98561 9.417*4 10. s82i6 10.01439 10. 59654 20 40J94 98558 41836 58164 01442 59606 19 42 40442 98555 41887 58n3 01445 59558 l8 43 40490 41939 J 58061 01449 59510 17 44 41990 <;3oio 01452 59462 16 45 1 40^6 9^ C 45 42041 57959 01455 594'4 15 46 40634 98541 42093 57907 01459 59366 '4 47 4068 ^ I 42144 5/856 01462 59318 13 48 40730 98535 i 42195 57805 01465 59270 12 49 40778 98531 j 42246 57754 01469 59-22 . II 50 9.408.15 19.4*29?' 10.57703 10.01472 10. ^9175 10 5 1 40873 98^25 41348 57652 01475 59*27 9 52 409 z r 98521 42399 57601 01479 5979 8 53 40968 98518 4:450 57550 0148* 59032 7 54 41016 9*5'5 42501 57499 1485 58984 6 55 41063 42552 57448 01489 58937 5 56 4:110 98508 42603 57*97 01492 58890 4 >7 ' 41158 98505 42653 57347 01495 3 : 58 ; 41205 98501 4 Z 74 57296 01499 58795 2 i 59 f 412^1 98498 42755 57245 01502 58748 I 60 i 4: :co 98494 42805 57195 01506 58700 'Co- line. bine. Co tang. Tangent. Co-fecant. Secant. M. 75 Degrees. TABLE V. Of ARTIFICIAL Sines, Tangents, and Secants. 15 Deg. M. Sine. Do-fiue. Tangent.! Co-tang. Secant. Co-fecanf. o 7.41300 98494 ). 42805 10.57195 10.01506 0.58700 60 I 4*347 98491 - 42856 57^44 01509 58653 59 I 4*394 98488 ; 42906 57094 01512 58606 58 3 41441 98484 4*957 57043 01516 5 8 559 57 4 41488 9 8 4 8i 43007 5^993 0151.9 5 5 J2 56 5 4'535 9 S 477 43057 56943 01523 58465 5,5 I 6 41582 98474 43108 56892 01526 58418 54 7 41628 98471 43158 56842 015*9 58372 53 8 41675 98467 43208 56792 01533 - 58325 52 9 41722 98464 _ 43258 5 6 74 l 01536 58278 5i 10 ? . 41768 ,98460 i 7.43308 io.5t.6gi 10.01540 0.58232 5 ii 4i8i5 98457 , 4335 s 56641 oi543 58185 49 12 41861 9 S 453 43408 56592 01547 58139 4^ 13 41908 98450 43458 56542 01550 58092 47 14 4*954 98447 43508 56492 oi553 58046 46 15 42001 98443 43558 5644 1 oi537 57999 45 16 42047 98440 43607 56393 01560 57953 44 17 42093 98436 43 6 57 56343 01564 57907 43 18 42140 98433 43707 56293 01567 57860 4* *9 42186 98429 4375JL 56244 01571 57814 41 20 9.42232 9.98426 9 43806 10.56194 10.01574 0.57768 40 21 42278 98422 43855 56145 01578 5772* 39 22 42324 98419 4395 56095 01581 57676 38- 23 42370 98415 43954 56046 01585 57630 37 14 42410 98412 44004 5599 6 01588 57584 36 ~-5 42461 98409 44053 55947 01591 57539 35 26 42507 98405 44102 55 8 98 01595 57493 34 i 27 42553 98402 44131 55849 01598 57447 33 23 4^599 98398 44201 55799 01602 57401 32 ! 29 42644 9$J9J 44250 5575 01605 57356 ;i 3O 19.42690 9.98391 {9.44299 io.5570i 0.01609 0.57310 >o 3 4-735 98383 I 4434S 55652 oi6iz 57265 29 1 32 42781 98384 ' 44397 55603 01616 57219 aS , 33 42826 98381 44446 55554 01619 57174 2/ ! 34 42872 9^377 44495 5555 01623 57128 26 35 42917 9*373 44544 55456 01627 570S3 25 36 42962 93/o 44592 5548 01630 57038 2 4 37 43008 98366 44641 55359 01634 56992 23 3$ 43053 98363 44690 553io 01637 56947 22 39. 43098 98359 4473* 515262 01641 56902 21 40 9-43H3 9.98356 9-44787 10.55213 10.01644 o. 56857 20 1 4i 43188 98352 44836 55164 01648 56811 1 9 i 42 43233 98349 44884 . 55116 01651 56767 ii 43 43278 9 8 345 44933 55067 01655 56722 17 44 433^3 98342 44981 55019 01658 56677 16 45 433 6 7 9^338 45029 5497 1 01662 56633 15 46 43412 9 8 334 45078 54922 01666 565*8 4 47 43457 98331 45i-6 54874 01669 56543 13 4 43502 98327 45i"4 548*6 01673 56498 i:. 49 43 54 6 98324 ' 452*2 54778 01676 56454 . r 50 9-4359 1 [9.9*320 19-4527J 10.54729 10.01680 10.56409 jo ' 51 43635 98317 453*9 54681 01683 563' J 5 9 5* 436^0 98313 453*7 54633 01687 56320 8 53 437M 9*309 45415 545^5 01691 56276 7 i 54 43769 98306 45463 54537 01694 563J 6 55 43813 98302 455" 54489 01698 56187 5 56 43*57 98299 45559 54441 01701 561-13 4 57 43901 98295 45606 54394 01705 56099 3 58 43946 98291 45^54 5434 6 01709 56054 2 59 43990 98288 45702 54298 01712. 56010 I 60- 44034 98284 4-750 54250 01716 56966 O Co. fine. Sine. Co- tang. 'Tan gent. Co-fecanti Secant. M. 74 Degree*, V. Of ARTIFICIAL Sines, Tangents, and Secants. 16 Degs. M. Sine, i Co-fine. Tangent. Co-tang. Secant. Co-fecant. o 9.44034 9.98284 9.45750 10.54250 10.01716 10.55964 00 I 4478 98281 45707 5I 2 3 01719 55922 59 2 44122 98277 45^45 54 Z 55 01723 55878 58 3 44166 9^273 45892 54108 01727 55834 57 4 44210 98270 4594 54060 01730 55790 ,-6 5 44^3 98266 45987 54013 01734 55747 55 6 44297 98262 46035 53965- 01738 55703 54 7 4454' 98259 46082 539i8 01741 55659 53 8 44?$ 5 58*55 46130 52870 01745 55615 . S2 9 44428 98251 46177 53823 01749 55572 51 10 9-4447* 9.98248 9.40224 10.53776 10.01752 10.55528 5 ii 44516 98244 46271 537^9 0175.6 55484 49 12 44559 98240 4 6 3 '9 5368i 01760 55441 48 1} 44602 98257 46366 53634 01763 55398 47 T 4 44646 98233 464*3 53587 01767 55354 46 r> 44689 98229 46460 53540 01771 553H 45 16 44/33 98226 46507 53493 01774 55267 44 I? 44776 98222 46554 53446 017-8 55224 43 18 44819 98218 46601 53^99 01782 55181 42 19 44862 98215 ; 46648 5335^ 01785 55U8 4i 20 9.44905 9.98211 9.46694 10.53300 10.01789 10.55095 40 21 44948 98207 46741 53259 ??7,9| 55052 39 22 44992 98204 46788 5 3 2r2 01796 55008 }8 f^3 4535 98200 46835 53165 01800 54965 3" *4 4577 98196 46881 53H9 01804 549*3 ^6 *5 45120 98192 46928 53072 01808 54880 3=5 26 45163 98189 46975 53025 01811 54837 34 27 45206 98185 47021 52979 01815 54794 33 28 45249 98181 47068 52932 01819 54751 3 2 29 45292 98177 47114 52886 01823 54708 31 3*5 9-45334 9.98174 9.47160 10.52840 10 01826 10. 54666 30 5 45377 98170 47207 52793 01830 54623 29 32 454 T 9 98166 47^53 5-747 01834 5458i 28 33 4<4 6 2 98162 47299 52701 01838 54538 27 34 4S54 9^59 4734 6 52654 01841 54496 26 3^ 4>S47 9811:5 4739^ 52608 01845 54453 2 5 3$ 45^0 98151 4743^ 52562 01849 544" 24 37- 45632 98147 474^4 52516 01853 54368 23 i 3? 45674 98144 4753 52470 01856 54326 22 39 45716 98140 475/6 52424 01860 54284 21 9-45758 9.98136 9.47622 10.52378 10.01864 10.54242 20 41 45 Soi 98132 47668 52332 01868 54199 19 f 42 45^43 98129 477*4 52286 01871 54 r 57 18 ! 43 45^5 98125 4776o 52240 01875 54H5 17 44 459 2 / 98121 47806 5 2 i94 01879 54373 16 i 4.5 45969 98117 478^2 52148 01883 5403 r 15 46 46011 98113 47897 52103 01887 53989 H 1 47 460 > 3 98110 47943 52057 01890 53947 n ' 4 s -4609 5 98 106 47989 5201 r 01894. 5395 12 49 46136 98102 4 8 35 51965 01898 53864 II 9.46178 9.98098 9.48080 10.51920 10.01902 16.53822 IO <;r 46220 98004 48126 51874 01906 53780 9 C.2 46262 98090 48171 51829 01910 53738 8 ! 53 46303 98087 4&U? 5'73 01913 53697 7 ; ^4 46345 9 S 83 48262 5'73 01917 53655 6 55 46386 98079 48307 51693 01921 536J4 5 <6 46428 98075 4 8 35,3 51647 01925 53572 4 " 46469 98071 4*398 51602 01929 5353 - 3 c8 46511 98067 4844? 5 r 557 01933 53489. 2 < ^9 46^2 98063 48489 5 T 5i J 01937 534,48. I 60 46594 . 98060 4 3c 34 31466 O 1 <-(-'. 55406 i Co fine. bine. 'Co- tang. Tangent. Co iecant. Secant. M. 73 Degrees. TABLK V. Of ARTIFICIAL bines, langents, and bccants. 17 Deg. M. Sine. Co-fine. Tangent. Co- tang. Secant. BTTi** Co- fecant. 9.46594 9,. 98060 ) 4*534 10 .51466 10.01940 10.55406 60 I 46635 98056 48579 51421 01944 53365 59 z 46676 98052 42624 5*32.6 01948 533H 58 3 46717 98048 4.8669 5*331 0195* 53283 57 4 46753 98044 48714 51286 01956 53242 56 5 46800 98040 48759 51241 01960 53200 55 6 46841 98936 48804 51196 01964 53159 54 7 46882 98032 48849 5"5* 01968 53^ 53 8 4 6 9 2 3 980^9 48894 51106 01971 53077 52 9 46964 98025 48939 51061 01975 53036 5^ 10 9.47005 9.98021 9.48984 10.51016 10.01979 10.52995 50 ii 47045 98017 49029 50971 01983 52955 49 I? 47086 98013 49073 50927 01987 52914 4 B 13 47127 ' 98009 49118 50882 01991 5 2 73 47 14 47168 4,98005 49 l6 3 50837 *&99S 52832- 46 15 47209 98001 49207 50793 01999 5 z7 9 i 45 16 47249 97997 49252 50748 02003 .5*751 44 17 47290 97993 49296 50704 . 02007 527TO 43 iS 47330 9/989 49341 50659 O2OI 1 52670 4- 19 47371 97986 49385 506 "15 02014 52629 4* 20 9.4741* 9.97982 9.49430 10.50570 I0.020J8 10.52589 40 21 474 5 i 97978 49474 50526 O2O2Z 5^54 39 Z2 47492 97974 49519 50481 0202.6 52508 3* 23 47533 97970 49563 504-37 02030 57.467 37 Z4 47573 97966 49607 50393 02034 52427 36 *5 476i3 97962 49652 50348 02038 5238- 35 26 4765$ 9795 s 49696 50304 02042 5 2 146 34 27 47694 97954 49740 50260 02046 52306 33 28 47734 9795.0 49784 50216 0205O 52266 V- 29 47774 97946 - 49828 50172 020s4 5^226 3i 30 9-47r4 " 9.97942 9,49871 lQ.5"OJ2o tO-0205,8 10. s-^86 3 1 47854 97938 49916 5 op? 4 02062 57.146 2 9 3P 47894 97934 49960 50040 01066 52106 28 23 47934 9793 50004 49996 02070 5206$ 27 34 47974 97926 50048 49952 02074 5^026 z6 35 48014 97922 50092 4'J9 S 02078 ^1906 2 5 3^ 48054 97918 50136 49864 ^20' i 5i94<> 24 37 48094 97914 50180 49820 ozo36 51906 2 3 38 48133 97910 502.23 49/7? O2OOO 51 Ho; 39 43i73 97906 50267 49733 0,'. 51827 40 ;.48*i3 9.97002 9.50311 10.49689 IO.02C 10.5;- 4 1 4*252 97M 50.355 49 64 5 U L i ,'. 5^74-3 42 48x9* 97894 50398 49602 Q2i05 si 70S ^8 43 4 8 332 97890 50442. 49558 O2 I iO 51665 44 48371 97886 50485 49515 021 14 51619 16 45 48411 . 97^8 ? . 5$29 49471 ozri3 5-15&9 i 5 46 48450 97878 50572 49428 O2 122 51550 14. 47 48490 97874 50616 49384 0-126 51510 T J 3 ! 48 48529 97870 50659 49341 02130 514/1 12 49 48568 97866 50703 49297 02134 5H32 1 1 50 9.48607 9.9786! 9 5 746 10.49254 10,02139 10.51393 IO fi 48647 9/857 50789 49211 02143 5M53 9 S^ 48686 97853 50833 49167 02147 5!3'4 8 53 48725 97849 50876 *4 9 i24 02151 5 '-75 .7 54 48764 97845 50919 49081 02155 5^36 i 55 48803 97 8 4i 50962 49038 02159 5JI97 5 56 48842 97837 5 r o5 48995 02163 5^58 4 57 48881 97833 51048 4*95* 02167 51119 -i 58 48920 97829 . 51092 4^908 0.1171 510SO 2 59 48959 97825 '5"35 48865 02175 5I04I 60 48998 97821 51178 48822 02179 51002 Co-fine. Sine. Co- tang. Tangent Co fecant. Secant. M. 72 Degrees TABLE V. Of ARTIFICIAL Sines, Tangents, and Socants. 1 8 Begs. M. Sine, i Co fine. Tangent. Co -tang. Secant. Co-leont o .48998 9.97821 9.51178 10.48822 0.02179 io. 51002 60 1 49037 97817 51221 48779 02183 50963 59 2 49376 97812 51264 48736 021*8 50924 58 3 49U5 97808 51306 48694 01192 50*85 57 4 49*53 97804 5*349 48651 02196 50847 56 5 49191 97800 51392 48608 O220O 50808 55 6 49231 97/96 5H35 48565 022O4 50769 54 7 49269 9779 51478 48522 02208 50731 53 8 49308 97788 51520 48480 02212 50691 52 9 49347 97784 51563 4 8 4?7 022l6 50653 51 10 .49385 9-97779 9.51606 10.48394 0.02221 0.50615 5 ii 49424 97775 51648 48352 02225 50576 49 \i 49462 97771 51691 48309 O2229 50538 4 S 13 49500 97767 51734 48266 02233 50500 47 M 49539 97763 51776 48224 02237 50461 46 15 49577 97759 51819 48181 O224I 50423 45 16 49<>i5 97754 51861 48139 02246 50385 44 l l 49654 W75 51903 48097 2250 50346 43 18 49691 9774 6 51946 48054 02*54 50308 4* 19 4973 9774* 51988 48012 02258 50270 41 20 3.4976$ 9-97738 9.51031 10.479-9 0.02262 to. 50232 40 21 49806 97734 52073 4:927 02266 50194 39 22 49844 97729 ' 52H5 47885 01x71 50156 38 23 498*2 97/25 52*57 47843 02275 501 18 37 24 49920 97721 52200 47800 oz27 9 50080 36 25 49958 977'7 52242 4775* 02283 50042 35 26 49996 977U 52284 47716 02287 50004 34 ^7 5034 97708 52326 476/4 C2292 49966 33 28 50072 97/04 52368 47632 02196 49928 3* -9 50110 97700 52410 475QO C2300 49890 3i 30 9.50148 9.97696 9.52452 10-47548 0.02304 10.49851 30 3' 50185 97691 5M94 47 56 02309 1 49815 2,9 32 50213 97687 5253 r > 47464 02313 49/77 28 ! 33 50261 97683 52578 47422 02317 49739 2? 34 50298 97679 52620 47380 02321 49701 26 35 50336 9/674 52661 47339 02326 49664 25 36 50374 97670 52703 47297 02330 49626 24 37 50411 97666 52745 47255 02334 49589 23 3S 50449 97662 5-7*7 47:i3 02338 49551 22 39 504*6 97657 5282.9 47i7i 02.343 49514 2 I i 4 9,50523 997fc53 9.52870 10.47130 10.02347 10.49477 20 . 4I 50^61 97649 52912 47088 02351 49439 19 4* 50598 97645 5*953 47047 0*35$ 49402 18 i 41 50635 97640 5 2 995 47005 02360 49365 17 44 5 c6 73 97636 53037 46963 02364 49327 16 1 4-5 50710 97632 53078 4697.2 02368 49290 *5 46 50747 97628 53120 46880 02172 49253 4 47 507?4 .97623 51161 .46839 02377 49116 13 4 ^c%^\ 97619 ' 53202 46798 02381 49179 12 i 49 50858 97615 53244 46756 023*5 49142 II 50 9. 50896 9.97610 9-53285 10.46715 10.02390 10.49104 IO 51 50933 97606 53327 46673 02394 49067 9 52 5*970 97602 53363 46632 02398 49030 8 53 510*7 97597 53409 46591 02403 48993 7 54 5*043 97593 5345 46550 02407 4 S 957 6 55 51080 97589 53492 46508 02411 48920 5 56 5HI7 975*4 53533 46467 02416 48883 4 57 5H54 97580 53574 46426 02420 48846 3 58 51191 97576 53 6 5 46385 02414 48809 2 59 57227 9/571 53656 4 6 344 02429 48773 I 60 51264 975 6 7 53697 46303 02433 48736 O i Co-fine. ' Sine. Co-tang. Tangent Coiecant Secant. M. Degree*, TABLE V. Of ARTIFICIAL Sines, Tangents, and Secants. M. Sme. Co-fine. Tangent. Co-tang, i Secant. C~-fecant- M o .51264 9-97567 3.53697 0.46303 0.0*433 10.4^:56 60 1 Sijci 97563 5373^ 46262 02437 48699 "9 2 5*338 97558 53779 4$2ZT 0244* 48662 58 3 5*374 97554 53810 46l80 02446 48626 57 4 51411 97550 53861 4<5l39 02450 48589 56. 5 5 '447 97545 5392 46098 02455 48553 55 6 51484 9754 1 53943 46057 Q24S9 48516 54 7 51520 97536 53984 46016 02464 48480 53 8 5 [ 557 97532 ' 54 2 5 45975 02468 48443 5 9 5- r 593 97548 : 54065 45935 02472 48407 5r 10 .5:629 ,>'97523 9. =54106 0.45894 0.02477 0.48371 50 ii 51666 97519 54H7 45853 02481 48334 49 12 5170* ; 975*5 54^7 458i3 02485 48298 48 13 5^738 - 97510 54228 4577* 02490 48264 47 4 51774 ' 97506 54269 4<73 T 02494 48226 46 5 51811 97501 54309 45691 02499 48189 45 16 51847 97497 5435 45650 02503 48153 44 17 51 88 3 97492 54390 45610 02508 48117 43 18 51919 97488 54431 45569 02512 48081 4* 19 5'9^5 , 97484 54471 455*9 02516 48045 41 20 .51991 9-97479 9.54512 o 45488 o 02521 10.48009 4 b 21 5202-7 97475 54552 45448 02525 47973 39 22 52063 97470 54593 45407 02530 47937 3 23 52099 '^7466 54633 45367 02534 47901 37 24 5 2I 35 9746i 54673 453*? 02539 47865 36 *s 52171 97457 54714 45286 02543 47829 35 26 52207 97453 54754 45246 01547 47793 34 27 52242 9744? 54/94 45206 Ci552 47758 33 ! 28 52278 97444 54835 45165 02556 47722 32 29 5 2 3i4 97439 54875 45 I2 5 O25'JI 47686 3i i 3o 9.^2350 9-97435 9-549 r 5 10.45085 0.02565 10.47050 30 r 31 52385 97430 54955 45045 02570 47615 2 ? 32 54-421 97426 54995 45005 02574 47579 28 33 5*456 974*i 55035 449*5 - 02579 47544 27 34 52492 97417 55075 449^5 04583 475o8 26 35 5:2527 974*2 55^5 44885 02588 47473 25 I 36 5*563 ' 97408 55155 44*45 02592 47437 24 1 37 52598 974^3 55^95 44805 02597 474C4 25 38 51634 97399 55235 447^5 0?.OOI 47366 22 39 52669 97394 55^75 44725 02606 47331 2T 40 -) 52705 9-97390 9-553*5 10.44685 10.02610 10.47295 20 4* 52740 97385 55355 44645 0261 J 47260 J 9 4* 5*775 9738r 55395 44605 02619 47225 18 43 52811 55434 4-4^66 02624 47189 17 44 52846 97372 55474 44:26 00628 47 J 54 16 45 52881 97367 555.M 444 6 02633 47119 '5 46 549 T 6 97363 55554 4444 6 02637 47084 H 47 52951 973^8 55593 44407 . 02642 4749 ij 1 4 * 51986 97353 55633 44367 02647 47014 ia 49 $302 1 9/349 55673 443*7 026 q i 46979 1 : ' i 1 50 9-53056 9-9/344 9.55712 10 44*88 10.02656 16.36944 10 ] 5i 53092 97340 5575 2 44248 026^:0 46908 9 52 53126 97335 5579i 44209 02665 46874 8 53 53161 97331 55831 44169 02669 46839 7 I 54 53i9 6 97326 55870 44130 02674 46804 6 1 55 53^31 97322 . 559*0 44090 02673 46769 5 1 56 53266 97317 -55949 44051 02683 46734 4 I 57 53301 97312 55989 44011 02688 46699 3 ' 1 5* 53336 57308 56028 43972 02692 46664 2 1 59 53370 97303 ^6067 4 7 ^33 02697 46630 I 11 6o 534^5 97299 56107 43*93 02701 46595 C 1 Co- line. Sine. Co-tang Tangent Co-fecant. Secant. M. j Degrees. . Of ARTIFICIAL Sines, Tangents, and Secants, do M. Sine. , ^o-fme. {Tangent. Co-tang. | Secant. Do-fecant. .53405 .972-99 . 56107 0.43893 O.O2/OI 0.46595 60 i 53440 97-94 56146 43*54 02706 46560 59 2 53475 97289 56185 438i5 O27H 46525 53 3 53509 972.85 56124 43776 01715 46491 57 4 53544 97280 56264 43736 02720 46456 56 5 53573 97276 56303 43697 02724 46422 55 6 536i3 97171 5 6 342 43658 02729 46387 54 7 53647 97266 563^1 4^619 0*734 46353 53 S 53 68z 97262 5^420 43580 02738 46318 52 9 537i6 97257 56459 43541 02743 46284 51 10 9-53751 .97252 9.56498 10.43502 0.^2748 0.46249 50 n 53785 97248 5 6 537 43463 0x752 46215 49 ii 53819 9/243 5 5 57 6 43424 02757 46181 48 13 53854 9,7M 56615 433B5 02762 46146 47 14 53888 97234 56654 43346 02766 46112 46 15 5392* 97229 56693 43307 02771 46078 45 16 53957 97224 56731 43268 02776 46043 44 17 53991 97*20 5 S 771 43229 02780 46009 43 18 54025 97215 56810 43i)0 02785 459/5 42 i' 54059 97210 56849 4JiSf OfcTJQ 41:041 4* 20 9-54v3 9.97206 9.56887 10. 43113 O.O2" ,4. 10.45907 40 21 54 I2 7 57201 56926 43074 02799 45873 39 : 22 54161 97196 56965 43035 02804 45 8 39 38 13 54*35 97192 57004 42996 02808 45805 37 4 544*9 97187 5704* 42958 4577 J 3* a 5 54263 9718* 57681 42919 02Sl8 45737 35 26 54297 97178 57120 42880 02822 457-03 34 '27 5433 1 97173 57158 42842 02827 45669 33 a8 54365 97168 57197 42803 02832 45635 32 29 54399 97163 5/235 41765 04837 45601 3i 30 9-54433 9,97159 9-572/4 10.42726 10*02841 10.45507 ?o 3 1 54466 97154 57312 42688 0^846 45534 la 32 54500 97149 57351 42649 <38 5, 455oo 28 33 54534 97H5 57389 41611 02855 45466 27 34 54567 97140 57428 42572 02860 45433 16 35 54601 97U5 57466 42534 02865 45399 25 36 54635 97130 57504 42496 02,870 45365 24 37 54668 97126 57543 42457 02874 45332 23 3 54702 97121 5758i 42419 02879 45298 22 39 54735 97116 57619 42381 028^4 45265 21 40 9.54769 9.97111 9*5765* 10.42342 10.02889 [0.45231 20 4 1 54 3oz 97107 57 6 96 4^304 02893 45*98 T 9 4* 54836 97102 57734 42266 02898 45i f 4 18 43 54869 97097 577/2 42228 02903 45U* l l 44 5493 97092 5;8fO 42190 02908 45097 :6 45 54936 97087 57849 42151 02913 45064 15 46 $49*9 97083 57887 4 2 H3 02917 453i H 47 5500-? 97078 5/9*5 42075 0:922 44997 J3 4 s 55036 97073 57963 42037 02927 44964 12 49 55069 97068 58001 41999 02932 44931 II 50 9,55'* 9.97063 9.54039 10.41961 10.02937 10.44.398 10 5 1 55 r 36 . 97059 58077 4197,3 02941 44864 9 52 55169 97054 58115 41*85 02946 44831 8 53 552G2 97049 5 Sl 53 41847 02951 44798 7 54 55235 . 9"/44 5^t9l 4.1809 02956 44765 6 55 55268 97039 58229 41771 02961 44732 5 56 5,5301 9703: 58267 41733 02965 44699 4 57 55334 97030 5*304 41696 02970 44666 3 ! 58 55367 97025 . 5*342 41658 02975 44 6 33 2 59 55400 97020 58380 41620 02; go 44600 X ; 60 -33 9/3*5 58418 41:581 02985 44567 o ; Co-fine. Sine. Co-tang Tangent Co-fecant. Secant, M. ; Degrees* TABLE V. Of ARTIFICIAL Sines, Tangents, and Secants. 21 Begs. M. ' Sine. Co-fine Tangen Co-tang Secant. Co-fecan f. 9-554*3 9.97015 9.^8418 10.41582 10.02985 10.44567 60 55466 97010 58455 454'5 02990 44534 59 55499 97005 58493 41507 02995 445oi 58 5553* 97001 5*53i 41469 02999 44468 57 t 55564 96996 58569 4*431 03004 44436 56 5J597 96991 58606 41394 ' 03009 44403 55 6 55630 96986 58644 41356 03014 44370 54 7 55663 96981 58681 4 r 3 T 9 03019 44337 53 8 55695 96976 58719 41281 03024 44305 52 9 5572* 9697,1 58757 A 124.3 03029 44272 5i 10 9.55761 9 96966 9-5^794 10 4:206 ro. 03034 lu. 44239 50 *' 55793 96962 58832 41168 03-338 44207 49 12 55826 96957 58869 41131 03043 44174 48 13 55*5* 06952 5*97 4 I0 93 03048 44*42 47 H 55891 96947 58944 41056 03Q53 44109 46 r 5 559*3 96942 5898' 4:019 03058 45 16 5^956 96937 59019 40981 03063 44044 44 17 55988 96932 5->56" 4-944 0306* 44012 43 18 56021 96927 50094 40906 03073 43979 42 *9 56053 9692.2 59 1 ? 1 40869 03078 43947 - 1 20 9.5*085 9 96917 59168 10.40832 0.03083 10.439.15 40 21 5^118 96912 59 i0 5 4795 03088 43882 39 22 5 6l< 5P 96907 59M3 4757 03093 43850 38 23 56182 96903 59280 40720 03097 43^8 37 H .56215 96898 59317 40683 03102 43785 36 25 .,'56247 96893 59354 40646 03107 43753 35 26 .56279 9 6S38 5939 1 40609 03) 12 43721 34 27 56311 96883 59429 40571 03U7 43689 33 28 56343 96878 59466 4534 03122 43657 32 29 56375 96873 595>3 4497 0?I27 43625 31 SG .56408 .96868 59540 0.4:460 0.03132 0.43592 30 3* 56440 96^63 59577 44 2 3 0337 43560 2 9 3* 56472 96858 59 6l 4 40386 03142 43528 28 33 5 6 54 96853 59651 40349 03H7 43 19 6 27 34 56536 96848 59688 40312 C3J5 2 43464 26 35 56568 96843 59725 40275 03157 43432 *5 36 56599 96838 59762 40238 03162 43400 24 37 56631 96833 59799 40201 03167 43369 23 38 56663 96828 59^5 40165 03172 43337 22 39 5.6695 96823 59 8 72 40128 03177 4?35 21 40 .56727 .96818 .59909 0.40091 0.03182 0-43273 20 4i 56/59 96813 59946 40054 03187 43M 1 19 42 56790 96808 599 8 3 40017 03192 43210 18 43 56822 96803 ; 60019 39981 03197 43*78 J 7 44 56854 96798 60056 39944 03202 43146 16 45 56886 96793 60093 39907 03207 43114 15 46 56917 96788 60130 39870 03212 43oS3 H 47 56949 96783 60166 39 S 34 03217 43051 13 48 56980 96778 60203 39797 03222 43020 12 49 57012 96772 60240 39760 03228 42988 I 50 .57044 96/67 60276 0-39724 0.03233 o 42956 O 5i S/075 96762 60313 39687 03-3* 4,925 9 52 57107 96757 60349 39651 03 2 43 4*893 S 53 57138 96/52 60386 396J4 03248 42862 7 54 57169 96747 60422 39578 03253 4283! 6 55 57201 96742 604^9 3954 1 03.258 4*799 5 56 57232 96737 60495 3955 0:5263 42/68 4 57 57264 96732 60532 39468 03268 42/36 3 58 57295 96727 60568 39432 03273 42705 2 59 57326 96722 60605 39395 03278 42674 i 60 57353 96717 60641 ?93"9 03*83 42642 Dp fine. Sine. p-tang.i Tangent. Cq-fecant Secant. vT 68 Degrees, TABLE V. Of ARTIFICIAL Sines, Tangents, and Secants. 22 Degs, ; M. Sine. Co-fine. rTangent< Co-tang. Secant i Co-fecant. o ) 573 v^ 9.96717 9.60641 10.39359 10.03283 10.42642 60 I 57389 96711 60677 393^? 03289 42611 59 i 57410 96706 60714 39286 03294 42580 5* 3 57451 96701 60750 $9*5? 03299 4 2 549 57 4 57482 96696 60786 39 ir 4 03304 42518 56 5 57514 96691 60823 39 r 77 03309 42486 55 6 57545 96686 60859 39*4* 03314 4H55 54 7 57576 96681 60895 39105 03319 42424 53 g 57607 96676 60931 39069 03324 4^393 5 2 ! 9 57638 96670 6oc,67 3933 03330 42362 5i i to 907669 9.96665 9.61004 10.38996 10.03335 10.4x331 50 i IZ 57700 96660 61040 38960 03340 42300 49 1 * 2 57731 9 6C 55 61076 . 3*9 2 4 334> 42269 48 13 37762 96650 61112 38888 03350 42238 47 4 57793 96645 61148 38851 03353 42207 46, Is 57824 96640 61184 3^816 03360 42176 45 ! 16 57^55 96634 6|220 38780 03366 42145 44 1 7 57885 96629 61256 3 8 744 03371 42115 43 18 579 l6 96634 61292 38708 03376 42084 4i 19 57947 96619 61328 38672 03381 4 2 53 4i 20 9.57978 9.96614 9.61364 10.38636 10.033^6 10.42022 40 21 58008 96608 61400 38600 03392 41992 39 22 58<>39 96603 61436 38564 03397 41961 3* i -3 58070 96598 61474 S S 5 iS 03402 41930 37 : 14 58101 96593 6ls08 38492 03407 41899 36 15 .8131 96588 61544 3S456 03412 41869 35 26 58162 '9658* 61579 3 8 4 zi 03418 4I 8 3 8 34 -7 58192, 96577 61615 38385 034^3 41808 33 28 58223 9657* 61651 38349 034-8 4 r 777 32 29 5^53 96567 61687 38313 03433 41747 3i 30 9.52284 9.96562 y. 61721 10 38278 10.03438 10.41716 30 31 58j4 96556 61758 ftp Q3444 41686 29 32 5^345 9 6 55 T 61794 38206 03449 4^655 28 33 34 58406 96546 96541 4l830 61865 38170 33i35 034'4 03459 41625 4 T 594 27 26 35 5&4.?6 9 6 535 61901 3809.9 03465 41564 25 36 58467 9653 61936 38064 034.70 41533 24 37 53497 96525 61972 38028 03475 4J503 23 38 58527 96520 62008 37992 03480 4H73 &a 39 5*557 9.6514 62043 37957 03486 4 r 443 21 4 9.39 96429 62609 3?39 r 03571 40961 5 ; 59 :: ^ 96424 62645 37355 03576 409$ 4 57 59098 96419 62680 37310 03581 40902 3 j ! <;8 59128 9 6 4'3 62^15 37^5 03587 40872 2 1 ^9 55158 96408 62750 37150 03592 40842 I j 60 591 8S 96403 62785 37215 03597 408 ii Co-fine. Sine. Co-tang. Tangent. Go-fecant. Secant. M. 07 Degrees TABJLE V. OfARTiFiciAi Sines, Tangents, and Secaa4:s. 23 Degs. M. Sine, j Cofire r ranged. Co-tang. Secant, ( ^"fccant. > 5.5^:0 >. 96403 x. 62785 i 0.37*15 0.03507 i "oTJobii bf I 59218 96397 62820 37180 o^''O3 40782 59 2 59-47 96392 62855 37 03008 4753 5.8 3 59 2 77 96387 62890 37110 03613 40723 57 4 59307 96381 62926 37074 03619 40693 56 5 59 62961 37039 ' 03624 40664 55 6 59366 96*70 62996 37004 03630 40654 54 7 59396 - 63031 36969 056:55 40604 53 59425 96360 63066 3^934 0364; 4575 .52, 9 59455 9 6 354 63101 36^99 0.364.6 40545 51 10 .59484 9-9349 ' 9. 63135 o. 36865 0,03651 10.40516 5 ii 595H 9 6 343 63170 36830 03657 40486 49 12 59543 96338 63205 36795 93662 4457 13 59573 96333 63240 36760 03667 , 40427 47 596-2 96327 63275 36725 03673 40^98 46 15 9632Z 63310 36690 03678 40368 45 16 59661 96316 63345 36655 03684 4339 44 17 59.690 96311 63379 36621 03689 * 40310 43 18 59720 96305 3658,6 03695 40280 19 59749 96300 63449 36551 03700 40251 r 20 9.59778 9.96294 9.63484 10.36^16 10 03706 r o . 40 2 2 2 40 21 59808 96,89 63519 36481 ' 03711 40192 39 22 59837 96284 63553 36447 03716 40163 38 23 59866 96278 63588 36412 03722 40*34 37 24 59 8 95 06273 63623 36377 03727 40105 36 25 59924 96:67' 63657 36H3 03733 40076 35 26 59,954 9-5^62 63692 36308 03758 40046 34 17 59983 96:56 63/26 36*74 03744* 40017 33 i 28 60012 96151 63761 36239 03749 39988 32 j 29 60041 96245 63796 36204 03755 39959 3 9.60070 9.96240 9.63830 10.36170 10.03760 l -3993 31 60099 96234 6386^ 36135 03766 39901 60128 96*29 .63899 36101 03771 39872 28 33 60157 96223 63934 36066 03777 39 8 43 2-7 34 60186 96218 63968 36032 03782 39 8l 4 26 3S 60215 96211 64003 35997 03788 397^5 2; 36 60244 96207 64037 03793 39756 . 2 4 37 60273 96201 64072 35928 03799 38 60302 96196 64106 35894 03804 ,39^8 22 39* 60331 96190 64140 35860 03810 21 40 9.60359 9.96185 9.64175 10.35825 10.03815 10.39641 20 41 60388 96179 64209 35791 03821 39611 J 9 i 42 60417 96174 64*43 * 35757 0^876 10 43 60446 96168 6 4 z 7 S 35722 39554 17 44 60474 96162 64312 35688 .6*838 39526 16 45 60503 96157 64346 35654 03843 39497 15 46 60532 96151 64381 35619 03849 39468 47 60561 96146 64415 355*5 03854 39439 13 48 60 :'$ 9 96140 64449 35S5 1 03860 39411 12 49 60618 96135 64483 03865 I I 5 9.60646 :;. 96129 9.64517 10.35483. 10/03871 10 -39 354 10 51 60675 9612? 64552 03877 393*5 9 '- > 60704 96118 64580 3 54 '4 0^882. 53 60732 96112 64620 353^0 03888 39268 7 54 . 60761 96107 64654 35346 03893 39 Z 39 6 55 SiJtovS _> 96101 64688 353*2 o ", 8 ci 9 3921 1 5 56 ^>6c 96095 64722 3527? 3 9.1? 2 4 5? 60846 96090 64756 35244 03910 39*54 3 58 60875 96084 64790 35210 07916 391*5 2 59 60903 96 79 64824 35176 03921 3997 I 60 60931 64855 35 142. o $9*7 39069 O Co fine siw Co-lang Tangt'ul.'Co-iicant. Secant- M. 66 i^egrgec V. Of ARTIFICIAL Sines, Tangents, and Secanfg. 24 Degs. M Sine,. f Co-'fme. Tangent Co-tang. Secant. Co fecant. o I 3 . 609 5 r, 60960 196073 ,6067 1.6.43 : 3 648 .2 to. 35, -42 35108 10,0.5927 03931 10.39069 39040 60 ] 59 2 60088 | 96062 04016 3574 0393! 39012 58 3 ' 61016 ' 96056 64960 35040 03044 38084 57 4 f^TO^s 900 ~o 6*4994 35006 03950 38955 56 | 5 * 01^73 96045 65028 34972 03955 38927 55 6 6 noi .90039 65062 3493^ 03961 58899 54 ] 7 61129 9' JO 34 65096 74904 O' ( r\66 38871 53 8 61158 q6o2$> 651 50 34^70 3972 58842 52 Q 1 /> [ I f ; , ! 022 65164 0:078 3^814 51 1 IO [9^96017 3 (J5I97 10. 54803 ^ -, sj 10.38786 5 1 i: 6t242 9 jo 1 1 65231 54/ 6 9 03989 38758 49 ! i i f> 1 2 ;o ! 96005 65*65 Q3995 38730 48 " 6 1 zy<$ 06000 $5199 ? 17OT 04000 38702 I 6 i 3 .z 6 I 95994 34667 04 .06 38674 46 i i 6 r 3 ,4 1 9 "98 -5 65366 3< 6 H 04012 38646 45 i'5 finite 9-9-2 6-400 04018 38618 44 6UIT i '>5 ( :~7 65434 34566 04023 ?8s89 43 18 61438 9597 1 654"7 34^33 04029 38562, 42 61466 65 ?oi 34499 04035 3^34 ' 20 9-61494 y .g - 6171; q 5008 65877 34^3 04092 38255 31 "I 3 9.6,77; 9 95902 9.65870 10.34130 10.04098 10. 38227 30 3' cr8oo 9-897 65004 34006 04103 38200 29 6r8;8 9^891 65937 34963 04109 38172 33 61856 9^885 65971 34029 4x15 38144 -7 34 61883 ^587^) 6 M o ? 4 0412 1 38M7 26 61911 95873 66038 3396.2 04127 38089 2$ ' 3" 619*9 95868 66071 339-9 04132 38061 24 37 61966 66104 33^-96 04^38 3?o34 23 38 61994 9 > 8 ; 6 661 }8 33862 04144 38006 22 ! ^ ') 62G2 I 95850 66T 7 T 33829 04150 37979 21 .40 9.62049 5.95544 ). 66704 10.33796 10.04156 10.37951 20 4* 620/6 95839 66238 33762 94161 379H '9 42 6.1IO4 9 s ?, ^ 3 66271 3^729 04167 37896 18 4> 6213 i 958*7 66304 33606 37865 17 4 4 6-1 ^9 9 5821 66337 33663 04179 378.4? 1 6 45 6218" 9^1-5 66371 3 -629 04185 37*14 '5 4'J _ 62214 66404 33596 04190 37736 H 47 62241 95^04. 66437 33563 04196 377 59 13 48 62168 9579? 66470 335.?o' 04202 3773* 12 49 6220,6 95792 '66501 04? 37704 ri : 5 y . ' z : S ; Q .957 ^ 6 9.6,653/7 10.33.^63 10.04214 .0.37657 IO 62 } ;o Q " ?2o 66570 33430 04 i 20 37650 9 ' 5^ 62177 95775 66603 33397 04.125 37623 8 ! 53 62405 66636 33364 04231 3:595 7 i 54 6*43 2 957 -5 66669 333 V 1 04*37 .37568 6 i 5 5 624-;) 95757 66702 33298 0424*3 3754 1 5 ! 56 62486 9575' 667*5 33265 04249 375 T 4 4 1 57 62513 9/5745 66768 332.32 0425? 374^7 3 ' 5^ 62541 95739 66801 33 T 90 04^61 37459 2 59 6c jjg- 95733 057^8 663*4 66867 33166 33' -3 0*11$ 042-2 3743- 37405 C>-inv:. Sine. Co tang. T;n gent. Co-fecant Secant. M. 65 rccs, V. Of ARTIFICIAL Sines, Tangents, aiad Secants. 23 Degs, , M.| Sine. Co-fine. Tangent Co-tang Secant. iCo-fecant 9.62595 957*5 9.66667 ro. 33133 10.04272 >o-37 05 ^ I 62622 95722 66900 33100 04278 373,8 59 2 62649 95716 66933 042-4 . 3735* 3 62676 95710 6< ; )66 33*34 04290 37,3*4 5V 4 61703 95704 66999 33001 04296 37^97 5 627^0 93698 67032 329^8 04302 3. -70 55 6 62757 95692 67065 3*935 04308 37243 7 62784 95686 67008 32(>02 943*4 37216 sit 8 62811 95680 67131 32869 04720 37l8q - ! ?v | 9 628-5 95674 67163 37877 04326 ? ' f ' - ! ? i 10 9 '. 6 2 8 6 9.95068 9.67 196 10 . 32804. 1 1 62892 9-5663 67229 3*771 04337 37106 12 62918 95657 67262 3273* 37082 d 8 13 62945 95651 67295 04349 37055 -7 ;^ 14 62972 95645 67317 32673 43 5 5 37028 4 i > 62999 95639 67360 326^0 04361 37001 45 1 6 63026 95633 67393 32607 04 i 6 7 30974 44 1 7 63052 95627 67426 2s?4 OA 3 - 3 36948 4? 18 63079 6 74. V s 3*542 04-79 36921 4? '9 63106 95615 67491 7 i 'Or, 04 >^ 4' 20 9-63133 9.95609 ^.67524 10.3.476 jio. 0^391 ~.-o->07~ 4 21 63159 95603 6/5>6 31444 04397 3*1:41 22 63186 955V7 6;<8 -., 2..+ I 1 i Oc4<>3 36814 ? *3 63*13 95591 6-^622 323-8 . 04409 36:3; 3V 24 63239 955*5 676^4 32346 { 0,44 15 36/61 36 j *5 63266 95579 67687 3 : ; i 3 0444 1 36734 3 26 6321,2 95573 67719 32281 04427 3 te 08 34 ; 27 63319 95567 67752 322 4 S 36681 i 28 63345 95561 67785 3*215 044 J9 >6 5> 3- 29 633:2 955S_5 - 67817 32J83 C 4445 36628 30 9.63398 J- 95549 9.67850 10. 32 i 50 10 044? i u. 30602 30 31 63425 93543 67881 32118 04457 36575 3* 63451 95537 67915 32085 04463 365^9 28 ! 33 63478 95531 67947 3-053 04469 27 i 34 63504 955*5 6 7y 8o 32020 04475 36496 26 35 63531 95519 68012 31^*8 04481 36469 2 < 36 635^7 95513 68044 31956 c; 44 8 7 36443 2 4 i 37 635*3 95507 68077 3*923 04493 3 6 4'7 2? 38 63610 68 109 31891 04^:00 36390 Zi j 39 63636 9 H-94 6*142 04506 ^364 21 j 40 9.63662 9-95483 9-6^174 10. 31826 1 . 04 5 1 2 0.3? 33S 201 4* 63689 9^482 68206 3^794 04^1^ 36511 *^ 42 6371 5 95476 68239 31761 045*4 36285 43 63741 9 5470 68271 31729 P453 362^9 1 7 ] 44 63767 95464 68303 3HV;7 04536 36-' 33 l6 ! 45 63794 95458 68336 316-4 ! 04542 30200 1C 1 : 4 6 63820 95452 68368 V^;_ 04548 36180 '4 I 47 63^46 9S446 68400 3 i 600 G 4>54 3 -: 6 1 "4 i > : 48 63872 9,440 68432 3*<#B 04 ; o 36128 12 49 638rS 95434 68465 3 '5:5 ^45()6 36102 II 50 : 9. 63 -24 954-7 51684^7 to 31 53 10.04573 0^3^07^ 10 51 63950 95421 68529 p 31471 04579 36050 9 52 63976 9 '+> 5 6^561 3'439 04585 jf'024 8 i 53 . 64002 95409 68593 -140; 04591 35998 7 : 54 64028 9543 68626 31374 0459 7 35974 6 i 5? 64054 95397 6 v 6r,8 04603 3 594-6 ; 56 64080 95391 68690 3I3IO 04609 35920 4 <7 64106 , 953^4 68722 31278 04616 5^,4 3 58 64132 68754 cjpiz | ^-;8C8 2 59 64158 9 5 3 7 j 68786 0^628 3 ^842 I ; 60 641X4 688.8 046^4 3 ; /: i 6 O i Co line. Mne. Co tang' TargeiJt. < Jo ft cant. 1 Se-ant. A3 j| V. "OF Sines, Tangents, and Secants 26 Degs, M. " Sine. Co- fine. |Tangent. ! Co-tang. Secant. C ^o-fecant ;. 041^4 9 .95366 f ; .63015 0.31182 i 0104634 0735816 ~ 60 i 64210 95360 688^0 31150 04640 35790 59 2 64236 95354 68882 31118 04646 35764 58 3 64262 95348 68914 31086 04652 35738 57 4 64288 95341 68946 31054 04659 357J2 56 5 643 T 3 9^335 68973 31042 04665 35687 55 6 6433} 953-9 6QOIO 30990 04671 3566! 54 7 64365 95323 69042 3 958 04677 35635 53 8 64391 95317 69074 30926 04683 35609 52 9 64417 95310 69106 30894 04690 35583 5 1 10 9.64442 9.95304 5.69138 10.30862 10.04696 io.3555 g 5 ii 64468 1 95298 69170 30830 04702 35532 49 12 64494 95292 69202 30798 04708 35506 48 I 13 64519 95286 ^9234 30766 04714 3548i 4; i J 4 64545 95279. 69266 30./34' 04721 35455 46 64571 95 2 73 69298 30702 04727 354 Z 9 45 . 16 64596 95267 69329,.. 30671 04733 354 C 4 44 17 64622 95261 69361 30639 04739 35378 43 18 64647 95254 69393 30607 04746 35353 42 *9 64673 694-5 30575 04752 35327 4* 9.64698 19-95*42 9.69457 tO.30543 10. 047 5 i 10.35392 40 21 64724 95236 69483 30512 04764 35276 39 I 22 64749 95229 69510 30480 047/1 352,1 38 1 23 64775 95223 69552 30448 047"7 35225 37 2 4 64800 95217 69584 30416 04733 35200 36 25 64826 95211 69615 30385 04' 35174 35 26 64851 95204 69647 30353 04796 35149 34 I 27 64877 95198 69679 30321 04802 35124 33 28 64902 95*9* 69710 30290 0480^ 35098 32 29 64927 95*85 69742 30258 048 1 - 3/073 3 1 30 9-64953 9.95179 - 9.69774. 10 30220 lo, 04*21 0.35047 3 31 64978 95 r ?3 69805 30195 04827 3^023 29 1 65003 95167 69837 . 30163 04S33 34997 28 33 65029 95160 69868 30132 04840 34971 27 | 34 65054 95*54 69900 30100 04846 349 + 6 26 1 So 65079 95x48 69932 30068 04852 34921 25 i 36 65104 95141 69963 3'*>37 04859 24 I 3? 65130 95*35 699-95 30005 04:^65 34870 23 65M5 95129 70026 20974 048^1 34845 Z2 1 ^ 65180 95 ii.i 7:0-8 29942 04878 34820 21 ! 40 9-65205 9.95116 9.700^9 10.2991 i 10.04884 10.34795 20 41 65230 95110 70T2I 19879 04890 34770 *9 S 42 65255 95103 70151 29848 04897 34745 18 43 65281 95097 70184 29816 04903 34719 17 44 6s 306 95090 702 r 5 29785 04910 34694 16 65331 95084 TOZ47 297^ 04916 34669 1 5 46 65356 95078 70278 297 :.z 04922 34644 14 47 95071 70309 2*9691 04929 34619 13 48 65406 95065 70341 29659 04935 ' 34594 . 12 ' 65431 95 0< !9 70372 29628 04941 34569 II "50" 9,65456 9.95052 9.70404 10.29516 10.04948 10.34544 IO 5 i 65481 95046 7043 5 29565 049 54 34^9 ( 5* 65506 950^9 70466 29534 64961 34494 8 53 65531 95^33 70498 29502 04967 34469 7 54 65-56 95027 70529 294/1 04973 34444 6 55 65586 70560 19440 04980 34420 5 65605 95014 70592 19408 04986 34395 4 57 65630 95007 7062.3 29377 04993 3437 58 1 656-5 95001 706 54 19H6 04999 34345 ^ 9 &5'6?o 9499; 70685 65005 34320 60 ] 6570' 94988 70717 9i8* 65012 34295 1 Co- fine. Sine. Co- tang . Tangent Co-fecant-' Secant. M. 63 Degrees TABLE V. Of ARTIFICIAL Sines, Tangents, and Secants 27 Degs. I M Sine. Co- line. Tangent- Co-tang. Secant. Co-fecan o 9.65705 9 949^ 9.70717 10.29283 10.05012 10.54295 60 I 65729 94982 70748 29252 05018 34271 59 2 6 5754 9497.? 70779 29221 05025 34246 8 1 65779 94969 70810 29190 05031 34221 57 4 6^804 94962 70*41 29159 05038 34*96 56 t 65828 94956 70873 29127 05044 34*72 55 6 65853 94949 70904 29096 05051 34H7 54 7 65878 94943 70935 29065 05057 34122 53 8 65902 94936 70966 29034 05064 34098 52 9 659-7 94930 70997 29003 05070 34073 5 r 10 9.65952 , -^~ 9 -949 2 3 9.71028 10.289:2 10.05077 10.34048 5 ii 65976 94917 7 I0 59 28941 05083 34024 49 12 66001 94911 71090 28910 05089 33999 48 13 66025 94904 71121 28879 05096 33975 47 J 4 66050 94898 7H53 28847 0510: 33950 46 1.5 66075 94891 71184 28510 05109 33925 45 16 66099 94885 71215 28785 05115 33901 44 17 66124 94878 71246 28754 05122 33876 43 18 66148 94871 71277 28723 05129 338 5 2 42 19 66173 94865 7^308 28692 05^5 33827 4i 20 9.66197 9.94858 9-7I339 10.28661 10.05142 10.33^03 40' 21 66221 94852 71370 28630 05148 33779 39 j 22 66246 94845 71401 28599 05155 33754 38 23 66270 94839 7i43i 28569 05161 33730 37 *4 66295 94832 71462 28538 05168 3370? 36 25 66319 94826 7 r 493 28507 05174 33681 35 26 66343 94819 71524 28476 05181 33657 34 27 66368 94813 71555 28445 05187 33632 33 28 66392 94806 71586 28414 05194 33608 32 29 66416 94799 71617 28383 0^201 33584 31 30 9.66441 94793 9-71648 0.28352 0.05207 rc> -33559 30 31 66465 94786 71679 28321 05214 33535 29 32 66489 94780 71709 28291 05220 335" 28 33 66513 94773 7174 28260 05227 33487 .27 34 66537 94767 "1771 28229 05-233 33463 26 35 66562 94760 71802 28198 05240 33438 2 4 36 66586 94753 71833 28167 05247 334H 24 37 66610 94747 71863 28137 05253 3339 23 38 39 ; 66634 66658 94740 947-4 71894 71925 28106 28075 05260 05266 33366 33342 22 21 40 .66682 94727" 71955 0.28045 0.05273 0-33313 2O 4 1 66706 94720 71986 28014 05280 33294 19 42 66731 947H 72017 27983 05286 33269 18 43 66755 94707 72048 * 27952 05293 33245 i/ 44 66779 04700 72078 27922 05300 33221 16 45 66803 94694 72109 17891 05306 33197 15 46 66827 94687 72140 27860 05 * i 3 33173 14 47 66851 94680 72170 27830 05320 33H9 13 4? 66875 94674 72201 27799 05326 33' 2 5 12 49 66899 94667 72231 27769 05333 33ior II 5 . 66cjz2 . 94660 772262 0.27738 0.05340 0.33078 10 5 1 66946 94654 72293 27707 0.534 6 33PS4 9 52 53- 54 66970 66994 67018 94647 94640 94634 72323 72354 72384 27677 27646 27616 05353 053^0 05366 : 33030 33006 32982 7 6 55 67042 94627 72415 27585 ''373 32-958 5 56 67066 94620 72445 27555 05380 . 32934 4 C7 67090 94614 72476 275M 05386 32910 GO 3 58 67113 94607 72506 27494 5393 32887 2 59 67137 94600 72537 274^3 Os4OO : 32*- 6 3 i 60 67161 94593 72567 2/4*3 05407 : 3 2.8 ^9 Co-fin^. Sine,. l Co- tang. Tangent. Jo leca: t, Seca: t, 5fJ TE 02 yegrees- TABLE V. Of ARTIFICIAL Sines, Tangents, and Secants. 28 Degs, M., Sine. Co-fiie. 'angent.j Co-tang. Secant. o-fecant. 67161 9 94593 72567 0.27433 i 0.05407 .32839 o 1 67185 945^7 72598 27402 05413 32^15 9 2 67208 945^0 72628 27372 05420 32792 8 3 67232 94573 72659 2734 1 05427 32768 7 4 67256 94567 72689 27311 05433 32744 6 5 67280 9456o 72720 27280 05440 32720 55 6 67303 94553 72750 27250 05447 32697 54 7 67317 94546 72780 27220 05454 32673 53 8 6735 9454 72811 27189 05460 32650 52 9 67374 1 9453? 72841 27159 0^467 32626 51 10 .67398 9., 4526 .72872 0.27126 0.05474 o. 32602 5 ii 67421 945*9 72902 27098 05481 32579 49 12 67445 94513 72932 27068 05487 32555 48 1 I3 67468 94506 72963 27037 05491 32531 47 14 6749* 94499 72993 27007 05501 32508 46 15 67515 94492 73023 26977 05508 32485 45 16 67539 94485 73-54 26946 05515 32461 44 17 67562 94479 73084 26916 05521 32433 43 18 67586 94472 73 IJ 4 26bS6 05528 324'4 42 19 67609 94465 73M4 26? 56 05535 32391 4i 20 .67633 9-9445* .73175 10.26825 0.05542 e. 32367 40 ZI 67656 94451 73205 26795 05549 32344- 39 22 67680 94445 73^35 26765 05555 32320 3 23 67793 94438 73265 26735 05 5 '-2 32197 37 *4 67726 9443i 73295 26705 05569 32274 36 *5 6775 94414 77326 26 6 1 A. 05576 31250 35 26 67773 94417 73356 26644 05583 32227 34 27 67796 94410 733^6 26614 05590 32204 33 28 67820 94404 73416 26584 05596 32180 32 *9 67843 94397 73446 26554 05603 3115' 3i 30 9.67866 9.94390 )./3476 io. 26524 10.05610 10-32134 30 3i 6781)0 943 s ? 7357 26493 05617 32110 i'? 31 6/913 94376 73537 26463 05624 32087 2? 33 6/9? 6 94369 73567 26433 05631 32064 27 34 67959 94362 73597 26403 05638 32041 26 35 679*2 94355 73^17 16373 05645 32018 25 36 68006 94349 73657 26543 05651 31994 2 4 37 68029 94 Hi 73687 26313 05658 31971 23 38 68052 94335 73717 26283 05665 3 '948 22 39 68075 94318 73747 26253 05672 3*925 21 40 9.68098 9.94321 9-73777 io. 26123 jo. 05679 io. 3190- 20 41 68121 943H 7307 26193 05686 3187-) 19 41 68144 94307 73837 26163 05693 31850 jS 43 68167 94300 73867 26133 05700 3183; 17 1 ,44 68190 94293 73897 26103 05707 31810 16 45 68213 94286 73927 26073 057(4 317*7 15 46 68237 94279 739S7 26043 05721 31/63 14 47 68260 94*73 739 8 7 26013 05727 3 I 74 13 48 68282 94266 74017 25983 05734 31713 12 49 68305 94 2 59 74047 25953 05741 3 l6 95 II 5> 9.68328 9.94252 9.74077 10.25923 10.05748 10.31672 10 S* 6835^ 94245 74'07 25893 05755 31649 9 5* 68571 94238 74'37 25863 05762 31626 8 53 68397 84*31 74166 25854 05769 31603 7 H 68420 942=4 74196 25804 05776 31580 6 55 68443 94217 74226 25774 05783 31557 5 5 6 68466 94210 74256 15744 05790 31534 4 57 68489 94203 74286 25714 05797 3I5U 3 58 68572 94196 74316 25684 05804 31488 2 59 68534 94189 74345 25655 05811 31466 I 60 68557 94182 74375 25625 P5 8r8 3H43 O Co-fine. Sine, Co-tangJ Tangent JCp-fecan Secant- M. TABLE V. Of ARTIFICIAL Sines, Tangents, and Secants. 29 Degs, M. Sine. Co fine. Tangent Co-tang. Secant. Co-fecant. o 9-^557 9.94182 9-74375 10.2^625 10.05818 10.31443 60 I 68580 94^75 744> 5595 05825 31420 59 2 68003 94168 74435 *556j 05832 31397 5* 3 6*625 94161 744 6 5 *5535 05839 3*175 57 4 6864* 94 '54 74494 25506 05846 3*35* 56 5 68671 94H7 745*4 15476 05853 31329 55 6 68694 94140 74554 25446 05860 31306 54 7 68716 94'33 745 8 3 25417 05*567 31234 53 8 68739 94126 74613 25387 05874 31261 5i 9 68762 94119 74643 25357 05881 3j?.33_ _5_'_ /o 9-6*784 9.94112 * 74673 1^.25327 jo. 05808 10.31216 50 n 68807 94105 74702 23298 05895 31193 49 12 68829 94098 7^732 15268 05902 37* 48 13 68851 94090 74/6* 25238 05910 31148 47 H 68875 94083 74791 25209 05917 31125 46 15 68897 94076 74821 25179 059*4 31103 45 16 68920 94069 74851 25149 05931 31080 44 *7 68942 94062 74850 25120 05938 31058 43 18 68965 94055 74910 15090 05945 31035 42 19 68987 94048 74939 25061 05952 3101^ 4' 20 9.69010 )-944 I 9.74969 10.25031 10.05959 1^.30^0 40 21 69032 94034 7499 s 25002 05966' 30968 39 12 6 95S 94027 75028 24971 05973 30945 38 23 69077 94020 75058 14942 05980 30923 37 24 69100 94012 75087 24913 05988 30900 36 25 69122 94005 75117 148*3 05995 30878 35 26 69144 93998 75M 6 248:4 06002 30856 34 27 69167 93991 75176 24824 06009 30833 33 28 69189 939 9 4 75205 24795 06016 30811 32 2q 69212 93977 75235 24765 06013 30788 3 1 3 9.69234 9.93970 9.75264 10.14736 10.06030 '0.30766 30 31 69256 939 6 3 75294 24706 06037 3-744 19 32 69*79 939 ; 5 75323 24677 06045 30721 28 . 33 69301 93948 75353 24647 06052 30699 27 34 69323 93941 7538i 24618 06059 30677 26 35 69H5 93934 75411 24589 06066 30655 25 36 69368 93927 7544 1 14559 06073 30632 24 37 69390 939 2 o 75470 14530 06080 30610 3 ; 38 69412 93911 75500 24500 06088 30588 22 39 69434 9395 75519 24471 06095 30566 11 40 9.69456 9.93898 9-75558 10.24442 10.06102 10.30544 2O 4 1 69479 93891 75588 24412 06109 30521 19 42 69501 93884 75617 . 24383 06116 30499 18 : 43 695 2 3 93876 75647 24353 06124 30477 7 44 69545 93869 75676 24324 06131 3455 16 45 69567 93862 75705 24295 06138 30433 15 46 69589 93355 75735 24265 06145 30411 J 4 47 69611 93847 75764 24236 06153 30389 13 4* 69633 93840 75793 24207 06160 30367 12 Ji. 69655 93833 75822 24178 0616" 3345 II 50 9.69677 _>. 93*26 ) 7^852 10. 24148 10.06174 o 30323 IO 5i 69699 93819 75881 24119 06181 30301 9 52 69721 93811 759 ro 24090 06189 30279 8 53 69743 93804 75939 24061 06196 3*57 7 54 69/65 93797 75969 24031 06203 30235 6 i 5 ! 69787 93/89 7599 8 24002 0621 r 30213 5 \ 5 69809 93782 76027 23973 06218 30191 4 I s l 69831 93775 760 <;6 *3944 06225 30169 3 58 69853 93768 76086 23914 06132 30147 i 59 69875 9376o 76115 13885 06240 30125 I 6c 69897 93753 76144 23856 06247 30103 | Co-fine. Sine. ' Co-tang. Tangent. |Co-fecant Secant. M. Oo a TABLE V. Of ARTIFICIAL Sines, Tangents, and Secants. 30 Degs. M. Sine. Co-fine. ,Tangei!t. Co-tang. Secant. Co-fecant. 9.69897 5-93753 9.76144 to. 238^6 10.06247 10.30103 60 I 69919 93746 76173 23827 06254 3008 1 59 2 69941 93738 76202 23798 06262 30059 58 3 69963 93731 76231 23769 06269 30037 57 4 69984 93/24 76261 23739 06276 30016 56 5 70006 93717 76290 23710 06283 29994 55 6 70028 93709 76319 23681 06291 499/2 54 7 70050 93702 76348^ 23652 06298 29950 53 8 70072 93695 76377 23623 06305 29928 52 9 70093 93687 76406 23594 06313 29907 Ji_ 10 9.70115 9.93680 9-76435 10.23565 10.06320 10.29885 5 IX 70137 93673 76464 23536 06327 29863 49 12 70159 93665 76493 23507 06335 29841 48 13 70180 93658 76522 23478 06342 29820 47 H 70202 93 6 50 76551 23449 06350 29798 46 15 7022.4 93 6 43 76580 23420 06357 29776 45 16 70245 93636 76609 23391 06364 29755 44 i? 70267 93628 76639 23361 06372 29733 43 18 70288 93611 76668 23332 063.79 29712 42 *9 70310 93614 76697 23303 06386 29690 4 1 20 9^70332" 9.93606 9.76725 10.23275 10.06394 10.29668 40 21 70353 93599 76754 23246 06401 29647 39 22 "0375 93591 76783 23217 06409 29625 3* 2 3 70396 935H 76812 23188 06416 29604 37 24 70418 93577 76841 23159 06423 29582 36 25 70439 93569 76870 23130 06431 20561 35 26 70461 93562 76899 23101 06438 29539 34 27 70482 93554 76928 . 23072 06446 29518 33 28 70504 93547 76957 23043 06453 29496 32 29 70525 93539^ 76986 23014 06461 29475 JLL 30 9.70547 9-93S3 2 9-77015 10.22985 10.06468 10.29453 3~ 3* 70568 933*5 77044 22956 06475 29432 29 32 70590 935'7 77073 22927 06483 29410 28 33 70611 9351 77101 22899 06490 29389 27 34 7633 935 02 77130 22870 06498 29367 26 35 70654 93495 77159 22841 06505 29346 25 36 70675 934 8 7 77i88 ' 22812 06513 29325 -4 37 70697 93480 77217 22783 06520 29303 2 3 '33 70718 9347* 77246 22754 06528 29282 2- 2 39 70/39 93465 77^74 22726 06535 29261 21 40 9.70761 9-93457 9-77303 10.22697 10.06543 10.29239 20 4 1 70782 9345 77332 22668 06550 29218 *9 42 70803 93442 773 61 22639 06558 29197 18 43 70824 93435 77390 22610 06565 29176 17 44 70846 934*7 77418 22582 06573 29154 16 45 70867 93420 77447 22553 06580 29133 15 46 70888 93412 774/6 22524 06588 29112 r 4 47 70909 9345 77505 22495 06595 29091 13 48 70931 93397 .77533 22467 06603 29069 12 49 7095^ 9339 77562 22438 o66ro 29048 I I 5 9.70973 9.93382 . 9-77591 10. 22409 10.06018 10.29027 10 5i 70994 93375 77619 22381 06625 29006 9 5 71015 933^7 77648 22352 06633 28985 8 53 71036 9336 77677 22323 . 06640 28964 7 54 71058 , 933S 2 77706 22294 06648 28942 6 ! 55 71079 93344 77734 22266 o66<;6 28921 5 i 56 71 100 . 