LIBRARY UNIVERSITY OF CALIFORNIA. "N GIFT OF Class ^ J^ ^ c ,*^>^ V POPULAR WORKS PUBLISHED BY J. & J. HARPER, 82 CLUT-ST., NEW-YORE- THE HISTORY OF MODERN EUROPE, from the Rise of the Modern Kingdoms to the present period. By WILLIAM RUSSELL, LL.D.. and WILLIAM JUNES, Esq. With Annotations by an American. In 3 vols. 8vo. THE HISTORICAL WORKS OF THE REV. WILLIAM ROBERTSON, D.D.: comprising his HISTORY OF AMERICA; CHARLES V.: SCOTLAND, and INDIA. In 3 YO!S. 8m With Plates, GIBBON'S HISTORY OF THE DECLINE AND FALL OF THE ROMAN EMPIRE. In 4 Tola. 8vo. With Plates. > ENGLISH SYNONYMES, with copious Illustrations and Explanations, drawn from the best Writers. By GKORGK CRABBK, M.A. STO. LIFE OF LORD BYRON. By THOMAS MOORB, Esq. In 2 YOU. 8 TO. W ith a Portrait. THE BOOK OF NATURE; being a popular Illustration of the general Laws and Phenomena of Creation, &c. By JOHN MASON GOOD. M.D. and FJl.'S. 8vo. With his Life. HOOPER'S MEDICAL DICTIONARY. From the last London Edition. With Additions, by SAMITEL AKERLY, M.D. 8vo. COOPER'S SURGICAL DICTIONARY. In 2 vols. 8vo. GOOD'S (On. JOHN MASON) STUDY OF MEDICINE. In 5 Tole. 8vo. A new Edition. With Additions, by SAMUEL COOPJCR, M.D. DOMESTIC DUTIES; or Instructions to Married Ladies. WORKS OF THE REV. ROBERT HALL, with Memoirs of bis Life, by Sir JAMES MACINTOSH. In 3 vols. sjvo. KEITH ON THE PROPHECIES. 12mo. LIFE OF LORD EDWARD FITZGERALD. By THOWAS MOORE, Esq. In 2 vols. 12mo. With a Portrait. PRESENT STATE OF CHRISTIANITY in all parts of the World. By the Rev. FREDERIC SHOBERL. 12mo. THE INVALID'S ORACLE; or, ART OF INVIGORATING AND PROLONGING LIFE. By WILLIAM KITCHINER, M.D. 18mo. THE COOK'S ORACLE, AND HOUSEKEEPER'S MAN- UAL. By WILLIAM KITCHINKR, M.D. Adapted to the American Public. 12mo. MODERN AMERICAN COOKERY. By Miss PRUDENCE BMITH. 16rao. GIBSON'S SURVEYING. Improved and enlarged. 8vo. ELEMENTS OF SURVEYING. With the necessary Tables and Plates. By CHAHLKS DAVIES, Professor of Mathematics at the Military Academy at West Point. 6vo. DESCRIPTIVE GEOMETRY AND SPHERICAL PRO- JECTIONS. By CHARLES DAVIXS. 8ro. TREATISE ON SHADOWS AND PERSPECTIVE. By CHARLES DATTKS. STO. SURVEYORS' TABLES. 12mo. BROWN'S DICTIONARY OF THE HOLY BIBLE. 8vo. BROWN'S (J.) CONCORDANCE. 32mo. WESLEY'S SERMONS AND WORKS. 8vo. LETTERS FROM THE AEGEAN. By J. EMERSON, Esq. 8ro. WORKS PUBLISHED BY J. & J. HARPER. THE HISTORY OF THE JEWS, from the earliest period to the present time. By the Rev. H. H. MILMAN. In 3 vols. 18mo. With Maps. THE LIFE OF NAPOLEON BONAPARTE. By J. G. LOCKHART, Esq. With copperplate engravings. 2 vols.'lSrno. LIFE OF NELSON. By R. SOUTHEY, Esq. Portrait. 18mo. THE LIFE OF ALEXANDER THE GREAT. By the Rev. J. WILLIAMS. With a map. 18mo. NATURAL HISTORY OF INSECTS. Illustrated by nu- merous engravings. 18mo. THE LIFE OF LORD BYRON. By JOHN GALT, Esq. 18mo. THE LIFE OF MOHAMMED. By the Rev. G. BUSH, A.M. With a plate. 18mo. LETTERS ON DEMONOLOGY AND WITCHCRAFT. By Sir WALTER SCOTT, Bart. 18mo. With an Engraving. HISTORY OF THE BIBLE. By the Rev. G. R. GLEIG. In 2 vols. 18mo. With maps of Palestine, &c. NARRATIVE OF DISCOVERY AND AD-VENTURE IN THE POLAR SEAS AND REGIONS. With illustrations of their Climate, Geology, and Natural History ; and an Account of the Whale Fishery. By Professor LESLIE, Professor JAMESON, and Hi GH MURRAY, Esq. With Maps, &c. 18mo. LIFE AND TIMES OF GEORGE IV., with Anecdotes of Distinguished Persons of the last Filly Years. By the Rev. GEORGE CROLY. With a portrait. 18mo. New and improved edition. NARRATIVE OF ADVENTURE AND DISCOVERY IN AFRICA, from the earliest ages to the present time. With illustrations of the Geol- ogy, Mineralogy, and Zoology. By Professor JAMESON, JAMES WILSON, Esq., an second section sgntninar Involution and Evolution. Tfee third section 4;mtainn- the nature and power of Logarithms, witrT their application, and the method of computing them. 'The fourth section ^oateinB- geometrical definitions, theorems, and problems, with the description and use of the sector, Gunter's scale, and other mathematical drawing instruments used by surveyors. Jhe fifth section^VontainEK Plane Trigonometry, right- angled and oblique, with a variety of rules and practical examples. The first section (Part the Second) gives an account of the chains and measures used in Great Britain and Ireland, methods of surveying and of taking inaccessible distances by the chain only, with some necessary prob- lems ; also a particular description of the several instru- ments used in surveying, with their respective uses. The second section contains the mensuration of heights and distances, with a great variety of problems and prac- tical examples. The third section contains the mensurajtion of areas, or the various methods of calculating the superficial con- tents of any field ; also several new rules and^problems, with practical examples, and various methods of finding the areas of maps from their geometrical construction ; two of which, more concise than, the rest, were first pub- lished in this work. Also, it contains four new and much more concise methods of determining the areas of sur- veys from the field-notes, or by calculation, than any hitherto published ; to these is added the method of cal- culating the area of a survey, by having the meridian pass through the east or west point of the survey, with the method of discovering these points from the field- notes, and the method of correcting the errors by the pen, when the survey does not close : also another new method for calculating the area, by having a parallel of latitude pass through the north or south point of the survey. The whole geometrically considered and de- monstrated.* * The remaining part of the Author's Preface I have altered according to the arrangement and improvement of this new edition. EDITOR. PREFACE. Vil The fourth section contains the nature of offsets, and the method of casting them up by the pen. The fifth section contains the method of finding the areas by intersections. The sixth section shows how to enlarge or diminish a map, or to reduce a map from one scale to another ; also the manner of uniting separate maps of lands which join each other into one map of any assigned size. The seventh section contains the method of dividing land, or of taking off or enclosing any given quantity. Section the eighth treats of surveying harbours, shoals, sands, &c. Section the ninth treats of levelling, adapted to the surveying of roads and hilly ground, with promiscuous questions. Section the first (Part the Third) contains the astro- nomical methods of finding the latitude, variation of the compass, &c., with a description of the instruments used in these operations. Section the second contains a description of the instru- ments requisite in astronomical observations. Sectiqn the third shows how to find the variation, of the compass ; with a description of the azimuth compass, and its use. In this edition is introduced a new set of accurate Mathematical Tables. Truth calls upon me to acknowledge, that the methods of calculation herein set forth got their rise from those of the late Thomas Burgh, Esq.* who first discovered a universal method for determining the areas of right-lined figures, and for which he obtained a reward of twenty thousand pounds sterling from the Irish Parliament. I" hope, therefore, it cannot be construed as an intention in me to take from his great merit when I say, that the methods herein contained are much more concise and ready than his. * This method, with very little alteration and improvement, in this country, is usually called the Pennsylvania Method of Calculation. ED. CONTENTS. PART I. Sect. Page 1. Decimal Fractions . . 11 2. Involution and Evolu- tion 22 3. Of Logarithms .... 28 4. Elements of Geome- try . . .' 40 Mathematical Instru- ments 64 5. Trigonometry .... 82 PART H. 1. The Chain 109 The Circumferentor . 121 The Theodolite ... 125 The Semicircle ... 128 The Plane Table . . ib. Mensuration of An- gles by these Instru- ments 131 The Protractor . . . ib. 2. Mensuration of Heights 137 Of Distances . 146 3. Mensuration of Areas 151 General Method ... 177 Pennsylvania Method 187 Of computing the A- rea of a Survey, ge- ometrically corisid- A3 Sect . ^ Page ered and demon- strated ....... 191 4. Of Offsets 200 5. Method of Surveying by Intersections . . 205 6. Changing the Scale of Maps 208 7. Method of dividing Land 213 8. Maritime Surveying . 220 9. Levelling 222 Promiscuous Ques- tions 229 PART IE. It Introductory Princi- ples 231 2. Description of Instru- ments 235 3. Variation of the Com- ' pass 243 LIST OF TABLES, Logarithms of Numbers. Sines and Tangents. Traverse Table. Natural Sines. EXPLANATION OF THE MATHEMATICAL CHARACTERS USED IN THIS WORK + signifies plus, or addition. " minus, or- subtraction. X or . " multiplication, -r " division. : : : : " proportion. = " equality. V " square root. f/ " cube root, &c. 05 " difference between two numbers, when it is not known which is the greater. Thus, 5 + 3, denotes that 3 is to be added to 5. 6 2, denotes that 2 is to be taken from 6. 7 X 3, or 7 . 3, denotes that 7 is to be multiplied by 3. 8 -r- 4, denotes that 8 is to be divided by 4. 2:3 : : 4:6, shows that 2 is to 3 as 4 is to 6. 6 + 4 = 10, shows that the sum of 6 and 4 is equal to 10. \/ 3, or 3 , denotes the square root of the number 3. y'S, or 5 3 , denotes the cube root of the number 5. 7 2 , denotes that the number 7 is to be squared. 8 3 , denotes that the number 8 is to be cubed. Et cetera* OF THE UNIVERSITY OF THE THEORY AND PRACTICE OF SURVEYING. THE word Surveying, in the mathematics, signifies the art of measuring land, and of delineating its boundaries on a map. The Surveyor, in the, practice of this art, directs his attention, at first, to the tracing and measuring of lines ; secondly, to the position of these lines in respect to each other, or the angles formed by them ; thirdly, to the plan, or representation of the field or tract which he surveys ; and fourthly, to the calculation of its area, or superficial content. When this art is employed in determining the variation of the compass, in observing and delineating coasts and harbours, their latitude, longitude, and soundings, together with the bearings of their most remark- able places from each other, it is usually denominated Maritime Surveying. This branch of Surveying, however, demands no other qualifications than those which should be thoroughly acquired by every land-surveyor who aspires to the character of an accomplished and skilful practitioner. Surveying, there- fore, requires an intimate acquaintance with the several parts of the mathematics which are here inserted as an introduction to this treatise. PART I. Containing Decimal Fractions, Involution and Evolution, the Nature and Use of Logarithms, Geometry, and Plane Trigo- nometry. SECTION I. DECIMAL FRACTIONS. If we suppose unity or any one thing to be divided into any assigned number of equal parts, this number is called the de- 12 DECIMAL FRACTIONS. nominator ; and if we choose to take any number of such parts less than the whole, this is called the numerator of a fraction. The numerator, in the vulgar form, is always written over the denominator, and these are separated by a small line thus f , or ;- the first of these is called three-fourths, and the latter five-eighths, of an inch, yard, &c., or of whatever the whole thing originally consisted : the 4 and the 8 are the denominators, showing into how many equal parts the unit is divided ; and the three and the live are the numerators, showing how many of those parts are under consideration. Fractions are expressed in two forms, that is, either vulgarly or decimally. AH fractions whose denominators do not consist of a cipher or ciphers, set after unity, are called vulgar ; and their denomi- nators are always written under their numerators. The treat- ment of these, however, would be foreign to our present purpose. But fractions whose denominators consist of a unit prefixed to one or more ciphers, are called decimal fractions ; the nume- rators of which are written without their denominators, and are distinguished from integers by a point prefixed ; thus T \, T 4 ^, T yj_, in the decimal form, are expressed by .2, .42, .172. The denominators of such fractions consisting always of a unit prefixed to as many ciphers as there are places of figures in the numerators, it follows, that any number of ciphers put after those numerators, will neither increase nor lessen their valjie : for T 3 , T \ 7 , and T Yo-V are a ll f tne same value, and will stand in the decimal form thus .3, .30, .300 ; but a cipher or ciphers prefixed to those numerators lessen their value in a tenfold proportion : for r \, T / , and yVro* which in the decimal form we denote by .3, .03, and .003, are fractions, of which the first is ten times greater than the second ; and the second, ten times greater than the third. Hence it appears, that as the value and denomination of any figure, or number of figures, in common arithmetic is enlarged and becomes ten, or a hundred, or a thousand times -greater, by placing one, or two, or three ciphers after it ; so in decimal arithmetic, the value of any figure, or number of figures, de- creases and becomes ten, or a hundred, or a thousand times less, while the denomination of it increases, and becomes so many times greater, by prefixing one, or two, or three ciphers to it : and that any number of ciphers before an integer, or after a decimal fraction, has no effect in changing its value. DECIMAL FRACTIONS. 13 SCALE OF NOTATION. Integers. Decimals. 7342186 875326 ifffff! f inn H;if** Hffrlf girli. -88.188.1 * GO C. & CO >-t .'* ~? <*> e+ ~ t\ * ' 011 g a* *S gf to * 3- cr I '"S ADDITION OF DECIMALS. "Write the numbers under each other according to the value or denomination of their places ; which position will bring all the decimal points into a column, or vertical line, by themselves. Then, beginning at the right-hand column of figures, add in the same manner as in whole numbers, and put the decimal point in the sum directly beneath the other points. EXAMPLES. Add 4.7832, 3.2543, 7.8251, 6.03, 2.857, and 3.251 together. Place them thus, 4.7832 3.2543 7.8251 6.03 2.857 3.251 Sum = 28.0006 Add 6.2, 121.306, .75, 2.7, and .0007 together. 121.306 .75 2.7 .0007 Sum= 130.9567 What is the sum of 6.57, 1.026, .75, 146.5, 8.7, 526., 3.97, and .0271? Answer, 693.5431, 14 DECIMAL FRACTIONS. What is the sum of 4.51, 146.071, .507, .0006, 132., 62.71, .507, 7.9, and .10712? Answer, 354.31272. SUBTRACTION OF DECIMALS. Write the figures of the subtrahend beneath those of the minuend according to the denomination of their places, as di- rected in the rule of addition ; then, beginning at the right-hand, subtract as in whole numbers, and place the decimal point in the difference exactly under the other two points. EXAMPLES. From 38.765 take 25.3741 25.3741 Difference = 13.3909 From 2.4 take .8473 .8472 Diff. = 1.5528 From 71.45 take 8.4837248. Difference = 62.9662752. From 84 take 82.3412. Diff.= 1.6588. MULTIPLICATION OF DECIMALS. Set the multiplier under the multiplicand without any regard to the situation of the decimal point ; and having multiplied as in whole numbers, cut off as many places for decimals in the product, counting from the right-hand towards the left, as there are in both the multiplicand and multiplier : but if there be not a sufficient number of places in the product, the defect may be supplied by prefixing ciphers thereto. For the denominator of the product being a unit, prefixed to as many ciphers as the denominators of the multiplier and multiplicand contain of ciphers, it follows that the places of de- cimals in the product will be as many as in the numbers from" whence it arose. DECIMAL FRACTIONS. 15 EXAMPLES. x Multiply 4.765 by .003609. .003609 438885 292590 146295 Product = .175992885 Multiply .121 by .14 Product = .01694 Multiply 121.6 by 2.76 2.76 7296 8512 2432 Product = 335.616 Multiply .0089789 by 1085. Product = 9.7421065. Multiply .248723 by .13587. Product = .03379399401. DIVISION OF DECIMALS. Divide as in whole numbers ; observing that the divisor and quotient together must contain as many decimal places as there are in the dividend. If, therefore, the dividend have just as many places of decimals as the divisor has, the quotient will be a whole number withouj. any decimal figures. If there be more places of decimals in the dividend than there are in the divisor, point off as many figures in the quotient for decimals, as the decimal places in the dividend exceed those in the divisor ; the want of places in the quotient being supplied by prefixing ciphers. But if there be more decimalplaces in the divisor than in the dividend, annex ciphers to the dividend, so that the decimal places here may be equal in number to those in the divisor; and men the quotient will be a whole number, without fractious* 16 DECIMAL FRACTIONS. When there is a remainder, after the division has been thus performed, annex ciphers to this remainder, and continue the operation till nothing remains, or till a sufficient number of decimals shall be found in the quotient. EXAMPLES. Divide .144 by .12. .12).144(1.2 = quotient. 12 ' 24 24 *~--.^. ^ Divide 63.72413456922 by 2718.^ 2718)63.72413456922(.02344522979 = quotient. 5436 9364 8J54 12101 10872 12293 1087$ 14214 13590 6245 5436 8096 5436 26609 24462 21472 19026 24462 24462 DECIMAL FRACTIONS. 17 There being 11 decimal figures in the dividend, and none in the divisor, 1 1 figures are to be cut off in the quotient ; but as the quotient itself consists of but 10 figures, prefix to them a cipher to complete that number. Divide 1.728 by .012 .012)1.728(144 = quotient. 12 52 48 48 48 *. ~ Because the number of decimal figures in the divisor and dividend are alike, the quotient will be integers. Divide 2 by 3.1416 3.1416)2.0000,0(0.636618+ = quotient. 1 8849 6 115040 94248 207920 188496 194240 188496 57440 31416 260240 251328 8912+ In this example there are four decimal figures in the divisor, and none in the dividend ; therefore, according to the rule, four ciphers are annexed to the dividend, which, in this condition, is yet less than the divisor. A cipher must then be put in the quotient in the place of integers, and other ciphers annexed to the dividend ; and the division being now performed, the deci- mal figures of the quotient are obtained. ;*,,. 18 DECIMAL FRACTIONS. Divide 7234.5 by 6.5 Quotient = 1113. Divide 476.520 by .423 = 1126.5+ Divide .45695 by 12.5 = .0365+ Divide 2.3 by 96 = .02395+ Divide 87446071 by .004387 = 19933000000 Divide .624672 by 482 = .001296. REDUCTION OF DECIMALS RULE I. To reduce a Vulgar Fraction to a Decimal of the same value. Having annexed a sufficient number of ciphers, as decimals, to the numerator of the vulgar fractions, divide by the denomi- nator ; and the quotient thence arisjng will be the decimal frac tion required. EXAMPLE. Reduce f to a decimal fraction. 4)3.00 .75=decirnal required. For f of one acre, mile, yard, or any thing, is equal to 1 of 3 acres, miles, yards, &c. ; therefore if 3 be divided by 4, the quotient is the answer required. Reduce f to a decimal fraction. Answer .4 Reduce if .48 Reduce ^ - .... .1146789 Reduce % .7777+ Reduce fi - .9130434+ Reduce |, i, {, |, and so on to Jg-, to their corresponding decimal fractions ; and in this operation the various modes of interminate decimals may be easily observed. RULE II. To reduce Quantities of the same, or of different Denominations^ to Decimal Fractions of higher Denominations. If the given quantity consist of one denomination only, write it as the numerator of a vulgar fraction ; then consider how many of this make one of the higher denomination, men- tioned in the question, and write this latter number under the former, as the denominator of a vulgar fraction. When this has been done, divide the numerator by the denominator, as directed in the foregoing rule, and the quotient resulting will be the decimal fraction required. DECIMAL FRACTIONS. 19 But if the given quantity contain several denominations, re- duce them to the lowest term for the numerator ; reduce likewise that quantity whose fraction is sought to the same denomina- tion, for the denominator of a vulgar fraction ; then divide as before directed. EXAMPLES. Reduce 9 inches to the decimal of a foot. The foot being equal to 12 inches, the vulgar fraction will be-^; then 12)9:00 .75=decimal fraction required. Reduce 8 inches to the decimal of a yard. 8 inches 1 yard X 3 X 12 = 36 36)8.0(.22+ = Answer. 72 80 72 8 Reduce 5 furlongs 00 perches to the decimal of a mile. 1 mile 5 furlongs 8 40 200 = vulgar fraction. 320 320 per. 320)200.0(.625 = decimal sought. 1920 800 640 1600 1600 Reduce 21 minutes 54 seconds to the decimal of a degree. Ans. .365. Reduce .056 of a polejx> the decimal of an acre. Ans. .00035. Reduce 13 cents to the decimal of an eagle. Ans. .013. Reduce 1 4 minutes to the decimal of a day. Ans. .00972+ Reduce 3 hours 46 minutes to the decimal of a week. Ans* 0224206+ 20 DECIMAL FRACTIONS. RULE in. To find the value of Decimal Fractions in terms of the lower denominations. Multiply the given decimal by the number of the next lower denomination which makes an integer of the present, and point off as many places at the right-hand of the product, for a re- mainder, as there are figures in the given decimal. Multiply this remainder by the number of the next inferior denomination, and point off a remainder as before. Proceed in this manner through all the parts of the integer, and the several denomina- tions standing on the left-hand are the value required. EXAMPLES. Required the value of .3375 of an acre. 4 = number of roods in an acre. 1.3500 40 = number of perches in a rood. 14.0000 The value, therefore, is 1 rood 14 perches. What is the value of .6875 of a yard ? 3 = number of feet in a yard. 2.0625 12 = number of inches in a foot. .7500 12 = number of lines in an inch. 9.0000 The answer here is 2 feet 9 lines. What is the value of .084 of a furlong? Ans. 3 per. 1 yd. 2 ft. 11 in. What is the value of .683 of a degree ? Ans. 40 m. 58 sec. 48 thirds. What is the value of .0053 of a mile ? Ans. 1 per. 3 yds. 2 ft. 5 in.+ What is the value of .036 of a day ? Ans. 61' 50" 24'" DECIMAL FRACTIONS. 21 PROPORTION IN DECIMAL FRACTIONS. Having reduced all the fractional parts in the given quantities to their corresponding decimals, and having stated the three known terms, so that the fourth, or required quantity, may be as much greater or less than the third as the second term is greater or less than the first, then multiply the second and third terms together, and divide the product by the first term, and the quotient will be the answer ; in the same denomination with the third term. EXAMPLES. If 3 acres 3 roods of lanoT can be purchased for 93 dollars 60 cents, how much will 15 acres 1 rood cost at that rate ? 3 acs. 3 rds. = 3.75 acres. 15 acs. 1 rd. = 15.25 acres. $93, 60 cents =$93.60 Then 3.75 : 15.25 : : 93.60: 15.25 46800 18720 46800 9360 ^ g 3.75)1427.4000(380.64 = Answer. 1125 3024 3000 2400 2250 1500 1500 I If a clock gain 14 seconds hi 5 days 6 hours, how much . will it gain in 17 days 15 hours? Ans. 47 seconds. If 187 dollars 85 cents gain 12 dollars 33 cents interest in a year, at what rate per cent, is this interest? Ans. 6.56+ 22 INVOLUTION AND EVOLUTION. SECTION II. INVOLUTION AND EVOLUTION. INVOLUTION is the method of raising any number, considered as the root, to any required power. Any number, whether given or assumed at pleasure, may be called the root or first power of this number ; and its other powers are the products that result from multiplying the number by itself, and the last product by the same number again, and so on to any number of multiplications. The index, or exponent, is the number denoting the height, or degree of the power, being always greater by one than the number of multiplications employed in producing the power. It is usually written above the root, as in the following EX- AMPLE, where the method of involution is plainly exhibited. Required the fifth power of 8 = the root, or first power, first multiply by - - 8 then multiply the product 64 = 8 2 = square, or second power, by 8 &c. 512 = 8 3 = cube, or third power. 8 4096 = 8 4 = biquadrate, or fourth power. 8 32768 = 8 5 = Answer. EXAMPLES FOR .EXERCISE. What is the second power of 3.05 ? Ans. 9.3025. What is the third power of 85.3 ? Ans. 620650.477. What is the fourth power of .073 ? Ans. .000028398241. What is the eighth power of .09 ? Ans. .00.00.00.0043046721. Note. When two or more powers are multiplied together, their product is that powet whose index is the sum of the in- dices of the factors, or powers multiplied. EVOLUTION is the method of extracting any required root from any given power. Any number may be considered as a power of some other number; and the required root of any given power is that EVOLUTION. 23 number which being multiplied into itself a particular number of times produces the given power; thus if 81 be the given number, or power, its square or second root is 9 ; because 9 X 9=9* =81', and 3 is its biquadrate, or fourth root, because 3X3X3X3=3 4 =81. Again, ifj!729 be the given power, and its cube root be required, the answer is 9, for 9 X 9 X 9=729 ; and if the sixth root of that number be required, it is found to be 3, for 3 x 3 x 3 X 3 X 3 X 3=729. The required power of any given number, or root, can always be obtained exactly, by multiplying the number continu- ally into itself; but there are many numbers from which a proposed root can never be completely extracted ; yet by ap- proximating with decimals, these roots may be found as exact as necessity requires. The roots that are found complete are denominated rational roots, and those which cannot be found completed, or which only approximate, are called surd, or irrational roots. Roots are usually represented by these characters or ex- ponents : N/, or * which signifies the square root; thus, \/9, or 9 2 =3. \ r or cube root ; ^64, or 64^=4. \V or * biquadrate root; v'lG, or 16 T =2, &c. Likewise 8 signifies the square root of 8 cubed ; and, in general, the fractional indices imply that the given numbers are to be raised to such powers s are denoted by their numerators, and that such roots are to be extracted from these powers as are denoted by their denominators. RULE For extracting the Square Root. Commencing at the unit figure, cut off pefi*s of two figures each, till all the figures of the given number are exhausted.* The first figure of the required root will be the square root 4fr* * In dividing a decimal, or a number consisting of a whole number with a decimal, into periods, the division must also commence at the unit figure or decimal point, and must be continued both ways, if there be a whole number ; and if there be an odd figure at the end of the deciijMil, a cipher, or if it be a periodical decimal, the figure that would next atise, from its continuation, must be annexed ; thus 417.245 will be divided thus, 4'17'.24/50: 41.66666, &c. thus, 41 / .66 / 66'66 : and .567 thus, 56'70, &c. See the Editor's " Elementary Treatise on Arithmetic, in Theory and Prac/zce,".page 219. ED. 24 . EVOLUTION. ^ of the first period, or of the greatest square root contained in , it, if it be not a square itself. Subtract the square of this figure from the first period ; to the remainder annex the next period for a dividend ; and for part of a divisor, double tjbie part of the root already obtained. Try how often this part of the divisor is contained in the dividend wanting the last figure, and annex the figures thus found to the parts of the root and of the divisor already de- termined. Thus multiply and subtract as in division ; to the remainder bring down the next period, and, adding to the divisor the figure of the root last found, proceed as before.* If any thing remain after continuing the process till all the figures in the given number have been used, proceed in the same manner to find decimals, adding, to find each figure, two ciphers, pr if the given number end in an interminate decimal, the two figures that would next arise from its continuation. To extract the root of a fraction, reduce it to its simplest form, if it be not so already, and extract the root of both 'terms, if they be complete powers : otherwise divide the root of their product by the denominator. The root may also be found by reducing the fraction to a decimal, if it be not such already, and taking the root of the decimal. "% . s ' EXAMPLES. Required the square root of 1710864. 1'71'08'64' 1710864(1308 = Answer. 