93337 777 6 3 22237 06663 28900 4 87 7:121 93329 7779 1 22209 06671 28879- 3 58 71142- 933* z 77820 22180 06678 28858 z "9 71163 93314 7/849 22151 06686 28837 i 60 / 1 1 4 9-3307 ?78_7? 22123 06693 28^16 Co fine. Sine- Co- tang. Tangent. Co-fecant. Secant. M. . -59 Degrees TABLE V. Of ARTIFICIAL Sines, Tangents, and Secants. 31 Degs. lM. Sine. Co- line. Tangent. Co-rang. Secant. Co-fecant o 9.71184 2-93307 9,77877 10.22123 10.06693 io.28i6 60 i 71205 93299 77906 22094 06701 28795 59 i 2 71226 93291 77935 22065 06709 ~- : 774 5S i 3 7(247 93284 77963 22037 06716 28753 5" 4 71268 93276 77992 22008 06724 28732 56 5 71289 93269 78020 21980 06731 28711 55 6 71310 93261 78049 21951 06739 28690 54 7 7I33I 93 2 53 78077 21923 06747 28669 53 8 93246 78106 1894 06754 28648 52 9 71373 93238 78135 21865 06762 28627 10 9-71393 9.93230 9.78163 10.21837 10.06770 10.28607 1o" ii 71414 93223 78192 21808 06777 28586 49 12 93215 78220 21780 06785 28565 48 13 71456 93207 78249 21751 06793 28544 47 M 71477 93200 78277 21723 06800 28,523 46 M 71498 78306 21694 06808 28502 45 16 71519 93184 78334 21666 06816 28481 44 17 7*539 931/7 78363 21637 06823 28461 43 18 71560 93169 78391 21609 06831 28440 J 9 71581 93161 78419 21581 06839 28419 4* 20 9.71602 9.93154 9.7*448 10.21552 10 .06846 10.28398 40 21 71622 93H 6 78476 21524 06854 28378 39 22 71643 9313? 78505 21495 06862 28357 32 23 71664 93i3i 78533 21467 06869 28336 37 24 71685 93123 78562 21438 06877 28315 25 71/05 93H5 78590 21410 06885 28295 35 26 71726 93108 78618 21382 06892 28274 34 ' 27 71747 93100 78647 21353 06900 28253 33 28 71767 93092 78675 21325 06908 28233 29 71788 93084 78704 21296 06916 28222 |5 30 9.71809 9.93077 9.78732 10.21268 10.06923 10.28191 30 3* 71829 93069 78760 21240 06931 28171 20 32 71850 93061 7*7*9 2I2I1 c/H)39 28150 23 i 33 71870 93053 78817 21183 06947 28130 - 7 ! 34 71891 93046 78845 2II55 06954 28109 16 35 71911 93038 78874 2II26 06962 28089 .25 36 71932 93030 78902 21098 06970 28068 '. 4 37 71952 93022 78930 21070 06978 28048 23 38 71973 93014 78959 2IO4I 06986 2*027 2i 39 - 71994 9 -,007 78987 2 10 1 3 06993 28006 2f 4 9.72014 9.92999 9.79015 10.20985 lO.O-CCf 10. 27u36 20 i 41 72034 92991 79043 20 957 07009 27966 9 42 72055 92983 .79072 209:8 . 07017 27945 J 43 72075 92976 79100 ' 20900 07024 27925 17 44 72096 92968 79128 20^72 07032 27904 16 , 45 72116 92960 79156 20844 07040 27884 r 5 46 72137 92952 79185 20815 07048 -7803 H 47 72157 92944 79213 20787 07056 27843 13 48 72177 92936 792^-1 20759 07064 2-7-23 12 ! -1L. 72198 92929 79269 20731. 07071 -27802 II ! 50 9.72218 9.92921 9.79297 to. 20703 10.07079 ro.2;7*>2 10 51 72238 9*9*3 79326 20674 07087 27762 9 : 52 "2259 92905 79354 20646 07095 27741 S 53 72279 928 Q7 79382 20618 07103 27721 7 j 54 72299 92889 79410 2r 590 07111 27701 6 : 55 72320 92881 79438 ' 20562 07119 27680 5 56 72340 92874 79466 20534 07126 27660 4 57 72360 92866 79495 20505. 07134 27640 3 58- 72381 gfc&s'S 79523 20447 07142 27619 2 59 72401 92850 79551 20449 07150 275^-9 I 60 72421 92842 79*579 071 <;8 Co.fme. Sine. Co-tang. Tangent. Co- recant .Secant JM. ; T/EI.E V. Of ARTIFICIAL. Sines, Tangents, and Secants. 32 Dcgs. M. Sine. Co- line. f Tan gent. Co-tnng. ( Secant. Co-fecant. : o 9-72421 9.92*4.-. 9-79579 0.20421 |io.07i;S 10.27579 00 i 72441 92834 79607 203:;^ 07166 2 7559 59 ! 2. 72461 9 z > -i o 79 6 35 20365 07174 27539 ^ 3 7x482 f ; 2 S 1 S ' 79^63 20337 0-182 27518 57 4 72502 92*10 79691 20309 07190 2749* 56 5 72522 9x863 797*9 20281 07197 27478 55 6 7**4* 9279S 79747 20253 07205' 2745^ 54 k *~f 72*6Z V ^ 7 "> " 79776 2022,4 07213 27438 53 8 7*5*1 9 - 7 " 9 79^04 20196 072*1 27418 52 9 72'->o2 i 9-7~ T 79832 20168 07229 27398 5 1 10 9.7. .02 2 3,92763 o . 791*60 0.20140 10.07237 10.27378 5 1 ii 72643 9275S ! 79**8 201 12 07245 -7357 49 ! 12 72663 9 2 7^7 j ,799 l6 20084 07253 27337 48 \ 13 72683 92739 79944 200^6 07261 2 73i7 47 14 72703 92731 7997-i 20028 07269 27297 46 1 *5 727-3 927-3 Scooo 2COOO 07277 2 7277 45 16 72743 92715 80328 .19972 07285 27257 44 *7 7-63 Q-7Q7 800^6 19944 07293 27237 43 18 7*783 92699 80084 19916 07301 27217 42 r 9 72803 9 a6c/r 80112 19888 07309 27297 4' 20 9 7^-3 j.9it>3 ;). 80140 10. 19860 0.07317 10.2717-7 40 21 72843 926^5 1 8ci6S I 9 ? 3 2 07325 27157 39 22 72^63 92607 80195 19805 07333 27 J 37 33 2 3 7^3 5-659 80223 J 9777 07341 27117 37 24 71902 92651 8c2sl 19749 07349 27098 36 *5 72922 92643 . 30279 197-21 07357 27078 25 26 72942 92635 80307 19693 07365 27058 34 2 7 729^2 92627 80335 19665 07373 27038 33 28 7-9^ 9z6i9 80363 J9 6 37 07381 27018 32 -9 73.002 9 2 6 1 r 80391 19609 07380 26998 3i 30 9 73022 7.92603 9.^041^ 10.19581 10.07397 10.26978 30 3 730|t 9*555 80447 J 9553 07405- 26959 29 32 73061 92587 80474 19526 07411 2^939 28 33 73081 9 2 579 80502 19498 07421 26019 27 34 73101 92571 80^30 19470 07429 26899 26 35 -5121 9*5$3 80558 19442 C 7437 26879 25 . 3* 7^140 9*555 80^86 19414 C 7445 26860 2 4 1 57 7^160 92546 80614 iu386 9745$ 26840 23 3^ 73180 9253^' 80642 9fs8 07462 26820 22 39 7 7 zoo 02 C JO 80669 J 9.ni 07470 26800 21 40 9.73219 .).9152i 9. 80697 10.19303 10.07478 10.26781 20 4' 732-39 925H 0725 19275 07486 26761 r 9 42 75259 91^6 80753 19247 07494 26741 18 43 ?3i7? 9249^ 80781 19219 07502 26722 7 44 7?iu3 92490 SoSoS 19192 07510 26702 16 45 7% l8 924^2 808.36 19164 07518 26682 15 46 73337 92473 80864 19-136 07527 26663 14 47 73357 92465 HoS 9 2 19108 07535 26643 13 48 73377 9 2 457 80919 19081 07543 2662-3 12 49 7339 6 92449 80947 19053 07551 26604 II i 50 Q.73416 9.92441 9 80975 ' 10.19025 10.07559 10.26584 10 5 1 71435 '-4. 7 3 81003 18997 07567 26565 9 5* 73455 92425 81030 18970 07575 26545 8 53 73474 024 1 6 81058 18942 075^4 26526 7 54 73494 92408 81086 18914 07592 26506 6 ! 55 735'3 -;2400 81113 18887 07600 26487 5 56 73533 92392 81141 18859 07608 26467 4 <7 7355 2 92384 81169 18*31 076-16 26448 3 5S 73^72 9*376 81196 18804 07624 26428 2 || 59 73691 92367 81224 18776 07633 26409 I 60 73611 92359 81252 18748 07641 26389 Co-fine. Sine. Co taug Tangent. Co-fecanl Secant. M. 5; degrees. TABLE V. Of ARTIFICIAL Sines, Tangents, ami Secants. 33 Degs. M. Sine. Co-fine. Fangf nt. Co-tang. Secant. Co -iecar.t. G .73611 9-9 2 359 ). 81252 o. .is 74 S lo. 67041 10. 203^9 Co { 1 73630 9*2351 81279 18721 07649 16370 59 2 9*343 81307 1^693 26550 5* 3 73669 92334 81135 18665 07 6f: 6 26331 57 4 73689 92326 81362 i86^S 07674 26311 56 5 73705 92318 81.390 186x0 07682 6|92 55 6 73/27 92310 81418 18582 07690 2^*73 54 7 73747 92302 81445 185^5 07698 26253 53 8 73766 9 2 293 81473 i 18527 07707 20234 9 73785 92155. 81500 iS;co 07715 2 c> 2 i 5 5* 10 73805 ^92277 5.81^28 ro. 18472 10.07-; 10.26/95 50 1 i 73824 92269 81556 1^444 07 ; jj 26176 49 12 73843 92260 81583 18417 07740 26157 48 13 7386 3 92252 81611 18380, 07748 26137 M 73882 92244 8:638 18362 07756 26118 4* 73901 0*2,35 81666 18334 07765 26099 45 j 16 73921 92227 81693 18307 O'/ 173 2.6079 44 | 17 73940 92219 81721 18279 07781 26060 43 i 18 73959 92211 81748 182^2 0-7789 26041 42 '9 73978 92202 81776 -.8224 07:<;S 20022 41 20 J- 73997 1.92194 19.81803 10,18197 0.07806 10.20C03 40 :: 21 74017 92186 81831 j 8 : 1 9 07814 259*3 39 ' 22 74036 92177 8i8>8 18142 07823 25964 38 : 23 74055 92169 18114 07831 25945 37 24 7474 93161 81913 i ?'o:'/ 07830 259-6 36 25 74093 92152 81941 18059 07x48 25907 35 26 74' r 3 92144 81968 18032 C 7 S 5 6 25-87 27 -92136 81996 18004 07864 25862 35 28 74151 92127 82023 J7.977 c 7" 7 } 25^40 32 29 74 '70 92119 82051 07881 2s8:o 3* 30 j. 74189 9.92111 9.82078 10.17922 "ic7c7?^9~" {To.2;8ix~ 30 i 3 1 74208 921 2 82106 07898 257 ^ 29 92094 82133 1786-7 07906 2577? 28 33 74246 02086 82161 17859 07014 25754 27 34 74265 92077 82188 I7&I2 07923 *573-5 26 741*4 92009 82215 17785 079-1 25716 2 5 36 74303 92060 82.43 17757 07940 *5 6 93 24 } 37 74322 82170 17730 0:948 2^678 2 3 1 38 74341 92044 82298 17702 079^6 2, "659 12 _J9_ 71360 9:03 ^ 82325 I767J 07965 ! 2 ^6*4.0 21 , ; 4 9 '743.79 .9 2? 4 7 7.82352 10 17648 10.079 "3 io,2>6ij[ . 41 74398 92018 82380 176-0 079-2 26-2 10 1 42 744 ] 7 92010 82407 17593 079^0 43 74-i ^6 92002 82435 17565 07998 2 ; -" :.'4 44 74455 91993 82462 17538 08007 2,; ^^; 16 45 74474 91985 82489"' 17^:1 cSo i N 2552*5 .5 1 46 74493 91976 2517 1 7.; "3 o')Oi4 25 1:07 47 74 <>2 91968 82-44" ' C - O -, 2 254^ '3 48 74531 l959 82571 0^04 r 2 54 u 9 12 49 7454-9 QiQ$r 82;:)Q 17401 ,to4 9 254U I 1 ^ 50 9. 74568 9.91942 9 82626 10.17374 i o . c x. ' 8 43 2 1 | 748 7 9J934 82653 17^7 cSc66 254*3 9 52 74606 91925 82,681 17519 2S394 53 74625 91917 82708 1-7292 25^:5 'i 54 74644 91908 82/35 1726) 08092 6 55 74662 91900 82762 17233 08. co 25358 5 ' 56 74681 91891 827^0' i ~2io 08109 4 1 74700 91883 82817 17^83 08 1 1 7 2 ;?co 3 f 58 74719 91874 82844 r7l6 081 6 25281 2 59 60 747 37 747 > 6 M' 1806 ,857 Sine. 82871 82899 17129 I7ior oS 1 34 08143 Co-lecant 25263 Sec.aiu. 1 o I Co- line. Co-tang. j Tangent $ egw TABLF. V. Of ARTIFICIAL Sines, Tangents, and Secants. 34 M. Sine. Co-fine. jTangent. Co-tang. Secant. Cofecant. 9 7475<> 9.91857 0.82899 10. 17101 10.06143 io.25H4 60 I 74775 91849 82926 17074 08151 25225 59 2 74794 91840 8*953 17047 08160 25206 58 3 7481* 91832 82980 17020 08168 25188 57 4 74831 91823 83008 1.6992 08177 25169 56 5 74850 91815 83035 16965 08185 25150 55 6 74868 91806 83062 16938 08194 25132 54 1 7 74887 91798 83089 16911 08202 25"3 53 8 74906 91789 831^7 16883 08211 25094 52 9 749-4 91781 83144 16856 08219 25076 5' 10 9-74943 9.91772 9.^3171 10. 16529 19.08228 10.25057 5 1 1 74961 91763 83198 16802 08237 25039 49 12 74980 91755 83225 16775 08245 25020 48 13 74999 91746 83252 16748 08254 25001 47 ! r 4 75017 91733 83280 16720 08262 24983 46 1 15 753 6 91729 83307 16693 08271 24964 45 , 16 75054 91720 83334 16666 . 08280 24946 44 : i? 75073 91712 83561 16639 08288 24927 43 r- 75091 9'7'->3 83388 16612 08297 24909 42 ! r 9 7st ro 91695 83415 16585 08^05 24890 4^ i 2 0.75128 9.01656 9 834^2 10.165 3 10.08 ; 14 10.24872 40 ' 21 75'47 91677 834/0 16530 08323 24853 39 i 22 75165 91669 83497 16^03 08331 24^35 38 f 23 75184 91660 83524 16^76 083-40 24816 37 24 75202 91651 83551 16449 08349 24798 36 *5 7v 7 -zi 9 l6 43 83578 16422 08357 24779 35 26 75239 91634 83605 16395 08366 24761 34 j 2? 75,*S* 91625 83632 16368 08375 2474* 33 1 28 752/S 91617 83659 1634? 08383 24724 3 2 i 2Q 75294 91608 836*6 16314 08392 24706 3i 30 J-753'3 9.91399 9 83713 10.16287 10-08401 10.24687 30 71 7533* 91591 83740 16260 08409 24669 2 9 3- 7535 91582 83768 16^32 08418 24650 z$ 33 75368 9'573 8 3795 16205 08427 24632 27 34 753*6 91565 8>*22 16178 08435 24014 26 35 75405 91556 83849 I (. i 5 1 08444 M595 25 16 754^3 9*547 833"6 16124 08453 24577 24 37 7544 1 9M38 83903 16097 08462 24559 2 3 38 75459 91530 839?0 16070 08470 24541 22 ?9 7547? 91521 83957 16043 08479 24522 21 40 9. 7 549 6 9.91512 9* 8 ,398.4 IO. lOGlO 10.084^8 to. 24504 20 4 1 755'4 91504 84011 15989 08496 24486 I 9 4.2 75533 9*495 84078 15962 08505 24467 18 43 75.55* 91486 84065 *5935 08514 24449 17 44 75569 9 T 477 84092 159.08 08523 24431 16 45 7 20 4' 76590 90969 14380 09031" 23410 19. 42 76607 90960 856*7 ! J 4353 09040 23393 18 43 76625 99 5 1 85674 14326 09049 233/5. jy 44 76642 90942 85700 14300 . 0905,^ 23358 r6 45 76.660 9003 3 85727 ' 14273 09067 233*40 15 46 76677 90924 85754 14246 090/6 23523 H 47 76695 90915 85780 14220 09085 23305 13 48 76712' 909-^6 85807 14193 09094 23288 12 49 7673 (50896 8*834 14166 09104 23270 II 50 9.76747 9.9,887 9.85860 10. 14140 10.09113 10.2J253 1 HO 5' 76765 90878 85887 14113 09122 23235 9 52 76782 90869 85913 14087 09I3I & 53 76800 90860^ 14060 09140 23100 7 54 76817 90851 5^7 14033 09149 23183 6 55 76835 90842 85993 14007 99158 23165 5 56 76852 90832 86020 13980 09168 . 23148 4 57 76870 . 90823 86046 13954 09177 23130 3 58 76887 9*3814 86073 13927 09186 * 23 1 *3 2 59 76904 90805 86rco 13900 09195 23096 1 60 76922 90796 86126 13874 09204 23078 o Co-fine. Sine. - Co- tang. Tangent. Co iecant. Secant. ' M. 54. Pfgtees, TABI,E V. Of ARTIFICIAL Sines, Tangents, and Secants, M. Sine. Co-fine. "angent. Co- tang. Secant. Co-fecant. o .76922 .90796 .86126 0.13874 0^09204 0.23078 60 1 76939 90787 86153 13847 09213 23061 59 2 7 6 957 90777 86179 13821 09223 23043 58 3 7 6 974 90768 86206 13794 0923* 23026 57 4 76991 90759 86232 13768 09241 Z3009 56 5 77009 90750 86259 13741 9 2 5 0v 22991 55 6 77046 90741 86285 13715 9 259 22974 54 7 77043 90731 86312 13688 09269 22957 53 8 77061 90722 86338 13662 09278 22939 5 2 I 77078 90713 86365 13635 09287 22922 5i 10 .77095 .90704 .86392 0.13608 0.09296 0.22905 50 ii 77112 90694 86418 13582 09306 22888 49 12 77130 90685 86445 13555 09315 22870 48 13 77H7 90676 86471 '3529 09324 22853 47 14 77164 90667 86498 13502 09333 22836 46 '5 77181 90657 86524 13476 09343 22819 45 16 77199 90648 86551 13449 09352 22801 44 17 77216 90639 86577 13423 09361 22784 43 fl 77233 90630 86603 13397 09370 22767 42 19 772.50 90620 86630 13370 09380 12750 41 *o .77^68 .90611 .86656 0.13344 0.09389 0.22732 40 21 77**5 90602 86683 13317 ,09398 22715 39 22 77302 959 a 86709 13291 09408 22698 3* 23 77319 905*3 86736 13264 09417 22681 37 24 77336 90574 86762 13233 09426 22664 36 *s 77353 90565 86789 13211 09735 22647 35 26 77370 90555 86815 13185 09445 42630 34 27 77387 90546 86842 13158 C 945.4 22613 33 28 77405 9053" 86868 I3 J 32 09463 22595 32 *9 774" 905*7 86894 13106 09473 22^78 31 30 77439 .90518 .86921 0.13079 0.09482 10.22561 30 | 3 1 77456 90509 86947 13053 09491 22544 2 9 32 77473 90499 86974 13026 09501 22527 28 1 33 7749 90490 87000 13000 09510 22510 *! 34 77507 90480 87027 12973 09520 22493 26 35 775M 90471 87053 !294: 09529 22476 25 36 77541 90462 87079 12921 09538 22459 24 37 77553 90452 87106 12894 09548 22442 23 3* 77575 90443 87132 12868 95 '! 22425 22 ! 39 77592 _JK>434 8715.8 12842 09^66 22408 21 lo~ 9-77609 9.90414 9~8 TISj ~ o 12*15 10.09576 0.22391 2O 4' 77626 90415 87211 12789 09585 22374 J 9 1 4* 77^43 90405 87238 12762 09595 22357 18 45 77660 90396 87264 12736 09604 22340 i? 44 7/677 90386 87290 12710 09614 22323 16 45 77694 90377 87317 12683 09623 22:506 15 i , 46 777H 90368 87343 12657 09632 22^89 '4 47 77717 935S 87369 12631 09642 22173 1 4 3 77744 90749 87396 12604 09651 22256 12 _49_ 7776r 90339 87422 12578 09661 22239 II ! 50 9-7777* 9.90330 9.87448 10.12552 10.09670 IO.2Z222 iO 1 5i 77795 90320 87475 12525 09680 22205 9 5^ 77812 90311 87501 12499 09689 22188 8 53 77*29 90301 87527 12473 09699 22I7I 7 H 54 77846 90201 87554 12446 09708 22154 6 55 77862 90282 87580 12420 09718 22138 5 56 77879 90273 87606 12394 09727 Z2I2I 4 57 77896 90263 87*33 123^7 09737 22IO4 3 5* 77913 90254 87659 12341 09746 22087 2 59 77S30 90244 87685 12315 09756 22O70 I 60 77946 90235 87711 12289 09765 22054 Co- fine. Sine. Co-tang Tangent Co-lecan Secant. M. 53 Degrees, TABLE V. Of ARTIFICIAL Sines, Tangents, and Secants. 37 Deg, M. Sine. Co-fine. Tangent. Co-tang. Secant. Co-fecant. o .77946 .90235 9.87711 0.12289 0.09765 0.22054 60 I 77963 90225 87738 12262 09775 22037 59 t 77980 90116 87764 12236 09784 22O2O 5* 3 77997 90206 87790 I22IO 9/94 22003- 57 4 78013 90197 87817 12183 09803 21987 5 6 5 78030 90187 87^43 12157 09813 21970 55 6 78047 90178 87869 IiI3I 09822 **953 54 7 78063 90168 8 7 S 9 5 12105 09832 21937 53 8 78080 90159 8792Z 12078 09841 21920 5* 9 78097 90149 87948 I20C2 09*51 21903 51 10 .78113 .90139 .87974 o. 12026 0.09861 0.21887 50 ii 78130 901^0 88000 I20OO 09870 21870 49 ' 12 78147 90120 88027 11973 09^80 21853 48 13 78163 90111 88053 II 9 47 09889 21837 47 1 M 78180 90101 88079 IIplI 09*99 21820 46 15 7*197 90091 88105 II895 09909 21803. 45 16 78213 90082 88131 11869 09918 21787 44 I i? 78230 90072 88158 II842 09928 21770 43 18 78246 90063 88184 Il8l6 09937 21754 42 T 9 78263 953 88210 II790 09947 21737 4i 20 .78280 90043 .88236 o. 11764 0.09957 21/10 40 21 78296 90034 88262 11738 09906 21704 39 22 733U 90024 8^289 11711 09976 21687 38 1 23 78329 90014 88315 11685 09986 21671 37 24 78346 90005 88341 11659 09995 21654 36 2 5 78362 89995 88367 11633 10005 2l6 3 8 35 26 7^379 89985 8*393- 11607 10015 21621 34 2 7 7*395 89976 88420 11580. 10024 21605 33 28 78412 89966 88446 i'554 10^34 21588 32 2<) 78428 89956 8X472 11528 1004.4 2IS72 3i 30 7*445 . 89947 9.8^498 o. 11502 o. 100^3 0.21555 30 31 784*' 8 9937 88524 11476 '10063 2I 539 29 3 2 78478 89927 8*550 11450 10073 21522 28 33 78494 89918 88577 11424 10081 21506 27 34 78510 89908 88603 1*397 10092 21490 26 35 78517 89898 88629 U37I IOIO2 21473 2 5 36 7S543 89888 88655 "345 IOII2 21457 24 37 78560 89879 88681 "319 IO12I 21440 ^3 I* 78576 89869 88707 11293 10131 21424 22 39 78592 ?9359 88733 11*67. 10141 21408 21 40 9.78609 9.89849 9-8S759 10.11241 0.10151 0.21391 2O 4* 78625 89*40 88786 11214 I0i6o 21375 19 42 7864* 89850 838i2 11188 IO!7O 21358 18 43 78658 89820 88838 11162 I0l8o 21342 17 44 78674 89810 88864 11136 IOI90 21326 16 45 78691 89801 88890 11 110 10(99 21309 15 46 78707 89791 88916 11084 10209 21293 T 4 47 78723 89781 88942 11058 10219 21277 13 48 78739 89771 88968 11032 10229 21261 12 4-9 78756 89761 88994 I TOo6 10239 21244 11 50 9.78772 9.89752 9 890:10 10. 10980 10. 10248 10.21228 10 5 1 78788 8 9742 89046 10954 102^8 2I2I2 9 52 78805 89732 890/3 10927 10268 21I 9 5 8 ! 53 78821 897.22 89099 . 10-501 10278 21179 7 i 54 78837 89712 89125 10875 102*8 21163 -6 1 55 7*85* 89702 89151 10849 10298 21147 .5 56 788(89 89693 89177 10823 10307 21 13! 4 ! ! 57 78886 89683 89203 10797 10317 2JII4 3 I s8 78902 89673 89229 10771 10327 21098 2 59 78918 89663 89255 1074$ 10337 2IOS2 I 60 78034 89^3 89281 10719 10547 2ie66 O Co fine Sine. Co-tang. Tangent. Cofec^nt Secant. M, 5 1 .Degrees. TABLE V. Of ARTIFICIAL Sines, Tangents, and Secants, Degs. IM. Sine. Co-fine. Tangent. Co-rang. Secant. Co-fecant 1 o T^si" 9.85653 9.89.81 10.10719 10. 10347 10. ^1066 60 I 78950 89643 89307 10693 10357 21050 59 2 78967 '69633 89333 10667 10367 21033 58 3 7?983 89^24 8935$ 10641 10376 21017 57 4 78999 89614 8938? 10615 10386 1001 56 5 79015 89604 . 89411 10589 10396 20985 55 6 79031 89594 89437 10563 1040)6 20969 54 7 79047 89584 89463 10537 16416 20953 53 8 79063 89574 89489 10511 10426 20937 52 9 79079 89564 .89.15 10485 10436 20921 5 L 10 9.79095 9-9J54 9.89541 ro 10459 10. 10446 10.20905 5 if 79111 89544 89567 10433 10456 20889 49 12 79128 89534 ?9593 10407 10466' 20872 48 \ '3 79*44 89524 896:9 10381 10476 20836 47 J 4 79160 89514 89645 10355 10486 20840 46 J5' 79176 89504 89671 10329 16496 20824 45 16 79192 89495 89697 10303 10505 10808 44 17 79208 89485 89723 10277 10515 20792 43 18 ?9z4 *9475 89749 10251 10525 20776 42 19 792 jo 89465 2^775 '10225 i5?5 20760 4i 20 9-:9-5<> 3-89455 9.898-1 10. 10199 10.105-45 10.20744 40 21 79^72- 89J45 898^7 10173 10555 20728 39 22 79285 &9435 89855 10147 10565 20712 38 2-3 7934 94*5 89879 IOI2I i57S 20696 37 I *4 79319 89415 89905 10095 K ie>5*5 ao68i 36 -5 79^35 89405 89931 10069 IOS95 20665 35 26 9 5i 89395 89957 10043 10605 20649 34 47 9 67 89385 89983 JOOI7 10615 20633 33 28 9^1 89375 90009 09991 1062.5 * 20617 r- a,*7 9 '-9 89? 4 9003J 09965 106 -6 20)01 ?i 3 3-79*15 >.9354 ).9')o6t 10.09939 ro. 10646 IO.20585 30 3i 79131 89344 90086 .09914 10656 2056} 20 32 79 J 47 30334 90112 9 888 10666 20>v3 2i5 33 79465 893*4 90138 09862 1 06 -;6 20537 ^7 34 79473 89314- 90164 09836 110686 20522 26 35 79494 89304 90190 OgSlO 10696 20506 25 i 36 795io 89294 90116 C^i i 10706 20490 24 37 79526 9284 90242 09758 10716 20474 23 3* 7954* 89274 90268 09732 10726 204 = 8 22 39 - 795J8 89264 902-4 09/06 10736 20442 21 40 9-79573 9-V54 9.90320 10.09680 10. 10746 10. 20417 20 4i 7)5*9 89244 90346 09654 10756 20411 ^9 4z 79605 89*33 90371 09629 10767 20395 18 i 43 70621 89223 90397 09603 10777 20379 17 44 79636 89213 90423 C 9577 10787 20364 16 45 79652 89203 90449 09551 10797 20348 15 46 79668 39193 90475 09525 10807 20332 14 47 79684 89183 90501 09499 10817 20316 13 42 ' 79699 3 9 i73 90527 09473 10827 2030f ' 12 49 797 I! i 89162 9055? 09447 10838 20285 11 !i 5 9-79731 9.8915? 9.90578 to. 09422 10. 10048 10.20169 10 1 51 79746 89142 90604 09396 10858 20-54 9 . 5* 79762 89132 90630 09370 10868 20238 O i 53 7977^ 89122 90656 09344 108* 2O2 Z 2 *J ; 5-1 79793 89112 90682 O 93 .l8 10888 202 7 Q ! 5S 79809 89101 90708 09292 10899 20I9I 5 ! 56 79 8 i5 89091 ' 90734 09266 10909 20175 4 i 57 79840 89081 90759 OQ24I 10919 20 1 :>0 3 ! 5* 79856' 89071 90785 9 2I5 10929 20144 2 59 79872 89060 93811 09189 10940 20128 I ; .60 79^87 89050 90837 09163 10950 20113 Co- fine. "*" , ,1 , Sine, Co-tang. Tangent. Cg-fecant Secant- ty, c ! J Degrees, ' TABLE V. Of ARTIFICIAL Sires, Tangents, and Secants 39 Degs. M. Sine. Co- fine. Tangent. Co-tang. Secant. [Co-Tecant o ,. 79*07 9.69050 9.90837 10.09163 10. 10950 10.20113 'bo I 7993 89040 90063 09*37 10960 20097 59 2 79918 89030 90889 cqr n 10970 20082 58 : 3 79934 89020 90914 090^6 109^0 20066 57 4 79950 8goo 9 90940 09060 10991 20050 56 5 79965 8 3d. ,9 90966 09034 1 IOOI 20035 55 6 79981 88989 90992 09008 I10II 20019 54 7 79996 8*978 91018 08982 11022 20004 53 8 Boo 12 88968 91043 08957 II032 1998*4 52 80027 8-638 qio69 08931 1 1042 1 99?3 ii 10 9.80043 9.83945 9.91095 ro, 08005 10. 11052 Fb. 199.57 5 ii 80058 88937 91121 08879 11063 19942 49 12 80074 88927 91147 08853 11073 ..',2.6 48 13 Sv. 089 88917 91172 08^28 I IO(i3 19911 47 88906 91198 08802 11094 19^95 46; 15 80120 91224 08776 ii 104 i^^So 45 16 80136 8S886 91250 087 ro 11114 19864 44 17 80151 88875 91276 O&7Z4 11125 1 9 : ; 4 9 43 18 80166 8*865 91301 08699 11135 19834 42 *9 . 80182 S3'*- 5 91327 08673 11145 19818 4* 20 9.80197 9.88844 9-9 l 353 10.0*647 10.11156 10.19803 40 21 88834 9*379 08621 11166 19787 39 22 8oiz8 888-24 91404 08.596 11176 1977* 38 23 '0244 88813 91430 08570 11187 19756 37 24 80259 88803 91456 08544 IH97 19741 36 25 88793 91482 0^518 11207 19726 35 26 8- 7 o 88782 91507 08493 11218 19710 34 27 80305 8X772 9 r 533 08467 11228 1-9695 33 28 80320 88761 9*559 08441 11239 19680 3* 29 So? 36 88751 91585 08415 11249 19664 3> 3 9 .803U 9.38741 9.91610 10.08390 jo. i 1259 lo. 19^49 30 31 80366 * ^8730 91636 0.8364 11270 19634 29 32 80382 88720 91662 08338 11280 19618 28 33 80397 88709 91688 08312 11291 19603 27 1 34 80412 88609 9*713 087.87 11301 19588 26 35 80428 8*628' 91739 08261 11311 19572 25 36 80443 88678 91765 08235 11322 19557 24 37 80458 88668 91791 08209 11332 19542 23 ! 3 80473 88657 91816 08184 11 343 19527 22 80489 88647 9fS42 .08158 II353 19511 21 i 4 9.80504 9.88636 3^7868 10.08132 10. i 1364 .0.19496 2O 41 80519 88626 9 T ^93 08107 IJ 374 19481 19 80534 88615 91919- 0^081 "385 19466 1 8. i 43 80550 88605 9*945 08055 1 1395 19450 17 ! 44 80565 88594 91971 08029 1 1406 J 9435 16 45 80580 88584 91996 08004 1 1416 19420 15 46 80595 88^73 92022 07978 11427 19405 14 ' 47 80610 88563 92048 07952 11437 13 48 80625 88552 92073 07927 1 1448 193^5 12 49 80641 88542 92099 O7QOI 114^8 '9352 11 5 ^.80656 9 88531 9.92125 10.07875^ ro . 1 1 4-t>v 10.19344 1O 5 1 80671 8*521 92150 07850 11479 19329 9 i 52 80686 88510 9>?7 07824 11490 19314 3 ; 53 80701 88499 92202 07793 11501 19*99 7 i 54 80716 8*489 92227 C7773 11511 192^4 6 i 55 80731 84 ?8 92253 077,17 11522 19769 5 ! 56 80746 88468 92279 07721 11532 10254 4 57 80762 88457 92304 07696 "543 19238 3 58 80777 88447 92330 07670 115-53 19223 2 59 80792 88436 07644 11564 19208 I 60 80807 88425 92381 0.76*9 H57J IQJ 9 3 Co- fine. Sine- Co-tang. Tangent. Co-fecaiit-' Secant. * ,^. J^^i-v-A^ic- TABLE V. Of ARTIFICIAL Sines, Tangents, and Secants. 40 Degs. M.j Sine. , Co-fine. Tangent. Co-tang Secant. jCo-fecant. .80807 .60425 >. 92381 10.07519 0.11575 10.1,193 60 I 80822 8S 4 i 5 92407 07593 11585 191-8 59 2 80^37 88404 $M33 07567 11596 19163 58 3 8oS<,2 8304 9245^ 07542 11606 19148 57 4 80*67 88383. 924^4 07516 11617 J 9 1 33 56 1 : 5 80*82 . 88372 92510 07490 11628 19118 55 ,i 6 80897 S3i62 9*535 07465 11638 19103 54 \ 7 80912 88351 92561 07439 11649 19088 53 8 80927 88340 97 07413 11660 19073 5* i 9 80942 88330 9ZUI2 07?Si 11670 19058 5i 10 .80957 ) 8*319 9. 92038 10.07302 cuiib&i 10.19043 5 ! ri 80971 8830$ 91663 07337 11692 19028 49 12 809*7 88i y 8 9i6S9 07311 U702 19013 48 ri 81002 8Sz<7 9-7 r 5 072*5 11713 1899* 47 J-r *I17 8*276 92740 07260 11724 1*9*3 4 J I 8 iO}t 8*266 92766 07234 H7H 18^68 45 1 6 8104) 882^5 9*7';* 07203 H74S 18954 44 17 81061 83 244 92^17 07183 ir 7 s6 18939 43 *8 81076 88134 S 243 07157 1 1706 18924 * l JO 81031 , 8g^ 3 9 -S68 07/32 '1777 1^09 4 r 10 . i i 106 9.6^212 ;.92>94 iO.O'/ iot> 0.1178$ 10 I 89.). 40 ii 81121 8Siot 0,2^1^0 07080 JI799 i-7', 39 22 ' 8it6 8v; 9 j 9*945 07355 11809 18864 ?s *3 8 M 5-1 88180 92^71 07019 11820 18849 37 14 81166 88ifc9 9x996 07004 11831 18834 36 15 8iiSo BSiqi 93022 009:8 11842 18^0 3 26 81195 ^8148 93048 66952 I I > 2 18^05 34 27 8 12 to 88.37 9373 06927 II8&3 18790 33 &i 8rzi5 88126 93099 06901 Il8^4 i775 3* *9 8 12 -;0 8X115 .93^4 06876 nS?j i8;6o 3i 30 9.81254 9.5^105 9.93150 10.06^50 10. 11^95 10- ^746 30 3i 81269 88094 93*75 06825 11906 18731 *9 3* 81134. 88083 93201 06799 11917 1^716 tl 33 81299 88071 93227 06773 11928 18701 27 34 81314. 88061 93*5^ 06743 11939 IS686 z6 35 813^8 88051 93*7^ 06722 I z 949 18672 *5 36 8n43 8*040 ^33^3 06697 11960 18657 *4 37 81358 88029 933*9 06671 11971 18642 *3 3* 81372 SBoiS ^3354 06646 11982 18628 22 Ijl Br?8? 88007 .93380 06620 11993 18613 21 40 9.81401 9.H799 6 9.93406 10.0651,4 10. 12004 10.18598 2O 41 81417 87985 93431 06569 12015 18583 19 4* 81451 7975 934^7 46543 12025 18569 18 43 81446 '87964 934'^* 06^18 12036 18554 17 44 81461 27953 93508 064;2 12047 18539 16 ' 45 8i475 2794* 93533 06467 12058 18525 15 ! 46 81490 87931 93S59 06441 12069 18510 H 47 81505 87920 93584 06416 12080 i8495 3 I 4 81519 87909 03610 06390 1 209 1 18481 12 ^49 81534 8789? 9^6^6 06 s 6-i I2I32 18466 II 5 9. 81549 9.87887 9.95^61 10.06339 IO.I21I3 10.18451 IO 1 5 1 81563 87^77 93687 06313 I2I23 18437 9 ; 5 2 81578 87866 937i* 06^88 12134 18422 8 i 53 8i 59 z 87855 93738 06261 12145 18408 7 54 81607 87^44 93/63 o6z37 I2IS6 18393 6 ! 55 81622 87833 93789 06211 I2l67 18378 5 56 81636 87821 9 3$ 14 06186 12178 18364 4 57 81651 87811 93840 06 1 60 12189 18349 3 5* 81665 87800 93f5 06135 1220O 18335 2 ' 2 87734 94018 05982 12^66 18248 6 5 81767 87723 94-044 05956 12277 18233 5 6 81781 877" 94069 0.5931 12Z58 18219 4 7 81706 87701 94095 05905 12299 18204 5? 8 81810 87690 94120 053^0 12310 18190 2 9 81825 87679 94146 0^854 I 212T 18175 5 1 10 .81^59 .87668 .94171 0.05829 io i 2332 o. iKi6i 5 ii 81854 87657 94197 0580? 1^343 18146 49 IZ 8i86S 87646 94222 0577? 12354 iSiji ifc 13 81882 87635 9424$ 05752 12365 18118 /; !4 81897 876^4 94 2 7'< 05727 12376 iSro3 /y 15 81911 87613 94-')9 05701 1^3*7, 18089 [5 16 81926 87601 9*3*4 05676 I2 399 18074 44 17 81940 87590 94350 05650 12410 18060 43 iS 81955 87579 94375 05625 1 1421 18045 |2 19 81969 87<6S 94401 05599 1143?. 18031 4' 20 .81983 87557 .94426 0.05574 0.12443 10. 18017 4^ 21 81998 87546 944?* 0554^ 12454 18002 39 21 82011 87535 94477 055^3 U4 6 5 i 7y S8 S8 23 82026 87524 94 ; .o3 0^497 1^4/6 1/974 J7 24 82041 87<5'3 94528 0547; 12487 ^7959 36 25 8*055 87501 94554 05446 12499 J 7945 }5 26 $2O'>9 8749 94579 0542 1 12510 17951 :H *7 81084 87479 94*04 O 5396 12 J2I 17916 jj 28 82098 87468 94630 05370 12532 17902 32 *9 82II2 2/457 94^55 o*345 12^43 i 7 88S 3' 30 9.82126 5.87446 9.94^81 0.05319 0.12^54 0.17874 3 3i 82141 87434 94706 0^294 12566 17859 2 9 3* 82155 874*3 94732 05268 12577 17845 28 33 82169 87412 9475? 05243 12588 17831 27 ! 34 82184 87401 94783 05217 1^599 17816 26 35 82298 8739 94^08 05192 12610 17802 2 5 3^ 822f2 87373 94834 05166 12622 I77?S 24 37 8Z226 87367 94859 05141 12633 J7774 2 3 38 82240 273S6 94884 05116 12644 17760 ^^ 39 55 87H5 9-jqio 05090 12655 T 7745 2. f 40 9.82269 9-37334 9-94935 10.05065 10. i:>66f> 10.17731 20 4i 82283 873" 94961 05039 12678 17717 T 9 42 82297 87311 94986 05014 12689 17703 18 43 82311 87300 95012 04908 12700 17689 ' 7 44 82326 87288 95037 04963 1271.2 17674 16 45 82340 8/277 95062 04938 12723 17660 15 46 47 82^68 87266 87255 95088 95 lr 3 04912 04887 12734 12745 1764^ 17632 J 4 13 4* 82382 87M3 55'39 04861 12757 17618 12 49 82396 87232 9 ', 1 64 04836 11768 .17604 If 5 9.82410 9.87221 9*95190 10.04^10 ic. 1-2779 10.17590 10 5i 824*4 87209 95215 04785 12791 1757^ 9 5* 82439 " 87198 95240 04760 12802 175,61 b 53 **453 87187 95266 04734 12813 J7547 7 54 82467 87175 95291 01709 12825 17533 6 55 82481 87164 95317 04683 11836 17519 5 56 82495 87153 95341 04658 12*47 i/S5 4 57 82509 87141 05368 04632 12859 r7 49 3 58 82523 87130 95393 04607 1 28 70 17477 2 59 82537 87119 95418 045#a 12881 17463 ) 60 82551 87107 95444 04556 12895 T7449 O 60 fine Sine. Co-tang. Tang"! t Co-fecant Secant. M . 48 Degrees . Of ARTIFICIAL Sines, Ta-ffgcr.ts, sad ec?,tits. 42 Degg. M.r Sine. Co-iin Tament., Co-tang. Secant. Co-fecant. f o .. 19.1*255 1 9.87107 ) -95444 i o . 04 5 5 6 ro. 12893 jo. 17449 <.o i 1 gz 5 6 5 870g6 95469 04531 12904 17435 59 2- 5*579 87085 95495 04505 12915 *74*l 5* 3 8*593 S7073 955*0 04480 ^12927 17407 57 4 82607 87062 95545 C4455 13938 *7393 56 5 8:621 87050 95571 04429 12^50 J 7379 55 6 826.55 87039 955^6 04404 12961 J 7365 54 7 82649 87028 95622 043/8 12972 17351 53 8 82663 87016 95 6 47 04353 12984 J7337 5* 9 82677 87005 95672 04^28 i ? -995 17323 . i 10 9-84691 9.86993 9.95098 (0.04302 to. 13007 10.17309 ~TO~ ii 82705 86982 ' 957*3 04277 13018 17295 49' 12 8^719 86970 9^74* 04252 13030 17*81 48 13 8 *733 869159 95774 04226 13041 17267 47 H 82747 86947 95799 04201 13053 J 7^53 46 15 82761 S6 93 6 95825 04175 13064 17239 45 16 82775 86924 95850 04150 13076 17225 44 i? 82788 86913 9.5875 04125 13057 17212 43 18 2S02 86902 95901 04099 13098 17198 42 ^12. 848X6 86890 95925 04074 131 ro 17184 4i 20 9-82830 j.. 86879 9 -9595* 10.04048 10. 13121 10. 17170 40 21 82844 86867 95977 04023 13*31 J 7i56 39 22 82858 868 < ;5 9600: 03998 I3H5 J 7U2 38 ! 23 82872 86844 96020 03974 '3 1 5 6 17128 37 i 2 4 828*5 86832 96053 03947 13168 17115 36 25 82899 86821 96078 03922 I3I79 17101 35 i 26 82913 86809 96104 03896 13191 17087 34 27 82927 86798 96129 03871 13202 17073 33 *3 82941 86786 96155 03845 13214 17059 3- ; 2Q | 82955 8677; 96180 03820 13225 . 17045 31 30 9.82968 86763 .96205 10.03795 0.13237 10. 17032 50 31 82982 86752 96231 03769 13248 17018 29 3* 82996 86740 96156 03744 13160 17004 28 33 S^OIO 86728 96281 03719 13272 16(^90 27 34 850Z3 86717 96307 0369? 13*83 16977 26 35 *3*37 86705 9 6 S3* 03668 13295 16963 25 36 83051 86694 9 6 357 03643 I33o6 16949 24 37 83065 86082 96383 03617 I33i8 16935 23 | '' 3 83078 86670 96408 03592 13330 16922 22 i ?9 83092 866*9 964^3 03567 I334J 16908 21 | i 40 q. 8 3106 86647 964^9 0.03541 I0 - 3353 10. 16804 20 4* 83120 86635 9 6 4 4 03516 13365 i6'j^o *9 : 4- 83133 86624 96510 0-490 13376 16^67 18 43 83147 80612 9 6 5?5 03465 13388 16853 *7 83161 S66oo 96^60 03440 13400 16839 16 : 45 83174 86389 96586 03414 I34* 1 16826 15 i 4 83188 86577 96611 03389 J3423 16812 H 1 47 83202 86565 96636 03364 13435 J& 79 3 13 4 X H>5 86554 96662 033*3 ' U446 16785 12 49 83229 86542 06687 03313 13458 16771 II 50 9 . 83242 86530 96712 0.032,08 0.13470 10.16758 10 5' 83156 86518 96738 03262 13482 16744 9 CT -> ** 83270 86507 96763 03137 J3493 16730 8 53 837.83 86495 96788 03212 13505 16717 7 54 83297 86483 96814 03186 13517 16703 6 83311 86472 96839 -03161 13528 16699 5 5& 83324 86460 96864 05136 J3540 16676 4 57 *333* 86448 96890 G ; i T o 13552 16662 3 58 8335r 86436 96915 03085 13564 16649 2 59 83365 86425 96940 03060 *3575 16635 I C 83378 86413 96966 03034 13587 16622 O Co-line. I Sine. o tang. Tangent. ^o-fecant Secant. M. 47 Degrees. TABLE V. Of ARTIFICIAL Sines, Tangents, and Secants. 43 Degu, *mamr*m M, Sine. Co-line ffangen Co-tang Secant. Co lecaht o 9-8337* 9.86413 9.96966 10.03034 10.13^7" iO. 160^2 60 1 8339 2 86401 96991 03009 *3599 16008 59 2 834 5 86329 97016 02984 1361 1 J 6595 5* 3 83419 86377 9/0^.2 02958 13623 16581 57 4 83432 86366 97067 02933 ^634 16568 56 5 83446 86354 97092 02908 13646- 16554 55 6 *3459 86342 97118 02682 13658 16541 54 7 8347; 86330 97143 02857 13670 16527 53 8 83486 86318 97-168 02832 13682 165x4 5* 9 83500 66306 9-7193 02807 13694 1 6 500 5i 10 9-83513 9.86,9, ') 9/219 .0.01781 10.13705 10. 16487 5 ii 83527 86283 97244 02756 I37I7 16473 49 11 83540 86271 97269 02731 137^9 16460 48 13 83554 86259 9/295 0270^ 13741 16446 47 H 83567 86-47 97320 02680 *3753 16433 46 15 83581 86235 97345 02655 J37-6, 16419 45 16 8 3594 86223 - 97371 02629 13777 16406 44 i? 8360* 86zi r 97396 02604 13789 16392 43 18 83621 86200 97421 02579 /3foo 163/9 42 J 9 83634 86i8S 97447 02553 13812 16360 4' 20 9.83648 9.86176 9.97472 0.02528 o. 13824 ..10352 4 5 2 I 83661 86164 97497 02503 13836 16339 39 22 83674 86152 97523 02477 13848 16326 38 23 83688 86140 97548 0/452 13800 16312 37 24 83701 86128 97573 02427 13872 16299 36 25 83715 86n6 975,98 0240* 13^84 16285 35 26 837^8 86104 97624 02376 J3*96 16272 34 27 83741 86092 97649 02351 13908 16259 33 23 837.'5 86080 97674 02326 13920 16245 32 29 83768 86068 97700 02300 ^3932 16232 3J 30 9.8378! 86056 .97725 0.02275 0.13944 o. 16219 30 31 83795 86044 97750 02250 13956 16205 29 32 83808 86032 97776 02224 13968 16192 28 33 83821 86020 97801 02199 13980 16179 27 34 83834 86008 97826 02174 J 399 2 16166 26 35 83848 85996 97851 02149 1400^ 16152 25 36 83861 85984 ' 97877 02123 14016 16139 24 37 83874 85972 97902 02098 14028 16126 23 3? 83887 85960 97927 02*73 14040 16113 22 39 83901 85948 97953 02047 *45*. 16099 21 40 9.83914 .85936 .97978 0. 02022 o. 14064 0.16086 20 4 1 83927 85924 98003 01997 14076 16073 T 9 42 83940 85912 98029 * 01971 14088 16060 x 18 43 83954 85900 98054 01946 14100 16046 17 44 83967 85888 98079 OI92I 14112 16033 16 45 83980 85876 98104 01896. 14124 16020 15 46 83993 85864 98130 Ol870 14136 16007 14 4/ 84006 85851 98155 01845 14149 15994 13 48 84020 85839 98180 Ol820 14161 15980 12 49 84033 85827 98206 01794 I4 J 73 15967 II 50 9 84046 .85815 .98231 0.01769 0.14185 0.15954 IO 5i 84<>59 85803 98256 01744 14197 I 5V4 I 9 52 84072 85791 98281 01719 14209 15928 8 53 84085 85779 98307 01693 1422 1 I59I5 7 54 84099 85766 9833 2 01668 14234 15901 6 55 84112 85754 98357 01643 14246 15888 5 56 84125 85742 9838^ 01617 14258 15875 4 57 84138 85/30 98408 01592 14270 15862 3 58 84151 85718 9^433 01567 14282 15849 2 59 84164 85706 98458 01542 ' H 2 94 15836 I 6c 84177 85 6 93 98484 01516 H307 T 5 ?23 Co-fine. Sine. Co-tang Tangent _o-fecant Secant. MJ 46 Degree?, TABLE V. Of ARTIFICIAL Sines, Tangents, and Secants. 44 M. Sine. Co-fine. Tangent Co-tang. Secant. Co-fecant | o 9.84177 9.85691 9.98484 ie. 05616 10.14307 10.15823 60 i I 84190 85681 98509 01491 14319 15810 59 2 84203 85669 98534 01466 14331 15797 58 3 84216 85657 98560 01440 1.4343 15784 57 4 84249 85645 98-585 ' 01415 56 5 84242 85632 98610 01390 14368 15758 55 6 84255 85620 98635 01365 14380 15745 54 7 84269 85608 98661 oi339 14392 53 8 84282 85596 98686 01314 14404 15718 52 9 84295 85583 98711 01289 14417 15705 5* 10 9.84308 9.85571 9-9 8 737 10.01263 10. 14429 10. J 5692 50 ii 84321 85559 98762 OI2 3 14441 15679 49 12 84334 .85547 98787 OI2I3 M453 15666 48 13 84347 85534 98812 OII88 14466, '5653 47 84360 85522 98838 OII62 14478 15640 46 15 84373 85510 98863 01137 14400 15627 45 16 84385 85497 98888 OIII2 i453 15615 44 17 84398 85785 98913 01087 14515 15602 43 18 84411 85473 9 8 939 0!O6l 14527 15589 4- 19 84424 85460 98964 OIO36 14540 20 9-84437 9.85448 9.98989 IO.G10I1 10.14552 10.15563 40 ZI 84450 85436 99015 00985 14564 39 , 42 84463 854*3 99040 00960 . 14577 1:037 23 84476 8^41 1 99065 00935 14589 i ^524 37 24 84489 85399 99090 OO9IO 14601 15511 8450- 85.386 99116 00884 14614 15498 35 26 845 15 85374 99141 00859 14626 15485 34 i ^l 4528 85361 99166 00834 14639 15472 33 i 28 84540 85349 99191 OOSOO 14651 15460 29 84553 85337 99217 00783 14663 '5447 31 j 30 9,84566 9.85324 9.99242 I0.0075S 10. 14676 10.35434 3o 84579 85312 99267 00733 14688 15421 2 9 3^ 84^92 85299 99 2 93 00707 14701 15408 28 33 84605 85287 99318 - OO682 14713 15395 27 34 84618 85*74 99343 00657 14726 15382 26 35 84630 85262 99368 OO632 ' H738 15370 2 ' 36 84643 85250 99394 00606 14750 J 5357 24 37 84656 85237 99419 0058l 14763 *5344 84669 852*5 99444 00556 H775 I533I " ! 39 84682 85212 99469 00531 14788 15318 21 40 9.84694 9. 85200 9.99.495 IO.00505 10. 14800 10.15306 2-0 ' 4 1 84707 85187 99520 00480 14813 15203 1 9 84720 85175 99545 00455 14825 1^280 iS 43 847 53 85162- 99570 00430 14*3 8 15267 17 44 84745 85150 00404 14850 1 6 84758 85137 99621 00379 14863 15142 15 46 84771 85125 99646 0354 i4 Q 75 15229 47 84784 85112 99672 00328 14888 15216 1 3 >', 43 84796 85100 i 99697 00303 14900 15204 12 1 49 84809 85087 99722 00278 H9I3 i c 1 9 1 ii - 9.84822 9.85074 9-99747 10. 002^3 10. 14926 10.15178 10 51 84835 85062 99/73 00227 14938 15165 9 52 84847 8 5049 99798 O0202 14951 15153 3 53 84860 8503-7 99823 00177 14963 15140 7 54 84873 85024 99848 OOI52 14976 15127 6 84885 85012 99874 OOI26 14988 15x15 . s . 56 84898 84999 99899 OOroi I ^OOI 15102 4 84911 84986 99924 00076 15014 15089 3 .58 84923 84974 99949 00051 15026 15077 2 "Q 84936 84961 99975 00025 15039 15004 I 60 84949 84949 10 .0000 ooooo 15051 1505: O Co-fine. Sine. Co-tang. Tangent. Co-fecant. Secant.' M j 45 Degrees. J.ABLE Yl IViERIDIOW AJ M. GOBI od. id 2d. 3d. 4 d. 5d. 6d. 7d. 8d. 9 _d. lOd. iid. ud. \jd. M. o 60 61 120 12 t 1 80 181 240 241 300 Hi 421 422 4 8~ 542 H3 603 604 664 665 725 726 78.7 7*8 o i 2 3 4 2 3 4 62 63 64 122 123 124 182 183 184 242 244 302 304 363 364 365 4*3 424 425 484 485 486 544 545 546 605 606 607 666 667 668 727 728 729 789 79 791 2 3 4 -5 6 5 6 65 65 125 iz6 186 245 246 305 306 366 367 426 427 487 488 547 548 608 609 669 670 731 732 792 793 5 6 7 8 8 67 6s 127 128 187 188 247 248 307 308 368 369 428 429 489 49 549 55 610 6n 671 672 733 734 794 795 / 8 9 g 129 189 249 309 370 43 491 55 1 612 673 735 796 _j 10 ii 13 14 10 ii 12 13 1/1 TO 7i 7 2 73 74 132 133 190 191 192 193 194 250 251 252 253 *54 3 IO 3' 1 311 314 371 372 373 374 37=; 432 433 434 435 492 493 494 495 496 552 553 554 555 556 613 614 615 616 617 674 675 676 677 678 736 737 738 739 740 797 798 799 800 So i 10 ii 12 13 "15 16 18 19 16 17 i? IQ 75 76 77 7S 79 135 I 3 6 137 '95 196 197 198 199 256 257 258 259 318 320 376 377 37^ 379 380 436 438 439 440 497 498 499 500 501 557 558 559 561 562 618 619 6ao 621 622 679 680 681 682 683 741 742 743 744 745 802 803 804 805 806 15 16 17 18 20 2) 22 23 24 20 21 22 Si 82 83 84 "140 141 43 144 200 20T 202 203 20 4 260 261 262 263 264 321 3*3 324 3^ ; 38, 382 383 3?4 .3* 5 442 443 444 445 502 503 504 505 506 563 564 565 566 567 6^3 624 62 s 626 627 68^ 686 687 688 689 746 747 748 749 750 80-7 808 809 810 811 20 21 22 2 4 26 27 26 27 2* 85 86 o _ 88 146 J 47 148 206 207 208 265 266 267 268 326 327 329 386 3*7 388 389 446 447 448 449 57 508 509 510 56* 569 57 629 630 631 632 690 691 692 693 752 "753 754 814 815 816 Sf- 26 27 28 29 29 Sc 149 209 269 330 390 450 51 i 572 J?l! 694 75? _i2 3' 32 33 34 30 31 32 33 90 9- 93 94 150 152 153 2 IO 211 212 2T 3 270 271 272 273 274 33 1 332 333 334 335 39 1 393 394 3 ) : 452 453 454 455 5 '3 514 5*5 516 573 574 575 57* 577 634 635 636 6 37 M 095 696 697 698 699 75 6 . 757 75? 759 760 8iS 819 820 821 822 3 31 32 33 34 35 36 37 35 36 37 1? 95 96 97 q8 155 156 157 158 2I 5 216 217 218 275 276 277 278 336 337 33* 3^9 39 22Q I 7 '289 34? 349 35 468 409 468 470 47i 529 530 590 59 1 592 6;i 6 5 t 653 712 713 714 77 i 775 776 836 JLH 47 48 49 50 5' 52 53 54 59 5 1 52 53 no III 112 114 170 171 172 T 73 T74 230 231 232 290 291 292 293 .--04 35 1 352 353 354 4 n 411 4'3 414 4 T 5 472 473 474 475 476 532 533 534 535 536 593 594 595 596 597 654 655 656 657 658 71?) 7 1 / 718 719 777 77* 779 780 839 840 842 5 5* 52 53 54 ~55 56 57 58 tg 55 56 57 ro 116 117 118 iro 1/7 178 I7Q 2 35 i 2y5 236 296 237 297 2 3 8: 2 9 3 239 290 356 359 416 417 418 419 420 478 479 480 481 537 539 540 541 598 599 600 601 602 659 660 661 662 663 720 721 722 723 724 7^3 784 "85 786 844 845 8J8 56 57 | M. od. id! zd.i 3 d-i 4'l.il^ J\ 7d.| d.i 9 d. lod irrt.^ d - ^yM* ' Q TABLE VI. Mi UDIONAL PARTS. V i. i 5d- icd, 7d. i 83. 9i. od. id. 2d. 3d. 2 4 d. 2 5 d. 26d. ,;- ' -*- M. 910 7 9 035 036 09* ^99 ib?. 1^3 225 22.6 289 290 354 355 419 420 1484 1550 1617 r6i8 1684 1685 o I 2 851 852 9*3 175 97 & 037 038 100 I IO! 16: 227 228 1291 1292 356 357 421 1422 1486 '4^ 7 1557 1610 [620 1686 1687 2 J 4 3<;; 915 077 040 1102 I .29 1294 358 1423 1^.88 621 [688 4 f 8 9 856 857 858 916 917 918 919 920 979 980 981 982 < 4 04?. 043 044 045 104 105 106 107 108 167 170 117, '3? 132 ^33 234 1235 1295 1296 1207 1298 I2 99 359 I 3 6c [362 1363 1424 142? 1426 1427 1428 1490 149 ! 1492 '493 f 557 r 55 b 15.59 '623 1 62^ 1627 ils^ 1690 .691 1693 1694 5 6 7 8 9 10 ii 860 861 862 921 922 923 924 984 985 986 046 047 048 0-19 109 I IO in 112 "73 1174 117 1237 1238 1239 IJOO 1301 I3O2 1303 i;6 1366 1.367 1368 1430 1431 1432 '4v. 1497 1562 IS 64 16 , 1695 696 '97 [698 ii 12 13 M 86; 925 987 050 r r r 17 1 140 1304 1369 T 43 1490 I ') i6v 1690 14 i<; 86 + 926 988 I0 5 I 1114 Ii; 1141 I3O5 137- '43 > J- ;, 1567 f^r 1700 I c 16 86; 927 989 1052 1115 H76 1242 I30n 1371 r 4 36 I50i '634 1/02 16 17 866 9*8 990 1053 nib 'I I 60 1247 1307 1372 '437 150; 1569 1635 170; i? 19 868 929 930 992 993 1054 1055 1117 1118 Il8z 1244 1 -45 I 7O9 1310 '573 1374 !1;9 '504 '57 1571 I ') 7 ' 1704 . ' , 18 n 20 869 934 9H 1056 II F9 ri8; 1246 I3II 1375 1440 r -o' i - i6T" I ; ;(> 20 2 870 932 ,99. '057 I 120 1184 1248 1312 [376 144-. 150 ' 57 " I .4^ 1707 21 2 871 933 9 6 i > " II2I 1 185 T249 1313 '377 '44 ? . ,08 I 7-. 1 r f70' 22 2 2 872 87- 934 9*5 99 998 i . 6c I 122 1186 nS- 1250 1251 1315 '37C 13*0 '44 4 '59 '577 -' M : 170., r-ri 23 ' t 8-4 936 ggc io6j 1*2 n -> 12^2 13 I ( I 3 8r 141- 1512 1578 i 7 2s 2 ? 7. 937 1000 1 06 1 ; 2 f 16, 1253 1317 1382 i. 6 171 i 26" 2 H 7f 9 v" 100 :otl t r ) 2 r 1 9. r*54 1318 138; 4^ 1514 I JoO 1647 17/4 27 2 939 IO^ 106; I i 2 119.1 125: ''319 13^4 15: . r N ! i r6^ 171 - 28 2 ^79 4i 100 ro6< /12<- 1192 1256 I32r 1^85 Uv i [640 i - 1 r. 29 3 48o 94 i IOO< 136. 1130 ii>: 1257 1321 138* '45 ] 1517 15*3 1650 1717 30 i 3 8f 943 100 106^ i r? t IQ4. 1258 I Hi I 1 2 i j '. r6? i 3 88 944 1009 r j 3 II ) 1250 172, '454 151 r ^ - r; r. ' 7- c 3 Z 1 j ; S3 945 946 ro? rn- f 196 1260 1267 '3* SO' r . 9 '455 45^ 15 2C r 2. i 1588 '^>5^ I '; q . 172: 33 34 I f 948 : 101 1072 to? "3 If9 T2OC I26A 132!; 1392 139- >4^ r '2 , 1589 1 6 - 6 ! 7 Zj '7-4 Ts 36 3 88 -49 101 IO~d 113 '20 126- 1320 179- 14 '.o 1525 I5Q - i') $ 8 37 1 - 8>i 95 C fOl IO/5 "3 Z~2 f :6 r 33 f t:-;6'. 1597. i'K'; 1726 38 1 * 88 Qfl I-i 107^ 1130 -O :*6 r 7 I r ; ' r i f> i r ?- 1593 1660 172 39 4 89 95 2 IQ1 1077 n;^ i04 126* T! :.? i | 146 i'^ ? t>59 166 1729 4 1 ^ ^9 353 101 io/r 114 20 1 J3 '4J53 15*9 '59 .662 4 1 \ 3 9; 95' 101 roi 107- io8c "1 120 127-: 1271 13 139 1466 1530 1597 1663 1 66 I7 3 r 1732 4 2 43 4 i 956 toi 108 1 11.4 1208 '27: M J! r ... 146 i;3- i - i6v '713 44 4 ) z " 1-2 ro ^3 114^ : , , 127: n.v ri LI.-, r < 34 i6c i ' J l>34 1 N 4 95 H I .-2 100 J 14 1 2 1C 1274 133- 1^0; 146. i; ; 160 166- 4 6 I 3 r -i r f 14 (21 127 '4 1/7 I5.V i6oa Tf.fi '737 47 1 360 10? ' T2 ? 1176 T 34 T (406 r 47' 1603 1670 173; 4S I ^61 ros , r - r ! ' ' i34< '4 '47- r -. ,S I 6 0.1 1671 1739 1 062 :c ; 1 i 127, 1343 14. x '473 153 160; 1672 r 7 40 To ; >o M i . . ( tz8o '34- f r N7'!- f >4< 1607 1671 1741 51 1 5 - 102 109 i 1 5 M 17 . r ^ j r r '47 T 4 1 r*i 8 1675 1742 11 10 . 102 l^f i i 5 128. i [41 M'* -476 I 42 l5: r6?6 <53 I 5 T4 ?7 ipa r T - I n r i-g 3 r 74 141: '47 15.1 16: 1677 '741 I ' Q6 '03 1093 r i tz8d i?4 v 14 r; '47' '5-'! : i6r: I 74(2 <;s 1 90 ',b- ro3 f ' C r i ; i- ^49 14^^ 148 154^ 161- i >79 J747 56 i c 9 "7 r 3 rt>9 r :. z r 28- 1 3 "o r : r 4^1 1547 16 1 168 r-4'' 57' f 1 c - ,71 f D 9 t I 12. 12^ I " 141- 14*^2 1548 16;; i69] 58 5 oo 7 '^" 1 .' 11 < r ? c? i ; . 148 rcj2 161 r68r '75'- 59 IJM d i,d i,d I. 9 d 2 od.| 2id .l2-d J, 3 d 2 4 d. 2 S d. z6d. 2 7 d.).M. TABLE VI, MERIDIONAL PARTS. JM. 28d. 2 ,a. 3 od. 3'd.J 3 2d. 33d. 34d.' *5^ 36d. 37d. 3 8 d . 3(id . l40d . 4id., M. j; o 1751 1820 1*88 1958 2028 2100 2172 2244 2318 239^ 2468|2i54<; 2623 2702 i 1752 1821 1890 T 959 2030 2101 2173 2246 23J9 2.394 2470 2^46 2624 2703 I i 2 3 1753 1755 1822 1823 1891 1892 1960 1962 2031 2032 2102 2103 2174 2175 \l% 232.' 2322 2395 2471 2472 2548 2549 2625 262- 2704 2706 3 ! 4 175(5 r824 1893 1903 2033 2104 2176 2249 2323 2398 2473 2550 262?. 2707 4 6 ?$ i82S 1826 1894 1964 1965 2034 2036 2IO6 2107 2178 2179 2250 22^2 232^ 2399 2400 2475 2476 2551 2629 2631 2708 2710 5 i '6 j 8 1759 1760 1828 1829 1897 1898 1966 1967 2037 2038 2IO8 2109 2 1 8.0 2181 *S3 2254 2327 2328 2401 4403 2|79 2 ^5 2632 41711 2712 8 i 9 1761 1830 1899 1969 2039 2IIO 2182 2255 2329 2404 248 2557 2635 2714 9 i 10 1763 1831 1900 1970 2040 2112 2l8d 2257 2330 240; 2481 263^ 2715 10 j ii i / 64 1832 190; 1971 2041 2113 2185 2258 23 52 2406 2482 2559 267^ 2711 ii 12 1765 '333 1902 1972 2043 2114 2186 2259 2333 2408 24?^ 2560 2638 2718 12 j 13 1766 1834 1903 1973 2044 2115 2187 2260 2 3H 2409 2485 2^62 2640 2719 13 14 1-67 1836 19,:.- 1974 2045 21 l6 uSK 2161 2335 24*1 c 2486 2;6? 2641 2720 14 15 1768 [837 . ,.00 1976 2046 2118 2IQO 226-, 2337 2412 2487 2S64 2642 2722 15 16 1769 '838 1907 '977 2047 2119 2I 9 I 2264 2338 2413 2,;S 9 2,66 2644 2/23 16 I 17 1771 1839 1908 1978 2049 2J20 2192 2265 2339 2 4 f 4 2490^2=567 2645 2704 17 18 1772 1840 1909 197'-) 2050 2IiI 2193 22.66 2340 2415 1491 2^68 2646 2726 18 : L I9 I773 184, 1910 1980 2051 2122 2195 2^68 2342 -417 -49? 2570 2648 ~7~7 19 20 1774 .842 1912 1981 2052 2123 2 196 2261; 2343 2418 2494 2S7' 2640 2720 20 21 1775 1*44 '9 T 3 f 083 2053 2i2; 2I 9? 2270 23 44 2410 2495 >57 >6 s'C 2730 21 22 * 770 l^ : 1914 1984 20 ^4 2126 2198 2271 234; 1420 2496 2^7; 2vTiJ2 21 ! 23 1777 1846 1915 19^ 2056 2127 2I9Q 2277 2 347 2-122 2498!* v7< 2^653 - 7 1 - 24 177* 1847 1916 1986 2057 2128 2201 2274 2348 24 n 24.99 25 1780 1848 1917 198- ^058 2129 2202 2275 2349 2424 2^.0 ~~ " - *< / 26 1781 .849 1919 1988 2059 2131 22C3 227; 242; 2sOI -7V' 27 1782 5850 1920 1990 2060 2132 2204 2277 2 ' 52 242- 2 ; o ~ 28 783 IX 5 2 1921 2062 2133 227. 2*53 242^ 2^04 2581 29 ..-84 r ^53 1922 1992 2,063 2174 2207 2429 2:0? 2582 33 : 7 -' . i.54 1923 1997 2064 213: 22^3 2201 2355 24 3C 2307 2,84 2742! 31 .'78- 1855 1924 2065 2137 2209 2282 2^57 2.452 2585 ,- fj f) ^ 32 1788 18^6 '925 1996 2060 2135 22 ID 2284 2358 2433 250. -si-'C. 33 X78 9 1857 1927 1997 067 2139 221 ! 2 2$ 5 2 ? 59 2434 2^10 2 > 8 8 1746 34 /7QO T8<^ 2928 1998 J 6 9 2140 2213 2286 2360 2435 1512 1-607 34 ! 35 1791 1860 1929 1999 2070 2141 22/4 2287 2361 2437 25I7|2590 36 '792 1861 1930 2000 2071 2143 2215 1288 236 3 i + l':- 2>92 3^ ! 3" 1 793 [862 193 1 2001 2072 4144 2216 2290 2364 ^43v 2 si ^ 2 593 2671 27 si 37 ; 3^ J 794 iV>63 1932 2OO3 2073 2145 2218 2291 2365 2440 2517 2594 267^ .'- 7 r > 2 39 1796 1864 1934 2004 2075 2146 22I 9 229 i 2366 2442 25l8 2595 2674 275-1 ,39 4 r/9; 1865 '935 2CO, 2076 -.14- 22 2O 229 .'i 2368 2447 25J9 2597 267; 40 4 1 '79* 1867 1936 2006 2077 2149 22^! 229-' 236., 2^4! 2521 4598 2.675 1756 41. 42 T79 > 1X68 1937 2007 2078 CO ^2i2 22 9 6 5370 -44' 2522 2599 267 2 7 c , ^ 42 43 ! 80 1^69 1938 2008 2079 2151 2224 2297 237* 244V 27lv 2601 2679 2755 4 3 44 ; So i 1870 1939 2010 208 1 2152 222^ Z37< z 44 v 268l 2760 44 45 1802 1871 1941 2011 2052 2153 2226 144-;. 2682 2762 45 46 1804 1872 1942 2OJ2 2155 222 7 2303 2'375 2451 2527 :60C 2^83 2763 46 47 1805 1873 1943 2QI3 2 ,.84 2156 222 | 2 3 O .:. a 52' :tio6 2684 2764 47 48 r'3o6 187^ 1944 2014 2085 2157 22^0 2303 2378 1J.C > 2 ; 3 o 2607 [2^86 48 49 1807 1876 *94> 2015 2087 2I 5 S 2131 2504 2379 -454 250 2608 2f;s 7 2767 '49 5 '877 1946 2017 2088 2159 22^2 1305 2300 145: 1532 :tS8 2768 5 51 1809 1878 2018 20 8 f) 210] 2*33 2}o- 2 "8 1 a 531 2M I z6()C 2770 52 1810 1879 1949 2019 2O')O 2/62 2308 ^2 45 8 2^3: 2612 26911:771 ^2 ' 53 1811 i8 c jo 19^0 2020 2O9I 1163 7, 2 7 6 2309 24>c 2^6 2614 ,6,,2 :7~^ 54 18:3 1882 1951 2O2 1 2093 2I(' 4 22.7 23 1 J 240 1 253-7 261 s I ;v.- ; ;_ 55 1814 1883 1952 2O23 2094 2166 z:'.}8 2 < i ?. 2,.-, 6 2463 2539 2616 56 5*7 1 3 r -, s 5 r 6 r88 4 1 38 5 r 953 1955 2024 2O95 2096 2167 2r6Sj 1241 2313 23 '4 2388 1189 246 ; 2 540 2*541 26jS Z ?J I 2696 1277' 56 ' ^7 5.8 1817 1956 2O26 2097 2316 2390. ,466 2^2 2620! 59 r8i8 1*87 1957 2027 2099 2170! 2243 123! 7 2391 246" 2544 zf)2I |M. 2^d.|29d. 3od. 3 id. 32d > jbd . ; 39'! . 1400'. | i HI. TABLE VI. MERIDIONAL PARTS. Ci2782:2i 2786 2866 2.67 17^92876 Z79Cj2SJ7l 2949 -95 2951 -953 *954 2 3 _4 6 8 12793 _2Z2* 10 '2795 11)2797 12 12790 2*;o;2963 131279912881 T 4 !2*OIJ2882 15 | J -> 3031 I : o ? - i 3116 '73, !!^iil! 2877(2960 2 9 6l 10 2i': 17)280512880 iS^Sof; 21 '2810 22 23 289 I 2892 9 5 ^;2_Si4J2896 2816 2897 ^i7J- 26lS J2 9 OO 2820 : 902 2J20Q4 2.V 2826 12908 2828)2910 i >529 (291 I 2830! "9 13 33 41 42 *3 44 45 46 47 29/5 2836 2 9 l8j 3 C02 96-, 2967 2 9 68 2971 297.2 *974 ^975 297- 2978 2979 2982 2984 2985 >c-33!3"v 3C34J3r2c 3036)3121 . 3038 3040 3041 if! 7 3044 3046 3047 304* 3050 305.3 3056 3060 3061 3063 ?6-} 5065 700" 506* 3070 3071 - 2991 ^995 1839 2840 2922 1343 :S 44 2845 2926 1928 2929 50J2-.0 j:o32 51 J35ij*933 852*2935 853 J 2 936 -5j*93* 53 2858(2940 zS; 9 U94* 2*6) 2862 u 944 3005 3006 3007 3009 3010 3012 3013 3077 307'^ 308S 3090 3 1 at 3127 3130 3130 3139 3140 314:. ^43 3146 3149 3to 3152 3155 3156 ill 8 3159 3 f ~ 3162 3163 3165 3166 3168 1169 3171 ill 2 P74 3176! 3178 111: 3-3 3204 3206 '3207 3209 3210 3212 3*i3 3215 3216 3*i7 3*i9 3220 3212 322? 3226 3228 -32 3-34 3235 5237 111- 5240 r-44 3246 ^^ 3250 3251 ^53 3093 30943l8l 3C 9 6hl82 3097)3184 ,,--.,,309^3185 301413100 3187 30.16 3101 3or 3104 3020 3023 3188 3190 3191 3106 3193 3IQ7J3 310813195 3024 3110 -i026{3ii 113198 3027;3!ili32ooJ3289 ^02Q!3II4!320I J720C i-57 3 2 59 ^260 326; 3266 3268 3269 3271 3272 3274 4d. j49d. J5od. 3*93 3384 329513385 3296 3299 3301 3302 .005! 33 C 7|3397 3387 338* 33^ 339^ 3393 3394 3310 34 OC 33^!345 3316 33i9 r 3410 411 33^5 3326 34H 3417 34/6 3478 3479 3484 34*5 3487 349 349^ 3493 3495 5_id. 356<] 357 357* 3574 3_5_75 35: 35S2 3583 3585 3590 349 6 i 3 5< 349 s 3500 3501 3504 35C7 3593 3594 ( 359 6 3598 3599 3601 3602 3328 3J^9i3_52 J3420 3514 3515 3517 3518 3520 3509 3604 3511 3606 5331 333 2 1334 Uli 3337 333^ 3422 3425 34=8 3430 3341 13433 3 343 i 3434 344 3346 3349 3437 -,439 344- 3442 3353 5355 3-6 44S 3447 344S 33593 3609 3610 3612 3614 3615 35-3|36i8 3525 3-5*6 3622 3_52 8 3623 35*9|3frsS 3531 3532' 3534 3536 3537 3539 3626 3628 3630 3631 3633 3635 3636 3641 345] 3547 3643 3362 3454 3548 3364 3456J3550 3277 3278 3280 3281 ^283 336- 33*7 3368 337 3372 '. 3 7 ? >7j355i 34^9 ^46 1 3553 3555 52^. 3665 3667 3669 3670 3672 3968 3970 397* 37*9 $870 J3973 377013872(3975 37M 376^13866 376713868 367, 3772|373!3977 774)3^75 3978 3980 3775|3 "77* 378013*82 37*2^ 3984 39 36 39*7 3677 3678 3680 3682 3685 3686 3688 3690 3691 3693 3095,^/7-ri . j; . - 3696 1379613^97 i4Q 1 3784|38 5 3989 399i 37 00.15003 863887 i77 3i9 3993 378913890(3994 37911389213996 3792|3 S 94^99 K 3794 4000 369813797^329914003 3/oo|3799;39 0: :4-5 3801 13902 400 380213924:4008 38041390614010 37oi 3:7o3 3704 3706 3709 37ii 37/3 3714 3806 3907 [401* 38o 7 J3 5 8o 9 h 3811 390914014 3812 13816 3718:3^17 37 J 9i38i9 372i {3821 37J38a2 37-4 3824 3726(3826 37*7 3827 3644 3646 7647 3649 3651 37*9 3731 3732 3734 37 3 6 3737 3739 374 1 374- 3829 3831 3833 3 C; 34 3836 3^39 3 8 4 r 3843 374413844 3746|3846 374713848 3749 3462 3556)365 3464 3358 3'654 375 2 7465 ^-59 !36s6! 3754 3284 337513*46713561 3286 3376|3468 < J3563 337 ? !347of3: 3379 1347" 1 3566 8 11347 3 35*7 3657I3756 3659J3757 3660:3759 3662J 3 76o 3664! 3762 3851 ^53 3*55 3856 39 T 3 39H 3916 39^ 3920 4017 4*9 402 j 4022 4024 4026 3923 jp*j 39*5 4 30 3926 4031 392814033 3930(4035 393* 4037 3 9 33 1403 8 3935 3937 3939 394Q 394* 3944 3945 4040 4042 4044 4045 447 4049 .051 3947 4053 3949 14054 3951 4056 395* ,4058 395414060 3956,4061 3958 4663 3959 4065 4067 3860 3963)4069 3861 5965(407 3864! ? 9 66|4O" 72 o i 2 3 _ 1 , 6 8 9 10 ii 12 13 ~15 1 6 17 18 20 2t 22 23 *4 *5 26 28 _29 31 3* 33 J4_ 35 36 I "40 4 r 42 4.3 44 45 46 47 48 49 5 5* 53 jJ4 55 56 .57 59 TABLE VI. MERIDIONAL PARTS. [M. o i 2 3 4 6 7 8 _9 10 ii 12 13 56d. 40 74 4076 4078 4079 4081 4183 4185 4186 4 i88 4190 -) j 4294 4296 4298 4300 4302 59d. 6od. 6id.' 4049 4651 4653 4656 4658 62d. 4775 4777 4779 4781 4784 4786 4788 4790 4792 4794 4796 4799 4?oi 4803 4805 4807 4809 4 Sn 48*4 4816 4820 48*2 4824 4827 4529 48^1 4833 4835 1*37 4839 4^42 4844 4846 ,848 4^50 4 8 55 4857 4|9 4863 P7z 4874 4876 48:9 4881 4,:. a 488 q 4887 4850 4X92 494 ^96 49 3 ^TT . 5040' 5042! 544 5046 5349 5179 51-81 5184 5186 ,188 5195 5198 5200 5203 5205 5207 5210 ^212 66d. 67d. 68d. 563! 5 6 34 5636 5642 6qd. 579! 5797 5803 5*06 M. i 3 4 4409 4411 44'3 4415 44 1 ? 45^7 4529 $1 4535 4537 4539 454 1 4-543 4545 4905 4907 4909 4912 4914 5324 5326 5329 3331 5333 5474 5477 5479 5482 5484 4083 4085 4087 4088 409 4092 4094 4096 4097 4099 4101 4103 4105 4106 4108 4192 4194 4196 4197 4*99 4201- 4203 4205 4207 4208 4304 4306 4308 43 1 1 4313 4315 4317 4319 432' 4419 4421 4423 4425 4427 4660 4662 4664 4666 4668 4916 4920 4923 4925 4927 4029 4932 4934 4936 49.38 494 4943 4945 494? 4949 4952 4954 4956 4958 4960 4^63 4965 4967 1-969 5051 5 C 53 5056 5058 5060 5336 5338 5341 5343' 5346 5353 5356 5487 5489 5495 5497 5500 5505 5508 5510 55 '3 5518 552o 552.3 5526 5528 5531 5533 5044 5 6 47 5650 5652 5*55 5660 5663 5666 5668 5809 5811 .5814 5817 5820 5 6 7 S 9 4429 443i 4433 4435 4436 4548 455 C 4552 4555 455 6 4670 4672 4674 4676 5062 5065 5069 5072 5828 5831 10 ir 12 13 IS 16 17 18 19 20 ' 21 22 23 24 4210 4212 4214 4216 4218 4220 4221 4223 4225 4227 4229 4231 4233 4234 4236 4238 4240 4242 4244 4246 4247 4249 4251 4253 4255 4323 4325 4327 4328 433 4438 444 4442 4444 4446 4558 4560 4562 45^4 4566 4568 457 4572 4574 4680 4682 4687 4689 5076 5078 50X1 5083 .52 x 5 5219 5222 5224 5227 5229 5231 5234 5363 5368 5T73 5376 5378 538i 5389 5571 5674 5677 5679 56 3 a 5655, 5687 5690 5^93 5696 5837 5840 5842 5845 5848 15 16 17 18 20 21 22 23 24 2 5 26 27 28 4110 4112 4114 4115 4117 4332 4334 4336 4338 4340 444' 4450 4452 4454 445^ 4458 4460 4462 4464 4466 4468 4470 4472 4474 4476 4691 (693 4695 4697 r 6 99 4701 4703 4705 .4707 47^2" 4714 4-716- 4718 4720 4723 4724 4726 4728 ILL 1 4733 47 > 5 4737 4739 ill 1 4743 4745 474-7 4750 AT 5 2 5085 508$ 5090 5092 5095 5097 599 5102 5106 5111 5H3 53 5125 5127 5130 5^3- 5134 .141 5851 5^54 5J57 26 j _2_9 3T 33 34 4119 4121 4124 4126 4128 4i3 4*32 4*33 4135 4137 4139 4141 4*43 4144 4146 4148 4^5 1111 4 r 55 4157 4159 4161 4163 4164 4166 4168 4170 4*74 4*75 :;79 7 4,181 4342 4344 4346 4348 4349 4351 4353 4355 4357 4359 436J 4363 436.5 4367 4369 437i 4373 4374 4376 4378 4578 4580 4582 4584 4586 4588 4590 4592 4594 4596 459? 4600 4602 4604 4606 ;239 5241 5M3 48 5386 539 5539 554 1 5544 5546 5549 5552 5554 5557 5560 5698 5701 -5704 5706 5709 5;7" 57^5 5717 5720 5/31 5734 5736 5739 5742 574 75? 575 5759 5761 5/04 % 5868 5874 5^76 4972 4974 49 Si 5-5 1 52.53 5255 5258 5260 5398 5401 5403 5406 5408 5*79 5882 5885 589, 30 3 1 32 33 34 35 36 37 38 J_9 40 42 43 _44 45 46 47 48 49 50 52 53 _54 55 56 57 59 44/S 4480 4482 4484 44J6 4488 4490 4492 4494 [496 449* 4500 4502 4504 45o8 4509 4511 4513 4515 49*3 4985 4987 5990 ~z1 3 5267 5170 -,272 54 IT 54 T 3 5416 -,421 54*3 5426 5428 5433 55^5 5567 557 5573 "5581 55^3 5? 3j" 5894 5^96 5X99 ^902 5905 5900 5911 5914 59*7 5C-20 5922 59 2- ,-928 593 > 5934 5937 5940 5943 35 36 37 38 "40 4 1 42 4? 44 45 46 47 48 5 52 - 1 53 5 5 56 57 58 s<>' 4257 4259 4261 4262 4264 4608 4610 4612' 46x4 4616 4618 4621 4623 4625 1627 4629 4631 4 6 33 4635 4 6 37 4994 4996 4999 NCOI 5003 500^ -OC5 5010 5012 5014 5-75 5*82 4266 4268 42.70 4272 4274 4276 4277 4279 4281 4283 4285 4287 4289 4291 4203 4380 4382 4384 4386 4388 439 4392 4394 4396 439S 5M4 5146 5 1 5 l 5^53 5155 5'58 5160 5 1 2 5JA5 5167 5160 i5'7* 51/4 5177 .a$7 5297 5299 5302 5304 5306- 5~3Ti ,-314 5436 343* 544 i 5444 5446 5449 545J 5454 5456 5_459 5461 54 6 4 54 6 9 559^ 5594 559^ 5599 5602 5^04 5605 5612 5615 4754 4756 J4758 14760 4762 5017 5019 5021 5024 5026 502^ 5030 5033 535 50?} 57^7 5770 5772 5775 4400 4401 4403 4405 4407 4517 4519 4521 4523 45 2 5 4*39 4641 4643 4645 4647 4764 4767 4769 47*1 14773 5618 5620 5623 5626 5784 5789 595 1 5954 5957- ^960 i N o 6 3 > 3 2 I TABLE VI. MERIDIONAL PARTS. -od. 7' ^66 3 -'975 4 _ii2l! 5 iS 9 8i 6 5984 7 5987 -4 5992 5995 5998 12 6001 i;J6oo4 1416007 010 16 ; 18 Si : Ol<; 6022 6025 ,oiS 6031 6034 6040 '043 .046 049 6052 605 6058 6061 606.; 067 6070 ' 073 'o ')07i oos: 3 ! v o 8 il 'oSS i ',609 3 l' )0 94 4J609 ') 1 O^ 610 610 6 ; e 61. 6iT 6fi 612 . 6127 6130 6i34 140 '49 ilP34J 161 {6351 ^4'6354 167 170 174 6364 177 6367 180 6371 \ '374 186 7^2 J 95 198 201 205 208 21 T 214 217 _|i!6753 6545 P757 6.S48 6 ?6o 6552:0764 655516768 65596771 6562 6775 0565 6779 242 *45 252 6 2 - > i 387 394 6400 404 6407 410 !74d. !7 5d. 7 6970 6990 6 9 94 6 95 8 7210 7214 '223 227 7231 / - j - /T7 v / / v y 7*3 5 (7494 7774 0569)0782 6572(6786 6576 16700 6 579'>793 63|6797 6586 6801 6590 6804 6593j6So8 659716812 6603 6607 6610 6614 6819 6823 6826 6830 54I3J66I7 6834 .61 1 ,68 38 '62416841 64816845 6849 6856 686c 6864 6477 6430 635 639 642 6646 >443 6447 6450 6457 6656 6 So 6 271 6467 i 74 6277 6?. 80 6284 62,87 6200 -293 647? ''477 6480 649. (1209 ^497 309 5653687 OI7 7472J7749 74767754 748517764 769 7 2 39 724? 7248 7252 7256 7260 7*73 041 045 056 7285 7289 7294 7298 73C2 7306 73" 080 84 05 J 7092 70 9 6 ;n6 016879 5667 6886 >9p[7i24 7562 7315 73^9 73^3 ^8 7332 ^349 7358 7.^6 7371 ,14)7128 '1817132 140 M5 H9 _ 6 90S 6688 6909 . 69i-3 66956917 |6 9 20 6924 6028 6702 6706 6507 6717 6932 936 6514 6517 632516524 ,286528 |->7 6720 6943 6-24 6947 6951 6 955 6059 ,..\W3 6742 (6967 739 7401 11 53 7406 157 7410 7161174^ 499 . 5037783 5Q 7788 "793 521 535 539 7*03 5257808 7822 -*i*i/ / 548^32 7837 7842 7847 -852 7857 7862 585 7872 7608 7612 7617 75897877 7594J78S2 7^ 7907 7626 - 7631 , 76367927 932 94^ '953 7958 7963 r o68 7973 7650 7654 7664 7668 7678 7165 7169 173 7181 -419 74 2 3 74^7 7432 743^ 190 7687 745 C 45^ 45 s : 771 J 79d. 8051 ^056 8062 So6^ 8od. 8 id. 82d 83d. \ 8375 538,7 5 ^98 5404 8410 8416 8422 8439 M45 8451 8457 8463 8469 8475 8480 8486 8492 8498 8504 8510 8516 8739 8746 8752 8758 8765 <*77' 8/78 8784 8791 ^'797 8804 8810 8817 8823 8830 88^6 8843 8849 8856 8863 9146 9160 9167 9174 9182 9189 9196 9204 921 1 92 It 9225 9 2 33 9240 9248 9606 9^614 9622 9 6 3i 9639 ",072 8077 8083 8088 8093 8099 8104 8109 9047 9656 9 5 64 9672 9681 9689 9697 9706 9723 5 1 3 I 1141 9255 9262 9270 9277 9285 9300 9307 93 J 5 93:2 9731 974= 9748 9757 9765 9774 9783 9791 9800 9809 8152 ^63 8168 Si 74 8876 8883 8889 8896 8903 8909 89:6 8927 8930 8179 Si8f 8,90 Hi 96 ^201 3207 8212 ^218 8223 ^234 ,]2 4 C ?245 8251 8256 '0262 8267 Sa-73 8279 8284 8528 8534 854 8552" 8558 8564 8]3 8589 8595 8607 86~i4 8620 8626 8632 13638 J86T 5 86^1 8657 8663 8670 9330 933^ 9345 9353 9360 9368 937^ 934 9391 939 r - 9407 9414 9422 9430 943^ 9453 946 946 94T7 948 949 950 950 95' 952 953 954 954 955 956 957 958 959 9^9 9817 9826 9835 9*44 9852 8936 5943 S 95 c 8957 8963 *970 8984 Sooi 9005 9012 9018 9025 9032 9039 9046 9053 9060 9067 974 9081 9089 9103 9861 9870 9879 9897 9906 99 1 5 9924 9933 994- 995' 9960 9969 9978 9987 ''S2QC 8296 3 3 OI ^307 )^3I2 9996 1COIC 10015 1002^ 1003; \. .-5318 1 8 32^ } 8329 ) 8 33f *8_34j 2834: 5 835: 3 335* : 836; i 837C 8676 868: 8688 8695 v/o? 10043 10052 10061 10071 icoSc 8707 8714 8 7 2C Vm 91 ic 9117 912^ 9131 913' 10089 10099 TOIO IOIl8 TOI2" 7v9^ ; 999 ^32 '004 8009 ?020 8025 8030 8035 3 32 655 33 35 36 37 38 39 40 4' 42 43 44 45 46 47 48 49 ' 50 5J S* 53 54 55 56 57 58 59 cd. J7 ld - . .,8od. j TABLE VII. MEAN HEFRACTION. FAL Dip. Hot .VIII. of the Dip. ^^IX. lax in Alt. j 1 /vpp. Ait. Refr. App. Alt. Refr. App. Alt. Refr. App. Alt. Refr. App. Alt. Refr. o. o o. 5 O. IO 0.15 0.20 0.25 0.30 0.35 0.40 o-45 33- o 52. ic 31.22 30-35 29.50 29. o 27.41 27. o 26.20 5- 5 5 5.10 5-i5 5.20 5.25 5-35 5.40 5-45 9-54 9.46 9.3' 9-3 9-3 9.15 9. 8 9. i 8.54 8.47 10. TO. 10 IO.2C T0.30 i o 40 10.50 11.^0 II. 10 I I . 20 11.30 5-15 5. 10 5 5 5. o 4.56 4.51 4-4 4-43 4-39 4-34 20. o 20. IO 2O.2O 20.30 20.40 20.50 2 . 2 .IO 2 .20 2 -30 2-35 2.32 2.31 2.20 i. 2* 2.27 2.26 2.25 2.24 34- o 34-30 35- o 35 -3c 3^- o 36.30 37- o 37-30 38. o 38.30 1.2^ 1.2: 1.21 1.20 ftV i. !(' I. I t r. 13 i. ii i 2 3 4 6 7 8 9 IO I. 21 1.43 i.Je 2. Q 2.21 2.33 2.44 2 -53 3- - o 10 20 30 40 55 9 9 8 8 7 6 5 60 /o 75 80 90 4 4 3 2 I o. ^o 0-55 I. C ' 5 I. 10 1.15 I . 2C 1-30 25.42 25- 5 24.29 23.20 22.47 22.15 21.44 21.15 20.46 5.50 5-55 6. o 6. S 6.10 6. iq 6.2Q JJ.2S 6 '-35 8.41 8.28 gii] 8. 9 8. 3 7-57 7.5i 7.4^ 11.40 11.50 12. C 12. 10 12.20 12.30 T2.40 12.50 13. o 13-10 4.27 4.23 4.20 4.16 4-13 4- 9 4. 6 4- 3 4 . o 2 .40 2 .50 2 . C 22. IO 2.23 2.21 2. JO 2.19 2.17 2. If 2.IC 2.14 2.1- 39- o 39.30 40. a 41. 42. c 43- o 44- o 45. c 46. o 47. o r. 10 I. r i. i i. 5 * 3 1-51 o-5> 0-5: ir 12 13 14 15 16 i7 18 *9 20 3.10 3.27 2Z.2O 22.30 22.40 23- o 23.10 3.50 3-57 4. 4 4-IT TABLti, X. Moon's Augmentat. Alt. ALI;II.?T. 4-17 o f ^/; I 3 4 6 7 3 9 IO II 12 'H 15 1 6 1.40 1.45 I. S '55 2. ~O 2 5 2.10 2.15 2.2C 2.25 20. l8 19.25 19. o i8.ii if. 48 17.26 17-. 4 16.44 6.40 6 ,45 6.50 6-55 7. c 7- 5 7.10 7- 15 7.20 7.25 7-40 7.30 7.25 7.20 7-15 7- IT 7* 6 7- 2 6.57 1^.20 13.30 (3.40 '3-50 14. o 14.10 14.30 14.45, 14.50 3-57 3-54 3-5^ 3-48 3-45 3-43 3 40 3-3* 3-35 3-33 23,20 23.30 23.40 23.50 24. o 24.10 24.20 24.30 24.40 24-50 2.12 ?. . IT 2. IO 2. 9 2. 8 2. 7 2. 6 2. 5 2. 4 2- 3 48. o 49. c 50. c 51. c 52. c 53- o 54. o 55. o 56. o 57. o 0.4^ 0.46 0,44 0.4. 0.41 0.40 o. 3^ 0.36 ~vT: 0/34 o-33 0.3:' O.JO o . 29 O.2( O.2s 0,24 21 22 2. 4 26 22 30 35 45_ 6 70 80 90 4,23 4-36 4.42 4.5-2 5- 5 5-1; 5-35 6. 4 6-27 o 5 IO 15 20 35 SO 55 60 70 So 90 2. 3 C 2 '35 2.40 2.4; 2-50 2-55 3- o 3- 5 3.10 3-15 10 ,24 1 6 . 4 15.45 '5-27 15- 5 14,52 14.36 14.20 14. 4 13-49 7-30 7-35 7.40 7-45 7.50 s! 5 o i'; 6-53 6.49 6.4: 6-37 6-33 6.Z9 6.25 6.22 15. c 15.20 15.30 15 40 IS- so 16. c I6.TC i6.:c 16.50 3-3 3, -8 3.26 3-^4 3.21 3- 17 25. o 15.10 15-40 25.50 >6. c 26.20 26.30 2. 2 2. I 2. C i'. 59 1.54 58. c 59. c 60. o 61 . o 62. 'o 63. o 64. o 65. o 56. o 67. o 6.46 7.2; 8. i 9'. 6 '- 7 " TABLE XI. Dip. At differ. Distances liom the Observer. 3-20 3-25 3-30 3-35 3-40 3 -,45 3-50 3-55 4. o 4 5 13-34 13,40 13. 6 '2.53 12.40 I2_.27 12. iq 12. 3 11.40 8.20 8.25 fe 8.40 8.45 8.50 8-55 9. o 9- 5 6. 1 1 6. 6. r 6. i 5-5* 5.55 5-52 5-45 16.40 rS. 5 c 17. o 17.10 17. 20 17.40 17.50 18 . c 18.10 3- 8 3 6 3- 4 3' 3 3- * 2.59 2.57 2 5 ". 2.54 2.52 26.40 z6. 5 o 27. o i/.IS 17.30 -7-4S 28. o zS.iq 28.30 1.53 1.52 1.51 1.50 1.49 1.43. 1 .4.7 1.46 1.45 1.44 6V c 69. c 70. o 71. o 72. o 73- c 74- c 75- o 76. o 77- c O.25 0.22 0.2J 0. IQ o.i 1 - o. 17 0.15 o. 14 o. 13 i 4 I r,' ; j *^ 1 i 5 Height f the Eye in Feet. _5 I T ; J S - 12' ii -3 54 12 t7 S 12 -- J 5 7 4 6 4 5 ? 4 3 4 .3 4 3 ( 4 - 3 ' 4- "~*4 '45 15 . 12 1C 8 7 6 T 5 4 -s 30' ^ 3! ro;z? '; n f2 14 O Ii 8 9 7 f ? 6< 7 6 k c 6 S 6 4.10 4.15 4.20 4.25 4-30 4-35 4.40 4-45 4.50 4 '55 11.29 ni 8 10.5$ 10.48 10.39 10.2',, f0.2C TO. I) 10. 2 9.10 9.15 9.20 9-25 9-30 9-35 9.40 9-45 9-5 9-55 5.42 5-39 5-36 5-34 5>3 g I?;;; 18.20 18*4 18.50 19. o 19.10 19. 20 19.30 19.40 19 50 2.51 2.49 2.47 2.46 2.44 2 . 4 3 2.41 2 45 a. 37 29. o 19.30 BO. o 30.31. 31 . o .3 r 3' 3i. o 33- c 1.42 1.40 I. }'. I . 17 i-33 lUs 78. o 79- c 80. o St. o 8*, o |: o t-l O. 12 O. 11 o. ic c. 9 o. 7 o. 6 o. 0. 2 o. c TABLE XII. A TABLE OF THE SUN's DECLINATION, For the YEARS 1806, 1810, 1814, i8iS. Eeing the Second after LEAP YEAR. an. Feb. V!h ,. w May tine Ju !y Aug. Sept. Od. vov Dec. i outh outh South N T orth Noi th STorth T orth North North outh outh uth Q J 2 3- 3 2.5* 7.12 43 : .20 4.23 4-47| 14.57 15.15 2. 2. 9 3. ic 3- 6 18.10 17-55 .28 . 6 3- i 3-M 4.19 4 . 3 s 1.46 '55 3 2.5: 6.37 .58 5.10 15. 33 2.16 3- i 17-39 .44 3.48 4-57 2. 41 4 2.46 6.00 35 5-33 '5 5i 2.2^ 2.57 17.24 32, 4.11 5. it < 2.40 6. 2 .11 5-55 10. 8 2.31 2.51 17. 8 .01 4-34 5-35 2.21 6 a- 33 5-43 .48 6.18 16.25 i-37 2.40 16.51 37 4-57 5-53 2.28 j 2.20 25 6.41 16.42 2.43 22.40 16.35 5.20 i6.n 2 2 35 8 2. l8 5- "^ 7- 3 16.58 2.40 22.3: 16.18 5-53 5-43 16.29 22.41! C) 2. \C 4.4- 4.38 7,26 17.15 2-55 22.27 16. i 5-30 6. 6 16.46 22.48) TO 2i . 1 14^2- l-i5 7-4* 17.31 3- o 22. 19 15.44 5- 7 6.2Q 17.03 22.54 I 1 2 .52 [4. b 3-5 1 8.10 17.46 23. 4 22.12 15.26 4.44 6.52 17.20 23. o 12 a -43 13.48 5.28 8.3ZJI8.. 2 23. b 22. 4 15. 8 ..22 17-3 23- 4' 2 .2' 13. 2h 3.04 2.41 9.16(18.3. 23.1 2 .47 14-3 3.36 8. o Is! 5 -3- 9 23-13 I 2 .12 12-4^ 9.37II8.4 23.1 14. i 3 12 8.2 18.2 23.16 16 11 . 12.2 'S3 9-591'y- c 23.2 2 .28 13. > 2.49 8. 4 A 18.4 23 J9 I 20. 4< (2. 5.30 10.20 I Q I* 13.2 2 .! 13-3 2.26 9- 18. 5 23.22 'I 20.3 11.4 i. 6 10.41 19,1 13.2 2 . b 13. i 2- 3 9.2 19. 23.24 l ao.a n.2 0.42 11.02*19.4 13.2 20.5^) 12.5 1.40 9-5 19.2 23.26' ;20 20. i 'ii. }.i8S. 11.23 li )- S i^.2 20.47 12.3 1.16 10. 1 19'- 3 23-27 2 19.5 10.4 o. 5^ (1.43*20. 23.2 20.35 12 . I 0.53 10.3 19.5 23.28 2 19.4 10. I ^.29 12. 4j20.1 20.2^ II.5 0.29 10.5 2.0. 23.28 2 15,3 9-5 T-53 12. 24)20. 3 2^.2 2O. 12 11 *3 o. 6N ii. i 20.1 23-28 a 19.1 9-3 1. 16 12,44 20.4 20. OC ii. 0.178 n-3 20.3 23-a7j ,2 ij* 9.1 (.40 13.0; 20.5 23.2 *9-4/ 1C. 0.41 11.5 7.0.4 23.26 2 is. 4 3 ^ * 3 13.2' 21. 23.2 19.34 10. i. 4 12. I 20-5 23.24 2 i*. 3 8.2 2.27 13.4: ii I 23.2 19.21 IO. 1.23 12.4 21. -3. fi 2 8.1 8. 2. to 14. ] 21.2 19. ' <* i.yi I 3 .C 21. I 23.19 ! 2 18. ? 14 14. 2C : ii . 3 * ^ T i S . c 132 ZI .2 27. l6 17-4 5-34 ) 21.4 23.1 18. 3< 9.1 2-sS V' 4 21.3 5 . , . 2 1-* 21.5 18.2 8.4 ' 14.0 13. 9 TABLE XII. A TABLE OF THE SUN's DECLINATION, For the YEARS 1807, 1811, 1815, 1819, Being the Third after LEAP YEA*. Jan. Feb. March April May June July Aug. Sept. Oft. Nov. Dec. : a? South South South *s otth North North North North Ncrth South South South Q > I 23- 4 17. 16 7-49 4.1* 14-53 21. 5 b 23.11 18.13 ^33 2. IS 14.14 21.44 2 22.59 1-6-59 7.26 4.41 15. IJ 22. 7 23- 7 I7.S 8. ii 3-19 H-34 21-53 3 4 "54 22.48 16.4.2:7. 3 16.246.40 5- 4 5.27 15. 29 15.46 22.14 22.22 23- 3 22.58 17-43 17-27 7-49 7.27 3-4^ 4- 5 H-53 15.12 22. 2 22.1 I ^ 22.42 16. 6J6.I7 5.50 16. 4 22.2922.53 17.11 7- 5 4.29 I5-30 22. 19 6 22.35 I 5-4 8 5-54 6.13 16.21 22.36|22. 4 7 16.^ 6.43 4.52 15.48 22.27 - 22.28 ^5.29 5-3i 6.3S 16.38 22.42 22.41 16.30 4. 20 5-15 16. 7 22.34 8 22.20 15.11 5- 7 6.5* 16.54 22.48 22.35 16.22 I.** 5-38 16.24 22.41 9 22.12 14.52 4.44 7.20 17.11 t*.53 22.28 16. s 5-35 6. j 16.42 22.47 to 22. 3 14.324 21 7-4 17.27 22.58 22.21 15.48 5- T 3 6.24 16.59 22 53 11 n. 54 H-isis-s? 3. s 17.43 23- 3 22.14 T 5-30 4-50 0-47 17. 16 22. 5 H 12 21.45 13.53 3-34 8.27 17.58 23- 7 22. 6 i;.i2 4-27 7- 9 17-33 23- 3 13 21. 3S '3-33 3.10 8.49 18.13 23.11 21.57 14.54 4- 4 T'3i 18.49 23. 8 '4 21.25 13-13 2.46 9.ic 18.28 ^3,.i5 ZI-49 14.36 3.41 7-54 18. s -3 I2 ( 1 5 21.15 12-53 2.23 9.52 18.43 23.1^ 21.40 T 4 .lS 3.18 8.17 18.21 23-I5, 16 21. 3 12.32 J-59 9-54 1^.57 23.20 - 1 3O 13-59 2-55 5.39 18.36 23.191 17 20.52 12. II '35 to. i; 19.11 ^3-^3 21.21 I3.4C 2.32 9. i 18.51 23.21 Ii8 20.40 II .fO I. 12 10.36 19.24 23.25 21. II 13.21 '- 9 9-2? r 9 . 6 23.24 19 20.28 11.29 0.4* ">.57 r 9 . 3 8 23-26 21. 13- 2 1.45 9-45 19.20 23.25! 20 20.14 ii. 8 0.24 ii. iS 19.51 23-27 20.49 12.42 1.22 to. 7 '9-34 i3 ^7 21 20. 2 10.46 o. iS. 11.38 :o. 3 23.2? 20.33 12.22 0.59 10.28 19-48 43.2? 22 19.49 i. 25 0.23N. 11.59 zo. is; 23-28 20.27 T2. 2 0.35 10.50 ZO. I ,3.28 2 3 I9-35 10. 3 0.47 12. 19 20.27 23.28 20. 15 11.42 O.I2N. ii. ii 20.14 ,3.2? H 25 19.21 19. 7 9.41 9.19 I, 10 i-34 t2 -39 12.59 20^9 :o.^o 23.27 23.26 20. 2 19.50 11.22 II. I O.I2S- 0.35 11.32 ii.5S 20. 27 jo. 39 23.271 23.26 z6 r8.52 8.56 i-57 13.18 21. I 23.24 19-37 10.41 0.58 12. I^ 20. si -3-24 2; T^.37 8.34 2.21 t3-37 11. I I 13.22 10 .24 10. 20 I. 22 12.3 :i . ? 13.2?. 28 18.11 8.12 2.44 13.57 11.21 23.20 19.11 9-S9 1 45 12.5 : i . t ? 13.20 29 18. 6 3- * 14.1; It. 31 23.17 18.57 9.38 2. 9 l3-*f :l .24 '.] 1 7 3 17.49 3-3i 14.3,! 2X.4I 23.14 'Ml 9.16 2.32 [3V3J .1.3^ -3.13 ji tii 17-33 3B imia 3-55 11.50 18.28 8-5. U3-5 .-,3.10 TABLE XII. A TABLE OF THE SUN's DECLINATION, For the YEARS 1808, 1812, 1816, Each being LEAP YEAR. an. eb. larch \pril lay June uly Aug. Sept. Oct. Nov. Dec. I 1 c uth b South ^orth orth STorth orth orth North outh outh South 1 1 ' 6 i b * o / o / / a , / , / J i- 5 7,2. 31 4-35 S . 6 22. > ? 8. 2 17 3- r 3 4.29 2 '- 5 ' 3. o 7 3 9 4-59 5.24 22. 13 3- 4 7.47 55 3-36 4.48 2Z.OO 11 3 22. 55 6 . 4t .46 5.22 5-42 22.20 2.59 7-3 T 33 4. oo 5- 7 22. 9 4 22 49 6 . 28 -3 v44 6.00 22.27 2.54 7. 15 . ii 4-*3 5.26 22.17 "43 6. ic 59 6. 7 6.17 7,2 34 2.48 ? c .4* 4 . 4 r 5-44 21.25]] ^ 12.36 5* 5 2 36 6.30 6.34 22.4-. 2.43 6-43 .26 5- 9 16. 22.32 22.2Q 5-34 13 6.52 i.ji 2.46 2.3') 6.26 4 ^32 i6.2b22.39|j | Z2.22 5-i5 .50 7-15 7- 7 2.S2 2.30 o, <: .41 555 16.3722.45(1 22.14 4.56 4.26 7-37 7.23 2.57 .-.2.23 5>V .18 6.1 16.55 22.51 j i 22. S 4-3 4- 3 7-59 7-39 23. 2 22. 1 i5-3 4.56 6.4 17.12 -5711 i 21.57 4.1 3 39 8.22 17-54 -3- 22. 1-5.1 3? 7- 4 17.28 23- 2J i 21,4 13-5 3.16 *-4 .IO 23.1 21.5 14.5 4. 10 7.2 17-45 ^3- 7 T 21.5 13-3 2.52 9- iS.a<5 23.1 - -5 14.4 3-47 7.4 18. i 23.11 : 21.2 13.1 2.28 9 iS.39 2 V I i .4 14.2 3 *4 8.1 18.17 23.I5 i 21. I 12 . <; 2. 5 9.4 18.53 23.2 2 .3 14. 3. i 8.3 18.32 girt I * 21. 12. 3 1.41 IO. I 19. 7 23.2 2 . 2 '34 2.38 V 15.47 23.21 1 " 20.5 12. I 1.17 10.3 19.21 23.2 2 . 1 13.2 2.14 9.1 ro. 2 23.23 1 ' 20.4 II-5 0.54 10.5 19-34 7,3.2 2 . ' 13- 1.51 9.4 19.17 23.25 1 x -O.3 H-3 0.30 ii. i 19.4- 23.2 20. 5 12.4 1.28 1C. '9-3J 23.26 1 2 2O. I H . I o.o6S. u-3 20. C 23.2 20.4 12.2 i. 4 IO,2 19.45 23.27 la 20. 10-5 o.i7N 11.5 20. I- 23.2 2O. 2 12. 0.41 10.4 19.58 2 3 . 2h i 2 !9-5 IO-3 0.41 12. I 20. 2/ 23.2 2O. I II.4 o.iSl II . :.o. ii 23.28 1 2 if3 IO. i. 5 12.3 20.31 2-3.2 2O. II . 2 o. 6S II. 2 2Q,i^ 23.27 1 2 19.: 9-4 1.28 12. 5 20-4 23.2 19.5 II. 0.29 11 .4 20.36 23. 26 J > 19.1 9.2 1.52 13-1 20. $ 23.2 19.4 IO.^ 0.53 12. 20.45 23.25 i ! 18. 5 9- 2.15 r 3'3 2 I . 23.2 19.2 10. y r.i6 12. 3 ;o. 5 c z 3 .2 3 r8.4 8. a*39 13-5 21 . I 23.2 T 9 .I IO. 1,40 12-5 ZI.IC 23.20 5- 18.2 8. 3- * 14.1 21 .2 23.1 19. 9*' 2. 3 I3.I 1 1 . 2 ] 23.1- r iS. 7- 3.26 H-3 21.3 23.1 18.4 9.2 2.26 13-3 21.3: 23.14 *? . 3-49 14.4 21.4 23- 18.3 9. c ! *. 50 1 3-. '1.4 23.10 17-3 4,1* 21. 5 iS.i 8<3^ ! 14. ^ :-3- 6 ^TL TABLE XII. ') i A TABLE OF THE SUN's DECLINATION, For Ike YEARS 1809, 1813, 1817, V jfe Being the Fir ft after LEAP-YEAR. Jan. Feb. March April May. June July Au-. Sept, j Oil. Nov. Dec, >. c South South South North North Nbrth N'ortii North North Soiith Sui'.-h juuth^ [ j 23. 2 17. 7 M7 4-30 IS- 2 22 . < -,^ 9 1 8. 6 8.22 3- 7 14.24 zx.49 1 2 22.36 16.50 7.14 4-53 15.20 22. II i3- S 17.51 3. o 33i! J 4-43 .5*j i i 2Z.5I l6 -33 r ) . ^ i 5.16 15-38 22.1^ 23. o J 7-3S 7v3 3-54 15. 2 :2. 7 4 22. 4^ 16. 15 6.28 5-39 T 5-55 22.26 22. SS 17.19 7.16 4-17 15.21 ^.15 5 22.38 15.57 6. 5 6. 2 I6.l-jj22.3-, 22.50 17. 3 6.54 4.40 15.40 22.23 6 22.31 IS 39 5.42 6.24 16. 30 22.39 12.44 16.47 6.31 5- 4 15- 5^ 2S. 30 7 22.24 15.20 5.19 6 -47 16.46 22. 4 c 22.38 16.30 6. 9 5-^7 i6.it 22-37 8 22.16 iv * 4-55 7- 9 17. 3 22. S l 22. V 16. 13 5-46 5-5 '6.33 12.44 9 22. 8 14.42 4-32 7.32 17.19 22.56 22.25 15.56 5.24 O.J3 16.51 22.50i ,10 21.59 14.23 4. 9 7.5417.35 23. I 22.17 r 5'39 5- I 6,35 17. 8 22.56 ri 11.50 '4- I 3-45 8.16 17.51 23. s 22. 10 15.21 4-j8 : 6.58 17- zt 23. J 12 21.40 13-43 3.21 8. 3 8!i8. 6 2 3*- 9 22. 2 15- 3 4.15 7.21 17.41 23. 6 IJ 2I.3& 13.23 4.58 9.ooji8.2i ^3-13 21. S3 I4-4S 3-5- 7.43 '7-^7 2-3 . 10 M 2I.2C J 3- 3 2,34 9.22 18 36 23.16 21.44 14.27 3.29 8. 6 is. 13 23-M 15 21. 9 12. 42 i. n 9-43 18.50 23.19 ^33 14. 8 3. 6 8.28 lS;2 9 *3*17 t6 20.5'^ f 2.22 1.47 10. C 19. 4 23.22 21.25 '3-49 2.43 8.50 ' 44 i 3 . 20 f 7 20.46 12. I *-*3 10.26 19.18 23. 24 ?. I . I n-3u 2.20 9-13 18.59 -3-23 iS J 9 20.34 20 . 2 ?. 11.40 II.lS 0.59 0.36 10.47 IT. 8 i9oi 19.44 23.2- 23-27 ii. 5 -o. 115 13.11 12. S2 1.57 9-35 [ 9-i3 r -33 1 9 -S6| '9 --7 23.25 2J ? S6 2C 2O. 10.57 O.I2S. 11.28 19-57 23.27 20.44 12-32 1 - 10 10.18 19.4^ 13.27 21 19.56 *0,35 O.I2K. i r.49j2o. 10 23.2,- :o. 32112. 12 Q-47N. 10.40 '9-55 13. si 22 19.42 10. i ; 3-35 12. 9 20.22 23.2-- iO. 21 II.5-: 0.23N. ir . i 20. * 23.28 2; 19. 2b 9-52 0.59 12.29 20.33 23.2: 20. 911.3: 0. O 1 1.22 20. 21 23.27 24 19.14 9.29 0.23 12.49 20.45 23.26 19.56 II. I I 0.248. "43 20.33 13.27 2 5 18.59 9- 7 i. 46 i. JO 13. 9,J20.s6 ^3-25 '9-44 19.30 I0. 5 J 0.47 t^. 4 1 2 . 2 ; ao4,S 2'. 57 zi.z; 2t 18.44 8.45 !3.zS 21. 6 '-3-^3 ro.^o I . IO 23.^3 27 18.29 '' . 2 2 $33 13.47 21.17 23.21 r 9- 17 to. 9 1.34 ia-4S 21. 8 23.21 2g 18.13 8. o 2.57 14. 6 21.27 23.19 '9- 3 9 4 ' r '57 '3- 5 Z C . J *3.Hg 2Q 17.57 3.20 14.25 2?. 36 23.it 18-49 9.27 2.ZI 3 r 2 5 U.-'j 23.15 ^0 f 7-4 T 3-43 14.44 21. 4^ :3- r^ 18.35 9- 5 2-44 17. 45 21.3., 23-11 31 17.24 4- 7 21.54 18.21 8.4-1 14. 5 -3 ", 1 - - TABLE XIII. For reducing the Sun's Declination to any Meridian, and to any Time under that Meridian, containing Proportional Parts of the Daily Difference of the Sun's Declination to every Hoar, and to every Fifteen Degrees of Longitude. )-" ' X.l" OOO ooo o r 000 000 OOO OOO OOO 000 ooo 000 ooo ^ co co o c o CO coo 000 ooo CO CO d d o CO ooo ooo CO or>^O O^ ' ooo' ooo * ^t- t- cl M ooo sH vo o vo vo o O "^ vo O vo. vo vo O ""> O vo t^ -0 d O <- to N t- r-. vo M 5 H vo tf ..COw O f~- vo cl t- - t3O OO ON ON 2 - OOO OOO ooo X 33 d J o w? ooo OOO o *^ o ooo ooo 6 o o 000 Xtt 000 d vo d rh co OOO 10 o O io rt -tf- t^-oo oo 000 2 ^ ON ON O 000 vo Q <>J i/-^ vo O vo 000 ooo I ^ -> vr-t m too vo ^,0 .00 o voO vo vo voo o O vo vo M tot- O M voj t- O ^ rt vo t- * M <3- - O - O r< o CO U-) M W M f-1 r- O r vo t^ O <* co n to t w-> HH ro M vo N rj- vo VD NO t- O ^ CO O 00 00 ON N "*-NO 000 000 1000 O M K, cl 000 1 UH i ooo 000 000 ooo 000 d f> o 000 S3- 6 OOO o' d d 2}* OOO d o o ooo M 4-NO ooo C 00 O ooo ooo " *< <* ^ c o * 000 - M H 000 N fl ro ooo rororf coo 000 * r 9 O VOO vo 00 ^0 tn ^00- O vo to o vo to PS. u~i f^i 1 O t*>- *-*"* i "^ O f *- r-. 10 r< v ro o ^ O O r^ ^ c ^t r) O t-- VO rt O VO M CO r^ 10 c) ^ ^ <* <* O r^ vo ^-10^, c5 d r^- ro vo vo lOVO ::I 000 r-oo o 000 t- Tt- VO ooo s o OOO vo r to i- .-, co ?)- x 000 000 0^0 w f) 000 "5- ^ 11 r p OOO 000 000 000 000 vo 8 o o VA o vo vo O vo o TcTr- vo. O vo * -* * o - rj- -i O o co^- ooo 000 O rt ro 000 A > 10 O 'O O 10 O vno^ v^o -^Ovo vo vo.O - OJL tor- O M vo t- O M fc ,000 f-f) r*> *C CO* * -t "* v^ 1 OOO ooo H W (D C ^ 000 d o o O o c ooo OOO odd OOO is, OOO 000 000 C ooo ooo 000 o o d ooo OOO ooo rj- 10 CO P- Tf ooo 000 OOO - C '-> s 3 "4 1 vo 10 o ^ o o vo o LO O VO voo too -, O vo O r*. vo r r- vo O r~~ . 000 ^ m ^f- 000 CO -sf >O M fl ro ro OOO 000 000 -|-< P 5 o t<~ 000 to O vo ^. H *- ~. coo ooo ooo OOO OOO 000 OOO OOO to O l/ ~> O vo o 00 ^ d ^ o N N CO ooo i^, d vo CO ^ ^J- O d vo d Q ir , O 'O O vo o to o .1 tot- O f vo r- O r-' C - O O Q O rt 10 ^ d vo t-- o M vo r-- ro ro ro 000 O r^r to ^^-Tf 000 r^ o <*> ri- ko w-. OOO o f* o VO to M .OOO C ooo 000 ooo 000 J ^ i-i ro rj- u~,vo r-oo ON - ^ ro T}- vo VO txor ON O >- CJ ro Tj- o rJ oo S"ro^ M on -j --v^ Daily Difference ofDe -i r^ M M O r^ to f-OO rf- rt N r*s OOO c O r^ O vo H. rj- rj- to 000 ^ O HI d s>3 c to co 2 M ? ri i-. ~ ri i> T r^ OOO 000 000 000 OOO toe ^ .o&>^. i- P TO 000 i- ii^ ^. '^.VO OOO OOO ^- to 0-00 to o o vo r> to .j 10 vr> <3- O vo O 4- r. ro i/-< o to vod o c - vn o to N H >- O l o C O >-" <-' '0 vo 000 -1 t-^ r- r-1 H W> OOO OO rf- O <^ * '* d V 10 ,00 ; O *^ O O '0 uoo ,00 - Otoo M i/^ t^ rl l ^ K .0 <4 *^o|" ^ 000 000 co rj- .-j- 000 K X X O o O ro e o o OOO OOO OOO OOO 000 000 OOO ooo OOO S 000 000 000 OOO OOO' o o* o OOO OOO o o lr e> o 1 o M <^ ro^o U~,V> C^ -X> Ov O 000 o 0*0 000 X M > 1.0 >3 P) vo o vo to E?!? too o rf- rr- to o o M 10 to ^57 ' 10 O to N O f^ tO f> to o o ri 6 N HI rj- Cv * OOO O r^ to O roft^ -r N M OOO <> O r^ C~00 rt ro ro ^4- 000 O | OOO OOO 000 000 000 OOO vo O l( ^ TJ- <^ rA 000 '0 M M r- M N O 000 10 >o " \D O 000 to O to ^ t^- co v-< vO w rt *"?, to O to tovo vo o" vo o fO M vo O vo *t- m M ON O -> 6 to ^}- ro f;,: M. g > X iy^ f-1 ^rt vo r- * O M to lo^-^ rj- co N ^ r>. l-i VO CO O t.r> *r\ vo o to r^. 6 N N >-< vo O to C '^ t^, C CO 1-1 _ ra 10 r^ rj-oo r^ 000 c-1 ^ p^ w to 1H fl M OOO t-- rl :> 4-x) rj ro on 000 s >-j j> X % N ^5-8 _O M M 000 t- c rj ff) r|- ^.^ ^S O C O -0 CNO OOO f P O i-l f! OOO OOO * M OOO i?; d OOO 4-co < 1*^ 000 O o c vo o 4 OOO OOO OO rJ vo C-l CO C*"i 000 33 > X S > X to C-J ^ ro HI to "~0 w rt m rj- t< ro r^> 6 cTo O to o c< vo ro M M ro ^J O l^. rf- xo to ^ 10 ro t^ to is Tj- r) 00 00 O "O'O l o o ' o fO M ^J- to O O t^ to CO M M - o i^ '0 fo to VO rJ O ^ COTj-^ r>. *o t^ 000 000 r* O f~ 000 2 ? to O to ^0 W M OOO " O 10 ^J. ^- Tf- 10 o-.d ^0 N O to o N t^^ rr, OOO to 6 vo \i". M "o~o~b ii' to O vo <""> c- O 000 to O OOO to o vr ^"^ ^ OOO a: 10 CT\ to O to XN M r^- co co ^0 M * to o O* N o -I T- M N f CO "O O vo *-- O N 1" 1^ o o to i^. o rl to m vo M '0 it. ro to o isi to o to t>. o *i O rj d vo o 6i5 000 ro vo c> 000 i -- O * N vo CT t -. M 'M O HI HI M t< 3?* n N oo ** O > coo vo ^ ^ uo O o O ^ O vo ** t^ O ti 000 0^0 u~i r^ C -< o o o OOO O M 10 OOO OO O N n fJ H ooo ^0 O O C rt '^ OOO t~- O r! <~> rt rj 000 >o r^ o 000 000 O N "> 000 ^^ ev rt r- 0*0 CTXN %0 OC M ^ r* o H >ooo M rj- t^* O -*or-|asw rj-vooc M -I ^ ^00-0 OOO -t-,o ^ oe o O rJ so odd ooo oo o H .Ot-VO M rj-vc ^000 oo O <^ t-t -' OOO *i-vc oo 00 O M ^0 000 r-. o o c o OOO OOO '^ '^ v^ 000 OOO OOO ; *-;- -j ^o o o OOO OOO OOO ooo OOO 000 000 OOO 000 O HI 000 000 o O -- "1*0 [ t- O f-N r^i O r-.r- o ^0 O 00 O OOO OOO OOO 000 boo rn ro ^J~ OOO OOO OOO O w 000 o o c ' o .0 '0 CN * - .06 O N f ^ O O c?"o o ro *->o r^. C> -I A r^o t-. C^ O -^^ OOO OOO OOO OOO OOO 000 000 000 OOO 000 1 b rn r-t O r- o 1 r~ O rJ vo r> O N >or^ O t* ^ r^ o c > ^0 t^ " r4 *fr .00 t- C> O i- " <~ N CT "OOO 10 so t""- 000 M l-< 000 000 e o o 0* " " 000 000 r^cxs o O.C o o o 000 OOO 000 i- ~ OOO : O o A - -,0 00 c; O ri d O O ^Ttlt^r 1 ./.O XC r- r- t- GO OO C- 0\0 rt f ^f-ioo i --oc' c 000 O M f$ ro rj- u-, CN O "< N r-l tl 000 OOO 000 000 OOO OOO OOO o o c OOO coo 000 ' = O Q oo r-- o ro o ao ^ .0 ,~ o to*-~ VO t-t- , O O OOOJOOO H OOO OOO 000 vo<) r-. 000 OOO 000 000 OOO '000 OOO OOO fO VO r, C^ 10 o r* "d- O i* bv* O >~O M C->*o~ I- -^ O M M f4 * c^ ^-OVC ..ooo poo . OOO OOO OO CX3 O 000 o o - - o ON-,.- N O o - rj fl rj ro C*"l ^" - C M ^.0*0 OOO COO 000 000 VO t-. t- o o o r-oc eo OOO O CT> O 000 o o 000 OOO OOO OOO OOO sVl rt *vC 00 O N ^^ C-| ^' ^iT jnm t> * oc OJ M M N Ml -. G | O o o * ! o o o OOO to ro ro i 14- ^- ^f I OOO O O C OOO OOO 000 000 OOO odd OOO I ba c j i r -h vo e? oo rf t 'iDiiy Difference of Declination ia Miles, and to every fix Seconds. TABLE XIV. SUN's RIGHT ASCENSION. Days Jan. Feb. Mar April May. June. July. Aug. Sept. o 37 8 3* 'o 34 12 26 14 i8|i6 26 iS 38 30 3i \ q-2 3Q ; 3: 8 .42 10 38 M 22 18 42 3* This Table is fufficiently exa& for finding when any Star comes to the Meridian, in order to obtain the Latitude ; but in all calculations for determining the true Apparent Time, the Sun's Right Afcenfion mufl be taken out of the Nautical Almanack, as it is there calculated to a greater degree of accuracy. If the Sun's Right Afcenfion be wanted in Degrees,it is readily found by converting Time into Degrees, by means of Table XVI. S s TABLE XV. The Right Afcenfions and Declinations of the principal fixer j Stars,, adapted to the Beginning of the Year 1806. Names of the Stars-. Rieht Afcenfion in Declination. An.Vai'. Time. Ann. Var s. -r- 3-06 3-31 12-89 3 3 3-o'z 3-34 3.12 3 85 3-55 3-39 3-4* 4.41 3-*i' 3-^4 5-3, 3;*4 3 69 3 2-4 3.20 3-7i 3-^ .^.69 2-39 a-T^ a 63 2-53 2-73 2 77 ^39 a- 03 2-92 2:03 1-44 28 7 2-96 2-2< 2 3 7 1 33 :*.6j '* 93 3-M 3 29 : 3-22 3*64 : 3-33 : Degrees. o49' o' 7 25 15 i'3 24 30 i* 33 30 28 i o 29 3 45 43 2 13 4."! 54 53 59 45 62 ii 45 66 12 o 75 35 45 78 41 o 86 10 o i-o 33 o Hi I/ O H. M. S o 3 id o 29 41 o 53 3^ o 58 54 i 52 4 i 5$ 15 2 5* 9 * 5.> 3 6 * J.> 59 4 S 4^ 4 i4 ^ 5 i a;, I -I ^4 5 44 40 7 2i 12 7 29 8 7 31 -5 I450' 5 3"N 55 28 3 88 16 10 34 35 26 41 23 18 22 32 24 3 19 29 - 40 n 54 _ 23 27 32 IT 9 o - 16 635- 45 47 21 6 9 47 7 21 36 j* 17 59 5 43 24 28 vy o i-J 3^ 5 12 54 38 - 57 25 9 ~ 62 47 48 57 i 33 50 27 14 20 II 50 27 53 44 27 22 34 N. 14 37 14 N. 12 42 49 N. 5* 31 2 N. 38 36 25 N. 8 21 39 N. 44 35 34 N. 61 46 o N. 27 i 51 N. 14 9 51 N. r 3' 57 45 149 30 15 162 30 45 162 54 45 iyi 23 15 -04 58 15 211 42 221 39 o *3* 37 o 256 27 o 261 29 o 268 I 45 1 277 35 3o 295 20 3o 308 42 15 318 29 o U3 35 45 ?43 4^ 45 22 36 45 76 18 15 94 54 45 99 8 45 139 30 30 r<;8 44 45 UO 2- -3D u6 39 o .44 22 45 Mi 43 *' 8 47 5 9 JS i 10 jo 3 10 Ji 39 !i 45 .33 !3 39 53 14 6 4^ l * 45 36 15 26 28 H 5 & 17 *.? 5 17 J2 ? r8 30 22 19 41 22 :o 34 49 -i i. 5^ ^ 54 23 55 7 i 30 27 5 5 iJ 6 19 3-; 6 36 35 9 18 2 3 14 59| 4 40 10} 5 6 36 * 17 3i! .1 46 J3 iREGULUS Upper Pointer . . Aliath Bcpctnuch. . Ar D HA M i Sec. ' j M JM S M ;M S M M S M M S M |M " 5 ; M M i S 1 Th i. i o. 4 61 14. 4 121 8. 4 Ihl .2. < 241 16. ^ i s ^c. 4 I i i 20. 8 62 J4-. ^ 122 8. *| 182 12. ; | 242 10. [ 30 20. ^ | O ?C 2 > 0. 12 6. 4- I- 123 8. i.: ,-i 3 12. K .0.12 30 5 20.1. ; o 4 3 | 40.1 c 64 4.16 ! 124 8.i(i; 184 12. "K i 244; i 6. if 30. 20. It I C 4 65 4.20 I2 5 8.20 18^ 12. 2C 24 t6.a ;i 30 20. 2C i i 5 6 o. 24 66 j.ii 126 8.24 136 12.24 2,4-' l6 . 2 3' c 12 : jjo.f: 73 4 52 8.52 193 12 3 1 iO. v6 3 3 C ! 4 . r 1 ' I. 75 5 o > 1 3 > 9- o 195 ! 3 c 2s- 17. c 35 2 1 . ' 3 4 i <; i 16 r 4 76 5- 4 136 9 . 4 196 n- ^ 2S6 '7. 4 3i 21. , 4 t. 16 i l " r. 8 77 5- 8 \yj ^ M 197 1.3. "i 17. ^ 21. L 4 i \ 18 r . 12 78 5.12 \ T 3- 9 . 12 j J 9% 13.12 7 - i - "31 21 . 12 4 3- 18" ' *9 i.it 79 j. it i '39' 9. It i'/ 9 13.10 17. jr i 31 .'I.I << 4 4s j 9 2C 1.20 80 $"- 140 9-2C 200 13 -.20 20C 17. 2C ! 32 2 I . 2C 5 c 20 2f|1.24 81 P* 2 -* 141 9-*4 Z$J J3 24 26 17.2." 32 21.24 5 15 21 2 2 | f . 2 S 82 ,-.28 142 9- 2 1 ". 202 13.2 26. 17 2 5* 22 r 3^- ,83 BA 5-32 s ?6 *43 9- 2(- .203 20^. 13-3 20' 17-32 32 il.32 S 4!? 6 o 13 : 2s 1.40 4 8 5 $.40 144 9 -.4, 20S 1 3 . 40 26 3 2 21 .40 6 r;. 24 i 2 C - 26 86 5-44 146 9-44 206 ^3-4^ 266 1.7 44 3z 2 1 . 44 6 ^o 26 j 27 87 147 9^48 - 207 i}. 4 8 26- I 7 '. 4 X 3 2 6 45 27 i 8,8 5-5- 148 9- 5 VsS 13.52 2 68 i?. r* 21. ^2 7 o 28 i 5-5f 149 9- 5' 2-09 tj,5* 269 32 2 1 . 5 f % 7 15 29 1 d j 90 6. 150 o. c 210 '4- t 270 3J : 2 . C' 7 30 30 i fip 9 1 6. '4 10. 4 2 t I 14. 4 271 ah 33 22. 4 7 4> 31 i 3U. -8 6. x 152 10. b;i 21- 14. Jy 2^2 rV. S 33 .S c 32 ' 3 i'-' 2 ! 9.3 6f2 ^53 10.12' 213 ,4.12 27 18 M J3 22.12 3 ic 33 34 94- 154 10,16 2I 4 14. 16 ' j8. 16 33m 22.16 8 30 34 3 9 1 * 6. 20 1 " S 1C. 2C -21 S 14. 2C %J.1 18,20- .jf 21': 20 8 45 36 57 ^ 6.24 6.2 157 10.2-^ IO.26 216' 21- 14.24 I 4 .28 2-7 ^.a^ I 8'. 2^ .iY zz'aS 9 9:1.5 27 38 6.3 158 10.32 218 4-3- 2yfc 18.32 22.32 3 ( j 99 6.36 ^59 10.36 219 4-3' 279 iX. 3 9 45 -^ i 40 :.4-j| loo o. 4 c 160 t0.4t ,;| 2240 4.40! Svjc 22.40 i C Cj 4^ : 101 6 . 44 161 io. 4 | 4V 48* 3- I2 108 . 12 \<& .12 228 15 12, . I 2 3.14 !2 Q 49 ^ . 161 109 . J< 169. i .16 22 9 r 5 ; . , t 289 9. I 6 349 5 . j , i 2 I< 49 53 1 10 .2C 170 C i 3 . 2 1 ' 12 ;c 50 S' ? 2.^; III 2 'i 17. 24 231 ^5.24 2 9 J 3 a $- HI .2 l-JZ i .28! 2U f5.28 '.) 2 " 352 i 3 1 . j2 1 13 173 11.32 253 15.3:; 193 .9-ri 353 -. j 54 1 14 7-36 174 1 1,. 36 234 2<>4 354 '3 3 54 [, 55 3-40 "5 7.40 '75 11.4 f -3 !; 5,4c '^95 '-> 4' j .3 5 c : : .^ r 3 4 56 ? -4-I 116 7.4-! 176 I . ^ -; 236 2 b 9.44 356 57 3-4- 117 17.4^1 Ml r i . 48 ^37 5.", 48 -97 9.48 ?S7 4 Ir :S ;.<;i ir8 178 1-52 - ;8 .5 '5 - ! ' 9 <" [ 9-5- 3SS ' 4 3t 9J3 .56. 119 1/9 i . 56 239 V C ( ' L 9 9-5* 3 ^ c i? . : ;c;j'-;4 4 . 60(4. oj 120 8. 'oj 180 2. 2JC 1 ft | ;oc -0. 3 6c i 4 .2c||i; c 60 TABLE XVIJ. To reduce the time of the MOON'S PafiTage over the Meridian of Greenwich to the Time of its Paffage over any other Meridian, Ship's Long. 30 ' 35 40 45 5 55 60 7 QC 95 100 105 no "5 J20 TzJ 130 J35 140 14, 150 155 i6o 165 170 175 180 Daily Va.iation of the MOON'S parting the Meridian. 42 4*' 46' 48' 4 8' 54 56' 58' 56' i 58' 60' 62' 64' 60' Time fiom J southing H. M. O O O 20 40 1 O I 20 1 40 2 O 2 20 2 4 3 o 3 20 3 4 4 o 4 20 4 4 5 o 5 20 5 4 6 40 7 o 7 20 7 4? 8 o "8 "20" 8 40 9 9 20 9 4 10 O 10 2J 10 40 TI O 11 20 II 40 IZ O TABLE XVIII contains the decimals to every minute in twelve hours, and is ufeful to find the proportion of time in twelve hours, by multi- plying it by the number found under the top hours in the column, and oppofite to the minute in the left hand fide column ; from the product cut off four figures from tfe right hand, the remainder is the proportion of time required, if there is no fraction. Fx AMPLE. If the difference in 12 hours is 6 minutes^ what will it be in 6 hours ? Decimal of 6 hours is = ,5000 X by 6 minutes 6 Anfwer 3 minutes j 3,0000 If the difference is for a proportion of time in 24 hours, multiply the difference by the decimal of half the time required j from the poducl cut pff four figures from the right, the figures to the left is the anfwcr. TABLE XVIII. Decimals to every Minute in Twelve Hours. j 1 2 J 4 5 6 7 $ 9 10 rr o j 2 3 4 .0013 ,0028 0042 0055 .0861 .087^ .08:8 1667 1680 '695 .1709 .1/22 .2500 2513 .2528 .2542 2555 3333 3346 3375 .3388 4167 4180 .4195 .4209 .4222 .5000 .50:3 50-iS . 50-2 -.055 5^33 .5846 5861 .5875 .5888 6667 .66So 6695 .6709 .6722 7500 7513 7 5 - i 7542 ^333 '*|ti 175 .8788 .9167 .91^0 9*05 .9206 5 .oofcg .09-2 i/-;0 2569 342 .4236 .5069 5 f ;o2 673* 7569 . 8402 9236 6 .oj83 .0916 I 750 5*3 3416 425 .5083 . 59 i6 .5750 "8416 . r ; 2 : 7 0097 .0930 1764 .2597 343 .4264 5-97 930^.6764 7 5 9 7 . 026^1 8 9 10 ii .0111 0125 oi.~9 0152 0944. .0958 .0972 .0985 .1778 -1792 1806 .1819 .261 1 2625 2659 .2652 3444 345* 3472 .4278 .4-292 .4^06 43 1 9 .5111 .5125 5944 595S 5972 59^5 .6819 761 r .7625 7*39 8444 .8458 84/2 .8485 9278 .9292 .9306 12 0167 . 10OO 1834 2667 35-o 4334 .5167 .0003 .68-4 7667 ~~: 13 4 5 ci8i 0194 0208 . 1014 1027 . 1041 .1248 .1861 '875 , 2681 .261)4 .2708 35H 357 354 1 434- 4375 5 1 ..*' i 5*94 .6014 .6027 . 604 1 . 6:^48 .6^61 6875 .7681 7694 7/c& .8514 .8527 ',34* 93^1 1 6 0222 '055 .1889 .2722 3555 43*9 .5222 .605^ .68:59 3 < ><; 17 0236 . 1069 .1903 .2736 3569 4403 5236 .0069 .6903 2736 .8;6u .0403 18 O2CO .1083 ,1917 -2750 35^3 .4417 52 so .6083 .0917 "7^0 * '& 19 0264 .1097 l( )3 1 27<>4 3597 44 3 ' .5264 4*97 6931 .7764 -597 20 0278 . X J 1 1 .1945 .2778 .3611 4445 527^ .611 / .6945 .8611 . Q44C 21 2 2 23 .G2y2 .0306 .0319 .1125 .1152 19^9 1973 .1986 .2792 .2So6 .2819 3^25 3639 .3652 4459 4473 .4486 5-9- .5306 53'9 6125 .6139 6152 .6959 .6973 .6986 . 7792 .7806 .7819 ".8639 9459 9473 .0486 24 333 . 1160 . 2000 2*33 ?6a6 .4500 -5333 .6166 7000 .8666 27 a 8 0347 o ,61 .0389 .1194 .1208 . 1222 .2014 .2028 .2042 . 2056 .2847 .2861 .2875 3680 3694 .3708 .3722 .4514 .4^28 454- 4556 5347 -36 5375 .6180 .6194 .6208 6222 .7014 .7028 .7042 .7056 7*47 .7861 7*75 .7889 .8680 .6694 .8708 ,87*2 V5 CO .9514 .9528 954^ 29 jV>j ' IZ 3 6 2070 .2903 373 6 457 5s 03 .6236 7070 7903 8746 OS70 3'-' 0417 .0431 .12^0 .1264 -2084 .2098 .2917 2931 375 3/64 .4584 4593 154*7 5431 6250 .6264 .7098 7917 7931 .8750 .8764 .9584 S^ .0444 .1*77 .2111 .2944 3777 . 46 1 j 5444 .6277 .7111 i7944 96 1 1 33 .045$ .1291 .2125 .2958 379' 462* .5458 - 6291 .7125 79 SB .8791 . ft 6 2 C 34 .0472 X 35 2139 .2972 . 3&os .4639 5472 6305 7139 7972 .8805 35 04*6 ' 3 1 ( J 2153 .29*6 3*19 4653 .5486 .6319 7 1 5 3 7986 .8819 . 06^7 36 .0500 1333 .2167 .3000 3833 .4667 55-0 6333 .7167 .8000 .8833 37 0514 .0528 1347 .1361 .2l8l .2195 .3014 3847 .3861 4681 4695 55*4 .5528 6 347 .6301 71*1 7195 8014 .884; .886: .9681 Q 6 O C 39 40 41 0542 .0556 .0569 1375 .1389 .1402 .2209 .2223 .22^6 .3042 .3056 . 3069 3*75 -3880 3902 4709 4727 .4736 5542 555* .5569 6 375 .6 4 C2 7^09 7223 .7236 804?. .8056 .8069 .^875 .8889 .8902 9709 9723 .9736 42 .0583 . 1416 .2250 .3083 3916 .4750 5583 .6416 .7250 .8083 .8016 .9750 41 44 .0597 .0611 .1430 ,1444 2264 .22-i 3097 393C 3944 .4764 .4778 5597 .561 1 .6430 .6444 .7264 7278 .8097 .8111 .8930 .8944 .9704 9778 4^ .0625 T 45^ 2292 3125 3958 .4792 5^5 64.8 .7291 .8l2C ;8.93i Q-Q> 46 .0639 .1472 .2306 3'39 3*72 .4806 5 6 39 .6472 .73.06 ;'8ltq 47 '.0653 . 1486 .2320 3 '53 .398.6 .4820 5653 .6486 .732.0 . S % i - 3 .8986 CS20 48 .0667 . 1500 2334 .3167 4000 .4834 5607 .b -oc .7734 . x i o' : . yOOC Q-*' 7,4. 4> 0601 I 5 I 4 .2348 3 f Si .4014 .4548 .5681 6 5l-4 .734 8 j S j .0,848 5 .0694 1527 .2361 3*94 4027 4861 5694 1-6527 .7361 8 j 94 .9027 . 9 6i 5 1 0708 J S4 1 *375 . ?2O* .4041 4875 57^ .6v)i 7375 .8.208 9 C 4 ' 5- 0722 1555 23^9 3222 4C55 .4889 V/22 6 555 73*9 8222 .905^ '^'80 53 .07^6 1569 .2403 3236 .4069 .4903 5-36 .6569 .^236 .9069 .<>903 54] .0750 '5^3 .2417 3aCO 4083 49'- 57jo .6^8^ 74 ' 7 >; 2 - c .9083 9V 1 7 j 55 .0764 1597 '2431 .3264 4097 493 5 "4 6597 7131 8264 .9097 .9931 57 58 59, .0778 .0802 .0806 .0819 .1611 1625 .1639 . 1652 2445 .2459 2473 .24S6 -3? 78 3392 33 J 9 .41 1 1 .4125 4"5i 4945 4959 4973 .4986* 5792 .5806 .5819 .6611 ,6625 .6630 .6652 '7445 7459 7473 8292 .8306 .8319 9111 .9-125 9139 .9152 9945 9959 9973 .9986 TABLE XIX. AMPLITUDES. 'La CP J >~i H to rh voso , ..^___ co _^ C'. x O Q -l -t- so '.-. ro ^ - so - o >st- - oc ^ -- ^ T^-^sO bo - ^cx~ f''' :<"' ^o en -^ o - i ro ! to Cl rT 7^T 77 **" ^1 so H, >S ^ s rf S es " z z rr rp ci * *j S 3 2 s r- , ro, ro ' -, *}- o -x* OO ^^ OO ~~~~^ TO SO .jO -TT, CO OO OC 00 00 00 CO 00 OO OO CO O> ON ON CN ON ON VO H, I g^ggg^ c-l ol N N CO ro ^^. ; r 3-^o CO-'c* ! ! O SO so O -^ *-O VO 3. so so so vf> -o so so s.- O SO NO VO so sC O - sO VO r>. r^ r o 1 ") *] I, at |:*i m ro ^- voip l>-C* CN o M M ro^-covo r^oo ON O HI M ro ^i- vov r*-OO ON O ^ r) ro TABLE XIX. AMPLITUDES. - i u o->ou 2 . - r , M d Lat. TABLE XX, ~^ La t. t r<- j ***;**+ O:, f! ro^,o ve r--oo CN o M r, ^^,^0 I! cc C l < M O N Tf-vO OO VO vo VO VO vo \O ON rl Tt-vD JO O | VO VO vo VO VO vO rt 3 O O O vo vo VC 2 _ M M VO VO VD VO VO VO VO OO O -! ro m - -i (M N N N vo VO VO VO vo vO C--OO O <* ^vO N r4 ro ro ro ro VO VO vo vo vo VO OO O >-i no vc OC VO vo VC VO VO \O vj-i vo vr, O VO vo 5 a 000 vo > cs - M ^ vo r- cr\ o c< rj- vo r- o o M < VC CO ON rr, vi- r- c "-> 000 vo ;^ ON o N ro O O O M i-. *f-vD C- CN O N VD vo VC' VO O vo VO VO VO VO vo VO VO VO VO VO vo vo vo vo vo vo VO VO VO NO VO VO VO vo - 2 000 vo vo vo o o o 2 VO vo VO vo vo" vo (4 M N M r4 r^' -! -rj- i/- t^ CN O ^- ^^ ~*T O O O ^ ro ^-'vo ^ r- O ; r<- vr vo 00 O ^ ^ -} |S . . . 