1 23 71 69 2608 I 20864 20864 * The principle on which the preceding rule depends is, that the square of the sum of two numbers is equal to the squares of the numbers with twice their product. Thus, the square of 34 is equal to the squares of 30 and of 4 with twice the product of 30 and 4 ; that is, to 900-J-2 X30 x4-[-16= 1156. Here, in extracting the second root of 1156, we separate it into two parts, 1 100 and 56. Thus 1 100 contains 900, the square of 30, with the remainder 200 ; the first part of the root is therefore 30, and the re- mainder 200-J-56, or 256. Now, according to the principle above men- EVOLUTION. 25 Required the square root of 16007.3104. I'60'07'.3r04 r 1 22 16007.3104(126.52 = Answer.' 60 44 246 I 1607 6 I 1476 2525 I 13131 5 I 12625 25302 I 50604 50604 EXAMPLES FOR EXERCISE, Required the square root of 298116. Ans. 546. Required the square root of 348.17320836. Ans. 18.6594. Required the square root of 17.3056. Ans. 4.16. Required the square root of .000729. Ans. .027. Required the square root of 17f. Ans. 4.168333+ TO EXTRACT THE CUBE ROOT. RULE I. Commencing at the unit figure, cut off periods of three figures each, till all the figures of the given number are exhausted. Then find the greatest cube number contained in the first period, and place the cube root of it in the quotient. Subtract its cube from the first period, and bring down the next three figures ; divide the number thus brought down by 300 times the square of the first figure of the root, and it will give the second figure ; add 300 times the square of the first figure, 30 times the product of the first and second figures, and the square of the second figure together, for a divisor ; then tioned, this remainder must be twice the product of 30, and the part of the root still to be found, together with the square of that part. Now, dividing 256 by 00, the double of 30, we find for quotient 4 ; then this part being added to 60, the sum is 64, which being multiplied by 4, the product 256 is evidently twice the product of 30 and 4, together with the square of 4. In the same manner the operation may be illustrated in every case. The rule, however, is best demonstrated by Algebra. See my Treatise on this subject, page 231, second edition. ED. B 26 EVOLUTION. multiply this divisor by the second figure, and subtract the re- sult from the dividend, and then bring down the next period, and so proceed till all the periods are brought down.* To extract the cube root of a fraction, reduce it to a decimal, and then extract the root ; or multiply the numerator by the square of the denominator, find the cube root of the product, and divide by the denominator. The cube root of a mixed number is generally best found by reducing the fractional part to a decimal, if it be not so already, and then extracting the root. It may be also found by reducing the given number to an improper fraction, and then working according to the preceding directions. EXAMPLES. 1. Required the cube root of 48228.544. 3 2 X 300=2700 3 X30 = 90 Divisor 2790 48'223'.644'(36.41 Root. 27 21228 Resolvend. 19656 Subtrahend. 32 x 300 X 6 = 1 6200 ) 3 X 30X6 2 =3240V 1572.544 Resolvend. 6 3 = 2 1 6 j 1 572. 544 Subtrahend. Subtrahend 19656 362X300=388800 36 X 30= 1080 Divisor 389880 36 2 X 300X4 =1555200) 36 X 30X4 2 = 17280 \ 4 3 = 64) Subtrahend. 1672544 Ex. 2. What is the cube root of 62570773 ? Ans. 397. Ex. 3. What is the cube root of 51478848 ? Ans. 372. Ex. 4. What is the cube root of 84.604519? Ans. 4.39. Ex. 5. What is the cube root of 16974593? Ans. 257. * The reason of this rule will appear evident from the following illus- tration. The cube n'25, for instance, is equivalent to the cube of 20 ad- ded to the cube of 5, t gether with the sum of 300x4x5+30X2X5x5 , or, wluch is the same thing, 25 is equal to 20+5, and therefore 25 cubed EVOLUTION. 27 2. To extract the Cube Root by another Method.* 1. By trials find the nearest rational cube to the given number, whether it be greater or less, and call it the assumed cube. 2. Then say, by the Rule of Three, as the sum of the given number and double the assumed cube is to the sum of the as- sumed, and double the given number, so is the root of the assumed cube to the root required, nearly. Or, as the first sum is to the difference of the given and assumed cube, so is the assumed root to the difference of the roots, nearly. 3. By using, in like manner, the cube of the root last found as a new assumed cube, another root will be obtained still nearer. And so on as far as we please ; using always the cube of the last found root for the assumed cube. EXAMPLES. 1. To find the cube root of 21035.8. Here the root is soon found between 27 and 28. Taking therefore 27, its cube is 19683, which is the assumed cube. Then, Ig6g3 21035.8 2 2 39366 42071.6 21035.8 19683 As 60401.8 : 61754.6 : : 27 : 27.6047, is equal to 20+5 cubed ; but 20+5 cubed is equivalent to 8000-J-300X 4x5+30x2X5x5+125, or to 203+(300x4+30x2x5+5x5)x5= 48228544. 20X20+5X20 +5x20+25 Multiplied, { 20X20+2X5X20^ = second power. 20X20X20+2X5X20X20+20X25 +5 X 20 X 20+2 X 20 X 25+125 20 X 20 X 20+3 X 5 X 20 X 20+3 X 20 X 25+1 25=r3d power or, SOOO+300 X 4 X 5+30 X 2 X 25+125. Here the rule is evident. In the same manner, the operation may be illustrated in every case. For a demonstration of this rule in general terms, the reader is referred to the Editor's " Treatise on Algebra, Theo- retical arfd Practical." ED. * This rule is found in Hutton's Mathematics. There have been differ- ent rules given for extracting the cube root, among which this, and another rule given in Pike's Arithmetic (by approximation), are very expeditious. B2 28 OF LOGARITHMS. Therefore 27.6047 is the root nearly. Again, by repeating the operation, and taking 27.6047 for the assumed root, it will give 27.60491 the root still nearer. 2. Required the cube root of 3214? Ans. 14.75758. 3. Required the cube root of 2 ? Ans. 1.25992. 4. Required the cube root of 256 ? Ans. 6.349. SECTION III. OF LOGARITHMS. LOGARITHMS are a series of numbers, so contrived, that by them the work of multiplication may be performed by addition; and the operation of division may be done by subtraction. Or, Logarithms are the indices, or series of numbers in arith- me.tical progression, corresponding to another series of numbers in geometrical progression. Thus, 0, 1, 2, 3, 4, 5, 6, &c. indices or logarithms. 1, 2, 4, 8, 16, 32, 64, &c. geometrical progression. Or, 0, 1, 2, 3, 4, 5, 6, &c. ind. or log. 1, 3, 9, 27, 81, 243, 729, &c. geometrical series. Or, 50*, 1, 2, 3, 4, 5, 6,&c.ind.orlog. 1, 10, 100, 1000, 10000, 100000, 1000000, &c. geomet- rical series, where the same indices serve equally for any geometrical series or progression. Hence it appears that there may be as many kinds of indices, or logarithms, as there can be taken kinds of geometrical series. But the logarithms most convenient for common uses are those adapted to a geometrical series increasing in a tenfold progres- sion, as in the last of the foregoing examples. In the geometrical series 1, 10, 100, 1000, &c. if between the terms 1 and 10 the numbers 2, 3, 4, 5, 6, 7, 8, 9 were interposed, indices might also be adapted to them in an arith- * In any system of logarithms the log. of 1 is ; for logarithms may be considered as the exponents of the powers to which a given or inva- riable number must be raised, in order to produce all the common or natural numbers, therefore by assuming x=a, then by squaring x=a a hence a 2 a, and consequently by division a=l, from whence it is evi- dent tint the log. of 1 is always = 0, in any system ; for more on this subject, and the algebraical form of the rule for computing logarithms, see Bonnycastle's Algebra, page 200, New- York edition ; or my Treatise on Algebra, page 332, second edition. ED. OF LOGARITHMS. 29 metical progression, suited to the terms interposed between 1 and 10, considered as a geometrical progression. Moreover, proper indices may be found to all the number^, that can be interposed between any two terms of the geometrical series. But it is evident that all the indices to the numbers under 10, must be less than 1 ; that is, they must be fractions. Those to the numbers between 10 and 100, must fall between 1 and 2 ; that is, they are mixed numbers, consisting of one and some fraction. Likewise the indices to the numbers between 100 and 1000, will fall between 2 and 3 ; that is, they are mixed numbers, consisting of 2 and some fraction ; and so of the other indices. Hereafter the integral part only of these indices will be called the index ; and the fractional part will be called the logarithm. The computation of these fractional parts is called making logarithms ; and the most troublesome part of this work is to make the logarithms of prime numbers, or those which caiwot be divided by any other numbers than themselves and unity. RULE For computing the Logarithms of Numbers* Let the sum of its proposed number and the next less num- ber be called A. Divide 0.8685889638+ by A, and reserve * The number 0.8685889638-}- is twice the reciprocal of, the hyper- bolic log. 2.302585093, which is the log. of 10, according to the first form of Lord Napier, the inventor of logarithms ,; which log. according to the excellent Sir I. Newton's method is calculated thus ; let DFD (PI. 14, jig. 1) be an hyperbola whose centre is C, vertex F, and interposed square CAFE=1. In CA take AB and Ab, on each side = JL, or 0.1 ; and, erecting the perpendiculars BD, bd, half the sum of the spaces AD and Ad will be =0.1 | 7 1 *7' + &c . and the half diff. = o_] + ^ + o.oo,i | o.oooooom &c< Which reduced will stand thus, 0.1000000000000,0.0050000000000 Sum of these=0.1 053605 156577=Arf 3333333333 250000000 And the diff. =0.0953 101798043=AD 20000000 1666666 In like manner putting AB and A6 142857 12500 each = 0.2 there is obtained 1111 100 Ad = 0.2231435513142, and _9 J_AD = 0.1823215567939. $1003353477310,0.0050251679267 Having thus the hyperbolic logarithms of the four decimal numbers 0.8, 0.9, 1.1, and 1.2 ; and since ^X^=2, and 0.8 and 0.9 are less than unity, adding their logarithms to double the log. of 1.2, we have 0.6931471805507, the hyperbolic log. of 2. To the triple of this adding the log. of 0.8, because Hgl 10, we have 2.3025850929933, the log. of 10. Hence by one addition 30 OF LOGARITHMS. the quotient. Divide the reserved quotient by the square of A, and reserve this quotient. Divide the last reserved quotient by the square of A, reserving the quotient still ; and thus pro- ceed as long as division can be made. Write the reserved quotients orderly under one another, the first being uppermost. Divide these quotients respectively by the odd numbers 1, 3, 5, 7, 9, 11, &c. ; that is, divide the first reserved quotient by 1, the second by 3, the third by 5, the fourth by 7, &c., and let these quotients be written orderly under one another; add them together, and their sum will be a logarithm. To this logarithm add the logarithm of the next less number, and the sum will be the logarithm of the number proposed. EXAMPLE 1. Required the logarithm of the number 2. Here the next less number is 1, and 2+l=3=A, and A 3 or 3 2 =9 ; then 3)0.868588964 9)0.289529654 -^ 1=0.289529654 9)0.032169962-^- 3=0.010723321 9)0.003574440-r 5=0.000714888 9)0.0003971 60-H 7=0.000056737 9)0.000044129-f- 9=0.000004903. 9)0.000004903-^ 1 1 =0.000000446 9)0.000000545-^-13=0.000000042 0.000000061 -M5=0.000000004 are found the logarithms of 9 and 11 : And thus the logarithms of all the prime numbers are prepared, that is, 2, 3, 5, 11, &c. Moreover, by only depressing the numbers above computed, lower in the decimal places, and adding, are obtained the logarithms of the decimals 0.98,0.99, 1.01, 1.02; as also of these, 0.998, 0.999, 1.001, 1.002. And hence, by addition and subtraction, will arise the.logarithms of the primes 7, 13, 17, 3T, &c. All which logarithms being divided by 2.3025850929933 therefore the triangles ABE, AD C are mutually equiangular, and consequently (by the last) AC : AE : : AD : AB ', where- fore AC multiplied by AB will be equal to AE multiplied by AD. Q. E. D. THEOREM XVIII. PL. 2.^-. 1. Triangles ABC, BCD, and parallelograms ABCF ana BDEC, having the same altitude, have the same proportion between themselves as their bases BA and BD. Let any aliqu6t part of AB be taken which will also measure BD : suppose that to be ^g, which will be contained twice in AB, and three times in BD, the parts Ag, gB, Bh, hi, and iD being all equal, and let the lines gC, AC, and iC be drawn: then (by cor. to theo. 13) all the small triangles AgC, gCB, BCh, &c. will be equal to each other, and will be as many as the parts into which their bases were divided ; therefore it will be, as the sum of the parts in one base is to the sum of those in the other, so will be the sum of the small triangles in the first to the sum of the small triangles in the second triangle ; that is, AB: BD:: ABC : BDC. Whence also the parallelograms ABCF and BDEC, being (by cor. 2, theo. 12) the doubles of the triangles, are likewise as their bases. Q. E. D. Note. Wherever there are several quantities connected with the sign (: :) the conclusion is always drawn fiom the first two and last two proportionals. THEOREM XIX. PL. 2. fig.Z. Triangles ABC, DEF, standing upon equal bases AB and DE, are to each other as their altitudes CG and FH. Let BJ be perpendicular to AB and equal to CG, in which let KB=FH, and let AI and AK be drawn. THEOREMS. 55 The triangle AIB=ACB (by cor. to theo. 13), and DEF; but (by theo. 18) El : BK : : ABI : ABK. That is, CG : FH : : ABC : DEF. Q. E. D. THEOREM XX. PL. 2. Jig. 9. If a right line BE be drawn parallel to one side of a triangle ACD, it will cut the two other sides proportionally, viz. AB : BC : : AE : ED. Draw CE and BD; the triangles BEC and EBD being on the same base BE and under the same parallel CD, will be equal (by cor. to theo. 13) therefore (by theo. 18) AB : BC : : (BEA : BEC or BEA : BED : :) AE : ED. Q. E. D. Cor. 1. Hence also AC : AB : : AD : AE ; for AC : AB (AEC : AEB : : ABD : AEB) : : AD : AE. Cor. 2. It alsotftppears that a right line which divides two sides of a triangle proportionally must be parallel to. the re- maining side. Cor. 3. Hence, also, theo. 16 is manifest; since the sides of the triangles ABE, ACD, being equiangular, are propor- tional. THEOREM XXI. PL. 2. Jig. 4. If two triangles ABC, ADE have an angle BAG in the one equal to an angle DAE in the other, and the sides about the equal angles propor- tional ; that is, AB : AD : : AC : AE ; then the triangles will be mutually equiangular. In AB take Ad=AD, and let de be parallel to BC, meeting AC inc. Because (by the first cor. to the foregoing theo.) AB : Ad (or AD) : : AC : Ae, and (by the hypothesis, or what is given in the theorem) AB : AD : : AC: AE ; therefore Ae=AE, seeing AC bears the same proportion to each ; and (by theo. 6) the triangle Ade=ADE, therefore the angle Ade=D and Aed=E; but since ed and /JCare parallel (by part 3, theo. 3) Ade^B, and Aed=C, therefore B=D and C=E. Q. E. D. THEOREM XXII. PL. 2. Jig. 5. Equiangular triangles ABC, DEF are to one another in a duplicate pro- portion of their homologous or like sides ; or as the squares AK and DJtf of their homologous sides. ^ Let the perpendiculars CG and FH be drawn, as well as the diagonals BI and EL. 56 GEOMETRICAL The perpendiculars make the triangles ACG and DFH equi- angular, and therefore similar (by theo. 16) ; for because the angle CAG=FDH, and the right angle AGC=DHF> the re- maining angle ACGDFH (by cor. 2. theo. 5). Therefore GC : FH : : (AC : DF : :) AB : DE, or, which is the same thing, GC : AB : : FH : DE, for FH multiplied by AB=GC multiplied by DE. By theo. 19, ABC: ABI: :(CG: AI or AB as before:: FH: DE, or DL): : DFE: DLE, therefore ABC: ABI: : DFE : DLE, or ABC : AK: : DFE : DM, for AK is double the triangle ABI> and DM double the triangle DEL, (by cor. 2. theo. 12.) Q. E. D. THEOREM XXIII. PL. 2. ./Eg-. 6. Like polygons ABODE, abcde are in a duplicate proportion to that of the sides AB, ab, which are between equal angles A and B and a and b, or as the squares of the sides AB, ab. Draw AD, AC, ad, ac. By the hypothesis AB : ab::BC:bc, and thereby also the angle Bb-, therefore (by theo. 21) BAC=bac ; and ACS =acb : in like manner EAD=ead, and EDA=eda. If there- fore from the equal angles A and a> we take the equal ones EAD-}-BACead-\-bac, the remaining angle DAC=dac, and if from the equal angles D and d, EDA=eda be taken, we shall have ADC=adc : and in like manner if from C and c be taken BCA=bca, we shall have ACD=acd', and so the respective angles in every triangle will be equal to those in the other. By theo. 22, ABC: abc : : the square of AC to the square of ac, and also ADC : adc: : the square of AC to the square t)f ae ; therefore, from equality of proportions, ABC : abc : : ADC : adc ; in like manner we may show that ADC : adc : : EAD : ead.. Therefore it will be, as one antecedent is to one consequent, so are all the antecedents to all the consequents. That is, ABC is to abc as the sum of the three triangles in the first polygon is to the sum of those in the last. Or ABC will be to abc as polygon to polygon. The proportion of ABC to abc (by the foregoing theo.) is Us the square of AB is to the square of ab, but the proportion of polygon to polygon is as ABC to abc, as now shown: therefore the proportion of polygon to polygon is as the square of AB to the square of ab. THEOREMS. 57 THEOREM XXIV. PL. I. Jig. 8. Let DHB be a quadrant of a circle described by the radius CB ; HB an arc of it, and DH its complement ; HL or FC the sine, FHor CL its co- sine, BK its tangent, DI its cotangent ; CK its secant, and CI its co- secant.. Fig. 8. 1. The cosine of an arc is to the sine as the radius is to the tangent. 2. The radius is to the tangent of an arc as the cosine of it is to the sine. 3. The sine of an arc is to its cosine as the radius to its cotangent. 4. Or the radius is to the cotangent of an arc as its sine to its co-sine. 5. The cotangent of an arc is to the radius as the radius to the tangent. 6. The cosine of an arc is to the radius as the radius is to the secant. 7. The sine of an arc is to the radius as the tangent is to the secant. The triangles CLH and CBK being similar (by theo. 16), 1. CL:LH:: CB : BK. 2. Or, CB : BK : : CL : LH. The triangles CFH and CDI being similar, 3. CF (or LH ) : FH : : CD : DI. 4. CD: DI:: CF (or LH ) : FH. The triangles CDI and CBK are similar; for the angle CID=KCB, being alternate ones (by part 2, theo. 3), the lines CB and DI being parallel, the angle CDI=CBK being both right, and consequently the angle DCI=CKB> wherefore, 5. DI : CD : : CB : BK. And again, making use of the similar triangle CLH and CBK, 6. CL : CB : : CH : CK. 7. HLiCH-.iBK: CK. 58 GEOMETRICAL GEOMETRICAL PROBLEMS. . 0. " if-vVj .-,\r ; ') Wsna^w iV\r> -T< "i> '' ;-^v;. . PROBLEM I. PL. 2.^.7. To wta&e a triangle of three given right lines B 0, LB, L 0, of which any two must be greater than the third. Lay BL from B to L', from B with the line BO describe an are, and from L with LO describe another arc ; from O, the intersecting point of those arcs, draw BO and OL, and BOL ijS the triangle required. This is manifest from the construction. PROBLEM II. PL. 2. Jig. 8. At a point B in a given right line BC, to make an angle equal to a given angle A. Draw any right line ED to form a triangle, as EAD, take BF =ADj and upon /Fmake the triangle BFG, whose side BG= AE, and GF=ED (by the last),, then also the angle B= A ; if we suppose one triangle be laid' on the other, the sides will mutually agree with' each other, and therefore be equal ; for if we consider these two triangles. to be made of the same three given lines, they are manifestly one and the same triangle. Otherwise, Upon the centres A and B, at any distance, let two arcs DE, FG, be described; make the arc FG=DE, and through B and 6r draw the line BG, and it is done. For since the chords ED, GF are equal, the angles A and B are also equal, as before (by def. 17); PROBLEM L PL. 2. Jig. 9. To bisect or divide into two 'equal parts any given right-lined angle BA C. In the lines AB and AC, from the point A, set off equal dis- tances AE=AD', then, with any distance more than the half of DE, describe two arcs to cut each other in some point JF; and the right line AF, joining the points A and F, will bisect the given angle BAG. For if ZXFand FE be drawn, the triangles ADF, AEF are equilateral to each other, viz. AD= AE, DF=FE, and AF common, wherefore DAF=EAF, as before. PROBLEMS. 59 PROBLEM IV. PL. 2. Jig. 10. To bisect a right line AB. With any distance more than half the line from A and B, describe two circles CFD, CGD, cutting each other in the points C and D; draw CD intersecting AB in E, then For, if AC, AD, BC, BD be drawn, the triangles ACD, BCD will be mutually equilateral, and consequently the angle ACE=BCE; therefore the triangle ACE, BCE, having AC=BC, CE common, and the angle ACE=BCE ; (by theo. 6) the base AE=the base BE. Cor. Hence it is manifest that CD not only bisects AB, but is perpendicular to it (by def. 10). PROBLEM V. PL. 2. fig. II. On a given point A, in a right line EF, to erect a perpendicular. From the point A lay off on each side the equal distances AC, AD; and from C and D as centres, with any interval greater than AC or AD, describe two arcs intersecting each other in n ; from A to B draw the line AB, and it will be the perpendicular required. For let CB and BD be drawn, then the triangles CAB, DAB will be mutually equilateral and equiangular, so CAB=DAB 9 a right angle (by def. 10). PROBLEM VI. PL. 2. fig. 12. To raise a perpendicular on the end B of a right line AB. From any point D not in the line AB, with the distance from D to B, let a circle be described cutting AB in E ; draw from E through D the right line EDC, cutting the periphery in C, and join CB, and that is the perpendicular required. EBC being a semicircle, the angle EBC will be a right angle (by cor. 5, theo. 7). ROBLEM VII. PL. 2. fig. 13. From a given point A t to let fall a perpendicular upon a given right line BC. From any point D, in the given line, take the distance to th given point A, and with it describe a circle AGE, make GJB= 00 GEOMETRICAL AG, join the points A and E by the line AFE f and AF will be the perpendicular required. Let DA, DE be drawn, the angle ADFFDE, DA=DE t being radii of the same circle, and DF common; there- fore (by theo. 6) the angle DFA=DFE, and FA a perpen- dicular. (By defl 10.) PROBLEM VIIL PL. 2. fig. 14. Through a given point A to draw a right line AB, 'parallel to a given right line CD. From the point A to any point F in the line CD draw the line AF', with the interval FA, and onefoot of the compasses in F, describe the arc AE, and with the like interval and one foot in A describe the arc BF, making BFAE', through A and B draw the line AB, and it will be parallel to CD. By prob. 2, The angle BAF=AFE, and by theo. 11, BA and CD are parallel. PROBLEM IX. PL. I. Jig. 17. Upon a given line AB to describe a square ABCD* Make BC perpendicular and equal to AB, and from A and <7, with the line AB or BC, let two arcs be described, cutting each other in D ; from whence to A and C let the lines AD, DC be drawn ; so is ABCD the square required. For all the sides are equal by construction ; therefore the triangles ADC and BAC are mutually equilateral and equian- gular, and ABCD is an equilateral parallelogram, whose angles are right. For B being right, D is also right, and DAC, DC A, BAC, ACS, each half a right angle (by lemma preced- ing theo, 7, and cor. 2, theo. 5), whence DAB and BCD will each be a right angle, and (by def. 43) ABCD is a square. SCHOLIUM, By the same method a rectangle or oblong may be described, the sides thereof being given. PROBLEM X. PL. 2. Jiff. 15. To divide a given right line AB into any proposed number of equal parts. Draw the indefinite right line AP, making any angle with PROBLEMS, 61 AB, also draw BQ parallel to AP, in each of which let there be taken as many equal parts AM, MN, &c. Bo, on, &c. as you would have AB divided into ; then draw Mm, JVn, &c intersecting AB in , F, &c. and it is done. For MN and mn being equal and parallel, FN will be par- allel to EM, and in the same manner GO to FN(by theo. 12) ; therefore AM, MN, NO, being all equal by construction, it is plain (from theo. 20) that AE f EF 9 FG, &c. will likewise be equal. PROBLEM XL PL. & fig. 16. To find a third proportional to two given right lines A and B. Draw two indefinite blank lines CE, CD anywise to make any angle. Lay the line A from C to F, and the line B from C to G, and draw the line FG ; lay again the line A from C to H, and through #draw HI parallel to FG (by prob. 8), so is CI the third proportional required. For, by cor. 1, theo. 20, CG : CH : : CF : CL PROBLEM XII. PL. 2. fig. 17. Three right lines A, B, C given, to find a fourth proportional. Having made an angle DEF anywise, by two indefinite blank right lines ED, EF, as before ; lay the line A from E to fr, the line B from E to /, and draw the line IG ; lay the line C from E to H, and (by prob. 8) draw HK parallel there- to, so will EK be the fourth proportional required. For, by cor. 1, theo. 20, 6? : El : : EH : EK. Ox,AiB::C:EK. PROBLEM XIII. PL. 3. fig. 1. Two right lines A and B given, to find a mean proportional. Draw an indefinite straight line, on which place AB=A and BC=B ; bisect AC (by prob. 4) in E, and describe the semicircle ADC, and from the point B erect the perpendicular BD (by prob. 5), then BD is a mean proportional. For if the lines AD, DC be drawn, the angle ADC is a right angle (by cox. 5* theo. 7), being an angle in a semi- circle. The angles ABD, DBC are right ones (by def. 10), the line BD being a perpendicular ; wherefore the triangles ABD, 62 GEOMETRICAL DBG are similar : thus the angle ABD=DBC, being both right, the angle DAC is the complement of BDA to a right angle (by cor. 2, theo. 5), and is therefore equal to BDC, the angle ADC being a right angle as before ; consequently (by cor. 1, theo. 5) the angle ADB=DCB; wherefore (by theo. 16), AB : BD :: BD: BC Of, A : BD ::BD: B. PROBLEM XIV. PL. 3.^.2. To divide a right line AB in the point E, so that AE shall have the same proportion to EB as two given lines C and D have. Draw an indefinite blank line AF to the extremity of the line AB, to make with it "any angle ; lay the line C.from A to C, and D from C to D, and join the points B and D by the line BD ; through C draw CE parallel to BD (by prob. 8), so is E the point of division. For, by theo. 20, AC : CD : : AE : EB. Or, C : D : : AE : : EB. PROBLEM XV. PL. 3. fig. 3. To describe a circle about a triangle ABC, or (which is the same thing) through any three points A, B, C, which are not situated, in a right line. By prob. 4. Bisect the line A C by the perpendicular DE, and also CB by the perpendicular FG, the point of intersection H of these perpendiculars is the centre of the circle required; from which take the distance to any of the three points A, B, C, and describe the circle ABC, and it is done. For, by cor. ^to theo. 8, the lines DE and FGr must each pass through the centre ; therefore their point of intersection H must be the centre. SCHOLIUM. By this method the centre of a circle may be found, by hav- ing only a segment of it given. PROBLEM XYL PL. 3. fig. 4. To make an angle of any number of degrees at the point A of the line AB, suppose of 45 degrees.' From a scale of chords take 60 degrees, for 60 is equal to the radius (by cor. theo. 15), and with that distance from A as a centre, describe a circle from the line A B ; take 45 degrees, PROBLEMS. 63 the quantity of the given angle, from the same scale of chords, and lay it on that circle from a to b ; through A and b draw the line AbC, and the angle A will be an angle of 45 degrees,, as required. If the given angle be more than 90, take its half (or divide it into any two parts less than 90 and lay them after each other on the arc, which is described with the chord of 60 degrees ; through the extremity of which and the centre, let a Ine be drawn, and that will form the angle required, with the given line. PROBLEM XVII. PL. 3. fig. 5. To measure a given angle ABC. If the lines which include the angle be not as long as the chord of 60 on your scale, produce them to that or a greater length, and between them so produced, with the chord of 60 from J5, describe the arc ed ; which distance ed, measured on the same line of chords, gives the quantity of the angle ABC, as required ; this is plain from def. 17. PROBLEM XVIII. PL. 3. fig. 6. To make a triangle BCE equal to a given quadrilateral figure ABCD. Draw the diagonal AC, and parallel to it (by prob. 8) DEt meeting AB produced in E ; then draw CE, and ECB will be the triangle required. For the triangles ADC, AEC being upon the same base AC, and under the same parallel ED (by eor. to theo. 13), will be equal, therefore if ABC be added to each, then ABCD =BEC. PROBLEM XIX. PL. 3, fig. It. To make a triangle DFH equal to a given five-sided figure ABODE. Draw DA and DB, and also EH and C F parallel to them, (by prob. 8) meeting AB produced in H and F; then draw DH, DF, and the triangle HDF is the one required. For the triangle DEA=DHA, and DBC=DFB (by cor. to theo. 13) ; therefore by adding these equations, DEA+DBC =DHA+DFB,if to each of these ADB be added; then DEA+ADB+DBC=ABCDE (^ DHF. 64 MATHEMATICAL PROBLEM XX. PL. 3. jig. 8. To project the lines of chords, sines, tangents, and secants vrith any ra&iuit. On the line AB, let a semicircle ADB be described ; let CDF be draWn perpendicular to this line from the centre C ; and the tangent BE perpendicular to the end of the diameter ; let the quadrants AD, DB be each divided into nine equal parts, ^very one of which will be ten degrees; if then from the centre C lines be drawn through 10, 20, 30, 40, &c. the divi- sions of the quadrant BD, and continued to BE, we shall there have the tangents of 10, 20, 30, 40, &c. and the secants C 10, C 20, C 30, &c. are transferred to the line CF, by describing the arcs 10, 10 ; 20, 20 ; 30, 30, viz. the half of 12. Any other aliquot part of a number may be used in the same way. In like manner, if the number proposed be too small to be made the parallel distance, it may be multiplied by some number, and the answer is to be divided by the same number. To protract angles by the line of chords. Case 1 . When the given degrees are under 60. 