'O "O \O 000 ... vo vo VO vo vo vo VO vo VO VO vo vC VO vo- VO VO VO VO vc vc VD vo vn O -o o "- 1 ro t- -~ rj ro r<-> rr- ro ro VO VQ" t - " 2 000 vo vo vo " VD l^> f T^ - vO vo VO VO vo vo VO vO VO VC VO VO J fo -^ ^> vC VD VO y :/ . g 000 6 o o o o -/o cs O - PI rh vovo r^ o o *- p X VO vo O vo vo vo vo vo VO VO vO vo VC vO VO VO vO VC VD VO vo vc o vo vo vo ro roro vo vo vo r^ ^" ? ; vO vo vo ^ O O O O O vo vo vo o vo vo Q -, t4 ro -^J" vo vo VO va vo VO VO vo r-- CN o - n M 1-1 M rj r-] cl VO vo vO VO vo vo Cl 'I rl cl c> tJ VO VO VO vO VO VO VD VD vo ""* ^ 2 000 OOOOOO O" 2 M * ' 5" VOVD r^oo CN o r. O p [r-v S ^ VO vo vO VO vo vp vO vo vO VO VO VO VO VO VC' VO -0 vo VO vo VO* VC vo vo VO VC vo VO VO VO 1 ^-t vo vc vo o 6 o a o o VO vo VO VO vo vo .~ 1 - - O o \0 vo VO vo VO VO VO vO vo VO VO vo vc VO VO VO vo sb - s O VD VO vo OOOOOO vO VO VO vo VO VO M M, M vo VO vo vO vo vc ^- M - M . vo VO vffl vo vo vc vo VD v vo vo vo VO vo :Z o -> O O O O O O -ro ON c >- cr: -u| O vo O vo VO vO O VO VO vO vo VO VO vc vO vo \O vo VO VO VD VO vC VO vo vo 5 y ;> OOOOOO vo f>> -vo oo o- O O O O O O >- O M M ro ro <* ^-,vo ^oo o- 0- o - Q 3 vO vO VO VO VO vo VO vo VO VC vo vo VO VO VO VO vo VO vo VO* VO VD. >O vo vO VC vO VO vo VD 36 5 C OOOOOO o vo r^ r^ o OOOOOO "^ O O ** N N ro Tj- T}- vr- vO vO Ir^oo ON s vo V7 vo vC WO VO VO VO VO vo vo vo vc vo VD vo VC VO vc vo VO VO '--' vO VO vC vO vo'vo'vo' 2 O O O Irj M ro i-O r- rf- OOOOOO >/"> I'-IVD VD r^ OO O O O G O O "O ON CN O O "-i o o o 2 2 M - * > - * ^f- a: vovovo vo vo' vo vo' vo vc" vo VO vo vo VO VO VO vo vo vo V vo vo vO vo vo vc vo VO VO VD ~ 000 O O* O O VO vo vo vn vr vo v.~ v." <^ VO VO V1 vO 3- 5 5 cT OOOOOO .O OOOOOO ON ON er\ O O O 2 vo vo vo VO VO vo vo VO VO vo vovovo vo vc VO vo VO vo vO vC vo VO vo vo vo vo -o vo vo s 8O - OOOOOO OOOOOO b o O o o o OOOOOO O O O ^ -0 VD vO vo VD vo vP VO vo vo vo vo vo vo vO VO VO vo vo vo VO vo vo vO vc vO VO vo VO f , 3 O O O o o o OOOOOO OOOOOO OOOOOO <~* ro -J- ^t- * Tf OOOOOO <* ^ vo' 000 3 vC O VC vo vo vo VO VO vo VO vo vo VO vo VO VO VO vo vc vo VD VD vo vo vo vo VO VC vo M s o o o OOOOOO OOOOOO OOOOOO O O O O O O O O 0^ i-O vo vO vD vO vo vo vc VO VO vo VO VO VO vo vO vo VD vo vo vo vo vo vo vo vo >o vO V.O VO S O O O o o o !O O O O " O O O O O O OOOOOO OOOOOO OOOOOO OOOOOO I O O O O ! o o o o o o O O [ O O O 1 } at. IvO --C vo T^TOTO^ vo vo vc vc VO vo vo vO v;5 vO vo vo |^ V roT^* > loo o o - - - JEL TABLE XX. * 1 OS & <2 *+ 100 i^oo C ro r^ ^o ro co r<- O M rJ rn rj. ^ J*_iV^_^ O I>-OO ON O *-i N co ^ oo t-^ oc N .x> i > o<- rj *^ X O ro K~ O O O r-^ r^ tv ^0 M " Jl " V "^ " r^ r^ t-x r^. (i. t^. O CTs N NO ON ** N . M CO CO rr, -4- r- r- r-. ^ r^ t^. t^ *- ui o 10 o **- t/vc o i- t^ tx t^OO 00 00 o ix r*. m o < y rt cl ro 5j- ^ x; oo oo oo oo TC 10 LT 00- OO CN ON ro ^ <; 10 O O NO r>> t^. O O it i- M r4 c^ r>- t^ t^ r^ t^- 1 ^ i^ O ~ r- o N <> ro m m Tf t^- r^. r^ r^ fx. t^ ^^1 *"'' <^ NO ^T ^ NO cri Q Q t^ ^ t^ t^-y^, (xJ ci r^ o ^ - 1 >- r< N ro } :o oo oo oo oo on M O ON O O |OO O cr N N s s O O M '0 LO o CONO oo 1-1 ^J-NO O O O w M ^ w M M n fv-i rn ro rj- rt- Co t^ c ,0 '^, - i^ ^. O M - - r-* i >- "-" M < N CO <^ <^ 5- 4- 1 ^ ^o 1 ^ S "o Z ^ N 1 r^ r~- r- r^ t^ t^ t^ oo oo ^ .v ^o rj CN t^ ro ro Tj- |OO OO OO O H 2 33 lO LO L/-. NO O O 1 o o. NH -^-o c~ o o o -, rh r^ c> r| iy M M l-l M d N Cv c4 NO ON f*"> |^- N CO rv> r, ^. ^J. | *^ O O NO M <^ >o >o O O " i- ** t^-oo oo oo oo ^1 Cs-C H ro 3O OO OO cr. 2 T 00 O N sj- u-> LO rhNO oo C ^i ^ u-i vr, o-, o O O r-v o . M' r> vi ro oo ro o ON rocxs rvioo TT ^f Wi 'O O O ^h o o - N M 5C 3 S l o r^ o 'I- ** 11 w~ M ^ c< d co m OO O 1-1 o O co TJ- -4- 10 vo o r^ r- r^ r- t^oo LO w t O i-i 00 00 00 NO O NO o NO NO NO NO r~- r^- t^ t^ r*>s r^ r^- t*.f. r^. t>.t>.'ix r^ 2 !-H <-) ri-o OO O i- rn >r-, l^ ^J- ^- 10 10 10 0- , ON N rf-NO ON - o I- ^t" r^- ON rl *-o O"* - - M <* rl f) NO O ^ OO o i t- N 00 >^-, o o o 2 x M ro "4- * *- ko vd -o 1/ ">O OQ ') - M '-f ^ ON ^ LO o 2 - ON O rn rv-) ^- 000 <*** T <* rr 10 ! u-. tin S> o O O ONONOOOOlNONONOVO t~^t^ o o -i H, ^1 M- l- 0". -S N M c CO CO r-> 5-^*o * co 1-1 ! N rn r "^ ro to c*j ^- 3- Tj- o-o v*o O H -i N N .t-> O T)h H ro co VO O O vO O NO NO O NO cl < ~ as' OS >-! C-l M ro rr VS VD en ro i->-oo O - en rj-o r-- e? rotoro^OroTj- t-'4-"4*'^-'^-'^" HH oo ly, 1-- CA to LO u-) LO NO O K-J OO TO <- 000-"- O ".Ni3 H- *i M 5 X l^OO CTv >O NO VO O -l <* "'NO S o. g. 5 5 rj- >^- y vo *0 10 ^> o o o o - * ** * O O N NO NO NO NO O NO O O NO NO o t-- t^ i> r-- r^ IN tx'l^ CN s X rj- LOO o eJ M r^cxs ON >-i N <^n N O rl ro t f * ^ W f >0 t>- C\ O <* ^ * Nt- ^ ^ N rj-NO OO M CO VO u , LO ^O O O NO OO l-> 00" VD NO NO NO NO NO NC NO NO O NO NO NO 2 X H <*"> "3" r) n M lO u-> o 1^ OO ON r) rt -s <^ ^ N > r) r^~, O CO en <-) ro CO ro OO CJN w t+ 2 x| CTv O l-i ! m r^ rf 100 l-^CX3 CTx O >-> M ro >o o r^ ON ;. - ro .^,vci 00 O^ 'J- -' U-l VO LT ; NO NO O NO NO O O NO O O NO O O NO NO NO O NO NO NC NO NO NO O NO O ! LO r- c i i- -vt TJ- NC 3 X r-o* &o sO NO NO C\O O " <^ -> r rt N rl ^f- tar, XAlvO t -OC CN O 1-1 N -4- ir-i N CO r^ CO ro ONO r> CN 04 1 vO NO NO O NO NO NO O O NO VC N/5 O O O 1 VO NT NO NO O NO NO NO NO NO NT) ,4*1-"-! iX |o 00 O NO NO NO O NT 00000 NO VO VO VO NO NO NO * ^ _i M r) M r^ rn ~, rf rj- 10 "-.0 r- t^ o oo a-, o p-i r) ro ^- '^> o r--oo 1 , 33 2 X 2~ 11 rCoooS O O O Nr> NO N.- NO v- 00 ) ir^ w^> w-^ O O O VONO O NO O NO o o o o o o t ^ r^ I ^ I ^ SO OO I CO C> CN ON O O O ~ M c-l rl rororj- MHIMM,-^ * M O NO O -0 NO ON&NOOOO .OOONONONO NONOOOONOlOOO 5 X. s 7" ^ r< "^ C r^, ,,, .-<, ro m ro o o o o o o ro r*-j ^v r)* TJ- r ^- O O O O O Tf- ^ TJ- 10 IJ-V VJ-| O O O O O O -i lo ^: . \c, vo o o o o o o o so r- r- O O O O o o o O NO NO i 000000 o o o o o o O O O O O O O O O O O O 000 O NO NT NO NT> NO O O O NO NC O NO NO r o NO NO O 'NO VO NO Lat. t< 4 f^l ^- "-.NO t--00 t> .-^ rh u-, <^rltor->rr>r">ci<-o rfTj-Tj-^-'i-Ti-i ot^oCNO- ^f^Tt-'ovor--C)OCNO ^-^-iO>0 8. o > 6,0 > 4. o .? o Ib. oz. ro. o 8. o 6. c 4. 8 3. o 2. 4 Ib. ot. 3- o 2.12 2. i. 8 I. 0. 12 44 45 46 49 8. 78 8. 8; 8. 9? 9- 7 9. 17 9. 26 320 330 350 360 380 390 .10 130 fto [.6 o 470 480 49 5. 67 4- 3 4- 39 4- 75 5. 10 5- 4' Hi. b 43- , 45- * 7- : 9- .' I. 2 6 4 3 2. ; i. 5 I . 0. 5 2. O ! 5 I. C 0. 1 o. 8 o. 6 o. 4 0. I 7 8 9 10 ii 12 14 '5 16 17 18 . 50 74 * 97 4. 18 4- 39 4. 58 50 11 65 70 75 80 85 90 95 00 05 til o. 25 o. 67 I. 07 1. 46 5- 79 6. 13 6. 46 6. 79 7- 43 (,oo 70? 800 900 ooo 100 200 300 4CO 500 600 7Q 2. 9 4- 5 7- 7 9 . 2 0. ( 4- 3* 18 12 < 9. c 6.' c 4- c 3- c Jaro iac: 4. S 4. o ' 3- o ) 2. i. 8 es. 4. 8 4. c 3- o 2. i. 8 i. 8 i. 4 I. I. O 0.12 4- 77 4- 95 5. 12 5. 2 9 5 45 5. 61 I. 83 2. 2C 2. 55 3- &9 3- 2 3 3- 5* 7- 75 8. 06 8. 37 8. 68 8. 98 9 . 29 2. J 3- ' 4- i 6. i 7- s 8. -, \\ 2.8 'all Pie O. 1C :es. 20 21 22 23 24 5- 77 6. 06 6. 21 6- 34 6. 4? 10 15 20 30 35 3. 88 4- '9 4- 49 4 7 f * 15. 08 5- 37 500 520 540 560 6oc 9 . q > o. 17 o. 74 ,i. 80 32. 41 8co ccc 3100 1300 0. C I. 2 2. c 3- : 4. * 76. c Musquc 0.12 0. ( ti. O. Piltol 6 o. ; Iff ; 25 26 27 28 29 31 3- 33 34 3 3 3 4 4 4 4 6. 61 6. 75 6. 87 7. oo 7- . 7 37 7.. 48 7. 60 7. 7 7. 8 7- 9 140 1 60 170 iSe 200 210 22O 230 240 15. 93 1 6. 20 16. 73 i7 . 2. S 17^75 1 3. 24 iS. 71 19. 17 19. 62 20. C( 20. 5< 620 640 660 680 700 720 740 760 780 32. 94 33- 47 33- 99 34- 5 35 co 35- 5o 3400 3500 3600 3700 3800' 3900 77- J 78. 3 79- 4 80. c 81. 6 82. ( N. B Theie proportions are with powder in good condition; it it is damp, or damaged, agrsat- T quantity will be neceflary. A TABLE of the :N 7 umbei and forts of Shot contained in the Grapes for the nature of Guns undermentioned. 35- 99 36- 47 36. 95 4000 4100 4200 4300 4400 4500 83. - f 34. 7 86. i 87. 8 88. 800 820 840 6o 880 90 92 94 96 98 37- 42- 37- 88 Pdrs. ^ ,hot. No. in each. No. in ach box 4 4 6 8 JO 12. 2O 42 24 18 12 9 6 4 4lb. 3 2 Oz. 8 6 9 9 9 9 9 9 9 9 8. o 8. i 8. 2 8. 3 8. 4 8. 5 8. 6 250 260 270 280 290 300 3IP 20. 92 21. 3 21. 7' 22. I. 22. 5 22. 9 i3- 2 38. 80 39- a 5 39, 69 40. i 40. 56 40. 9 41 . 4 4600 4700 4800 4900 5000 iM 89. 90. 91. 92. 93- 96. TABLE XXIII. For finding the Latitude by two Altitudes of the Sim 1-iaU elapfed Time. o Hour. j Hour. M. o' 1 10 20" 30" 40'' g M. o" 10" 20" 30' 40" so" o i 2.36018 '3833 29324 83730 66121 18409 53627 13334 43936 09695 i 0.58700 57999 5858, S7S3 58465 5^-48 57653 58231 5753^ 5 * > 5 2 3 05916 02440 8595.9 99221 8373- ^6225 3j6i 3 93422 79593 90790 77663 2 .3 57310 56633 57190 56521 5*40* 56970 5629?; 56X57 56745 560*6 i 4 5 6 75^4 66125 58208 74042 64701 57018 72339 55861 70700 Si 986 54733 69121 60690 53634 67597 59431 52561 4 5 6 55960 553" 54660 5585" 55203 54559 5574^ 55095 54*53 5563- 5498- 54347 5552 s 54 2 4i 554F9 54773.! 54136 '' 7 8 9 51515 45718 40605 50494 44823 39*09 59496 43946 39017 46520 43086 38258 47566 4224 < 3753 46632 41417 36762 7 9 54 3 1 534 fc 52791 5330? 52690 5382:. 53200" 52580 53^97 43014 52995 535'Q 1C ii 1.36032 31896 353 1 : 34609 30600 33915 29967 29342 3255* 28727 10 i f 0.52186 51589 52080 51400 51986 51592 51886 51294 5^7^ ^HQ6 516881 -1099 \ | 12 20I2O 27522 26931 26349 25774 25207 12 5IOQ 4 50905 ^oSo - '071 '.Ko6i i "0510 j M 24647 21432 18440 24095 20919 17961 2 354'' 20412 17487 23010 19910 17018 22477 19415 16554 21952 18925 1609 , 13 50423 49^52 49290 50327(50232 49758149664 49197 49104 ;oi 37 49570 4901; 5004: 48 9 ?.( - -> ' +994 7. < 49383i l6 15642 15192 14748 1430; 13872 1344-' 1 6 4 8 73 6 48644 4*553 48462 o 4.0 11 1 48280 " 17 I30I3 12590112171 "757 11346 109*1, 17 48180 48090 48009 4"QI< J.7^2C 4-7" ?O i' iS 19 10536 08193 1013609740 07814)07439 09348 07067 08960 06698 0857, 06 33-.- i' 4765q 47561 47031 4747- 4694.- 47J8, 468^6 4729- 4 6 " 6- 47207 ; 16681 1 20 1.05970 05610 5254 04901 0455- 04202 20 0.46595 46 ^oS 464^1 4^335 .Ifc24( 4.6163 | i 21 22 03857 01845 01516 03*75 01192 0283* 00870 02504 00550 02172 002 5 - 2 I 2- 46077 45567 45992 45583 45907 45399 45822 45737 4 <; '> 7 i 45652 ; 24 0.999IS 98077 99606 97777 99296 97480 989X8 97184 9^682 ^689; 9837* 96600 - 3 24 45064 4456; 44981 44485 44898 44403 448 1 5 44321 4475 44230. -> : 1 4- / | 44649 1 , 25 26 963:0 94614 92 9 'i2 90025 9433- 92716 95738 92452 95454 v379o 92189 95172 93519 91928 94892 93250 91669 26 27 4477 43593 43114 4399' 439'5 435^J434.33 4303 5142951 43^34 433 5 ; 4287- 4375" 43*7-3 4279 43673 ' 43193 -12 "2 I 28 2 9 914II 89894 94^54 %<>47 90899 89401 90646 89156 9394 88913 9014 88671 20 4264^ 42176 4256^)4248- 4*09 (4202. 42409 4194.- 41^6; 42253 41792 1 3 | 3 34 I 35 - 36 0.88430 87015 85644 84317 83030 81780 80567 88191 86783 85420 84100 82819 81576 80368 ^79.53 86553 83884 82609 81372 80170 87717 86324 84976 83669 82401 81169 79973 8748. 86096 ^4755 *2?93 80967 79777 8724. *53 7 c H53- 8324: 8x986 2076- 79581 30 3 1 32 33 34 35 0.41716 41261 40812 40368 39930 39497 39060 41 i So 40738 4029; 39857 39425 #998 41 564 41111 40664 40222 J978? 39353 3802- 4148 x 4103' 40590 4014(5 3928: 3885' 41412 4096 40516 40076 39641 3921! 58786 40442 40003 j 39569 i 39140 ' 58716 37 33 39 79327 78239 77122 79193 78051 76938 79001 77863 76756 78809 77677 76574 78618 7749 1 7659?. 7842^ 77^0' 7621? I 39 3*646 38227 3 S 57 6 3774.5 38506 38089 38020 38366 3795' 3754.1 3/882 37473 40 0.76035 75854 75676 7549v 753^3 7514; 40 0-3740-J37337 37*6$ 37202 37 n- 37068 4* 74972 '/4797 74624 7445 i 742/9 74107 4' 37001 36934 36867 36800 -673 56668 42 43 73937 72926 72760 73597 72595 73429 72430 73?6i 72266 73093 72103 42 36602 36206 36536 36141 36470 360.76 36404 3601 1 36272 44 45 71940 70976 7I77 8 70818 71616 70660 7H55 7050-3 71295 70346 7"35 70190 44 35816 354.30 35366 35686 35302 35622 3555:- 35494 4 6 47 48 49 70034 691*3 68212 67330 09879 68962 68064 67185 6-9/2 s 68811 67916 67040 69571 6866.., 67/6 66896 69418 68510 67622 66752 6926; 08361 67476 666oq 4- 47 49 .3504', 34669 34296 54984 3460--, 34234 33864 34921 34544 34i 7 ^ 33803 34*> 3448.' 34110 34795 3404 1 - 34732 3435^ 33986 ^3620 50 5 1 5 2 53 54 o. 66466 65620 64791 63978 63181 66324 65481 63844 6305;. 66182 65342 64519 63711 62919 66041 65204 6.4383 63578 62789 65066 6424? 6344; 62659 6 57 6c 64928 -4113 63313 62520 50 .5 3 54 o.3.<559 33197 3283, 32134 3349$ 33*37 32780 32426 32076 S'3438 33077 32720 32367 3 20 1.8 3337^ 32661 32300 3.1 060 3295- 3225^ 33258 : $2809 > 2 543 ] 32102 : n^A * 55 62400 62271 62/42 62014 61886 01759 5< 31787 31729 31672 5 1 6 1 ^ 3l 557n?.on 5 b 61632 61506 61380 6125..; 61129 61004 3 r 44? 31386 3I32Q U272 57 60879 60755 60631 6050!'" 6o?8<; 60262 57 31103 31046 30900 :o 9 34 50878 ioitfL 5 s 60140 60018 59896 59775 59654 59534 30766 50710 3065 <; 30544304^ Is? 594*4 59294 59*75 5905' 5893"? 58818 59 30433 303 78*303* 3130268 50M3 ! 3 o 15 3 TABLE XXIIL For finding the Latitude by two Altitudes of the Sun. Half Elapfed Time. i 2 Hours. ii 3 Hours. IV o'' 10' 20'' 30" 40" NO" MJ o" 10" 2C'' jc/' 4/' 50' 0.3010; ,0048 9994 2 9939 29885 29^31 0.15051 1 5O2O] 149 .5 14957 1492 14594 29771 1974; 29668 2961^ 29560 29507 1 14863 14832 14800 1476^ '4738 14707 29453 -9399 29346 29295 29239 29186 2 141 ',(. 14645 1^614145'* 145^2 f 452i j 29133 i ( ->* - 2902- 2A| 974 48921 28869 14490 14^60 14429 14398 43 ('8 J 4337 Z9#X4 1876 28 1 1 2*659 28607 2855^ -, 4Jo/ 14276 14246 1421, 1418 14155 2 3 5 o . 28450 18 ^9^ 834' 2829; 28243 5 14094, 14004 14034 14004 U974 2768 28089 28037 27986 ? 79 35 t 394 1388^ IT } f i f r 3794 : 74: S 274*Si -737 9 27327 , / 13585 ?355? 135*^ I3O^ t 13441 *JV1 7227 -71/7 27127 -7077 2702S Q '34 1 3382 '~'3^3 1332. 1321)5 13266 c .16972 26379 26^C 267*1 26/31 o I j -i 5 / 13208 '1317 1 3 , 5 13121 '3093 j *668.2 .663 16/5^:6535 26486 26478 11 13064 r 3035 13007 1297'' 1 2 95- 12921 26339 ' '' ;~jc 26292 2624^; 2619 c 26/47 19 Ti' < 9 ^ 1^864 12830 1*807 1 2 7 v r2 75 i i 26091; 26051 .occ; *595f 25907 258^9 i ,' 12/23 '269*; 12606 f263i 126IC . & 25811 2570 57-6 2566^ 25621 ? 5573 '4 1*554 T2526 12499 1247; I2 443 2415 25526 i 54/S 4 5' j- ~ 53^ ^ 25338 2529 '. i ; 123*7 12360 12332 U3 O 5 12277 12249 j 25244 2519 25' 50 25 \O 2505: 25011 1 6 1 2 i 2 I 1219; 12167 r 2 140! 121 17 120^5 I ' 24964 2491 14^72 24*2: ^477') 24733 17 1205*, (2031 12004 11977 1194- 11922 2468, 2454 -4595 24 c j<- 245'4 244 "8 Ii 1189: 11868 ' 1^42 11815 11788 11761 i j t 24417 2436- 24322 2427^ 24231 24166 19 i'7vt 1708 Il68l 11654 1162 s - 11601 c 0.2 4J j, 24096 2405. 24001' 23 ,6 i 23916 \C 0.115-: 11548 11522 11495 1 1469 "443 1 I 2 3 8 7i -3827 23782 13738(2 -60 < 2? (54-9 2 f 1141' 11390 11364 H3.33 11312 11285 j i 23605 Z 356<- H 516123472 2 J42* 133*4 1 2 11259 1 12731:1207 uiSi 11155 11130 j -334^ 23-9' ^3252127200 23165 23122 -3 II 104 1 167811 1052 11027 I1COI I0 975 2 4 23078 2303- '.299111294*! 2 .862 24 10950 10924110899 10873 1084^ 10^22 | 2 f 22819 2277. 21690 22647 22604 2-5 10797 I0772JI0746 10721 10696 10671 2t 22561 225lr 22476 -'24^3 22391(22349 10646 106201 1059; 10570 1054: 10520 '27 2230^ 2226^ i2222 22I/5C 2 - ' 3 X ;2Oy6 27 1049: 10471 10446 10421 IO3Q6 10371 1 i2b 22054 22012 il'97O 2192ft 21887 21845 2b 10747 1032. 10297 10272 10248 10224 ! ic - 21803 il76: 21720(21679 21^3'" 21 sg6 >9 icigc. 1017; 10I5I 10I2f IOIO2 10078 30 0.2155. 2151 "473 21432 21391 21350 30 o. 1005 (10029 10005 09981 C 9957 9933 i 31 21309 I.I26 2J22* 2II87 21147 21 I 06 3' 0990^109885 09861 09837 09813 09789 32 21066 208? 4 2IO25 20784 20985 20/44 20945 20704 20905 20^64 20665(20625 3- J3 09765(09741 0962" 09599 09718 09576 09694 09552 09670 09529 09647 09506 34 2058: 20545 2O506 20466 2042-7(20387 J4 09482 09459 09435 09412 09389 09366 35 20348 20309 20269 20230 20191 20152 35 093471093 19 -9296109273 09250 09227 : 3* 2OI I 7 19880 19640 200/4 19841 19611 20O35 (9803 19572 19996 19764 19957119919 19726 196^7 19496 1 945^ 36 J7 09204109 18 1 ',091 58 109 1 36 09067109044 09022 08999 0893 i;o l >)909Jo8886|o8864 09117 08976 08842 09090 08954 08819 39 I942O I 9 ^2 |344 19306 19269 1923; 39 08797:08774 0875208730 0870;; 08686 4 1 o 1919,- 1896:^ 19156 ,893, 19118 19081 18857 10043 18820 I9CO6 l8 7 83 40 4 1 0.0&66/. 08551 08641 08619,08597 08488)08466 08575 08444 08553 0? 4 22 :4 2 18746 i8;0 1867^ 1863; 18595 18561 08401 0837908357108336 08314 08293 i4 7 18525 18488 18451 1841 5 18378 18342 41 08271 38250 0822808*07 08185 08164 44 18306 18269 18233 18197 18161 18124 M 08147 o8j2iio8rcco8o7f; 08058 08036 '4 ; 18089 18053 18017 17981 J 794^ 17909 4- 08015107994 0797i07952 07931 0791O 4' I7 ; 374 17838 17502 17767 1773* 17696 46 07889(07868 0784^ 078^7 07806 07785 47 17660 l/62s 17590 '7554 I75I9 174*4 47 07/6: 07744 ^7723 07703 07682 0766! 48 J7449 I74M 17379 17344 '7309 17274 1-8 07641 ^7620 07600 07579 07559 07539 A' 17239 1720- 17170 r 7 r 35 17101 17066 40 0751- 0749 s - 07478 07458 0743; 07417 5' o. 17032 16997 6963 16928 16*594 i6S6o CO 0.0739" D 7^77 07357 7337 07317 07297 5 J 16526 16792 16724 16690 16656 ^I 0727; -7- -.: 07237 07217 07197 071/8 16622 16588 6554 16520 ,6487 16457 >2 0715* 3713' 07119 07009 07060 : 5 '-' 16419 1636' &35* 16^19 1628*; 16252 53 07040 3/02! 07OOI 06982 06962 06943 54 1 6 2 ; g 16186 6152 16119 16086 16057 54 06925 06904 06885 c6S6; 06846 06827 5 16020 1598 5954 15921 15^88 .5856 55 06808 ^6780 6770 06751 06731 06712 - 15827 579C 575 s 15725 1569? i s66o 56 06693 0667. 3665(5 06637 06599 5 15628 '559.' 1 5563 15530 1549^ 15466 ^7 06580 065' I 0650.^ 06^0; 06487 j5- 154^4 IC402 15370 1533S 15306 15274 58. 0646^ 0644^ 06431 36412 06394 06375 f [55 15242 15210 1517* 15140 1 5 1* 5 71083 59 06357 06 33 ? .6320 067,0; 06283 .6*65 TABLE XXIII. For finding the Latitude by two Altitudes of the Sun. Half Elapfed Time. 4 Hours. 5 Hours. M o" i j" 20' 3' 40" 50'' M o" 10'' zJ' 30 s 40" 50'' 0)0.06247 06229 0621 1 06192 0,174 06156 o 0.01506 0149; 01489 01480 01472 01464 06138 06120 06102 06084 36^66 06048 i 01455 01447 01439 01430 01422 01414 06030 06012 0599505977 05959 0^94! 2 0140^ 01393 01390 01381 0137.: 01365 05024 05906 05888105871105853 0583' 3 oi35/|oi349 01341 "333 01317 05818 05801 05783 05766 0574^ 0^731 4 01310 01302 01294 OK'. 8(J 01478 OI2/O 05714)05690 35679 05662 05645 05627 s 01263 01*55 o 1 247 OI2AC 01232 01224 0561005593 05576 5559 '554* 0552 01217 01209 01202 01I 94 01187 OII79 05508)05491 35474 0545- 054+0 o<;42^ 7 01172 01164 0115- OII 5 ,: 01142 01135 05406 .,5389 053--' 8 01 123 01 120 OI1I3 01 100 OICQv 01091 0530', 052JO 05273 5 57 -.52400522 9 oio-/; 01077 OI07C 0106? 01056 01049 10 0.05207 05191 05174 0515* 0514205125 1C. o 01042 01035 01028 ' 1O21 01014 01007 i 05109 05093 65076 05060 05044 0502 i i oiooc 00993 009^.7 00 9 KO 0097; 00966 i 05012 04996 G4q3o|o4964 04943 oAi) ; ; j2 00960 00953 00946 00940 0093? 00926 I 04916 34'fOO 04884 04868 04^37 13 00920 00913 00^07 00 9 OC 00894 OO&87 i< 04821 04805 04789 04774 0475^ 14 00381 00874 oo86 00*62 0085- 008 49 i 04727 0471 J 04696 0468 04.665 04645 I 5 00843 00836 o 830 00824 ooSzfc 00.* 1 ( 16 04634 046(9 04603 04588 0457J 0-155 i 6 OO'to; 00799 00703 0078 7 '.07 :' i 00775 i 04542 04527 345 1 a 34496 04466 17 00769 00763 00757:007 51 00745 ou ; 3 9 ib 0445' 04436 04421 04406 04391 o f37& i , 00733 00728 00722 00716 00710 00704 19 04361 04 ?4< 043?* 04317 34302 04,87 '9 00699 0069? 00687100682 00676 00670 20 0.04272 6415 04243 0422- H 21 4 04*99 2.O 0.00665 00659 00654.00648 00643 00637 2 04 ) 8 ? 04170 04 1 5 5 3414( '4127 04112 21 00632 00626 0062 00616 00610 00605 i 2 04098 04083 04069 HO 5 5 04040 04. -2'; 22 00600 00594 00589 00584 00579 00574 I \Z 040 it O399 1 "' 03983 03969 03955 03941 23 00566 00563 00558 00553 00548(00543 j 2. 0391? 03913 03^85 033/1 03857 M 0053^ 00533 0052^ -10523 00518(00513 2 03843 03829 j 3 8 1 q 03^0:. 03788 03774 -5 00508 00504 30499 00494 00489 00484 2(> 03760 0374 >3733 03719 03706 0^692 20 00480 00475 00470 00461100461 00456 27 03675 o 3 ( 1 6 ; 0365" 03638)03624 03611 if 00452 00447 0044? 0043^100434 00429 28 03597 03584 3357f 03557 J 3 544 03531 28 00425 00420 00416 0412 00407 00403 29 03517 03504 33491 0347^ 03465 0345- 29 00399 00394 00390 6o$86 .-.0382 00377 30 0.0343^ 34*3 0-54.2 03399 03386 03373 30 0.00373 00369 00365 00361 357 o353 31 03360 03 H* 33335 03322 03309 03296 00349 00345 00341 30337 00333 00329 32 03283 03271 03258 0324^ 3323 3 33220 32 00325 00321 00317 0031: 00310 00306 33 03207 03195 03152 03170 03 157 3 T 45 13 00302 00298 029 ; 00/91 00287 00284 34 03132 33120 03107 03095 03083 03070 34 00280 00276 00273 00269 00266 00262 35 03058 03046 03034 03021 03009 02997 35 00259 00255 032 52 3024C) 0024=; 00242 36 02985 02973 02961 01949 02937 00239 00235 00232 30229 0022 i 00222 ,37 02913 02901 02889 02877 02865 02853 37 OO2 1C) 00216 OO2IJ 0210 00207 OO2O3 3* 02841 0:82., 02818 02806 02794 32 83 OO200 00197 00194 00191 COlg'"' 00185 139 02771 02759 02748 02736 02724 0271; 19 OOIS3 00180 00177 00174 OOITJ co 1 68 40 0.02701 02690 0267^' 02667 02656 0264^ 40 o. 00166 00163 00160 00157 oo 1 55 0:152 j 41 02633 02622 02610 32599 02588 02577 4! 00149 00147 3GI44 OOI42 OOJ39 00137 i 42 02565 02 5 54 02543 02532 0252f 02510 tr. 00134 00132 OO 1 2 () 00127 00124 OOI22 143 02499 02488 0247; 02166 024,55 02444 1-3 OOI2O 00117 OOII5 001 1 - oono OOI08 44 02433 02422 02-11 I 0240:-, 02390 02379 44 OOIC6 00104 30102 00099100099 oo95 45 02368 02357 02.347 02336 02326 02315 45 00093 00091 OOO8q 00007 00085 00083 46 02304 02294 02283 02273 02262 32252 46 00081 00079 00077 00075,00074 00072 147 02241 02231 Q.2227 022 10 02200 02190 47 00070 00068 OO066 0006- 00061 f- 02179 02169 021 50 02 140 02139 02128 OOO6C 00058 00056 00055 00053100052 J49 02118 02roS 0209? 020S". 02068 49 000^0 OOO49 30047 00046 DO044JOOO43 5 0.020^8 02048 0203^102021 02013 02009 50 0.00041 OOO4O 00039 00037 0^0561 00035 !5 01999 01989 01979 Olg^O 01960 0195* 51 00033 00032 OOO3 ! 00030 00029 00028 52 01940 01331 0192: 01912 31892 52 00026 00025 OOC24 00023 00022 OO02I {53 01883 01873 01864 01854 53 OO020 00019 OOOlS OCOI7 OOOI/ 00016 54 01826 01817 01808 UI7$S 0X780 3*780 54 OOOTC, 00014 36013 ^00.12 ooo r i . 01771 01761 - T f ~ j,-, j . OOOj^lOOOOg 30 ""oBi - OCOO7 I 56 01716 01707 31698 >i6So 01671 6 OOO 10 OOOc6,OOCO6 00005 cooo 5 00004 r 57 01662 JI <>53 3*644 016.3^ 31626 31618 00004 3a.3c $ .0300.3 00002 OOC02 ( 5"> 01609 o r 600 31591 31583 31 5.74 31565158 cooo?- ooo: JOOOJ OOCOI OOOOI j 59 T 01557101548 31540 3/531 01523 > r 5 r 4|S9 OOOOO OOOOQ JOOOO | TABLE XXIir. For finding the Latitude by two Altitudes of the Sub, Middle Time. ' o hours. i i Hour. i M o'' i 10" 20" 3o" 4 o" ^o ; ' MJ o" 10' , id' 30" 40" 50" o 2.OOOOO 1627*: 0373 .3982 76476 S6i67 o 4-7I403 71521 71638 71755 71072 71988 i 1^94085400779 06578 11694 16269 20408 i 72104 7222072335 72450 72565 72670 2 3.2418727603 3 oi 8 a 33878 36681 39313 2 7^793 7*967730*0 73133 73246 73358 3J 4* 79 & 44H4 4| 54289 ,6061 46371 57/64 48490 5943 50510 00982 52440 62506 3 4 7347 74137 73582 73694 74357 73805 74466 739 16 74575 74027 74684 5[ 6397^540- 6l 718951.73085 66781 74^ 68117 75370 6 94 I 3 76469 70672 7754 2 5 6 74792 75437 74900 75544 75002 75650 75116 75756 75223 75862 75330 75967 i 7 75on 76909 80607 81583 82537 "3471 7 76072 76177 76281 76385 76489 76593 b 343*5 !J52.8e 56157 87017 87860 88636 8 76697 76800 76907 77006 77106 77210 9 8r>49 x 9^-'.M 91076 51845 92600 93341 9 773 I2 77413 77514 77615 77716 77817 ! 10 3.94071 947^ 95494 9618- 90^72 9754-J 10 4.77917 78017 78117 78217 78316 78415 f u 98207 99503 00136 00761 01376 1 1 78514 78613 78809 "8907 79004 i 124.01983 02581 .3172 03754 04329 04896 12 79101 7919^ 79295 79392 794'^ 79584 i ] 3 05456 0600- J&5M 07093 07626 08251 1 ^ 79680 797/6 79871 79966 8006 1 ^0156 1 '4 08671 00184 09691 10193 106*8 11178 '4 80251 8034; 80439 8o533 80627 80720 * J 5 11663 1214?. 126 if 13085 '3549 14007 80813 50906 80999 8 1091 81275 ' 16 ' 17 14461 17090 i49 I M I 5355 '/SiS '79.3^ 18346 18757 16663 16 81367 81914 81459 82004 81550 8x094 81641 82184 81732 82274 81823 82364 ! 18 19567 T99-7 20363 10755 1 8 S2453 82542 82631 82720 82808 82806 |.r 9 21910 22289 2266^ 23405 23770 9 82984 ^3072 43160 ^3247 83334 3|4 I 20 4.24133 14493 2464, 15202 '^553 25901 20 4.83508 83595 ^3682 83768 83854 8394 i 21 26246 i' 5-v> ^692? 2726 q ^7590 -7931 ii 84026 541 u 54196 84281 54366 84451 22 28260 ^587 28911 19*33 '3553 29870 i - 84536 84620 84704 84/88 84872 84956 1*3 30185 ^0497 ^0807 114*1 31725 25 85039 85122 8520; 85288 85371 3 5454 i 24 32026 ?ij26 52623 32919 .13212 3353 24 85618 55700 ^5782 85864 85945 i 25 33791 34080 H36 - 34649 34931:3521 1 86026 3610^ 36i38 86269 86350 86430 [26 35489 35765 36040 56313 365^416853 26 865^0 ^6590 8^670 86750 86830 869IO [ 27 371x1 5738; 5765. 379M 3817538474 27 86989 ^7068 87147 87226 87304 3/382 2.1 38692 38949 59-4 59709 39960 28 87460 8753S $7616 57694 8/772 87850 zq 40209 104 5 <> 40702 40--47 1119041432 '9 87927 88004 88081 88158 88*35 883II ! 3 4,41673 41912 42150 42386 ^2622 42856 50 4-88387 58 4 6 3 ^539 PIC 88691 88 7 6 7 31 43088 3*6 43550 43779 44007 44233 3 1 88842 88917 88992 89067 89142 89217 32 444 "9 44083 44906 45127 H34 8 45568 3 2 89291 39365 39439 89513 89587 89661 ' 33 45736 4600 : ^6219 46434 4664846861 J3 89735 ^9808 -59881 ^9954 90027 9OIOO 134 470/3 17284 47494 47702 47910-48117 J4 90173 50246 90318 90390190462 90534 .35 4 8 3*3 485*7 48934 4913649336 90606 90678 90750 90821 90892 90963 36 4953'- 4973549933 50130 30326 50522 ;6 91034 91105 91176 91247 91317 91387 37 <;O7i6 509 to 51 I0> 51294 5148? 51675 ^7 9H57 91527 91597 91667 91737 91807 i 3- 51864 52052 52240 52426 52612 52797 ^8 91876 91945 92014 92083 92152 92221 1.39 529*1 53165 5334- 535^-9 537ie 53891 39 92290 92358 92426 92494 92562 92630 :4 - 54M9 54427 54604 5478o 5495 6 40 1.92698 92766 9^834 92901 9296893035 '41 55131 55306 55479 55652 55824 55996 -H 93102 93169 93236 93303 9336993435 4- 56166 56336 56506 ^6674 56842 57010 41 93501 93S67 93633 93690 93/65^93831 ;43 57^77 57343 ;7^oS 57673 57837 58000 n 93897 94027 94092 94157194222 144 58163 58325 5*487 58648 58808 58968 44 94287 94352 944 1 7 94481 94545 94609 i 45 59127 59*85 59443 59600 59751 59913 45 946/3 947.37 94801 94865 94929 94993 i 46 60060 60224 60378 60532 60685 '0838 95056 95182 95245 9530895371 [47 '60990 61141 61292161443 61593 61742 47 95434 95497 95559 95621 95683:95745 4* 61^91 62039 62187 62334 ^2481 62627 4? 95807 95869 95931 9599396055196117 49 62773 62 9 r8 53063 63207 335.1 ''3494 49 96178 96239 96300 96361 9642296483 50,4.03637 63779 63921 64062 64103 64343 50 4.96544 96605 96665 (6725 96785 96845 5.1 64483 64622 64761 64899 6503- 05175 5 1 96906 96966 97026 97086 97145)97204 S^ 65312 6 544 s 65584 65720 6585; 65990 52 97264 97323 973^3 97442 97501 97560 i 53 6612; 66259 66792 6652; 66658 66790 53 97618 97677 9773$ 9/794 97853 979H i 54 66922 ^7053 6718,- '* 7 3 1 4 67444 r >7574 54 97969 9X027 98085 98143 98201 98259 55 67703 67832 67961 $8089 68217 68344 55 98316 08374 98431 98489 98546 98603 56 68471 68597 ^8725 68S4C 68974 ''9^99 56 98660 98717 98774 98831 98887198944 5" 69224 69348 69472 69595 69718 69841 57 99000:99057 99113 99169 99225 q928l 58 59 69063 70689 7008 ; 70809 70207 70928 7032? ; 7 1-047 70449 71166 70569 58 59 9933799393 99670199725 99780 99504 99^35 9955999615 99890^99945 TABLE XXIII. For finding the Latitude by twaAltitudes of the Sun* Middle Time. 2 Houis. 3 Mours. M c/' ' 10'' 20" I 10" 40" i 50" M c" LO'-' .O 7 jo 1 '4***' &>* 050 -QOC 000,5 OOIO- o Jib 302180027 5.15052 r 151 1 ., 1514 1517; 15209 I 0^3:7 jo 3 s i ^-'435 00459 oo 543 '005 90 i 15240 1527 1 530 , 1536- 15396 z 00650 00704 00757 soSic 086410091 2 1542 1545 1 ^4" i '552 I 555' 15552 3 00970 01023 ; 1 7 00, 21., 01 182)01234 : 1561 i ,04 567^ 1570 J 5735 15700 4 01287 013^9 1392 01444 01406 Olf;y -524 02574 02625 0267^ >75 02:7' 8 16516 1654 1657; 1660 16633 16662' 9 02 26 0287? 02926 0297 0^026 070- 9 1669 16 2 167 ^ 1677 16808 16837 10 5-03125 03i7u 03224 03275 03322 0,37 i 5.16066 1689 1092^ .695 16982 17010 j i 03421 03470 J s > I C 03:6 03617 0366 1 1 17039 1706 I709C 1712 17153 17182 12 03714 03 7<> 3 03*1 1 03859 0390* 03956 12 17210 1723 17267 1-729 17324 17352 ; 13 04004 04052 3410C 04148 4 1 9' 04244 13 1 7380 1740 ! 74"?7 1746 17491 17^21 14 04292 ^4340(04387 0443s 04482 04530 14 1754 i 757" 17604 1763 17060 17688 15 0-4577 04624 04671 04718 0476;, 04812 t 5 17716 1774 '77/1 1779 17826 17854 16 04859 04^00 0495 04999 ,504'.) 0509 1 6 1788 1790 17936 1796 17990 18018 17 05139 0518 05231 o - 7 " 353.24 05370 '7 1804 18072 18099 1812 18154 18181 18 05416 0546 0550* 0555- ^5599 0564 18 1820 1823 (8261 1822 1^342 19 O^G 057^6 05781 35827 0587, 05-U7 i 1836, 1839 .8422 x -44 18475 18502 20 5.05962 06007 06052 0^97 ,,14 0618- 20 5.1852 i*55 18581 i860 18634 18660 21 06232 06274 0632 ' ,636- 03410 06454 21 1868- [871 18739 1876 187,1 18818 22 06498 06543 06587 06631 0667 ^ 07619 22 18844 18896 1892 18948 18973 2 3 06763 06807 ^6-851 068-^4 0693 0698 2 T, 1899, 1902 19051 1907 19102 19128 24 07O25 07068 07112 0715; 07198 1.7241 2 + 19-25 19179 19204 1923 1.9*5-5 1928; 07284 07328 373-71 07413 07456 07499 2r 19300 ^933 19357 1940-7 19432 26 07542 07584 07627 07670 07712 07754 2 I945- '948 r v^ 19583 2" ' 07797 0783. 07881 07923 0796" 08007 27 196^3 '9 '3 19657 19682 19707 19732 23 08049 08091 08133 0^17 08216 08258 .8 19756 1978 19806 1983 19^5; 19879 19 o8-3or 08341 08385 084*4 :8 4 6 5 08507 29 1.990^ 19925 1995, 1997 2000'! 2002 r 30 5-08548 08589 0563P 0_,07l .8712 08753 30 5.20050 20074 20098 20 12 20146 20170 08794 08834 08875 ^8916 08956 08997 3i 20194 2O2I5S 20242 20266 202GO -3 r 1 3 2 09037 09072 091 ib 0915^ o 9 1 9 >. 09239 3 ; - 2033^ 20362 .0385 2040 2043 20456 33 09279 09518 09319 09558 09359 09597 09399 09637 09438 09670 09478 09716 3 33 20480 23621 .'.050, 20527 2055 2069 20714 29597 2C737 35 9755 19794 09834109873 09912 09951 35 20760 20-8, 20807 20* 3 C 26876 3* 09990 10029 1006* IO1O7 10146 10184 36 208 9 c, 2092. 10945 20v'7 10)00 2ior? * 3? 10223 10262 1030-. 10330 10377 10416 3 21036 105 *Ic?ii 2 : ic. il i 2 7 2 1 149 38 10454 10492 10531 : o ^ o L, 10607 10645 3^> , 2117 2 1 1 94 2121; 21239 21261 712 84 j 39 10683 10721 1 07 .-i, 10797 1.3834 10872 '9 21306 2132, 2T37. 21395 21417 40 5. 10916 10947 10985 I 1O22 i io5c 11007 40 5- 2 143 V 21462 21506 2 1 5 i 8 21550 ] I-IIJ5 11172 11209 11246 11283 11320 41 21572 21593 1615 2163; 1659 2l68l 1 42 43 44 H357 11797 ii394 II834 11431 11652 11870 I 1468 I 150-1 i I688JJ 1725 11906111942 11542 11761 11979 42 43 44 21702 21832 21960 21724 2185 21982 -1875 -2003 2176- 2180- 22O2.1 I7*j 204 : 2l8lO 22067 45 12014 I20sO r2oS6 I2I22JI 21^6 12104 45 22O83 2210; 2130 ^21 \ j 2172 22193 ! 46 12229 1226c 1230: 12336 12371 12407 46 22214 -223. 225; 2*27- 229; ^2318 47 12445 24?S 2513 12549 12584 12619 47 2233 21359 4380 2240-0 2421 ^2442 ; 12654 12689 12724 12759 12794)12829 22461 .248; 250; 2252^ 2544 -2564! 149 12864 12898 293? I2968|l300a(l30^7 49 2258, 2z6c- 2625 2264 2666 5 5.1307' 13106 3140 I3I75 1320:, 13243 50 5.22706 2726 2746 z766 2 7 5 () -2^06 ' 5i 13277 I33.il F3345 13379 13413 U447 51 22826 2846 2866 12886 906 2925 i I 52 13481 13 "49 135*3 13616 13650 52 **945 2965 2984 1 5 Oo^i 5024 3043 136^4 I37I7 '3751 '37*4 13818 13*51 t^ ^ 2306; joSi .310 1-3121 3141 i 5 ! 13884 3917 1895 J 1:398414017 14050 54 23180 5190 3218 1323 325: 3276 5^ 14083 41 16 I 4 1 4v 14182 14215 14247 55 23295 33M 333 * ^3352. 339* 56 .14180 4313 '4345 14375 14411 r 444.' 50 23410 342s; 3447 1346' 348 ^504 57 "U475 4508 14540 H573 14605 14637 7 2 35 2 3 /3542 3560 13570 ? > 9 -' >8 ' 146.69 47ci 14733 14765 14797 14829 58' 23635 365. 367: .3601 3709 3728" 59 14861 4893 14925 149 5V 15020 59 23746 376? 37*3*3 . , ^ Uu TABLE XXIII. For finding the Latitude by two Altitudes of the Sun. Middle Time. j 4 Hours. r 9 Hours. : M o" 10" 20 V 30" 40* j 50" M o'' 1C" - c" 30"' jcf j-' ' .23856 374 13892 13911 13929 23947 5.28597 8606 8614 1502- 8031 23b39| I 2396^ 3983 140O1 24019 14.03 7 24055 I 28648 065,. 8664 28673 S68i 1^689! 31 24073 4091 14IO8 24126 24144 24162 2 28697 8 70S ^7' 3 28722 ^73- -8/38) 3 4*97 J42I5 24.232 242 sc 24267 3 28746 ^754 876; 28770 8778 rtlU 4 24285 -4302 :4320 *4^7 24355 243/2 4 28793 SSoi 8^09 28817 882-- ^8833 5 24389 24407 14424 24441 1445? 14476 5 28840 8848 8856 2^8b< 8871 6 *4493 .4510 Z 47 24544 24561 24578 6 28886 8894 8901 28909 8q. 28924 7 24595 24612 24629 14646 2466? 24680 7 28931 8939 8, )4 6 2895^ ^961 28968} 8 24697 24714 14730 2476? 24-780 Q 2*975 898} 8990 2899; 9004 29012! 9 24797 -48 1 5 24830 24846 486; 24*79 9 29019 9026 9033 2404C 9047 290541 10 .24896 .4912 24919 24945 4961 -4973 o 5.29061 906^ 9075 1906 9089 29096 i ir 24994 25010 25027 25043 559 25075 M 2910.; 9110 9116 2917; 9130 29^37! ' 12 25091 2510: 25123 15:39 5*55 15171 2 29143 9150 9157 2916^ 9170 29177} i r'2 25187 25203 2521912523; 5*5* 25266 3 29183 9 T 9 C 9196 19207 9209 29216 i 14 25282 '.529'* Z 53 14125329 5345 15360 4 29222 9229 9235 29241 9248 29254^ 15 25376 15392 25407 2542^, 543* 25454 5 29260 9207 .9273 9285 29292! 16 25469 25484 25500 2551 <; 5530 7.5546 6 19298 9304 9310 293ic 93*2 29328 17 25561 25S76 2 5591 25607 5621 15637 7 29334 9340 29346 29352 935 5 29364) 18 25652 15667 25682 25697 5712 25-27 g 29370 9375 29387 9393 2 9399| '9 25742 25757 15771 25786 5801 25816 9 2^404 9410 29416 29421 9427 2943 7 20 5.2583' 25845 25860 25*75 25889 25904 0,5.29438 29444 29449 29455 9460 29466 21 25918 25933 iS 94^ 25962 25970 25991 l 2^471 9477 9482 2947 9493 29498 22 2600? 26020 26034 16048 26063 26077 2 29503 9509 29514 29519 -9524 29529 23 26091 -6105 26120 26134 2614!) 26162 3 29535 29540 29545 29550 955^ 29560 26176 26190 26204 26218 Z62 3 2 16246 "4 49565 29570 29575 29S8o 29^85 295901 25 26260 16274 26288 26301 2()3is 26329 2s 29595 19599 29604 29609 -9614 29619 76 26343 26357 163/0 26384 26397 26411 6 29623 -9628 29633 29637 20642 19647' 27 2642 5 26438 26452 26461; 26479 26492 27 29651 296.56 29660 29665 19669 29674 i 28 26506 26519 '-6532 26546 26559 16572 28 29678 49683 29687 29691 19696 29700 2 9 26586 16599 16612 26625 26638 26651 29 29704 79709 29713 29717 9721 29726 j i 3 5.2666^ 26678 26691 16704 26717 26730 30 5.29730 29734 29738 29/42 29746 29750 ! 3 1 26743 26755 l6 7 6S 26781 26794 26807 31 *9754 29758 29762 29766 29770 - 9 7 74 ; 32 ! ^ 26820 26896 26832 26908 26845 26921 26858 26870 26946 26883 269^8 ! 3 29778 29801 2980" 2978^ 29808 2979C 29811 29793 29816 i<)Tyf\ 29814! | 34 26971 26983 26996 27008 27020 17033 H 29823 29827 29830 29834 19837 298^.1 | 35 2704^ 27057 27069 27082 27094 17106 5.5 19844 29848 298^1 298 ; 4 298 s8 10801 j 36 27118 27130 27142 27154 27166 27178 29864 29868 27871 20874 29878 19h8l ! 37 27190 27201 27214 17226 27238 27250 J7 2988*, 2988; 29890 29893 298*6 2990^ r 38 2726;. 27274 272*5 27297 27309 17320 $8 29903 29906 29909 29912 19915 29918; 39 2733- 27344 27355 27567 27379 27390 ?9 29920 2992.- 29926 19929 19932 2993"! 40 5-2740- 27415 27455 27436 2/447 27459 4- 5.29937 29940 2994: 29946 19948 2995 ' ' 41 27470 27481 27495 27504 2751; 27526 -(.i 2995. 29956 2 9959 19961 19964 20066 4* 1 43 27538 17604 27549 1*7615 27560 27626 17571 27637 27581 27648 27593 27659 43 29969 29983 29971 29986 29974 29988 29976 29990 29979 2998; j 29993 2999^ i | 44 27670 27681 27692 27/03 27713 2772 4 K 2999- 29999 30001 30004 5000613003, 45 27735 27746 2775^ 2776" 27777 27788 45 30010 30012 300 u; 300 1 C 56018130020 i 46 27799 27809 27&2C 27830 27841 2785 46 30022 30024 30026 3002^ '30029(30031 1 4 2786: 27872 27882 2789 27903 27913 47 3003^ 30035 30037 3003^ 3004.0130042 27924 h 27934 279441*7954 27964 2797 -}S 3004 3004 30047 30048 30050 30051 i 4 27995 2800< jzbo i 2g02 2^03 l ( . 3005 30054 30056 30057 ^00 5 <; 30060 5 C 5.2804. iSot;: 2806 = 2807 2808 c 28094. 5 5.3006 3006 30064 ^oo6( 50067 30068 51 2810^ ^ 28 1 14 2*1^ 2813 iZo r A " 28l< 5i 30070 3007 J00 7 2 3007 50074 30075 C2 2816- 2817: 18182 28191 28201 2821 52 3007 3007 30075 ^ooSc 30081 30082 53 i8r.2C 2827' .2823C 2828^ l82 3 f 2829< l82 4 c 2830; 18258 2826 183142832 53 3008 3008 3008* 3008 3oooc 50086 3.0090 30o6 30091 50087 30091 si 2833: - 28342 235 i8 3 6c 28369 2837 ,< 3009 3009: 30094 3009 50095 30096 2838- ,2S}9( 2840 2841^ 28423 284^ ^ 3 C 9 30091 3009- '3000 3009 fc ^0099 57 2844 r 28450 ) 2845^ 18468 28477 2848 3009 30 IDC 5oioc 50100 5OI03 30101 5? 2849. ^Sso: iSckilzJJciOhSxzolaS.sJ $j 3010 3010: 50ic; 3010 3310; "^0102 ,28^55128565)285721285802858 39 301033010. 3010. 3010 3010-; ,3010: TABLE XXIII. For finding- the Latitude by two Altitudes of the Suri. Log Rifing. o Hour I i Hour. iSj 0' if? 3 ' 40 5 M o" 10" ' 2 30" 40" 50" {.oooo? J.223 324?fc 765-r ^2642' Oi02 4 o ^534-3 534 8 *;537*i 53959 54197 54434 97860 I25O ia^4b 3079 f 22 3 ,0^0!) i 3-54670 54905:55140 55375 55608 55*4i 2 ). 58006 $50ff 7 I 45i 74^8 -705. 8319 2 56074 5630656537 56767 56997 57226 - 93184 1/18271 >79o 118-17 3*43 ; 2522- 3667 3 S o. 071. ^i6cc 4575 4708 3 4 57455 58814 57683 57910 59038159261 5^37 59486 58363 59?oS ^5*9 59930 ; 3765? 4.0501 43*5 4593' 4^5^ ^1041 5 60152 60373 60593 60813 61032 61251 t 5 3488 6687; 7*474 55868 58184 6 8920! 70'.) 1 7 80265^2019 0440 2869 ^7 3V .1639 74770 S+zi >474 ^0646 <7C*c 6 7 8 6 H 6 9, 62766 64043 61686 62980 64254 61903 63194 64465 62120 63407 646 7 s 62336 63620 Ms 62551 63832 65094 V 83-01 902979186. ^399 490 *6394 9 65302 65510 65717 65924 66131 66337 10 t 97854 )9**9 00699 0^09 0345? 04805 10 3.66542:66747 66952 67156 6/359 6 7 cf,2! 2 .6131 >74J-7 08 7 2 09991 11240 12472 ii 67/65 67067 68163 68369 6S5 7 c 68770 2 1368, 14** 5 i6o6< 7223 ,83*2 '9517 12 68969 69169 69367 69566 69763 69961 2063* 21744 1283 -39 '5 24980 16033 '3 70157 703.54 70550 70745 70940 71135 4 27077 28100 7.9110 3 l Zc jll 12 52093 14 71329 71 7I7I6 71909 72101 72293 2306 24.023 34972 1.59 K 5^39 J77$l *5 72485 72676 72867 73057 7,3247 73436 16 2866; 19567 404 5 7 433 + 22H f3o?5 1 6 73625 ^3813 74COI 74189 74376 74563 1 J 7 43 C <3 1477 45<>i6 ,6447 17270 f 8o8< 17 74750 7493 6 75I2I 75307 75491 75 r >76 18 48895 r/693 5048 :i27] ;-iO-0 ;2Sn tX 75860 76043 76227 76409 76952 76774 r 9 JS5 54344 -,5096 : S S 4 l 56580 ^7312 ''9 7^955 77137 77318 77498 7767* 77858 20 2. 5303<, 5 8 7-S9 5947 60182 6o3 SSK .10 3.78057 78216 7*395 7*S7S 7*75 78928 i 6227, 62960 6364 64316 J497 J5652 21 7910*; 79282 79458 79634 79809 79985 22 66312 56967 j/OI ^262 6890, 6 953 8 22 80159 80334 ^0508 80682 80855 8loz': 2 3 70169 70796 7141 8 7ZO30 7264, --3258 2 3 81201 81373 81545 81717 Si868 52059 2 ! 73863 /44 6 4 75060 75^ji 76241 76825 24 82230 82400 82570 82739 ^2 908 83077 25 77405 77982 7*55i 79li4 796^9 50251 2 5 83246 83414 83582 *3749 839 1 ? 8408 '. 2u 8oSr q ^1363 81914 81461 ^300; i35 4 t z6 84-250 84416184582 84748 8 4v i3 8507* 27 8408? 84617 35148 3567J S6Z99 06720 2 7 *5M2 85406 1557? 8 57^4 85*97 86060 28 87*38 57753 i8i6^ *773 89179 89782 28 8622^ 8638586547 86709 868-0 87031 29 OOiS 90779 912/3 91765 92254 92740 2 9 87192 8/3528/513 47672 87832 8790} 3^ 131 2.972^3 96067 93703 9 6 $3 J4^ J ,6994 946 5<: ;74^ 95129 ^7912 95599 9 8 3 6 7 30 31 riiiso 89097 883098^07 79254 ^H 88025 89567 ^733 -9/23 88940! x 9 8 7v 31 98820 99270 99718 00164 co6oS 01049 3* 90034 90189 50344 90498 90653 90807 33 3.0148* 01925 02360 32792 03223 03650 33 909-60 91114 92167 9H 2 o 91572 9.'7-4i 34 04077 04501 04922 3534* 05700 06176 34 91871 92028 9- 1 ? ?233i 92482 92632 J- 0659 07001 07411 07*$ 1 9 08225 08630 35 92782 92932 93- 93232 93381 9353 3" 09032 09431 09830 10227 -.0624 1 1015 3 b 93679 93^27 93975 9412: 94271 94418 3~ 11406 11796 1218^ ri;70 12954 f3337 37 94566 94712 9459 9S G; 95M 1 95297 3 13718 14097 1447^ ^50 1522^ 15597 3* 9 544:J 955*S 95733 953^ 96023 96167 39 1596- '6338 I.-) 706 t 07? 1743 1 7 800 39 . 9631 96455 9 6 599 96742 96585 9702- 40 J.lSlO. 1852 liSSi ijift *9594 19946 40 3.97170 973*3 97455 97S97 9773^ 9788* 41 2030 20653 2IOO *35 .'.1695 22044 4* 98021 98162 98302 9844: 98583 9872; 4 2S3?. i*7J* 237 23414 *3753 24090 42 98862 99002 9914' 99250 ^9419 9^557 41 2442 14764 2509 2542h 2 575v 26089 43 996c;(j 99 8 34 99972 ooloc 00247 00384 4-1 2641 26745 27072 i739'> 27720 2**42 44 4.00521 00657 0079, 00930 11066 OJ2O2 4- 2336 286S: ii^OO2 29320 29637 29952 45 oi33/ 01473 0160. 0174; oiS 77 J2OI2 ' 46 3026 30579 3089 i i :o 31512 3lS20 4" 0214'. 02280 02414 0254; 02681 02814- 47 3212 >'*434 327^ 3304- 33347 33 6 49 47 0:947 03080 03212 P334^ 0347- 03608 45 3395'- 14250 '345 4. 3447 -3514^ 35459 49 03740 03871 0400^ -^4134 04265 343 9 c 49 35?: *6oaS ?6>z ^66 1" 3690^ V '9 ; 49 0452- 04656 47 8( 049 1 ( 05045 -.517; 5 MTSSa 37770 3805 3^343 ^86? 389" So 4.0530, J >443 0556' 05690 05818 05946 39*95 >9477 ^97S< 4.0030 403^ 4>>97 5 J 06074 06202 06330 06457 -.6584 0671 1 5* 40875 41151 8.124 4170 41976 42250 s2 0683 06965; 07091 37*17 07343 0^69 i 42527 . 2794 4306. 43334 4^o; 43871 53 .0759: -7720 07^45 07970 08095 'S.2C 5* 44'3S .4404 44 6 7^ 4493 45199 45462 C 4 ,08344 08468 08592 ^.^716 08840 08904 55 4572. 15986 4614 46507 46765 47024 ^0908 ; 09210 09333 o 9 4?< 0957 C970J rf 47282 f?539 ^779 48050 4830; 4Ss5V :6 09823 39945 1006 roiSl 1 . 10310 104:1 57 48811 19064 4931 49566 49816 50066 '57 10552 10673 10794 1091 ; 1 103 - IH5< S 503M 576S8 3 4 708 - 71197 7092* 71250 ; . 9 8 . 71036 71357 710X9 71411 7^43 71464 4 87728,87769 8780987850 S> 0528809 3 siijl 68?73 ! 5 71518 71624 71678 71731 71784 r. 882i3'!S8*5^ 88294 88334 $9414 6 7183 7189 171943 71996 72049 72102 6 88454(^494 88534 88^4 88614 "8654 j I I 7*155 72471 7220? 7*5*3 7 226c 72576 7231317236'', 7*6*817*681 72418 7273^ 7 8 8809488734 89012 88814 89052 88*53 8 909 1 89???: I 9 72785 72838 72890 72942 729,4|7304(' o 89i7i!'892io 89250 89281, 8932^ 89368 . 10 4.73098 73150 73202 73^54 73306 7335* 1C, .4.89407 89447 89486 -9525 ^9564 89604 i i If 734 1 - 73462 73565 73 6l 7 ^736.68 r ! 89643 896^2 59721 8 9; 60 -,9799 59838 ' i 7^720 737-2 7j8.23 73^74 7392'; 73977 Ii 80877 8991^ 8 9955 89994 933 ',0072 ! ' 3 7401* 74080 74*3' 74182 742 3 - 7428', i ? 901 i i 9014^ 9018! 90227 ")026C- OOJOJ ! 1 4 743 3 ; 74386 74437 744 s 74539 74590 r 4 90345 90381 90421 90451 904*:- 90536' i ; 7464' 74692 7474 ^ 74793 74^44 74894 I s 90575 00613 90652 90690 ^07*8 ;O/07 16 74945 74995 7504675090 75147 75197 16 90^4, 90.8$ 2 90920 90952- '-50996 ; 17 75-47 7529 7534> 753gS[7544^ 7549^ 17 91034 OtO/ 3 9 1 1 1 I 91140 9118- 'JI225 J 18 "5S49 75*99 75649 ,75699 7^74^ 75/9- 18 91263 9130! ?'339 }*4M H45* 19 7584? 75808 75948 7 5 '9 7 76047 76097 19 91490 9J528 91566 9160? > i 6..1 4! 1 1679 j 20 4.76146 76196 7624; 7629. 76.?44 76394 20 4,91716 91754 91792 91830 y 166 VI') 'V - 1 * ' 1 21 76443 #492 70542 765.)! 76640 7668p .'. i 91942 9I9/ C ; 92017 92054 9209? 9215 9 22 7*7** 76 -S 76836 76934 7698;- 2 2' 9216?, 92203 92241 9227^ 923 1 r >*3S* 1*3 1 24 7 032 7 7 i - - 77081 77373 j 7 1-30 77422 7/179 77470 77227 77519 77276 2 4 92390 92612 92427 92649 lltll 92501 9253^92575, 9276^92796 ' 2 ; . 77614,77664 7776i 77809 77857 2s 9283:; 92870 ^907 9294.;. )29S,|;joi7 j i **' 779 ' ^8 oo 78050 -309?: 78146 26 93054 93090 > 3 1 2 - 93164 i *V - 73r:iv'i7-'T4? 7^29- 78338 78385 78433 Z 7- ' 93273 933 IC ) 1 14^ 93383 )34 I 5 , ! ' 4 5 5 i 1 *8 7 8 ' u r ' " 8 " 78;7< 78624 78671 78 7 ic. aa 97402 Q ^ ^ ? > ) 5 s ^4 ^ -. (, - - 7^7 7 7886 78908 78956 7900: -9 93709 93745 ; JO 1 *3*54 LT v I -* 4-790*1 ?99 7914 79192 79 H' 794*7 J; 4.9392,', 93962 9399- ,403,! )406c ,410- ) i 3 r 7-j ^i 7942^ 7947^ 79522 7956? J ! 94141 94177 H- 1 " 94240 ,43 zo. i 3' 2 796) 7966- 797-6 79802 79849 32 94556 943^ 7^4^j 1449 i 33 7989 7994-! 799^9 80035 80082 f 1 2 J 35 94^7 94:0; 9467t 9471^ , -'7-T7 ' 34 8cT 7 : 80221 80267 80314 80360 8040' J4 94782 9481?- 748 5 : ^48^.- ia.6 2 c, ,.;Cj '9 35 8045 80498 So 544 8o'v;l io6^7 80687 94994 95029 9 506 - ^10^ )^ IT, \ -i s J 70 , 36 8072, 867.75 80820 ^0.8-, 6 30912 80958 ^ 95205 "J5 2 4- n~~^ ) 5 3 ' c 'v34> 37 8roo 8 1049 8ro 95 > r 1 4 ; 81186 81232 37 3S450 95485 95520 95'5Si >5>^9 ' 38 .* 7 - 8,323 8136: 2 1450 3l505 ?8 95624(95659 ^694 Q57* ; - 95765 .55798 * 39 8150'; 8159-. 8164.1 81686 8173? $1776. 3<7 9 ;S32j0586: >59toa 95Q 56 >6or>5 J 40 4. 8 1 x 2! J3 [86;- i I 9 r i 31950 82001 82046 40 4. 9604019607.^ 96109 )0 4 , o i 77 9*1213 ;l ! *i .^209 i 82136 ^zi - i|8 222618227 1 82}!; 4' 9624.''!. ,6280 ^631 :' 96349 3 x ^ ,6417 ' i 4- 82 $6>-.)82405 8244918249482538 ^2583 4- 96453 76486 )(>52C 6vga, )6lijl 43 82o-> ^(82672 8.i7T6JS276i 8280; ^2850 43 96656 ;66gc 76724 )6/58 6792: 44 45 8289, 82938 8320? ; 302618 7071 83-2 4? 8 ^9 $33 3 <; 83M5 44 96860 9706... -;68 94 96927 96961 >7i6; wSii ;^i? - . 46 534:7 83467 ^'c T4 *3 598)8 3.642 4" 972^ ,729^ >~t 33 '736- ^7398 -, 74 ; z ' 1 47 8368- 837aaWs773J33# 16 83860181903 47 9746: 9753- 975i >7 S9^ 7 ^ 3 2, I 48 S 3947J s 399a|'H034 8407~!S-4i2o; / 4J6-j 9/665 ;7<'9'.; 9776$ 5>779'*97^}*1| 49 84207^4250 M*93i' 5 4337j s >43-cj ; '44-v: 49 9786; 07^9- 1793 ] T964 97.<)9^i^ W ' r '3 J| 50 4- 8446^184 <;o-j 84 5^2 >4>;9v . ''46.51 vO 4-. 98063 ^809' pl2tl 9>5r<;-; ;> 1') ') -j -).'. ^ ^ J 5? 84724 84767 848 ro. ^4852 8489.184938 Cl 98261 ^829-, J%26 ''*35-- ,8392 9^25 ! ' 52 8498, 85023 85066 ! 5108^85 )^J S;io* ^2 0^4,5" 93490 0852; V X 55 1 ;8 ^S. 1 - 9:620! 53 ^23-6 8527* 85321 85363:85406:^5448 53 98653 98718 93751 i??3-. -;8.- 1 5 ! , ' 54 *549WJ533 8557; ^5^:7185659 85701 54 j8b8: 98913 9*94 c ^976; .^9010 5^ 85744 85786 5$82? 5870 '^59 1 71859 54 55 99042 99074 99107 09139 ^9' 7 ' 99203! : ! 56 8590 860 } 7 86070 86121 86i6?j36ao5 -,6 99*35 99267 993 CC 9933--. nn' ! 4 99396. - 57 i 59 86246)862$? 86496 8651* 80745186786 86330 mil 86^72 ^6621 86415^6455; 57 8666286704.53 86910^6957(59 99619 99810 99651 99842 0949 ? 99873 9952- 999 TABLE XXIII. For finding the Latitude by two Altitudes of the Sun. Log Rifing. 6 Hours. 7 Hours. M o" 10" 1 20" 30" 40'' 50" M o" IC/' 20" 30'' 40" 5 o ^.00000 30031 2006; 00094 00125 -0156 5.09996 IOO2C 10044 0068 10092 10116 i 00188 00219 3O250 00282 00313 00345 i 10140 10164 0188 O2 1 2 0236 10260 3. 00376 00407 J043& 00469 00501 00532 2 10484 10308 10332 0356 0380 10404 3 00563 -595 00657 00689 00720 3 10429 10453 10477 0501 0525 '0549 4 00751 00782 00813 00844 00875 :0 95 10573 10596 10620 0643 0067 10691 e 00936 00967 00998 0.1028 01059 01090 c 10714 1073 10761 0785 10809 10832 6 OI12I 01151 01 182 01213 01244 >I27 ; 6 10856 10879 10903 0926 0950 10974 7 01305 01336 01367 0x398 01428 01459 7 10997 11 O2 I 11044 1068 11092 11115 8 01490 01520 01550 01580 01611 01641 j 11139 III62 1118, 1 12O: 11231 1125 9 01671 01701 01732 01762 01702 01822 9 11278 1 1301 [ t3--r IM4- 1137- "393 JO 5-01853 0,883 01913 01943 01973 0200<. c 5.11417 1144 11463 11486 H50 V '1532 02034 02064 02094 0*125 O2 I S s 2185 1 1 H556 "579 11602 1162- 1 164^ 11671 2 02215 02245 0227? 02304 02334 023C4 2 11694 11717 117^0 1 176; 11785 11808 3 02394 0242} 024 v? 02483 O25 12 -1542 1 < 11831 11854 1676 11899 I19Z2 "945 4 02572 02602 02631 oz66i 02691 C2720 4 1196 11990 12013 12036 12058 12O30 02750 02780 ,2810 02^39 Oi86 9 02899 1 5 12104 12126 12149 12172 12195 I22I7 6 02928 02958 0198. 03016 03045 030 7 4 12240 12263 122^5 12307 12329 12352 - - 03104 03162 03191 03220 03250 17 12374 12396 .2419 12441 12463 124*6 i 03279 03308 033 v; 03366 03396 03425 i 12508 14^30 12557 2 57: 1259 12619 9 03454 9 H 8 3 03512 0357J 02600 9 12642 12664 2686 2709 12731 '2753 i. c 5.0362 03658 0368: 0*715 3744 03773 iO c 12776 '2795 12^20 12841 12863 12*85 . I 0380 038:003^59 03887 03916 03945 21 12907 1292-.; 12951 '2973 '3995 13-JI7 2. 03974 04002 04031 04.60 04088 04117 :2 13039 1306* 13083 13104 13126 13148 3 04146 04174 04203 04232 04261 04289 13170 13192 13214 <3236 '325 13*80 24 04318 04346 -4374 04402 044 '50104451; *4 13302 '33*; '3345 13366 133** 13409 25 04487104515 04543 04571 04600 04628 -5 I343I *H5 2 1 3474 '3495 I35I7 13^38 26 04656-04684 04740 04769 04797 z6 13560 '353' 15602, i 3624 13646 73667 1 27 04825*048^3 0488, 04910 04938 04966 2 7 13689 13711 13732 13753 '3775 13796 28 04994 05022 05050 05077 05105 05133 2* 13816 13839 13860 i } t> * i 13902 13923 -9 05160 05188 05116 05243 5*7f 05299 29 13944 13966 139*7 14008 14029 14050 30 5.05327 05354 05382 05410)05437 05465 2,0 5.14071 14092 141 13 14134 '4 155 14176 31 5493 05520 0.5548 05576 05604 05631 3 t 14198 14219 14240 14261 14282 14303 32 05659 05686 057*3 05740 05768 05795 2 14324 14345 14366 14386 14407 1442* 3 7 05822 05849 05876 05904 OS93' 059 & 3 14449 144^9 14490 14511 14^31 14552 34 0^985 06013 06640 06067 06094 4 H573 '4593 14614 1463; t 4 6;6 14676 35 06149 06176^6203 06220 0625806285 14697 147 16 1473^ '4759 14780 14500 30 06312 06339506365 06392 00419 06445 6 14821 14842 [4862 14882 14902 14923 37 06472 0649906526 06553 06579 06606 7 14943 14963 14984 15004 15024 15045 06633 06660(06686 06712 06740 06766 Q 15065 15085 15106 15126 15146 i<;i66 39 06793 06820 06847 0687, 06900 0692; 39 15187115207 15227 15248 15266 15288 49 5.0695.} 07111 06980 07138 7 66 07164 07033 07190 07059 07217 07085 07243 4 41 5.15309 15428 1532-9 15448 15349 15468 15369 15488 1538 15508 (5408 .5528 42 07260 07295 07322 0734? 07174 07400 I 2 15548 15568 15588 15608 1562* 15648 1 43 44 07427 07584 07453 07610 07479 07636 07505 07662 07532 07687 0755 s 0771' 44 15667 15787 156^7 15^07 15707 15826 ! 5 846 5747 15865 15767 j i 5 S8 5 | 45 07739 07765 07791 07816 07^42 07868 1C 15904 15924 r 5943 15963 16983 IOOO2 46 1 47 07894 08049 0792010794? 08074^8100 07971 08126 07997 08152 08022 08178 46 16022 16139 16041 ,6158 16061 16178 16080 16197 16100 46217 16119 16237 48 I 49 0820; 08356 08229 08381 0825408280 08406108432 0830* 08457 0833- 084*2 48 16256 16371 16275 16390 16295 16410 16314 16429 16333 16448 16352 '9467 "Jo 5.o3so8 08533 08558 08584 08609 08634 O 5.16486 16505 16525 16544 16563 16582 i *i 08660 0868; 08710 08736 08761 08787 1 16601 16620 16640 16659 16678 16697 U 08812 088?" 08862 088? 7 08911 0893* 2 16710 1673- 1675:4 16773 16791 lift. 53 08961 08986 090*1 09036 09061 O9"o8f ^3 .16829 16848 16866 16885 16904 16923 54 09111 09136 09160 09185 =92100923. 5- 16942 16960 16979 (699?; 17017 17036 09260 0928,- 09310 OQT7C 0936009385 s s .17054 17073 17091 17111 17129 17148 5< 58 S'j 09409 0955? 09703 5.09850 09434 09581 09727 09874 0945809483 09605)09629 0975^09776 09899*09923 0950709532 09654109678 098010982, 0994710997. 5" 5" 58 S'y 17167 17277 i7i5 17296 17406 1751- T72O;: I73H 17425 ^7533 17222 17333 17443 17554 17241 17351 17462 17572 17259 17369 17480 TABLE XXIII. For finding the Latitude by two Altitudes of the Sun, Log Rifing. 8 Hours. M. o" 10" 20" ?o" 40'; 50" " 5.17609 5.17627 5^7645 5.17663 5ii?68i 5.17699 r 5- r 77i7 5-17735 5-17753 5 17772 5.17790 5.17808 - 2 5.17826 5.17844 5.17862 5. 17*480 5.17*98 5.17916 3 5-*7934 5.17952 5.17970 5.17988 5 18006 5-18024 4 5.18042 5.18060 5.18078 S.IJPSI 5.18113 5. 18131 5 5.18148 5.18166 5-18184 5.18201 5.18219 5.18237 6 5-18255 5.18272 5.18290 5.18308 5 l8 325 5.1*343 7 5.18361 5-18378 5.18396 5.18414 5.1843! 5.18449 5.18467 5.18484 5.18501 5.18519 5.18536 5-18553 9 5.18571 5.1*588 5.18605 5.18-623 5.18640 5.18657 JO 5.18675 5.1*692 5.18709 5- '3727 5.18744 5. 18761 ir 5-18779 5.18796 5.18813 5.18831 5.1884* 5.18865 12 5.18*83 5.18900 .5.18917 5.18934 5.18951 5.18968 *3 5.18985 5. 19002 5.19019 5- I 935 5.19052 5.19069 '4 5.19086 5.19103 5. 19120 5- I 9 I 37 5-J9r54 5.19171 IS 5.19188 5.19205 5.19222 5-l9 2 39 5. 19256 5- I 9 2 73 16 5.19290 5-I9307 5-193*3 5.19340 5.19356 5'i9373 J7 5.19390 5.19406 5.19423 5.19440 5.19456 5-19473 xS 5.19489 5.19506 5.19523 5-i9^39 5- J 9556 5.19572 19 5-195*9 5. 19606 5. 19622 5.19639 5.19656 5.1967* 20 5.19689 5.19705! 5-19721 5'i9738 5-J9754 5 i9"70 2.1 5.19786 5-19803 5.19819 5 '9*35 5-19851 5.19568 22 5.19884 5. 19900 5.19917 5-19933 5.19949 5.19965 *3 5.19982 5.19998 5.20014 5.20030 5.20047 5.20063 24 5.20079 5.20095 5.20111 5.20127 5.20143 5.20159 t 2 5 5.20175 5.20191 5.20206 5.20222 5.20238 5 202 54 26 5.20270 5.20286 5.20302 5.20-318 5.20334 5.20350 ^7 5.20366 5.20382 5.20398 5.20413 5-20429 5.20445 28 5.10461 5.20477 5.20492 5.20508 5.20523 5.20539 29 5.20555 5.20570 5-20586 5.20601 5.20617 5.20633 30 5.20648 5.20664 5.20679 5.20695 5.20710 5.20726 3 r 5.20742 5.20757 5.20773 5.20788 5 . 20804 5.20819 3* 5.20835 5.20850 5.20865 5.2o->Si 5.20896 5.20911 33 5,20926 5.20943 5.20957 5.20972 5.20987 5.21002 34 5.21018 5.21033 5.21048 5.21063 5.21079 5.21094 35 1.21109 5.21124 5.21140 5.21155 5.21170 5.21185 36 5.21201 5.21215 5.21230 5 21245 ;.2iz6o 5.21275 37 5.21290 5.21305 5.21320 5-21335 5.21350 5.21364 38 5-*i379 5.21394 5.21409 5.21424 5-2*439 5.21454. 39 5.21469 5.21484 5-21499 5.21513 5.21528 5-21543 40 5.21558 5.21573 5.215*7 5.21602 5.21616 5.2.1631 4* 5.21645 5.21660 5.21675 5.21689 5.21704 5.21718 42 5-2J733 5.21747 5.21762 5-21777 5-21791 5.21806 43 5.21820 5-21835 5.21849 5.21864 5.21878 5.21893 44 5.21908 5.21922 5.21936 5.21950 5.21964 5.21979 45 5.219.93 5.22007 5.22021 5.22036 5.22050 5.22064 46 5.22078 5.22092 5.22107 5.22121 5.22135 5.22149 47 5,22164 5.22178 5.22192 5.22206 5.22221 5.22235 48 5-22249 5.22263 5.22277 5.22291 5.22305 5.22318 JlL 5,22332 5.^2346 5.22360 5-^2374 5.22388 5 . 22402 50 5.22416 5.22430 5-22444 5.22457 5.22471 5.22485 51 5.22499 5-22513 5.22527 5-22541 5.22555 5.22569 5* 5.22583 5.22596 5.22610 5,22623 5-22637 5.22659 53 5.22664 5.22678 5.22691 5.22705 5.22718 5,22732 54 5.22745 5.22759 5-22773 5.22786 5.22800 5.22813 55 5.228:7 5.22840 5.22854 5.22868 5.22881 5.22895 56 5.22908 5.22921 5.2293-5 5 . 22948 5.22961 5-229/4 57 5.22988 5.23001" 5.23014 5.23027 5.23040 5-23054 58 5.23067 5. 23080 5.23093 5-23107 5.231*0 5- 2 3i33 59 5-23146 5.23160 5 23173 5.23186 5.23199 5. 232 f 3 TABLE XXIV. OFNATUEAE SIN-ES-. f o 1 2 3 4 [ M. N lint I N col. N flne>J cot N fiat :!N cof . N fin X cof.'.N fn< - N cof M. i 2 J 3 4 5 6 2 8 ii i 7 iOGOOC OOOC oooc oooc cooc COOv. oocc > ' 77< > j So > T 03 - i lS')2 i 189) ![ I 9 2C i 98. 98. - 9* 98, 98 j g&l 349^ c 35" 3577 3601 3635 366-: 9993 935 93' 93. 93: 5^3 526 529 532 535 537 540 J $6i 700 : 860 703^ 8^8 706.3 857 7092 855 7121 854 7150 7^ 75^ 746 744 60 H 57 55 54 8 9 to ii 12 26 29 3 1 34 10OOOC i oo7c OOOC oooc 99995 0990 194 197 2CO 205 206 209 > 59 s 9 8c 9 *c 975 97!^ >9977 97<; 976 975 974 ' 3723 375' 3810 999-32 931 93C 929 926 513 546 549 555 558 99852! 717-0 851 720^ 849! 7237 847 7266 846] 7295 740 73^ 734 73' 53 52 50 49 48 s 16 iS 37 40 43 46 49 52 99999 999 99 C J 999 999 999 212 215 218 221 f 224 226 j8fc 39*6 3955 39*4 4 OI 3 92^ 9 2Z 9 2I 919 561 5640 566 5698 572- 9984 ?3 83 7.35 : 73^2 7440 7469 749 b 99/29 727 "25 723 721 719 47 46 45 44 43 42 '9 20 21 23 6r 64 66< 698 99998 9998 9998 9998 9998 99997 997 977 997 996 996 U3? ^35 2 S -4' 2472 250 2530 2500 2618 97 97 97 : 97 4042 407 4100 4129 4r59 799 f - 917 916 912 5785 581, 54, 5873 5902 593 < 9983 83 82 82 lit 824 75 2 7 7556 7614 7643 7672 7701 773- 7759 7788 7817 7846 7H 712 710 705 40 39 38 37 36 2 5 26 2 7 28 2? 7c6 785 844 S7; /99 968 967 96* _9*c ) 96 963 963 96, 96! 4217 4275 433? 4362 ,.99 1 j 910 .9 C 9 907 906 905 5960 59? 6018 6047 60 7 f 6105 6134 6163 6192 6221 6250 6279 99822 8i( 8.7 815 813 99703 70-] 699 696 694 692 35 34 ?3 32 3* 30 31 32 33 34 36 9-J2 9 6c 989 1018 104, 99996 9 9 < 995 995 995 995 264? 2071 2705 273^ 276: 2792 25 5t 2908 2 9 jS 296; 4420 4449 447,8 457 >9904 902 901 9 cc 89^ 8 9 7 9,89* 894 893 892 890 9812 810 808 8ot 804 80 7 8904 7933 79^ 799 1 80,20 ; 9 68 9 | 687 68s 683 678 29 28 27 26 24 37 38 39 40 42 1070 ,1105 1134 1164 1193 1222 99994 994 994 99? 993 993 9960 959 959 958 957 45 6 5 4594 4623 4653 4682 4711 6308 6337 6366 6395 6424 6453 9801 799 797 795 79: 792 8049 8078 8107 8136 8^4 )9 673 671 668 666 664- 22 21 20 '9 ]8 43 44 45 46 47 48 12.80 1309 1338 1367. 99992 99- 991 991 991 2996 302J 3083 3U2 3141 9955 554 95 1 ? 952 95* 95' 4740 4769 4793 4^27 4885 8Sc 883 882 88. 6482 6511 6540 65.69 6 59 8 6627 979 75 7 8t 78 H 782 780 8223 *J 52 83!' 8339 8368 59661 659 657 654 652 649 17 16 15 12 49 52 53 54 1425. '454 154! 1571 99990 9 8 8426 8484 8513 8542 8571 8600 8629 8658 8716 644 642 639 637 J>3_5 630 627 62^ 622 6i 9 II IO 9 8 7 6 __ . 4 3, o 55 56 59 60 1600 1629 1658 1687 1716 1745 99987 987 9 S6 9-6 3345 3374 343 343,2 3461 9944 943 942 941 940 939 5088 5117 5146 5 f 75 5234 870 869 867 866 -864 86: 6831 6860 6889 6918 6947 6976 99766 764 762 76. 75* 75^' N fine M. -; cof. V fine N T cof. V fiat V cof. Vfine v cof Vcof. ^ fine M. 89" 88 | *7* ,86 85 TABLE XXIV. OF NATURAL 5" 6 7 6 9 V M. N fin Nco'.jNfu Ncof N fin N cof N fm N cof.!N fine Ncof i\J . o t i 3 4 5 6 871 874 877 880 883 836c 883; 9061 6! 611 61, 6oc 6o ; 6ot 1045 4 s 5i 54 56 59 62 9945' -449 446 443 44 437 434 1218' ' zif 24. 74 302 33' 360 11385 4jv 44: 476 504 53 99 2 55 251 248 244 240 237 23^ ^9*30 226 222 2r 9 215 211 39: 64? 97. 1400^ 033 061 090 9902: 02; QIC or < on 006 002 1564] 67, 7cr 73c 758 787 816 9^765 76-j 760 755 75-i 746 74 1 60 59 53 57 <56 55 54 53 52 5i 50 49 48 7 1 8 9 10 I! 12 891- 8947 * 97 ( 9005 9034 906^ 99602 599 590 59^ 591 588 995^ 5^3 580 57 148 177 1 205 234 26 ? 98998 99-1 99 C 986 982 978 ,5845 873 902 93' 959 0fb 9S737 732 728 723 71* / r -; *3 r 4 15 16 17 18 9092 9121 9150 9179 920!; 92^7 1082 85 83~ 916 94 97. 59412 409 406 402 399 . 39" 1256- 59 1 620 64. 678 706 f2 73~5 764 793 82; Jji 8^0 99208 204 200 197 J 93 if 9 99^6 18: 178 J 7S 171 167 1429 3 Z 34 37 40 43 ( 9^973 969 965 96] 957 953 9894S 944 940 936 93i 927 16017 04', 74 103 132 160 :;7C9 7^4 700 69? 690 6b6 9l6Si 676 671 667 662 657 47 46 45 44 43 42 4i 40 ' 39 3* 37 36 19 20 21 22 23 24 9266 9495 9.124 935- 9382 9411 1 1 002 03 o6c 08, nS 147 99393 39 3$6 3$3 3?o _377 9371 370 367 364 36* 357 1446^ 493 522 55 580 608 16189 2lS 246 .275 3<; ^333 16361 390 4 rg 447 476 505 25 26 27 2$ *9 30 3i >i* 33 34 35 36 9440 946 (, 9498 95*7 955' 95?5 9553 55' 548 545 542 540 11176 205 23^ 26: 291 _J20 II349 37S 407 436 465 494 12908 937 966 99; 13024 v 99163 160 156 152 148 144 f4 6 37 666 695 723 752 781 OS9*3 919 914, 910 906 902 5 S6 5 : 648 643 638 633 629 35 34 3* 3* 3 30 j 9614 9642 9671 97-x 9?2 V 0758 9537 534 53i 528 52') 523 9354 35i 347 344 34 r 337 13081 u 139 i$8 f 97 226 99141 J 37 133 129 125 122 14810 83* 867 896 925 954 98897 893 880 884 8Sc 876 16^33 562 59i 620 64* 677 9*624 619 614 609 604 6oc *9 i 2* 27 26 25 2 4 37 3 39 40 4i 42 9787 9816 9*45 9874 993 9932 9,5c 5*7 5i4 5u 508 506 11523 552 580 609 638 667 9334 33' 3*7 324 320 ji7 13254 283 312 34' 370 399 )9 1 ** 114 I 10 106 102 098 99094 091 087 083 079 075 14982 15011 040 069 097 126 98871 867 863 858 854 849 16706 734 763 792 820 849 16878 906 935 964 992 17021 9*595 590 685 580 575 57 9856? 561 556 55 1 546 54i ^3 22 21 20 ig 17 16 15 H 13 ^ 43 44 45 46 47 4* 9961 9990 10019 048 077 106 99503 500 497 494 491 488 11696 72 5 754 7^3 8ra 840 9314 310 307 303 300 297 f34 2 7 45* 4?5 5M 543 572 ^'155 184 212 24] 27O 299 93-45 841 *36 832 827 823 49 53 5 5* 53 ! 54 10135 164 19' 221 2 5 C 2 7 -., 99485 482 479 476 47j 470 W4&7 4 r >4 46. 8 455 452 11869 898 927 95* 9^5 201 4 9293 290 286 2*3 279 276 13600 620 6<8 68 - 716 744 99071 0(>7 063 ot;^ 55 oi '5327 356 385 414 442 47' 98818 814 809 805 800 796 17050 07* .107 !36 164 ]92 3 S 53 6 53' 526 52' 516 5JM ii 10 8 9 55. 56 57 5? 59 60 10308 3?7 36.6 39< 4'-s 45j no43 071 129 IS8 187 9272 269 * 262 258 255 U 73 802 8u 860 880 917 99047 043 039 035 03' 07.7 15500 529 557 586 6X5 6^3 ;&7qi /8/ 782 77* 77? 769 17222 250 279 308 336 365 98506 502 496 491 486 4Si 5 4 3 2 I o M. N cot" V lint. S col". |N fine N T c. ; f V fm ; s* cor N hritf X Cof. N T fine M. 84 | 8i^ | 8 80 B5H55 TABLE XXIV. Or NATURAL SIITES. 10 11 iz 13 l M N fine N cof- N fine N cof. IS fine N cof-;N fine N cof. \ fino N cof. M . o i 2 3 4 6 i73 6 5 39 ? 422 45i 479 508 537 9848 i 476 471 466 461 455 450 19001 109 13? 167 J 95 224 252 9*163 157 152 146 140 135 I2Q 20701 820 848 877 90 c 93* 962 97815 809 803 797 79 < 784 77* 22495 523 552 580 6cS 637 _!L5 1 26') 3 722 75 778 807 s? ^ np- 3 8 9 2 920 94 977 23005 97437 43^ 424 417 411 404 3^8 9739 1 3*4 373 37 T 36^ 358 24192 220 249 277 305 333: 362! 97030 023 015 008 COI 9 6 994 987 60 59 S^ 57 56 55 54 7 \ 9 10 ii 12 f 755 594 627 6s'i 680 708 98445 44c. 435 43c 42; 420 19281 300 338 366 395 42 ? 19452 481 509 538 566 595 9 124 11* IJ2 10 101 20990 21019 047 076 104 132 9777* 766 760 754 748 742 24390 418 446 474 503 53'j 96980 973 966 959 952 945 53 5* 5i 50 49 48 '3 H IS 16 17 18 19 20 21 22 23 24 17737 766 794 823 852 88e 9*4:4 409 44 399 394 3*9 98090 984 079 c?5 067 065 21161 1*9 218 246 275 ' ."03 97735 729 723 717 71 T 705 97351 345 33? 33i 3*5 318 24559' 587 615 644. 672 700 9 6 937 930 9^3 916 909 902 47 46 45 44 43 4 2 17909 937 966 995 18023 052 >3<>3 378 3/3 36* 362 357 i9 62 3 65- 680 709 737 765 98056 050 044 039 033 027 21331 360 388 4 1 / 445 474 97698 692 686 680 673 Cf.-j 23033 062 090 11% 146 175 ;73'i 3 C 4 298 291 2^54 278 24728 756 784 813 841 869 96894 887 880 873 866 858 4i 40 39 38 37 36 ~ 5 26 27 28 29 3Q 3 1 32 33 34 35 36 150*1 io< 138 166 T 9. ; 224 ^8352 347 34 1 336 33' 3^5 19794 823 85 r 880 908 937 98021 016 CIC 004 97998 992 21502 & 559 616 644 97661 655 648 642 63^ 6 3 c 23203 231 26c z8S 3'6 345 97271 264 257 251 244 *37 24897 925 953 982 25010 038 96851 844 837 829 822 815 35 34 33 3^ 3i 3& 18252 281 309 33? S^} 395 98320 315 310 304 299 294 98288 283 277 . 272 267 261 19965 994 ZC022 5 I 079 108 97987 981 975 969 9 6 3 958 21672 701 729 758 786 814 97 62 3 617 6n 604 59 8 _59* 975^5 579 573 566 560 553 ^3373 401 420 45 S 486 54 97*3^ 223 217 2IC 203 196 v7T8<> 182 176 169 162 _J_5_5 ,7.148 141 134 12" 120 11 3 25066 094 122 151 I 79 20/ 96^07 8co 793 786 77* 771 29 28 27 26 *5 24 23 22 21 2O 19 18 | 39 40 4 1 4-2 I 8424 452 48, 509 538 567 201^6 165 193 222 250 279 9795* 946 94 934 928 922 2184^ 871 899 928 956 985 aj54* S7i 59' 62'; J$( 684 i 5=3 ( ; 263 291 32C 348 376 9676-; 756 749 742 73-1 72; 43 44 45 46 47 48 18595 624 652 6Si 710 738 98256 250 245 240 234 229 20307 3^6 364 393 421 45 97916 910 905 899 893 887 22013 041 070 098 126 155 22183 212 240 268 2*7 3^5 22353 3^ 410 438 467 495 97547 54i 534 528 5- 1 5*5 975 0? 502 496 4*9 483 476 97470 4 6 3 457 45 C 444 437 2371^ 740 765 797 Sa; 853 .540/5 432 460 4'6S 516 545 96719 712 7? 5 697 690 682 i? 16 *5 14 13 12 ri~ 10 9 8 6 ~~5~~ 4 3 2 I 49 5 5i 5* 53 54 18767 795 824 852 88 1 910 9*223 218 212 207 201 196 20478 507 535 563 592 62 cof. I \ fine cof. J \ line cof. fine N cof- M o 2 3 4 6 5882 910 938 9&(; 994 60:2 050 6593 585 578 570 362 555 547 i?5 6 4 592 620 6 4 < 676 704 73' 6126 : 118 no IO2 09^ 086 078 9237 265 293 3 21 348 376 404 5630: 622 613 60 s 596 588 579 0902 929 957 .985 1017 040 068 106 097 08? 079 oil 052 557 54 612 639 66; 6 94 722 S'455 J 54^ 532 5^3 SH 50'-; 49.^ 60 59 58 57 56 55 54 7 s 9 10 it 12 6079 10; 135 163 191 219 6540 532 524 5i7 509 502 '7759 7*7 815 & 899 6r;o - 062 054 046 037 049 943 2 4.60 487 515 543 57i 5571 562 554 545 536 528 1095 I2 3 15' i; 206 233 5043 033 024 015 006 1997 4988 979 970 961 952 943 749 .777 .804 83* 859 87 944 8 5 476 46 (. 457 447 43 94428 41$ 400 399 390 3c 53 52 51 5 49 J_ 47 46 45 44 43 42 13 H J 5 16 17 18 6247 275 303 33i 359 W3*7 64^4 486 479 47i 463 456 17927 '955 983 28011 039 06.7 6021 ' 013 005 599" 9*9 9 8j 19599 626 654 682 710 737 55*9 5ii 502 493 4*5 476 1261 28 <; 316 344 372 399 2914 942 969 997 3024 051 J9 20 21 22 23 14 6415 443 471 500 528 556 6448 440 433 425 417 410 28095 123 150 178 206 234 5972 964 956 948 94 Jill 95923 9 T 5 907 898 890 882 29765 III 849 8 7 C 904 5467 459 450 44' 433 424 1427 $ 5 ic 537 5^5 4933 97.4 :9i5 906 897 888 379 106 134 161 189 aofi 9437 361 35 1 342 332 32? 4 r 4.0 39 38 37 _1 6 _ ' 35 34 33 S 2 3i 3 ! 25 a6 27 28 29 30 : 6584 612 640 668 6^6 724 6402 394 386 379 37J 3 fi LN cof.'N fin M 1 74" 75 7** 7i 70 1 X X2 TABLE XXIV. OF NATURAL II 20 21 22 23" 24 Ji M N'fim N cof N fm< 1 N cof N fir e Is cof N' fim N cof N fin, . K c-of-j M I 2 3 4 34202 28^ 36' 955 945 935 925 35*3' 86, 891 91* J^-'4 97: '9335* 34* 33' 32; 3c6 T328; 26^ ! **' 5 ^746 48? 51 54* 5 6 S 59. 62: ! 9 2 7 1 i 70 >i 6 9' r f r , > 67 66^ 65: 5907; ICC 1 S' i3c 20: 23^ 9205< C3< O2i Ol/ oo 9199, 98 406 7* 7oc 72- 75. 7 8c 8o( 83. >9 r 35. > 34 33 31; > 30- > 29 ! 28" > 60 J 59 58 ? 57 i 56 5 55 5 54 7 9 10 12 J439: 421 44? 47 ; 5*5 53 < ' 88,' 875 869 8,9 849 30027 08* tai J 3 ? 162 37645 67* 703 73C 757 92642 631 62C 609 598 587 J9 6c 28: 3^ 34 1 36: JQ^ 9197 95< 94.5 93< 92 Q It 408 6< 88< 9: 93 96^ 992 > 9127 > z6< I 24^ I 23< 22^ 211 53 52 50 49 4J 13 *4 1 5 18 58, 612 63', 66< 694 829 819 809 799 7S V }6J9C 21 7 244 27 1 2 t 93222 21 J 201 190 169 83$ 8 9 j 919 946 9 "s^ 554 54- 39421 448 474 501 528 555 9190- 89] 8 7 c 856 845 4ioif 04 - 07: 09^ 151 9I20C 47 46 45 44 43 42 19 20 21 21 23 24' 77<; 80? 830 85; )3779 76, 759 728 36352 379 4 c6 434 461 488 93159 137 127 116 106 ,7973 999 38026 . 053 o3c 107 409 488 477 466 595*J 6oS 63 661 68S 91833 822 8ic 799 787 775 1 f T "5 20^ 23 25- 284 9112^ 116 104 092 c8c 068 91056 '044 032 0?0 008 90996 4' 40 39 38 37 25 26 27 28 29 '2 33 34 35 36 34884 912 93" 966 993 $5021 93718 708 698 68S 677 667 36515 542 569 623 650 36677 704 73i 7 5 5 812 36839 867 294 948 975 3095 08^ 06 : Ji* 93C3I O2C OIO 92999 998 92967 959 945 935 924 161 215 241 268 432 421 399 388 366 355 343 332 321 795 822 848 875 91764 752 74' 729 7iS 706 41337 363 39 416 443 469 35 34 33 32 ***~ 28 27 26 075 102 130 93 6 57 647 637 626 616 606 93596 585 575 565 555 544 389S 349 376 4J i9 928 955 40008 35 91694 683 67, 660 41496 522 549 5/5 602 628 909^4 972 96 94 93 924 . 37 38 39 40 42 239 2 9 ; 347 33456 510 537 564 59' 92310 n? 276 265 254 40062 088 ii ; 168 r 95 91625 6 '3 590 H 6 55 707 734 760 9091 1 899 887 863 851 23 22 21 20 II 43 44 45 46 47 4* 49 i 50 .J 53 54 35375 402 429 456 484 5*i 93534 524 5 J 4 53 493 4*3, 37002 029 056 083 110 137 92002 892 881 870 859 849 38617 64.4 671 69? 7*5 752 )2243 231 .220 209 T6 40221 27<; 3oi .355 ^555 543 59 508 496 ^4 472 461 449 437 425 41813 840 866 892 919 945J 90839 814 802 90766 753 74 J 729 717 704 ^0692 68c 66S 64: 631 17 16 *5 13 12 3553* 5 6 5 592 619 647 674 462 " 452' 441 420 7'% 191 218 245 272 299 827 816 805 704 784 5&77S< 8os 832 m 912 ?2i75 164 152 130 119 ^0381 408 434 461 488 5H 41972! 998 4.2024 051 077 104 II 10 9 8 7 6 55 2 56 . 5* ; 59 ; 60 570193410- 728 400 75? 383 782 379 *37 3'*! 7326 353 38o 407 434 401 7 d* 75 T 740 729 718 8939!' 966 993 9020 075 J2J07 096 085 073 002 050 ,0541 c 567 594 621 ,1414 402 390 37* 366 355 J.JI30 156 183 20C 235 202 5 4 .3 2 I O M N cofJX fnp lv i "" cof.JN fine 1 v cof. r ^ fine s ct'i.jN finplN cof. s fine M '"( 6.S j 67 66 6s TABLE XXIV. OF NATURAL SINES; 26 N cuf. 2 S fine 7 25 N line" 46947 973 999 47024 050 076 101 ^ N cof. 281 267 254 .'.240 226 213 19 M. M fine N cof. S fine N cut,! N fine 506 53 * 557 608 N cof. 57462 44' 434 420 406 391 377 M. i 2 3 4 6 2262 288 341 367 394 420 50631 618 606 594 557 43837 863 889 916 942 968 994 59879 867 854 841 8z8 816 803 45399 477 5^3 5^9 554 89101 087 074 06 1 048 035 C2I 60 57 56 55 54 7 8 9 10 II 12 42446 473 499 5*5 55^ 57^ 90545 53- 520 57 43 44020 046 072 098 114 441/7 203 229 255 281 307 59790 77 7 764 75- 739 726 45580 606 6r : 68 4 710 8900^ $8905 968 955 942 47127 153 178 204 229 88199 185 158 144 130 ' 684 710 735 786 87363 349 33: 3*1 306 292 53 49 4* '3 4 i5 16 18 (.2604 631 6^7 683 709 73J .,0470 458 433 4" 40' 19713 700 687 674 662 649 45736 762 787 839 86; 38928 91; 90:. 8-75 862 47181 306 33J 409 88117 10 ; 08; 07 S 062 ;fli 888 915! 55717- 2 5 C 33* 221 2O7 'l78 I 3 6 121 47 46 45 44 43 42 19 20 21 22 2 4 42^62 815 841 897 J3- 35S 33j 443 3 i 359 385 4" 4^7 464 89636 623 610 50 7 5^4 5V i 45891 917 94- 968 994 460.10 812 808 795 782 474-4 460 537 562 $8034 020 os6 ^7993 979 965 4*964 989 49014 040 06^, OQO 40 39 37 36 25 26 27 28 29 30 42920 94 6 972 999 ,0321 309 20,6 284 271 2^9 4449 516 542 565 594 620 ^9558 5* 9 506 493 097 123 149 75- 741 728 701 475* 639 66^ 690 ^795i 937 923 99 896 882 49116 141 166 192 217 242 .9268 ? 9 | 344 369 394 '445 470 495 52' 546 6710} 093 ' 079 064 036 35 34 33 32 3 1 . 3 3t 33 34 35 36 43077 104 130 150 182 209 9024^ 23 ' 2 - 1 -! I 5 6 IS 4464'. 67^ 698 724 776 s 9 4$o 467 454 441 428 46201 226 2*2 278 3 C 4 330 67^ 661 647 634 6:.o 55607 593 5 8c 566 553 535 88526 $*> $} 47- 45? 4774J 767 793 844 87868 854 840 826 812 87021 ^99? 978 964 94? 29 28 27 26 25 24 23 2* 21 20 i9 10 37 38 39 40 42 43*35 261 287 34" 4339 2 418 445 47* 497 ^ 158 146 133 I2C ' 108 "^828 88c 906 9^2 376 363 35 337 433 484 4/89' 920 946 971 997 l8o i: -57784 770 756 743 729 715 86935 921 87* 43 44 45 46 9009; 082 070 057 045 032 4495* 984 45010 036 062 088 8932;. 311 29^' 185 272 25 46510 587 6* 3 4^04- 07 _^ 091 12. ICC 17- 47701 687 67' 6 5 c 645 631 49571 59' 62: 6 4 7 67, 834 . 8c>f 791 17 16 15 14 13 12 49 50 5i 5* 53 54 43549 575 602 628 654 680 90019 007 89994 981 963 956 45114 140 1 66 192 in* 247 89145 232 210 206 T ^6664 716 74-' 79 T 88445 431 40.: 39 r - 377 252 177 30? 32^ \^-^ \ 379 405 430 4v 48 60! 58'. 1 J9 74 S 771 79' 84- ^6762 74^ 73' 7' 6 9 c II T.O 9 S 6 55 56 57 58 59 60 43706 733 759 7? 5 Sn 837 S 994 > 93C 9.1* 90s 892 879 4520-. 295 321 347 37? 399 8916; 153 14 127 114 IOJ 870 921 94' ~~i '836- 34 L 33 1 322 308 205 518 50^ 490 47 C 462 ''89' 95 C 97 ; 5CCCE 661 646 632 5 4 3 i i M. Nf. N cor. 6 N fine 4 1 N cof. | 6 N fine 3" N fine 1 N cof fc N line N c:.f ( N fin? TABLE XXIV. OP NATURAL SINES. M. 30 31 3 N fine 52992 53017 041 066 091 Ms 140 2 N cof. 84801 789 774 759 743 728 712 33 ; 34" N fine N cof. N lintjN cuf. N fine 54464 488 5*3 .537 561 586 610 N cof. X fine N cof. M. 60 59 58 57 56 55 54 i 2 3 4 6 fOOOC 02; 050 076 101 126 i "i $6603 588 573 559 544 530 . '5 1 < 51504 529 554 579 604 625 653 35717 702 687 672 657 642 627 83867 851 835 819 788 77* 943 968 992 56016 040 064 oc OC 00 00 00 00 0vO O N *>i Wn ^J 00 O N> -0 '^1 - v -fc, 7 8 9 ! 10 II ' 12 16 iS 50176 201 227 252 2/7 30: ^6501 471 457 442 4 2 7 $1673 703 728 753 7755 803 51828 852 96 a 927 952 0612 597 582 567 55' 536 53164 189 214 23- 263 288 681 66c 650 635 619 659 683 708 732 756 74 724 708 igi 676 56088 112 160 208 52790 773 757 74' 724 708 53 5* 5 49 48 47 46 45 44 43 42 40 JL 35 34 - 33 3i 50327 35- 377 42^ 453 1i 354 340 506 49 j 476 461 337 36 i 38< 411 435 ^ 57' 557 54* 526 805 ' 829 854 ST> 902 645 629 613 56232 256 280 205 329 353 82692 675 659 643 626 610 i J? 24 5047* 5*8 551 50628 654 679 704 729 754, 295 266 251 $62^7 222 207 IQ2 1/8 163 051 076 TOJ 401 37 355 53460 484 509 534 ssf 583 ^4511 495 480 464 448 433 54927 975 999 55024 048 33565 549 533 5'7 501 485 56577 401 42C 449 473 497 82593 5": 544 528 29 30 52I2t 2CO 22% 2=;c 4 5 340 310 -94 279 264 5360; 632 6 5 C 681 70; 730 54417 407, 386 370 355 339 5507* 097 121 169 194 ^3469 453 437 42. 405 3*9 56521 545 569 593 617 $3 54 51079 104 129 179 204 85970 956 94 r 926 911 896 52572 597 621 646 671 696 ^5066 051 035 020 005 84989 54049 073 097 122 146 171 84135 120 104 072 0^7 555<>9 53. 557 58. 605 630 S 3 i 79 163 147 115 098 56952 976 57000 024 047 071 82198 181 165 148 17 16 14 13 12 51229 254 279 304 329 354 85881 866 851 821 8c6 52720 745 770 794 819 844 84974 959 943 92* 913 54 r 95 220 244 269 293 $4041 009 83994 978 962 55654 678 702 726 775 83082 066 050 034 017 OO7 57095 119 '167 215 8209*) 082 o6<; 048 032 015 II 10 9 3 7 6 55 56 5*379 404 429 454 479 5* 85792 777 762 747 732 77 52*69 893 918 945 967 99- 8 4 S82 866 851 S2C 54342 366 440 464 83-946 930 915 899 883 867 55/99 823 847 87, oro 82985 969 953 936 920 904 57238 262 286 3?4 358 81999 982 965 932 9 J 5 5 4 3 z i o N cof. N line Ncof. STinelN cuf.JNT fine N cof. N fine N cof. N fine M. 59 J 550 57 56* : 55" i TABLE XXIV. OF NATURAL SINES, 3. S /int > N cot'' 81915 899 865 848 832 36- 37" ,38 V 39'' M. N line t\ cof' iO 9 O2 8Ss 867 850 833 8l6 799 N fine 60 1 8 1 205 228 274 2 9 S 32i Ncof. 79^ 846 82C, 811. 793 7/6 75S IN line JN cot. 78801 7S 3 765 74: 729 /n 693 N fine 955| 977 63000 022 04 s 068 :s cof.; 777~i5 696 678 660 641 623 6o S M. i z 2 3 4 6 5735^ 381 405 42, 453 477 501 5*77$ 802 826 849 873 896 920 61566 589 612 635 65? 68j 704 01720 749 772 795 841 60 59 57 56 55 54 J 53 ! 50 49 48 8 9 10 1 1 12 57524 548 572 596 6iq 643] 3l 7*r 765 748 "W 58943 96; 990 59H 037 061 2*0782 765 743 730 7*3 696 60344 367 39 414 437 460 7974 1 723 706 688 671 653 7^676 658 642 604 586 7* 5" 6 8 55<> 53- 406 47 ''- 630,0. 113 I 80 203 77586 568 550 531 5i3 494 13 It 16 17 18 57667 691 715 738 762 7 86 81698 681 664 . 647 614 59^4 10' 154 201 ^0679 662 644 627 610 593 60483 506 5-9 553 576 1599 79635 6oc 565 547 01664 887 909 932 955 978 271 3/6 /? 458 439 421 402 384 47 46 45 44- 43 42 j 20 21 22 2 4 "833 881 904 928 8'597 580 563 546 530 5T3 59225 240 3?8 342 50576 SS 8 54* 524 ^07 4 S 9 60622 645 668 691 *7?4 807 830 853 876 7953C 512 494 4"9 441 &2COJ 024 046 oo 9 09^ I Is 1*& 44^ 4-'- 4 405 387 36 9 78351 .333 27 2/3: 03301 401 428 45 J 473 ; 73 66 347 329 310 273 4 * 39 ' 37 36 ! 26 27 28 -9 '7952 970 999 047 070 58094 118 141 165 31496 479 462 445 428 412 593^5 41? 43 < 459 482 ^0472 455 420 403 386 79424 40 ( 353 335 6>13>- i6d 206 22f 251 63496 513 54 5^3 7/255 236 21 J 199 181 35 34 33 32 3 1 ; 3 o j 32 i 33 34 35 36 ^395 378 344 3^7 59506 529 55^ 576 599 612 ,50368 35' 334 316 299 282 60890 922 94' 968 99' 61015 793'* 2 ij 247 022:4 ao; 342 3 6 5 388 2Z C 20 ( I7C 15- ?65 3 72C < 42 77^44 125 oSb 070 651 28 27 26 25 24 37 33 39 40 42 58236 260 283 307 33^ 354 81293 276 259 242 225 20* 59646 660 693 716 739 763 80264 247 230 2f2 195 178 61038 061 084 10; 130 IJL 43 >: 45 < '479 502 524 xi 098 07, 0370; 83^ 8.H 87- 7/033 014 76906 95' 940 2 ; 2 I 20 59 18 43 44 45 46 47 48 58378 40 r 4*5 449 472 40 6 81191 174 '57 140 106 59786 809 832 856 879 902 5992: 949 972 9 9 s 60019 042 So 1 60 143 1 08 091 073 61176 222 2 4 < 201 79105 087 069 051 03. 7^9~> 980 962 944 926 908 62547 592 66c 780 ; 5 OC7 779^ 97 95^ 63*99 9:2 944 76921 go' sa U: 791 754 17 16 13 1 2 I I 10 9 8 7 6 ' 5 4 3 ; 2 I O M 49 50 52 S3 54 58519 6^4 81089 072 055 038 02 1 004 80056 038 02 r 003 79986 61314 337 360 3*3 406 429 6268; 728 75 ' 7,74 79$ 77916 879 801 84, 82^ 6^033 078 ICC TJ ^ 64 1 1>7 190 21 : -34 279 55 56 57 59 63 58661 684 708 731 755 779 80987 970 953 936 919 902 6006 1, 089 112 '35 181 /995 1 934 916 899 881 61451 474 497 520 ; 543 s-66 78891 7 1 85; 819 So i 62810 842 88- 93-' 7 6c 75' 733 7*J 76698 079 66 1 642 623 604 M. tfcof N fjne N cof. Nfine N cof. N fin, Ncof. N fir.t X i]m . . 54" 53 ; ; o TABLE XXIV. OF NATURAL SINES. 40 41" 42 N fine o N col'. 44 C M M i\ lint N cof. N fmt ,N cof. N fine- N" cof. N fine N cof. o r 2 3 4 6 64279 301 323 346 36S 390 41: 76604 5*6 S^'/ 548 53 C 5 11 492 6560'; 628 650 672 694 7 I6 7j8 7547' 452 433 'V 39 f 37f 35J& 66913 >35 956 97* 66900 67021 043 0*7064 086 107 125 151 172 743 J 4 2 9 < 276 2<6 ij? 217 198 68200 22) 24* . 264 285 306 3*7 73H5 Ii6 096 076 056 036 016 69466 4*7 508 529 549 570 59i 71934 914 894 873 53 833 i; 60 59 58 57 56 55 54 8 9 10 ij ! 12 6443; 457 479 $o > 5^4 546 7 6 4;3 4;; 43' 4' 39 - go 657^9 7Si 803 82'; *4 : 869 75337 3i8 190 280 261 241 7417^ 159 *39 1 20 loo 080 68349 370 391 412 433 455 68476 497 08 539 561 582 72996 976 957 937 917 897 69612 633 654 675 6,^6 717 7I79 2 77* 752 73^ 711 691 53 52 5' CO 2 IB 4 {i T7 lg 64568 590 612 3< 6^7 670 7636 i 34^ 3*5 304 *S(. 267 "624* 229 2rc 192 173 154 6589, 913 935 956 078 66000 75222 20? l8 4 J6 5 146 126 67194 215 237 2<8 28c 30] 74061 041 022 002 739^3 9 6 3 72877 1]? 8i7 797 777 72757 737 717 697 6/7 657 69737 758 779 800 82! 842 71671 650 630 6ic 590 569 47 46 45 44 43 42 *9 20 21 22 *3 *4 64701 723 746 ?6S 790 812 $4*34 856 878 901 9i3 945 66C22 044 066 0*8 109 yi 6615^ '75 JQ7 2lS 240 262 75JO7 088 069 050 030 Oil ^73i" 344 366 387 409 430 6745- 47- 49; 5< 53? 559 73944 924 904 88; 865 846 68603 62^ 645 666 688 709 6g86z 883 904 9 ;: 946 966 ?i549 3Z 2 <;o^ 488 468 447 4' 40 39 3* 37 _J6__ 35 34 33 T- 3i 30 29 28 27 26 25 24 *S 16 27 zS *9 30 sV~ 3 33 34 35 36 37* 38 39 40 41 42 7613; 116 097 07^ 59 041 "49 9 i 973 953 93^ 91- 8 9 f 73'^ 806 787 767 747 728 6^73C 75' 772 793 814 3 f 72637 617 597 577 557 537 69987 70008 0:9 049 070 091 71427 407 386 366 345 325 6496 989 6501 1 13 .55 077 76022 oo? 759^4 96^ 946 927 66284 306 327 349 372 393 74^76 857 838 8,8 '799 7 9) 67580 602 62? 6 4 ; 666 688 73708 688 66q 649 629 610 6SS 5:7171517 87&J 497 899! 477 9201 45: HI 437 962 417 70112 132 153 174 i9> 215 71305 284 264 -43 223 203 650'A 122 14-5 166 1*8 210 7>9* 889 870 851 832 8r? 66414 436 45? 480 501 523 74760 74 1 722 703 683 664 67709 730 752 773 795 816 73590 570 55' 5P 5 11 491 68983 69004 02 c 046 067 oS8 72397 377 357 337 3i7 297 70236 257 277 2 9 V 3'9 539 71182 162 141 121 100 080 2 3 22 21 2O '9 18 43 44 45 46 47 ~~iL- 49 5 5i 5* - 53 54 654** *54 276 2 9 ^ 3>c 342 75794 775 756 73* 719 69:, 66545 566 588 610 632 653 74644 6 2 c 606 586 567 54? 67*37 8^9 88c 901 923 944 73472 452 43- 412 393 373 .69109 IjO i>i J 7 2 193 21.1 7" 7 7 5? 236 216 196 176 70360 ' 38' 401 422 443 463 7 jo5q 639 OJO 70998 97* 957 70937 916 896 87S 55 834 17 16 15 H 13 12 6536., 386 40^ 430 45? 474 756Sc 661 642 3 004 585 66675 6 9 7 718 740 762 78| 7452% 509 489 470 ,45* 43i 67965 955; 6800; c_9 051 072 73353 333 314 294 *74 254 69235 56 277 298 319 34 72156 136 lie i 095 075 055 70484 505 525 546 567 58.7 II 10 9 8 7 6 55 56 58 59 60 ',5496 518 540 5 s 2 5^4 606 75566 547 528 509 49 47' 66805 S27 848 870 S 9 r _9*1 ^T"* 4 74412 392 373 35? 334 3M 68093 US 136 157 79 2OO 7323=* 215 195 J75 *55 J 3 : 69361 382 43 424 44 5 466 72035 015 7199- 974 954 934 70608 62 649 6?c 690 711 70813 793 772 752 73' 711 5 4 3 2 I O M N cof. XTine N fine Ncof.jN fmc N cof. N fine Nrof. N fine M 40 47 46 e 45 TABLE XXV. PROPORTIONAL LOGARITHMS. 1 s. h m h m h m h m h m 1) n o 5 h m i) n h m S J4-334 2.25 1.954 1.778 1.653 1.556 i477 L4IC 1.3522 I >4'33 248 95 775 65* 554 475 469 35 T 3 2 13-73- 24 947 773 649 553 474 408 354 3 I3.S56 234 943 771 647 55 2 473 407 3495 4 3-43' 227 940 768 646 55 472 406 3486 5 3-334 220 936 766 644 549 471 405 3477 6 3-255 213 933 763 642 547 469 404 3468 8 3.130: 207 200 929 926 761 759 640 639 546 544 468 46? 403 402 3459 345 9 3-079 19^ 922 757 637 543 466 401 344 r 10 U 12 3-033 2.992 954 'l32 176 1.919 916 912 '754 712 750 1.635 633 632 1.542 540 539 1.465 464 462 1.400 398 397 1.3432 3423 *3 919 887 170 I6 4 909 906 747 745 628* 537 536 461 460 39 6 395 3406 3397 16 18 857 829 803 77 I 5 8 152 146 I 4 I 93 8999 896 893 743 739 736 626 6*5 625 621 535 533 532 459 458 457 45^ 394 393 392 391 33*8 3379 3371 3362 *9 754 *35 8904 734 620 5*9 454 3910 3353 so 2.7324 2.130 1.8873 1.732 i. 618 1.528 *-453 1.3900 1.3345 21 22 7112 6910 671- 124 119 114 8842 8811 8781 730 7 z8 725 616 615 613 526 5256 5242 452 45'4 4502 3890 3880 3870 3336 3327 33^9 24 6532 109 8751 7 2 3 611 5229 3860 Z 5 2 7 28 6355 610} 6021 5863 104 098 093 088 8721 8691 8661 721 719 7154 610 608^ 6069 60-53 5 aij 5202 5j89 4480 446 b 4457 4446 3851 3841 3831 330i 3 2 93 3*84 2276 29 _57io 084 8602 7136 5166 4435 3812 3267 30 2.55 6 3 .079 1-8573 1.7112 .602 .5149 1.4424 1.3802 3 2 59 3' 32 33 34 35 36 37 38 39 5283 5 r 49 5 OI 9 4894 477i 4652 4536 4424 0744 069 0649 0603 557 0467 0422 0378 8544 8516 848; g 459 843' 8403 8375 8348 8 ? 20 709 7071 7050 7030 7010 6990 6970 6950 6930 6005 5989 5973 5957 594i 5925 5909 5894 5878 5136 5123 5110 5097 5071 5058 5045 5032 4412 4401 439 4379 43 58 4357 4346 4335 4325 3792 37*3 3773 3764 3754 3745 3735 3726 3250 3242 3233 3216 3108 3191 3^3 40 42 43 44 45 46 , 47 48 2.4314 4206 4102 4000 3900 3802 370/ 3613 3522 7412 334 0291 0248 0206 016^ OI22 Oo8l 0040 oooo 9960 .8293 8266 8239 8212 8186 8159 8133 810; 8081 80-5 .6910 6890 6871 6851 6832 6812 6793 6774 6755 6736 .5863 5816 580! 5786 577i 5755 5740 572$ .5019 5007 4994 4981 4969 4956 4943 493 1 4918 4906 4314 4303 4292 428, 4270 4260 4M9 4238 4228 4217 3707 3697 3688 3678 3669 3660 3650 3641 3632 3623 -3*74 3166 3158 3M9 3141 3133 3116 3108 3100 50 52 53 54 55 56 57, 58 59 , ^3345 3^59 3174 3091 3010' 2852 2775 2700 2626 9920 9881 9842 9803 9765 9727 9690 9652 9615 9579 8030 8004 7979 7954 7929 7904 7879 7830 1.6717 6698 6679 6642 6624 660^ 6587 6568 6550 5710 5695 56.80- 5666 5651 56^6 562 r 5607 5592 55^ 4881 4869 4856 4844 4832 4820 4808 4795 4783 .4206 4185 4175 4164 4154 4*43 4122 4ri2 3613 3604 3595 3586 3576 3567 3558 3549 3540 353i 3091 3083 3075 3067 359 343 334 3026 3118 60 ^553 954- 7782 .6532 5563 ) 47/1 4102 3522 3010 h m m i m h m m i m h m h m rn > ' * 2' 3 3' 4' c * S' < > 6 , ,, * 8' TABLE XX.V. PROPORTIONAL LOGARITHMS. h m h m i m h m i in i m h m i m h ni s. > 9' o' 10' ,,/ D IZ 1 9 13' M' * I 3S 2488 2080 1707 1363 1045 0749 0471 0210 10 .2931 1.2481 .2073 .1701 .1358 . 1040 .0744 .0467 1. 02O6 TI 2923 2474 2067 1695 1352 1035 07?9 0462 O2O2 j 12 2915 2467 2061 1689 1347 1030 0734 0458 0197 13 2907 2460 2054 1683 1342 1025 0730 0453 0193 14 2890 2453 2048 1677 1336 1020 0725 0449 0189 15 2891 2445 2041 1671 1331 1015 0720 0444 0185 16 2883 2438 2035 1665 1325 1009 0715 0440 0181 j 1 7 2876 2431 2028 1660 1320 IOO4 0711 0435 0176 i 18 2868 2424 2O22 1654 1314 0999 0706 0431 0172 T 9 2860 2-4*7 20l6 164$ 1309 0994 0701 0426 0168 20 .4852 i .2410 .20O9 . 1642 <33 I .0989 1.0696 .04221 i .03*4 21 2845 2403 2003 1636 1298 0984 0692 0418 0160 22 2837 2396 1996 1630 1292 0979 0687 0413 0156 23 2829 2389 1990 1624 1287 0974 06^2 0409 0151 24 2821 2382 1984 1619 1282 0969 0678 0404 0147 2814 2375 1977 1613 !2 7 6 0964 0673 0400 0143 26 2806 2368 1971 1607 1271 0959 0668 0395 CT 39 27 2798 2362 1965 1601 1266 0954 0663 0391 OI 35 28 2791 2355 J958 J595 1260 0949 0659 0387 0131 29 278? 2348 1952 1589 1255 0944 0654 0382 0126 30 .2775 1.2341 I.I946 1.1584 .1249 1.0939 I . 0649 1.0378 .0122 3* 2768 2334 1939 1578 1244 934 0645 374 0118 2760 2327 1933 1572 1239 0929 0640 0369 0114 33 2753 2320 1927 1566 1233 0924 0635 OIIO 34 2745 2313 1921 1561 1228 09 1 9 9631 0360 0106 2738 2307 1914 '555 1223 0914 0626' 0356 O1O2 36 2730 2300 1908 J 549 1217 9 0/) 0621 0352 0098 ;' 37 2722 2293 1902 *543 1212 0904 0617, 0347 0093 38 2715 2286 1896 1538 1207 0899 0612 0343 0089 39 2707 2279 l88 9 1532 I2OI 0894 c6oS 339 0085 40 i .2700 r . 2272 I.I883 1.1526 r . 1196 1.0889 1.0603 1-0334 I.OOSl 4 1 2692 2266 1877 1520 .1191 0884 0598 033" 0077 268- 2259 I3 7 I 1186 0880 0594 0326 00 7 3 43 2678" 2252 1865 1500 1180 0875 0589 0321 0069 44 2670 2245 lg; 1503 117 0870 0585 0317 0065 45 2663 2239 I8 5 2 149$ 1170 086; 05^0 0313 Oo6l 46 265=; 2232 1846 14^2 116* 0860 0575 0308 0057 47 2648 2225 1840 1486 1159 085 c 057 j 0304 0053 4* 2640 2211 1834 1481 II'5/ 0850 0566 0300 0049 49 26*13 2212 1828 147 : i A' oS 45 01562 0291 0044 5 1.2626 I .220 1.1822 1.1469 1. 114 1 .0^,1, 1.0557 i .02-.; s ! . ' 51 261: 219? 1816 146. 1 1? 0835 o 5 ; 0,87 0036 52 2611 2192 1809 1458 1 1 \ o3 3 i 6548 o y. 8 2 0032 53 2604 2183 1803 1452 112 6543 o? 7 ' 0028 54 2596 2178 179- 144 112 0821 0530 0024 55 2589 217. 179 144 II 1 0816 0534 0270 0020 2582 2165 178 143^ III 0811 026; doi6 57 2574 2159 1779 1430 110 0806 52. 0261 0012 58 2567 2152 1773 I4M iro oSej 0520 0257 00(^3 59 2560 176-7 109 079- 05U-. 0:52 0004 60 255 7 1*2,13 -.176 i . 141 i . 109 r .0/92 r psii 1.024"* 1 . ocx o h m ( h m h m h m h m h nV h in h ni h in j .'? q/ 1 T ' , , ' | Q , , , 0* T] 14/ o i 5' 9 16' o r? / 1 TABLE XXV. PKOPORTIONAL, LOGARITHMS. 1 M h m I h m 10 1 h m Q 20 h m 21 Ih in 022 h m 02 3 h rr 02 4 h n 02 5 h m O Q 26 h re o 27 h m o 28 li m 02- 969 947 9262 906 8873 8691 *S*6 834* SJ86 8030 7^79 21 991 968 946 9 25Q 9060 as ?o 8688 8513 ^34,- 8183 8027 7877 22 99 r 968 9464 925 9057 8867 868 8510 834; 8i8r 8025 78/4 -3 990 967 9460 9252 9053 8 ; ]64 8082 8507 83.39 8178 7^ 24 99 967 9456 9249 9050 8861 8679 8504 83317 8r 7 s 80. -.0 7869 2 5 999 967 9453 9245 9047 8857 8676 8^02 8334 8i7S 8or? 7867 26 9*9 9667 9449 9242 9044 8854 8673 84^0 8331 8170 8014 7864 27 989 9664 944- 9 2 3^ 9041 8851 8670 8328 8167 8012 7^62 23 988 9660 9442 92:5 9037 8848 8667 8493 8326 816,- 5ToO9 7859 29 988 9656 9439 9232 9034 8845 86f 4 8490 8323 8007 7^57 3 90-5 96 w 9435 922S 93i 8842 8661 8487 8320 8,159 800^ 7855 3i 987 9649 943i 9225 9028 8839 8658 8484 8318 8157 8002 -852 32 987 9645 9428 9222 9024 8836 86^ 8482 83X5 8r S4 7999 7850 33 9 S6 9 9641 9425 9218 90^1 8*3? 8652 8479 8312 8152 7997 7847 34 9863 9638 9421 9215 9015 8S 3 o 8649 8476 8309 8149 7994 7845 35 986 9634 9418 9212 9015 8827 8646 8473 8307 8146 799 2 7842 36 985* 9630 9414 9208 9012 8824 8643 8470 8304 8144 7989 7840 37 98 >4 9626 9411 9205 9008 8821 8640 8467 8301 8141 7987 7837 ) 3S 9850 9623 9407 9201 9001; |*i 7 8637 8465 8298 8138 7984 7835- 39 9 8 4 r 9619 9404 9198 9002 8814 *6 3 .5 8462 8296 8136 798 r 7832 40 9842 9615 9400 9'95 8999 8811 8632 8459 8293 8133 79/9' 7830 } 4i 9838 9612 9397 9191 8996 8809 8629 8456 8290 8131 797k 7?aS 42 9834 9608 9393 9188 8992 8805 8626 84S? 8128 7825 43 9830 9604 9390 9i3s 8989 8:302 8623 84^1 8285 812. 797r 7823 | 44 9*27 9601 9386 9181 8986 8799 8620 8448 8282 812; 7969 7820 1 45 9^23 9597 938.3 9178 8983 8796 8617 8445 8279 8120 7818 46 9819 9593 9379 9*75 8 9 8c 8>93 8442 827-7 8117 7964 78 1 > ! 1 47 9-,, 9590 93/6 9172 8g/7 8790 84V. X 274 7961 7813 48 98u 9S86 9372 9168 $973 S6o8 84V 8271 7959 7811 49 9807 9582 9369 9165 8970 8784 8434 8269. 8110 7956 7808 50 9803 9579 9365 9162 8967 8781 843t 8266 8107 7954 5i 9800 957< 9362 9^8 8 599 8428 8 2 6< 8104 795i 52 9796 957i 935^ 9 r 55 896 f 877S 3.97 842, 8261 8102 7949 53 979- 9508 9355 9152 89^8 8772 5594 842; 54 9788 9564 93$r 9148 8 9 54 8 7 6q 8^91 8420 8097 7944 7796 55 9/84 9561 934* 9H5 8951 8588 841, 825? 8094 794i 56 9780 9557 9344 9142 8948 876; 58.5 C 4i ; 8250 8091 57 9777 9553 93.41 9138 8945 8760 8582 8411 8247 8.0^9 7936 58 9773 955^ 9337 9*35 8942 Sv79 8409 8.244 59 9769 9.46 9334 9132 89^9 8754 8576 84..; 8242 8o?4. 7931 60 9765 9542 9331 9128 ^93^ 8751 8575 840, :O^T S. i m m i m h ni m 'i m i m i m 1 o* u' 1 9' * zc' 5 21' o 2 a' 1 zS "25 3 2S'! 29' j y < 2 TABLE XXV-. PROPORTIONAL LOGARITHMS. 1 1 h rn i m i m h m i m i rn i m h m i m j h m h m - h m S JG 3 0' . jji 32' 33' 34' ^ 35' S 36' 3 37' 38' :> 39' 4 ' o 4 i' o 7782 7639 7501 7368 7238 7112 6990 6871 6755 6642 6532 6425 I 7779 73/ 7499 7365 7236 7110 6988 6869 6753 6640 6530 6423 2 7777 7634 7497 73 6 3 7234 7108 6986 6867 6751 6638 6529 6421 3 7774 7632 7494 736i 7232 7106 6984 6865 6749 6637 6-527 6420 4 7772 7630 749 2 7359 7229 7104 6982 6863 6747 66^ 6525 6418 5 7769 7627 7490 7357 7227 7102 6980 6861 674S 6633 6523 6416 6 7767 7625 7488 7354 7225 7100 6978 68^9 6743 6631 6^21 6414 7 77 6 5 7623 74 ? 5 7352 7223 7098 6976 6857 6742 6629 6519 6413 8 7762 7620 7483 735 7221 7096 6974 6855 6740 6627 6<;i8 6411 9 7760 7618 7481 7348 7219 7093 6973 6853 6738 6625 6 5I 6 6409 10 7757 7616 7479 7346 7217 7091 6970 6*51 6736 6624 6^14 6407 ii 7755 7613 7476 7344 7215 70% 6968 6849 6'/34 6622 6512 6406 12. 7753 7 1> 1 1 7474 734 1 72ia 7087 6966 6847 6732 6620 6510 6404 13 775*- .7609 747- 7339 7110 7085 .6964 6845 6730 6618 6509 6402 14 7743 7607 7470 7337 72oS 7083 6962 6843 6728 6616 6507 6400 5 7745 7604 7467 733*5 7206 7081 6960 6841 6726 6614 6505 6398 16 7743 7602 74 6 5 7333 7204 7079 6958 6840 6725 6612 6^03 6397 I? 7741 7600 7463 733 7202 7077 6956 6838 6723 6611 6501 6 395 18 7718 7597 7461 7328 7200 7075 6954 6836 6721 6609 6500 6 393 19 7736 7595 7458 7326 7198 7073 6952 6834 6719 6607 6498 6391 ao 7734 7593 7456 73 2 4 7196 7071 6950 6832 6717 6605 6496 6390 21 773 1 759 7454 7122 7193 7069 6948 6830 6715 6603 6494 6388 22 7729 7588 7452 7320 7191 7067 6946 6828 6713 6601 6492 6386 23 7726 7<86 745 7317 7I 8 9 7065 6944 6826 6711 6600 6401 6384 24 7724 7S83 7447 73J5 7187 7063 6942 6824 6709 6598 6489 6383 2 5 77?2 7581 7445 7313 7 i5 7061 6940 6822 6708 6596 6487 6381 26 T7J9 7579 7443 7311 7'*3 7059 6938 6820 6706 6594 648 s 6379 27 7717 7577 744 ' 7309 7181 7057 6936 6818 6704 6592 6484 6377 28 77H 7574 7438 7307 7179 7055 6934 6816 6702 6590 6482 6376 29 7712 7572 7436 734 7*77 7052 6932 6814 6700 6589 6480 6 374 30 7710 7570 7434 7302 7*75 7050 6930 6812 669!* 6<58 7 6478 6372 31 7707 7567 7432 7300 7172 7048 6928 6810 6696 658; 6476 6371 1 32 7705 7565 7429 7298 7170 7046 6926 6809 6694 6583 6475 6369 33 7703 7563 7427 7296 7168 7044 6924 6807 6692 6^! 6473 6367 34 7700 7560 74*5 7294 7166 7042 6922 6805 6691 6579 6471 6365 35 7698 7558 74*3 7291 7164 7040 6920 6803 6689 6S78 ,6469 6364 I 36 7696 7VS6 7421 7289 7162 7038 6918 6801 6687 6576 6467 6362 37 7693 7554 7418 7287 7160 7036 6916 6799 6685 6 574 6466 6360 3 7691 755 1 7416 7285 7158 7034 6914 6797 6683 6572 6464 6358 1 39 7688 7549 7414 7283 7156 7032 6912 6795 6681 657P 6462 6357 ! 40 7686 7547 7412 7281 7154 7030 6910 6793 6679 6568 6460 6 355 i 4 1 7684 7544 7409 7279 7152 7028 6908 6791 6677 6567 6459 6353. | 42 7681 754 2 7407 7276 7H9 7026 6906 6789 6676 6565 6 4 S7 6351 43 7679 7540 7405 7274 7M7 7024 6904 6787 66/4 6563 6455 63^0 ! 44 7677 7538 7403 7172 7H5 7022 6902 6 7 8s 6672 6;6i 6453 6348- | 45 7674 7555 7401 7270 7143 7020 6900 6784 6670 6559 64Si 6346 46 7672 7533 7398 7268 7141 7018 6898 6782 666i 6558 6450 6 344 47 7670 753i 7396 7266 7139 7016 6896 6780 6666 6<;s6 6448 . 6 343 4* 7667 7528 7394 7264 7137 7014 6894 6778 6664 6554 6446 6341 49 766s 7^6 7392 7261 7135 7012 6892 6776 6663 6552 6444 6 3 39 50 7663 75*4 7390 7259 7133 7010 6890 6774 6661 6550 6 443 6338 51 7660 7522 7387 7257 7i3i 7008 6888 6772 6659 6548 644 6336 5* 7658 75 r 9 7385 7255 7129 7006 6886 6770 66S7 6>47 6439 6 3 H 53 7*SS 7517 7383 7253 7127 7004 6884 6768 66 S S 6<4<; 6 4r 6332 54 7653 75r. 738i 725 * 7124 7002 6882 6766 6653 6543 643 6331 55 7651 7513 7379 7H9 7122 7000 6881 6764 66si 6<;4i 6474 63 29 56 7648 7510 7376 7246 7120 6998 6879 6763 6650 6 539 6432 6327 57 7646 7508 7374 7244 7 nS 6996 6877 6761 6648 6^8 6 43 c 6325 53 7644 7506 7372 7242 7116 6994 6875 6759 6646 <>53 6 6428 6324 59 7641 7503 7370 7240 7114 6992 6873 6757 6644 6534 642 6322 j 60 7639 7501 73^8 7238 7112 6990 687 675_ 6642 6S3* 642 6320 S h m h m h m h m h m h m h m h m h m ii m h re h rn i o 30 - 3* o- 31 o 33' o 34' o*35 0*36 o 3 7 o 3 X' o39 Q 40 o 41' TABLE XXV. PROPORTIONAL LOGARITHMS. h ra I h ra h m h m h m h m h m h m h ra h m h m h m s. o 42' o*43' o 44' o 45 o 46' o47' o 4 8' 3 49' o" 50' Q g 5* 0=52 o53' 6320 6218 6ng 6021 59*5 5832 5740 5651 55 6 3 5477 5393 5310 i 6319 6216 6117 6019 5924 5830 5739 5649 55<>2 5476 539i 5309 2 6317 6215 6115 6017 5922 5829 5737 5648 556o 54/4 539^ 5307 3 6315 6213 6113 6016 5920 5827 5736 5646 5559 5473 5389 53<>6 4 6313 6211 6112 6014 59 J 9 5826 5734 5645 5557 547i 5387 5305 5 63*2 6210 6110 6013 59 1 ? 