1. With any radius on a centre, describe the arch. 2. Make the same radius a trans- verse distance between 60 and 60 on the same line of chords. 3. Take out the transverse distance of the given degrees, and lay this on the arch, which will mark out the angular distance required. 72 MATHEMATICAL Case 2. When the given degrees are more than 60. 1. Open th sector, and describe the arch as before. 2. Take or of the given degrees, and take the transverse distance of this ^ or , and lay it off twice if the degrees were halved, three times if the third was used as a transverse distance. Case 3. When the required angle is less than 6 degrees ; suppose 3. 1. Open the sector to the given radius, and de- scribe the arch as before. 2. Set off the radius. 3. Set off the chord of 57 degrees backwards, which will give the arc of three degrees. Given the radius of a circle (suppose equal to two inches), re' quired the sine and tangent of 28 30' to that radius. Solution. Open the sector so that the transverse distance of 90 and 90 on the sines, or of 45 and 45 on the tangents, may be equal to the given radius, viz. two inches ; then will the transverse distance of 28 30', taken from the sines, be the length of that sine to the given radius ; or if taken from the tangents, will be the length of that tangent to the given radius. , But if the secant of 28 30' was required ? Make the given radius, two inches, a transverse distance to and at the beginning of the line of secants ; and then take the transverse distance of the degrees wanted, viz. 28 30'. A tangent greater than 45 s (suppose 60) is found thus. Make the given radius, suppose two inches, a transverse dis- tance to 45 and 45 at the beginning of the scale of upper tan- gents ; and then the required number 60 may be taken from this scale. Given the length of the sine, tangent, or secant of any degrees, to find the length of the radius to that sine, tangent, or secant. Solution. Make the given length a transverse distance to its given degrees on its respective scale : then, In the sines. The transverse distance of 90 and 90 will be the radius sought., In the lower tangents. The transverse distance of 45 and 45, near the end of the sector, will be the radius sought. In the upper tangents. The transverse distance of 45 and 45, taken towards the centre of the sector on the line of upper tangents, will be the centre sought. In the secant. The transverse distance of and 0, or the beginning of the secants, near the centre of the sector, will be the radius sought. Given the radius and any line representing a sine, tangent, or secant, to find the degrees corresponding to that line. Solution. Set the sector to the given radius, according as a sine, or tangent, or secant is concerned. DRAWING INSTRUMENTS. 73 Take the given line between the compasses ; apply the two feet transversely to the scale concerned, and slide the feet along till they both rest on like divisions on both legs ; then will those divisions show the degrees and parts corresponding to the given line. To find the length of a versed sine to a given number of de- grees, and a given radius. Make the transverse distance of 90 and 90 on k the sines equal to the given radius. Take the transverse distance of the sine complement of the given degrees. If the given degrees are less than 90, the difference between the sine complement and the radius gives the versed sine. If the given degrees are more than 90, the sum of the sine complement and the radius gives the versed sine. To open the legs of the sector so that the corresponding double scales of lines chords, sines, and tangents may make each a right angle. On the lines, make the lateral distance 10 a distance be- tween 8 on one leg and 6 on the other leg. On the sines, make the lateral distance 90 a transverse dis- tance from 45 to 45 ; or from 40 to 50 ; or from 30 to 60 ; or from the sine of any degrees to their complement I Or on the sines, make the lateral distance of 45 a transverse distance between 30 and 30. OF THE PLAIN SCALE. The divisions laid down on the plain scale are of two kinds, the one having more immediate relation to the circle and its properties, the other being merely concerned with dividing straight lines. Though arches of a circle are the most natural measure of an angle, yet in many cases right lines are substituted, as being more convenient ; for the comparison of one right line with another is more natural and easy than the comparison of a right line with a curve : hence it is usual to measure the quan- tities of angles, not by the arch itself, which is described on the angular point, but by certain lines described about that arch. The lines laid down on the plain scales for the measuring of angles, or the protracting scales, are, 1. A line of chords marked CHO. 2. A line of sines marked SIN., of tangents marked TAN., of semitangents marked ST., and of secants marked SEC. ; this last 'is often upon the same line as the sines, because its gra- dations do not begin till the sines end. D 74 MATHEMATICAL There are two other scales, namely, the rhumbs marked RV, 'and longitudes marked LON. Scales of latitude and hours are sometimes put upon the plain scale ; but as dialling is now but seldom studied, they are only made to order. j The divisions used for measuring straight lines are called scales of equal parts, and are of various lengths for the conve- nience of delineating any figure of a larger or smaller size, ac- cording to the fancy or purposes of the draughtsman. They are, indeed, nothing more than a measure in miniature for laying down upon paper, &c. any known measure, as chains, yards, feet, &c., each part on the scale answering to 1 one foot, one yard, &c., and the plan will be larger or smaller as the scale contains a smaller or a greater number of parts in an inch. Hence a variety of scales is useful to lay down lines of any required length, and of a convenient proportion with respect to the size of the dr^aw- ing. If none of the scales happen to suit the purpose, re- course should be had to the line of lines on the sector ; for, by the different openings of that .instrument, a line of any length may be divided into as many 'equal parts as any person chooses. Scales of equal parts are divided into two kinds, the one simply, the other diagonally divided. Six of the simply divided scales are generally placed one above another upon the same rule ; they are divided into as many equal parts as the length of the rule will admit of; -the numbers placed on the right-hand show how many parts in an inch each scale is divided into. The upper scale is sometimes shortened for the sake of introducing another, called the line of chords. The first of the larger or primary divisions on every scale is subdivided into ten equal parts, which small parts are those which give a name to the scale : thus it is called a scale of 20, when 20 of these divisions are equal to one inch. If, therefore, these less divisions be taken as units, and each repre- sents one league, one mile, one chain, or one yard, &c., then will the larger divisions be so many tens; but if the sub- divisions are supposed to be tens, the larger divisions will be hundreds. ! To illustrate this, suppose it were required fo set off from either of the scales of equal parts f f, 36, or 360 parts, either miles or leagues. Set one foot of your compasses on 3, among the larger or primary divisions, and open the other point till it falls on the sixth subdivision, reckoning backwards or towards the left hand. Then will this extent represent f , 36, or 360 miles or leagues, &c. and bear the same proportion in the plan as the line measured does to the thing represented. DRAWING INSTRUMENTS. 75 To adapt these scales to feet and inches, the first primary division is often duodecimally divided by the upper line ; there- fore, to lay down any number of feet and inches, as, for in- stance, 8 feet 8 inches,, exte'nd the compasses from 8 of the larger to 8 of the upper small ones, and that distance laid down on the plan will represent 8 feet 8 inches. Of the scale of equal parts diagonally divided. The use of this scale is the same as those already described. But by it a plane may be more accurately divided than by the former ; for any one of the larger divisions may by this be subdivided into 100 equal parts ; and, therefore, if the scale contains 10 of the larger divisions, any number under 1000 may be laid down with accuracy. The diagonal scale is seldom placed on the same side of the rule with the other plotting scale. The first division of the diagonal scale, if it be a foot long, is generally an inch divided into 100 equal parts, and at the opposite there is usually half an inch divided into 100 equal parts. If the scale be six inches long, one end has commonly half an inch, the other a quarter of an inch, subdivided into 100 equal parts. The nature of this scale will be better understood by consider- ing its construction. For this purpose, First. Draw eleven parallel lines at equal distances ; divide the upper of these lines into such a number of equal parts as the scale to be expressed is intended to contain ; from each of these divisions draw perpendicular lines through the eleven parallels. Secondly. Subdivide the first of these divisions into ten equal parts, both in the upper and lower lines. Thirdly. Subdivide again each of these subdivisions, by drawing diagonal lines from the 1 Oth below to the 9th above ; from the 8th below to the 7th above ; and so on, till from the first below to the above ; by these lines each of the small divisions is divided into ten parts, and consequently the whole first space into 1 00 equal parts ; for as each of the subdivisions is one-tenth part of the whole first space or division, so each parallel above it is one-tenth of such subdivision, and conse- quently, one-hundredth part of the whole first space ; and if there be ten of the larger divisions, one thousandth part of the whole space. If, therefore, the larger divisions be accounted as units, the first subdivisions will be tenth parts of a unit, and the second, marked by the diagonal upon the parallels, hundredth parts of the unit But if we suppose the larger divisions to be tens, the first- subdivisions will be units and the second tenths. If D2 76 MATHEMATICAL the larger are hundreds, then will the first be tens and the second units. The numbers, therefore, 576, 57,6, 5,76, are all expressible by the same extent of the compasses : thus, setting one foot in the number 5 of the larger divisions, extend the other along the sixth parallel to the seventh diagonal. For, if the five larger divisions be -taken for 500, seven of the first subdivisions will be 70, which upon the sixth parallel, taking in six of the second subdivisions for units, makes the whole number 576. Or, if the five larger divisions be taken for five tens, or 50, seven of the first subdivisions will be seven units, and the six second subdivisions upon the sixth parallel will be six tenths of a unit. Lastly, if the five larger divisions be only esteemed as five units, then will the seven first subdivisions be seven tenths, and the six second subdivisions be the six hundredth parts of a unit. Of the line of chords. This line is used to set off an angle from a given point in any right line, or to measure the quan- tity of an angle already laid down. Thus, to draw a line that shall make with another line an angle containing a given number of degrees, suppose 40 de- grees. Open your compasses to the extent of 60 degrees upon the line of chords (which is always equal to the radius of the circle of projection), and setting one foot in the angular point, with that extent describe an arch ; then taking the extent of 40 de- grees from the said chord line, set it off from the given line on the arch described ; a right line drawn from the given point through the point marked upon the arch will form the required angle. \ The degrees contained in an angle already laid down are found nearlyin the same manner. For instance, to measure an angle : from the centre describe an arch with the chord of 60 degrees, and the length of the arch contained between the lines measured on the line of chords will give the number of degrees contained in the angle. If the number of degrees are more than 90, they must be measured upon the chords at twice : thus, if 120 degrees were to be practised, 60 may be taken from the chords, and those degrees be laid off twice upon the arch. Degrees taken from the chords are always to be counted from the beginning of the scale. Of the rhumb line. This 4 is, in fact, a line of chords con- structed to a quadrant divided into eight parts or points of the compass, in order to facilitate the work of the navigator in lay- ing down a ship's course. DRAWING INSTRUMENTS. 77 Of the line of longitudes. The line of longitudes is a line divided into sixty unequal parts, and so applied to the line of chords as to show, by inspection, the number of equatorial miles contained in a degree on any parallel of latitude. , The graduated line of chords is necessary, in order to show the latitudes ; the line of longitude shows the quantity of a degree on each parallel in sixtieth parts of an equatorial degree, that is, miles. The lines of tangents, semitangents and secants serve to find the centres and poles of projected circles in the stereographical projection of the sphere. The line of sines is principally used for the orthographic projection of the sphere. The lines of latitudes and hours are used conjointly, and serve very readily to mark the hour lines in the construction of dials : they are generally on the most complete sorts of scales and sectors; for the uses of which see treatises on dialling. OF THE PROTRACTOR. This is an instrument used to protract or lav down an angle containing any number of degrees, or to find how many degrees . are contained in any given angle. There are two kinds put into cases of mathematical drawing instruments ; one in the form of a semicircle, the other in the form of a parallelogram. The circle is undoubtedly the only natural measure of angles ; when a straight line is therefore used the divisions thereon are derived from a circle or its properties, and the straight line is made use of for some relative convenience : it is thus the par- allelogram is often used as a protractor instead of the semi- circle, because it is in some cases more convenient, and that other scales, or CD, the three similar triangles CLH, CBK, CDI give the following proportion (by theo. 14) : 1. CL : LH : : CB : BK ; whence the tangent is known, being a fourth proportional to the co-sine, sine, and radius. 2. CL: CH:: CB:CK; whence the secant is known, being a third proportional to the co-sine and radius. 3. HL : LC : : CD : D7; whence the co-tangent is known, being a fourth proportional to the sine, co-sine, and radius. 4. HL : HC : : CD : C7; whence the co-secant is known, being a third proportional to the sine and radius. As for the logarithms, sines, tangents, and secants in the tables, they are only the logarithms of the natural sines, tangents, and secants calcu- lated as above. TRIGONOMETRY. 8$ Fig. 1. As S.C : AB : : S.A : EC. That is, as the sine of the angle C in the tables is to the length of AB (or sine of the angle C in a circle whose radius is A C), so is the sine of the angle A in the tables to the length of BC (or sine of the same angle in the circle whose radius is AC). In like manner the tangents and secants represented by making either leg the radius will be proportional to the tangents and secants of a like arc, as the radius of the given arc is to 10.000000, the radius of the tables aforesaid. Hence it is plain, that if the name of each side of the triangle be placed thereon, a proportion will arise to answer the same end as before : thus, if AC be made the radius, let the word radius be written thereon ; and as BC and AB are the sines of their opposite angles, upon the first let S.A, or sine of the angle A, and on the other let S. C, or sine of the angle C, be written. Then, When a side is required, it may be obtained by this propor- tion, viz. As the name of the side given is to the side given, So is the name of the side required to the side required. Thus, if the angles A and C and the hypothenuse AC were given, to find the sides ; the proportion will be Fig. 1. 1. R : AC : : S.A : BC. That is, as radius is to AC, so is the sine of the angle A to BC. And, 2. R : AC : : S.C : AB. That is, as radius is to AC, so is the sine of the angle Cto AB. When an angle is required we use this proportion, viz. As the side that is made the radius is to radius, So is the other given side to its name Thus, if the legs were given, to find the angle A, and if AB be made the radius, it will be Fig. 2. AB: R:: BC: T.A. That is, as AB is to radius, so is BC to the tangent of the angle A. 88 TRIGONOMETRY. After the same manner, the sides or angles of all rigW angled plane triangles may be found, from their proper data. We here, in plate 4, give all the proportion requisite for the solution of the six cases in right-angled trigonometry ; making every side possible the radius* In 'the following triangles this mark in an angle denotes.it to be known, or the quantity of degrees it contains to be given; and this mark ' on a side denotes its length to be given in feet, yards, perches, or miles, &c. and this mark , either in an angle or on a side, denotes the angle or side to be required. From these propositions it may be observed, that to find a side, when the angles and one side are given, any side may be made the radius ; and to find an angle, one of the given sides must be made the radius. So that in the 1st, 2d, and 3d cases any side, as well required as given, may be made the radius, and in the first statings of the 4th, 5th, and 6th cases, a given side only is made the radius. RIGHT-ANGLED TRIANGLES. CASE I. The angles and hypothenuse given, to find the base and perpendicular. PL. 5. fig. 4. In the right-angled triangle ABC, suppose the angle A= 46 30' ; and consequently the angle C=43 30' (by cor. 2y theo. 5); and AC 250 parts (as feet, yards, miles, &c.) ; re- quired the sides AB andJ?C. 1st. By Construction* Make an angle of 46 30' in blank lines (by prob. 16, geom.)^ as CAB ; lay 250, which is the given hypothenuse, from a scale of equal parts, from AtoC; from C let fall the perpen- dicular BC (by prob. 7, geom.), and that will constitute the triangle ABC. Measure the lines BC and AB from the same scale of equal parts that AC was taken from, and you have the answer.* * It is proper to observe, that constructions, though perfectly correct in theory, would give only a moderate approximation in practice j on account of the imperfection of the instruments required in constructing them ; they are called graphic methods. Trigonometrical methods, on the con- trary, being independent of all mechanical operation, give solutions with the utmost accuracy : they are founded upon the properties of lines called sines, co-sines, tangents, &c., which furnish a very simple mode of express- ing the relations that subsist between the sides and angles of triangles. TRIGONOMETRY. 87 2d. By Calculation. I. Making A C the radius, the required sides are found by these propositions, as in plate 4, case t. R : AC : : S.A : BC. R:AC::S.C:AB~ That is, as radius =90 is to AC, =250 So is the sine of A=46 30' to BC, =181.4 As radius =90 is to AC, =250 So is the sine of C=43 30' toAB, = 172.1 10.000000 2.397940 9.860562 2.258502 10.000000 2.397940 9.837812 2.235752 If from the sum of the second and third logs, that of the first be taken, the number will be the log. of the fourth; the number answering to which will be the thing required ; but when the first log. is radius, or 10.000000, reject the first figure of the sum of the other two logs, (which is the same thing as to sub- tract 10.000000), and that will be the log. of the thing required. 2. Making AB the radius. Secant A: AC:: R: AB. Secant A': AC : : T.A : BC. That is, as the secant of A=46 30' 10.162188 is to AC, =250 2.397940 So is the radius =90 10.000000 to AB, =172.1 As the secant of A =46 30' is to AC, =250 So is the tangent of A =46 30' to^C, = 181.34 12.397940 2.235762 10.162188 2.397940 10.022750 12.420690 2.258502 * For finding the logarithmic sine, co-sine, &c. of any number of de- grees and minutes, in the table, also the degrees, minutes, &c. of any logarithmic sine, co-sine, &c., the reader is referred to table 2, at the end of this treatise. TRIGONOMETRY. 3. Making BC the radius. Sec. C : AC Sec. C : AC That is, as the secant of C is to AC, So is the radius : R : BC. : T.CiAB. =43 30' 10.139438 =250 2.397940 =90 10.000000 toBC, =181.34 As the secant of C =43 30' is to AC, =250 So is the tangent of C=43 30' 12.397940 2.258502 10.139438 2.397940 9.977250 12.375190 to AB, =172.1 2.235752 Or, having found one side, the other may be obtained by cor. 2, theo. 14, sect. 4. 3d. By Gunter's Scale. The first and third terms in the foregoing proportions being of a like nature, and those of the second and fourth being also like to each other ; and the proportions being direct ones ; it follows, that if the third term be greater or less than the first, the fourth term will be also greater or less than the second : therefore the extent in your compasses from the first to the third term will reach from the second to the fourth. Thus, to extend the first of the foregoing proportions ; 1. Extend from 90 to 46 30', on the line of sines; that distance will reach from 250, on the line of numbers, to 181, for BC. 2. Extend from 90 to '43 30', on the line of sines ; that distance will reach from 250, on the line of numbers, to 172 r for A B. If the first extent be from a greater to a less number ; when you apply one point of the compasses to the second term, the other must be turned to a less ; and the contrary. By def. 20, sect. 4. The sine of 90 is equal to the radius ?. and the tangent of 45 is also equal to the radius ; because if one angle of a right-angled triangle be 45, the other will be also 45 ; and thence (by the lemma preceding theo. 7, sect. 4) the tangent of 45 is equal to the radius : for this reason the line of numbers of 10.000000, the sine of 90, and tangent of 45, being all equal, terminate at the same end of the scale. TRIGONOMETRY. 89 The first two statings of this case answer the question without a secant ; the like will be also made evident in all the following cases. 4th. Solution by Natural Sines. From the foregoing analogies, or statements, it is obvious that if the hypothenuse be multiplied by the natural sine of either of the acute angles, the product will be the length of the side opposite to that angle ; and multiplied by the natural co- sine of the same angle, the product will be the length of the other side, or that which is contiguous to the angle. Thus : The given angle =47 30' Nat. Sine=.725374 Nat. Cos.=.688355 Hyp.= 250 250 36268700 34417750 1450748 1376710 Perpend.= 181.343500 Base= 172.088750 CASE II. The base and angles given, to find the perpendicular and hypothenuse. In the triangle ABC, there is the angle A 42 20', and of course the angle C 47 40' (by cor. 2, theo. 5), and the side AB 190 given ; to find EC and AC. ' \ 1st. By Construction. Make the angle CAB (by prop. 16, sect. 4) in blank lines> as before. From a scale of equal parts lay 190 from A to B t on the point B erect a perpendicular BC (by prob. 5, sect. 4), the point where this cuts the other blank line of the angle will be C ; so is the triangle ABC constructed : let AC and BC be measured from the same scale of equal parts that AB was taken from, and the answers are found. 2d. By Calculation. 1. Making AC the radius. S.C-.ABi : R:AC. S.C lABi: S.A : BC. 90 TRIGONOMETRY. That is, as the sine of C=47 40' is toAB, =190 So is radius =90 to AC, =257 As the sine of C =47 40' is to AB, =190 So is the sine of A=42 20' to BC, =173.1 2. Making AB the radius. R:AB::T.A: EC. R:AB:: Sec. A : AC. That is, as radius =90 is to AB, =190 So is the tangent of A 42 20' to EC, As radius is to AB, =190 So is the secant of J.=42 20 = 173.1 =90 to^tC, =257 3. Making BC the radius. T.C: AB: : Sec. C : AG T.C:AB::R: BC. That is, as the tangent of C=47 10' istoAB, =190 So is the secant of C=47 40' 9.868785 2.278754 10.000000 12.278754 2.409969 9.868785 2.278754 9.828301 12.107055 2.238270 10.000000 2.278754 9.959516 2.238270 10.000000 2.278754 10.131215 2.409969 to AC, =257 As the tangent of C=47 40' isto^tf, =190 So is the radius =90 10.040484 2.278754 10.171699 12.450453 2.409969 10.040484 2.278754 10.000000 12.278754 to BC, = 173-1 2.238270 TRIGONOMETRY. Or, having found one of the required sides, the other maybe obtained by one or the other of the cors. to theo. 14, sect. 4. 3d. By Gunter's Scale. 1. When AC is made the radius. Extend from 4? 40' to 90 on the line of sines ; that dis- tance will reach from 190 to 257, on the line of numbers, for AC. 2. When AB is made the radius, the first stating is thus per- formed : Extend from 45 on the tangents (for the tangent of 45 i equal to the radius, or to the sine of 90 as before) to 42 20' ; that extent will reach from 190, on the line of numbers, to 173, for BC. 3. When BC is made the radius, the second stating is thus performed : Extend from 47 40', on the line of tangents, to 45, or ra- dius ; that extent will reach from 190 to 173, on the line of numbers, for BC; for the tangent of 47 40' is more than the radius, therefore the fourth number must be less than the second, as before. The first two statings of this case answer the question without a secant. 4th. Solution by Natural Sines. SofC. SofC Nat. S. of C. Side ABxR. Thus, .739239)190.000000(257.02, &c.=AC. 147 8478 4215220 3696195 5190250 5174673 1557700 1478478 and, .673443 =Nat. S of 190= side AB. 60609870 673443 127.954170 92 TRIGONOMETRY. Nat. Sof C.739239)127.954170(173.09=.BC. 73 9239 5403027 5174673 2283540 2217717 6502300 6653151 CASE III. The angles and perpendicular given, to find the base and hypothenuse. PL. 5. fa. 6. In the triangle ABC, there is the angle A 40, and conse- quently the angle C 50, with BC 170, given, to find AC and AB. 1st. By Construction. Make an angle CAB of 40 in blank lines (by prob. 16, sect. 4) ; with BC 170 from a line of equal parts draw the lines EF parallel to AB (by prob. 8, sect. 4), the lower line of the angle, and from the point where it cuts the other line in C let fall a perpendicular BC (by prob. 7, sect. 4), and the triangle is constructed : the measures of A C and AB, from the same scale that BC was taken, will answer the question. What lias been said in the two foregoing cases is sufficient to render the operations in this, both by calculation, Gunter's scale, and natural sines, so obvious, that it is needless to insert them ; however, for the sake of the learner, we give for Answers, AC 264.5, and AB 202.6. IV. The base and hypothenuse given, to find the angles and perpendicular. PL. 5. fig. 7. In the triangle ABC, there is given AB 300 and AC 500;. the angles A and C and the perpendicular BC are required* TRIGONOMETRY. 1st. By Construction. 93 From a scale of equal parts lay 300 from A to B ; on B erect an indefinite blank perpendicular line ; with AC 500 from the same scale, and one foot of the compasses in A, cross the perpendicular line in C ; and the triangle is constructed. Byprob. 17, sect. 4, measure the angled, and let BQ be measured from the same scale of equal parts that AC and AB were taken from ; and the answers are obtained. 2d. By Calculation. I. 