5824 5733 5643 5556 54/c 53S6 C3O3 6 6310 6208 6108 601 1 5916 58*3 573 1 5641 5554 5469 5384 J J 3 5302 7 6 3 =S 6*06 6107 6009 59 J 4 582! 5730 5640 5553 y 5467 5383 5300 8 6306 6205 6105 6oc8 59*3 5819 57-8 5639 555J 5466 5382 5299 9 6 305 6203 6103 6006 5911 5818 5727 5637 5550 5464 538o 5298 10 6303 6201 6102 6005 5909 5816 5725 5636 5549 54 6 3 5379 5296 ji 6301 6200 6100 6003 5908 5815 57H 5635 5547 5467 5377 5295 12 6300 6198 6099 6coi 5906 58i3 5722 5633 5546 5460 5376 5294 13 6298 6196 6097 6000 5905 5812 5721 5632 5544 5459 5375 5292 14 6296 6195 6095 599* 5 9 3 5810 5719 5630 5543 5457 5373 5291 15 6294 6193 6094 5997 5902 5809 57i8 5629 5 54* 545 6 5372 5290 16 6293 6191 6092 5995 5900 <;8o7 5"i6 5627 5540 5454 5370 5288 17 6291 6190 6090 5993 5898 5806 5/15 $6z& 5538 5453 5369 5287 iS 6289 6188 6089 5992 5897 5804 5713 5624 5537 5452 5368 52^ 19 6288 6186 6087 5950 589< 5^03 5712 5623 5536 545 5366 5284 20 6286 6185 6085 5989 5894 5801 5710 5621 5534 5449 5365 5283 21 6284 6183 6084 5987 5892 5800 5709 5620 5533 5447 5364 528l 22 6282 6181 6082 5985 5891 5798 5707 5618 553i 5446 5362 5260 I 23 6281 6179 6081 5984 5889 5796 57o6 5617 553 5445 536i 5 2 79 H 6279 6178 6079 5982 5888 5795 5704 5615 5528 5443 5359 5277 Z 5 6277 6176 6077 5981 5886 5793 5703 5614 5527 5442 5358 5276 26 6276 6174 6076 5979 5884 5792 5701 5613 5526 544 5357 5 2 75 27 6274 6173 6074 5977 5^3 5790 5700 5611 5524 5439 5355 5273 28 6272 6171 6072 5976 5881 57^9 5698 5610 55*3 5437 5354 5272 29 6271 6169 6071 5974 5880 5787 5697 5608 552i 5436 *5353 52/1 30 6269 6168 6069 5973 5878 5786 5 6 95 5607 5520 5435) 53U 5269 31 6267 6166 6067 59/1 5877 5784 5 6 94 5 6 5 55'8 5433 535 5268 3 2 6265 6165 6066 59 6 9 5875 5783 5692 5604 5517 543* 5348 5266 33 6264 6163 6064 5968 5874 578i 5691 5602 55^6 543 5347 5265 34 6262 6161 6063 5966 5872 578o 5689 5601 55'4 5429 534 6 r 5264 35 6260) 6160 6061 5965 5870 57/8 5688 5599 55 r 3 5428 5344 5262 36 6259 6158 6050 59 6 3 5869 5777 5686 5598 55H 5426 5343 5261 37 6257 6156 6058 5961 5867 5775 568 s- 559 6 5510 54*5 534 1 5260 38 6255 6155 6056 5960 5866 5774 5683 5595 5508 5423 534 -> J-T 5 2 5$ 39 6254 6i53 6 55. 5958 5864 5772 5682 5594 5507 542: 5339 _> j 5257J 40 6252 6151 6053 5957 5863 577i 5680 5592 5506 5421 5337 5256 41 6250 6150 6051 5955 5861 5769 5679 559i 5504 5419 533 6 5254 4* 6248 6i 4 g 6050 5954 5860 5768 5 6 77 5589 5503 5418 ''ms 5253 43 6247 6146 6048 5952 5858 5766 5676 5588 55oi 54i4 5333 5252 44 6 *45 6145 6046 5950 5856 5765 5 6 74 55*6 4488 4420 4 5223 5144 5066 498-; 49 X 3 4766 4695 4624 4555 4486 4419 5 5222 5064 49 S8 4912 4833 4765 4 6 93 4623 4554 44*5 4418 6 5221 S'4 1 5063 4986 4911 437 47" 64 4692 4622 4552 4484 44 1 7 7 5219 5140 5062 4985 4910 4836 4/ 6 3 4691 4621 4551 44*3 4416 8 5139 5061 4984 490? 4834 4762 4690 4619 455 4482 4415 ; 9 5217 5137 5059 4983 4907 4833 .4760 4689 4618 4549 44*1 44i4 10 5215 5136 15058 4981 4906 4*32 4759 4688 4617 454* 4480 4412 II P3S 557 4950 490;- 4831 4758 4686 4616 4547 4479 4411 12 5 2I 3 5*33 5055 4979 490: 4830 4757 4685 4^15 4546 4477 4410 13 S2II 5132 S54 4977 4902 4828 4756 4684 4614 4544 4476 4409 H 5210 5131 553 4976 4901 4827 4/54 4683 46 rz, 4543 4475 4408 5209 5 I2 9 4975 4900 4826 4753 4682 4611 4-542 4474 4407 16 5207 5128 5050 4974 4899 48*5 475 2 4686 4610 454 1 4473 4406 -. 5206 027 549 4972 4897 4823 475 1 46-70 4609 4540 4472 4405 18 5205 5048 4971 4896 4.822 4750 4678 4608 4539. 447 1 4404 1 19 S203 5124 5046 4970 4 s 9 5 4748 4677 4607 4538 4469 4402- 20 5202 5143 5045 496, 489; 4820 4/47 4676 4606 4536 4468 4401 2 I <520I 5122 5-44 4967 4892 4819 4746 4675 4604 4535 44<>7 4400 ' 2 5*99 5120 5043 4966 4891 4817 4745 4673 4603 45 H 4466 4399 ! 23 5119 5041 49 6 5 489.: 4816 4744 4672 4602 453? .4465 439* H 5 r 97 5118 5040 4964 4889 4*M 4742 4671 4601 4532 4464 4397 : -5 5*95 5116 539 4962 4887 4814 4741 4670 4600 4S3 1 44 6 3 4396 ! 26 5194 5115 4961 4886 4812 4740 4669 4599 4530 4462 4395 27 5193 5114 5036 4960 4*8$ 4811 4739 4668 4597 4528 4460 4394 1 28 5191 5112 535 4959 48 8y 4810 4738 4666 4596 4527 4459 4393 -9 5190 5111, 5034 4957. 488'2 4809 4736 4665 4595 4526 445 s 4391 1 30 5189 5ii3 5032 4956 4881 4808 4735 4664 4594 4525 4457 4390 ' 5108 ^031 4955 4880 4806 4734 4663 4593 4524 4456 4389 32 5186 5107 5030 4954 4879 4805 4733 4662 4592 4523 4455 43*8 ' 33 5*85 5106 5028 4952 4877 4804 473^ 4660 459 4522 4454 4387 34 5^3' 5105 5027 495 J 4876 4803 4730 4659 4589 4520 4453 4386 35 SIS* 5103 5026 4950 4875 4801 4729 46 S* 458$ 4519 4452 43*5 ! 36 5181 5102 502 < 4949 4874 4800 4728 4 6 S7 4587 4518 445? 4384 : 37 5*79 5101 5023 4947 4873 4799 4727 4656 4586 4517 4449 4383 5178 599 5022 4946 487 r 479^ 4726 4 6 55 4585 4516 444* 4381 39 5177 5098 5021 4945 4870 4797 4724 4653 4584 45*5 4447 4380 40 5*75 5097 5019 4943 4869 4795 47*3 4752 4^82 45M 4446 4379 4 * 5174 595 5018 4942 4868 4794 4722 465' 458i 4512 4445 4378 5 J 73 594 5017 4941 4866 4793 4721 4650 4^80 4511 4444 4377 [ 43 5172 5016 494 4865 4/92 4720 4 6 49 4579 4510 4443 4376 44 45 46 51-70 5169 5168 5 OJ 4 5 OI 3 5012 4938 4937 493 6 4864 4863 4861 4789 4788 4717 4716 4648 4646 4645 4578 4577 4575 4509 4508 4507 4441 4440 4439 4375 4374 4373 . 066 ! ' 5088 5011 4935 4860 4787 4715 4644 4574 4506 4438 4372 516^ 5086 5009 4933 4859 4786 47 H 4 6 43 4573 4505 4437 4370 ; 49 5164 50S> 5008 4932 4858 4784 4712 4642 4572 4503 4436 4*369 5 5162 ^084 5007 493i 48 S6 47^3 4711 4640 457i 4502 4435 4368 -j 061 5083 15035 4930 4782 4710 4639 4570 4501 4434 4367 5160 ^081 5004 4928 48 ,-4 478i 4706 4638 4569 4500 4433 4366 53 5158 5080 5003 4927 4780 4708 4 6 37 4^67 4499 4431 43 6 5 54 5157 579 5002 4852 4778 4707 4636 4566 449 S 4430 4364 55 5077 5000 4925 4 8<;o 4777 4705 4635 45 6 5 4497 4429 43 6 3 5*54 5076 4999 4923 4849 4776 4704 4633 4564 4495 4428 43^1 i ^ 5 J 53 5 7 5 499 s 4922 4848 4775 4703 4632 4565 4494 4427 436* \ ^ 5073 4997 4921 4847 4774 "4702 4631 4562 4493 4426 4359 5150 5072 4995 4920 4845 4772 4701 4630 4560 449 z 4425 4358 | 5'49 5071 4994 4918 4844 47/1 4699 4692 4559 4491 4424 4357 i S. h m h m h m h m li m h m h m h m h m h m h m h m c 54' o'55"o56' 0*57' o 58 o 59 I* 0' 1 I i y 3' I? A' 1 2 "' TABLE XXV. PROPORTIONAL LOGARITHMS. | h Ttxl h m i m m i m h m h m h m h m i m \ h m n in i S i 6' Q i Q g, a 9 10' ii' 9 12' 9 i3' Q '4' Q jsj i 1 6' 3 17' o 4357 4292 4228 4164 4102 4040 3979 3919 3860 3502 3745 3686 | i 435 6 4291 4^7 4163 4101 4 3 9 397* 3919 3*59 3801 3744 3687 : 2 4355 4290 4226 4162 4100 4038 3977 39i* 3*58 3800 3743 36^6 3 4354 4289 4224 4161 4099 437 3976 3917 3*57 3799 374* 3685 ] 4 4353 4288 4223 4160 4098 4036 3975 39 l6 3*S6 m* 374i 3684 i 5 4352 4287 4222 4159 4097 4035 3974 3915 3*56 3797 3740 3683 6 43 5 4** 5 4221 4158 4096 434 3973 39H 3*55 379 6 3739 3682 7 43 *! 42*4 4220 4*57 4095 4033 3972 3913 3*54 3795 3738 36*1 8 4349 4283 4219 4156 4093 4032 3971 3912 3*53 3794 3737 3680 9 4347 4282 4218 4155 4092 4031 39/c 39" 3852 3793 3736 3679 10 4346 4281 4217 4154 4091 4030 39 6 9 3 9 to 3*5i 3792 3735 3678 ii 4345 4280 4 2l6 4153 4090 4029 3968 3909 3*50 3792 3734 3677 12 4344 4279 4215 4153 4089 40^8 39<>7 3908 3*49 379 1 3733 3677 J 3 4343 4*7* 4214 4151 4088 402- 3966 397 3*4* 3790 3732 3676 r 4 4342 4277 4213 4150 4087 4026 -39 6 5 3906 3*47 37*9 373i 3675 15 434i 4276 4212 4149 4086 4025 39 6 4 3905 3846 37** 3730 $6H 16 434 4*/5 4211 4H7 4085 4024 39 6 3 394 3*45 3757 37*9 3673- : 17 4339 4274 42IO 4146 4084 4023 3962 3903 3*44 3786 37*8. 3 6 7* i 18 4^8 4*73 4209 4 1 45 4083 4022 3961 3902 3*43 37*5 3727 3671 19 4336 4271 4207 4144 408? 4021 3960 390i 3*42 37*4 3727 3670 : 20 4335 4270 4206 4143 4081 4020 3959 3900 3841 37^3 3726 3669 21 4334 4269 4205 4142 4oSo 4019 395* 3^99 3840 3782 37*5 36.68 : 22 4333 4268 4204 4141 4079 4018 3957 3 8 9 b 3*39 37?I 37*4 3667 23 43 3 ^ 4267 4 2 3 4140 4073 4017 3956 3*97 38}* 3780 37*3 3666 24 433 T 4266 4202 4139 4077 4016 3955 3*96 3*37 3779 372* 3665 j *5 4330 426^ 4201 4138 4076 4015 3954 3*95 3*3^ 3778 3721 3664 26 4329 4264 4200 4i37 4075 4014 3953 3*94 3835 3777 3720 3663 1 27 43 zS 4263 4/99 4i36 4074 4013 395* 3*93 3*?4 3776 3719 3 6 ^3 z8 4327 4262 4198 4i35 4073 4012 395 1 3*92 3833 3775 37i8 .66; 29 43^6 4261 4197 4 T 34 4072 4011 3950 3*91 3532 3774 3717 3661 30 4325 4260 4196 4133 4071 4010 3949 3890 3773 37> 6 3660 3i 43*3 4259 4 i 9 c 4*32 4070 4009 394* 3880 3*3 3772 3715 3^59 32 4322 4 2 S 8 4194 4131 4069 4008 3947 3*88 3829 3771 3714 ^S 33 4321 4256 4*93 4130 40 5 ; 4007 394 6 3887 3828 3770 3713 3657 34 4320 4255 4192 4129 4067 4006 3945 3886 3*27 37<>9 371* 3656 35 4319 4254 4191 4128 4066 4005 3944 3885 3826 3768 37U 3655 I 3<5 43i8 4*53 4189 4127 40^5 4004 3943 3884 3*2^ 3/ 6 * 57io 3654 1 37 43*7 425- 4188 4120 4c6 4 4003 3942 3883 3824 3767 3709 3'J53 . 33 43x6 4251 4187 /j.1 2 > 4063 4002 3941 3*82 3*23 3766 3709 3652 39 4315 4250 4i8f 4124 4062 400 1 3940 388: 3822 3_7j }7o8 3 6 5i 40 43H 4249 4185 4'22 4061 4000 3939 jfeb 3*21 3764 3707 36$0 4 1 43^3 4248 4184 4121 4060 3999 393 s 379 3820 37^3 370.6 3649 42 43*i 4247 4183 4I2O 45*9 399* 3937 3878 3820 376:. 3649 43 43 10 4246 4182 4119 40^8 3997 3936 3*77 3819 3761 3704 3648 44 4309 4245 418 41 lb 4056 399 6 3935 3876 3*iS 3/ 6 3703 347 45 4308 4244 4 iBc 411" 40-5 3995 3934 3^75 3 8 ' 7 3759 370Z 3646 46 4307 4 2 43 4 l 7 c 411 40^4 3993 3933 3816 375* 3/01 3'>45 47 4306 4241 4178 4^5 453 399?- 393* 3*73 381,' 3644 48 4305 4240 417- 4114 /o-:. 599' 393i 3*72 3'4 3643 49 43C4 4239 4 '7 411 4051 3930 3871 3813 37v< 3 :; 4i 50 43Q3 47.38 4112 4050 39*9 3929 3870! 3812 3754 3697 3641 5i 4302 42.37 417 411 4040 3988 3928 3869 3811 3753 ^696 3640 52 430i 4136 417 411 4H8 3-9*7 39*7 3868 3810 3752 3^951 3639 53 4300 4235 4 1 / 410 4047 3986 39*6 3*67 3800 375 ' 3^94 3638 j 54 4298 4234 4*7 410 4046 39*5 39*:> 3866 3808 3750 3693 3637 1 55 4297 4 2 33 416 410 4045 39*4 3924 3865 3*07 3693 3636 56 4296 4232 416 4 1 o 4044 39*3 3923 3*64 .3806 ^692 3635 57 4295 42 3 r 416 410 4^43 39*2 3922 3.8.c 5 ^691 3635 58 4294 4230 416 4104 398r 3921 374, 3690 3634 59 4293 4229 4'I-(j 4*01 404.1 3980 ,3920 3861 T4" 3689 3633 60 4292 4228 416 4. 1 02 4040 3979 39'9 3860 3^ 3632 S h m h m h rr h. m h m h m h n h m h m h m 'i m h m i 7 jO i 9 1 JO 1 IT r 12 i 3 13' I' I4'it iV . i&fi 17' ' : TABLE XXV. PROPORTIONAL LOGARITHMS. mjh m i m i m j m m i m i m i m h m > m m , s 1 8' i r 19' 20' z\' " 22' 23' 9 24' <*5' 26' t 27' aS' 29' o 3632 35/6 3522 3468 34 i 5 362 310 3 2 59 3208 3158 1 08 059 i 3631 35/6 3 5 2I 3467 34H 3361 3309 3258 3207 315? 107 058 z 3630! 3575 3520 3466 34'3 360 308 3257 206 3i5 6 106 Oj7 3 3629! 3574 3519 34 6 5 3412 359 307. 3256 zof 3155 105 056 4 3628 3573 351* 3464 34" ^358 306 3255 204 3154 105 056 5 36-27 3572 3517 34^3 34ro 358 306 3254 3204 3*53 104 55 6 3626 357i 3516 34 6 3 3409 3357 3305 3253 3203 3153 103 054 7 3625 3570 3515 3462 3408 335^ 3304 3253 3202 3152 102 053 8 3624 35 6 9 35M 346i 3408 3355 3303 3252. |20I 3i5i IOI 052 9 3623 3568 35*4 3460 347 3354 3302 3251 3200 3150 101 052 10 3623 3567 35*3 3459 3406 3353 3301 3 2 5 3199 3H9 IOO 051 ii 12 3622 3621 3566 3565 3512 35ii 345* 3457 3405 3404 3352 335i 3300 3300 3249 3248 3198 3198 3148 3H8 099 09? 050 049 13 3620 3565 35io 3456 343 335i 3299 3247 3197 3147 097 3048 H 3619 3564 3509 3455 3402 3350 3298 3247 3196 3H6 096 3047 15 3618 3563 35o8 3454 34oi 3349 3 2 97 3246 3195 3H5 096 3047 16 3617 35^ 3507 3454 3400 3348 3296 3 2 45 3194 3144 3095 3046 17 3616 3561 3506 3453 3400 3347 3295 3244 3193 3H3 3094 345 tl 3615 .3560 2506 3452 3399 3346 3294 3*43' 3193 3H3 3093 344 19 3614 3559 3505 345 1 339* 3345 3294 324- 3192 3142 3092 3043 20 3613 355^ 354 3450 3397 3345 3293 3242 3*9 T 3H 1 091 3043 21 3 6!2 3557 3503 3449 339 6 3344 3297. 324 r Sift 3H 09! 3 42 22 3611 3556 352 3448 3395 3343 3291 3240 3'&9 3 J 39 090 3041 *3 3610 3555 35i 3447 3394 3342 3290 3239 3188 3138 089 3040 24 3610 3555 3500 3446 3393 3341 3289 3*38 3188 3138 088 3039 = 5 3609 3554 3499 3446 3393 3340 3288 3237 3187 3137 087 3039 26 5608 3553 3498 3445 3392 3339 3288 3236 3186 3136 3087 3038 27 3607 3552 3497 3444 339J 3338 3287 3236 3185 3135 3086 3037 28 3606 3551 3497 3443 3390 3338 3286 '235 318^ 8i34 3085 3036 _iL 3605 355 3496 3442 3389 3337 3285 3234 3183 3133 3084 3* 30 3604 3549 349 3441 33S8 3336 3284 3233 3183 3'33 3083 334 3i 3 6 03 3548 3494 344 338 7 3335 3283 3232 3182 3132 3082 3034 3* 3602 3547 349 3439 3386 3334 3282 3231 3181 3i3i 3082 3033 33 3601 3546 349 34-38 33*6 3333 3282 3231 3180 3130 3081 303* 34 3600 3545 349 343* 3385 3332 3281 3230 3179 3129 3080 3031 35 3599 3545 349 3437 3384 3332 3280 3229 3178 3129 3079 3030 36 359?! 3544 348 3436 333 333^ 3279 3228 3178 3128 3078 3030 37 359* 3543 ,48 343^ 3382 3330 32/8 3227 3i77 3^27 307? 3029 3? 359" 354* 348 3434 338i 3329 3277 3226 3176 3126 3077 3028 39 3596 354 348 3483 338o 3328 3276 3225 3175 3125 3076 3027 40 3595 3540 348 3432 3379 3327 32/6 3225 3174 3124 30/5 3026 4 1 3594 3539 348 343i 3379 3326 3275 3224 3i73 3124 3074 3026 42 3593 3538 348 343 3378 3325 3274 32*3 3173 312 3073 3025 43 3592 353 348 3430 3377 3325 3273 3222 3172 3122 307 3024 44 359 1 353 348 34-9 3376 3324 327a 322 3171 312 3072 3023 45 359 353 348 5423 3375 3323 3271 3220 3170 312 307 3022 46 3589 353 348 342" 3374 3322 3270 322 3169 3U 3070 3022 47 3588 353 348 34* 3373 332 3270 321 3168 3" 306 3021 48 3587 353 347 342 3372 3320 3*69 321 3168 311 306 3020 49 3587 r 353_ 347 3424 337 33i 3268 321 3167 311 3c6 3019 5'o 3536 353^ 347 342 337 33 1 3-267 321 3166 3U 306 "3018 5i 3585 3530 347 342 3370 33i 3266 321 3165 3n 306 3018 52 3584 3529 347 342 336 33* 3265 321 3164 3 11 306 3017 53 3583 3528 347 342 336 33i 3265 321 3163 3ii 306 3016 54 3582 3527 347 342 336 33* 3264 321 3163 311 306; 3015 55 358i 3526 347 34i 336 33i 3263 321 3162 311 306' 30H I 56 358o 3525 347 34 x 336 33i 3262 zai 316! 3" 306 3 OI 4 57 3579 352; 347 34i 336 33i 3261 321 3160 3ii .306 3 01 3 53 3578 35^4 347 341 336 33i 3260 320 3i5 f 3" 306 3012 59 3577 3523 346< | 34 1 336 33i 325? 3 20C 1 3TS 310 306 3011 "Co j 3576 3522 346^ 34 1 336 33i 325^ 320^ 5 315 310 305 3010 S h mjh m h n i h rr h rn h IT h n h n i h n h h h m i** iS'ji? 19 I* 20 'lt 2 1 2 1-2 1-24 l*j ' 1 2( 1 2 i 2 i 29' TABLE XXV. PROPORTIONAL LOGARITHMS. h ID h m h m h m h h n i h n i h rn i h h i h i n h m s ! 3 i 31 ' i 32 i 3 1 3 ' 35 ' i 3, o 301 29 '>2 291 286 252 277. 273< > 268 5 264 259 255 - 2510 i 300 2962 291 286 282 277 5 272 ) 268- 1 264 259 2 55 i 2509 2 300 2961 291 286 282 277 272 268 J 263 259 '55 i 2508 3 300 2960 291 286 28l 277 272 268 3 263 259 2 55 i 2507 300 29S9 201 286 28l 27- 272 26^: i 263 2<9 2 55 -j 2507 c 300 2958 201 286 z8i 277 272 268 263 259 2 54 9 2506 6 300 29^ 291 286 281 277 272 268 i 263 2 59 254 3 2505 7 300 295 290 286 281 277 272 268c > 263 259 254 i 2504 8 300 295 290 286 281 276 272 267$ > 263 259 2 54 / 2504 9 300 295 290 286 281 276 272 267* 263, 2 59< 254 3 2503 10 300 295 290 286 281 276 272 2078! 263 2 5&< 254 5 2502 ii 295 290 28S 281 276 272 267/1 263 258^ 254. 5 2502 12 300 295 290 285 281 276 272 2676 263 258^ 254. 2501 13 300 295 290 285^ 281 276 272 2675 263 25*' 2 54; 2500 14 299 295 290 285 281 276 271 2675 2530 258^ 254: 2499 1 5 209 295 290 285 281 276 271 2674 2629 2585 254 = 2499 ! ' 16 290 290 285 280 276 271 2673 2629 2585 2541 2498 j !7 299 294 290 285 280 276 271 2672 262.8 2584 2540 24.0*7 1 18 2 99 294 290 2o }i 280 276 271 2672 2627 25^3 25^0 2 497 | 19 2 99 294 2900 285 280 276 271 2671 2626 2 5 8 3 2539 2496 20 299 294 2899 285 280 276 271 2670 2626 2582 2 53^ 2495 i 21 299 294 2898 28s 280 276 -714 2669 2625 2581 2538 2494 j 22 299 294 2898 28s 280 275 2713 2669 2624 2580 2 537 2494 | -3 299 294 2897 28so 2804 275 2713 2668 z6zq 2580 2536 2433 24 299 294 2896 2849 280 275 2712 2667 2623 2579 2535 2492 299 294 2895 2848 2802 2756 2711 2666 2622 2 57 S 253; 2492 j 26 298 294 2894 2848 280 2756 2710 2666 2621 2577 2534 2491 i ; 27 298 294 2894 2847 280 2755 2710 266; 2621 2577! *533 2490 | 28 298^ 2940 28q2 2846 2845 2800 2799 2754 2753 2709 270'^ 2664 2663 2620 2619 -576 2575 2533 2532 2489 | 2489- 3 2986 2939 2891 2845 2798 *753 2707 2663 2618 2574 2531! 2,8.8 3 1 2985 2938 2891 2844 2798 2752 2707 2662 2618 2574 2530 2487 j 32 298 2937 2890 2843 2797 2751 2706 2661 2617 2573 2530 2487 33 2084 2936 2889 2842 2796 2750 -705 2660 2616 2572 2529 2486 34 2983 293- 2888 2842 2795 2750 2704 2660 2615 2572 2528 2485 35 2982 2935 2887 284, 2795 2749 2704 2659 2615 2571 2527 2485 36 2981 2934 2887 2840 2794 274* 2703 2658 2614 -570 2527 2484 37 2981 2933 2886 2839 2793 2747 2702 2657 2613 569 2^26 2483 2980 2932 288q 2838 2792 2747 2701 2657 2612 569 2525 24*2 ; 39 2979 293. 2884 2838 2792 2746 2701 2656 2612 503 2s25 2482 | 40 2978 2931 2883 2837 2791 2745 2700 1655! 2611 S67 2, -24 2481 2 977 2930 2883 2836 2790 2/44 2690 2655' 2610 566 2 5 2: 2480 42 2977 2929 2882 283^ 2744 2698 2654 2610 566 2 5 22 2480.: 43 2976 2928 288l 2835 2788 2/43 2698 2653 2609 56; 2522 2479 ! 44 2975 2927 2880 2834 2788 2742 2697 2652 2608 5<>4 252) 2478 , 45 2974 2927 2880 2833 2787 2741 2696 2652 2607 2564 2520 2477 1 46 2973 2926 2879 2832 2786 2741 2696 2651 2607 2563 2520 2477 j 47 ^973 2925 2878 2831 2785 2740 2695 2650 2606 2562 2519 2476 i 48 2972 2924 2877 2831 2785 2739 2694 2649 26os 2561 2 5 I* 2 475 j 49 2971 2924 2876 2830 2784 269? 2649 2604 2561 2517 2475 j ; 5 2970 2923 2876 2829 2783 2738 -.692 2648 2604 2560 2517 2474 5 r 2969 2922 2^7S 2828 2782 2737 2692 2647 2603 2559 2516 2 473 2969 2921 2874 2828 782 736 691 2646 2602 25 sS 251 ; 2472 53 2968 2920 -873 282/ 781 735 2690 2646 2601 2515 2472 : 54 2967 -920 2873 2826 780 73S 689 264s 2601 2 5 j7 2514 2471 55 2966 2919 2872 2825 779 734 689 2644 2000 2556 251? 2470 56 2965 .918 2871 2825 779 733 688 2643 25991 55* 2^12 2-? 5 1650 161? 8 1979 194 1903 1866 l82Q 179 1750 1720 1684 1649 1614 9 1978 194 10 i86 5 1828 179 1755 I7I9 1684 1648 1613 10 '977 193 1902 186 1828 179 1755 1719 1083 164^ 1613 ii 1977 '93 1901 1864 1827 179 J 754 17!' 1683 1647 1612 12 1976 193 1901 1863 1827 179 1/54 171-. f62 1647 1612 XI I97S r 93 1900 186 1826 178 i/ S. I7 T 7 1681 1640 1611 14 !975 193 1899 1862 1825 178 1752 1717 1681 164^ i6ro 15 .1974 193 iS'99 1862 1825 178 1752 1716 1680 1645 1610 16 1974 193 189*5 186 1824 17* 1751 J7I5 1680 164^ 1609 17 J 973 193 1898 1860 1823 178 175 1715 1670 1644 1609 18 1972 1974 1897 1860 1823 1786 T 75Q 1714 1678 1643 1608 19 1972 193 1896 1859 1822 178, i 7 49 1714 1678 1643 1607 20 I9"i T 93 1896 1859 1822 1/8 J 749 1713 6;; 1642 1607 21 1970 J 933 1895 i8<8 iSfci 1785 1748 1712 1677 1641 1606 22 19^0 193- T8-H i8S7 1820 1784 1748 1712 1676 1641 1606 23 1969 1931 1894 1 8, -7 1820 1783 1747 1711 1676 1640 1605 24 1968 193 1893 i 5 6 1819 1783 1746 171: 1675 1640 1605 25 1968 1930 i*93 r8$ 5 1819 1782 1746 1710 1674 1639 1604 26 1967 1929 1897. .855 1818 1781 1745 1-709 1674 1638 1603 27 1967 1929 1891 i8 H 1817 1781 1745 1709 1673 1638 1003 28 1966 192* 1891 1854 1817 I 7 ': C '744 1708 1673 1637 1602 2 9 1965 1928 1890 1853 1816 1780 174? I70> 1672 1637 1602 30 1965 1927 1889 1852 1816 1770 1743 1707 1671 1636 1601 ! 31 1964 1926 1889 1852 1815 1773 '74* 1706 1671 1635 1600 ! 32 1963 1926 1888 1851 1814 I7?8 1742 1706 1670 r ^35 1600 33 1963 1925 *3S8 1850 1814 1777 1741 170^ 1670 1634 '599 34 196:1 1924 1887 i843 (l 1403 i37o 1337 1304 1271 1239 20 1572 1538 1503 1469 1456 1402 1369 1336 1303 1271 1239 21 1571 1537 i53 1469 H35 1402 1368 '335 1503 I2 7 C 1238 22 1571 1536 1 502 1468 H35 1401 1368 1335 1302 12/0 1238 23 I5 7 c 1536 1502 1468 J 434 1401 1367 ^334 1302 1269 1237 24 1570 1535 1301 1467 H33 1400 1367 1334 1301 1269 1237 25 1569 1535 1500 1467 J43.? J 399 1366 1333 1301 I?-68 1236 26 1569 1534 1500 1466 *43- J 399 1366 1333 1300 1268 "35 27 i S 6b 1534 1499 4*$ i43^ 'J98 1365 i,'3 2 1300 1267 1235 28 r>6 7 1533 1499 146; J 43i I3Q8 1365 133^ 1299 J26 7 1234 29 1567 i;32 1498 1464 r 439 1397 1364 i33i 1298 1266 1234 30 ^566 *532 1498 1464 H3Q '397 1363 i33i 1298 1266 i*33 31 1566 i53i 1497 1463 1429 1396 1363 1330 1297 1265 1233 3^ ,J56<; '53J 1496 1463 1429 1396 1362 1329 1297 1264 1232 33 1565 1530 1496 1462 1428 1395 1362 1329 1296 1264 1232 34 1564 r 53 H95 1461 14^ 1394 1361 1328 1296 1263 1231 35 fS<3 1529 '495 1461 1427 1394 1361 1328 1295 1263 1231 36 1563 1528 1494 1460 i4 2 7 1393 1360 1327 1295 1262 1230 37 1562 1528 1494 1460 1426 1393 1360 1327 1294 1262 1230 3 1562 W H93 T 459 1426 1392 J359 13^6 1294 1261 1229 39 1561 1527 H93 *459 1425 J 392 '359 1326 1293 1261 1229 40 1561 1526 1492 MS* 1424 1391 1358 1325 1292 1260 1228 4i 1560 1526 1491 '45* 1424 I39 1 1357 r 3 2 5 1292 1260 1227 42 J 559 1525 1491 H57 J 423 139 I3S7 1324 1291 1259 1227 43 1559 1524 1490 1456 142^ 1389 1356 J3*3 1291 1259 1226 44 55 8 i5M 1490 1456 1422 13^9 130 1323 1290 1258 1226 45 1558 15*3 1489 1455 1422 1388 J 355 1322 1290 1257 1225 46 1557 1523 1489 T 455 1421 1388 J 355 132* 1289 1*57 J22 5 47 1556 1522 1488 J 454 1421 1387 J 354 1321 1289 1256 1224 48 1556 1522 1487 H54 1420 1387 1354 1321 1288 1256 1224 49 1555 1521 1487 '453 1419 1.386 1353 1320 1288 1255 122? 5 J 555 1520 1486 1452 1419 1386 1352 1320 1287 1 2; 5 1223 5? *554 1520 1486 1452 1418 13 ? 5 1352 1319 1287 1254 1222 5* 1554 1519 148*; 1451 1418 13*4 I35 1 1319 1286 I2 54 1222 53 '553 1519 148 s 1451 1417 '384 135* 1318 1285 1*53 1221 54 1552 1518 1484 1450 1417 1383 1350 1317 1285 I2 53 1221 55 1552 Mi* 1483 1450 - 1416 W83 1350 1317 1284 1252 I22O 56 >55i I5i7 1483 M49 1416 1382 1349 1316 1284 1252 1219 57 i55i 1516 1482 1449 1415 1382 1349 1316 1283 ? 2 5* 12J9 58 1550 1516 1482 1448 1414 i.3*i ms 1315 1283 1250 1218 59 1550 '5*5 1481 1447 1414 1381 1348 1315 1282 12^0 12l8 60 1549 I5i5 1481 1447 Ui3 1380 1347 i3H 1282 1249 1217 S. h m h m li rn h m h m h m I K m h m h m h m h m . ** 5') 2 6') 2 Q ?' Z- 8' * 9' 2 Q 10' 2 II' 2 12' i 13' 2*14' 2 6 15' TABLE XXV. PROPORTIONAL LOQARITHMS. ii ru Ii r.i ii in 1, in h in | ii m j h m Ii m j (i m h m h m i s. ^ 1 6' }J M' 2 IS' 2 y 19' i 2..' 2 *l'-l w 22' ** 23'' I2 4 ' i2 '2 5 ' 1 26' o 1217 1186 1154 1123 I0 9 I 1061 1030 0999 0969 93-' 0909 i 1217 i i8s M53 1122 1091 io6c 1029 99 v 969 939 909 2 . 1216 1184 1153 1122 I09C 1060 1029 998 9 68 3 1216 1184 1121 logo 10^9 1028 998 9 68 938 908 4 *5 1183 1152 /12L loVo 1058 1028 997 967 9^7 907 5 1215 1183 1151 I12C jo8v 1058 1027 997 967 937 907 6 1214 1182 1151 I 119 i oS i 1057 1027 996 9 66 936 906 7 1214 1182 IlfO 1119 108^ 1057 1026 996 966 936 906 8 1213 1181 1150 1118 1087 1056 1026 995 965 93S 905 9 1213 1181 1140 iu^ 10^7 1056 1025 995 965 935 905 10 1212 1180 1149 1117 1086 10 55 1021; 0994 0964 0934 0904 n llll 1 1 80 1148 1117 1086 1055 1024 994 964 934 904 12 I2II 1179 -1148 Hit 108: 1024 993 963 933 93 13- 1210 1179 1147 1116 1085 1054 1023 993 963 93 H 1210 1178 1147 iii- io s 4 IQ53 10.? 3 992 962 932 902 15 1209 1178 1146 1115 1084 1053 1022 992 9 62 93^ 902 16 I2C9 1177 1146 1114 108;- 1052 IO22 991 9 6l 93^ 901 17 120i 1177 114; 1114 1083 1052 1021 991 96l 901 18 1208 1176 1145 1 1 1 ? ICS: 1051 IO2I 990 960 93^ 900 19 I2D7 1175 1144 IIJ 3 io8i 1051 1020 990 960 900 20 1207 1175 "43 1112 I Oft) 10^0 JO20 0989 959 0929 0899 21 1206 1174 1143 1112 1081 1050 ioj 9 989 959 929 899 22 1206 1174 114: 111 I 1080 1049 1019 985 958 928' 898 23 1205 1173 1142 mi 1080 1040 1018 988 9^8 928 898 24 I2C5 1173 1141 I 1 1C IC79 1048 1018 987 957 927 897 *5 1204 1172 1141 IIIO 1079 1048 1017 987 95" 927 8 9 7 26 1204 1172 1140 HOC 1078 1047 1017 986 9^6 926 896 27 I2O3 1171 1 140 1109 1078 1047 1016 986 956 926 896 28 1202 1171 1139 I 10? 1077 1046 1016 98,- 9<5 925 895 29 I2O2 1 170 IT 39 noS 1076 1046 1015 985 955 925 895 ! 30 (201 1170 1138 IIC7 1076 1045 1015 0984' 095:4 0924 0894 31 1201 1169 1138 1106 1075 1045 1014 984 954 924 894 3 1 12OO 1169 1137 1106 1075 1044 1014 983 953 9-3 893 33 I2QO 1168 IIO^ 1074 1044 1013 983 953 893 34 II 99 1 1 68 1136 IIOs 1074 1043 1013 982 9^-2 922 892 35 II 99 1167 1136 1104 1073 1043 1012 982 95 2 922 892 .36 IIQ8 1167 JI 35 1104 1073 1042 IOI2 981 95 1 921 89! 37 1198 1166 H35 1103 1072 1042 ion 981 921 891 38 1197 1165 i 1 34 1103 1072 1041 ion 980 950 920 890 39 II 9 7 11(35 1134 1102 1071 1041 IOIO 980 950 920 890 - 40 1196 1164 1133 Hp2 1071 1040 1009 0979 0949 0910 0889 I 196 1164 1132 IIOI 10701 104*0 1009 979 949 919 889 42 II 9 5 1163 1132 I1OI 1070 1039 1008 978 948 9iX 888 I 43 1195 1163 IJL 3 T IIOO 1069 1039 1008 978 948 918 888 44 1194 1 162 1131 noo 1069 1238 1007 977 947 917 887 1 45 1193 1162 1130 1099 1068 1037 1007 977 947 917 887 46 1193 1161 1130 1099 1068 1037 1006 976 946 916 886 ; 47 II 9 2 1161 1129 1098 1067 1036 1006 9-76 946 916 886 , 48 1192 1160 1129 1098 1067 1036 1005 975 945 9*5 885 ! ! 49 II9I 1 1 60 1128 1097 1066 1035 1005 975 945 9V5 885! 50 I 19* n 59 1128 1097 1066 1035 1004! 0974 0944 0914 0884 j 5 1 H9O 1159 1127 ^096 1065 1034 IC04. 974 944 914 884! i 52 1190 1158 TI27 1096 1065 1034 1003 973 943 913 883 i 53 1189 1158 I 126 1095 1064 IP 3 3 1003 943 913 883 j 54 r 189 1157 1126 IO 9S 1064 1033 1002 972 942 912 883 55 1188 1157 II2 S 1094 1063 1032 IOO2 972 942 912 882 | 56 1188 us6 1094 1063 1032 IOO1 971 941 911 882 1 57 1187 1156 1124 1093 1062 1031 1001 97i 941 91 1 8?t 5* 1187 1155 1724 1092 1062 1031 IOCO 970 94 910 88 1 59 1186 1154 1123 1092 1061 1030 I COO 970 940 910 880 1 60 n36 H54 1123 1091 ic6f 1030 09 9 9' 0969 939 0909 0880 S. h rn h m h m h rn h m h m h m h m h m h m h m i Z Q I 6' 2 17' , -? / -,O , , ' O , ~.' L 2O 2 21' ,*,2' 1 2 2 3 : c 2 -i ' 22 S ' 2'': TABLE XXV. PROPORTIONAL LOGARITHMS. h m h m h m h m h m h m h m h m h m h m h m | s. 1 27' i 25' 2 2 9 ' 2 }0' 2 3i ; 2 31' 2 33' 1 34 ^35' I" 3 0' zo / 0880 0350 02I 07'>2 0763 0734 0706 0678 0649 0621 0594 i 879 850 820 791 762 734 705 677 640 621 593 z 879 849 820 7 9 I 762 733 705 677 64 621 593 3 S 7 3 849 819 790 762 733 7: 676 648 620 59 2 4 8 7 5 84* 819 79 761 732 704 676 64- 620 592 5 8?7 848 818 789 73 2 703 675 ' 64, 619 59i 6 877 847 to 8 789 73 1 73 675 647 619 59i 7 876 3 4 7 817 788 760 731 73 674 646 6r8 591 8 876 846 817 .8 759 73 702 674 64!. 618 590 9 875 846 816 787 759 730 702 673 645 617 59 10 0875 0845 0816 078? 0758 0730 0/0 0673 '064; 0617 0589 IX 874 845 816 7*7 758 729 701 672 644 616 589 IZ 874 84.; 8if 786 757 729 700 672 644 616 588 13 873 844 l l > 786 757 .728 700 671 643 615 588 14 873 843 814 7*5 756 728 699 671 643 615 'S 8 ?- 15 872 843 814 785 756 727 699 670 642 615 587 16 871 842 ! 13 784 755 727 698 6 7 o 642 614 586 17 871 842 813 78 4 755 726 698 670 641 614 586 18 871 841 812 783 7^4 726 697 669 64, 613 5^5 19 870 841 812 783 _754 725 697 669 641 613 5^5 zo 0870 0840 o3n 07?2 0753 0725 0606 066* 064: 0612 05*5 i 2I 869 84.0 Su 782 753 724 696 668 640 612 584 22 869 839 810 781 752 724 695 667 639 6 ij 58 4 *3 868 839 8xo 781 752 723 695 667 6 39 611 583 2 4 868 838 809 780 75^ 723 695 666 638 610 583 *5 867 838 809 780 751 722 694 666 638 610 58z 26 867 837 808 779 75i 722 6 94 665 637 609 5*z 17 866 37 808 779 750 721 693 665 637 609 58i 28 866 836 807 778 750 727 693 664 636 609 581 ' 29 865 836 807 778 749 721 692 664 630 60'^ S*o 30 o86s 0835 0806 0/77 0749 0720 0692 0663 0635 0608 0580 31 864 835 806 777 748 720 691 663 635 607 579 3* 864 834 805 776 748 719 691 663 635 '6QJ 579 33 863 834 805 776 747 7I 9 690 662 634 606 579 34 863 834 804 775 747 7 l8 690 662 634 606 578 35 862 833 804 775 746 718 689 661 633 605 578 36 862 83? 803 774 7 4 6 717 689 661 633 605 577 1 37 861 8 3 z 803 774 745 71- 683 660 632. 604 577 33 86 1 832 802 774 745 7 I6 688 660 632 604 5/6 39 860 831 802 773 744 716 687 659 63, 603 576 40 0860 0831 0801 0773 0744 0715 0687 0659 0631 0603 0575 41 859 830 Soi 772 743 715 686 658 630 602 575. 4* 859 830 80 1 772 743 714 686 658 630 602 574 43 8 = 8 829 800 771 742 7H 686 657 629 602 5/4 I 44 858 829 800 771 742 713 685 657 629 601 573 45 857 828 799 770 74i 713 685 656 628 601 573 46 857 828 799 770 741 712 684 656 628 600 573 47 856 8*7 79 769 740 712 684 655 628 600 572 856 827 798 769 740 711 6?3 655 627 599 572 49 855 826 797 768 740 7i 683 655 627 599 57i 5 o*55 0826 0797 0768 0/39 0711 0652 0654 0626 0598 057i 5i S 5 5 825 796 76 7 739 710 682 654 626 598 570 5* 854 825 796 767 738 7K 68 1 653 625 597 570 ! 53 854 824 795 766 738 709 681 653 625 59.7 569 j ' 54 853 824 795 766 737 709 680 6<2 624 596 569 1 55 853 823 794 76s 737 708 680 6,2 624 596 568 j 1 56 852 823 794 765 736 708 679 651 623 596 568 ! 1 57 85. 822 793 764 736 707 679 651 623 595 5 68 i ! 5* 851 [ 822' 793 764, 735 707 678 650 622 595 567 | 59 J*5i 82, 792 763 735 706 678 650 622 594 567 j J 6o 0850' 082J 0792 0763. 0734 0706 0678 0649 0621 0594 0566 i S. h m h rn h m h m h m : h m h m h m h m h m h m : .12 7 ' 1 Z?,' ,0 -, , 1 > 30' a 2" g *33' z" H' 2 35' 36' TABLE XXV. PROPORTIONAL LOGARITHMS. i m h m h m > m i m h m h m h m i rn h m h m I s. 4 38' - 7 39' 4 c 2 4 I' "42 i 43'.2 Q 44' z 45 ' 2 46 *, 47' '. 4 y 0566 0539 0512 0484 0458 043 1 0404 0378 035 2 0326 0300 i 566 538 511 484 457 43 i 44 377 351 325 299 2 $65 548 511 484 457 430 4 3 377 '35* 325 299, 3 :5?5 537 510 483 456 430 403 377 35 3M 298 4 564 537 510 483 456 429 43 376 350 324 2 9 S 5 564 536 509 482 455 429 402 376 349 323 297 6 563 536 509 4 8 2 455 428 402 375 349 323 297 7 563 536 508 48l 454 428 401 375 349 323 2 9 7 S 562 535 508 4 8l 454 427 401 374 348 322 296 9 562 53 5 507 480 454 427 400 374 348 322 296 10 CK62 0534 0507 0480 0453 0426 0400 0374 0347 0321 c2 95 ir 5 6l 534 57 480 453 426 399 373 347 321 295 12 5 6l 533 506 479 452 426 399 373 346 320 294 13 560 533 506 479 45* 425 399 372 34 6 320 294 H 560 532 505 .4/8 45i 425 398 372 34^ 39 294 15 559 532 55 478 45* 424 398 37* 345 3i9 293 16 559 53i 504 477 450 424 397 37i 345 319 293 17 558 53i 54 477 450 423 397 370 344 3^8 292 18 558 53i 53 476 450 4*3 396 37^ 344 3i8 292 19 557 53C 503 4/6 449 422 396 370 343 3i7 291 20 0557 0530 0502 0475 0449 0422 0395 0369 0343 0317 0291 21 557 529 502 475 448 422 395 369 34* 316 291 22 5<6 529 502 475 44* 421 395 368 342 316 290 23 556 528 501 474 447 421 394 368 34 2 316 290 M 555 528 501 474 447 420 394 367 34 1 3^5 289 25 555 527 500 473 446 420 393 367 34 1 3*5 289 26 554 527 500 473 446 41$ 393 366 34 3 J 4 aW 27 554 5^6 499 472 446 419 392 366 340 314 288 28 553 526 499 472 445 418 392 366 339 313 288 29 553 526 498 47i 445 418 391 365 339 313 _i!z 30 0552 052=; 0498 0471 0444 0418 39 J r036<; 339 0313 0287 31 55* 5^5 498 47i 444 4 J 7 39 1 364 338 312 286 32 552 5*4 497 470 443 4'7 390 364 338 312 286 33 55i 524 497 470 443 416 390 363 337 3u 285 34 55 1 523 496 469 442 416 389 363 337 3U ZS 5 35 55 523 496 469 442 4*5 389 363 336 310 285 36 550 522 495 4*8 442 4*5 338 362 336 3io 284 37 549 522 495 468 441 4*4 388 362 336 3io 284 38 549 521 494 467 441 414 388 36i 335 39 283 39 548 521 494 467 440 414 387 361 335 309 283 40 0548 0521 0493 0467 0440 0413 03*7 0360 0334 0308 0282 4i 547 520 493 466 ; 439 4*3 386 360 334 308 282 4* 547 520 493 466 439 412 386 360 333 37 282 43 546 5i9 492 465 43.8 412 3^5 359 333 37 . 281 44 546 519 492 465 43$ 411 385 359 333 307 281 45 546 518 491 464 438 411 384 358 332 3c6 46 545 518 491 464 437 410 384 35* 332 306 280 47 545 5*7 490 463 437 410 384 357 S3 1 35 279 48 . 544 517 ; 490 463 436 410 .383 3<7 33' 305 279 49 544 517 .4^9 462 436 409 3^3 356 330 304 279 5o 0543 0516 0489 0462 43: 0409 0382 03 5 <> 033 0304 0278 5i 543 516 4-89 46 z 435 408 382 356 3^9 34 278 5* 54* i*5 488 461 434 408 38i 355 329 303 277 53 : 542 515 4 88 461 434 407 38: 355 329 303 277 54 541 5'4 487 460 434 407 381 354 328 302 276 - 55 541 5H 487 460 433 406 380 354 328 302 276 56 541 5i3 486 459 433 406 380 353 37 301 276 57 540 5i3 486 459 432 406 379 353 327 301 2/5 1 5* 54,0 5' 2 485 458 432 4 5 3/9 353 326 300 275 59 ' 539 5*2 __5 45 S 4 5 378 35* 326 300 274 60 539 0512 0484 0458 43i 0404 0378 0352 0326 0300 0274 .; S. h ni h m h m h m !) ni h m h m h nf h m h m h m 2 C 38' t 3 y 2 4.*'44-'- 'S 45' V 4* TABLE XXV. PROPORTIONAL LOGARITHMS. 1 h m h mi h JTI| h fti h m h m h n h n h i n m h m | 2 Q 49' z 50' 2 tt 51' 2 U s2 2 U 53 2" 54' 2 9 55 z 56 2 5 O ,c '- 5 s S 59' o 0274 0248 0223 019" 0172 0147 OJ22 009^ 0^7 004 0024 I -73 24^ 222 I 9 - 1/2 147 121 97 7 4 24 2 273 1 247 a 22 197 171 146 122 97 7 4 23 3 273 247 221 19^ I7i 146 121 96 7 4 23 i 4 272 247 221 196 171 146 121 96 7 4 13 5 272 246 221 T 9:> 170 145 120 96 7 4 22 6 271 246 220 19 s I~O F45 120 95 7 4 22 1 7 271 M5 220 194 169 144 119 9*> 7 C 4 21 8 270 245 2KJ 194 169 144 II? 94 70 4 21 I 9 270 244 210 194 169 143 no 94 6 4 21 ' 10 0270 024*4 O2I9 Olg^ oi6S 0143 cub 0093 oo6f 004 OO20 II 269 244 21*! J 9 7 1 68 nS 93 6b 44 20 12 269 243 218! 192 167 142 117 93 6Jr 44 19 13 268 243 217 192 167 142 117 92 68 43 19 4 z6t 242 217 192 160 141 1 17 92 67 43 19 I 267 242 216 191 166 141 116 9 1 67 42 18 16 267 241 216). 191 160 141 116 9 1 66 42 18 17 267 241 2 I () I(j- 16^ 140 11 ; 9' 66 42 17 iS 266 241 21 5 190 165 140 "5 90 66 4 1 17 19 266 240 215 189 164 114 90 65 17 20 0265 0240 O2 14 0189 0164 0139 0114 0089 006 v 0040 0016 21 26; 239 2I 4 189 167 179 114 89 64 40 16 22 264 21 3 1 8 I6J 138 113 89 64 40 '5 23 264 t3i 213 1 88 163 1 13 64 39 1.5 24 264 2?8 213 1^7 162 177 I 12 88 39 15 ! 1^ 263 23$ 2 I 2 187 162 *37 112 87 65 3^ H 26 263 237 212 l>7 161 136 112 8? 62 3 3 27 262 237 211 186 161 136 III 87 62 38 13 8 262 36 211 186 161 136 III 86 62 37 13 29 261 236 21 I 185 1 60 I 10 86 61 37 12 30 0261 0235 0210 018^ 0163 0135 01 10 oo? 5 0061 0036 OO12 3J 261 235 210' JS4 J 59 134 I 10 85 6c 36 12 32 260 235 2O9 184 '59 IOQ 84 60 36 II 33 260 234 209 r$4 15* J 34 109 84 6c 35 II 1 34 259 234 208 158 133 108 84 5 r 35 10 35 259 2 33 20S !3 TOS 5- 34 10 36 258 233 20S 182 rs? 132 1-07 58 34 IO 37 25* 233 232 207! 181 156 I] 107 82 57 34 33 9 | 9 39 257 206! 181 156 13 1 1 06 82 57 33 S 40 02^7 0231 02o6j 0181 0156 0131 OlOt) OOil 00^71 0032 0008 4 1 256 231 20 C i8c J 55 1 3 105 81 56 33 8 42 2^6 230 205 180 155 130 105 So 56 3' 7 43 255 230 205 179 1^4 129 10; 80 55 3 l 7 44 -55 230 204 179 154 129 104 80 55 3' 6 45 2^ 229 204 179 r 53 129 104 79 55 3 C 6 46 254 229 20; 178 128 103 79 54 3 6 47 254 228 20; 17? 1^3 128 103 ?j .54 19 5 | 48 228 202 177 152 127 107 7* 5? 20 5 40 253 227 lOi 177 152 127 IC2 77 p ic 4 5 0252 0227 O202 0176 0151 0126 OT02 O077 oo;v co:.' 0004 ] 5* 2^2 227 201 1/6 151 126 101 77 >2 2". 4 ;z 25 2 226 20T 176 151 126 101 76 5* 2~ 3 53 226 2CO J 75 150 125 IOC 76 5 1 27 3 54 2 'I 225 2OO 175 150 12*; ICO 75 5 1 2; 2 55 45<3 22s 200 174. 149 124 100 75 51 it 2 i 56 ifb 2,24 199 74 149 1 >4 099 75 50 26 2 *7 2 sO 224 199 174 148 124 00 74 50 2 ' 1 58 249 24 J 9 V *n 148 123 008 74 4V 2; I 59 2 49; 2 = 3 19^ g 12-3 098 73 49 Z- 60 0248 C27. ; 0107 0172 OTJ7 C122 OOgS c c ; : 004^1 09*4 COCO 1 S i m h m h m h m h hi h ;n ft m h 01 h m h m i m ^ o , ../ 2 Q 'I' l * ^' - y 53' 2 54' - 55' z' J 56' : Q '?' =j& TABLE XXVI. For computing the Effefts of Parallax on the MOON'S Difiance from the SI-N or a STAR. I .= * "5 5 Apparent Diftance. Add the Difference of the two Numbers out of this Table, if the Appa- rent Diftance is lefs than 90, and fubtradt it if above M. ; S 10 10 ii 12" ^r 4" 10 U 1 7 o 19 " 20 ~~r -7T 4~ 25 ~r ! 29 3 ~ j 3 5 6 1C i < I? 2C j 3 r I 2 4 2 4 I 2 4 I 2 3 I 2 3 i -2 3 O 2 3 c 2 2 O I 2 c I ,.2 I o 1 2 i 1 i '! ' i i i i U 12 13 ' 15 16 17 18 T 9 20 Z\ 22 23 2 4 2 q r 6 g 9 1C 5 6 7 9 5 7 8 4 6 7 S 4 S 6 4 4 5 6 7 3 5 6 6 3 4 6 6 3 4 5 6 ' 3 4 5 3 3 4 4 5 3 3 3 4 5 3 3 4 3 3 3 2 2 2 2 2 2 2 3 4 4 5 6 4 4 4 3 3 3 1 1 13 r 4 16 18 10 12 i3 15 16 f 1 1 12 9 IO 1 1 13 8 9 IO 12 13 8 9 IO ii 12 7 8 9 10 ii 7 8 9 IO ii 6 8 9 10 6 7 8 8 9 6 6 8 9 6 6 7 8 9 6 6 8 5 6 8 5 , 6 7 7 5 6 6 6 7 r 6 6 7 4 r 6 6 22 2C 29 20 22 24 26 33 3 k 4 r 18 20 22 24 26 i; 18 2C 22 24 15 17 18 20 22 16 17 19 21 13 15 16 18 19 ii 15 17 18 12 13 H 16 17 i) 12 M 15 1 6 10 12 13 10 U 12 13 M 10 ii ii 12 13 9 10 ii ii 12 9 10 10 II 12 8 9 10 10 ii 8 9 9 10 u 7 8 9 9 10 7 8 9 9 10 1 1 12 13 15 7 8 9 10 10 II 12 [4 7 7 9 IO ii 12 26 27 28 ~~~3~I 32 33 34 39 45 28 30 3 - 34 37 20 28 30 32 34 24 26 28 30 32 34 36 38 43 22 24 26 28 29 31 33 35 38 40 21 22 24 25 2~ 21 22 24 25 18 21 22 24 17 ib 20 21 22 16 17 19 20 21 16 18 20 15 I 7 18 13 16 18 15 16 17 12 4 15 16 it 13 15 16 u 12 J3 J 4 45 5' 54 46 49 39 4* 44 37 39 44 46 29 3 1 33 35 37 27 29 31 33 35 25 27 29 31 33 24. 2 N 27 2 9 31 23 24 25 27 29 22 23 24 25 27 21 22 23 24 21 22 23 24 18 20 21 22 18 20 21 23 i? 18 19 21 22 16 17 19 20 21 16 17 18 19 20 15 16 ^7 18 IQ 17 18 19 34 35 S3 60 52 55 4/ 5 C 36 37 38 39 6 67 7 5 79 58 61 65 6s 72 53 56 59 62 66 49 52 55 58 61 45 48 53 42 45 47 50 52 4 42 44 46 49 37 4 1 43 46 35 37 39 43 33 36 38 40 31 32 34 36 3* 29 31 32 34 36 27 29 32 34 26 28 2 9 31 32 25 26 28 2 9 24 *5 27 28 30 23 24 26 27 JO 3 2 33 35 36 40 42 43 45 47 49 50 52 22 23 24 26 *7 29 2 32 33 35 36 3S 40 _43 45 47 4? 50 52 21 22 23 24 26 2 21 27 24 25 20 21 12 23 24 25 27 28 30 32 33 35 36 T? 4 1 42 44 Jl 47 49 5 1 53 54 41 i 42 43 44 45 83 8? 9 1 96 too 76 80 88 92 IOO 104 rap 117 121 126 136 69 73 76 8c 9 1 95 99 107 IIT 115 120 T24 64 6? 70 59 62 64 67 70 55 60 63 66 54 56 59 61 64 97 7o 73 76 48 50 53 55 58 60 63 6s 69 47 49 52 ~~57 59 61 64 67 T 9 72 74 77 80 42 44 47 49 JI 54 61 63 66 68 73 40 42 44 46 53 55 57 60 40 42 43 46 48 49 5 2 55 S7 3" 3* 39 4' 45 47 50 52 54 56 58 60 65 34 36 38 39 33 35 36 38 40 42 43 45 46 5 53 55 57 59 "62 64 66 68 70 3* 33 35 36 40 42 43 45 46 49 53 54 27 29 30 32 ?5 38 39 4* 43 45 46 48 49 26 28 29 30 32 33 35 36 38 39 41 43 44 46 47 46 47 48 49 50 51 52 5< 5 57 52 5 r 60 61 6? 105 109 Hi 119 1 2; So 84 S7 95 74 77 8} 87 9' 95 98 102 ro6 69 72 73 81 89 9 2 95 99 43 45 47 49 I 39 144 '55 r6o 166 r^2 178 9* 106 no 79 83 86 89 92 74 8c 83 6 62 65 67 70 72 59 61 64 66 69 53 55 60 6> \ J4C i r 5 T J 5 6 [162 129 133 138 '43 148 123 127 '33 '37 no 114 ilii ^28 103 107 no "5 n 9 96 99 1 06 I 10 89 93 96 100 103 83 86 90 93 97 79 82 88 9 1 75 80 83 86 74 76 79 82 68 70 73 75 7- 65 67 69 72 74 61 63 65 67 56 60 62 53 55 59 61 53 55 57 49 53 55 56 184 f90 10* ^671153 173 158 141 145 J3i '35 4 122 12 ' II3JI07 I F7 IIO IOC 103 94 97 19 89 9 2 20 & 5 8cj 76 rFiiF 72 75 24* 6c, 7? 7? 66 69 63 6( I? 61 63 5 27 56 ! 1 s ! XXVI. For computing the Effects of Parallax on the MOON'S Diftance from the SUN or a STAR. <: I 3 8 5 _; *sj "SiT 5 8 10 II 11 13 14 I< Apparent Diftance. Add the Difference of the two Numbers taken out of this Table, if the Apparent Diftanct- is iefs than 90, and fubtracl it if above. J i ~fT Ii! *// 134 M' 5 6' 37|3i 39" ]4o 41 41 |43' 44 V 45 4 6 47 4 49 |5 5'" a O O o I " c r C C J J I i i 2 O| I it 2 o i i 2i c i i I i i _J_I i a _L J I o I I I o I 1 I c 1 ] 1 o o I 1 o I i i 2 2 2 c c ] ] 2 2 2 c 1 1 2 2 I I I I 2 o ] 1 ] I 2 c i i i i i 2 i i J i i c J I I I 1 3 3 4 4 i 5 6 ~~6 1 9 3 3 4 4 5 6 6 7 1 S _9 9 10 ir 12 13 2 3 2 3 a 3 3 2 2 - 2 2 2 2 16 17 18 19 20 3 4 4 5 5 3 4 4 5 5 3 4 4 3 3 4 2 3 3 2 3 3 2 3 3 2 3 3 3 4 2 3 3 3 4 2 3 3 3 4 2 3 3 3 2 3 a 3 3 2 2 3 3 3 2 2 3 3 3 2 2 3 3 3 2 3 3 2 2 2 3 3 2 2 3 3 2 3 7 4 4 c. c 6 6 6 I 2 2 3 3 3 3 3 4 4 i 5 4 4 4 21 22 23 24 2 s ; 6 6 8 9 10 10 1 1 12 6 6 7 ^ 9 9 10 1 1 12 < 6 6 $ 6 6 : 6 t 7 r t; 6 6 ^ 5 5 6 4 5 <; 6 6 4 5 5 6 6 4 5 5 6 6 4 4 q 5 6 4 4 5 ; 6 4 4 4 r 5 4 4 4 c , 5 4 4 4 5 3 3 4 4 5 3 3 4 4 5 5 5 6 6 6 26 27 28 29 30 9 10 ii 12 13 h 9 9 10 TI S 9 9 10 ii g 8 9 10 7 8 9 10 8 8 9 9 7 7 8 9 9 7 8 9 9 7 7 8 S 9 6 7 8 8 6 6 7 g 6 6 7 7 8 6 6 7 8 6 6 7 7 5 5 6 6 7 5 5 6 6 6 3i 3* 33 34 t 35 1 4 ij 16 i/ iH J 4| 13 15; M 16; 15 '- ' 6 17 17 13 14 4 15 16 12 13 ! 4 14 i j :; 14 4 1 1 n 12 13 M ii ii 17 13 10 10 ii 12 13 10 1C 10 IJ 12 10 10 10 11 12 9 10 1C IJ II 9 9 10 10 ii 8 9 1C 10 II 8 9 9 1C 10 8 9 c 1C 10 8 8 8 9 9 8 9 _9 10 1C II 12 '3 7 7 8 8 9 10 ii 12 12 7 7 8 S 9 1C i j ii 12 6 6 7 7 8 36 37 3S I 39 40 1 4' i 41 43 44 1 45 46 47 48 49 5 51 5* 53 54 ;<; 57 5* 59 60 ~6~ 6?. M7 19 20 2 I 22 _1! 24 26 *7 28 -9 3C '3* 33 35 3' i 16 J 9 20 21 22 17 18 19 20 11 i? 18 19 20 21 16 17 18 19 20 15 16 17 ii! 19 H 15 16 r 7 18 i^ 15 1 6 ll 13 14 16 Z 13 13 J 4 15 16 13 '3 '4 i ^ 16 J2 12 13 H i- i: i 12 13 14 i ' II 1 1 12 13 - J 4 1 1 11 12 I? M II II 12 3j J 4 10 1C 12 I 13 9 10 ii ii 12 i 23 2s 26 2-7 28 23 H 2^ 26 27 22 23 24 25 26 21 ^22 23 24 25 20 21 22 23 24 J 9 20 21 22 *3 19 20 21 22 23 iS 9 20 20 21 J 7 rg 18 19 20 18 18 19 20 16 J7 i? 18 19 1 5 16 16 17 18 15 i:; 16 16 17 M 15 i ; ll i/ "4 IS 15 16 16 14 M 14 i; 15 J 3 14 M 14 14 13 13 *3 13 J 4 13 .3 13 13 12 13 r 3 J 3 13 2 9 30 3* 33 35 28 Z 9 31 32 33 28 30 3' 32 26 27 2 9 3 3i 25 26 2? 2 9 30 24 26 *1 28 29 2 4 2; 26 | 22 23 i 2 4 26 27 21 22 23 24 26 20 22 23 -4 26 J 9 21 22 2 4 25 *9 20 22 23 4 18 20 21 22 2 3 is 1 9 2C 2J 22 22 23 24 2; 26 17 18 19 20 21 22 22 2 3 2 4 25 16 17 iS >9 20 21 21 23 24 l^ 1 6 17 18 19 20 2O 21 22 23 4 15 16 17 18 J 9 T 9 20 21 22 I|*.MMM|MMMIMM i- O vD nc- oo-i e>Lr.-^ H 15 16 17 18 Ts 18 J 9 19 20 33 39 4i 42 4.1 36 35 39 4i 42 44 45 47 4* 5<5 5 2 54 35 36 3S i 39 \k 42 44 i 45 47 $L 50 s^ 33 35 36 3 39 3* 33 35 36 38 3 1 32 33 35 36 3 3 3* 33 3J 2 9 30 31 3 1 33 28 2Q 30 3' 32 27 28 2 9 3 3J 26 27 2S 2 9 30 25 26 17 28 29 24 *5 26 27 28 = 3 24 as 26 27 45 47 49 5i 52 M 4* 42 44 45 17 4* 50 39 4t 42 43 45 ;" 4 6 !4S 38 39 4? 4* 43 44 4 L 36 37 3> s fS 35 33 36 35 ll * 4J 4 c. 43 4' 32 33 35 3^ n 38 4c 31 3^ 35 34 '35 36 3-S 3 3i 32 33 34 3 r 36 29 3^ 3* 32 33 34 35 2* 2 9 3 C 3^ 3* 33 34 4 7 z* 29 3c J 1 3* 33 26 2/ 28 29 30 ~3~i 3J 2<; 26 27 2S 20 30 31 24 2 ' 26 2" 28 "29 30 23 24 zt; 26 27 ~rt 29 22 23 24 2=; 26 a~ 28 21 22 3 2 4 2 s ; "26 27 !:,'" Hta 3^39 40 HM 43 C 44^ 45 46 47 4* J 49 ( 5 cr <;il TABLE XXVI. For computing the Effefts of Parallaron the MOON'S Diftance from the SUN or a STAR. xl Apparent Dittance. Add the Diffeicnce of the two Number* taken out of this Table, if the Apparent Diftance I is lefs than f)0, and fubtradr it if above. 1 .X < ?< 53 5* 5^ <6c 57 5 ,o 59 120 6o c "S 65^ IIO 70 105 ,o. 7 5 | 8o c 95 9 o- 9S 100 105 IIO 115 120 M. 7 J " " " "I" ' " " ; c c c o o o c o c c 8 c o o o o c o c c c 10 o c c c c o c n o o c o o o c c. o o o o o 12 o c o o o c c c o c o 13 I 1 I I I 1 1 o c o c c c T 4 15 I I I 1 I 1 I I 1 1 c o c c o c 1 6 1 I I I ] I I 1 I Jj c o c c c 17 ,o 2 2 2 I I 1 I I 1 1 c o c o c 19 3 2 2 2 2 2 2 2 2 I ] o c 20 3 2 2 2 2 2 2 2 : i 1 i c o 21 3 3 3 2 2 2 2 2 1 1 c o 22 3 3 3 3 3 3 2 2 2 2 ! c c c 23 3 3 3 3 3 3 3 3 2 2 J c 2 4 4 3 3 3 3 3 3 3 3 21 1 o 2C 4 4 4 3 3 3 3 3 1 2 I c 26 5 4 4 4 4 4 3 3 3 3 2 c c 17 j 5 5 4 4 4 ff 4 ; 3 2 c c 28 6 5 5 5 5 5 41 4 4 3 2 2 c 29. 6 5 5 5 5 5 4 4 4 2 2 ( o 30 6 5 I 5 5 5 4 4 4 I 3 2 c 3* 6 I 5 5 5 5 c 4 4 3 2 c c 32 6 5 5 5 5 5 5 5 ; 4 7 2 c 33 6 6 6 S 5 5 5 S j 4 3 2 c o 34 7 C 6 6 6 6 S S 4 2 c ' 3S 8 7 7 6 6 6 6 6 c 4 2 c c 1 36 b 8 7 7 7 7 6 6 6 g 4 3 2 1 o 1 37 9 9 8 8 8 7 7 7 6 5 4 3 c I c 3^ 10 ID 9 9 9 8 8 7 7 s 4 * 3 ^ I 39 n 10 10 9 9 9 S 8 7 4 3 2 I 40 ii II 10 10 9 9 8 8 8 6 s 3 2 I 4< 12 12 1 1 10 10 10 9 9 5- 6 5 3 2 1 c 42 I i 12 n II 10 10 9 9 * 9 S 4 2 I 43 12 12 1 1 II 10 10 9 9 9 c 4 2 I c 44 12 12 ii 11 II 10 10 9 9 f, 4 2 I c 45 IT. 12 r.2 II 1 1 1 1 10 10 9 6 4 2 1 46 13 13 12 12 12 II 1 1 10 10 8 - 5 '3 I c 47 M 14 13 12 12 12 n II 1C 8 7 5 3 I c ' 4*3 15 J -i 1 3 *3 12 12 12 11 I! 9 7 15 i 2 c 49 1 6 I> 14 14 14 I? 13 12 II 9 - s 2 o 5 17 16 15 15 M 11 13 12 12 10 * 6 4 i , c 5i 17 16 1C is is 14 14 '3 12 10 6 4 2 52 T7 I- 16 16 1^ H M I? 10 (i 61 4 2 c 5.3 iK p8 17 16 1 6 15 M I? 10 6i ; 2 54 55 19 18 1-3 \] 16 17 16 16 15 16 15 IS M II I [ r; ?! 