'Making AC the radius. AC: R::AB : S.C. R:AC::S.A:BC. That is, as AC is to radius, Sois^LB =500 =90 =300 2.698970 10.000000 2.477121 12.477121 to the sine of C,= 36 52' 9.778151 By cor. 2, theo. 5, 90- 36 52'=53 08', the angle A. As radius =90 10.000000 isto.dC, =500 2.698970 So is the sine of A =53 08' 9.903108 to BC, Making AB the radius. AB:R R-.AB That is, as AB is to radius, So is AC =400 AC: : sec. A. : T.A : BC\ =300 =90 =500 to the secant of A,=53 08' As radius =90 is to AB, =300 So is the tangent of A= 5 3 08' toBC, =400 2.602078 2.477121 10.000000 2.698970 12.698970 10.221849 10.000000 2.477121 10.124990 2.602111 Or BC may be found from cor. 2, theo. 14, sect 4. 94- TRIGONOMETRY. 3d. By Gunter's Scale. 1. Making AC the radius. Extend from 500 to 300, on the line of numbers ; that ex- tent will reach from 90, on the line of sines, to 36 52' for the angle C. Again, extend from 90 to 53 08', on the line of sines, that extent will reach from 500 to 400, on the line of numbers, for BC. 2. Making AC the radius, the second stating is thus per- formed. Extend from radius, or the tangent of 45, to 53 08', that extent will reach from 300 to 400, for BC. 4th. Solution by Natural Sines.* RxAB .ACxSofA nn =SofC; and s =BC, AC R Thus, AC, AB, 5,00)300.0000,00 .600000 =Nat. sine 36 52'. and, Nat. sine of 4=53 8'=.800034 AC = 500 400.017000=5C. CASE V. The perpendicular and hypothenuse given, to find the angles and late. Pi. 5. fig. 8. In the triangle ABC there is BC 306 and AC 370 given, to find the angles A and C and the base AB. 1st. By Construction. Draw a blank line from any point, in which at B erect a perpendicular, on which lay BC 306, from a scale of equal parts: from the same scale, with A C 370 in the compasses * For finding the natural sines and co-sines, the reader is referred to table 3. TRIGONOMETRY. 95 draw the first drawn blank line in A, and the triangle ABC is constructed. Measure the angle A (by prob. 17, sect. 4), and also AB, from the same scale of equal parts the other sides were taken from, and the answers are now found. The operations by calculation, the square root, Gunter's scale, and natural sines are here omitted, as they have been heretofore fully explained : the statings, or proportions, must also be obvious, from what has already been said. Answers. The angle A 55 48' ; therefore the angle C34 12', and AB 208. CASE VI. The base and perpendicular given, to find the angles and hypothenuse.^ PL. 5. fig. 9. In the triangle ABC, there is AB 225 and BC 272 given, to find the angles A and C and the hypothenuse AC. 1st. By Construction. Draw a blank line, on which lay AB 225, from a scale of equal parts ; at B erect a perpendicular ; on which lay BC 272 from the same scale ; join A and C, and the triangle is constructed. As before, let the angle A and the hypothenuse AC be measured, in order to find the answers. 2d. By Calculation. 1. Making A B the radius. AB: R:: BC: T.A. R:AB: : sec. A : AC. 2. Making BC the radius. BC: R::AB: T.C. R:BC : : sec. C: AC. By calculation, the answers from the foregoing proportions are easily obtained as before. But because AC, by either of the said proportions, is found by means of a secant, and since there is no line of secants on Gunter's scale, after having found the angles as before, let us suppose AC the radius, and then l.S.A:BC::R: AC or 2. S.C-.AB: : R : AC. 96 TRIGONOMETRY. These proportions may be easily resolved, either by calcula- tion or Gunter's scale, as before ; and thus the hypothenuse AC may be found without a secant. From the two given sides the hypothenuse may be easily ob- tained, from cor. 1, theo. 14, sect. Thus, the square of AB= 50625 Add the square of C=73984 65)346 325 703)2109 2109 From what has been said on logarithms, it is plain, 1. That half the logarithm of the sum of the squares of the two sides will be the logarithm of the hypothenuse. Thus,* The sum of squares, as before, is 124609 ; its log. is 5.095549, the half of which is 2.547774 ; and the corresponding number to this in the tables will be 353, for AC. 2. And that half of the logarithm of the difference of the squares of AC and AB, or of AC and .BC, will be the loga- rithm of EC, or of ^5. The following examples are inserted for the exercise of the learner. Ex. 1. In the right-angled triangle AB C, n . ( the hypothenuse AC 540 perches, > A ( 1?C300 Given,} ^33045, J Ans 'UB449 To find the other two sides. Ex. 2. In the right-angled triangle AB C, p. $ the base AB 162 chains, . ) Glven ' I the base AS 180 poles $ Ans * ) To find the angles and perpendicular Ex. 5. In the right-angled triangle ABC, the hypothenuse .AC 1198 ) r' Ans. 1 < C 35 09 BC 980 chains 3 ( AB 690 ic angles and base. Ex. 6. In the right-angled triangle ABC, n . t the base AR 735.9 links, the > . ) ^ ~ So on> Given, < D/-I ortrk * Ans. < <.A 23 3(X I ) perpendicular BC 320 $ - / Ar< eno * % j 111 I _/L \-/ c F^.O To find the angles and hypothenuse. V OBLIQUE-ANGLED PLANE TRIGONOMETRY. BEFORE we proceed to the solution of the four cases of Ob- lique-angled triangles, it is necessary to premise the following theorems. THEOREM I. PL. 5. Jig. 10. 1 In any plane triangle ABC the sides are proportional to the sines of their opposite angles ; that is, S.C : AB : : S.A : BC, and S.C : AB : : S.B : AC; also, S.B : AC : : S.A : BC. By theo. 10, sect. 4, the half of each side is the sine of its opposite angle; but the sines *of those angles, in tabular parts, are proportional to the sines of the same in any other measure ; and therefore the sines of the angles will be as the halves of their opposite sides ; and since the halves are as the wholes, it follows that the sines of their angles are as then* opposite sides ; that is, S.C : AB : : S.A : BC, i|n of tangents, and keeping the left leg of your compasses fixed, move the right leg to 71 40'; that dis- tance laid from 45 on the same line will reach to 23 30', the half-difference of the required angles. Whence the angles are obtained, as before. The second proportion may be easily extended, from what has been already said. .\, CASE IV. PL. 5. fig. 17. The three sides given, to find the angles. In the triangle ABC, there is given AB 64, 4C47, J3C34; the angles A, B, and C are required. 1st. By Construction. The construction of this triangle must be manifest, from prob. 1, sect, 4, TRIGONOMETRY. 105 2d. By Calculation. From the point C let fall the perpendicular CD on the base AB, and it will divide the triangle into two right-angled ones, ADC and CBD, as well as the base AB into the two seg- nents AD and DB. AC 47 EC 34 Sum 81 Difference 13 By theo. 3 of this sect. As the base or the longest side AB 64 is to the sum of the other sides AC and JBC, 81 So is the difference of those sides 13 to the difference of the segments of the base AD, DJ5, 16.46 By theo. 4 of this sect. To half the base, or to half the sum of the segments \ Q0 AD and DB, . $ d Add half their difference, now found, 8.23 Their sum will be the greatest segment AD, 40.23 Subtract, and their difference will be the least seg- ment,DB, In the right-angled triangle ADC, there is AC 47 and AD 40.23 given, to find the angle A. This is resolved by case 4 of right-angled plane trigonome- try, thus : AD : R : : AC : sec. A 40.23 : 90 : : 47 : 31 08' Or it may be had by finding the angle ACD, the complement of the angle A, without a secant, thus : AC : R : : AD : S.ACD 44 : 90 : : 40.23 : 58 52' 90_58 52'=31 08', the angle A. Then by theo. 1 of this sect. BC : S.A : : AC : S.B -- 34 : 31 08' : : 47 : 45 37' E3 106 TRIGONOMETRY. By cor. l,theo. 5, sect. 4, 180 the sum of A and B=C. ' JL31 08' B45 37 180 76 45=103 15', the angle C. 3d. By Gunter*s Scale. The first proportion is extended on the line of numbers ; and it is no matter whether you extend from the first to the third or to the second term, since they are all of the same kind : if you extend to the second, that distance applied to the third will give the fourth ; but if you extend from the first to the third, that extent will reach from the second to the fourth.* The methods of extending the other proportions have been already fully treated of. RULE 2. Either of the angles, -as A, may be found by adding together the arithmetical complements of the logarithms of the two sides AB, AC, containing the required angle, the log. of the half- sum of the three sides, and the log. of the difference between the half-sum and the side opposite the required angle ; then half the sum of these four logarithms will bf the logarithmic co-sine of half the required angle, f It is required to find the angle A, in the last problem, by this rule, the sides remaining the same. AC=47 Api Co. 7.327902 Ar. Co. 7.193820 2)145 Half-sum 72.5' Log. 2.860338 Difference 38.51 Log. 2.585461 2)19.967521 Cos. i A, 15 34' 9.983760 Whose double 31 08' is the angle A. * The reader is referred to Hutton's Mathematics, vol. ii. New- York edition, for the method of investigating Plane Trigonometry analytically. t The demonstration of this rule is evident from theo. 5, and the nature of logarithms ; but in working the proportion by logarithms, we omit TRIGONOMETRY. 107 If the other angles were required, they can be found by Case 1, or by theo. 1 of this sect. RULE 3.* Add the three sides together, and take half the sum and the differences between the half-sum and each side : then add the complements of the logarithms of the half-sum and of the dif- ference between the half-sum and the side opposite to the angle sought, to the logarithms of the differences of the half-sum and the other sides : half their sum will be the tangent of the angle required. Example. In the triangle ABC, having the side AB 562, AC 800, and BC 320, to find the angle ABC. AC=80Q Sum 1682 #=841 Ar. Co. 7.075204 HAC=4l Ar. Co. 8.387216 HAB=279 log. 2.445604 HBC=52l log. 2.716838 Sum 20.624862 i- Tang, of 64 2' sum 10.312431 Whose double 128 4' is the angle AB C. Whence other angles can be easily found by theo. 1 of this section. An example in each case of oblique-angled triangles. 1. In the triangle ABC, having AB 106, AC 65, and the angle B 31 49', to find the La A and C and the side BC. Ans. The L. C=59 17' or 120 43', the LA 27 28' or 88 54', and the side BC=43.2 or 123.2. 2. In the triangle ABC, having the sideAB 2200, the L A 35, and the L B 47 24', to find the sides AC and BC and the L C. Ans. The LC 97 36', the side AC 1636, and the side BC 1272. 3. In the triangle ABC, having the side AB 240, AC the log. of the square of radius or 20, which is just equivalent to re- jecting 20 from the sum of the four logarithms, which should be done, because for every arithmetical complement that is taken 10 must be re- jected : but the Ar. Co. of the two sides containing the required angle is taken ; consequently 20 should be rejected, which is equal to the log. of the square of radius. * For the demonstration of this rule the reader is referred to Leslie's Geometry, prop. 12, p. 372. 108 TRIGONOMETRY. 263.7, and the angle A 46 30', to find the other angles and the side BC. Ans. The L.C 60 31', the L.B 72 59', and the side BC 200. 4. In the triangle ABC, having the sides given, viz. AB= 144.8, BC=W9, and AC=76, it is required to find the angles by each of the three rules given to Case 4. Ans. The least angle 29 49', next greater 54 07', and the greatest 96 04'. Additional exercises, with their answers. QUESTIONS FOR EXERCISE. 1. Given the hypothenuse 108, and the angle opposite the perpendicular 25 36' ; required the base and perpendicular. Ans. The base is 97.4, and the perpendicular 46.66. 2. Given the base 96, and its opposite angle 71 45' ; re- quired the perpendicular and the hypothenuse. Ans. The perpendicular is 31.66, and the hypothenuse 101.1. 3. Given the perpendicular 360, and its opposite angle 58 20' ; required the base and the hypothenuse. Ans. The base is 222, and the hypothenuse 423. 4. Given the base 720, and the hypothenuse 980 ; required the angles and the perpendicular. Ans. The angles are 47 17' and 42 43', and the perpen- dicular 664.8. 5. Given the perpendicular 110.3, and the hypothenuse 176.5 ; required the angles and the base. Ans. The angles are 38 41' and 51 19', and the base 137.8. , 6. Given the base 360, and the perpendicular 480; re- quired the angles and the hypothenuse. Ans. The angles are 53 8' and 36 52', and the hypothe- nuse 600. 7. Given one side 129, an adjacent angle 56 30', and the opposite angle 81 36' ; required the third angle and the remain- ing sides. Ans. The third angle is 41 54', and the remaining sides are 108.7 and 87.08. 8. Given one side 96.5, another side 59.7, and the angle opposite the latter side 31 30' ; required the remaining angles and the third side. Ans. This question is ambiguous, the given side opposite the given angle being less than the other given side (see Rule 1); OF THE CHAIN. 109 hence, if the angle opposite the side 96.5 be acute, it will be 57 3', the remaining angle 90 52', and the third side 114.2; but if the angle opposite the side 96.5 be obtuse, it will be 122 22', the remaining angle 26 8', and the third side 50.32. 9. Given one side 110, another side 102, and the con- tained angle 113 36'; required the remaining angles and the third side. Ans. The remaining angles are 34 37' and 31 47', and the third side is 177.5. 10. Given the three sides respectively 120.6, 125.5, and 146.7 ; required the angles. Ans. The angles are 51 53', 54 58', and 73 9'. The student who has advanced thus far in this work with diligence and active curiosity is now prepared to study, with ease and pleasure, the following Part, which comprehends all the necessary directions for the practice of Surveying. PART II. THE PRACTICAL SURVEYOR'S GUIDE. SECTION I. Containing a particular Description of the several Instruments used t Surveying^ with their respective Uses. THE CHAIN. THE stationary distance, or merings of ground, are measured either by Gunter's chain of four poles or perches, which con- sists of 100 links (and this is the most natural division), or by one of 50 links, which contains two poles or perches : but be- cause the length of a perch differs in many places, therefore the length of chains and their respective links will differ also. The English statute-perch is 5| yards, the two-pole chain is 1 1 yards, and the four-pole one is 22 yards ; hence the length of a link in a statute-chain is 7.92 inches. For the more ready reckoning the links of a four-pole chain, there is a large ring, or sometimes a round piece of brass, fixed at every 10 links ; and at 50 links, or in the middle, there are 110 OF THE CHAIN. two large rings. In such chains as have a brass piece at every 10 links, there is the figure 1 on the first piece, 2 on the second, 8 on the third, &c. to 9. By leading therefore that end of the chain forward which has the least number next to it, he who carries the hinder end may easily determine any number of links : thus, if he has the brass piece number 8 next to him, and six links more in a distance, that distance is 86 links. After the same manner 10 may be counted for every large ring of a chain which has not brass pieces on it ; and the number of links is thus readily determined. The two-pole chain has a large ring at every 10 links, and in its middle, or at 25 links, there are two large rings; so that any number of links may be the more readily counted off, as before. The surveyor should be careful to have his chain measured before he proceeds on business ; for the rings are apt to open by frequently using it, and its length is thereby increased, so that no one can be too circumspect in this point. In measuring a stationary distance, there is an object fixed in the extreme point of the line to be measured ; this is a di- rection for the hinder chainman to govern the foremost one by, in order that the distance may be measured in a right line ; for if the hinder chainman causes the other to cover the object, it is plain the foremost is then in a right line towards it. For this reason it is necessary to have a person that can be relied on at the hinder end of the chain, in order to keep the foremost man in a right line ; and a surveyor who has no such person should chain himself. The inaccuracies of most surveys arise from bad chaining, that is, from straying out of the right line, as well as from other omissions of the hinder chainman : no person, therefore, should be admitted at the hinder end of the chain of whose abilities, in this respect, the surveyor is not previously convinced ; since the success of the survey, in a great measure, depends on his care and skill. In setting out to measure any stationary distance, the fore man of the chain carries with him ten iron pegs pointed, each about ten inches long ; and when he has stretched the chain to its full length, he at the extremity thereof sticks one of those pegs perpendicularly in the ground ; and leaving it there, he draws on the chain till the hinder man checks him when he arrives at that peg : the chain being again stretched, the fore man sticks down another peg, and the hind man takes up the former ; and thus they proceed at every chain's length con- tained in the line to be measured, counting the surplus links contained between the last peg and the object at the terminar tion of the line, as before : so that the number of pegs taken OF THE CHAIN. Ill up by the hinder chainman expresses the number of chains : to which, if the odd links be annexed, the distance line required in chains and links is obtained, which must be registered in the field-book, as will hereafter be shown. If the distance exceeds 10, 20, 30, Strand $ * Widow J. G.'s part of Grange . 1 2 3 4 5 6 7 . 80 . 79 . 76 . 41i '. 87^ . 14 . 89 17. 65 18. 50 28. 00 20. 00 14. 83 19. 41 24. 53 Close at the first station. Explanation of the Remarks. Mr. J. D's part of Grange bounds or is adjacent to the sur- veyed land from the first to the third station ; Mr. L. P's part of Portmarnock bounds it from the third to the fourth station ; the strand then is the boundary from thence to the sixth ; and from the sixth to the first station, the widow J. G's part of Orange is the boundary. It is absolutely necessary to insert the persons' names, and town-lands, strands, rivers, bogs, rivulets, &c. which bound or circumscribe the land which is surveyed, for these must be ex- pressed in the map. In a survey of a town-land, or estate, it is sufficient to men- tion only the circumjacent town-lands, without the occupiers' names : but when a part only of a town-land is surveyed, then it is necessary to insert the person or persons' names who hold any particular parcel or parcels of such town-land as bound the part surveyed. When an angle is very obtuse, as most in our present figure are, viz. the angles . at A, B, C, E, and 6?, it will be best to lay a chain from the angular point, as at J., on each of the containing sides to c and to d ; and any where nearly in the middle of the angle, as at e : measuring the distances ce and ed ; and these may be placed for the angle in the field-book. Thus, No. Sta. Angle. ch. L ch. L 1. 03 1.09 ,- 17 ' 65 For when an angle is very obtuse, the chord line, as cd, will be nearly equal to the radii Ac and Ad ; so if the arc ced be swept, and the chord line cd be laid on it, it will be difficult to deter- OF THE CHAIN. 119 mine exactly that point in the arc where cd cuts it : but if the angle be taken in two parts, as ce and ed, the arc, and the angle thence, may be truly determined and constructed. After the same manner any piece of ground may be surveyed by a two-pole chain. PROBLEM II. To take a survey of apiece of ground from any point within it, from whence all the angles can be seen, by the chain only. PL. 6. fig. 6. Let a mark be fixed at any point in the ground, as at H, from whence all the angles can be seen ; let the measures of the lines HA, HB, HC, &c. be taken to every angle of the field from the point H ; and let those be placed opposite to No. 1, 2, 3, 4, &c. in the second column of the radii : the measures of the respective lines of the mering, viz. AB, BC, CD, DE, &c. being placed in the third column of distances, will complete the field-book. Thus : Remarks. No. Radii. ch. I. Distance. ch. I ki %C 20. 00 17. 65 2 21. 72 18. 50 3 21. 74 28. 00 4 25. 34 20. 00 5 17. 20 14. 83 6 29. 62 19. 41 7 21. 20 24. 53 Close at the first station. If any line of the field be inaccessible, as suppose CD to be, then by way of proof that the distance CD is true, let the mea- sure of the angle CHD be taken by the line 00, with the chain : if this angle corresponds with its containing sides, the length of the line DC is truly obtained, and the whole work is truly taken. Note. That hi setting off an angle, it is necessary to use the largest scale of equal parts, viz. that of the inch, which is diagonally divided into 100 parts, in order that the angle should be accurately laid down ; or if two inches were thus divided for angles, it would be the more exact ; for it is by no means necessary that the angles should be- laid from the said scale .with the stationary distances. 120 OF THE CHAIN. PROBLEM III. To take a survey by the chain only y when all the angles cannot be seen from one point within. PL. 6. fig. 7. Let the ground to be surveyed be represented by 1, 2, 3, 4, &c. Since all the angles cannot be seen from one point, let us assume three points, as A, #, C, from whence they may be seen ; at each of which let a mark be put, and the respective sides of the triangle be measured and set down in the field-book ; let the distance from A to 1, and from B to 1, be measured, and these will determine the point 1 ; let the other lines which flow from A, J5, C, as well as the circuit of the ground, be then measured as the figure directs ; and thence the map may be easily constructed. i There are other methods which may be used ; as dividing the ground into triangles, and measuring the three sides of each; or by measuring the base and perpendicular of each triangle. But this we shall speak of hereafter. PROBLEM IV. How to take any inaccessible distance by the chain only. PL. 8. fig. 8. Suppose AB to be the breadth of a river, or any other inac- cessible distance, which may be required. Let a staff or any other object be set at J5, draw yourself backward to any convenient distance C, so that B may cover A ; from U, lay off any other distance by the river's side to E, and complete the parallelogram EBCD : stand at D, and cause a mark to be set at JF, in the direction of A ; measure the distance in links from E to JP, and FB will be also given. Wherefore EF : ED : : FB : AB. Since it is plain (from part 1, theo. 3, sect. 4, and theo. 2, sect. 4) the triangles JEjPDand BFA are mutually equiangular. If part of the chain be drawn from B to C, and the other part from B to E ; and if the ends at E and C be kept fast, it will be easy to turn the chain over to Z>, so as to complete a parallelogram ; by reckoning off the same number of links you had in BC, from E to D, and pulling each part straight. THE CIRCUMFERENTOR. 121 THE CIRCUMFERENTOR. THIS instrument is composed of a brass circular box, about five or six inches in diameter ; within which is a brass ring, divided on the top into 360 degrees, and numbered 10, 20, 30, &c. to 360 : in the centre of the box is fixed a steel pin finely pointed, called a centre-pin, on which is placed a needle touched by a loadstone, which always retains the same situa- tion ; that is, it always points to the north and south points of the horizon nearly, when the instrument is horizontal, and the needle at rest. The box is covered with a glass lid in a brass rim, to pre- vent the needle being disturbed by wind or rain at the time of surveying: there is also a brass lid or cover, which is laid over the former to preserve the glass in carrying the instrument. This box is fixed by screws to a brass index or ruler of about 14 or 15 inches in length, to the ends whereof are fixed brass sights which are screwed to the index and stand perpendicular thereto : in each sight is a large and a small aperture or slit, one over the other; but' these are changed, that is, if the large aperture be uppermost in the one sight, it will be lowest in the other, and so of the small ones : therefore the small aperture in one is opposite to the large one in the other, in the middle of which last there is placed a horse-hair or fine silk thread. The instrument is then fixed on a ball and socket, by the help of which and a screw you can readily fix it horizontally in any given direction, the socket being fixed on the head of a three- legged staff, whose legs, when extended, support the instrument while it is used. To take field-notes by the Circumferentor. PL. 6. fig. 6. Let your instrument be fixed at any angle as A, your first station ; and let a person stand at the next angle J5, or cause a staff with a white sheet to be set there perpendicularly for an object to take your view to : then having placed your instru- ment horizontally (which is easily done by turning the box so that the ends of the needle may be equidistant from its bottom, and it traverses or plays freely) turn the flower-de-luce, or north part of the box, to your eye, and looking through the small aperture turn the index about till you cut the person or object in the next angle B with the horse-hair or thread of the opposite sight ; the degrees then cut by the south end of the F 122 THE CIRCUMFERENTOR, needle will give the number to be placed in the second column of your field-book in a line with station No. 1, and expresses the number of degrees the stationary line is from the north, counting quite round with the sun. | Most needles are pointed at the south end, and have a small ring at the north : such needles are better than those which are pointed at each end, because the surveyor cannot mistake by counting to a wrong end, which error may be frequently com- mitted in using a two-pointed needle. Two-pointed needles have sometimes a ring, but more usually a cross towards the north end ; and the south end is generally bearded towards its extremity, and sometimes not, but its arm is a naked right line from the cap at the centre. Having taken the degrees or bearing of the first stationary line AB, let the line be measured, and the length thereof in chains and links be inserted in the third column of your field- book, under the title of distances, opposite to station No. 1. It is customary, and even necessary, to cause a sod to be dug up at each station or place where you fix the instrument, to the end that if any error should arise in the field-book it may be the more readily adjusted and corrected, by trying over the former bearings and stationary distances. Having done with your first station, set the instrument over the hole or spot where your object stood, as at J5, for your second station, and send him forward to the next angle of the field, as at C ; and having placed the instrument in a horizon- tal direction, with the sights directed to the object at C, and the north of the box next your eye, count your degrees to the south end of the needle, which register in your field-book in the sec- ond column opposite to station No. 2 ; then measure the sta- tionary distance BC, which insert in the third column ; and thus proceed from angle to angle, sending your object before you, till you return to the place where you began, and you will have the field-book complete ; observing always to signify the parties' names who hold the contiguous lands, and the names of the town-lands, rivers, roads, swamps, lakes, &c. that bound the land you survey, as before ; and this is the manner of taking field-notes by what is called fore-sights. But the generality of mearsmen frequently set themselves in disadvantageous places, so as often to occasion two or more stations to be made where one may do, which creates much trouble and loss of time ; we will therefore show how this may be remedied, by taking back-sights, thus : let your object stand at the point where you begin your survey, as at A ; leaving him there, proceed to your next angle JB, where fix your instru- THE CIRCUMFERENTOR. 123 nrent so that you may have the longest view possible towards C. Having set the instrument in a horizontal position, turn the south part of the box next your eye, and having cut your object at A, reckon the degrees to the south point of the needle, which will be the same as if they were taken from the object to the instrument, the direction of the index being the same. Let the degree be inserted in the field-book, and the stationary dis- tance be measured and annexed thereto in its proper column ; and thus proceed from station to station, leaving your object in the last point you left till you return to the first station A. By this method your stations are laid out to the best advan- tage, and two men may do the business of three, for one of those who chain may be your object ; but in fort-sights you must have an object before you, besides two chainmen. It was said before, that a surveyor should have a person with him to carry the hinder end of the chain, on whom he can de- pend : this person should be expert and ready at taking offsets, as well as exact in giving a faithful return of the length of every stationary line. One who has such a person, and who uses back-sights, will be able to go over nearly double the ground he could in the same time by taking fore-sights, because of overseeing the chaining; for should he take back-sights he must be obliged, after taking his degree, to go back to the fore- going station, to oversee the chaining, and by this means to walk three times over every line, which is a labour not to be borne. Or a back and a fore-sight may be taken at one station, thus : with the south of the box to your eye, observe from B the ob- ject Aj and set down the degree in your field-book cut by the south end of the needle. Again, from B observe an object at C, with the north of the box to your eye, and set down the de- gree cut by the south point of the needle, so have you the bear- ings of the lines AB and BC ; you may then set up your in- strument at D, from whence take a back-sight to C and a fore- sight to E : thus the bearings may be taken quite round, and the stationary distances being annexed to them will complete the field-book. But in this last method care must be taken to see that the sights have not the least cast on either side ; if they have, it will destroy all : and yet with the same sights you may take a survey by. fore-sights, or by back-sights only, with as great truth as if the sights were ever so erect, provided the same cast con- tinues without any alteration ; but, upon the whole, back-sights only will be found the readiest method If your needle be pointed at each end, in taking fore-sights F2 124 THE CIRCUMFERENTOR. you may turn the north part of the box to your eye, and count your degrees to the south part of the needle, as before ; or you may turn the south of the box to your eye, and count your de- grees to the north end of the needle. But in back-sights you may turn the north of the box to your eye, and count your degrees to the north point of the needle ; or you may turn the south of the box to your eye, and count your degrees to the south end of the needle. The brass ring in the box is divided on the side into 360 de- grees, thus : from the north to the east into 90, from the north to the west into 90, from the south to the east into 90, and from the south to the west into 90 degrees ; so the degrees are num- bered from the north to the east or west, and from the south to the east or west. The manner of using this part of the instrument is this : hav- ing directed your sights to the object, whether fore or back, as before, observe the two cardinal points of your compass the point of the needle lies between (the north, south, east, and west being called the four cardinal points, and are graved on the bottom of the box), putting down those points together by their initial letters, and thereto annexing the number of degrees, counting from the north or south, as before, thus ; if the point of your needle lies between the north and east, north and west, south and east, or south and west points in the bottom of the box, then put down NE, NW 1 SE, or S W, annexing thereto the number of degrees cut by the needle on the side of the ring, counting from the north or south, as before. But if the needle point exactly to the north, south, east, or west, you are then to write down N, S, , or TF, without an- nexing any degree. This is the manner of taking field-notes, whereby the con- tent of ground may be universally determined by calculation ; and they are said to be taken by the quartered compass or by the four nineties. To find the number of degrees contained in any given angle. Set up your instrument at the angular point, and thence di- rect the sights along each leg of the angle, and note down their respective bearings, as before ; the difference of these bearings, if less than 180, will be the quantity of degrees contained in the given angle ; but if more take it from 360, and the remainder will be the degrees contained in the given angle. Ex. Let the angle proposed be GAB (pi. 6, fig. 6) ; place the instrument at A, with the flower-de-luce towards you ; then THE THEODOLITE. 125 direct the sights to .B, and observe what degrees are cut by the south end of the needle, which let be 250 ; then turning the instrument about on its stand, direct the sights to G, note again what degrees are cut by the south end of the needle, which sup- pose are 172. Then 250 1 72 = 68 = the L GAB ; but if the degrees cut should be 298 and 105, then 298 105 = 193, which taken from 360 leaves 167 = the L. GAB. THE THEODOLITE. Fig. 1. Frontispiece. THIS instrument is a circle, commonly of brass, of ten or twelve inches in diameter, whose limb is divided into 360 de- grees, and those again are subdivided into smaller parts, as the magnitude of it will admit ; sometimes by equal divisions and sometimes by diagonals drawn from one concentric circle of the limb to another. In the middle is fixed a circumferentor with a needle; but this is of little or no use, except in finding a meridian line, or the proper situation of the land. Over the brass circle is a pair of sights, fixed to a moveable index, which turns on the centre of the instrument, and upon which the circumferentor-box is placed. 'This instrument will either give the angles of the field or the bearing of every stationary distance line from the meridian, as the circumferentor and quartered compass do. To take the angles of the field. PL. 6. Jig. 6. Lay the ends of your index io 360 and 180 ; ^turn the whole about with the 360 from you ; direct the sights from A to G 9 and screw the instrument fast ; direct them from A to cut the object at B ; the degree then cut by that end of the index which is opposite you will be the quantity of the angle GAB to place in your field-book ; to which annex the measure of the line AB in chains and links ; set up your instrument at JB, unscrew it, and lay the ends of your index to 360 and 180 ; turn the whole about, with the 360 from you or 180 next you, till you cut the object at A ; screw the instrument fast and direct your sights to the object at C, and the degree then cut by that end of the index which is opposite to you will be the quantity of the angle ABC. 126 THE THEODOLITE. Thus proceed from station to station, still laying the index to 360, turning it from you, and observing the object at the fore- going station, screwing the instrument fast and observing the object at the following station, and counting the degrees to the opposite end of the index, will give you the quantity of each respective angle. LEMMA. All the angles of any polygon are equal to iwice as many right angles as there are sides, less by four. Thus, all the angles A, B, C, D, E, F, , are equal to twice as many right angles as there are sides in the figure, les* by four. PL. G.Jig. 6. Let the polygon be disposed into triangles by lines drawn from any assigned point // within it, as by the lines HA, HB, HC, &LC. It is evident, then (by theo. 2, sect. 4, part 1), that the three angle's of each triangle are equal to two right, and consequently that the angles in all the triangles are twice as many right ones as there are sides : but all the angles about the point H are equal to four right (by cor. 2, theo. 1, sect. 4) ; therefore the remaining angles are equal to twice as many right ones as there are sides in the figure, abating four. Q. E. D. SCHOLIUM. Hence we may know if the angles of a survey be truly taken ; for if their sum be equal to twice as many right angles as there are stations, abating four right angles, you may conclude that the angles were truly taken, otherwise not. If you take the bearing of any line with the circumferentor, that bearing will be the number of degrees the line is from the north ; consequently the north must be a like number of de- grees from the line ; and thus the north, and of course the south, as well as the east and west, or the situation of the land, is ob- tained. \ To take the bearing of each respective line from the meridian ; or to perform the office of the circumferentor, or quartered, compass, by the the" odolite. Set your instrument at the first station, and lay the index to 360 and 180 with the flower-de-luce of the box next 360; unscrew the instrument, and turn the whole about till the north and south points of the needle cut the north and south points in the box ; then screw it fast, and the instrument is north and south, if there be no variation in the needle ; but if there, be, and its quantity known, it may be easily allowed. THE THEODOLITE. 127 The circuraferentor-box may then be taken off. Direct the sights to the object at the second station, and the degree cut by the opposite end of the index will be the bearing of that line from the north, and the same that the circumferentor would give. After having measured the stationary distance, set up your instrument at the second station ; unscrew it, and set either end of the index to the degree of the last line, and turning the whole about with that degree towards you, direct your sights to an object at the foregoing station, and screw the instru- ment fast ; it will then be parallel to its former situation, and consequently north and south ; direct then your sights to an object at the following station, and the degree cut by the oppo- site end of the index will be the bearing of that line. In the" like manner you may proceed through the whole. If the brass circle be divided into four nineties, from 360 and 180, and the letters N, S, , VFbe applied to them, the bear- ings may be obtained by putting down the letters the far or op- posite end of the index lies between, and annexing thereto the degrees from the N or S, and this is the same as the quartered compass. If you keep the compass-box on, to see the mutual agreenlent of the two instruments : after having fixed the theodolite north and south, as before, turn the index about, the north end or flower- de-luce next your eye, and count the degree to the opposite or south end of the index, and this will correspond with the de- gree cut by the south end of the needle. At the second or next 'station, unscrew the instrument and set the south of the index to the degree of the last station ; turn the whole about, with the south of the index to you, and cut the object at the foregoing station ; screw the instrument fast, and with the north of the index to you, cut the object at the next following station ; the degree then cut by the south of the index will correspond with the degree cut by the south end of the needle, and so through the whole. Some theodolites have a standing pair of sights fixed at 360 and 180, besides those on the moveable index; if you would use both, look through the standing sights with the 180 next you to an object at the foregoing station : screw the instrument fast, and direct the upper sights on the moveable index to the object at the following station, and the degree cut by the oppo- site end of the index will give you the quantity of the angle of the field. Two pair of sights can be of no use in finding the angles from the meridian ; and inasmuch as one pair is sufficient to 128 THE SEMICIRCLE PLANE TABLE. find the angles of the field, the second can be of no use : be- sides, they obstruct the free motion of the moveable index, and therefore are rather an incumbrance than of any real use. Some will have it that they are useful with the others for setting off a right angle in taking an offset : and surely this is as easily performed by the one pair on the moveable index : thus, if you lay the index to 360 and 180, and cut the object either in the last or following station, screw the instrument fast and turn the index to 90 and 270, and then it will be at right angles with the line. So that the small sights, at those of the circle, can be of no additional use to the instrument, and there- fore should be laid aside as useless. This instrument may be used in windy and rainy weather, as well as in mountainous and hilly grounds; for it does not require a horizontal position to find the bearing or angle, as the needle doth,, and therefore is preferred to any instrument that is governed by the needle. THE SEMICIRCLE. THIS instrument, as its name imports, is a half-circle, divided from its diameter into 180 degrees, and from thence again, that is, from to 360 degrees. It is generally made of brass, and is from 8 to 18 inches diameter. On the centre there is a moveable index with sights, on which is placed a circumferentor-box, as in the theodolite. This instrument may be used as the theodolite in all re- spects, but with this difference ; when you are to reckon the degree to that end of the index which is off the semicircle, you may find it at the other end, reckoning the degree from 180 forwards. THE PLANE TABLE.* A PLANE TABLE is an oblong of oak, or other wood, about 15 inches long and 12 broad. They are generally composed of three boards, which are easily taken asunder or put together for the convenience of carriage. * This instrument is not much used by surveyors at present. THE PLANE TABLE. 120 There is a box frame, with six joints in it, to take off and put on as occasion serves ; it keeps the table together, and is like- wise of use to keep down a sheet of paper which is put thereon. The outside of the frame is divided into inches and tenths, which serve for ruling parallels or squares on the paper, or for shifting it, when occasion serves. The inside of the frame is divided into 360 degrees, which, though unequal on it, yet are the degrees of a circle produced from its centre, or centre of the table, where there is a small hole. The degrees are subdivided as small as their distance will admit ; at every tenth degree are two numbers, one the number of degrees, the other its complement, to 360. There is another centre-hole about one-fourth of the table's breadth from one edge, and is in the middle between the two ends. To this centre-hole on the other side of the frame, there are the divisions of a semicircle, or 180 degrees ; and these again are subdivided into halves, or quarters, as the size of the instru- ment will admit. That side of the frame on which the 360 degrees are, sup- plies the place of a theodolite, the other that of a semicircle. There is a circumferentor-box of wood, with a paper chart at the bottom, applied to one side of the table by a dovetail joint fastened by a screw. This box (besides its rendering the plane table capable of answering the end of a circumferentor) is very useful for placing the instrument in the same position every remove. There is a brass ruler or index, about two inches broad, with a sharp of fiducial edge, at each end of which is a sight ; on the ruler are scales of equal parts, with and without diago- nals, and a scale of chords ; the whole is fixed on a ball and socket, and set on a three-legged staff. To take the angles of afield by the table. Having placed the instrument at the first station, turn it about till the north end of the needle be over the meridian, or flower- de-luce of the box, and there screw it fast. Assign any con- venient point, to which apply the edge of the index, so as through the sights you may see the object in the last station, and by the edge of the index from the point draw a line. Again, turn about the index with its edge to the same point, and through the sights observe the object in the second station, and from the point, by the edge of the index, draw another line ; so is the angle laid down ; on that last line set off the distance to the second station, in chains and links ; apply your instrument F3 130 THE PLANE TABLE. to the second station, taking the angle as before ; and after the like manner proceed till the whole is finished. This method may be used in good weather, if the needle be well touched and play freely; but if it be in windy weather, or the needle out of order, it is better, after having taken the first angle as before, and having removed your instrument to the second station, and placed the needle over the meridian line as before, to lay the index on the last drawn line, and look back- ward through the sights ; if you then see the object in the first station, the tafcle is fixed right, and the needle is true ; if not, turn the table about, the index lying on the last line, till through the sights you see the object in the first station : and then screw it fast, and keeping the edge of the index to the second station, direct your sights to the next ; draw a line by the edge of the index, and lay off the next line ; and proceed through the whole without using the needle, as you do with the theodolite. If the sheet of paper on the table be not large enough to con- tain the map of the ground you survey, you must put on a clean sheet, when the other is full ; and this is called shifting of paper, and is thus performed.. PL. 6.^.8. Let ABCD represent the sheet of paper on the plane table, upon which the plot , jP, Gf, JFT, /, K, L, M is to be drawn : let the first station be E ; proceed as before, from thence to F and to G ; then proceeding to I/, you find there is not room on your paper for the line GH, however draw as much of the line GH as the paper can hold, or draw it to the paper's edge. Move your instrument back to the first station JS, and pro- ceed the contrary way to M and to L ; but in going from thence to K, you again find your sheet will not hold it ; however draw as much of the line LK on the sheet as it can hold. ! Take that sheet off the table, first observing the distance oo of the lines GH an ' " AE : R : : AF : & 1.325 90 1.15 60 13'. Its complement 29 47' will give FAE, as before. PRACTICAL QUESTIONS. Ex. 1. At 170 feet distance from the bottom of a tower the angle of its elevation was found to be 52 30'. Required the altitude of the tower. Ans. 221.55 feet. Ex. 2. From the top of a tower, by the seaside, of 14.3 feet high, it was observed that the angle of depression of a ship's bottom, then at anchor, measured 35. What then was the ship's distance from the bottom of the wall ? Ans. 204.22 feet. Ex. 3. From a window near the bottom of a house which seemed to be on a level with the bottom of a steeple, I took the angle of elevation of the top of the steeple, equal 40 ; then from another window, 18 feet directly above the former, the like angle was 37 30'. What then is the height and distance the steeple ? An J hei g ht **&6. 3 * { distance MP9.50. Ex. 4. Wanting to know the height of an inaccessible tower at the least distance from it, on the same horizontal plane, I 150 OF DISTANCES. took its angle of elevation, equal to 58 ; then going 300 feet directly from it, found the angle there to be only 32. Re- quired its height and my distance from it at the first station. Ang (height 307.53. ' \ distance 192. 15. Ex. 5. Being on the side of a river, and wanting to know the distance to a house which was seen on the other side, I measured out for a base 400 yards in a right line by the side of the river, and found that the two angles, one at each end of this line, subtended by the other end and the house, were 68 2' and 73 15'. What then was the distance between each station and the house ? . ( 593.08 S< \ 612.38 Ex. 6. Wanting to know the breadth of a river, I measured a base of 500 yards in a straight line close by one side of it, and at each end of this line I found the angles subtended by the other end and a tree close to the bank on the other side of the river to be 53 and 73 15'. What then was the perpen- dicular breadth of rife river? .^^/^-4t^Ans. &t&. 4&ry aids. Ex. 7. Two ships of war, intending to cann1fna(fe Jrfort, are, by the shallowness of the water, kept so far from it that they suspect their guns cannot reach it with effect. In order there- fore to measure the distance, they separate from each other a quarter of a mile, or 440 yards ; then each ship observes and measures the angle which the other ship and the fort subtend, which angles are 83 45' and 85 15'. What then is the dis- tance between each ship and the fort ? Ex. 8. A point of land was observed by a ship at sea to bear east by south ; and after sailing north-east 12 miles, it was found to bear south-east by east. It is required to determine the place of that headland, and the ship's distance from it at the last observation. Ans. 26.0728 miles. Ex. 9. If the height of the mountain called the Peak of Teneriffe be 21 miles, as it is very nearly, and the angle taken at the top of it, as formed between a plumb-line and a line conceived to touch the earth in the horizon, or farthest visible point, be 88 2' ; it is required from these measures to determine the magni- tude^f the whole earth, and the utmost distance that can be seep cm. its surface from the top of the mountain, supposing the form of the earth to be perfectly globular. . ( distance 135.943 > -, Ans ' \ diameter 7916 \ miles ' TO FIND THE CONTENTS OF GROUND. 151 Ex. 10. Wanting to know the extent of a piece of water, or distance between two headlands, I measured from each of them to a certain point inland, and found the two distances to be 735 yards and 840 yards ; also the horizontal angle subtended between these two lines was 55 40'. What then was the dis- tance required? Ans. 741.2 yards. Ex. 11. Wanting to know the distance between a house and a mill which were seen at a distance on the other side of a river, I measured a base line along the side where I was of 600 yards, and at each end of it took the angles subtended by the other end and the house and mill, which were as follows, viz. at one end the angles were 58 20' and 95 20', and at the other end the like angles were 53 30' and 98 45'. What then was the distance between the house and mill ? Ans. 962.5866 yards. Ex. 12.* Wanting to know my distance from an inaccessible object on the other side of a river, and having no instrument for taking angles, but only a chain or cord for measuring dis- tances ; from each of two stations, A and .B, which were taken at 500 yards asunder, I measured, in a direct line from the ob- ject 0, 100 yards, viz. AC and BD, each equal 100 yards; also the diagonal AD measured 550 yards, and the diagonal BC 560. What then was the distance of the object from each station A and B1 A i A 526.81. An8 ' \B 500.47. SECTION III. MENSURATION OF AREAS, OR THE VARIOUS METHODS OF CALCULATING THE SUPERFICIAL CONTENTS OF ANY FIELD. Definition. THE area or contents of any plane surface in perches is the number of square perches which that surface contains. * These practical examples are taken from Button's Mathematics, vol. ii. seventh London edition. 152 TO FIND THE CONTENTS OF GROUND. PL. 7. Jig. 1. Let A BCD represent a rectangular parallelogram, or oblong ; let the side AB or DC contain eight equal parts, and the side AD or BC three of such parts ; let the line AB be moved in the direction of AD till it has come to EF, where AE or BF (the distance of it from its first situation) may be equal to one of the equal parts. Here it is evident that the generated oblong ABEF will contain as many squares as the side AB contains equal parts, which are eight ; each square having for its side one of the equal parts into which A B or AD is divided. Again, let AB move on till it comes to GH, so as GE or HF may be equal to AE or BF; then it is plain that the oblong AGHB will contain twice as many squares as the side AB contains equal parts. After the same manner it will appear that the oblong ADCB will contain three times as many squares as the side AB contains equal parts ; and, in general, that every rectangular parallelogram, whether square or oblong, contains as many squares as the product of the number of equal parts in the base multiplied into the number of the same equal parts in the height contains units, each square having for its side one of the equal parts. Hence arises the solution of the following problems. PROBLEM I. To find the contents of a square piece of ground. 1. Multiply the base in perches into the perpendicular in perches, the product will be the contents in perches ; and be- cause 160 perches make an acre, it must thence follow that Any area, or contents in perches, being divided by 160, will give the contents in acres ; the remaining perches, if more than 40, being divided by 40, will give the roods, and the last re mainder, if any, will be perches, Or thus : 2. Square the side in four-pole chains and links, and the product will be square four-pole chains and links : divide this by 10, or cut off one more than the decimals, which are five in all, from the right towards the left : the figures on the left are acres ; because 10 square four-pole chains make an acre, and the remaining figures on the right are decimal parts of an acre. Multiply the five figures to the right by four, cutting five figures TO FIND THE CONTENTS OF GROUND. 153 from the product, and if any figure be to the left of them it is a rood, or roods ; multiply the last cut off figures by 40, cutting off five, or (which is the same thing) by 4, cutting off four; and the remaining figures to the left, if any, are perches. 1. The first part is plain, from considering that a piece of ground in a square form, whose side is a perch, must contain a perch of ground ; and that 40 such perches make a rood, and four roods an acre ; or, which is the same thing, that 160 square perches make an acre, as before. 2. A square four-pole chain (that is, a piece of ground four poles or perches every way) must contain 160 square perches ; and 160 perches make an acre ; therefore 10 times 16 perches, or 10 square four-pole chains, make an acre. Note. The chains given or required, in any of the following problems, are supposed to be two-pole chains, that chain being most commonly used ; but they must be reduced to four-pole . chains or perches for calculation, because the links will not operate with them as decimals. EXAMPLES. PL. I. Jig. 17. Let ABCD be a square field, whose side is 14cA. 291. ; re- quired the contents in acres. By problem 4, section 1, part 2, 14cA. 292. are equal to 29.16 perches 29.16 17496 2916 26244 5832 A. R. P. 160)850.3056( 5 1 10, contents. 40)50(1 rood. 10 perches. Or thus: 14cA. 29Z. are equal to 7ch. 29Z. of four-pole chains, by prob- lem 1, section 1, part 2. 63 154 TO FIND THE CONTENTS OF GROUND. eh. I 7.29 7.29 6561 1458 5103 A. R. P. Acres 5|31441 contents/ as before, 5 1 10. 4 Rood 1 [25764 40 Perches 10J30560 It is required to lay down a map of this piece of ground, by a scale of twenty perches to an inch. Take 29.16, the perches of the given side, from the small diagonal on the common surveying scale, where twenty small, or two of the large divisions are an inch : make a square whose side is that length (by prob. 9, geoin.), and it is done. PROBLEM II. To find the side of a square whose contents are given. Extract the square root of the given contents in perches, and you have the side in perches, and consequently in chains. EXAMPLE. It is required to lay out a square piece of ground which shall contain 12A. 3R. 16P. Required the number of chains in each side of the square ; and to lay down a map of it by a scale of 40 perches to an inch. A. R. P. 12 3 16 4 51 40 2056 TO FIND THE CONTENTS OF GROUND. 155 2056(45.34+ perches =22c/i.33|/.byprob. 6. sect 1, part 2. 85)456 903)3100 9064)39100 &c. To draw the map. From a scale where 4 of the large or 40 of the small divi- sions are an inch, take 45.34 the perches of the side, of which make a square. PROBLEM m. To find the contents of an oblong piece of ground, Multiply the length by the breadth, for the contents. EXAMPLE. PL. I. Jig. 3. Let ABCDbe an oblong piece of ground, whose length^.1? is I4tch. 251. and breadth Sch. 371. Required the contents in acres, and also to lay down a map of it, by a scale of 20 perches to an inch. ch. I. perches. 15732 3496 A. R. P. 160)506.9200(3 27 contents. 26 perches, or near 27. Or thus: four-pole ch. ch. I ch. I B ? P rob ' X sect ' 5075 2175 2900 31682 156 TO FIND THE CONTENTS OF GROUND. Acres 3(16825 4 Rood |67300 ' 4 Perches 26|9200 . To draw the map. Make an oblong (by schol. to prob. 9, geom.) whose length, from a scale of 20 to an inch, may be 29 perches, and breadth 17.48 perches. PROBLEM IV. The contents of cm oblong piece of ground and one side given, to find the other* Divide the contents in perches by the given side in perches, the quotient is the side required hi p.erches ; and thence it may be easily reduced to chains. EXAMPLE. There is a ditch 14cA. 251. long, by the side of which it is required to lay out an oblong piece of ground which shall con- tain 3A. OR. 27P. What breadth must be laid off at each end of the ditch to enclose the 3A. OR. 27P. ? A. R. P. 3 27 4 12 40 perch. cTi. I. 29)507(17.48=8 37, breadth. 217 140 240 8 The map is constructed like the last. TO FIND THE CONTENTS OF GROUND. 