1 2 2 c c 56 2C i f > iS iS 17 16 16 15 15 12 , - - 2 o 57 21 20 X 9 ig 19 18 17 16 I c 12 c 7 s 2 o 5 s 22 21 20 20 iS 17 16 1 6 13 1C 7! < 2 c 59 2-t 22 2] 2 1 20 10 rS 17 ij I? 1C 7 S 2 c 60 24 2: 2Z 22 11 20 19 18 1 3 14 1 1 8 c 3 c 61 25 24 2: a 3 22 21 20 19 z$ IS 1 1 81 <; 3 62 2f 2; 24 23 22 21 20 19 16 9 f 3 c i M. 5-, * >'' -1 All^l S7 J? lillE i6 5 < 7c ; 75J8oJ8 2 Jj A 2 TABLE XXVI. In working by the method sliewn in page 238, should the distance CH the objects be above 90 degrees, you must look in Table 26, with the Apparent Distance at the top, and the Moon's Correction on the left hand side column, the number found subtracted from 20, leaves the third correction. In the same column, and corresponding to the difference of corrections, is another number, vhich, when subtracted from 20, leaves the fourth correction. N. B. The different numbers found under 5, 100, 105, 110, H5o,120.. & c . sub- tracted from 20, will leave the numbers as are in the little Table annexed. TABLE XIII. The first page contains the Proportional Parts of the Declination of the Sun to every five Minutes of Time, and every Degree and Jo Minutes of Longitude} and to every Minute, and every six Seconds of the daily Variation of the Sun's Declination. The second and third page of the Table con- tain the Proportional Parts of the Sun's Decli- nation to every Hour in the Day, and to every 15 Degrees of Longitude, and'to every Mi- nute and every six Seconds of the daily Varia- tion of the Sun's Declination. Ex. 1. I demand the proportional Part answer- ing to six Hours,(or 90 of Longitude) when the Sun's daily Variation in Declination is 13 Mi- nutes 24." Under six Heurs (or 90) and op- posite 13' in left hand col. is 3' Under six Hours (or 90) and op- pcitte '24", in left hand col. is .... ,...0 15", 6 ,0 Answer 3 21,0 W hich is to be added or subtracted, according as the Sun's Declination is either encreasing or de- creasing. Lx. 2. What is the proportional Part answer- ing to eight Hours 40', (or 130 of Longitude, '.rhcn the Sun's daily Variation in Declination) is 18 minutes and 42 second:. Under 8 Hours, & opposite to J 8' !s 6' O/', ...42'' is C' 14", 40 minutes ,....,..18' is 0' 30'/, Q 42"is C' \'.i] 2 Answer 6' 45;'^ g Applicable a* the first Example, ~r 1 GO LJ JO !_'! 201 . 5 ZO iO 20 2C 20 20 8 20 20 20 20 20 20 IO 20 20 2L 20 20 20 ii 20 2O 2O 20 2O 20 12 20 2O 20 20 2O 2O 13 20 ZO 2O 20 20 '4 2O 20 2O 20 19 IQ '5 20 20 2O 2C 21 19 16 20 2O 2O 2 19 ~*9 17 20 20 20 20 19 18 2O 2O 20 19 19 rt '9 ZO ZO 20 19 18 20 20 20 19 19 18 21 20 20 J 9 ~19 '9 iS 22 2O 20 '9 it 18 23 2O 20 19 19 18 if 24 2O '9 19 18 17 *5 2O 19 J 9 T 9 18 17 26 20 19 J 9 ~7s , 7 "17 27 2O Iy 1Q 18 17 17 28 2O 19 iS iS 17 16 29 2O 19 18 18 16 30 ZO 19 18 17 16 16 31 ZO 19 "7s ~i~7 T6 J6 32 20 19 18 17 16 15 33 ZO 19 18 1 - 16 15 34 2O '9 18 16 i5 15 35 20 1 9 18 1 6 16 15 36 19 i$ ~ ~f~6 15 '4 37 '9 18 7 16 15 38 19 18 17 16 15 13 39 19 18 17 16 15 3 40 '9 18 17 15 IZ 41 ! 9 18 "i? 15 ~ 12 4* *9 18 16 15 13 I I 43 19 18 1 6 *5 13 II 44 19 18 16 II 45 J 9 iS 1 6 '4 13 II 46 19 17 15 ^3 12 10 47 19 17 15 12 10 48 18 17 15 13 II 9 49 18 17 15 13 I I 5 18 16 14 12 10 8 5 1 18 ~i6 M "7:2 10 8 5* 18 16 12 IO 7 53 18 16 I> 12 10 7 54 18 16 13 II 9 6 55 18 16 17 II 9 6 56 ~IiT T<;~ 13 1 I 8 5 57 18 .15 jq IJ 8 5 18 15 1 ^ 10 4 59 60 18 17 15 12 10 9 6 3 2 ~6~i~ 17 15 1 2 9 5 2 1 62 17 14 1 I 8 4 I M. 95*: 100 To! I 1C n, I2C TABLE XXVII. LATITUDES AND LONGITUDES OF TH E PRINCIPAL PORTS, HARBOURS, CAPES, SHOALS, ROCKS, &c. IN THE WORLD; Deduced from the Obfervations of the mod celebrated Navigators and Aftro noniers ; comparetl with the lateft and molt accurate Charts, Maps, &c. The Longitudes are reckoned from the Meridian of Greenwich. Coafls of Great Britain and Iflands adjacent. Places. Lat. Long, South Coajl iff' England. j Blackhead, F. S. . '. M. S. jo i i:N. D. M. 5 4 oW. Places, Lat. Long. n . C n * j Lizard Point . . , Mount's B. (Pcnz.) ^9 57 40 50 7 40 5x146 -oNDON(St.Paul's) 51 30 49N.c Greenwich Obf. .J5i 28 40 < More . . .'51 28 o i No. Foreland Light 51 22 40 Deal Cattle . . .[51 13 5 S. Foreland Lighth. 51 8 26 Dover Caftle . 51 7 47 ) 5 47 W. 5 O 3 46 o E. t 26 22 ' *3 59 t 22 6 i in i Runnel Stone Wolf Rock Land's End (Stone) Longfhips Lighth. S.Mariiii'bDay-mark St. Agnes Lighth. . Seven Stones .1 iO I 2O ^9 57 20 50 4 7 50 4 20 19 58 29 *9 53 37 50 6 20 S 39 o 5 47 45 5.41 32 5 44 30 5 14 39 5 19 23 5 47 20 Dungenefs Lighth. 15055 i '0574^ H aftings Bcachy Head Sear'ord Brighton Church . Shoreham 50 52 o o js o 50 44 23 o 15 12 50 47 20 k> 7 o 50 49 32 o ii 55VV, 50 49 59 o 1 6 IQ V'cR Coitfl of England. Cape Cornwall ...150 7 5cN.]5 42 oW. St. Ives Point . ;o 13 20 5 2 6 o Arundel Owers Light . Selfey Bill . . Portfmouth Church . 50 49 o |o 35 15 5 39 57 P 39 15 50 44 5 o 48 o 50 47 26 ji 5 57 Cow ana Calf Portlfiac . .. Hartlaad Point . . . Barnft.ible 5 r- 45 50 36 5110 50 7 20 $ 2 22 4 16 o 4 25 o 430 of Brittol Channel 51, 12 o 470 Ijlc of Wight. Lundy Uland . . ,i 13 o _). / U 4 32 o Flatholm Lixl;^jpMfe!c i ?.c o 3*7 O Bembridge Point . ,Princefl"a Shoal, S.B. Dunnofe Point St. Catherine 'sToweT Needles Light Cowes Hurft Lighthoufe . Chrift Church Mead BrankfeaCaft.(Pool) ;St. Al ban's Head ' 50 40 5 9 N. 5.0 39 30 50 37 7 5 35 33 5 39 53 5 45 37 50 42 23 51 43 57 53 41 19 5 33 3 4 25W. >4 25 ii 36 17 5' 33 5S 16 15 32 50 45 10 57 * 2 Nefs Point Mumble's Light . Worms Head Caldy lfl a nd . . St. Ciowan's Point St. Ann's Lights . Small's Lighthoofe Hates and Barrels . St. David's Hed . J - J ~ 51 29 30 5 1 3 6 45 5i 35 2 5 51 44 20 51 40 10 5^ 43 45 51 45 40 5i 45 15 5155 o / W 2 35 2? 3 3 1 5 3 55 413 o 4 26 30 4 47 o 5 i 5 28 o 5 20 15 ? 8 o ;Wey mouth .ShaniDlesShoal.Mid. 50 36 15 50 32 o 26 40 22 Strumbl-'s Heid . . Dinus Point 52 i 15 52 i 10 5 o o 1 ^O O Portland Upligot Lyme Cob i Berry Head, F.S. Dartmouth Start Point, F S. Bole Head,F. l>. 50 31 32 5 43 10 '50 24 o 50 " 2 O 5 *3 -6 50 13 15 26 55 2 55 29 3 2* 14 3 34 o 3 3 o 3 48 3 Cardigan Iflmd New Key Head ... Aberiftwith Aberdovey Bannouth PenkelLm Head. .. 52 7 45 52 10 40 52 ii 30 52 33 o S2 42 30 52 47 30 T J w l^") O 4- T Q 3 59 400 400 j! 3.2 o Rame Head Plymouth Old Ch. cuyitone Lighth 50 IS 5^ SO 2i 13 5 10 54 4 12 29 4 7 32 415 2 B.udl"'Y Jfland,So-Pt Porthoi.iilcyn Head 52 44 30 52 56 30 4 46 30 4 34 o jDeuaman's Pr F. S. r O I ; 2. 4 47 8 jPejidennis Caftle . .> ^ * j * w 50 8 49 5 J 44 TABLE XXVII. Or LATITUDES AND LONGITUDES, 1 Karnes of Places. Lat. Lon* Hnlyheadlfl. W. P. D. M. S, D. M. 53 18 4N. 4 40 loW. jLcrr/V T/lands. | Skerries Lighthoufe 53 2 4 50 .. ? 4 36 30 ["Point Linas Light . 53 24 30 4 17 45 Names of Places. Lat. [ Long; ; i Great Orms Head . c i 20 o D. M. S. 'D. M. ' | Point of Aye Lighth. I Lake Lights ) Liverpool . . 1 Form by Point i Lancajfter j J ** w \J 53 *i o 53 *3 o 53 23 3o 53 35 45 54 3 o j 16 o 380 2 27 O 3 5 o > c T o Bernera Ifland .... ; GrienHead, Bara Ifland Ruardvula,So. Uiit III. Hyflcere Ifland, W. P. Cafamul Ifland 56 48 cN. 7 56W 57 o o ,7 53 57 12 o 7 49 57 28 30 ; 8 o 57 34 20 ;8 o ; Selker Rock 54 16 30 * _> * u 3 27 o iRennifli Head 57 41 o |7 16 ; St. Bees Head Lighth. 1 White haven Workmgton * . . -! Mary Port Carlille 54 30 15 54 32 30 54 38 o 54 43 o 54 55 45 3 42 J5 3 34 45 3 30 o ? 27 o - 55 * jToe Head .... jGlafh Ifl md Light ... GallenHead Flannen Ifles St. Kilda Ifle .... 57 49 30 ; 7 25 57 5 o 6 56 58 10 30 7 24 58 14 o 7 51 57 50 o -8 18 / n : ' : But of the Lewi? 58 15 o 6 24 58 28 30 6 34 IJk oj Mem. Calf of Man .(54 i N. 4 o ShctlanJ Tjks. Skcrryvore lUcks .56 15 45 Dufkier Rock .'<;6 34 o Tire-e.v-IfLsN W.P. 56 33 o Hcliker Ittandi .. .[56 56 o Sunk Rocki, to the, weftwjrdorHellker 56 55 o CotlJfl.md,Ea!t End 56 41 o 7 24. o 7 20 o 7 16 o 6 59 o 7 3 o 6 At n Sucnburgh Head ...i59 5 1 N. Hang Cliff ...60 7 o Brafl'a Sound, Lerwick J6o lo o Whalfey Ifland 60 25 o Unft Ifland, N. E. Point 60 42 30 Foullihnd 60 25 o c 50 o 53 o 39 O I 20 .Rum Ifland, Eail End' 57 o o 43 o 6 -jo o 1 Cana Ifland, E.ift Ft. 57 3 6 44 o Ferro Ijles. D.mvegan Head . . . 57 33 o 74o */ Valernefh Point . . 57 35 20 6 54 o Monk Rock, which ap.| Rea Head 57 50 o 620 pears like a Sail J6l 18 oN. 6 3i\V More Head Stower Head Cape Wrath - ... L5 8 4 40 , 58 13 30 58 36 o 5 39 o 5 37 o 5 19 o Fulae Ifland 62 14 30 6 10 62 4 30 7 20 Mygenefslflind, E. Po. Rona I/land 'B:-.rj, or Suliikcr Ifl. 58 54 45 5 s 54 o 6 16 o 6 28 o Eq/1 Coijl of Scotland and England. Far-out Head <8 \Q O 4c r o , Dunnet Head . . . tJ J.S 58 42 o jj u 3 27 o NofsHead . .-. . . | 5 g 33 3 oN.'3 8W Duncan^ley Head . . 52 40 o 3 8 o Clythnefs ....[58 23 O J3 15 Ord Hea-l ... 158 12 30 1 T7 ~~^ rir TarbetNefs ....|575545 349 TABLE XXVIF". OF LATITUDES AND LO Names of Places. Lat. D. M. $. Long. D. M. Names of Places. J.ar. Long. D. M. S. " . M Cromarty Inverness 57 42 3oN. 57 3* 4 i oW 480 Mizzen Hea '. BantryB.Sheep'sH. ,i z; cN. 5 34 9 47 oW 9 49 o Fort George 57 3 8 460 Grelagh Rocks 5 31 30 10 S Brugh Head 57 44 30 3 31 o Durfey Jfle, W. end 5 36 10 12 . Kennaird'sHead Lt. 57 39 30 2 I O Bull Rock . .1$ 37 o io 16 o Peter Head 57 3* o T 47 o Cod's Heud . 42 o TO $ Buchan Nefs >7 29 3 i 47 o Hog Iflands 5 47 o ro 14 o New Aberdeen 57 9 o 290 Bolus Head .... 5 50 45 160 Limerick 52 41 o & 42 o Rocky Bank, Mid. . 56 r r o ill o Ba! lards Point . . . 52 42 30 9 54 o Holy Ifland, N.E. P. 55 43 30 i 53 o Hags Head 52 55 9 42 o Bambatgh Cattle . . 55 39 o i 4^ o Black Head ... 53 6 30 9 2* o Staple's Light 55 40 o i 43 o - Galway i3 I 5 9 ii o Fern Ifland Light. . 55 3* o i 45 o N ArranllTe,W.End 53 7 o to 5 o Coquet Ifland 55 22 30 r 30 o Skird Rocks ... 53 16 o ro ' 18 o Tinmouth Light 55 4 o r 20 o Sline Head ... .15^ 25 30 ro 29 o Hartiepool 54 44 3o i 7 o Shark Iflp ..': 53 3^ 45 io 36 o Stockton .... 54 3'> o I 18 Ennis Turk L ...(53 41 o io 24 o Whitby -4 2* 30 o 50 o Cla e!fl.md,WeftZnd|53 46 15 10 iS o Scarborough . . . 54 zo o o 23 o Achill Head ... 53 58 30 io 30 o Filey Brig 54 l6 3 J I Black Rock ' ...J54 5 o io 35 o *'Flamborough Head 51 io 30 o 3 cE. Urris Head . . >4 20 30 ro 18 o Spurn Lights 53 39 o 24 o Outer DowfingSj N. W. end 51 44 3 o i 18 o North Coajl of Ireland. Haddock Bank . . . Shoal to the We ft ward of Outer Dowfing | Dudgeon Lights . . ) Inner Dowfing . Cromer Bank Lemon andOwers,M. 53 46 o 53 44 o 55 3 55" io 33 53 25 o 53 21 o i 39 o o r } 5 o (70 o 42. o i 34 o 15^0 Ktd Iflss Three Tuns Rocks . Down Patrick Head. Killala Sligo Wheaten Rock 54 oN. 54 23 30 ,4 21 O 54 i 3 33 54 16 45 54 2I 15 io 8 - oW io 4 o 93-60 9.27 o 8 41 o 8 55 o Sherringham Shoal Haiborough Sand, S. Buoy 53 9 1 - ? o O Z 2 15} o Donnegal . . . Tellen Head Douras Head ... 54 3^ 30 54 41 3 54 5i o S 14 o 8 5$ o $ 42 o Hammond's Knowl Smith's Knowl, Buoy The Ridge Cromer Lights . . . > J W W 52 5~i o S- .59 o 53 o o 53 6 o i 53 o i 26 i 43 o I 20 Arr-ininof-e I. N . End Bloody Foreland .. Tory Island . . . Horn Head 55 5 45 >5 10 30 55 17 45 55 r 4 o .8 36 'o 55 17 o S ir o 7 57 o j Yarmouth 52 39 o r 44 o Mulloy 55 r 7 o i LeoftofF Lights South wold si 29 2O S* 20 o i 46 30 i 4} 35 Bucm's Head - Dunaff Head . . . '5 *7 45 ;S 17 30 7 47 o 7 3* o Albro' N apes Orfordnefs 52 9 o 5250 I 43 o i 34 14 Mullin Head Enniftrahul Rocks . 55 2 4 55 29 IS 7 24 o 7110 Keetifh Knock . . . " 3 51 42 }o i 36 30 Ca)odah Head . . . Inifhon* Head 55 21 55 15 45 77Q 6 51- o Londonderry 55 i o 7 *6 o Wcjl Coa/2 vf Ireland. Giants Caufewav . . . 55 17 30 6 10 o i Rachllhl. W. End 55 2I T 5 C S c Cape Clear . : i 22 3oNT. 9 30 cW/T ,ir Head 55 '4 45 640 Fartnct Rock . < r J 9 $> 934 o |Toi Head 55 *3 3 6 i o uCrookhaven . . : r zr> 30 f i 41 40 1 TABLE XXVII. OF LATITUDES AND LONGITUDES. 1 Ea(l Coq/l of Ireland. Cattcgat and Sound. Names of Places. ' Lat. Long. Maids Rocks D. M. S. 54 57 2oN. 0. M. 5 37 c\V Names of Places. Lat. 0. M. S. Long. P- M. Black Head 54 46 3 5 35 o 'aternofters 7 55 oN. I 27E. Carrickfcrgus . . . 54 4 20 5 45 o flarftrand Light 57 4 o 1 35 Bclfcft 54 34 3 5 56 o /ingo Beacon 57 3$ 45 I 37 Mew Ifls and Light. 54 40 45 5 ^3 o Jothenburgh 57 42 30 1 59 South Rock. Light . 54 20 50 5 22 o effiou I. Eaft Point . . 57 18 45 11 IO Dundrurn . . . 54 13 *5 5 50 o Weft P. 57 15 o ro 50 Ncwry . . 54 5 30 6 12 Yindel Rock 57 19 o ii 7 Dundalk 5? 58 30 6 1-6 o 3rafholm . . 57 *9 o 10 36 Clougher Head . . 53 49 30 6 20 uicringen Shoal 57 o o 10 29 Drogheda Bar 53 44 o 6 14 o Jiddingen Lights . . . 57 18 o ii 55 St. Patrick's Ifland .153 35 20 5 57 o Warberg 57 6 30 12 16 Lambay lil.md 53 3 o 5 5 6 o Rocky Shoal, Little M. Howth Head Light . 53 22 30 630 Ground 56 57 20 IZ DUBLIN . ..J53 21 45 6 16 o "alkenburgh . . . . 56 54 *o 12 29 Wickiow Lights ..'.z 59 o 6 i o c6 4.0 ^o 12 ?2 Arklow ... 51 50 o 670 An hoi: Light 5 T" J u 56 45 o ** j * i r 40 Glafcarrick ....51 39 15 6 10 o Knobbin .... S 6 45 11 53 Wexrord ... ^2 ?. z 30 6 17 o Waderoe I. Weft P. 56 28 o 12 33 Koll Light 56 19 20 12 27 South Coaft of Ireland. Lyfle Ground 56 19 o , ,I 4 8 Carnfore Point .... ^2 12 30N. 6 7 o\V Kifell IH and 56 12 11 42 Tufker Rock 52 14 o 5 5 s o Stains Head 56 35 20 10 51 Salttes Rocks Hook Light Waterford Tramore Dungarvon Urdmre, orRaniHd Youghall .... Dogi Nofe Cork Kinfale, Old Head . . Seven Heads Dundedy Head . - RoTs ;z 6 o V 4 30 5 2 n o ^2 7 52 4 o 5" 5* 30 5 r 57 o i i 48 30 5 1 55 30 51 38 30 51 36 o 5i 34 51 37 o 6 23 o 6 45 o 7 59 o 6 59 o 7 29 o 7 33 7 41 o 890 8 25 o 8 27 o 8 35 o 8 57 o * 56 30 Granan Chalk Ground, Shoal Navaren Shoal efnefs Ground, Shoal Haftens Ground, Ditto Nackr^i^vet Lights . . Cronenburgh Light Elfeneur Huen I. Wortk P. . . . Salthclm, North P. ..anfdfcrone . . . COPENHAGEN r alfterbro Light 56 25 o 56 % 5 o 36 23 30 56 17 o 5 d 15 o 56 6 30 56 3 20 56 i o 55 55 *o 55 4i 3 55 52 20 55 40 3> 55 21 10 10 55 ii 52 - 1 o -o 53 : i IO 12 21 2 37 (2 35 12 40 rz 48 12 51 12 35 12 48 Stags off Toe Head . 51 29 o 9 8 o Baltimore Si 30 o 9 20 o Baltic or Eajl Sea. , Coaft of Holland and Jutland, from Calais to the Scan-. Lubeck 'Dars Head Bornholm Lt. N.W. P. 53 51 3oN. 54. 28 o 55 *4 30 10 47E. 12 36 14 46 Calais 50 57 3oN i 50 5 6E Weft P. 55 8 20 15 I 7 Gravelines . ; o 59 15 2 10 Dantzick Heel 54 38 o 1 8 40 Dunkirk 51 2 II 2 22 Dantzick .... 54 21 45 18 31 Newport .... 51 8 20 2 45 o OJand Light, South P. 56 ii 20 16 25 Oftend .... 5i 15 3 2 55 o i North P. 57 23 o '-1 5 Wakheren I.Weft P 51 32 o 3 24 o Gothland, South P. . . 56 54 18 16 Goret Ifland,N.W P 51 49 3 5 o North P. . . 57 5 30 r8 54 Schowen Ifl. Lights. 51 40 45 3 37 o Faro I. N. E. P, ... 57 55 20 19 31 Bruges SI 13 3O l j y o Goltfke I ,8 16 o f q j North Gatt .... j * * 3 J 51 54 20 5 * j w 450 STOCKHOLM 5V 18 45 17 52 Rotterdam .... 51 54 4 29 o Brufter Ort Lights . 54 5 2 30 1 9 54 AMSTERDAM . . 52 22 O 4c j 30 m* j C C A I O 21 i Texel, N. Point . . 53 ii 20 j * j w 4 34 o Domefnefs Lights . . . j j ^ 57 45 3-3 -i2 31 Bremen .... 53 3 30 8 51 o Runoe Light 57 4* 2 o *3 8 Elbe River, Red B. c 2 t(Q t c 8 18 o R;a r5 C7 o i^ c6 Heiligcland Light .. ? -j ^ y j 54 9 30 800 Swafverort Light J *-* J / vj 57 54 3o J 3" i 1 59 | Holmen * . . . 57 8 30 8 35 o * I Robfnout .... 57 *7 30 9 39 Scaw .... 57 4i 45 10 39 o TABLE XXVII. OF LATITUDES AND LONGITUDES. Gulf of Finland. The Coqft- of Iceland. Names of Places. Lat. Long. Names of Places. Lat. Long* D. M. 3. D. M. D. M. S. D. M. Dagerort Point 58 57 3N zz IE Reikianefs I. ape . 63 55 ION . 22 4;; OW Odenholmlflands 59 *9 o 13 21 y'v eftman's Ifland . .63 z 25 '21 9 o Hango Ifland and Light 59 49 -3 20 1'airixford . 65 36 6 24 9 o Packerort Light v- 2 4 30 24 5 Straumnefs . . . 65 40 13 24 30 o Surp Point and Light 59 28 10 2428 ^orth Cape . 66 34 20 23 10 o f Kafch Skar Light ... 59 38 20 25 9 Grims Ifland 67 o 30 21 46 O ' Hoogland Ifland, N. enc 59 58 o 27 7 Rikefiord ,67 o 45 17 35 o See Skar Ifland, N. end 59 56 25 18 30 ongnofe . 66 45 10 12 19 O Wyburgh . . 69 40 o 2 9 55 Jiaanefs . . >6 2 15 12 21 Tol Beacon Light . . 60 i o 19 40 cnchuifen Ifland . . 65 o 25 10 5 o Cronftad 59 57 3 29 54 Engelhoaft . . 04 32 10 f 2 19 O PETERSBURGH .... 59 58 4 30 20 reeland Ifland '4 5 5 13 19 o Cape Hekla 63 12 20 16 54 o The Coaft uf Norway and Lapland, from Chrijtiana to Archangel. Davis' s Straits. Chriftiana 59 5 2 45 N 10 52 h. ^'ape Riefoluton . . 62 40 2oN. 46 43 oW Frederickftad 59 10 15 II 2 'ape Comfort 62 45 45 47 35 o Stromftad 58 55 10 ri 13 -Fope Harbour 63 55 o 47 55 o Faerder Light .... 59 2 35 10 39 Gilbert's Sound . . 64 15 20 47 5* Aiundal .... 58 40 o 8 57 ooken Sound . . . 64 50 16 48 3 o Chriftanafand 58 19 o 8 14 s. Chriftian River 66 7 25 47 13 o j Naze 58 7 20 7 15 Vlufketo Cove . 64 55 3o 52 56 o i Walbert's Head 58 32- o 5 5 6 lomcl Fort . . 67 22 15 45 53 o Bommel Head 59 3i 30 5 Diico I. S.W.Point 69 6 45 44 43 o Ulfter's Iflands 59 24 o 4 5 Vaygate Ifland 7 o 40 50 44 13 o Bergen 60 14 o 5n ames I. C.Bedford 68 30 o 50 12 o Ronde Light 62 22 O 5 4 Jumberld.l. S. Point 66 o 12 60 35 o Drontheim 63 26 30 10 20 jy of Good fortune 64 20 25 6 1 34 o Werro Ifland 67 40 o II 26 ej'olution Illand . . 62 5 15 64 35 o j North Cape 7i 9 45 26 I ape Warwick . . . 6140 64 35 o North Kyne Cape . . 71 6 10 7 A A Wardhur's Ifland |OifterHaven,Fiflier'sI. 70 30 30 70 3 o T*f 50 4 o 31 41 oajl of Trance, Spain, and Portugal, : Terrybem Point 6q Ij 20 33 58 from Calais to Gibraltar. Nagle Ifland, N. Point 68 33 12 35 40 J CspeSweetnofe .... 67 58 45 37 30 alais . . 50 57 30ls. 50 5 6E. Lambachoe Point . . .. 5 7 34 30 38 30 ape Grifnefs 50 52 30 35 30 Cape Orlogenofe 6 7 i 35 39 21 oulogne 5 43 30 36 30 Crofs Ifland, N. Point 56 21 o 38 45 Staples . . . 50 31 o 38 o Onega .... 63 36 o J T^ J 17 20 . Val. fur Somme 50 no i 38 o Cape Donega 64 45 20 55 42 ieppe 4-9 55 15 040 Archangel 64 30 3 o ^ 59 . Valery in Caux 49 52 30 040 Blue Point .... 55 19 20 38 5 ccamp 49 46 o 21 O ; Cape Bona Fortuna . . 56 24 10 .0 24 ape de Caux . . 49 42 30 II M odium Ifland, M. 56 39 20 .0 40 ape de laHeveLt. 49 30 30 o 4 10 Cape Candinofe .... 58 22 30 .1 25 avre . . . 49 29 15 060 Nova Zembla 78 6 o 6 20 ontflcur A U TO 49 25 o o 15 o The Coaft of Greenland. AKlb . J ointde Conebar 3 :. de la Percee . . 48 51 15 J. 9 22 30 f9 23 25 2. iO 15 o 31 3oW o 56 o John May en's I lid. . . . 71 10 25N. 9 *?oW t. Marcou, Ifland. ^9 29 49 i 8 50 Gael Hamkes Bay . . Sontokoe Ifland 75 o 40 73 27 20 6 51 9 36 apeBarfleur Light icrbourg f-9 4i 45 19 38 29 i 1 6 j 6 i 37 o TO C I r 1 TT . 1fl - _ ^ Dangy li'land / -> * 5 67 23 10 22 23 Z 7 25 l.ierney I. N. end y 4 J i J 9 45 ' 55 30 2 10 50 Ht j rjoifs-Nefs 65 3 o jfket Lights , \ 9 45 o 2 25 50 Whales Ifland 62 30 5 39 9 uernfey I. b. Pierre 9 29 o 2 33 o Cape Difcord 60 51 o 40 o ark I. Windmill . 9 23 32 2 24 45 Cape Prince Chrift. . . . Cape F rewel 59 55 45 59 38 30 V 35 42 44 erfey I.CapeGrifT- nefs . . . J 9 '5 '5 2 14 .Cape Dciolation 52 o 9 46 12 Sc. Aubin . . ; 9 10 50 a jo 30 TABLE XXVII. OP LATITUDES AND LONGITUDES. Names of Places. Lat. D. M. S. D L M g ' I] Names of Places. Lat. D. M. S. Long. D M. Corbier 49 10 45N. 2 15 cWi C. Fefaraon ^9 31 oN. 9 4 o\V, Chofey I Middle . . 48 52 20 49 TO Burlings ,9 28 o 9 23 o Coutances 40 2 50 27 25 Lifdon Rock (Cape) ;S 45 15 9 26 o St. Margaret 48 56 10 32 30 Lifbon {8 42 o 970 Granville Light 48 50 13 36 4 C. : pichel 3^ 25 o 9 jo o Avranches 48 41 o 20 o St Ub.es 38 31 o 8 42 o Mount St. Michael 48 38 o 30 o Sines 37 55 o 8 46 o St Malo 48 39 I 2 J 14 C St. Vincent . 37 2 30 9 i 3o .Tower de laConche 48 41 4 2 2 40 Lagos 37 8 30 8 39 o Cape Frehel Light 43 4 1 5 2 18 47 C. St Mary .. 36 56 o 7 51 o St/Brieux 48 31 o 2 44 30 Pt des Humjma . . 57 5 45 7 3 -o Brehat I. North end j8 51 20 2 55 45 Pt Avenilla .... >7 5 6 6 57 o Rock Douver, Mid. [9 5 20 2 53 o St. Lucar 36 45 6 16 30 Seven Island Mid. 48 55 o 3 24 o Seville 36 59 o 5 5 o TriangleRocks,E.e. 48 54 o 3 36 o Cadiz 36 32 o 6 16 o Rock Blanch ... 49 i 30 3 56 50 C. Trefalgar . . . 36 10 o 600 Mo of Baa N. end . 48 45 40 400 Gibraltar,EuropaPt.i36 6 30 5 19 3 Le Four Hie 48 36 o 4 45 30 Ufliant Light . . . Point Matthews . . 48 28 8 4-8 19 34 5 3 6 4 45 39 ' North Coajt of the Mediterranean. Breft Point Raz Saints Rocks Point L' Abbe Glenan Mands . . . 48 22 42 48 4 o 48 5 o 17 4* 40 47 42 o 4 29 4 4 45 o 5 3 '5 4 23 o 400 Malaga - .. Mod rill Almeria C. de Gatt 36 43 3oN. 56 44 50 36 51 o 36 43 50 4 zi o\V 3 32 o 2 30 2 12 5 Quimperlay . L'Orient Quib r on, S. Point Jfle de Groas,E.Pt. Belle Me, W.end Houatlfland, Middle Hedic Ifland Me deDieujN.W.e. Auray . Van lies Croiiie .... Nantes NoirmoufHer I.N.e. 47 5i 53 47 44 30 47 2$ O 5-7 37 o 47 22 50 (.7 23 o 47 20 45 46 43 o 47 39 TO 47 39 H \1 17 9 47 12 45 47 2 o 3 33 o 3 22 3 4 o 3 24 o 3 *4 55 2 57 42 2 51 5 2 24 2 58 5 .2 44 45 2 28 30 i 32 45 2 J7 20 Point Cape . . Carthagena Cape Pallas Alicant C. St. Martin Denia Valencia C. Oropefo R!verEbro,Entrance Terragona Barcelona C. St. Sebaftian . . Bay of Rofes .... 57 25 20 37 3' 40 37 36 30 38 20 41 3 8 47 20 38 52 20 39 26 o 40 6 o 40 43 o ji jo 30 41 23 8 4i 53 o 42 14 o I 26 100 o 41 15 o 28 10 o 12 3oE. 050 o i 8 30 W o 8 8E. o '55 o I I? 2 IO O 3^0 311 o St. Gilles 46 4 1 3 i 56 o Cape Creux 42 19 10 3 21 O Roche Bon |.6 1 6 o 2, 24 Collicure .... 42 3 ^ 45 350 Me of Ree, Light . }6 14 49 i 33 25 Perpignaa 42 42 G 2 56 MeofOIeronN-P:. 46 3 o i 24 45 Narbonne 43 ii 20 310 Cordova i Li^l.t . . . Royan Bourdeaux . . . 45 35 14 ' >5 3 o 44 51 o i 9 55 I 2, O o 34 o Agde r ort Brecon Cette Lights 43 19 43 i 6 30 23 3 3 28 o 3 30 15 3 42 o i C. Feret 44 40 o i 16 30 Montpelier 43 37 o 3 53 C. Breton i Bayonne St. Jean de Luz - . 43 39 43 28 30 43 24 o i 25 o I 2,8 26 i 30 o Aigues Light * Tour de Bouc. . . . t ,Vjarfeilles 43 32 30 43 22 30 43 17 50 4110 5 4 o 5 23 o 1 C Machicaco . . j Bilboa 43 29 o 43 15 2, 2 4O 2 43 o La Ciotat Toulon 43 10 20 43 7 16 5 4i 5 55 3 1 C. Mayor St. Vincent Vilhviciofa f Gijon C. P.enas 43 3- f3 23 43 34 o 43 35 43 43 o 3 38 o 4 15 o 5 ao o 5 38 o 5 48 o f-TIo'-p" 43 7 45 43 2 30 43 8 o 43 26 o 43 17 o 680 670 6 44 o 6 43 o 6 43 o Gien C. Taillar Frejus St. Tropez Aviles 43 35 5 53 o C. Gros 43 32 o 79 Rebadeo 43 33 10 720 Cannes 43 33 7 O O C Qrtegal C. Finifterre C. Corobedo Vigo Vienna TJ J J 43 4 6 37 42 53 42 39 o 42 14 o 41 47 o 7 5* 9 J 6 J5 o 10 30 8 39 45 8 43 o Antibes ... 43 34 4O St.Marguerite,Ifland 43 31 20 Nice [43 42- o Villa FrancheLight|43 4 3 CapeMeile 143 5 8 7 9 o 7 4 o 7 17 o 7 2 f o S 21 Q o Oporto C. Mondego 41 9 o 40 10 50 8 46 o ] 8 52 o i Savona '44 1 7 2O Genoa -J4-4 2 4 5 o 2 ^) O 3 59 o TABLE XXVII. OF LATITUDES AND LONGITUDES. ' "\ames of Places. '^ . Long. D. M. Names of Places. tat. D. M.. S. T ong. D. M. Pappallo 44 *& ^'- 9 17 o> Smyrna ^ 23 7 K.2-7 6 33 E. ' ov-.t Venere . . - 4 1 2 o 9 46 o ''.ape *"olpe 36 38 o 27 43 o Pi fa 4'* A3 o 10 23 o z8 31 30- lorence > 43 -1^ 35 ii 15 o apes . . : i *> O 28 37 o Leghorn . . ! 4l 3 3 10 16 30 CapeChelidoni ... 36 20 ,0 21 C. Mount Ncio . . 43 24 o 10 23 o ofa 1 1 and . . . 36 iz o o Vada ''4' T 9 ** 10 37 o Satalia .... 57 2 3o o :i o Cape Troy ....,42 49 O 10 44 o i-'ape 'Vaurronre "6 27 o 32 o o Point Hercole 42 23 10 II 12 - avelero Point .. . 36 30 o ^3 5 Civi K a. Vecchia . . . 42 6 o II 46 1 ape Urio Rome 4 1 53 54 12 27 41 Yaff.> 36 44 o ^640 Cape d'Anzia .... 41 24 o i* 37 o Me/.andretta or Cercello Point ... 41 12 1350 Sca.jJeroon ' o >6 15 o Gaeta ' .... 41 iz o 15 31 o Cape Porco 36 14 o ?5 48 o n aples 40 ^.o 16 o Cape >t. Mary ... 39 40 O 17 32 o 17 38 o 18 53 o Danjietta . . . Cape Bourlos .... Rofetta 31 31 o 31 43 30 31 22 45 32 o o 31 16 o 30 43 30 Cjpe Otranto . . 140 5 o 1950 : Aboukir .... 31 19 o 30 25 o j;rirvJi 1 . . 40 40 o 18 3 o Neifon's Ifland 31 21 30 23 o Manfredonia . . 41 30 o 16 17 o Cairo 30 2 21 31 18 30 Ortona . . 42 36 o 14 <;2 o Alexandria 31 II 20 30 II I5 Ancona 43 37 54 13 28 52 Cape Rofe 3 59 o 29 25 o Comachio 44 2 5 12 3 o Cape Selomon . . . ,i 43 30 25 ii o Chiozra . . . 4? '> 12 4 o C, i'azatin 32 28 -o 23 15 o Venice . .>4< 40 o 12 21 Derne * . , 32 51 o 21 5S C Tiiefte .... 45 49 J 3 53 o Cape 'a a fat 33 i 20 27 Rovigno 45 12 o 13 49 o C-'.pc ' enfurito . . . 32 7 o 15 II 30 Segnia 45 ii o 15 19 o Tripoli 3^ 54 o 13 18 o Zara 44 26 3 16 j 30 Cape Gergis 33 59 o i 1 35 Sebenico .... 44 3 16 34 30 Cape Paul .... 35 I1 ii 90 Kare-ita . . 42 52 o '830 Suza .... 35 39 o 1*45 o CapePalli, N. P. . 41 21 o 19 44 o Cape Bon .... 37 5 3 II 5 20 Capa Leng-uetta . . '40 30 o 19 48 o i unis .... 36 46 o 10 16 c Butrinto .... 39 5 o 20 19 o Cape Blanco .... 37 27 o 10 7 o Cape St Nicholas . 39 34 o 20 ]Q Cape Kofo 17 20 o 920 Larta .... 39 3 o 21 22 Cape t erro 3 , i < o 7 45 o Coron . . . 36 47 26 21 58 37 Cap^e Bugaroni . . . 37 6 o 7 13 o Cape Matapan ..36 23 20 22 29 15 Cape Tedels .... 3 6 54 4 i* o Cape St. Angelo ..(36 26 30 23 13 o Cape Cagines . . . 36 47 O 3 12 o Napoli .... 36 43 30 23 i o Algiers .... 36 43 o * H o Corinth 37 53 22 23 2 O Cape Tennis .... }6 33 o i 36 o Cape Doro Rock . - 38 9 59 24 37 4 Cape errat *5 55 o o 43 a Salonica .... 4 39 12 45 o Cape alcon ; . 4 6 o 46 Lagos .... 40 58 o 25 3 o Cape Figalle 35 32 o i 3 30 Cape Maori 4 35 o 25 37 o Cape Tre- Forcas . 7.8 a 54 o Dardanels . . . IO 10 26 18 o* Cape "Negril ?5 41 o 515 o Galipoli 4 2 5 33 ^6 38 o ',5 29 o 5 21 o CONSTANTI- Cent a Point .... 5 50 o 5 16 9 NOPLE 41 i ro 2* ^ T- Tangier .... 1 S 4^ o 5 49 Cape ..parrel .. ^ 4-> o ; 5s o South Coaft of the Mediterranean Sea. I /lands in the Mcditcrra.scan. Scutari _ ... 41 o 2oN. 2858 oE. Alboran ... 35 56 cE. 3 o oW Cape janifari 40 2 30 26 4 o Zaftarina '5 ri . 21 Cape ;:aba 39 45 25 56 o ; 7 cn.icteiTa C. Mofa 38 37 : T -8 c Adramietta 39 34 o 26 58 o ivica N. E. Point .\^-.j 3 o i 37 TABLE XXVII. OF LATITUDES AND LONGITUDES. Names of Places. Lat. D. M. S. Long. D. M. Names of Places. Lat. D. M. S. Long. D. M. Ivica S. Point 38 49 oN i 25 oE. Alicudi 38 41 ON. J 4 23 oE. olumbrctes 39 5 6 o 39 o Uftria, Weft Point 38 47 o 13 17 o Cabrera 39 6 300 El Navio . . . 38 47 30 14 48 20 Majorca. Levanfo . 18 3 o iz 29 o C. Formentor 39 5 8 3 16 o Maritime 38 z o 12 21 20 S.Po'mt, C. Salmi . 39 H 3 380 Favouillane . 38 o o 12 30 . Point, C. Pera . <9 43 o 3 33 o Galiti, Eaft Point . . 37 48 o 9 18 o Dragonera Ifle 39 33 o 2 27 Efquerques 37 47 o 10 58 50 Palma 39 32 o 2 42 Pantellaria, N- Point 36 54 50 12 II Minorca, C. Bajoli . 40 i o 3 49 o Linofa, N . Point . . 35 5 6 !3 3 30 Poit Mahon 39 5 2 o 4 25 Lampidofa, N. Point 35 4 3 12 49 o Corf ic a. Goza, N.W. Point . 36 5 o 14 7 o | Cape Corfe 43 i 3 9 22 Malta, C. Comoneto 36 i 30 14 18 o Saint Fiorenzo 42 35 o 9 19 o U Valetta 55 53 3 3 14 30 30 Calvi 42 34 o 8 43 o '. Marza Sirocco . 35 5 H 34 o ' Ajaccio . 41 50 o 8 42 o Gulf of Venice. South Point . 41 22 9 12 o ; ano .... 40 2 20 40 O Tower Diana 42 8 o 9 34 Pelegofa .... 42 23 o 16 32 o Baftia .... \* 4 2 o 9 z7 o Plana 42 13 o 16 o o Sardinia* I'remite .... 42 13 o '5 43 C pe Longo ardo . 41 14 3^ 980 Lifla, South Point . . 42 55 o 16 30 o Aimari, N.E. Point 41 8 o 8 23 o J omo 43 io o M 43 30 Cape Caccia 40 34 o 8 4 45 -onga, S. E. Point . 44 io 40 15 34 3o C- ot. Marco . . 39 5* 38 8 26 o Coronate, N. W. P. 44 io o J 5 37 o 1. S. Pedro, W. P. 39 8 o 870 Saniego, S. Point 44 36 o 14 30 20 C Teulada 38 51 o 8 36 o 3razza 5 N. W. Point 43 20 o 16 56 o Ifle Toro (Rock .. 38 50 o 8 17 o -'alermo, I. Lufma . 43 i* 3 16 51 oW Caglaria 39 '4 o 970 Curzula,W. Point . . 42 47 o 17 oo C . Carbonera 39 7 o 9 28 o Aguita, N. Point .. 42 35 o 17 4 o C . Ferrato .... 39 23 30 9 42 o Melida, W. Point . . 42 31 o 17 40 o C. Bellavifta 40 2 30 9 52 o Cephalonia, S. Point 37 55 o ii 17 o C. Coiiiiiio ^o 34 o 9 53 3 Cape Vifcardo . 38 24 o 21 3 20 I. Eiche 4t 5 30 9 35 o Corfu Point, Timon 39 38 o 19 58 o Gorgona 43 25 o 9 54 Paxu, N. W Point-: 39 18 o 20 23 Capraria .... 43 o o 9 49 o Zantf,S. Point .. 37 32 30 11 II O Elba, Weft end .. 42 44 o io 3 o Archipelago Pianoza ..... 4* 34 o io 4 o Pt. Timone, i. Corfu 39 38 o 19 58 oE. Formigues .... 42 23 30 io 7 o Paxo, N.W. Point . 39 J8 o 20 23 Monto Chrifto 4= 20 30 Jo 18 o Cefalonia, S. Point . 37 55 o 21 17 O GiUo .... 41 21 o io 54 o Cape Fifcardo . 38 24 o 2130 Gaaulo 4* 14 o n 5 o Zante, South Point 37 33 21 12 O Palroaria \Q 56 o 12 51 O Cerigo, South Point. 36 8 o 22 57 o Ponza, South end . 40 54 o 13 o o Cerigotto . . 35 49 23 17 o i fern a, South Point 40 40 30 *3 55 o Milo Mown 36 41 42 24 22. 12 Capri, S.W- r oint . 40 32 o 14 14 o Scio, Town . . . 38 17 o 26 6 o Sicily. Meffina. Mytelene Town . . 39 IO 26 26 o Cape Orlando . . j8 8 o 14 53 o Tenedos . . 39 43 25 52 o Cape Cera la 38 i 30 14 7 o Lemnos, N.E. P. . 40 o o 2,5 26 o Cape Cafrano 58 9 o '4 34 o Landia. Palermo 38 6 45 13 25 30 Cape Crio . . . 35 io o 23 25 o Cape Gallo 38 12 30 13 24 20 Cape Spada 35 4i o -3 40 o Cape St. Vito 38 12 12 54 o Suda 35 23 24 5 o Trapano ?8 2 12 42 Cape Sufa 35 28 o ^5 7 o C . 3 Fontani . 37 35 o 12 47 30 Candia 35 18 40 15 18 o Cape Alicante 37 3 o 14 o o Cape Sidera 35 io o 26 17 o Cape Saramis 36 47 o 14 36 o Cape Salamone . . * 35 i " 26 26 o Cape Paflaro 36 40 o 15 17 ' Shacufa M 7 o 15 22 O Goze, South Point, 34 50 o 13 50 o Cape Moline 37 36 o 15 19 o Panto, N.E. P. 35 49 io 26 58 o Stromboli 38 48 o 15 28 o Rhodes, Town 36 27 o 18 30 o Lipavi, South Point 38 31 o ,15 ii o Cape Tranquillo 3 6 S o 27 30 o i oaiina, E*ft Point . 39 19 o |i5 9 o Cyprus. Ftlicuri, . .. 38 40 o 114 42 o Gape Andrew f . . . 35 4i o 34 aS o TABLE XXVII. OF LATITUDES AND LONGITUDES. Names of Places. Lati P. M. S. Long . D. M. S. Names of Places. Lat. D. M. s. Long. i D . M. S. Cerina 35 14 .oN, 32 48 oE. River Volta 5 53 oN. I 2C O Cape Salizano .... 7500 31 41 o Cape at. Paul 5 52 o j I 4O O Cape de Gatt .... 34 34 23 5 o Whidah 6 25 o A 4J.W ** 3J 7 O | i. ape Grego 35 7 20 34 2 o Formofa River 5 53 o * j y 6 10 o C. Formofa 4 30 o 6 40 o " New Cal'abu- Rive; 4 23 o 800 Coaft of Africa, from Cape S part el to \ the Cape of Good Hope. Cameron River . . . John . . . Gabon River 3 20 c i '15 o 000 IO 9 23 o 927 O C.deLopez'oonfalvez o 47 o3 *J V 91 ~> O Cape Spartel . . 35 49 N 5 55 oW Sefto River T ' ** " 2 16 ** J q 7 c o Larafli New Sale, or Rabat. 35 12 o 34 3 660 6 47 o Alvary r'ay Congo River . . , 3 27 o 4 35 7 O -> w 10 40 ii 5 o Mazagan .... .3 18 30 8 25 o Ambris River 6 45 o 12 O O 1C. Blanche 33 1 o 8 38 o Capt- Ledo 9 50 o 12 3 o C. Cautin Saffia, or AzifHa . 32 34 32 20 o 950 920 v Philip de Bengtiela C: pe Negro 12 18 o 1 5 o o 12 35 o nAA n Mogadore Ifland . . 31 27 o 9 36 o T.gers Ifland . 1 6 30 o T'r M 12 O O | Cape Geer .... i Santa Cruz .... 30 38 o o 27 30 9 52 o 9 40 o *"ape Frio C Ro .'erode Pedro iS 40 o 2300 13 42 o 14. o o ! Cape Nun ] Cape Blanca . . . Cape Bajador .... 28 40 o 17 57 o 26 14 o n 15 o 12 54 o r 4 3 1 Angra Pequena Cape das - oltas . . St. Helen's Bay Cape 26 35 o 29 o o 15 40 o 16 45 'o Korn Ifland, Entrance St. Martin's 12 At: n or'Rio do Ouro . . 2 3 35 3 15 18 q S,ildannah Cay . . . )* ^5 17 45 o 1800 Cape das Barbas . . ifle de Lobo . . . i f 1 *-. ^^ D1 22 15 30 21 7 10 16 39 45 17 15 o Cape of Good Hope 34 29 o 18 23 o I V-.ape Blanco . . 1 Cape St. Ann j Cape Mynck . , 20 55 30 :o 42 30 [9 12 30 17 29 55 16 35 o r6 21 o IJlands, R.cks, and Shoals, / the North | Portendick 18 6 20 16 4 o Atlantic Ocean, and ^outh Atlantic,^ Barbary Point, En- or Southern Ocean. trance of Senegal B . 5 1 53 16 31 15 Cape Verd .... Breakers, off Ditto . Goree Ifland Cape Naze .... Cape St. Mary, En- 14 46 o 14 50 30 14 40 50 14 24 o 17 51 o 17 40 o 17 16 Rockal ...J57 13 oN. Atkins Shoal &$ 6 o Chapel Rock, D. . . 47 34 o Rock,D. ... 46 25 o Rock "- ~ 14 1 3 oW ii 32 o 7 12 o 13 12 O ] trance to the River Gambia . . Cape Roxo . . Cape Vergu Delos Ifles C. Sierra Leon . . . 3 17 o 12 23 9 52 o 9 29 o 8 2 9 30 16 56 o 17 10 o 14 56 o 14 7 o 13 48 o Steen Ground Jofyna Rock Bermudas Ifle ... Breakers Azoic*, or Wefiirn IJlmds. 3 7 - 45 o 30 46 o 32 35 o 32 35 o 23 u o \ 21 25 j - r 41 ' | 03 28 o j : 7 45 o i Cape Anne . . Cape Mount Cape Monferado . . i Cape Baxos seftos River Cape Formofa Cape Palma St. Andrew's River . Cape Maho Cape Appolonia . . Axim .... 770 6 46 o 6 16 o 5 28 o 5 27 o 5 8 o 4 25 o 4 58 o 5 12 o 4 59 o 4 52 o J 3 27 o 1 1 42 o u 17 o 10 7 o 9 47 o 9 39 o 8 15 o 6 30 o 5 12 o 3 ii o 2 36 Corve, South Point. Flores, Pt. Delgada Fayal, S.E. Point . Pito, Sumeries Point de Elpert.il Eaft Point Sc.G.orgfjS.E.Point Graciofa -Villa da Praya Terceira, Angta > . St. Michael 39 4i 13 39 33 29 34 30 12 38 27 o 38 ,6 o 38 22 38 30 45 39 2 70 38 38 10 3i 73 I 31 7 C 1 z* 4i 3<> i :8 2'S o -8 36 30 8 6 o i 27 50 o ^7 59 o '7 13 34 C. Three Points .. Dix Cove ... Sakondee Elmina . t . Cape Corfe Caftle . . Devil's Hill Annamaboe Fort . . 4 40 o 4 48 o 500 5 10 o 5 12 5 24 o 5 10 o 5 30 o 2 38 2 22 O i 59 o i 40 o i 48 o o 50 o i 7 o o 16 o Pta. Delgada ... Pta. Ferraria North Eafi Point Form i gas, or Ants . St. Mar/, Town . . -We a Point Punta da Caftello Mad ir., ///,.-. , 37 44 o 37 54 15 37 5 2 30 37 17 10 36 57 40 36 58 45 36 57 o 25 44 30 25 5* 18 5 14 30 "4* 54* o -5 13 o 2516 o 25 6 o "arracoai . f . - - - 5 53 o ! i 29 o Forto Santo, Town 32 58 15 16 25 o TABLE XXVII. OF LATITUDES ADD LONGITUDES. Names cf Places. Lat. Long. Names of Places. Lat. D , M . 5 Long. DM S Madeira Abrolhos Shoals . 18 6 oS 39 36 oW - Lorrnzo Point. . 32 43 oN. 26 47 oS. Afcenfao . 20 25 3 40 o Triftam Point 3* 54 17 25 o Trinidad I. S.E.Point 20 30 o ^9 16 o Funchai 32 37 30 1750 Martin Vas 20 2^ O 28 40 o S. Dezertos Saxemburg 30 45 o 19 40 o South Point ... 32 22 16 36 o Tiiftan de Cunha . . 36 27 o 13 17 o Salvagea, Middle . . 30 8 15 11 53 o Diego Ah-arez . . . 38 53 o id 40 o Piton 3 I 3 8 1660 Coughs Ifland 40 10 o 2 l6 O t.a.na'"y IJJes- ,Pepy'b Ifiand 45 30 35 3 o Palma,TownS.Cruz 28 37 o 17 46 o He Grande 44 40 o 40 36 o North Point South Point Feiro, V 'lv-; j rde . . Gomero, Port ' . 28 53 50 28 30 o 27 47 35 28 6 30 ^7 55 15 17 53 o 17 5^ o 17 8 50 Falkland ICaidi --- Po;t Egmont . . . Cape Percival. . . Ckrift;ua&Bay,I.De 51 10 o 51 ~7 o 60 16 o 61 18 o *Tenerifte fulation . . . 48 41 c 68 53 13 Hidalgo Point 28 36 10 16 21 o Aurora Ifland . < 52 6 o 48 17 -o Oratava 28 24 40 16 35 o 5^ 33 o 48 6 o Te;;a Point . 28 20 16 57 o ?c; 'ib Georgia* Peak ^ n o 16 39 o Cape Duller 53 58 30 37 40 o PortChviftianos 2 3 ;6 45 o WalJisI;.and 54 o o 38 2 Santa Cruz . . 28 28 o 16 16 o Cape Saunders 54 6 30 36 57 39 Canary, N.E Point 28 13 o 15 25 o Cape North 54 4 45 38 15 o Painus 28 7 o 15 26 o Cape George . . 54 17 o 36 32 30 Souih Weft Point 7 55 o 15 52 6 Sandwich Bay 54 4* *o 36 12 Fuerteventura (^Charlotte's Cape 54 32 o 36 11 30 PJnt Gorda 28 46 o 13 52 Cooper's Ifland 54 57 o 6 4 30 South Weft Point ,8 4 4 o 14 32 o Cape Difappointment 54 52 o 6 15 o ftmzarote, S. Point Puerto de Naos 28 51 o 28 58 o 13 47 o '3 33 3 Green I es Pickerf^ill Ifland . 54 59 o 54 42 30 " 36 15 o 36 58 o Punta del Fanoa 29 15 o 13 29 o Clerk's "Rocks .... 55 5 30 34 4* o Graciofa .... 29 17 o 13 31 o Sandit.uk Land. S k Claire 29 18 3o 13 32 o Cindlemaslfiands . . 57 jo o 27 13 o Alegranxa . Ca A -t P'-rd Jjland. St. Antonio 29 25 o 13 3; 30 Saunders' 1C e C.ipe Montague . . . Cape Briitol 58 o o 8 33 o 9 f 2 30 26 58 o 26 46 o w 26 51 o Santa Craz . 17 13 o 25 15 o Fiie"and Peak . . . 59*2 26 55 30 South End 16 58 o 25 28 o Southern Thule . . . 59 34 o 27 45 o St. Vincent 17 i o 25 6 o St. Lucia, S. Point 16 46 o 24 55 St.Nicholas,N Point Eaft Point Salt I. South Point 16 50 o 16 30 o ,6 38 15 24 37 o 24 12 O 2'z 56 O i The C'jfift afid adjacent IJlands from the t Cape of Good Hope to Canton . Bonavift;:, N. Point 16 3 40 22 45 o May--, S. Point . 15 6 o 23 10 o E.irtrrnCoaft of Africa St, Jago ^ape of Good Hope . 34 2 9 oS 18 23 oE. Port Pray a *4 53 4 23 31 o jFalfe Cape 34 16 o 18 44 o Fogo. North P/mt. T 4 57 a 24 24 o JGape Aguihas 34 44 o 20 15 o Biava, South Point 14 50 o 24 43 o Cape St. Brafs . . . 34 *8 o 2! 59 . Cape Ta'.hado 33 27 o 24 7 o Porgas Bank, N. end 17 50 o 19 10 o Cape Delgado 33 38 o 24 10 o - South enri H 45 19 45 c Ala^ou Bay 1? 30 o 26 35 o Penedode St. Pedro, Firft Pt. of Natal 32 it o 28 51 o crSt. Paul's . o 55 o 27 14 o Mid die Ft. of Natal 30 45 o 30 20 J F rnandez Po 3 28 o 8 40 oE. Port. Natal 29 50 o 30 57 o Prince's Ifland i 1 37 o 7 40 o Sm;>K.' Cape 27 7 o 32 15 o r.omas's Ifle o 19 o 6 42 o Delagoa Bay St. Matthew's i 35 oS. 7 30 oW Cape St Mary. , 25 i o ?3 16 o -umabona, N. end i 25 o 5 45 E - Cane Corrientes 23 37 o 3 6 35 o Afce.ifi'jn 7 57 o 14 15 Cape St. Sebaftian . . 21 35 o 36 25 o St. Helena Soiala . . 20 15 o 35 3^ o ; James Town . j Fernand de Noronha '5 55 o 3 56 o 5 43 32 24 o A.igoxa .... ] udio ... . }6 II O 21 29 39 27 o 39 26 o Rocks 3 5 6 34 30 P Mozambique 14 56 o 40 29 o j ----------- ' . . ' TABLE XXVII. OF LATITUDES AND LONGITUDES. Barnes of Places. Lat. T) M S Long. Names of Places. Lat. * Long. D M $ Cape Delgado - 10 6 oS. 41 15 oE Co~ ,-,,* id Co^. Quiloa . 8 41 o 39 40 o *Cape Comotin 8 4 cN 77 33 5 oE - Mombas 3 34 o 41 30 o Manapar Point 8 29 o 78 15 o MclinJa 2 45 o 4: 47 o Trinchindore Pagod 8 37 o 78 24 o Magadofha 2 20 ON 46 25 Point Calymere . 10 73 o 79 54 Ca e Bafias 4 50 o 49 20 Negapatam . 10 32 o 79 53 Cape Orfui ro 29 o 151 38 o Pranquebar JO 56 O 7'v 4 3 : Cape Guardafui . ii 47 o (51 35 o Devicotra .... J 1 21 79 47 The i\e 'fi. 1 Porco Nova ii 30 o 79 45 3 ' Cape Babelmandel Socobro I. E. Pt.- . . Cape Fartalh Suez ' ( Judda ! Mecca \, . . . Moka 12 38 O 12 15 o 15 29 o 50 2 21 29 ai 40 o 13 16 o 43 47 o 54 55 o 52 5 o 32 28 30 39 22 o 41 o o 44 o o 2uddalore . . i^ondicherry Madras ... ^oint Divy Mafulipatam Point Gordewar . Coringa Bay . . Vifigapatam ii 41 o u 42 o l6 2 O 16 16 o 16 45 o 16 58 o 17 46 o 79 37 45 ! 79 59 o ] 80 35 o j 812- o | 81 24 o j 82 37 o i 82 30 o 83 5 o Ccaft of Arabia. Gamjam 19 25 o 85 7 o ! Cape Aden 12 45 o 45 7 o [agernaut Pagoda . 19 48 o 85 57 o ' Cape More bat 1716 o 54 19 Jlack Pagoda 19 51 o 86 10 o Cape Pedro '7 54 o 55 2 7 "o ? a!fe Point .... 20 17 86 --i o j Cape Ifolette .... 19 4 o 57 18 o Point Palmiras ... 20 44 o 87 10 o 1 Great Mazeira I. . o 15 o 58 31 o Jalafore . . . 21 21 O 87 21 Ca e Rofalgate . . . 22 36 59 54 o Jngerlee Pagoda. . . 21 50 88 ii o Mufcat 23 30 o 58 16 o Cedgeree . . 21 48 88 50 a Gttipk of pf fla. Cape Muffeldom. . . t Cap* Jafk 26 17 o 25 57 o 56 17 o 57 15 o *Calcutta .... Fort William . . Chandernagor 2 34 45 2 51 88 27 56 88 30 o. Gambaroon . . 27 18 o 56 6 o pfg-n. i Baffora 30 31 o 47 3* o Iflamabad/or Chitta- i Molabar Coaji. jCapeMonze Point Gigat j*Diu Point j Cambay .... 25 o o 23 30 o 20 44 2 23 36 o 66 18 o 68 35 o 9 50 o 72 17 o gong Aracan River Cheduba I Jape Negrais .... Diamond iile .... 22 2O O o 17 o 8 45 q 680 5 50 o o 93 o 93 37 o 94 9 o 94 J 7 54 _ + M I ; Damaun .... 20 22 72 20 o 73 2 45 iVJ(J/t2J* 'avay Point 3 37 o 97 44 o 1 Omergon . ... 2O IO 30 7* 56 30 Mergui .... 2 10 30 98 19 15 St. John's Cape... . Baffeen Fort 20 6 <9 19 o 7a 34 o 72 55 2.4 unk Seylon 'ul Penang, or P. 8 15 o 98 2 u Bombay .... J 8 55 4i 72 54 24 of Wales I. ! Lighthoufe .... 18 53 o ' J^ T 72 52 54 Fort Cornwallis 5 27 o oo 25 o iCoullabal. 18 37 20 72 c6 30 Malacca 2 12 02 II Bancoot .... 17 56 40 / J J v 73 7 54 .. Cape Komania . . . I 15 o o, 5 o i Severndroog * . . 17 47 30 73 9 o iam .... 4 18 o oo 55 o Dabul 18 o o 75 29 o Clnva. ' Ghei-iah 6 37 o "3 22 24 jjmboja Point 8 45 o 3 45 o Vin'gorla Rocks .... 5 55 3 73 30 o Cape Avarello .... 2 54 Q 07 50 o ; Goa . . . ^ 3 1 O ^ti Ifi Oantn r j r Q ; Aguado Point > > C 28 ec 73 55 o r R ' ' 07 15 o j : Curwar Head .... i i 55 4 47 o 74 12 33 Vlacao 12 13 GO 30 o j 13 52 o 1 Barcelore 3 53 o 75 2 o Grand Ladrone .... 12. 2 O 13 56 o j ; Pcrmira Rocks . . . 3 13 o 74 4 o Canton 3 6 57 13 16 7 ; Mangalore .... 30 o 75 35 o i Mounc Dilly . . . 250 J J J 75 35 o Cananore Sacrifice Rock .... I $'. O i 28 o 75 2 5 o 531 5 IJlandsy Rocks, and Sbaah t in the Calicut I 20 5 50 o Indian Ocean. Cranganore .... o 17 o 76 6 o Cochin .... 9 58 o 76 15 34 larfeveen ii ro oS. ' 20 46 oE. Quii ,n .... 8 c-2. 30 76 37 o 3enia $:j 4> o 20 25 o Anjango Roads 8 39 *5 76 50 o fortune Sh.oal ?3 8 o 43 5 o P TABLE XXVII. OF LATITUDES AND LONGITUDES. Names of Places. | D L *' g Long. D. M. S. Names of Places. Long. 0. M. S. Long. D. M. S. Augufta Shoal .... Dutch Bank 33 44 t.S 37 20 o 36 16 oE. 38 52 o Eagle I. ..... Seychelle I 5 10 cS. 4 35 o 55 37 cE. 55 35 " o ! r. Edward's Ifles, North end . 46 39 30 78 2, Id Sandy Ifland 15 10 o 55 5 o South end ... 46 52 30 ' J z 30 37 47 o j\323retn Bdnjc* N. E oart . . 12 5 C o 5 1 4.4. o Kergulen'sLand - S. W. part . . . T J J ,) ^ 1 6 45 o So o o Bligh's Cape 48 29 o 68 38 15 St Brandon . . 16 34 o 62 50 o i Chriftmas Harb. 48 41 15 69 2 Roderigos ... 19 40 o 65 10 o | Cape Digby . . 49 23 30 70 32 o Port Louis . . , 20 9 44 57 a8 15 Cape George .... 49 54 30 70 12 L'Ifle Mauritius . . . 2o IO O 57 35 ' i ort 'al lifer 49 3 15 6 9 35 Bourbon, ; Amfterdaml. r; 5 1 o 77 44 o St. Dennis .... * 5i 43 55 3 St. aul .... ?S',44 o 11 18 o South Roquepiz . . . to 30 o 64 32 o Cloatts I . 21 45 o 93 27 o Speaker's Bank . . . 4 45 o 72 57 o ' Try^l Rocks . . > o 40 o 'OA. Cn r\ p^ R 1 Chriftmas liland . .. ro 35 o IWij. ^intSalatan,'S.E.P. 4 15 oS 114 25 o Cape Lopatka .... 5i o 15 156 42 30 PomcSambar,S.W.P. 2 45 109 2$ o Cape Gavareea .... 51 20 158 36 o . i . St. Peter & St. Paul S^ 5i 45 15* 4 6 30 Banguey 7 17 o 117 30 o Kronotflcos Nofs . . . 54- 43 162 13 30 Balambangan I. 7 30 oN. 117 20 Karafchatka Nofs . .(56 i 3 163 18 30 Palawan, S. Point . . 8 28 o 117 30 o Thadeus Nofs 62 50 o 179 5 North Point .... 11 20 6 I Tf) ^ ft O Cape Ifchukot/koi . . 64 14 30 173 -31 Sooloo, E. Point . . . 5 57 o 121 21 o EaitCape 66 5 30 169 9 30 Sooloo I. S. Point . 5 57 o rat tq 30 i Sard 3 Kamen 67 3 o 171 54 3oW Temontanges . .. 5 57 o iao 53 30 Cape North 68 56 o f79 ii 30 PbUlppme I/lands. ... Mindanao Graf ton Ifland 20 4 o 120 o e. PC. St. Auguftinc 6 15 o rrnofa I. S. end . . 22 5 )20 50 O -'Mindanao, S. Pt- 5 34 o' j O Tayoan .... 22 40 I 2O 2O O Goat 1 Hand .'-... 13 55 o - North end ..... 25 15 122 13 Luconi.u N. Point. 18 45 o 20 45 o Great Lequeo, S. P. 25 15 128 30 o Manilla . . . 14 36 8 zo 51 15 i North Point .... 28 o o 128' 30 o iXuno J. S. Point. . . 31 30 131 50 o rvoiLn roint .. . 34 45 o 131 30 o I/hinds, Rucks* ami Shoal*, in the Niphon I. South end - North end 33 3 41 o o 135 o o 142 o o China Sru. Matoofmaee .... 42 30 o 140 30 o iMednos Ifland 54 27 r< 5/ 55 45 PuIoBrata .... 445 X - I0 " 3 E Beerings Ifland . . . 55 3 6 167 46 o Ridang 1 6 zo o jjoz 37 o St. Lawrence Ifland 63 47 o 171.45 o PaloCoron ... .| 7 17 o i O 2 ^ O O PuloWay '10 rG2 34 o PuloUby . .. S 30 o Two Brothers ..... 8 $2, o . o The Co/til of' .iVet; 1 Holland and adja- Pu!o Condor ... 8 40 o ico 31 3 7 cent Ijlands. Pulo Sapata sio 4 30 : O Elephant 1. . . . 10 4 o roS 42 o Swilley Ifland .-.'43 55 s 147 7 3k i Pitt's I. 10 55 "4 35 o South Cape 43 42- o 146 58 o Sandy 1 10 40 o nz 48 o South Weft Cape.. .,43 37 ^ 146 5 30 Smalikey 10 37 o 1 1 2 44 o Mew Stone 3 47 J 5 146 26 30 Long I, IO 20 I 12 36 Tafman's Head ... -43 33 3 147 33 3 New J. .... 10 10 ; ( z ?. 3 o Adventure Bay ....'43 21 20 147 31 4 Firit Shoal jio 14 o r 12 24 o Cape Howe ' ... 37 3i 15 '45 3.1 o i Second Shoal .... 10 4 o 1 12 i s o Point Dromedary 36 18 o 150 5 o , Third Shoal 10 5 o ijz 10 o ,Cape St. George . .. 35 19 o 150 18 o Reef JO I C O I1Z O O Red Point .... IA- *o o 151 15 o j Scarborough Rocks . 15 117 12. Botany Bay .... JT S 34 6 o 151 23 o Macclesfield Shoal, Port Tackfon 33 5 <> i>i 25 o NorthPoint jl6 6 c 114 10 o i Port Stephens ... 32 40 o 152 9 o South Point 1515 o 114 20 o iCape Havvke 32 14 o 152 30 o Triangles, N. Point 17 o o in o o ^Smoaky Cape (near) 30 31 o. 153 6 o South Point 16 c o in 31 o Cape Byron 27 27 30 153 30 Pratas Roek, N, fide 2^ 57 30 116 57 30 'iPomt Danger ... 28 8 22 153 33 10 S W fide 2O 4.2 O T i (S 4.0 o 'Indian Hc^d * 2C ? O Paracel's, N. part . . 16 30 o no c o ;Cape Moreton * J 3 v 25 56 o r: ;s r- South part ii 37 o Tog 30 o : ;BuftardBay ... 24 4 o 151 44 o Hainan, N. Point . . 2O 2. O 110 i^ o jSandy Point ... 24 45 o 1 53 9 South Point .... 18 12 o j o |Cape Capricorn 23 29 o 151 2 O |Cape Townihend . . . 22 15 o 150 17 o The Coqil and adjacent J, , c^Pafmerfton ". ' .' 22 10 21 30 149 42 o 149 6 o C union to Cape Nor tit. Cape Conway 20 36 ^48 32 o Caps Gioucerter .. . 19 59 1^8 ir o Canton ... 2 3 6 Sf&jttJ 1 6 ?E. Cape Upftart 19 36 o 147 28 o Macao .... 2 213 o ji? :z o Cape Sandwich .... 18 17 ii 146 I 13 jGrand Lad roue . ..|22 2 o 113 c6 o TABLE XXVII. OP LATITUDES AND LONGITUDES. Names of Places. Lat. I). M. S. Long. D. M. Names of Places. Lat. D. M. S. Long. D. M. S. | O&DC Grafton . i 6 57 OS 14. > fA oE Weft Point I *o c S TA& 1O oE. jCape Tribulation. .. 1660 *TJ -I'T VJ ^ 145 21 Stephen's Island 22 14.0 gw 139 39 Endeavor River. . . . 15 26 o 145 14 41 Duruur's Island . . . i 15 o 143 21 o Cape Bedford .... 15 16 o '45 '5 o Matty's Island . . i 45 .0 143 z o Cape Flattery .... .4 56 o '45 *7 o Admit ally IjlanJ:*. Cape Weymouth . . . 12 42 142 45. o Mid. of the Jargeft 2 l8 O 146 4$ o Cape Granvilie .... II 5 8 142 22 O Portland Isles, Mid. 2 27 148 3 o York Cape .0 37 o 141 36 o Cape Byron . . . 2 30 149 2 Cape Cornwall .... 10 43 o 141 o o Duke of York I 49 1ST 20 Endeavor Straits . . ro 39 o 141 24 o New Ireland, E Pt. 5OO 152 30 o -Weft Point ... 2 20 F4.S 20 Cape St. George . . . 4 53 30 ^ 152 19 o I/lands and Recks, &c. in the Pacific <}ueen Charlotte's Foreland . . . 2 29 O 148 27 o Ocean. Sandwich IslandPeak 2 53 o '49 17 N. Britain, E. Pt. . . 4 53 o 153 9 o Sled e Ifland 64 30 oN.li66 !i oE - Weft Point 600 149 20 Clerk's Ifland 61 15 o 169 40 cW Port Praslin 4 49 2 7 r 53 6 30 Ander o 's liland . . 60 17 o 162 31 o \ T ine Islands .... 4 36 o 154 17 o ; Gore's I. C. Upright 6(3 22 172 26 o iouganville Straits . 7 5 o 158 56 o iKey's I. S. W. end 59 42 o 143 8 30 ''>>/ JjQftdi, Round Ifland ... S8 56 30 i53 3=> Cape Deception .. . 8 26 o r59 14 o S. Hermogenes 111. 58 15 o 15213 o iCepple't Island .... 10 15 o 165 4 o Trinity Ifland . 56 35 o *54 53 Edgecomb's Island. . II 10 165 14 o Foggy Ifland 56 12 157 19 30 Ourry's Island .... II 10 165 19 o Oonemak Ifland. ... 