1&7 PROBLEM V. To find the contents of apiece of ground in form of an ollique angular par- ttttlogram) or of a rhombus or rhomboidet. RULE I. Multiply the base into the perpendicular height. The reason is plain from theo. 13, geom. EXAMPLE. Let ABCD be a piece of ground in form of a rhombus, whose base AB is 22 chains, and perpendicular DE or FC 20 chains. Required the contents. ch. 22 ^l 10 Acres 11|0 ch. Or, 160)1760(11 acres. 160 The converse of this is done by prob. 4, and the map is drawn by laying off the perpendicular on that part of the base from whence it was taken, joining the extremity thereof to that of the base by a right line, and thence completing the parallelo- gram. RULE n. As rad. (viz. S. of 90, pr tang, of 45) Is to the sine of any angle of a parallelogram, So is the product of the sides including the angle : To the area of the parallelogram. That is, DA x AB x nat sine of the angle A = the area.* PI. 7, fig. 2. * Demonstration. For, having drawn the perpendicular DE the area by the first rule L* ABxDE ; but as radius 1 (S. L. E) : S. L. A : : AD : r 158 TO FIND THE CONTENTS OF GROUND. EXAMPLE. How many acres are in a rhomboides whose less angle is 30 and the including sides 25.35 and 10.4 four-pole chains ? Ans. 13A. OR. 29.12P. (Rad.) 1 : .500000 (Nat. S. of 30) : : 263.640 ( =25.35 X 10.4) : 131.82 = the area in four-pole chains ; which divided by 10 (because 10 square chains are an acre) gives 13.182 acres, or, 13 A. OR. 29.12P. Note. Because the angle of a square and rectangle are each 90, whose sine is 1, this rule for them is the same as the first. PROBLEM VI. To find the contents of a triangular piece of ground. Multiply the base by half the perpendicular, or the perpendicu- lar by half the base ; or take half the product of the base into the perpendicular. The reason of this is plain from cor. 2, theo. 12, geom. EXAMPLE. PL. 1. jig. 16. Let ABC be a triangular piece of ground whose longest side or base BC is 24cA. 38/., and perpendicular AD^ let fall from the opposite angle, is 13cA. 28?. Required the contents. ch.L. ch.l 1. Base 24.38 = 12.38 ). , , . ) 3 39 S four 'P le cnams> Acres 4] 19682 4 Rood 178728 40 Perches 31|49120 Contents, 4 A. OR. 3 IP. DE=S. -Ax DA ; therefore, DE xAB=ABx S./LAx DA = the area, or, 1 : S.L.A : : DAxAB : S.l-AxDAxAB = the area oftheparal lelogram. .Q. E. D. TO FIND THE CONTENTS OF GROUND. 159 ch. I ch.l Or,2dly. Perp. 6.78 of four-pole chains. base 6.19 6102 678 4068 4|19682=4A. OR. 31P. ch. I Or, 3dly. Base 12.38 four-pole chains. Perp. 6.78 9904 8666 7428 83.9364 Its half =4J19682=4A. OR. 31P. Or the base and perpendicular may be reduced to perches, and the contents may thence be' obtained, thus : ch. I. perches. By prob. 4, sect. 1, part 2. Perp. 13.28=27.12} Half the perp. 13.563 perches, ch. Z. 1. Base 49.52=24.38 i perp. 13.56 29712 24760 14856 4952 160)671.4912(4A. OR. 31P. 31 160 TO FIND THE CONTENTS OF GROUND. perches. 2. Perp. 27.12 Half-base 24.76 16272 18984 10848 5424 671.4912=4A. OR. 31P. But square perches may be reduced to acres, &c. rather more commodiously by dividing by 40 and 4, than by 160; thus, 4|0)67|1 4)16. 31 A. 4. 0. 31 * - perches. 3. Base 49.52 Perp. 27. 12 9904 .4952 34664 9904 1342.9824 671.4912=4A.OR. 31P. The map may be readily drawn, having the distance from either end of the base to the perpendicular given ; as may be evident from the figure. PROBLEM VII. The contents of a triangular piece of ground and the base given, to find the perpendicular. Divide the contents in perches by half the base in perches, and the quotient will give you the perpendicular in perches, and 1 so in chains. TO FIND THE CONTENTS OF GROUND. 161 EXAMPLE. PL. I. fig. 16. Let BC be a dilch, whose length is 24ch. 40J., by which it is required to lay out a triangular piece of ground, whose contents shall be 4 A. 1R. 10P. Required the perpendicular. ch. I. Perches. Base 24.40=49.6 Half the base=24.8|v J7 40 Perches. 24.8)690(27.82 1940 64 Perches, ch. I. Answer, perp. 27.82=13.45 This perpendicular being laid on any part of the base, and lines run from its extremity to the ends of the base, will lay out the triangle (by cor. to theo. 13, geom.) so that the perpen- dicular may be set on that part of the base which is most con- venient and agreeable to the parties concerned. PRACTICAL QUESTIONS. Ex. 1. What is the area of a parallelogram whose length is 12.25 and its height 8.5 four-pole chains ? Ans. 10A. 1R. 26P. Ex. 2. What is the area of a square whose side is 70.25 two-pole chains? Ans. 124A. 1R. IP. Ex. 3. What is tne area of a rhombus whose side is 60 perches, and its height 45 perches ? Ans. 16 A. 3R. SOP. 162 TO FIND THE CONTENTS OF GROUND. Ex. 4. What is the area of a rhomboides whose less angle is 40 and the including sides 80 and 25 four-pole chains ? Ans. 128 A. 2R. 9P. Ex. 5. What is the area of a triangle whose base is 12 and its perpendicular height 6 two-pole chains ? Ans. 1A. 3R. 8P. LEMMA. PL. 8. fig. 9. If from half the sum of the sides of any plane triangle ABC each particular side be taken, and if the half-sum and the three remainders be multiplied continually into each other, the square root of this product will be the area, of the triangle. Bisect any two of the angles, as A and B, with the lines AD, BD, meeting in D ; draw the perpendiculars DE, DF, DG. The triangle AFD is equiangular to AED; for the angle FAD=EAD by construction, and AFD=AED, being each a right angle, and of consequence ADF^ADE ; wherefore AD : DE : : AD : DF; and since AD bears the same proportion to DF that it does to DE, DF=DE, and the triangle AFD= AED. The same way DE=DG, and the triangle DEB= DGB, and FD=DE=DG; therefore Dwill be the centre of a circle that will pass through E, F, G. In the same way, if A and C were bisected, the same point D would be had ; therefore a line from J) to C will bisect C, and thus the triangles DFC, DGC will be also equal. Produce CA to H, till AH=EB or GB ; so will HC be equal to half the sum of the sides, viz. to AB-\-^AC-\-BC ; for FC, FA, EB are severally equal to CG, AE, BG ; and all these together are equal to the sum of the sides of the tri- angle ; therefore FC+FA+EB or CH are equal to half the sum of the sides. FC=CHAB, for AF=AE, and HA=EB-, therefore HF=AB, and AF=CHBC; for CF=CG, and AH= GB ; therefore BC=HA+FC, and AC=CHAH. Continue DC till it meets a perpendicular drawn upon H in K ; and from K draw the perpendicular KI, and join AK. Because the angles AHK and AIK are two right ones, the angles HAl and K together are equal to two right ; since the angles of the two triangles contain four right : in the same way FDE+FAE= (two right angles =) FAE+IAH ; let FAE be taken from both, then FDE==IAH, and of course FAE= K', the quadrilateral figures AFDE and KHAI are therefore similar, and have the sides about the equal angles proportional; TO FIND THE CONTENTS OF GROUND. 163 and it is plain the triangles CFD and CHK are also propor- tional: hence, FD : HA : : FA : HK FD:FC::HK: HC. Wherefore, by multiplying the extremes and means in both, it will be the square of FDx HKx HC=FC xFAxHAx HK : let HK be taken from both, and multiply each side by CH; then the square of CH X by the square of FD=FCx FAxHAxCH. It is plain by the foregoing problem, that ABxDE +{BC xDG+ACxFD = the area of the triangle; or that half the sum of the sides, viz. CH x FD == the triangle ; wherefore, the square of CH x by the square of FDFC xFAx HA X CH, that is, the half-sum multiplied continually into the dif- ferences between the half-sum and each side will be the square of the area of the triangle, and its root the area. Q. E. D. Cor 1. If all the sides be equal, the rule will become s/faXi aX aXa=%aaV3, for the equilateral triangle whose side is a. Hence the following problem will be evident. PROBLEM VIII. The three sides of a plane triangle given, to find the area. RULE.* From half the sum of the three sides subtract each side severally; take the logarithms of half the sum and three remainders, and half their total will be the logarithm of the area : or, take the square root of the continued product of the half-sum and three remainders for the area. EXAMPLES. PL. 8. Jig. 9. 1. In the triangle ABC are (AB=W.64\ Given < AC= 12.28 > four-pole chains ; required the area ( CB= 9.00 ) Sum 31.92 * The demonstrat ; on of this is plain from the foregoing lemma, and the nature of logarithms. 164 TO FIND THE CONTENTS OF GROUND. Half-sum 15.96 Log. 1.203033 C 5.32 0.725912 Remainders 1 3.68 0.565848 (6.96 0.842609 2)3.337402 Answer, sqr. ch. 46.63 log. 1.668701 or, 4.663 acres. Or, 15.96X5.32X3.68X6.96=2174.71113216; the square root of which is 46.63, for the area, as before. 2. What quantity of land is contained in a triangle, the three sides of which are 80, 120, and 160 perches respectively ? Ans. 29A. 7P. 3. What quantity of land is contained in a triangle, the three sides of which are 20, 30, and 40 four-pole chains ? Ans. 29A. 7.579P. 4. How many acres are in a triangle, whose sides are 49, 50.25, 25.69 four-pole chains? Ans. 61A. 1R. 39.68P. fc PROBLEM IX. Two sides of a plane triangle and their included angle given, to find the area. RULE.* To the log. sine of the given angle (or of its supplement to 180 if obtuse) add the logarithms of the containing sides; the sum less radius will be the logarithm of the double area. Or, As radius Is to the sine of any angle of a triangle, So is the product of the sides including the angle : To double the area of the triangle. , ABxACxNu. S. of /-A /Tn e That is, (PL 5, fig. 17) = the area. * Demonstration. This follows from rule 2, prob. 5, and from the na- ture of logarithms, because a triangle is half a parallelogram of the same base and height. Or thus, PL. II, fig. 3. Let AH be perpendicular to AB and equal to AC, and HE, FCG parallel to AB ; then making AH (AC) radius, AF(=CD) will be the sine of CAD, and the parallelograms ABEH (the product of the given sides) and ABGF(ihe double area of the triangle), having the same base AB, are in proportion as their heights AH, AF ; that is, as radius to the sine of the given angle ; which proportion gives the operation as in the rule above* TO FIND THE CONTENTS OF GROUND. 165 EXAMPLES. PL. 5. fig. 16. Suppose two sides AB, AC of a triangular lot ABC form an angle of 30 degrees, and measure one 64 perches, and the other 40.5, what must the contents be ? Given angle 30 sine 9.698970 Confides 2)1296 log. 3.112605 160)648(4A. 8P., Answer. 8 Or thus : .500000 sine LA 64 AB 32.000000 40.5 AC 2)1296.0000000 160)648 4A. 8P. 2. Required the area of a triangle, two sides of which are 49.2 and 40.8 perches, and their contained angle 1441 degrees. Ans. 3A. 2R. 22P. 3. What quantity of ground is enclosed in an equilateral triangle, each side of which is 100 perches, either angle being 60 degrees ? Ans. 27A. 10P. PROBLEM X. To find the area of a trapezoid, viz. a figure bounded by four right lines, two of which are parallel, but unequal. RULE.* Multiply the sum of the parallel sides by their perpendicular distance, and take half the product for the area. * Demonstration. The trapezoid ABCD (pi. 14, fig. 8) is equivalent to the rectangle contained by its altitude and half the sum of the parallel 166 TO FIND THE CONTENTS OF GROUND. EXAMPLES. 1. Required the area of a trapezoid, of which the parallel sides are, respectively, 30 and 49 perches, and their perpen- dicular distance 61.6. 61.6 0+49=79 2)4866.4 Answer, 2433.2=15A. 33.2P. PL. 9. fig. 10. 2. In the trapezoid ABCD the parallel sides are, AD 20 perches, BC 32, and their perpendicular distance AB 26 ; required the contents. Ans. 4A. 36P. PROBLEM XL To find the contents of a trapezium. RULE I.* Multiply the diagonal, or line joining the remotest opposite angles, by the sum of the two perpendiculars falling from the other angles to that diagonal, and half the product will be the area. sides BC and AD. For draw CE parallel to AB (prob. 8), bisect ED in F, and draw FG parallel to AB, meeting the production of .BC in G. Because BC is equal to AE, BC and AD are together equal to AE and AD, or to twice AE with ED, or to twice AE and twice EF, that is, to twice AF ; consequently, AF=%(BC-\-AD). Wherefore, the rectangle contained by the altitude of the trapezoid and half the sum of its parallel sides is equivalent to the rhomboid BF : but the rhomboid EG is equiva- lent to the triangle ECD (theo. 12, cor. 2) ; add to each the rhomboid BE, and the rhomboid BFis equivalent to the trapezoid ABCD. Note. On this proposition is founded the method of offsets, which enters so largely into the practice of land surveying. In measuring a field of a very irregular shape, the principalpoints only are connected by straight lines, forming sides of the component triangles, and the distance of each remarkable flexure of the extreme boundary is taken from these rectilineal traces. The exterior border of the polygon is therefore considered as a collection of trapezoids, which are measured by multiplying the mean of each pair of offsets or perpendiculars into their base or intermediate dis- tance, which is one of the other sides, because the parallel sides are per- pendicular to it. * Demonstration. For the trapezium ABDC =; the triangles ABC-\- TO FIND THE CONTENTS OF GROUND. 107 EXAMPLE. PL. 7. fig. 3. Let ABCD be a field in form of a trapezium, the diagonal AC 64.4 perches, the perpendicular Bb 13.6, andZW 27.2; re- quired the contents. Diagonal =64.4 ),., 13.64+27.2=40.8 J Multiply. 2)2627.52 160)131 376(8A. 33fP., Answer. 1280 33 perches. Note. The method of multiplying together the half-sums of the opposite sides of a trapezium for the contents is erroneous, and the more so the more oblique its angles are. To draw the map, set off Ab 28 perches, and Ad 34.4, and there make the perpendiculars to their proper lengths, and join their extremities to those of the 'diagonal. Note. When one of the diagonals and the four sides of a trapezium are given, it is divided into two triangles whose sides are given ; the area of each triangle may be found (by prob 8), and their sum will give the area of the trapezium. RULE II.* If there be drawn two diagonals cutting each other, the pro- duct of the diagonals multiplied by the natural sine of the angle of intersection of the diagonals wilTbe double the area. And this rule is common to a square, rhombus, rhomboides, &c., as well as to all other quadrilateral figures ; that is, 2 = the area. PI. \4, fig. 9. Or, as radius :S.LR:: ACX BD : the area. Note. Because the diagonals of a square and rhombus in- tersect at a right angle, whose sine is 1, therefore half the pro- duct of their diagonals is the area. * Pemonstration. P1.14,fig.9. For the trapez. = the four &sARB,BRC> CRD, DRA=.(ARxRB-\-BR xRC+CRx RD-\-DRxRA) xlS.LR =(AR+RCxBR+CR-\-RAxDR)x1}S./L_R=AR+RCxBR-\-RD XS.LR=ACxBDx]iS. , Q ,. .- Q i produces the circum. Circum. divided ] D *.\ quotes the diam. EXAMPLES. 1. How many acres are in a circle of a mile diameter ! 1 mile = 320 perches, log. 2.505150 2.505150 5.010300 0.104909 4|0)8042J5 log. 4.905391 4)2010.25 Answer, 502 A. 2R. 25P. H 170 TO FIND THE CONTENTS OF GROUND. -$ 2. A gentleman, knowing that the area of a circle is greater than that of any other figure of equal perimeter, walls in a cir- cular deer-park of 100 perches diameter, in wjiich he makes an elliptical fish-pond 10 perches long by 5 wide. Required the length of his wall, contents of his park, and area of his pond. Answer. The wall 314.16 perches, enclosing 49A. 14P., of which 39| perches, or of an acre nearly, is appropriated to the pond. PROBLEM XIII. The area of a circle given, to find its diameter. RULE. To the logarithm of the area add 0.104909, and half the sum will be the logarithm of the diameter. Or, divide the area by .7854, and the square root of the quotient will.be the diameter. EXAMPLE. A horse in the midst of a meadow suppose Made fast to a stake by a line from his nose : How long must this line be that, feeding all round, Permits him to graze 'just an acre of ground ? Area in perches 160, log. 2.204120 0.104909 2)2.309029 Diameter 2)14.2733 log. 1.154514 Answer, 7.13665 per.= 117ft. 9in. PROBLEM XIV. Allowance for roads. It is customary to deduct 6 acres out of 106 for roads ; the land before the deduction is made may be termed ihe t gross, and that remaining after such deduction the neat. RULE. The gross divided > ^ j 06 $ ( l uotes ^ e neat< The neat multiplied $ ^ ( produces the g^oss. TO FIND THE CONTENTS OF GROUND. 171 EXAMPLES. 1. How much land must I enclose to have 850 A. 2R. 20P. neat? 4020 4 2.5 Acres. A. R. P. 850.625X1.06=901.6625=901 2 26, the answer. 2. How much neat land is there in a tract of 901 A. 2R. 26P. gross ? 40 26 2.65 Acres. A. R. P. 1.06)901.6625(850.625=850 2 20, the answer. 848 &c. Note. These two operations prove each other. PROBLEM XV. To find the area of apiece of ground , be it ever so irregular, by dividing it into triangles and trapezia. PL. 7. /gr.4. We here admit the survey to be taken and protracted ; by- having, therefore, the map, and knowing the scale by which it was laid down, the contents may be thus obtained. Dispose the given map into triangles by fine pencilled lines, such as are here represented in the scheme, and number the triangles with 1 , 2, 3, 4, &c. Your map being thus prepared, rule a table with four columns, the first of which is for the number of the triangle, the second for the base of it, the third for the perpendicular, and the fourth for the contents in perches. Then proceed to measure the base of number 1, from the scale of perches the map was laid down by, and place that in the second column of the table, under the word base ; and from the angle opposite to the base open your compasses so as when one foot is in the angular point, the other, being moved backward and forward, may just touch the base line, and neither go the least above nor beneath it ; that distance in the compasses, measured from the ame scale, is the length of that perpendicu- lar, which place in the third column under the word perpen- dicular. H2 J72 TO FIND THE CONTENTS OF GROUND. If the perpendiculars of two triangles fall on one and the same base, it is unnecessary to put down the base twice, but insert the second perpendicular opposite to the number of the triangle in the table, and join it with the other perp'endicular by a brace, as Nos. 1 and 2, 4 and 5, 6 and 7, 9 and 10, &c. Proceed after this manner till you have measured all the triangles, and then, by prob. 6, find the contents in perches of each respective triangle, which severally place in the table op- posite to the number of the triangle, in the fourth column, under the word contents. But where two perpendiculars are joined together in the table by a brace, having both one and the same base, find the con- tents of each (being a trapezium) in perches, by prob. 11, which place opposite the middle of those perpendiculars, in the fourth column, under the word contents. Having thus obtained the contents of each respective triangle and trapezium which the map contains, add them all together, and their sum will . be the contents of the map in perches, which being divided by 1 60 gives ifhe contents in acres. Thus, for EXAMPLE. No. Base. Perpend. Contents. 1 2 24.8 17.0 ) 16.35 412.92 3 28.2 16.0 225.6 4 5 39.8 19.6) 16.25 712.42 6 7 49.4 29.0 > 15.0 5 1086.8 8 38.7 6.7 129.64 9 10 40.0 17.0 > 13.05 600 11 12 42.8 10.2) 12.3 5 481.5 13 26.2 17.9 234.49 14 15 24.0 11.6 > 10.05 259.2 Contents in perches 4142.57 TO FIND THE CONTENTS OF GROUND. 173 This being divided by 160 will give 25A. 3R. 22P.,the con- tents of the map. Let your map be laid down by the largest scale your paper will admit, for then the bases and perpendiculars can be mea- sured with greater accuracy than when laid down by a smaller scale, and if possible measure from scales divided diagonally. If the bases and perpendiculars were measured by four-pole chains, the contents of every triangle, and trapezium may be had as before in problems 6 and 1 1 , and consequently the whole contents of the map. If any part of your map has short or crooked bounds, as those represented in plate 7, fig. 5, then by the straight edge of a transparent horn draw a fine pencilled line, as AB, to balance the parts taken and left out, as also another BC : these parts, when small, may be balanced very nearly by the eye, or they may be more accurately balanced by method the third. Join the points A and C by a line, so will the contents of the triangle ABC be equal to that contained between the line AC and the crooked boundary from A to B t and to C : by this method the number of triangles will be greatly lessened, and the contents become more certain ; for the fewer operations you have the less subject will you be to err, and if an error be committed the sooner it may be discovered. The lines of the map should be drawn small and neat, as well as the bases, the compasses neatly pointed, and the scale accurately divided ; without all which you may err greatly. The multiplications should be run over twice at least, as also the addition of the column of cpntents. From what has been said it will be easy to survey a field by reducing it into triangles and measuring the bases and perpen- diculars by the chain. To ascertain the contents only it is not material to know at what part of the base the perpendicular was taken ; since it has been shown (in cor. to theo. 1 3 geom.) that triangles on the same base and between the same paral- lels are equal : but if you would draw a map from the bases and perpendiculars, it is evident that you must know at what part of the base the perpendicular was taken, in order to set it off in its due position ; and hence the map is easily con- structed. 174 TO FIND THE CONTENTS OF GROUND. PROBLEM XVI. PL. 8. fig. 5. To determine the area of a piece of ground, having the map given, oy reducing it to one triangle equal thereto, and thence finding its contents. Let ABCDEFGH be a map of ground which you would reduce to one triangle equal thereto. Produce any line of the map, as AH, both ways ; lay the edge of a parallel ruler from A to C, having B above it ; hold the other side of the ruler, or that next you, fast ; open till the same edge touches B, and by it, with a protracting pin, mark the point b on the produced line ; lay the edge of the ruler from b to Z>, having C above it, hold the other side fast, open till the same edge touches C, and by it mark the point c on the pro- duced line. A line drawn from c to D will take in as much as it leaves out of the map. Again, lay the edge of the ruler from H to F, having G above it ; keep the other side fast, open till the same edge touches 6r, and by it mark the point g on the produced line ; lay the edge of the ruler from g to JE, having jP above it, keep the other side fast, open till the same edge touches F, and by it mark the point /on the produced line. Lay the edge of the ruler from /to J), having E above it, keep the other side fast, open till the same edge touches E, and by it mark the point e on the produced line. A line drawn from D toe will take in as much as it leaves out. Thus have you the triangle cDe, equal to the irregular polygon ABCDEFGH* If, when the ruler's edge is applied to the points A and C, the point B falls under the ruler, hold that side next the said points fast, and draw back the other to any convenient distance ; then hold this last side fast, and draw back the former edge to B, and by it mark b on the produced line ; and thus a parallel may be drawn to any point under the ruler as well as if it were above it. It is best to keep the point of your protracting pin in the last point in the extended line till you lay the edge of the ruler from it to the next station, or you may mistake one point for another. This may also be performed with a scale or ruler which has a thin-sloped edge, called a fiducial edge, and a fine-pointed pair of compasses. Thus, Lay that edge on the points A and C; take the distance from the point B to the edge of the scale, so that it may only touch it, in the same manner as you take the perpendicular of a tri~ s* The demonstration of this is evident from prob. 19, Geom., page 63 of this box>k. TO FIND THE CONTENTS OF GROUND. 175 angle ; cany that distance down by the edge of the scale par- allel to it to b, and there describe an arc on the point 6, and if it just touches the ruler's edge the point b is in the true place of, the extended line. Lay then the fiducial edge of the scale from b to -D, and take a distance from C that will just touch the edge of the scale ; cany that distance along the edge till the point which was in C cuts the produced " line in c j keep that foot in c and describe an arc, and if it just touches the ruler's edge the point c is in the true place of the extended line. Draw a line from c to D and it will take in and leave out equally : in like manner the other side of the figure may be balanced by the line eD. Let the point of your compasses be kept to the last point of the extended line till you lay your scale from it to the next station, to prevent mistakes from the number of points. That the triangle cDe is equal to the right-lined figure ABCDEFGH will be evident from problems 18, 19, geom. ; for thereby, if a line were drawn from bfa C, it will give and take equally, and then the figure bCDEFGH will be equal to the map. Thus the figure is lessened by one side, and the next balance line will lessen it by two, and so on, and will give and take 1 equally. In the same manner an equality will arise on the other side. The area of the triangle is easily obtained, as before, and thus you have the area of the map. It is best to extend one of the shortest lines of the polygon ; because if a very long line be produced, the triangle will have one angle very obtuse, and consequently the other two very acute ; in which case it will not be easy to determine exactly the length of the longest side, or the points where the balancing lines cut the extended one. This method will be found very useful and ready in small enclosures, as well as very exact ; it may be also used in large ones, but great care must be taken of the points on the extended line, wliich will be crowded, as well as of not missing a station. PROBLEM XVII. A map with its area being given, and its scale omitted * It either draton or mentioned, to find the scale. Cast up the map by any scale whatsoever, and it will be As the area found Is to the square of the scale by which you cast np, So is the given area of the map To the square of the scale by which it was laid down. The square root of which will give the scale. 176 TO FIND THE CONTENTS OF GROUND. EXAMPLE. A map whose area is 126 A. 3R. 16P. being given, and the scale omitted to be either drawn or mentioned, to find the scale. Suppose this map was cast up by a scale of 20 perches to an inch, and the contents thereby produced be 31A. 2R. 34P. As the area found, 31A. 2R. 34P.=5074P. Is to the square of the scale by which it was cast up, that is, to 20X20=400, So is the given area of the map 126 A. 3R. 16P.=20296P. To the square of the scale by which it was laid down. 5074 : 400 : : 20296 : 1600, the square of the required scale. Root. 1600(40 16 8) 00 Answer. The map was laid down by a scale of 40 perches to an inch. PROBLEM XVIII. How to find the true contents of a survey, though it be taken by a chain that is too long or too short. Let the map be constructed, and its area found, as if the chain were of the true length. And it will be, As the square of the true chain Is to the contents of the map, So is the square of the chain you surveyed by To the true contents of the map. EXAMPLE. If a survey be taken with a chain which is 3 inches too long, or with one whose length is 42 feet 3 inches, and the map thereof be found to contain U20A. 2R. 20P. ; required the true contents. ^L As the square of 42ft. Om. = the square of 504 inches = 254016 Is to the contents of the map, 920A. 1R. 20P. 147260P., So is the square of 42ft. 3t*9. = the square of 507 inches = 257049 To the true contents* COMPUTATION OF AREAS. 177 P. P. 250416 : 147260 : : 257049 : 149019 A. R. P. 160)149019(931 1 19, Answer. METHOD OF DETERMINING THE AREAS OF RIGHT-LINED FIGURES UNIVERSALLY, OR BY. CALCULATION. Definitions. PL. 8. fig. 7. 1. MERIDIANS are north and south lines, which are sup- posed to pass through every station of the survey. 2. The difference of latitude, or the northing or southing of any stationary line, is the distance that one end of the line is north or south from the other end ; or, it is the distance which is intercepted on the meridian, between the beginning of the stationary line and a perpendicular drawn from the other end to that meridian. Thus, if NS be a meridian line passing through the point A of the line AB, then is Ab the difference of latitude or southing of that line. 3. The departure of any stationary line is the nearest dis- tance froimone end of the line to a meridian passing through the other end. Thus Bb is the departure or easting of the line AB : but if CB be a meridian, and the measure of the sta- tionary distance be taken from B to A, then is BC the differ- ence of latitude, or northing, and .AC the departure or westing of the line BA. 4; That meridian which passes through the first station is sometimes called the first meridian ; and sometimes it is a me- ridian passing on the east or west side of the map, at the dis- tance of the breadth thereof, from east to west, set off from the- first station. 5. The meridian distance of any station is the distance 178 COMPUTATION OF AREAS. thereof from the first meridian, whether it be supposed to pass through the first station or on the east or west side of the map. THEOREM L In every survey which is truly taken, the sum of the north- ings will be equal to that of the southings ; and the sum of the eastings equal to that of the westings. PL. 9. jig. 1. Let abcefgh represent a plot or parcel of land. Let a be the first~ station, b the second, c the third, &c. Let NS" be a meridian line ; then will all lines parallel thereto, which pass through the several stations, be meridians alscH; as a0, bs t cd, &c., and the lines bo, cs, de, &c., perpendicular to those, will be the east or west lines or departures. The northings, ei+go-\-hq=ao+bs-\-cd-\-fr,l}\e southings: for let the figure be completed ; then it is plain that go-\-hq+ rk=ao+bs+cd, and ei rk=fr. If to the former part, of this first equation ei rk be added, and/r to the latter, then #0+ hq-\-ei=ao+bs-\-cd-\-fr, that is, the sum of the northings is equal to that of the southings. ' The eastings, cs-{-qa ob+de+if+rg+oh, the westings. For aq-\-yo (az) de-\- if -\-rg-\-oh, and 00 cs yo. If to the former part of this first equation cs yo be added, and bo to the latter, then cs-\-aq=ob-^-de-\-if-{-rg-\-oh ; that is, the sum of the eastings is equal to that of the westings. Q. E. D. SCHOLIUM. This theorem is of use to prove whether the field-work be truly taken or not ; for if the sum of the northings be equal to that of the southings, and the sum of the eastings to that of the westings, the field-work is right, otherwise not; Since the proof and certainty of a survey depend on this truth, it will be necessary to show how the difference of latitude and departure for any stationary line, whose course and dis- tance are given, may be obtained by the a table usually called the Traverse Table.* * This table is calculated by the first case of right-angled plane trigo- nometry, taught in the fifth section of the first part of this book> where- the hypothenuse and an acute angle are given, to find the legs. In the right-angled triangle ABC (PI. 8, fig. 7), given the distance or hypothenuse AB 91 chains, links, or perches, the course or one of the acute angles ABC 41 ; it is required to find the legs, or the difference of latitude and departure.. m COMPUTATION OF AREAS. 179 To find the difference of latitude and departure by the Traverse Table. This table is so contrived, that by finding therein the given course, and a distance not exceeding 120 miles, chains, perches, or feet, the difference of latitude and departure is had by in- spection : the course is to be found at the top of the table when under 45 degrees, but at the bottom of the table when above 45 degrees. Each column signed with a course consists of two parts, one for the difference of latitude, marked Lat., the other for the departure, marked Dep., which names are both at the top and bottom of these columns. The distance is to be found in the column marked DisU, next the left-hand margin of the EXAMPLE. In the use of this table, a few observations only are ne- cessary. 1. If a station consist of any number of even chains or perches (which are almost the only measures used in survey- ing), the latitude and departure are found at sight under tjae bearing or course, if less than 45 degrees, or over it if more, and in a line with the distance. 2. If a station consist of any number of chains and perches,. and decimals of a chain or perch, under the distance 10, the lat. and dep. will be found as above, either over or under the bearing ; the decimal point or separatrix being removed one figure to the left, which leaves a figure to the right to spare. If the distance be any number of chains or perches, and the decimals of a chain or perch, the lat. and dep. must be taken As radius 90 10.000000 is to AB, 91 1.959041 So is the sine of B 41 9.816943 to AC 59.70 1.775984 As radius 90 10.000000 is to 315, 91 1.959041 So is the sine of A 49 9.877780 to BC 68.68 1.836821 Hence AC is the departure and BC the difference of latitude which correspond to those in the table. In the same manner the difference of latitude and departure to every degree in the table is calculated, by which the practitioner can at any time proxe the exactness of those in the table. 180 COMPUTATION OF AREAS. out at two or more operations, by taking out the lat. and dep* for the chains or perches in the first place ; and then for the decimal parts. To save the repeated trouble of additions, a judicious sur- veyor will always limit his stations to whole chains or perches and lengths, which can commonly be done at every station save the last. 1. In order to illustrate the foregoing observations, let us suppose a course or bearing to be S. 35 15' ., and the dis- tance 79 four-pole chains. Under 35 15', or 35| degrees* and opposite 79, we find 64.51 for the latitude, and 45.59 the departure, which signify that the end of that station differ in latitude from the beginning 64.51 chains, and in departure 45.59 chains. Note. We are to understand the same things if the distance is given in perches or any other measures, the method of pro- ceeding being exactly the same in every case. Again, let the bearing be 54| degrees, and distance as before ; then over said degrees we find the same numbers, only with this difference, that the lat. before found will now be the dep., and the dep. the lat., because 54f is the complement of 35 de- grees to 90, viz. lat. 45.59, dep. 64.51. 2. Suppose the same course, but the distance 7 chains 90 links, or as many perches. Here we find the same numbers, but the decimal point must be removed one figure to the left. Thus, under 35JL, and in a line with 79 or 7.9, are Lat. 6.45 Dep. 4.56 the 5 in the dep. being increased by 1, because the 9 is re- jected ; but over 54f we get Lat. 4.56 Dep. 6.45 3. Let the course be as before, but the distance 7.79, then opposite 7.70 Lat. 6.29 Dep. 4.43 976 7.79 6.36 4.49 Or opposite 7.00 Lat. 5.72 Dep. 4.03 .79 .64 .4ft 7.79 6.36 4.49- COMPUTATION OF AREAS. 181 THEOREM II. When the first meridian passes through the map. If the east meridian distances in the middle of each line be multiplied into the particular southing, and the west meridian distances into the particular northing) the sum of these products will be the area of the map. PL. 10. fig. 1. Let the figure abkm be a map, the lines ab, Ik to the south- ward, and km, ma to the northward, NS the first meridian line passing through the first station a. The meridian ( zd X ao > . ( am distances east \tu X ox (bq) y ~ ;a ( ow The meridian < efxgx ) = . < xp distances west \hhXga (my) $ ' \ gl These four areas am+ow-\- xp-\-gl will be the area of the whole figure cmswiprlc, which is equal to the area of the map abkm. Complete the figure. The parallelograms am and ow are made of the east meridian distances dz and tu multiplied into the southings ao and ox ;. the parallelograms xp and gl are composed of the west meri- dian distances ef and hh multiplied into the northings xg and ga (my) : but these four parallelograms are equal to the area of the map ; for if from them be taken the four triangles marked Z, and in the place of those be substituted the four triangles marked O, which are equal to the former, then it is plain the area of the map will be equal to the four parallelograms. Q. E. D. THEOREM III. If the meridian distance when east be multiplied into the southings, and the meridian distance when west be multiplied into the northings, the sum f these less by the meridian distance when west multiplied into the south- ings is the area of the survey. PL. 10. fig. 2. Let abc be the map. The jgure being completed, the rectangle af is made of the meridian distance eq when east multiplied into the southing an ; the rectangle yk is made of the meridian distance xw, mul- tiplied into the northings cz or ya. These two rectangles, or parallelograms, af-\-yk, make the area of the figure dfnyikd ; from which taking the rectangle oy, made of the meridian dis- tance tu when west into the southings oh or bm, the remainder * 182 COMPUTATION OF AREAS. is the area of the figure dfohikd, which is equal to the area of the map. Letbou = Y, urih=L, ric=O, wrc=Z, akw=K f cfb=B, and ade=A. I say that Y+Z+B=K+L+A. F=Z+O; add Z to both, then Y+Z=L+O+Z: but Z + O=K, put K instead of Z+O, then Y+Z=L+K\ add to both sides the equal triangles B and A, then Y+Z+B=L +K+A. If therefore B+Y+Zbe taken from abc, and in lieu thereof we put L-\-K-\- A, we shall have the figure dfoHikd =abc', but that figure is made up of the meridian distance when east multiplied into the southing, and the meridian distance when west multiplied into the northing less by the meridian distance when west multiplied into the southing. Q. E. D. COROLLARY. Since the meridian distance when west multiplied into the southing is to be subtracted, by the same reasoning the me- ridian distance when east multiplied into the northing must be also subtracted. SCHOLIUM. From the two preceding theorems we learn how to find the area of the map when the first meridian passes through it ; that is, when one part of the map lies on the east and the other on the west side of that meridian. Thus, RULE. The mend. ( east ) muhi lied into the < southings, ) dist. when } west > $ northings, ) sum is the area of the map. But, TheineriiL < east > d pliedintathe $ *hings, \ the sum dist. when ( west $ ( southings, ^ of these products taken from the former gives the area of the map. These theorems are true when the surveyor keeps the land he surveys on his right-hand, which we suppose thrgugh the whole to be done ; but if he goes the contrary way, call the southings northings and the northings southings, and the same rule will hold good. COMPUTATION OF AREAS, 183 General Rule for finding the Meridian Distances. 1. The meridian distance and departure both east or both west, their sum is the meridian distance of the same name. 2. The meridian distance and departure of different names, that is, one east and the other west, their difference is the me- ridian distance of the same name with the greater. Thus, in the first method of finding the area, a& in the follow- ing field-book, The first departure is put opposite the northing or southing of the first station, and is the first meridian distance of the same name. Thus, if the first departure be east, the first meridian distance will be the same as the departure, and east also,, and if west it will be the same way. The first meridian distance 6.61 E. The next departure 6.61 E, The second meridian distance 13.22 E. The next departure 1.80 E. The third meridian distance 15.02 E. At station 5, the meridian distance 5.78 E. The next departure 7.76 W The next meridian distance 1.98 W. At station 1 1, the meridian distance 0. 12 W. The next departure 5.84 E. The next meridian distance 5.72 E. PL. 10. fig. 9. In the 5th and llth stations, the meridian distance being less than the departures and of a contrary name, the map will cross the first meridian, and will pass, as in the 5th line, from the east to the west line of the meridian ; and in the llth line it will again cross from the west to the east side, which will evidently appear if the field-work be protracted, and the me- ridian line passing through the first station be drawn through the map. The field-book cast up by the first method will be evident 184 COMPUTATION OF AREAS. from the two foregoing theorems^ and therefore requires no- further explanation ; but to find the urea by the second method take this RULE. When the meridian distances are east, put the products of north and south areas in their proper columns, but when west in their contrary columns ; that is, in the column of south area when the difference of latitude is north, and in north when south : the reason of which is plain from the last two theo- rems. The difference of these two columns will be the area of the map. Construction of the Map from either the first or the second Table. PL. 10. Jig. 3. Draw the line NS for a north and south line, which call the first meridian ; in this line assume any point, as 1, for the first station. Set the northing of that stationary line, which is 3.54, from 1 to 2, on the said meridian line. Upon the point 2 raise 4 perpendicular to the eastward, the meridian distance being easterly, and upon it set 13.22, the second number in the column of meridian distances from 2 to 2, and draw the line 1, 2 for the first distance line : from 2 upon the first meridian set the northing of the second stationary line, that is, 9.65, to 3, and on the point 3 erect a perpendicular eastward, upon which set the meridian distance of the second station 16.82, from 3 to 3, and draw the line 2, 3, for the distance line of the second station. And since the third station has neither northing nor southing, set the meridian distance of it 33.02, from 3 to 4, for the* distance line of the third station. To the fourth station there is 29.44 southing, which set from 3 to 5 ^ upon the point 5 erect the perpendicular 5, 5 ; on which lay 13.54, and draw the line 4 to 5. In the like manner proceed to set the northings and south- ings on the first meridian, and the meridian distances upon the perpendiculars raised to the east or west ; the extremities of which connected by right lines will complete the map. COMPUTATION OF AREAS. Field-book, Method I. 185 No. St. Bearings. C.L. Lat. and halfDep. Mend. Dist. Area. Deduct. 1 NE 75 13.70 N 3.54 E 6.61 6.61 E 13.22 E 23.3994 o NE 20 10.30 N 9.67 E 1.80 15.02 E 16.82 E 144.9430 3 East. 16.20 0.00 E 8.10 24.92 E 33.02 E 4 SW 33i 35.30 S 29.44 W 9.74 23.28 E 13.54 E 685.3632 5 SW76 _^_ 16.00 S 3.87 W 7.76 5.78 E 1.98 W 22.3686 6 North. 9.00 N 9.00 0.00 1.98 W 1.98 W 17.8200 7 SW84 11.60 S 1.21 W 5.77 7.75 W 13.52 W 9.3775 8 NW531 11.60 N 6.94 W 4.64 18.16 W 22.80 W 126.0304 9 NE 36 19.20 N 15.38 E 5.74 17.06W 11.32 W 262.3828 10 NE 22 14.00 N 12.93 E 2.68 8.64 W 5.96 W 111.7152 11 SE 76 12.00 S 2.75 E 5.84 0.12 W 5.72 E 0.3300 12 SW 15 10.85 S 10.48 W 1.40 <.32 E 2.92 E 45.2736 13 SW 165 10.12 S 9.69 W 1.46 1.46 E 0.00 14.1474 Contents in chains - - - 1285.1012 178.0499 178.0499 1107.0513 186 COMPUTATION OF AREAS. The foregoing Field-look, Method II. It it needless here to insert the columns of bearing or distances in chains, they being the same as before. No. St. Lat. and halfDep. Merid. Dist. N. Area. S. Area. 1 N 3.54 E 6.61 6.61 E 13.22 E 23.3994 2 N 9.65 E 1.80 15.02 E 16.82 E 144.9430 3 0.00 E 8.10 24.92 E 33.02 E 4 S 29.44 W 9.74 23.28 E 13.54 E 685.3632 5 S 3.87 W 7.76 5.78 E 1.98 W 22.3686 6 N 9.00 0.00 1.98 W 1.98 W 17.8200 7 S 1.21 W 5.77 7.75 W 13.52 W 9.3775 8 N 6.94 W 4.64 18.16W 22.80 W 126.0303 9 N 15.38 E 5.74 17.06W 11.32W 262.3828 10 N 12.93 E 2.68 8.64 W 5.96 W 111.7152 11 S 2.75 E 5.84 0.12W 5.72 E 0.3300 12 S 10.48 W 1.40 4.32 E 2.92 E 45.2736 13 S 9.69 W 1.46 1.46 E 0.00 14.1474 Area in chains, ; 178.0499 1284.1012 178.0499 is before, 1107.0513 COMPUTATION OF AREAS. 187 A Specimen of the Pennsylvania Method of CALCULA- TION; which for its simplicity and ease in finding the Me- . ridian Distances is supposed to be preferable in practice to any thing heretofore published on the subject. Find, in the first place, by the Traverse Table, the lat. and dep. for the several courses and distances, as already taught ; and if the survey be truly taken, the sums of the northings and southings will be equal, and also those of the eastings and westings. Then, in the next place, find the meridian distances, by choosing such a place in the column of eastings or westings as will admit of a continual addition of one, and subtraction of the other ; by which means we avoid the inconvenience of changing the denomination of either of the departures. The learner must not expect that in real practice the columns of lat. and those of dep. will exactly balance when they are at first added up, for little inaccuracies will arise, both from the observations taken in the field and in chaining; which to ad- just, previous to finding the meridian distances, we may observe, that if in small surveys the difference amount to two-tenths of a perch for every station, there must have been some error committed in the field ; and the best way in this case will be, to rectify it on the ground by a resurvey, or at least as much as will discover the error. But when the differences are not within those limits, the columns of northing, southing, easting, and westing may be corrected as follows : Add all the distances into one sum, and say, as that sum is to each particular distance, so is the difference between the sums of the columns of northing and southing to the correction of northing or southing belonging to that distance : the corrections thus found are respectively additive when they belong to the column of northing or southing which is the less of the two r and subtractive when they belong to the greater ; if the course be due east or west, the correction is always additive to the less of the two columns of northing or southing. The correc- tions of easting and westing are found exactly in the same manner. The following example will sufficiently illustrate the manne* of applying the rule. % 188 COMPUTATION OF AREAS. , o> CO r ' >o (N O5 i> ^ "* co CO r-H VT3 1 w CO CD CO 00 r^ 1C Cx o li 1 CO o CO N Q. OQ CO o 05 CO 00 i* CQ W os (N o r-4 N 02 * CD l-H o r I 1 s 00 N' "^ O ' OS rt ? ^ J? co OS r I o CO S 5 B r-t II 8 m t^ (NO ? tf n W CO CO GO Sfci o E"" 1 u CD ,3 CD r-, t^ -^ o ^ a QQ CO OS c* CO 00 00 || H 2 rv l-H N (M PH 05 _ o O ?J5 3 ij ^ CO o i s ii ? os GO 2 s CO 00 CO 1 1 1 ' the additive corrections < ' ( 00.0 ) (.07 And consequently, by neglecting .04 and .03, and using .1 for each of the two .06 and .07, the northings when corrected are 62.9, 101.2,54.0, 00.1. In obtaining these corrections, it is commonly unnecessary to use all the significant figures of the distances : thus, for the ratio of 791 to 70, we may say, as 80 to 7^ The latitudes and departures being thus balanced, proceed to insert the meridian distances by the above method, where we still make use of the same field-notes, only changing chains and links into perches and tenths of a perch. Then by look- ing along the column of departure, it is easy to observe, that in the columns of eastings opposite station 9 all the eastings may be added, and the westings subtracted, without altering the denomination of either. Therefore, by placing 46.0, the east departure belonging to this station, in the column of me- ridian distances, and proceeding to add the eastings and subtract the westings, according to the rule already mentioned, we shall find that at station 8 these distances will end in 0, 0, or a cipher, if the additions and subtractions be rightly made. Then multiplying the upper meridian distance of each station by its respective northing or southing, the product will give the north, or south area, as in the examples already insisted on, and which is fully exemplified in the annexed specimen. When these products are all made out and placed in their respective columns, their difference will give double the area of the plot, or twice the number of acres contained in the survey. Divide this remainder by 2, and the quotient thence arising by 160 (the number of perches in an acre), then will this last quotient ex- hibit the number of acres and perches contained in the whole survey; which in this example may be called 110 acres, 103 perches, or 110 acres, 2 roods, 23 perches. 190 COMPUTATION OF AREAS. FIELD-NOTES of the two foregoing methods, as practised in Pennsylvania. Cast up by perches and tenths of a perch. N. Courses. Dist. N. S. E. W. M. D- N. Area. S. Area. 1 N 750 00' E 54.8 14.2 52.9 235.3 288.2 3341.26 2 3 N 20.30 E 41.2 38.6 14.4 302.6 317.0 11680.36 East. 64.8 64.8 381.8 446.6 4 5 6 S 33.30 W 141.2 117.7 77.9 368.7 290.8 43395.99 S 76.00 W 64.0 15.5 62.1 228.7 166.6 3544.85 North. 36.0 36.0 166.6 166.6 5977.60 7 8 9 10 S 84.00 W 46.4 4.9 46.1 120.5 74.4 590.45 N 53.15 W 46.4 27.8 37.2 37.2 00.0 1034.16 N 36.45 E 76.8 61.5 46.0 46.0 92.0 2829.00 N 22.30 E 56.0 51.7 21.4 113.4 134.8 5862.78 11 12 S 76.45 E 48.0 11.0 46.7 181.5 228.2 1996.50 S 15.00 W 43.4 41.9 11.2 217.0 205.8 9092.30 13 S 16.45 W 40.5 38.8 11.7 194.1 182.4 7531.08 f 229.8 229.8 246.2 246.2 30745.16 66151.17 30745.16 Area i 2 35406.01 i perches 177030.05 COMPUTATION OF AREAS. 101 Note. Tn the foregoing methods the first meridian passes through the map ; but as it is more convenient to have it pass through the extreme east or west point of the same, I have given the folio wing -example to illustrate this method. Of computing the area of a survey by having the bearings and distances given, geometrically considered and demonstrated. Let BCDEFGHA, pi. 14, fig. 1 1, represent the boundary of a survey of which the following field-notes are given ; it is re- quired to find the area. EXAMPLE. * Sides of the land. Bearings. Length" in chains. BC East. 4.00 CD N9 E 4.00 DE S69 E 5.56 EF S 36 E 7.00 FG S42W 4.00 GH S75W 10.00 HA N39W 7.50 AB N42E 5.00 RULE I. Find the difference of latitude and departure answering .to each course and distance by the Traverse Table or right- angled plane trigonometry, according to the directions already given, and place them under the succeeding columns North or South, East or West, according as they are north or south, east or west ; then if the survey does not close, correct the errors fey saying,* as the sum of all the distances is to each * This arithmetical rule was given by Mr. Bowditch in his solution of Mr. Patterson's question of correcting a survey in No. 4 of the Analyst. Also, the editor, Dr. Ad'.ain, has given precisely the same practical rule, 192 COMPUTATION OF AREAS. particular distance, so is the whole error in departure to the correction of the corresponding departure, each correction be- ing so applied as to diminish the whole error in departure : pro- in his elegant solution of the said question, analytically demonstrated. As the demonstration of this important rule may give great satisfaction to those who have not an opportunity of seeing the Analyst, I have inserted Mr. Bowditch's demonstration of said rule, which is as follows, viz. Demonstration 1. That the error ought to be apportioned among all the bearings and distances. 2. That in those lines in which an alteration of the measured distance would tend considerably to correct the error of the survey, a correction ought to be made ; but when such an alteration would not have that ten- dency, the length of the line ought to remain unaltered. 3. In the same manner, an alteration ought to be made in the observed bearings, if it would tend considerably to correct the error of the survey, otherwise not. 4. In cases where alterations in the bearings and distances will both tend to correct the error it will be proper to alter them both, making greater or less alterations according to the greater or less efficacy in correcting the error of the survey. 5. The alterations made in the observed bearing and length of any one of the boundary lines ought to be such that the combined effect of such alterations may tend wholly to correct the error of the survey. Suppose now that ABODE (pi. 14, fig. 12) represent the boundary lines of a field, as plotted from the observed bearings and lengths, and that the last point E, instead of falling on the first A, is distant from it by the length AE. TJhe question will therTbe, what alterations BB', CC", DD'", &c. must be made in the positions of the points JB, C, D, &c. so as to obtain the most probable boundaries AB'C"D'"A1 If AB' be supposed to be the most probable bearing and length of the first boundary line, the point B would be moved through the line BB\ and the following points C, Z), E would in consequence thereof be moved in equal and parallel directions to C', D', E', and the boundary would become AB'C'D'E'. Again, if by correcting in the most probable manner the error in the observed bearing and length of BC (or -B'C'), the point C' be moved to C", the points I)' and E' would be moved in equal and parallel directions to D" and E", and the boundary line would become AB'C"D"E". In a similar manner, if by correcting the probable error in the bearing and length of CD (or C"D'") the point D" be moved to D'", the point E" would be moved in an equal and parallel direction to E'", and the boundary would become A B' C"D"'E"". Lastly, by correcting the probable error in the bearing and length of the line.DE (or D"'E'") the true boundary AB'C"D'"A would be obtained. If we suppose the lines BB'CC"DD'", &c. to be parallel toAE, it would satisfy the second, third, fourth, and fifth of the preceding principles. For the change of position of the points B, C, &c. being in directions parallel to AE, the whole tendency of such change would be to move the point E directly towards A, conformably to the fifth principle ; and by inspecting the figure, it will appear that the second, third, and fourth principles would also be satisfied. For, in the first place, it appears that the bearing of the first line AB would be altered considerably, but the length but' little. This is agreeable to those principles, because an increase of the distance AB would move the point E in the direction Eb parallel to AB, and an altera- tion in the bearing would move it in the direction Eb' perpendicular to COMPUTATION OF AREAS. 193 ceed the same way for the corrections in latitudes. These corrections being applied to their corresponding differences of latitude and departure, that is, add when of the same name and AB. Now the former change would not tend effectually to decrease the distance AE, but the latter would be almost wholly exerted in producing that effect. Again, the length of the line BC would be considerably changed- without altering essentially the bearing ; the former alteration would tend greatly to decrease the distance AE, but the latter would not 1 produce so sensible an effec,t. Similar remarks may be made on the changes in the other bearings and distances, but it does not appear to be necessary to enter more largely on this subject. It remains now to determine the proportion of the lines BB', CC", DD'", &c. To do this we shall observe, that in measuring the lengths of any lines the errors would probably be in proportion to their lengths. These supposed errors must, however, be decreased on those lines where the effect in correcting the error of the survey would be small, by the second and fourth principles. In observing the bearings of all the boundary lines equal errors are liable to be committed ; however, it will be proper, by the third and fourth principles to suppose the error greater or less in proportion to the greater or less effect it would produce in correcting the error of the survey. Now the error of an observed bearing being given, as for example GFI (pi. 14, fig. 13), the change of position GI of the end of the line G would be proportional to the length of the line FG (=FI), so that the supposed errors both in the length and in the bearing of any boundary line would produce changes in the position of the end of it proportional to its length. There appears, therefore, a considerable degree of probability in supposing the lines BB', C'C", D'D'", &c. to be respectively proportional to the lengths of the boundary lines AB, BC, CD, &c. The main point to be ascertained before adopting this hypothesis is, whether a due proportion of the error of the survey is thrown on the bearings and lengths of the sides. Now it is plain by this hypothesis that the error in any boundary line is supposed to be wholly in the bearing if the line be perpendicular to AE, and wholly in its length when parallel to AE ; and if the length be the same in both cases, the change of position of the end of the line would in both cases be exactly equal. Thus, if FGH be the boundary line, GI the change of position of the point B in the former case, and OH in the latter, we should in this hypothesis have GI=GH. To show the probability of this hypothesis it may be observed, that in measuring the lengths of a line FGH of six or eight chains of fifty links each, an error of one link might easily be committed by the stretching of the chain or the unevenness of the surface. This error would be about ~j of the whole length. If we, therefore, suppose GI to be ^ of FG, the angle GFI would be about 10'. Now, with such instruments as are generally made use of by surveyors, it is about as probable that an error of KX was made in the bearing as that the above error, | part, was made in measuring the length. We shall therefore adopt it as a principle, that the most probable way of apportioning the error of the survey AE is to take BB 1 , C 1 C", ,D"D"', &c. respectively proportional to the boundary lines AB, BC, CD, &c. Hence the following practical rule for correcting a survey geometrically. Draw the boundary lines ABCDE by means of the observed bearings and 194 COMPUTATION OF AREAS. subtract when of different names, then the corrected difference of latitude and departure will be obtained, and the table will stand thus : s PQ $ 4> W dh- O5 i> W< i- 1^ w 00 OS CO CD o 1C CX) q W" CO CO CO r^' o> . r^ o OJ CO CO CO CO 8j O o 8 ^5 o J> I 1 >' w w o o Tj< CO CD 05 T 1 rj 1 1 1 1 Tp *o CO CO 00 < w < 1> i I 1 1 D N D (N f* ^ o5 O5 O5 OD ?O c4 s W II ? CO p-t a5 H 10 O5 w 00 c< > CD . ^ ( -i 00 N w CO CO CO C 1 1 1 5 -^ 6 Q T rp in J> -^ r i o J> iti Courses. CO . cS w W O5 W 05 co 05 W co CO GO CO Tj< 05 ^ o i> 72 O5 CO & w N "* ^ CO -o TO o- PQ Q O ' W Q fe .W O fo O 4 W pa O> | Tjt I rl I CO ' I O ^ I 8 I 8 | | 8. | S | 3 | 8 [ 8 g * , I d s a RULE H.J The difference of latitude and departure being found and cor- rected as in the preceding rule. * This is not the first station in t^ie actual survey, hut only the most westerly point of the survey as calculated by the foregoing method from the field-notes, which, for convenience' sake, I call the first station in mak- ing out this table. t The meridian distances in this column are the sum of two adjacent meridian distances ; but at the most westerly point the meridian distance is nothing, hence the first dep. is the first meridian distance, and, in like manner, the last dep. is the last meridian distance. J Demonstration. Let us consider that every tract of land has an ex- treme southerly point, as H ; and we reckon so much as any other point is distant from the east and west line IK (PL 14, fig. 11), that passes through 108 COMPUTATION OF AREAS. As beginning at the most northerly or most southerly point of the survey admits of a continual addition of the one and subtraction of the other, make choice of either of these points in order to calculate the area of the survey. 