54 3 3 167 31 o Egmont Isle, 'Cooper^ I. S. Ft. .. 54 24 o 169 o o C. Byron, N. E. . . . 10 40 o 166 49 o ,Oonalafka 53 54 45 1 66 26 o Lord Howe's Island II 10 164 43 o Sulphur Jfland . 24 48 o 141 20 New Hebrides. North Ifland 25 14 o 141 14 o Cape Cumberland . . 14 39 30 166 47 o South Illa'hd 24 22 30 141 24 o 2ape Queros .... 14 5 j o 167 20 o Tinian 14 58 o 145 5 o Leper'sisland, N E. 15 16 45 168 10 45 St Andrew's Ifland 5 18 o 133 40 o South Weft ... 15 30 o 167 4^ 30 Dangerous Shoal . . 2 53 o 136 10 o r 16 30 o 167 58 30 Freewill, or St. Da- Vfaskeylyne's } 16 33 45 i 68 i 30 vid's Islands o 50 o 137 51 o Islands j i 6 32 30 167 59 30 Pelew Iflands .... 7 19 o 134 40 o / 16 33 o 167 59 is Pifcadores, N. end . II 20 O 165 44 o Mallicolo, S. Cape . 16 38. o 167 42 30 -~ South end II O O 1 66 4S o S. W Cape 1631 o T f\ *7 J f\ "*C\ Oeyhee, N. Point, . 20 17 "55 5') - Cape Sandwich . . . 16 28 o JO/ J U ^{J 167 59 o South Point . . . 18 54 30 15; 48 o Sandwich Harbour . 1 6 25 20 167 53 o Eaft Point ... 19 33 o 154 5^ Cape Lifburne . ... J5 40 45 t66 57 o Mowee, E. Point. . 20 50 70 '55 55* o St. Bartholomew I, 15 42 o 167 17 30 South Point 20 34 30 156 12. 3O Aurora, North end . 14 52 o i6S r3 o Weil Point . . . 20 53 30 33 South end .... 15 24 o 168 20 45 ^ersjegoa .... 19 28 o 156 2 15 Table Lland 15 38 o 167 7 o Tahowrooa .... 20 38 r;6 36 o Whittuntidel.N.end 15 28 30 i6S 21 30 Moozokinnee 20 39 o 156 25 30 South en 1 16 o 25 1 68 19 o Rannai, S. Point . . 20 46 30 156 55 3"o Ambryml N.E.end 16 4 o 168 21 25 Morotai, VV. Point . 21 1O O t57 17 o Weft end 16 15 o 168 3 30 (Woodhoo 2 1 A2 3O T r 3 w "lr\ rj [670 o i63 28 4" Tahoora .... ai 4 2 30 1 S 3 * y 1 60 24 30 Apee, S. end 16 53 30 i6S 37 o . Oreehowa 22 3 160 6 30 -N.W. end ... 16 39 o 168 i3 o ;Oimea Road 21 57 o i59 39 3 Shep^ard's j From 16 56 o 168 41 25 Oneeheow .... 21 49 30 i 60 13 30 Island I to 17 3 30 168 43- 30 Whyteeie Bay .... 17 30 20 157 50 23 Three Hill Island .. 17 4 o 168 35 o Owhyee, Whyrnea Reef off W end... 17 8 30 168 28 30 Ro'ad ..'.... 21 57 3 '59 4 r 45 One Hill Island . . . 17 7 30 6 o Chriftmas, or Noel I. 1 57 45 *57 35 Two Hill Island .. . 17 13 5S J 5 Soconal. Middle . . . 18 48 o (10 IG Monument 7 14 25 i6S 38 zs :Cape Falfe 8 40 oS. r?6 30 oE. Hinchinbroke I. . . . c7 25 o r6S 38 o Eaft Point 6 20 148 o o Montague Island . 17 26 o 168 31 30 LouifiadelHes, E.Pt. 10 35 o 154 o o TABLE XXVII. OF LATITUDES AND LONGITUDES. Names of Places. Lat. Lat. Names of Places. Lat. i. - ***_ Long. D. M. S. D. M. S. D. M. S. D. M. S. Sandwich 5 F f0in 17 29 cS 68 20 scE. Port Refuge . 8 18 3 oS. 73 56 oW I Hand ) to 17 53 o 168 45 25 Savage Island .... 19 2 15 69 30 30 Traitor's Head 18 43 30 69 20 30 Agyoau '9 39 15 74 43 o Small Island off . . . . 18 41 o 169 26 c Hapae, North Point 9 41 o 74 37 20 inmer 19 16 o 169 46 o Mattafoa 19 44 30 74 47 o T I ' d 5 From 19 j6 30 169 21 O Turtle Island 19 4 8 45 77 57 o i to '9 5* 30 69 43 o Annamooka . 10 15 2, 74 5^ 55 ,Port Refolution . 19 32 24 169 43 o Tongotaboo, Bander- Inanama .... 19 31 o 170 21 O main Koad 21 4 15 74 56 24 ,Enar.um .... 20 IO 170 4 o Annamoke Ette . . . o 17 45 74 32 30 Neiv Caledonia* Commango Ette . . 20 l8 20 174 28 o ;Balleabea Island . . . 20 7 o 164 22 , Commango 2O 19 20 74 26 o Pudyoua Obf. .. . 20 I 8 10 164 4.1 12 . Tonamai . . 2.0 28 74 3i 3 Cape Colnet . . 20 30 o 164 56 o Tellefageo 20 3 I 15 174 29 i5 1 2, C O 167 8 o Morotoi * 21 n O 156 44 o Queen Charlotte's * 3 w I V f U VJ Eaoowe .... 7 21 20 30 '74 34 o Forebnd .... 22 15 167 12 4 Pylltaart's Island . . . 22 23 3 174 48 o Isle of Pines 22 38 167 38 o Oheteroa , ... 22 27 150 47 o Botany I. anch. oft". . 22 z6 40 167 16 45 Toobovai . . ^3 25 o 129 40 30 Norfolk Iiland . 29 i 45 i6S 10 o i (Paimerfton Island . . 18 o i 162 57 o Ne 5 w Cape Colvillc 36 26 o '75 33 o Sciily Island 16 28 o 156 22 ; Mercury Bay 3 6 47 o 175 56 o Ohamaneno 16 45 32 151 39 40 Cips Runaway 37 3* o 178 12 -lowe's I. . . 7. 1 6 46 30 154 6 40 EtitCape 37 4* 30 r/9 o o Marua Island 1 6 25 40 152 32 40 Mount Edgecumbe . 37 59 o 166 5; o Bolabola Island 16 32 30 151 51 53 Toiaga Bay 38 22 24 179 13 o Ulietea . . 16 3i 30 152 57 o Poverty Bay 38 42 o 178 24 o Huaheine .... 16 43 o 150 52 o Albatrofs Point . . . 38 4 o 175 18 o Owharre Harbour . 16 44 45 151 9 40 Cape Table 39 7 o J78 24 o Lord Howe's I. . . 1 6 46 o 155 25 o Mount Edgecumb . . 39 16 o 174 45 o D. of York I. ... 17 28 o 151 14 o Table Head 39 17 o 177 59 37 Emio 17 30 o 149 54 o !Shambles 39 20 o 178 20 45 Otaheite, Obf. ... 19 29 15 149 32 30 Portland . . . . 39 2 5 178 12 Point Veaus 17 29 20 149 36 45 Cape Kidnappers . . . 39 43 o 177 36 o Oaitepeha bay . . * 17 46 30 149 14 24 |Cape Turnagain.. . . 4 34 o 177 5 o Ofnaburg 17 48 o 148 10 o jC. Stephens (I. off) 40 37 o 174 54 o Pallifer Island . . . 15 38 15 146 30 15 ^Banks's Island . . , . 43 32 o 173 30 o Chain Island 17 25 o 145 38 53 'Cape Saunders . . . . 45 44 o 167 48 o Oheterooe 22 30 36 150 48 45 JSouthCape . . . . 47 19 o 167 48 o Toobouai . 23 25 o 149 20 30 'Knight's Island . . . 48 15 o 1 66 44 o Taookaa Island 14 30 30 145 9 3** JGohuidcr*! Island . . . 46 31 o 167 ii o Adventure Island . 17 6 20 144 17 45 Weft Cape 45 54 o 166 43 o Furneaux Island . . . 17 ii o 143 6 40 jDufky Bay 45 47 3 166 18 9 Refolution Island . . *7 2 3 i5 ,41 .45 o Cape Farewell . . . . 40 33 o 174 o o Bird Island 17 48 i43 35 Q^ Charlotte's Ent. . 41 o o 175 i'5 o Groups, S. Emoft. . r8 12 o 142 42 o Sound 41 6 o 174 18 30 Bow Island, E. end. 18 23 o 141 12 O Cape Campbell 41 44 o 176 15 o Prince Henry's I. . . 19 o o 141 6 o Cape Pallifer 4i 34 o 176 7 o Cumberland Island . 19 18 o 148 36 o Pch?t Rodney 36 15 o 175 7 o Gloucester Island . . 19 ii o 140 4 o ; Two Sifters Skirmifh Bay 43 4J o 43 49 o 177 II 176 35 o (^Charlotte's I. .. Egmont Island 19 ig o rg 20 o 138 4 o 138 30 o Cape Young 43 48 o 176 5,8 oW Whitfunday Island. . 19 26 o i37 56 o Friendly JJJes. Lagoon Island 18 47 o 139 28 o D.of York's /. ... 8 29 o 172 22 O Thrumb Cap 18, 35 o 139 48 o Wallis's Island ... jKeppel's Island Bofcawen'a Island . . '3 18 o '5 53 o 15 5 o o 178 3o o 176 18 o 176 15 o Ofnaburg Island . Blight Lagoon I. . . Pitcairn's Island . 17 51 o 21 38 75 * o 147 30 o 140 37 o 133 30 o TABLE XXVII. OF LATITUDES AND LONGITUDES, i Names of Places. I at. D. M. S. Long. D. M. S. Names of Places. Lat. o. M. s. Long. D. M S . Oparo ^ 1 36 oS. 144 i 32W Point Blaquire .... 5 6 39 cX. 32 20 OW . Point Stanhope 56 2 o 32 22 6 Hood's Island .... 9 26 o 138 52 o Point Highfield . 56 34 o 132 12 o Ohevahoa 9 4 3 6 139 I 22 Point Le Mefurier. . 55 46 o 32 2 Ohitahoo Harbour. . 9 55 3 139 8 40 Point Warde .... 56 9 o 131 49 43 Onateaya 9 58 o 138 51 o ?ape Camaano .... 55 29 o 131 43 o r ii 10 25 30 _ -O A Q 'oint Stewart .... - r > ^ j _ ; ^ j 36 O IVl;i2[QI4 127 52 o Point Pelew 60 51 o 147 3 o Deep Sea Bluff ... 50 52 c 12731 o Point Freemantle . . 60 57 o 146 26 o Point Boyles So 51 o 127 8 o Cape Hinchinbrook. 60 16 30 146 4 o Cape Scott .... So 48 o i28 20 Point Riou 59 47 o 140 43 o Woody Point ... 5 o 6 o 127 43 o Knight's Island . . . 59 44 o 139 9 Broughton Arch. . . . 5o 35 126 41 o 1 Piint Latouch .... 59 51 o 139 15 30 Point Duft' 50 48 o 126 50 o Cape Fairwcather . . 58 50 30 137 40 o Mount Stephens . . . Si i o 126 40 o nCapeCrofs , ... 57 5 8 30 136 4 30 Nootka Sound .... 49 34 20 126 28 30 Point Dundas . . . 58 21 r 35 59 Point of Breakers . . 1-9 25 o 126 28 o Point Adolphus . . . 58 16 o Point Chatham vo ,9 30 125 1.5 o Point St. Mary's . . . 58 43 3o 134 58 o Point Mudge 50 o o U4 51 o Point Converden . . . 58 12 134 53 Peint Sarah > 4 5 '24 34 30 Point Retreat .... 58 24 o 134 48 o Point Marmal .... 49 48 o 122 12 30 Point Parker 57 37 o 134 31 o Savery'sl. .... 4-9 57 3 124 5 3 o Point Sullivan .... 56 38 o 134 30 Deftrudlion I. 1-7 37 o 124 ii o Point Ellis 56 30 o 134 4 o Scotch Firpoint .... 49 42 o (23 43 o Point Malmefbury. 56 17 30 134 2 o Point Upwood 49 28 30 123 36 o Point Salisbury .... 58 o o 133 57 o Point Gower .... 49 23 o 123 9 o Point Macartney . . 57 i 30 133 48 o Point Grey .... 49 19 o 122 54 o Point Stylernan .... 57 53 o 133 38 o Anvil J. 19 30 o 122 57 o Point Windham. . . > C*7 *? r r\ Point Roberts . . 18 v> o [22 40 O Cape Fan/haw .... 5/ 3 l 57 J i o 133 15 30 Point Partridge . . . t 3 J ' M 48 16 o 122 29 Point Hood ,5 6 44 o 132 49 o Point Willbn .... '.8 10 o 122 29 Point St. Albairs . . & 7 o 132 42 o Birch Bay ^ 53 3 :22 27 o j Point Mjtcnamara . . 56 21 30 132 4,6 30 Strawberry Bay .... j.S 3') 30 Jr22 26 o 1 Port Difcovery .... 48 7 JJ22 3} 30 TABLE XXVII. OF LATITUDES AND LONGITUDES. Names of Places. Penn's Cove Oak Cove Pofl'effion Sound . . . ;Vmt Grenville. . . . ; Admiralty Inlet. . . . Cape Dif*ppointment Point Brown Colombia River.. .. Mount St. Helens . . Reiteration Point- . . Cape Lookout C. Foulweather .... Cape Perpetua Cape Gregory Cape Blanco ..... Cape Mendecino. . . Point D'Arena .... Port Bodega Point de Los Revs . Port St. Franeifco . . Mo n terry Point Sal Port St. Diego . .. Point Converfion... Point Fermin ... Guadaloupe,S. Point Cape St. Lucas .... Cape Corrientes . . . Aquapuico .... Point Remedies. .-. . iRealejo .... Point St. Catherine :Cape Blanco Point Burcia .... Quibo I. S. E. Point Cape Mariato .... v Lat. D. M. S. 48 17 oX. 47 53 o 47 53 o 47 22 o 47 3 46 19 o 47 o o . . 46 19 o 46 9 o 47 30 o 45 3a o 44 49 o 44 12 o 43 23 o 43 6 a 40 to o 3 s 56 o 3 8 21 38 o o 37 48 30 36 36 20 34 57 7 34 42 3o 34 9 53 42 30 28 54 o 2.2 52 2O 22 O i7 o o 13 29 o 12 29 ID 29 o 9 30 o 810 7 21 .0 7 13 o 7 24 o 900 5 35 o 4 12 o 3 56 o 2 50 2 26 I 36 o 57 o o j4_8^_o_ "o n 275: O IO O 120 2 II l8 5 12 o 800 12 2 O 12 I 56 [ 7 3 6 T 5 18 26 40 -7 i o Z 9 54 33 33 i 30 36 42 54 38 22 30 39 5* Lon. D. M. S. 122 22 OW 122 24 122 13 f4 r 30 122 42 123 5i o 123 53 o f2 3 53 o Names of Places. Chiloe, N. part . . . South part Cape Defeada Cape Noir .... Cape Horn .... Lat. n. M. s. 4 r 4S oS. 43 5 o 53 4 25 54 32 30 55 59 o Long. D. M. g. 73 5 o\V 73 5 o 74 18 o 72 3 15 67 26 c 121 6 1 \l\\\ o \ncF-aJlCoail o> 123 56 o J for n to Cape I2 3 55 Ijlands and Shoe 124 10 o 1-4 iS O lro ti America, j Florida, tls adjacent 55 53 oS. 54 47 10 55 i o 53 8 o 52 30 >2 24 ;o 17 o 19 i o o from Cape with the 68 13 \V 63 47 o 65 27 d 69 50 o 69 6 o 68 28 o 68 44 o 66 24 o 64 42 o 64 40 o 57 16 o S6 45 o 58 23 30 56 13 15 (.S 46 o 15 16 o 13 6 o \Z 10 41 6 o 40 2$ 39 28 o 40 27 o 39 58 o 37 6 o 35 4 o 35-16 o 35 46 o 41 59 o 45 38 o 48 24. o 50 46 o 50 15 o 52 io o 55 15 6 57 7 o 58 3 o 58 15 o 60 5 o 62 45 o 63 12 63 52 o 64 50 o 124 27 o 123 z8 o 122 39 122 36 o .22 7 3 r - r 34 J 5 120 16 30 116 53 o uS 51 o 117 57 o US 22 109 44 o 105 20 15 99 59 3o 89 41 o 87 3 o 85 41 o 84 40 o 82 55 o Si 36 o 80 4z o 79 56 o 79 27 o/ ^7-23-0 77 20 o oo 7 o 78 15 o 1 78 30 o 78 55 o 79 30 o &# 80 o o 80 59 45 79 20 C2 80 35 o 78 35 o 76 53 o 76 54 o 71 13-0 70 ii o 7100 7i 15 45 71 31 8 73 6 1 3 74 37 o 73 26 30 Statenlfhnd, Cape St. John . . Le Maire's Straits, C. GoodSuccels Str. of Magellan, Point Porpafs .... Point Poflefllon . . . Cape Virgin Mary . Sra. Cruz, Harbour i'ort Defire Cape Blanco Port St. Antonio . . . Cape Corrientes. . . River Plate, Cape St. Antonio Buenos Ayres Montevideo . . . St. Catherine's I. .. |St. Sebaftian ^7 56 o (.7 20 o [.o 51 o jS o o 36 23 o :4 36 45 34 54 4 8 27 21 13 50 o 23OO ^3 o o 21 4Z 2O 12 O 18 o o 16 45 o 12 58 O 10 ^4 o 8 34 o . 6 48 c 7 J2 3 2 o 2 27 O o 30 o o 32 o i 50 N. 4 56 o 5 57 4 6 21 10 6 44 o 6 ^5 ^o 8 28 o io 48 30 n 24 o II O II O Cape Frio Cape St. Thomas . . . 'Efpiritu Santo jAbrolhos Shoals .. Porto Seguro . . B, Todas Santos . . R. St. Franeifco .. . Cape St. Auguitine Pernambuco .... Cape St. Roque . . . Cape Baxas St. Louis dje Maran- i Panama .... Cape Corentes Point Chirambiza . . JfkndMalpelo Illand Gorgona .... Point Gufcama .... Point Mangles .... Emerald River .... _ Point Galcra >_, CapePaiTado .... Cape de Lorenzo . . 'Guayaquil Paita Truxiilo .... Cailao" Lima jYlo River Para, entr. . River Amazon, entr. _ * Cayenne . . River Surinam, ent. River Berbice, entr. RiverDemerava, ent. River Ellequibo.ent. River Oronoco,entr. Cape Ties Puntas . . Teftigos Isle . Copespo 'Cotjuimbo : Valparaiso Conception .... Mocha Iiland .... ; VaidivU Margarita I. E. Poin* - W. Point TABLE XXVI f. OF LATITUDES AND LONGITUDE?.' Lor" T -,t j Names of Places. 1 D/ *' s< LtfUUg, D. M. S. Names of Places. D. M. S. D. M. S. iBlancal. North End n 52 oN. 64 41 oW Las' Ar~as .... 20 10 ON. 92 5 cW Tortuga, Eaft end. . 55 30 65 12 Campeeche 2O 2 IO 90 25 o Weft Point 10 57 o 65 25 o Vera Cruz, . . 19 5 o 96 o o Cuigua 10 50 o 64 1 6 o Capf Roxa ... 21 41 o 92 10 o Cumana .... 10 27 64 15 o Maiiiic- Bar 23 42 'o 97 23 o Barcelona 10 8 o 64 46 30 Boca Chica 25 21 45 97 4 o P&ritu 10 4 o 6; 16 o Mouth of Rio Brava 2 5 53 o 97 3 o Cape Codera .... 10 36 o 66 6 o Horfe Channel 28 9 o 97 10 o ^>Mf Guayra 10 37 30 66 58 o Point Culebas 29 9 o 96 52 o Port Cabello 10 29 30 63 4 30 Ent. of the River Mi f- i ' Point Tuceacas . . ro 54 o 68 19 o fiflippi. . . . 29 i o 3 9 10 o Cape St. Roman . . . 12 II 70 6 o New Orleans 29 54 30 90 9 o Orchilla I. E. Point ii 51 o |66 2 o St. Bias Cape 29 36 o 85 3- o Weft ditto ... ii 52 o 66 10 o Egmont I. Entr. of Rocca, Eaft Point ... i* 59 3 66 36 o Spiritu Santo Bay 27 37 o 82 43 e Grande Key, E. Pt. ii 49 o 66 3^. o Boca Grande, Entr. Sak Key, Eaft end . Ii. des Aves ii 48 o |66 51 o 12 O 67 30 of Carlos Haruour.26 40 o Cape Roman . .126 i o $2 13 81 50 o Buen Aire, N. Pt. . 12 20 o 68 25 30 Dry Tortugas-Sli. Point de Lacre .... ii 55 30 68 x& o S.W. Point ... 24 30 o 82 53 o Curasao, 1 J'ooe Key . . 24 29 o 81 32 o [Savenet's Bay .... 12 iS O 169 12 Cay o Largo 14 5 o . So 37 o St. Crux, Bay .... 12 12 J69 7 30 C. Florida . . 25 42 o So 12 30 JAmfterdam Harbour 12 8 69 o o Xe\v Inlet 26 22 O 80 9 o : Orua Isle, E. end . . 12 24 O 69 59 o Granville Inl^t .... 26 45 20 3o 6 o ! N.W. end 12 38 30 70 9 o Hil Kborough I. S.Pt. 27 1-6 10 80 15 o iThe Monks Mid. . 12 27 /o 54 o C. Canavaral 28 18 o 80 30 o Cape Chivacoa Cape de la Vela . 12 l6 12 IO O 71 18 o 72 14 o Shoal off ditto, S.E.Pt. N. E. Point . . . 28 13 o 28 24 o ?o 14 o 80 12 'Needle Point .... II 2O 74 10 30 St. Auguftiu 28 49 o Si 35 o i .Carthagena 10 z5 19 75 2 7 o St. John's River, ent. 30 20 o 8 i 50 o 1 'ifland Puerto .... 921 o 7 6 12 Talbot Ifland, S. end 30 28 o Si 57 o ;Pta. deS.Blas .... 9 35 78 44 o Sunken Rocks, off jPuerto Bello 9 33 o 79 33 o ditto 30 22 15 81 27 o Port of Cartago 9 19 30 80 o o jSandy Point 10 39 o 82 35 o jSt. John's Harbour Corn I. N. end ... 10 41 o i 39 o 83 10 o 82 14 o The Weft -India Ijlands. St. Andrew's Id. N. Key iz 37 o So 48 o I. Barbadoes, S. Pt. 13 i joN.jSf 4* w Cape Gracias a Dios '15 o o 8246 o CapeCamaron -..:i6 I o 85 7 o Bridge T Lambert's (orN.) 13 6 25 59 49 o C* T-T A T f\ * y-\(x-fy* r\ 17 17 O 59 49 iCape Three Points 15 22 O 8S 39 o Ifland Tobago, * j I Bonacca Island, ; 'N. E. part IT 21 60 20 o South Weft Point 1 r6 26 30 85 54 o Melville's Rocks 1115 o 60 30 o Rattan I. Port Royal Scarborough . . . .' IT 60 43 o Harbour ,...ji6 22 20 86 27 o Brown's Point . ro "9 o 60 54 o Utila, Eaft end . . . 16 7 30 87 4 o Ifland of Trinidad, Glover's Reef, North Galera Point .. 10 5, r j 3 5 !) O 1 end 16 4-? o 87 37 o Galgara Point . . 10 q 61 o o Bokell Key Viciofa, E. Point . . 16 56 o 1900 87 47 o 84 38 o Soldier's Ifland . Jaque Point .... 10 3 I :.) 'Z 20 . 6z 5 o 6 1 58 o Mifteriofa,N. Point'i9 41 o 84 20 Ape's Ifland ro 42 o 6 1 47 o ,Confumel I. N. Pt. 20 8 36 34 o I. Grenada, [Loggerhead Key, N. 1 Point 21 37 45 86 51 o St. George Salin'sS^W. Pt. 12 I O 1 * 5 ) 61 55 o 61 57 o Catouch Cape .... Alacran .... 21 26 10 22 25 86 55 o 89 27 o LeGrandMAr^uis Goave 2 7 5 12 12 61 42 o 6 1 54 o Bermegi I. Mid.. . . 22 34 o 91 20 o GrenadaBk.with only Sandy I/lands 22 7 O 91 25 o 3 Fathom about the / - - New Bank 21 50 O OT A8 O Middle oi it 11 55 Triangles, Nmoft. 22 58 30 92 47 o TABLE XXVII. OF LATITUDES AND LONGITUDES. Names of Places. Lat. D. M. S. Long. b. M. s. Names of Places. Lat. D. M. S. Long. D. M. S. Urenadines, it. Bartholomew, Rifle Levora . . 12 i? SON. 6 i 42 o\V Eart Point 17 54 oN. 62 46 oV'^ llfle Rumle . . 12 21 61 41 o St. Martin, S Point 1800 ^ 63 4 ' o BCarriacovi r2 28 30 61 31 o North Point 18 8 30 67 2 O 1 Little Mavtinico 12 31 61 28 e Anguilla, N. E. Point 18 18 o J ** v 6 3 o o R Union .... 12 36 9 61 32 o Prickly Pear . . . 18 20 o 6 j 11 o [.Sail Rock 12 40 20 61 27 o Santa Cruz, j j Maycro 12 40 O 6 1 28 o Eaft Point 17 45 o 64 -;o o Canouan . . . Kibudiques 12 4 2 30 12 51 10 61 27 o 61 18 o S.VV. Point .... Virgin Iflands, 17 38 30 i j 64 49 30 Ballefu 12 <;5 o 61 16 o Anegada, W. Pt. iS 46 o 64 21 O Ballewya 12 58 15- 61 15 o Horfe Shoe, with Bequia ' .... I30O 61 24 o only from 2 to 6 Voting's Ifhnd 13 7 o 61 21 o Feet oft" ditto, S.E. f. St. Vincent, Point .... iS 33 o 64. 6 o Kingllown,' N. P. . . Chateau Belair, S. P. T 3 9 o 13 17 o 6r 23 o 6l 2Z Virgin Gordo, E. end Tortrtla, W. end . . . 18 31 o 1 8 25 30 ^ " ^ 64 13 o 64 40 o Spanifli Point Point Colonery . . . 13 21 15 13 12 61 19 o i 16 o St. John's, S. PC. . . . Bird's Key t8 20 18 15 o 64 39 o 64 47 o Rabifhi T 3 9 i 18 o St. Thomas, E. Pt. . 18 iS o 64 46 o We St. Lucia, Bequa, or Crab Ifland, Cape Grofe Le Cap. . .. 13 56 o i 6 o Eaft Point 18 9 30 6c iz o Cape SaWe 13 42 o 150 Porto Rico, J Moulacique Point . . . T 3 33 *5 I IO O Cape St. Juan, N. Pittoa Point 13 37 o 61 18 o E. Point 18 23 o 6 5 33 o Martinico, * Fort Royal 14 37 ro 6190 Cape Mala Pafqua Los Momllos . . . 17 58 o 17 58 o 6 5 43 Q 67 7 o St. Pierre Pearl Rock, W. Ft. Point Caravella . . . 14 45 50 14 5 r o 14 45 o 61 18 o 6 1 24 o 60 59 o Point Bruquen . . . Mona Ifland, E. Pt. St. Domingo, li 30 20 i* 3 45 67 4 o 67 44 o _ Point Salines, S.E. P. 14 26 o 60 57 o Saona, Eaft Point . . 18 12 30 68 28 o Diamond Rock . . 14 30 o 5i 13 Alto Vela 17 26 30 71 19 o Dominica, Abacou Point . . 18 2 18 73 44 # Scott's Head . . . *5 14 30 6r 31 o Cape Tiberon .. 18 20 o 74 2 9 o Rofeau 15 '8 45 61 32 o Cape Donamaria 18 36 o 74 25 o Prince Rupert's Bay 15 32 o 61 38 o Port au Prince . ^ 3 1 5 72 18 o Point Jaquet 15 36 o /5i 37 o C. St. Nicholas Mole 19 50 o 73 2I o Mulatto Point 15 l8 20 61 27 o Point Ifabella r 9 5^ 45 71 10 o Mary gal ante, Old Cape Francois . . 19 39 o 69 51 o Town _ Sunken Rocks off '5 54 30 61 30 o Cape Cabron Cape Raphael 19 22 30 19 i 30 69 n o 68 51 o ditto, S. E. Pt 15 51 o Cape Enganio,or Falfe Guadaloupe, Cape 18 33 o 68 18 o S. Point 5 57 o 6 1 40 o St. Domingo Town 18 26 30 69 48 o N. Point l6 22 O 61 45 o Tortuga, E. Point . 20 I 30 72 32 o Grand Terre, S.E.P. 16 13 o 61 8 o 16 29 30 t6 21 61 26 30 6r a o I/lands and Shoals North of Jamaica iDefeada, N. E. Pt. . . . | S. W. Point .... 16 13 o 6150 and Cuba. Saints Iflands 15 53 o 61 37 o ', Montferrat, EaftReef,Middleofit 20 6 3oN 6S 40 oW North Eaft Point . . 1 6 47 50 62 9 o Superb Shoal, Middle 20 5$ o 69 O O Redonde 16 56 o 62 20 O Silver Keys, Southern An^gua, E. Point 1760 6 1 40 o Reef 20 14 67 27 o Engliih Harbour . . 17 2 6 1 46 o North Eaft Point of Barbuda, North Pt. . . 17 43 o 61 50 o ditto 20 30 o 69 23 o St. Chriftopher, S. E. Weftern Edge, Silver Point 17 12 62 36 o Keys 20 28 69 57 o 1718 o 6 1 4.0 o Nevis Town 17 7 o 62 35 o Square Handkerchief Saint Euftatius, - N. E. Point . . 2140 70 27 o Town 17 30 30 63 o o S. W. ditto . . 20 52 15 /o 54 o Ifland Saba 17 39 30 63 12 O TABLE XXVII. OF LATITUDES AND LONGITUDE?. Names of Places. Lat. D.M. S. Long. D. M. 6. Names of Places. Lat. D. M. S. Long. D. M. S. Grand Turk I'liand, Morant Keys, N. E ; N. E. end 21 32 oN 71 3 oW Point . ij 26 oN 75 57 oW Sand Key, Middle . Great Caycos Ifland, South Point 21 IO 30 21 32 15 71 10 o 71 26 o S. W. Point - - . Formigas Shoal,M5d. Portland Rock .... 17 22 1 8 31 30 17 ii o 76 o o 75 45 o 77 12 o Cape Comet Caycos Shoal, S.E.Pt. 1 S V V Pt 21 43 20 58 2O 20 58 o 71 24 o 71 31 o 71 51 o Little Cayman I. S. Point ^ Great Cayman, E.Pt. 19 40 o 19 28 o 79 47 o 80 36 o Little Caycos Ifland, North Point 2.1 41 72 26 o S, W. Point . . . Swan Island, Middle Kj 27 17 24 8130 83 3^ o Providence Caycos I. North End 21 49 o 72 19 o IJland of Cuba. Heneaga Id. N .E. Pt. zi 17 30 73 2 o S. E. do* 20 59 30 73 4 o Cape Mayfi 20 13 oN 74 o cW , S. W. do. 20 52 o 73 39 o Cumberland Harbour [9 53 ro 75 12 o ~ W. do. . . 2170 73 37 o Cuba .... [9 57 o 76 4 o Little Heneaga Ifland, Cape Cruz : . . 19 48 30 77 3* Eaft Point 71 28 72 56 o IfleofPines,S.W.Pt. 21 19 52 54 o" Hogfties, Middle part 21 38 7349 0" Cape Corientes . . . 21 42 15 S 4 23 o Mayaguana Id. S. Pt. 22 1 S 2 5 72 47 o Cape Antonio 21 55 o 8455 o , N. W. do. 12 27 20 73 6 o Honda Bay .... 22 54 10 8360 . S. W. do. 22 22 73 8 o Havannah 23 -8 20 32 17 French Keys, Middle 22 38 O 73 30 o :*an Matanzas 2300 81 35 o Atwood\sKey,N.E Pt. 23 10 30 73 3* o Cattle Island 22 6 3O 74 1 6 o Crooked I; N.W. Pt. Mira Para, Vos Keys, 22 47 30 74 13 3o United States of America, Middle 22 5 O 74 28 o Watland Island, S. erid *3 5? 74 34 o Cumberland I. S. end 30 44 I5N. Si 58 oW Rum Key, Middle . . 2 3 33 3 74 56 o Savannah Riverjent.' 5 2 3 o Si o o Little Island, S. end . . 2 3 49 33 75 16 o 3 ort Royal, ent. 32 12 80 44 o Key Verde .... 22 75 3 o Caftletown Light. . r- 45 o So 5 o Yuma I. S. E. Point . 22 >o 40 -4 45 o Cape Roman . .(33 3 30 79 2" o North end ' . . . 23 ;o o 75 9 o George Town .... 33 27 20 79 25 o ; Gunahana I. S. Pt. . *3 58 "5 3 o Cape Fear 33 5 J 5 78 29 o ! North Point . . . 24 37 3 75 47 o r rying-pan Shoal, offj Powel's Point "* 4. \S O 76 74 O djtto . . .|?3 .31 30 78 18 o T J w 1 c 27 o / w J T ^ 77 24 o Cape Lookout 34 2 3 o 77 10 o New Providence, Naf- - j ** i ** / / ~t ** hoal off ditto S4 9 71 5 , fau Town -54 77 37 o Cape Hatteras 35 8 .0 7') 2 ' Aadrosl. N. Point . 25 25 o ?S 22 Shoals off ditto . . . H 47 ?o 75 27 o i South Point . . \ 24 4 o 78 7 o Cape Henry 36 57 o 76 10 o Greatlfaacl. N. Pu- 25 55 o 79 20 o Cape Charles }7 12 76 2 O Cat Keys .... 25 24 o 79 i 8 30 Chingoteak Island 38 -o o 75 20 o- Hole in the Wall 25 58 o 77 35 Thirteen Feet Bank 38, 6 20 74 47 o Little Baham Bank, 1 N.W. Point ... 27 48 o 79 15 o Cape James V8 46 30 75 8 o Memory Rock Orange Keys, Mid. Double-headed Shot 27 4 o M 33 30 79 6 o 79 9 o Cape May Philadelphia Sandy Hook L'ghth 39 o o 39 56 30 40 '26 30 74 58 o 75 l l o 74 6 o Kevs, W. Point . ~3 56 20 So 12 New York V 4 1 45 74 8 o Anguilla, S. E. Pt. . -3 ^9 o 79 12 o Montuk Point .... 4 5 72 6 o Block Island Point Judiih . fill O 41 23 o 71 38 30 IJland of Jamaica* NewportjRhocIel . 41 29 o 7115 o Gay Head . . . jfr 22 o 70 57 30 Morant Pt. S. E. end'iy $3 oN. 76 7 3o\V Sandy Foint Lighth. Port Royal 1 7 57 o 76 53 o Nantucket Island }I 31 70 4- o 1 Portland Point .... 17 42 o 77 12 o Southern Breakers. |o 43 30 70 o o South Negril .... 1815 o ;S 35 o Cape Cod Lighthoufe- J.2 5 70' 1 8 o Montego Bay 18 32 o ;3 7 o BoftonLighthoufe. \.iz iz o -o 54 o Galina Point i? 30 o -6 57 o Bofton Town .... .z 19 o 71 50 1 Port Antonio 1 8 14 o 7627 O ! Marbie Head +4 3* 9 TO 54 o 1 i ~ ^-~ D TABLE XXVII. OF LATITUDES LONGITUDES. Names of Places. La*. D. M. S, , Lc " S ' || Names of Places. 1 ' JVI w v Lat. Long. 12 14. aON 70 CCW ^fasrdalen I. N E^P. , Baker's Island Light. . 42 35 ^5 /^ is" '0 fO S. W. ditto 47 41 oN 47 12 5 6 1 4* Cape Anne Lighth. Entry!. 47 J 5 3 6 1 21 Thatcher's Island .. 42 40 10 7 39 headman's I. 47 15 20 61 53 Newberry PortLights. . 42 48 30 7 5 l . of AntecorU, E. P. ,. 49 8 35 61 59 Portsmouth Town .... ii O O 67 9 '. Efcnniinac . 4.7 i 4.? /- Wolves Iflads "T T .} v 44 47 5 66 55 St. John's Ifle, N. Cape T/ *f J 47 2 ao 63 54 Ifland of Campo Hel- Weft Point 46 34 '5 64 1 6 lo, or Weft Paf i . Eaft ditto 46 27 o 61 53 fage, Paflamaqua - .., . , . Bear Cape 46 o 10 62 ,S civ Bav A A CO O 67 o iilfborough Bay . . 46 6 12 6-7 o Sante Croix River. . . . T*f J 45 o o / 7 67 6 Cape St. George . . . 45 SJ J5 u j W 6 1 49 Gutj)i Canfo, N. entr. 45 42 20 6 1 27 From the Rkcr St. Croix to Cape Canfo [ufta Corp I. toi t Hood N ... 45 56 10 45 57 o 61 27 6 1 z_5 in Nova Scotia. C. North I. off C.Breton 47 I 5 60 15 \ Mocgone's Ifland, entr. of St. John's River C. Spencer 45 18 2oN. 45 '7 l6 56 4 W 6 5 55 Port Dauphin Spauifh Bay Flint Ifland 46 23 30 46 18 15 46 it 35 60 iS 60 2* 59 1-8' C. Chignefto, entr. of Bafon of Mines Hauto I. .... | Annapolis Royal ! Breyer's Ifland 1 St. Mary's Cape ' C. Forchu 45 24 20 45 19 12 44 47 10 44 J 9 o 44 10 i s 43 3 5 ; Bird Iflands 47 55 20 '60 41 Funk Ifland 50 I 15 5 z 17 Brion I. ... 47 S^ i 61 o Cape Free Is 49 34 ic 53 o I. - . _ _-_._.__. j ^ TABLE XXVII. OF LATITUDES AND LONGITUDES. Names f Places, Lat. Long, i Names of Places. ! **\ Long, Wadham Iflands 49 54 5^. 53 30\V Mount Joli .... 50 5 oN. Si 35W i Gander Bay . .9 40 16 54 15 Little Mecatina Ifland 50 28 15 59 32 Fogo Ifland f - O 12 53 54 Great Mecatina Point 50 52 14 59 13 Twiliingate Iflands 50 3 20 54 40 Jaha Bay * . . 50 52 20 59 7 Bay of Notre Dame 50 o o 55 35 ifcMjimaux Bay . . 51 28 10 57 5 Cape Sr. John Ho lie Iflands 56 10 P 56 91 45 5538 56 51 Gran^ Point 'orteau Bay .... 51 24 o 51 30 20 57 17 ' 57 o White Bay' 50 15 15 5 6 25 Red Clifi-s 5 1 33 40 36 50 , Hooping Harbour 50 46 o 5$ 18 Black Bay 51 40 2> 56 47 jGreen Ifland 50 47 20 55 35 ; Red Bay .... 5i 44 5 5i 25 Groais Ifland 5 55 5 55 45 fork Point 51 57 10 55 57 Hare Bay 51 15 10 56 i Cape Charles . 54 3 " 55 30 St. Anthony's Cape .. 51 17 30 55 44 jreat Bay of Efquimaux 54 ao o 57 35 iQuirpon Harbour . f Belleifle 51 40 20 5i 55 *5 55 39 55 30 Cape Harrifon St. Peter's Harbour 54 54 IS 56 28 10 5^ 50 | 60 50 Cape Norman 51 40 5 56 2 nchanted Cape 56 4,0 20 60 55 Bay St. Barbe > - 5* *5 1 7 5<> 53 Saddle I0ands . . . 57 13 3 60 50 Point Fertile 57 3 o 57 ii uft Jt>an 1 . . . 57 45 6l 20 St. John's I (land 50 50 20 57 23 Steel Point . . . 5* 7 10 61 50 Ingornachoix Bay Bay St. Paul 50 38 30 49 5 5o 57 25 57 55 Cardinal's JL ... Falfe Black Head . . . 58 50 40 59 20 20 63 o 69 19 [Cape St. Gregory 49 22 15 5* 17 Black Head ' 59 5 15 63 37 [South Head P ..... 49 7 40 58 26 Button's Iflands 60 47 50 ' 65 21 JGape St. George 4^ 30 45 59 '3 Cod Roy Ifland (.Cape Ray 47 52 10 47 37 o 59 3 59 X 5 Hudfons Bay. iGrcat Barrifway Burgeo Iflands 47 37 15 47 35 o 57 45 57 37 Button's Iflands .., 60 47 5N. 65 *i\V Runney Ifland 47 32 20 57 30 ^owe's Savage Ifland . 6j 48 20 66 25 Penguin's Iflands . . . 47 24 15 57 15 Terra Nieva 62 4 30 68 5 Fortune Bay . 47 16 10 55 35 Saddle Back Ifland 62 10 10 68 15 Burnet 47 15 35 56 i Great Bear Island .... 54 4 2 -P 80 i ;Great Miquelon (Langley Inland . . 46 55 '5 46 42 20 56 21 56 ao [ce Cove ..-.. Baker's Dozen 62, o o 57 o 5 69 5 :St. Peter's Ifland 46 36 po 56 ii Great Savage Island- . . 62 25 25 70 5 iCape Chapeau Rouge 'Bay of Placentia 46 52 o 47 o 10 55 " 54 35 North Bluff .... God's Mercies 62 26 15 62 28 o 70 53 |Cape St. Mary's 4$ 52 5 54 7 Salifburv Island 63 3o 45 76 55 6c. Mary's Bay 46 50 15 53 35 Nottingham) . end . . 63 3^ 30 76 50 jCape Pine 46 4O 20 53 *o Cape Charles, . end . . 62 50 22 74 * _ /- * Weft end .... 62 4 5 76 > Fro?n Quebec to Hudfons Bay. Cape Walfingham .... Cape Diggs .... 62 40 10 62 45 20 78 5 78 53 \ Mansfield, N. en3 ... 62 40 15 7S 5 :Quebec . . . 46 55 uN. 169 53\V South end .... 61 35 20 81 35 ;St. Paul's Bay 47 30 ?.j 69 15 Sleeper's Island .... 60 jo 40 8? 35 [Bay of Rocks 4* 5 5 M 43 Great ditto . .... 5 8 35 25 81 35 iLgvai Bay 4$ 55 30 68 50 Gape Pembroke .... 62 57 15 82 15 St. Nicholas's Bay 49 28 41 67 5 Large Jfwan's Neft .... 62 20 6 *3 35 'Trinity Bay 49 37 *4 66 32 |Cape Southampton .... 62 10 o 86 15 iThe Seven Ifland Bay CO 7 l6 ^S 5 Churchill River ;8 47 IO Q4 12 JGrand B.ay, St. John's j *** / * v 50 22 5 64 5 Charton Island J u *T / r*f 52 3 io VT 79 10 Mjngan L ... 50 16 10 63 20 Port Nelfon's Shoals . . 57 35 '5 9* 35 Ef^uimuux Illands 50 12 30 63 5 Hay Rive? 57 10 20 93 5 XXVIII. TABLE XXVIII. A GENERAL TIDE TABLE, Shewing the Times of High Water at the Full and Change of the Moon, at the principal Places on the Coafts of EUROPE and AMERICA. N. B. r. denotes the vertical rife of fpring tides, and//, feet. H. M. Aaron Ifland, France; r. 45/r. 6 30 Abbeville, France .. . . 10 30 Abb's Head, (St.) f offing,} Scot- land . . . . . . 4 30 Aberdeen, Scotland .. ..1245 Aberdovy, Wales ; r. 1 8 //. .. 730 Abrevrack, France . . . 4 30 I Achill Head, Ireland . . ..60 i Adventure Bay, North Holland 4 36 Agnes Lighthoufe, (St.) Scilly 3 45 Aix, Fiance . . ..30 Alban's Head, (Si.) England . . 7 30 Aldborough Bay, England ; r. Alderney Ifland, Britifh Channel ; ;. z8//. Alemouth, Scotland Alloa, Scotland A Itona, Germany .. . Amazon's River, America Ambleteufe, France Amcland i. German Ocean Amelia Harbour, America Almwch Port, Anglefea ; r. 24 ft. Amilcrdam, Holland ; r. 7 ft. Angra Bay, Terceira, A cores ; r.8//. ' Anholt Ifland, Denmark Ann Cape, America ; r. 12 ft. Annamoeka, Pacific Ocean Anticolti,Weft end Antwerp, Brabant Arbroath, Scotland . ... Archangel, Ruflia Archangel River (entrance of j White Sea Arklovv, Ireland Arran Ifle, Scotland; r.gft. Arundel, England ; r. 16 ft. Avranches, France Ay re Point, Ifle of Man Babelmandel (Straits of; Red Sea Balafore Road, India ; r. 12 ft. Ballinikellik^s Bay, Ireland Bailey Cattle, Ireland Baltimore, Ireland Brjitry Bay, Ireland Bardfey Ifle, Wales Barfleur, (Cape) France Barmouth, Wales; r. 14 ft. 10 45 6 o 2 15 2 30 6 o 6 o 11 O 10 30 9- 10 30 3 o 11 45 12 O II 30 6 o 3 30 6 o 1 45 6 o 6 30 8 15 11 15 9 20 6 o 10 30 12 O 10 30 3 15 5 45 3 45 3 45 8 15 7 30 7 45 H. M. Barnflaple Bar, England ; r. 26ft . 5 50 Bas (Jflesof) Britifh Channel r. 2? ft. .. 3 45 Baudfey Cliff, England JO 30 Bayeux, France . 8 15 Bayonne, Spain . 4 45 Bayonne, France . . 3 30 Beachy, on the Shore, Eng- land ; r. 20 ft 945 Beachy Head, (offing) England n o Bear Island, Hudfon's Bay 12 o Beaumaris, Wales ; r.z^ft. 10 15 Bee's Head, (St.) England n o Belfaft, Ireland . . . 10 30 Belle Isle, Bay of Bifcay . 3 o Bembridgc Point, Isle of Wight 1 1 40 Bergen (N.) and thence to the Stadtland, Norway . . i 30 Bermudas I. Atlantic Ocean ; Berwick, England ; r. i6/>. Bic Island, Canada Biddeford, England Bilboa, Spain ; r. is//. Bifcay, Coaft of, Spain Blakeney, England; r. 16 ft Blanco Cape, Africa Block Island, America; r. $ft. Blythe, England ; r. 12 ft. Bgy or Bog Point, Devon? England Bojador, (Cape) Africa Bolt Head, England ; r. 20 ft. Bombay, India Borkum Isle, German Ocean Bofton, England Bofton, (Lighthoufe) America; Botany Bay, N. Holland Botany Island, N. Caledonia Boulogne, France Bourdeaux Road, (entrance) and thence to Ufhant, France Bray Head, Ireland BreeBank, FJanders .. Bremen, Germany Breft Harbour, France Bride's Bay, (St.) Wales Bridgewater, England; r. 22 ft 15 45 7 3 9 45 7 37 * 45 5 20 12 O 5 55 ii 15 10 30 7 15 11 30 8 o 10 30 10 45 3 30 6 o 3 45 6 o 6 45 TABLE XXVIII.. HIGH WATER. H. M. Bridlington or Burlington, Eng- land; r. 13 ft. - 4 Brighthelrnftone, England ; r. - 10 - i f f o - 6 Buchan Neis, Scotland - 12 Burry Ifland, Wales; r. 14 ft. 6 ' Buftard Bay, New Holland ; . Brill, Holland ; r. 20 ft. Briftol, England ' Button's Hies, Hudfon's Bay 6 Cadiz, Spain - 4 Caernarvon Bar, Wales; r. lift. 9 Calais, France; r. iZ ft. -' n Calcutta, India - 3 Caldey Ifle, Wales ; r. 34/7. - 6 Calf cf Man, Irifli Sea - 10 j_ Callao, Port of Peru - 6 i Oainperdown, Holland Canaria Ifland, Atlantic Ocean 3 Cancale, France - - 7 Canio Cape, America Cantire, (Mull of,) Scotland; r.$ft. - - -9 Cape Ann, America; r. J2//, - II Charles, America - 7 i. Churchill, Hudfon's Bay, .7 Clear, Ireland - 3 -. Cod, America ; r. 6% ft. II Cornwall, England ; r. 22 ft 4 Corunna, Spain - 3 Donega, White Sea ; r. 6 ft. 6 Fear Bar, America - 7 Finifterre, Spain - 3 ~ Griznefs, France - II La Hogue, France - 12 Henlopen, America ; r.jft. - 8 Henry, America; r. 4ft. 7 St. Mary, Nova Scotia; r.llft. - 9 May, Delaware, B. Ame- rica, 8 Ortega!, Spain - - 3 Sable, Nova Scotia ; r. 9 ft. 8 Cappel, (Weft,) Holland - 12 Cardiff, Wales - 6 Cardigan Bar, Wales ; r.zoff. 7 Carlingford, Ireland; r. I4//.- 9 Carhfle, England - 12 Carmarthen Bar, Wales; r. 24 f I. 6 Carrickfergus Bay, Ireland ; r. 8//. - - 10 Caflcets, Brit. Channel ; r. ag//. 8 Catherine's Point, (St.) Ifle of Wight - - 8 Catnefs or Catfnofe, White Sea, 5 Charleftown, America; r.6ft. 7 Chatham, England - I Chepflow, England - 7 Cherbourg, France ; r. ao ft. 7 H. M. Chefter Bar, England ; r. 26 ft. 10 30 Chiloe Ifland, South America 12 30 Chittagong Bar, India - i o Chriftmas Sound, South America 2 30 Chriftmas Harbour, Kergulen's Land - - to o - 3 30 16 30 - 4 30 3 o 45 645 3 o 4 15 II O 5 10 6 o 6 o II O 9 o 2 15 10 30 3 30 6 30 Coaft, (Cape) Africa Condore, (Pulo) China Sea ; Copeland Ifland, Ireland - 10 Coquet Ifland, England ; r. IS ft. .2 45 Cork Harbour, (entr.) Ireland ; r. i8//. Cornwallis Port, P. of Waters Ifland; r. uft. - - i Cornwallis Port, Andaman I. TO Cowes, Ifle of Wight; r.\$ft. II 15 Cracatoa, (I.) Straits of Sunda; Cromarty, Scotland; r. 14 //. n Cromer, England ; r. 16 ft. Crookhaven, Ireland Crofs Ifland, White Sea Cumbry Lighthoufe, Scotland Curreufe Ifland, Almerantes Dartmouth, England, r. 18 ft. David's Head, iSt.) W T ale Deal, England ; r. 15 //. Delaware River, (ent.) Amor Denbigh, Wales Dieppe, France ; r. i$ft. Dingle Bay, Ireland Donegal, Ireland Dorfes, Ireland - -30 Dort, Holland . - -30 Dover Road, England; r. 14 ft. n 6 Douglas, I. of Man; r* 21 ft. 10 30 Downs, England; r. 15 //. ii o Drogheda, Ireland - 10 43 Dronthiem, and along the Coaft of Firnnark to the N. Cape - Dublin, Ireland ; r* 12 ft. Dunbar, Scotland Duncanfley Head, Scotland - 10 ^ Dundalk Bay, Ireland - JO 45 Dudgeon Light, North Sea - 7 30 Dundee, Scotland Dungarvon, Ireland Dungdnefs, England ; r. Dunkirk, Flanders ; r. Dunnofe I. of Wight Durfey Ifland Dulkey Bay, N. Zealand Dyiart, Scotland Eaoowe, Pacific Ocean Eagle Ifland, Afia Eafter Ifland, Chili Eddyftone, Britifh Channel ; r. i8//. Egmont, Holland Elbe, (red Buoy,) German Ocean 2 15 9 45 I 30 - 2 30 - 4 30 24 ft. jo 51 18 ft. u 15 - 8 55 30 10 57 2 15 - 3 70 3 30 o - 2 - . 5 50 - 4 30 TABLE XXVIII. HIGH WATER; H. M. Elizabeth Ifland, America 9 o Embden, Germany - ia *o Endeavor River, N. Holland i 30 Before the Eaftcro and Weftern Ems, German Ocean -90 Etaples, France 3 15 Exmouth Bar, England, r. 14 ft. 6 a5 Eyden River, German Ocean, ja o Exuma Bar, Bahamas - 6 35 Eyemouth Harbour, Scotland, a 15 Fair Ifle, North Sea -40 Falkland Ifland, America -50 Falmouth, England ; r, 18 ft. 5 45 Falfe Bay, Cape of Good Hope o Fayal Road, Azores ; r. 4^ ft. i ao Fearn Ifland Light. North Sea 3 30 Ferolle Point - - n 15 Fifenefs, Scotland - 4 30 Finifterre (Cape) to Cape St. Vincen^ - % 30 Finmark (Coaft of) in general, a 15 Flamborotfgh Head and Filer, 4 30 Flats (Kentifh), England * la o Flatholm Ifland, Briftol Channel 6 40 Flemifh Banks, North Sea - 3 o Florida Keys, America - 8 50 Flufliing, Holland - I'D Fly (or Vlie) Gateway, Hol- land - 6 45 Fly, or Vlie, Road, Holland - 7 30 Folkftone, England; r. ao/if. - 10 51 Fort George, Scotland - ia o Fbrt St. John, Newfoundland 9 o Forteau Bay, America - no, Foul Ifle, near Shetland -30 Fowey, England; r. i6ft. - 5 30 Frith of Tain, Scotland - n o Funchall, Madeira ; r. 7 ft. - 10 30 Gallopper andGabbard,Thames Mouth ;r. i6//. - ia 45 Galway Bay, Ireland - 4 30 .Galloway, (Mull of,) Scotland n 15 Gambia, (River, ent) Africa 10 15 Gafpe Bay, America - i 30 Gay Head, America; r. 7 ft. 7 37 George's River, America'; r. 9/A - - 10 45 George Town Bar, America - 6 40 Gibraltar, Spain - - la O Glafgow Port, Scotland - n 30 Goa, India - 4 30 Goodwin Sands, Back pf the, i 30 Gore, .near Margate, England, ia o Goree Gatway, German Ocean, i 30 Grangcmouth, England - a 30 Granville, France - 7 30 Graveljines, France, r. 1 8 ft. - 11 45 Gravefend, England; r. i6ft i 30 I Greihplm, near Milford Haven, 7 30 Guayaquil (Port) South America 6 30 Britifh Channel ; r.foft. - -60 Gulf of Corry vrechan, Lewises ; r. n/r. - - 4 30 H. M. Gut of Canfo, America - 8 30 Haerlem, If olland 9 o Hague, Holland - 6 15 Hcgue*. (Cape JLa,) France ; r. i6VV. - 8 45 Halifax, Nova Scotia ; r. 8 //. 7 30 Hamburgh. Germany 6 o Hampton Quay, England - ia o Hanford Water, England ; r. 16 ft. - - ia o Hartland Point, England , - 6 o Hartlepool, England - 3 45 Harwich, England ; r. I4//. n 30 Hafborough, England - 7 30 Hafborough Sand, North Sea - 8 o Haftings, England - 10 36 Havre de Grace, France 5 r f ^^ft t - - 10 30 Helena, (St.) Atlantic Ocean a ij Helena, (Cape St.) America 4 o Helford, England ; r. 1 8 ft. 5 15 Heilegoland, German Ocean, I a o Helen's (St,) England; r, ibft, II 45 Helvoetfluys, Holland - i 30 Henlopen, (Cape) America 8 54 Henriette Marie, (Cape,) Hud' fon's Bay * - ia O Holms, (Flat and Steep,) Briftol Channel ; r. 36 ff. - 6 40 Holy Head Bay, Wales; r. 14 ft, 10 o Holy Ifland Harbour, Scotland; r. 15 ft. - - a 30 Honfleur, France - -90 Hook of Holland -30 Heoringottah River, Eaft-Indias ia O Horn, (Before the,) German Ocean - ia o Horfe Race, America ; r. 5 ft. 10 30 Hofley Bay, England, r. iift.il o Hull, England ; r. i%ft. - 6 O Humber (Entr.) England - 5 15 Hung Road, F.ngland ; r. 4,6 ft. 6 45 Hurft Caftle, England - 9 30 Ice Cove, Hudfon's Bay - 10 o Ila, (E. fide and Sound of;) r, 5ft. - - 3 15 Ilfordcombe, England -60 Ingella, India - i r o Inverkeithing, Scotland - a 45 Ipfwich, England - I a o Ireland, N. W. Coaft, from Milen Head to Balliconnel ; r. lift. , W. Coaft in general, 3 o . . . . , Havens on the S. Coaft - 5 51 Ifle of Man, South fide - 10 ao Ives, (St.) England; r. 24ft. - 5 1,5 ackfon (Port) New Holland 8 15 ago (Ifle) Africa - - 7 45 aneiro, (Rio) Brazil . 4 30 ohn's, (St.) Newfoundland -60 ean de Luz, (St.) France -60 erfey Ifland ; r, i$ ft. -60 TABLE XXVIII. HIGH H. M. Juan, (Cape St.) America -40 Julian, (Port St.) Patagonia - 4 45 Jutland, (along the Coaft of,) 12 o Karakahoo Bay, Sandwich I* 3 45 Kedgerea, India - - n 30 Kenmare River, Ireland - 3 45 Kennebeck, America; r.gft. 10 45 Kentifh Knock, off the Thames, il 30 Kilduyn, Lapland - 7 30 Killybegs, Ireland - 6 45 Kingroad, near Brifto!; f. 6,1ft. 6 48 King's Channel or Swin ; ;. i6//. - IZ o Kinghorn, Scotland - a 30 Kinlale, Ireland - - 5 15 Kinnaird's Hea.d, Scotland - IZ o Kirkaldy, Scotland - Z IS Kirkcudbright, Scotland - n 15 Kirkduyn, Holland, near the Texel; r. izft. - -7 30 Komaroo, ^Cupe) N. Zealand - 9 30 Labradore Harbour, (Straits of Belleifle) - - - n 30 Lambanefs, N. end of Shet- land ; r. 5 ft, - ~9 Lancedora, Canaries - - 12 45 Lancailer, England - 11 15 Land's End of England - 4 30 Leith Pier, Scotland; r. 15 ft. 2 20 Lcrwick in Shetland - I 30 Lewis and Harris, (along the Shores of,) Scotland; r. lift. 6 o Le. wiles vButt of the) - 6 45 Lieh -12 o Limekilne on the Frith of Forth 3 30 Limerick, Ireland ; r. j 6 //. - 6 30 I iibon, Portugal - a 15 Liverpool, (entr. of the Har- bour;) r.i6jt. - 10 30 Lizard Point, on Ihore, England, 5 o Loch don - - 4 30 Lochlairne, Scotland - 9 45 Loch Swilly, Ireland -' 7 30 Lochihill, Holland -60 Loire River, entr. France -30 LONDON ; r. 19 ft. - a 46 Londonderry, Ireland -60 Long liland, America -30 Long Sand Head, Riv. Thames, n 30 Longfhips, England - 4 30 Loop Head, Ireland 4 30 Louifburg, America - - 7 15 Loweftoff, on Ihore, England ; r. jft. - -90 Loweftoff Road - 910 Loweftoff and Orfordnefs (offing between) - - II 15 Lundy Ifland, Briftol Chanmel ; r. $oft. ^ - 545 Lynn Regis, England -75 Lymington, Englan'd - n 15 Lynn Deeps, England ; r. 20 ft. 6 o Machias, America ; r. 12 ft. - II o Madeira Iflund, r. 7 ft. - i% 4 H.M. Madre de Dios, Pacific Ocean - a 30 Maes and Maiflair* Holland ^ o Magnus's Sound, (St.) Ur^ncy ; r. 8ft. * . 8 15 Malacca Road, India - 10 30 Maloes, (St.) France ; r< 45//. 6 30 Marble Head, America; r.izft. u 30 Margate Roads, Engl. r. id ft. n 45 Martha's Vineyard, America 9, o Martinique Ifland, Weil Indies 7 30 Mary, vSt.) Scilly. - 4 40 Mauritius, (Illes) - la 30 May, (Cape) America - 8 45 May Ifle, Scotland - I 30 Mcrqui, India ; r. is .ft. - 12 o Miquelon, Newfoundland; r. 7 ft. 9 o Milford Haven ; r. 36 ft. -60 Minehead, England; r, 36 ft. -60 Mizen Head, Ireland -30 Monaftry Ifland, White Sea; r. 6ft. .7 30 Montrofe, Scotland - I 30 A Ion terry, Pa c ilk Ocean - 30 ! TvTorlaix, France; r. 30 ft Morocco, (along the Coaft of,) 2 15 Mount Defert, Maflachufetts ; r. izft. - -no Mount's Bay, England ;r. 19 ft. 4 30 Nangafachi, Pacific Ocean - 6 e Nantucket Shoals, America; r. 5i/7. - - 10 30 Nantucket, America ; r. 6 ft. iz 3 Nantz, France -40 Nantz (before the River of) - 3 .o Nafiau, New Providence - 7 30 Natal River, Africa ; r. izft. - 10 o Naze, Norway - - u 15 Naze of Effex, England - n ao Needles I. of Wight ; r. 9 ft. - 8 56 Nevyn Bay, Wales ; r. 2,0 ft. - 8 45 Newcaftle-upon-Tyne -40 New Bedford, America ; r. 5 ft. 7 37 Newburgh, Scotland - 12 30 Newburyport, America;r. loft, n 15 Newhaven, England; r. ao//. 10 16 Newhaven, America; r. 8 //. n o New London, America; r. 5. //. 854 Newenham, (Cape) Pac. Ocean iz o Newport, Flanders - IZ O Newport, Wales ; r. 24 ft. - 6 45 Newry, Ireland - - IZ o New York, America ; r. 5 //. 8 54 New Zealand, (Bays,&c.) Paci- fic Ocean; r. 7^ ft. - -80 Nicholas (before St.) - 6 45 Noddy Harbour, Newfoundland 5 35 Nootka Sound, America ; r. 9 ft. 12 20 Nore, R. Thames ; r. 14 ff. - 12 IS Norfolk Sound, North Holland i o Normandy and Picardy (Coaft- of) - - ic 30 North Berwick, Scotland - i 30 TABLE XXVIII. HIGH WATER, North Cape, Lapland. North I- v . '._.. ' J'neland Nr- H. M. - 3 o - ii 15 '.nd South Rocks. Ireland n Nottingham lilands, Hudfon's Bay - io Oh?maneno Uliateah, Pacific Ocean - ii Opcrto, Portugal - 3 Orfonkieis, England - io Orkney lilands, in general ; r. 8//. Ormfhead-s Vales - - io Orotava Tenet iffe, Atlantic Ocean 3 Ortegal, (Cape,) Spain - 3 O fiend,, Flanders ; r.ibfl. - 12 Otahita Ifle, Pacific Ocean - * _ Owharre Bay, America - n 50 Oivers, near Spithead ; r.i$ft. 9 36 Owhyhe t ilflie) Pacific Ocean - Padftow, Ergland: r. 27 ft. - 5 Paffamaquodd) River, America; r. -if ft. - II Pejimark Point, France - 3 Penobicot River, America; r. ' io//. - - ro Pentland Frith ; r. % ft. - io Penzance, England ; /'. I9//. - ,' Peterhcad, Scotland - 12 Peter and Paul, (St. Kamfchatka 4 dphia, America - i Piel of Foudray, Coaft of Lan- caftiire - - n Pillefowder - - io Plymouth, England; r. 18 //. 6 Plymouth^ America; r. 6} //. II PodeiTemeck (before) - 6 Pomona or Main Land, Orkney 3 Poole, England; r. 7 ft. - 9 Porto Bello, America - 8 Port Hood/Cape Breton; r. 8//. 7 Port Howe, Nova Scotia; r. 8//. 8 Port Refolution, (Tanna) New M'jbrides - - - - 5 30 Pudyona, North Caledonia Pulo Penang, India ; r. loft. Pwcllheli Bar, Wales; r.tofl. Quebec, Canada Queda Road, India ; r. 6 ft. Queenborough, England Quibo Ifland, Pacific Ocean Rachlin or Ratlin Ifland Ram Head, England Rammekins, Holland Ramfey, Ifle of Man Ramfgate, England Ray Ca.pe, Newfoundland Rci'olytion Bay, Marquefai, America Rhe Ifle, Bay of Bifcay Rhode Ifland Hariiowr, Ame- rica ; r. i5//. Robin Hood's Bay, P^ngland, - Rochefort, France Rochelle, France Rochefter, England Rodrigues Ifland, Indian Ocean Roman, (Cape) America feonaldma, Orkney * Roicnefs, Orkney Rotterdam, Holland Rouen, ftttnce Rye Harbour, England; r. 2\ft.. Sable, (Cape) Nova Scotia; r.gft. - Sable, (Ifland) America ; r. 7 ft. Salvadore,- (St.) South America Savannah, (exit, to) America - jjScaw, Denmark ; ; r. \$fi. Scbaftian, ''St.) Spain Senegal River, Africa St. Aiban's Head;- England St. Anaftatia's Ifland, America, St. Andrews, Scotland St. Avguftine, Florida St. David's Head, Ua-les St. Gowan'd Head, Wales; M. 3 3 o io o 15 30 3 45 30 30 o 8 - n 30 Jackfon, Nova Scotia ; - 8 '7-A Portluul I-iil, England; /. 8//. 9 Portland Road, England ; r. 1 ft. 6 Portbnd, America; r. yft. - io . Portugal - 'j PortJ'ri'va, Cape Verd Iflands, ii ; Port R(>Ve\vay, Nova Scotia ; //. - - 8 Port Royal, Virginia - 8 Port Royal,, Jamaica \r. i ft. PortRviih, Ireland,^ 6 ft. 5 Port Seat on, Scotland - 2 Portl'mouth Huibour, England- .-. i8//. - - ii Poitl'moutli, America ; r. id ft. II Portugal, . Coall oi',} in general 3 > r.'.ul Point, Epcland - 5 Pretlr.n land - % i'urflect, River'! b&nicsj r. i;//. i St. Helen's, near Spithouu; r. i6fl. St. John's River, Bay of Fundy, St'. Simon's Bar, America St. Simon's Sound, Am elf ic a Salcombe, England ; r. 20 ft. Salem, America; r. 12 ft. Saltees, Ireland Sana-Ifland, Scotland; r6//. Sandwich, England - ^ Sandwich Bay, Nova Scotia ; r. %ft. Sandy Hook, New York; r-5//. Scarborough, England; r. I3//. Scheveling, Holland Scilly Illands, Britifh Channel ; Scotland, Eaft CoaH in general ; r. i or 1 4 ft. S--v.f->rd, England ; r. 2,0 ft. 3 o 55 3^ 3<5 30 o o 37 30 45 - 4 40 I - ro 16 ; THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW INITIAL FINE 25 CENTS OVERDUE. 1933 3 1933 MAR 11 MAY OCT 24 1935 FEB 23 1936 SEP 25 1942 APR 08 1988 LD 21-50m-l,'33 TC 62530 U.C. BERKELEY LIBRARIES