1. It is necessary to calculate the several latitudes in order to find the most northerly or most southerly point of the survey, which may be done from Table I., thus : The first lat. is .02 south, which is the difference of latitude between the second point of the survey and the first, when the survey is corrected from the next departure 3.93, which is N., subtract .02 and their difference 3.91 is equal to the difference of latitude between the third point and the first, which is N., and 3.91 2.02 1.89 = the difference of lat. between the fourth point and the first ; which is also N. .But as the next differ- ence of, lat. is south, therefore 5.71 1.89=3.32 = the differ- ence of lat. S. between the fifth point and ihe first ; and 3.82+ 2.99=6.81= the difference of lat. S. between the sixth point and the first ; and 6.81+2.65=9.46 = the difference of lat. S. between the seventh point and the first ; and 9.46 5.77 = 3.69 = the difference of lat. S. between the eighth point and the first; and 3.69 3.69=0 ; hence it is evident that 9.46 is the greatest lat. S. = the difference of lat. between the seventh point and the first; therefore, the seventh point of the survey is the most southerly point ; and, in like manner, 3.91 = the difference of lat. between the third point and the first, is the greatest lat. N. ; hence, the third point is the most northerly point of the survey. H, to be its latitude north, or the difference of latitude between the points H and A ; EL the lat. of B ; CM the lat of C ; &c. Thus, if from the contents of the figure MB CDEFK, the contents of the figure FKIAHG be subtracted, the remainder will be the area of the survey. The multangular figure IABCDEFK is composed of all these trape- zoids, viz. IABL, B CML, CDNM, EOND, and FKOE ; but (by Prob. 10) (1A -\-LB) X ZL = twice the area of the trapezoid IABL, and (LB-\-CM) X LM = twice the area of the trapezoid B CML, and so for the rest ; and IA-\-LB = the sum of the northings of the points A and B from the line IK, and IL = the easting of the pqkit B from the point A. In like man- ner the area of every other trapezom is found ; but these are the east col- umn areas, that is, (IA-\-BD X IL +(#!+ CM) X LM-}-(CM+DN) X MN-)-(DN+EO)xNO-}-(EO-\-FK) X OK= twice the area of the figure IAB CDEFK = the sum of the east area column. And in like manner we demonstrate that (FK-\-PG)xPK = twice the area of the trapezoid FKPG ; but FK+PG = the lat. of F+ the lat, of G and PK = the dep. or westing of the point G from the point F, and PGxPH= twice the area of the triangle PGH, and lAxIH twice the area of the triangle IAH\ hence (FK+PG)xPK+PGxPH+lAxIH = twice the area of the figure FKIAGH = the sum of the west area column. Therefore (/.#+ JgL) X IL+ (BL-4-CM) x LM+ ( CM+DN) x MN+ (DN+EO) x NQ +(EO+FK) x OK- ((FK+PG) X PK+PG X PH+IA X IH] = twice the area of the survey ; consequently, the sum of the east area column . the sum of the west area column twice the area of the survey. Q. E. IX COMPUTATION OF AREAS. 199 Now, by calling the most southerly point of the survey the first station, and proceeding to find the latitudes for the several lines in the order in which they were surveyed ; that is, the first difference of lat. will be the first lat., which place in the column of latitudes, opposite the said difference of latitude ; to the same lat. add the said difference of lat., to which sum add the next difference of lat. if it be of the same name, but sub- tract if of a different name, and place it in the column of lati- tudes ; in like manner continue to add or subtract the difference of lat. twice, and the last lat. comes out nothing, if the addi- tions and subtractions are rightly performed. Multiply each of the upper numbers in the column of latitudes by the corres- ponding dep., and place the products in the column of east or west area, according as the dep. is E. or W. The difference of these columns will be equal to twice the area, half of which will give the area of the survey ; as in the following table. Il i ! I oq 53 ? IS I 22 gi MS 3 3 S I "* 2 200 OF OFFSETS. Each of the numbers in the column of latitudes is twice the mean latitude of two adjacent latitudes ; but at the most south- erly point the latitude is nothing ; hence the first difference of latitude is the first lat., and in like manner the last difference of lat. is the last latitude. It is also to be remarked that the first station used in this table is not the first station in the actual survey, but the most southerly point of the survey, as calculated by the foregoing method from Table I. SECTION IV. OF OFFSETS. IN taking surveys it is unnecessary and unusual to make a station at every angular point, because the field-work can be taken with much greater expedition by using offsets and in- tersections, and with equal certainty ; especially where creeks, &c. bound the survey. Offsets are perpendicular lines drawn or measured from the angular points of the land, that lie on the right or left-hand to the stationary distance, thus : Let the black lines represent the boundaries of a farm or township ; and let 1 be the first station : then if you have a good view to 2, omit the angular points between 1 and 2, and take the bearing and length of the stationary line 1, 2, and in- sert them in your field-book ; but in chaining from 1 to 2, stop at d opposite the angular point , and in your field-book insert the distance from 1 to d, which admit to be 4ch. 25/., as well as the measure of the offset ad, which admit to be Ich. 12/., thus : by the side of your field-book, in a line with the first station, Say at 4ch. 25/. L. Ich. 12/., that is, at 4ch. 251. there is an offset to the left-hand of Ich. 121. This done, proceed on your distance line to e opposite to the angle &, and measure eb ; supposing then le to be 7ch. 40/., and eb 3ch. 401., say (still in a line with the first station in your field-book) at 7ch. 401 L. 3ch. 401, that is, at 7ch. 401 there is an offset to the left of 3cA. 40/. ; proceed then with your distance line to/ opposite to the angle c, and measure fc'j suppose then If to be I3ch. and/c Ich. 25/., say, in the same line as before, at 13cA. L. leh. 25L Then proceed from f to 2, and you will have the measure of the entire stationary line 1, 2, which insert in its proper column by the bearing. OF OFFSETS. 201 In taking offsets, it is necessary to have a perch chain, or a staff of half a perch, divided into links for measuring them ; for by tliis means the chain in the stationary line is undis- turbed, and the number of chains and links in that line from whence, or to which, the offsets are taken, may be readily known. Having arrived at the second station, if you find your view will carry you to 3, take the bearing from 2 to 3, and in mea- suring the distance line, stop at I opposite g ; admit 21 to be 4ch. 10/., and the offset Ig Ich. 20Z., then in a line with the second station in your fiefd-book, say at 4ch. 10/. R. Ich. 20/., that is, the offset is a right-hand one of Ich. 201. Again, at fn, which suppose to be Wch. 251. from 2, take the offset mh of Ich. 15/.,and in a line with the second station, say at lOeA. 251. R, Ich. 151. -In the same line, when you come to the boundary at t, insert the distance 2z, 13cA. 10/., thus, at 13cA. WL ; that is, at 13cA. 10/. there is no offset. At n, which is I5ch. from 2, take the offset nk 45/., and still opposite to the second station say at I5ch. L. 451. Let the line 3, 6 represent the boundary which by means of water, briers, or any other impediment, cannot be measured. In this case make one or more stations within or without the land, where the distances may be measured, and draw a line from the beginning of the first to the end of the last distance, thus : make stations at 3, 4, and 5, take the bearings, and mea- suring the distances as usual, which insert in your field-book, and draw a mark like one side of a parenthesis, from the third to the fifth station, to show that a line drawn from the third station to the farthest end of the fifth stationary line will ex- press the boundary. Thus, No. Sta. Deg. ch. L [3 172^ 5.45 4 200 13.25 5 250 3.36 Suppose the point p of the boundary to be inaccessible by means of the lines 6p or p7 being overflowed, or that a quarry, furze, &c. might prevent your taking their lengths : in this case take the bearing of the line 6, 7, which insert opposite to the sixth station in your field-book with the other bearing ; then direct the index to the point p 1 and insert its bearings on the left side of the field-book, opposite to the sixth station, annexing thereto the words Int. for boundary ; and having measured and inserted the distance 6, 7, set the index in the direction of the line 7p, and insert its bearing on the left of the seventh station 13 202 OF OFFSETS. of the field-book, annexing thereto the words ipt. for boundary ? the crossing or inter section of these two bearings will deter- mine the point p, and of course the boundary 6j7 is also de- termined. If your view will then reach in the first station, take its bear- ing, stationary line, and offsets as before, and you have the field-book completed. Thus, The Field-book. Remarks and Inter. N. St. Deg. ch. I. OFFSETS. 318 Int. to a tower 1 358 22.12 At 4ch. 25LL.lch. 121 at-7cA.40Z.L.3cA.40/. at 13cA. L. Ich. 251 231|Int. to ditto 2 297f 22.12 At4cA. 10/.R. lcA.20Z. at lOcA. 251 R. IcA. 511. at 13cA. IQL 0. at \5ch. L. 45Z. r 3 1721 5.45 4 200 13.25 I 5 250 3.36 1551 Int. for bound. 6 125 15.15 Ktlch.2QLL.2ch.20L 274 Int. for ditto. 7 1051 15.10 at7cA.45/.L.2cA.32Z. atllcA.25Z.O.atl2cA. 251. R. 36Z. Close at the first station. If you would lay down a tower, house, or any other remark- able object in its proper place, from any two stations take bearings to the object, and their intersection will determine the place whe^p you are to insert it, in the manner that the tower is set out in the figure, from the intersection taken at the first and second stations of the above field-book. A protraction of this will render all plain, on which lay off all your offsets and intersections, and proceed to find the con- tents by any of the methods in section the fourth. OF OFFSETS. 203 . The'foregoing Field-book may be otherwise kept, thus : Remarks and Intersection. No. St. Deg. L. hand Offset. ch.L Dist. ch.l R.hand Offset. ch. I 318 Int. to a tower - 1 358 1.12 4.25 3.40 7.40 1.25 13.00 232^ Int. for ditto - - 22.12 2 297 4.10 10.25 1.20 1.15 13.10 '' ' **-* * ; ' j 0.45 15.00 21.21 3 4 1721 200 5.45 13.25 5 250 ** 3.36 155^ Int. for boundary 274 Int. for boundary 6 125 15.15 7 105 2.20 2.32 1.20 7.45 11.25 12.25 0.36 15.10 , How to cast up offsets by the pen. PL. 11. Jig. 2. 1, 2 l/=2/,2/ -le=fe, leld=ed. Then Id X da=lda, and ed X (da+eb) =beda, %(eb+fc) X fe=befc, and 2/Xi/c=c/"9; the sum of all which will be Io>c21 ; the area contained between the stationary line 1, 2 and the boundary Iac2. In the same manner you may find the area of ZihgZ, of j"3i,j as well as what is without and withinside of the stationary line 7, 1. If therefore the left-hand offsets exceed the right-hand ones, it is plain the excess must be added to the area within the sta- tionary lines ; but if the right-hand offsets exceed the left-hand ones the differencs must be deducted from the said area, if the OF OFFSETS. ground be kept on the right-hand, as we have all along sup- posed ; or in words thus : To find the contents of offsets. 1. From the distance line take the distance to the preceding offset, and from that the distance of the one preceding it, &c. in four-pole chains ; so will you have the respective distances from offset to offset, but in a retrograde order. 2. Multiply the last of these remainders by half the first offset, the next by half the sum of the first and second, the next by half the sum of the second and third, the next by half the sum of the third and fourth, &c. The sum of these will be the area produced by the offsets. Thus, in the foregoing field-book the first stationary line is 22cA. 12/., or llch. 12/. of four-pole chains. See the figure. ch. L ch. L ch. L From 11. 12 = 1, 6.50 = 1/ 3.90 = le Take 6.50=1/ 3.90=le 2.25=ld 4.62=2/ 2.60=e/ l.Q5=ed ch.l 1<2=2.25 X 32?., half the first offset, .7200 ed = 1.65 X IcA. 26Z., half the sum of the 1st and 2d, = 2.0790 e f =2.60 X IcA. 32Z M half the sum of the 2d and 3d, = 3.4320 2/=4.62 X 37/., half the last offset, = 1.7094 Contents of left offsets on the first distance in ) square four-pole chains, > In like manner the rest are performed. The sum of the left-hand offsets will be 14.0856 And the sum of the right-hand ones 3.6825 Excess of left-hand offets in sq. four-pole chains, 10.4031 Acres 1.04031 Perches 6.4496 Excess of left-hand offsets above the right-hand ones, 1 A. OR. 6P., to be added to the area within the stationary lines. OF OFFSETS. 205 SECTION V. To find the area of a piece of ground by intersections only, when all the angles of the field can be seen from any two stations on the outside of the ground. PL. I*, fig. 1. Let ABCDEFG be a field, H and I two places on the out- side of it from whence an object at every angle of the field may be seen. Take the bearing and distance between H and /; set that at the head of your field-book, as in the annexed one. Fix your instrument at H, from whence take the bearings of the several angular points ABCD, &c. as they are here represented by the lines HA, HB, HC, HD, add Angle C40 30', sine 9.81254 ) Side BG 61.26 per. Side BC 60 per. Angle B 100 0', sine 2)3619.8, log. As CBG= 1809.9 Co. Ar. 1.78718 1.77815 > add 9.99335 3.55868 Isto jEjPG?= 2913.4, log. Soissq.BG61.26, log. To sq. FG 77.72, Ans. BF= 16.46 perches 6.74235 3.46440 1.78718 1.78718 2)3.78111 1.89055 add By the application of this method a tract of land may be divided accurately, in any proportion, by a line running in any assigned direction. Note. When the practitioner would wish to be very accu- rate, it will be much better to work by four-pole chains and links than by perches and tenths ; one-tenth of a perch square being equal to 6^ square links. '218 DIVISION OF LAND. EXAMPLE V. The following Field-notes (from A. BURNS) are of a piece of land, which is proposed, as an example, to be divided into three equal parts by two right lines running from the sixth and seventh stations : and proved by calculating the contents of the middle part. St. Bearing. 4-P. eh. 1 N.E. 561 21.60 2 N.E. 26i 13.44 3 S.E. 711 18.96 4 S.E. 261 13.44 5 S.W. 711 18.96 6 S.E. 45 8.47 7 S.E. 63i 13.44 8 N.E. 45 8.47 9 S.E. 261 13.44 10 S.W. 45 8.47 11 S.W. 63 13.44 12 N.W. 76 24.73 13 N.W. 36| 30.00 Area, 167A. 1R. 24P. EXAMPLE VI. PL. 8. Jig. 5. The plot ABCDEFGHA is proposed to be divided geometri- cally, in the proportion of 2 to 3, by a right line from a given point in any boundary or angle thereof, suppose the point D. Reduce the plot to the triangle cDe, as already taught; divide the base ce in the point N, so that cN be to Ne in the ratio of 2 to 3, by prob. 14 ; draw DN, and it is done. DIVISION OF LAND. 219 EXAMPLE VH. PL. 12. fig. 3. Example second may likewise be performed, geometrically. Produce CD both ways for a base, and reduce the whole to a triangle, making / the vertical point ; then bisect the base in N, and draw IN. But, Notwithstanding this geometrical method is demonstrably true in theory, it is not as safe, on practical occasions requiring accuracy, as the calculation, even when performed with the greatest care ; for which reason we will not enlarge on it here. EXAMPLE vm. Suppose 864 acres to be laid out in form of a right-angled parallelogram^ of which the sides shall be in proportion as 5 to 3 ; required their dimensions. For the greater side, multiply the area by the greater num- ber of the given proportion, and divide by the less, or, for the less side, multiply by the less number, and^ivide by the greater ; the square root of the quotient will be the side required : thus, 864A.= 138240P. 1.38240 5 3 3)691200 5)414720 Ans. V 230400=480. V 82944=288 EXAMPLE IX. If it be required to lay out any quantity of ground, suppose 47 A. 2R. 16P., in form of a parallelogram, of which the length is to exceed the breadth by a given difference, for instance, 80 perches, then add the square of half this difference to the area, and take the square root of the sum ; to which add half the difference for the greater side, and subtract it therefrom for the less : thus, 47A. 2R. 16P.=7616 perches, 1600 V 9216=96 1600 half diff. ; add and subt. 40 ( the length =136 ( the breadth=56 Ans K2 220 OF SURVEYING HARBOURS, &c. Any proposed quantity of ground may be laid out or enclosed in the form Square . . by prob. 2d, \ Parallelogram, one side given, by prob. 4th, f . Triangle of a given base, . by prob. 7th, f Circle by prob. 13th, ) It is sometimes most convenient, when land is to be laid out adjacent to a creek, river, or other crooked boundary, to measure offsets to the angles or bending thereof, from a right line or lines taken near such boundary, and to deduct the area of these offsets from the given quantity, and then to lay off the remainder from the right line or lines, in the desired form. In laying out new lands, attention must be paid to the allow- ance for roads, as exemplified in prob. 14th. SECTION VIII. OF SURVEYING HARBOURS, SHOALS, SANDS, &c. PL. 19. fig. 1. THERE are three methods whereby this may be performed ; for the observations may be made either on the water or on the land. Those made on the water are of two kinds ; one by the log-line and compass (as in plane sailing measuring) the course and distance round the sand ; and then to be plotted as a large wood, or any enclosure taken by the circumferentor. This method I omit, for two reasons : first, because it is to be deduced from the writers of navigation ; and, secondly, be- cause the distances thus measured are liable to the errors of currents, which generally attend shoals or sands near the shore. . The second method, when there are no distances to be measured on the water, though still there is one inconvenience, common also to the former, because the bearings or observa- tions are to be taken on that unstable element (an error scarce mentioned by practical artists), I shall briefly hint at ; and so rather choose a third, which is liable to neither of these imper- fections. Let a boat be manned out with a signal flag, a log and line, lead and line, and, to observe the bearings of any landmark, a compass with sights. Take two or more objects or places, as A, B, C, on the OF SURVEYING HARBOURS, Answer. Perp. desc. 2 17.6 links= 143.6ft. J With the angular elevation or depression in the third column, and the oblique distance in the fourth (as course and distance) are found the horizontal distance in the fifth, and the perpen- dicular ascent or descent on the sixth, for each station (as dif- ference of latitude and departure) : then, with the bearing and horizontal distance, we get the difference of latitude and de- parture in the last two columns. The ascents and descents in the sixth column are distin- guished by the letters E and D in the third, signifying eleva- tion or depression ; and being added separately, the difference of their sums is set at the bottom of the column with the name of the greater, and shows the perpendicular descent of B below the horizontal level of A. In like manner the northings and southings in the seventh column are distinguished by the letters N and S in the second, &c. PROMISCUOUS QUESTIONS. 1. The perambulator, or surveying wheel, is so contrived as 230 PROMISCUOUS QUESTIONS. to turn just twice in the length of a pole, or 16 feet; what then is the diameter ? Ans. 2.626 feet. 2. Two sides of a triangle are respectively 20 and 40 perches ; required the third, so that the contents may be just an acre. Ans. either 23.099 or 58.876 perches. 3. I want the length of a line by which my gardener may strike out a round orangery that shall contain just half an acre of ground. Ans. 27f yards. 4. What proportion does the arpent of France, which con- tains 100 square poles of 18 feet each, bear to the American acre, containing 160 square poles of 16.5 feet each, considering that the length of the French foot is to the American as 16 to 15? Ans. as 512 to 605. 5. The ellipse in Grosveiiur Square measures 840 links the longest way, and 612 the shortest, within the rails : now the wall being 14 inches thick, it is required to find what quantity of ground it encloses, and how much it stands upon. Ans. It encloses 4 A. 6P., and stands on 1760^ square feet. 6. Required the dimensions of an elliptical acre with the ..greatest and least diameters in the proportion of 3 to 2. Ans. 17.479 by 11. 653 perches. 7. The paving of a triangular court at ISd. per foot, came to WOl. The longest of the three sides was 88 feet: what then was the sum of the other two equal sides 1 Ans. 106.85 feet. 8. In 110 acres of statute measure, in which the pole is 161 feet, how many Cheshire acres, where the customary pole is 6 yards, and how many of Ireland, where the pole in use is 7 yards ? Ans. 92A. 1R. 28P. Cheshire ; 67A. 3R. 25 P. Irish. 9. The three sides of a triangle containing 6A. 1R. 12P. are in the ratio of the three numbers 9, 8, 6, respectively ; re- quired the sides. Ans. 59.029, 52.47, and 39.353. 10. In a pentangular field, beginning with the south side, and measuring round towards the east, the first or south side is 2735 links, the second 3115, the third 2370, the fourth 2925* and the fifth 2220 ; also the diagonal from the first angle to the third is 3800 links, and that from the third to the fifth 4010 ; required the area of the field. Ans. 117A. 2R. 28P. 11. Required the dimensions of an oblong garden containing three acres, and bounded by 104 perches of pale fence. Ans. 40 perches by 12. 12. How many acres are contained in a square meadow, the diagonal of which is 20 perches more than either of its sides t Ans. 14A. 2R. IIP. INTRODUCTORY PRINCIPLES. 23t 13. If a man six feet high travel round the earth, how much greater will be the circumference described by the top of his head than by his feet? Ans. 37.69 feet. N. B. The required difference is equal to the circumference of a circle 6 feet radius, let the magnitude of the earth be what it may. 14. Required the dimensions of a parallelogram containing 200 acres, which is 40 perches longer than wide. Ans. 200 perches by 160. 15. What difference is there between a lot 28 perches long by 20 broad, and two others, each of half the dimensions ? Ans. 1A. 3R. PART III. Containing the astronomical methods of finding the latitude, variation of the compass, $c., with a description of the instruments used in these operations. SECTION I. INTRODUCTORY PRINCIPLES. DAY and night arise from the circumrotation of the earth. That imaginary line about which the rotation is performed is called the axis, and its extremities are called poles. That towards the most remote parts of Europe is called the north pole, and its opposite the south pole. The earth's axis being produced will point out the celestial poles. The equator is a great circle on the earth, every point of which is equally distant from the poles ; it divides the earth into two equal parts, called hemispheres : that having the north pole in its centre is called the northern hemisphere, and the other the southern hemisphere. The plane of this circle being produced to the fixed stars will point out the celestial equator, or equinoctial. The equator, as well as all other great circles of the sphere, is divided into 360 equal parts, called degrees ; each degree is divided into 60 equal parts, called minutes ; and the sexagesimal division is continued. Note.^- The ancients, having no instruments by which they could make observations with any tolerable degree of accuracy t supposed the length of the year, or annual motion of the earth,, to be completed in 360 days : and hence arose the division of 232 INTRODUCTORY PRINCIPLES. the circumference of a circle into the same number of equal[ parts, which they called degrees. The meridian of any place is a semicircle passing througn 1 ' that place, and terminating at the poles of the equator. The other half of this circle is called the opposite meridian. The latitude of any place is that portion of the meridian of that place which is contained between the equator and the given place ; and is either south or north, according as the given place is in the northern or southern hemisphere, and there- fore cannot exceed 90. The parallel of latitude of any place is a circle passing through that place parallel to the equator. ( The difference of latitude between any two places is an arch of a meridian intercepted between the corresponding paral- lels of latitude of those places. Hence, if the places lie be- tween the equator and the same pole, their difference of lati- tude is found by subtracting the less latitude from the greater ; but if they are on opposite sides of the equator, the difference of latitude is equal to the sum of the latitudes of both places. The first meridian is an imaginary semicircle, passing through any remarkable place, and is therefore arbitrary. Thus, the British esteem that to be the first meridian which passes through the royal observatory at Greenwich ; and the French reckon for their first meridian that which passes through the royal observatory at Paris. Formerly many French geogra- phers reckoned the meridian of the island of Ferro to be their first meridian; and others, that which was exactly 20 de- grees to the west of the Paris observatory. The Germans, again, considered the meridian of the Peak of Teneriffe to be the first meridian. By this mode of reckoning, Europe, Asia, and Africa are in east longitude, and North and South America in west longitude. At present the first meridian of any coun- try is generally esteemed to be that which passes through the principal observatory, or chief city, of that country. i The longitude of any place is that portion of the equator which is contained between the first meridian and the meridian of that place ; and is usually reckoned either east or west, ac- cording as the given place is on the east or west side of the first meridian; and, therefore, cannot exceed 180. The difference of longitude between any two places is the intercepted arch of the equator between the meridians of those places, and cannot exceed 180. There are three different horizons, the apparent, the sensi- ble, and the true. The apparent or visible horizon is the ut^ most Apparent view of the sea or land} the sensible is a plane INTRODUCTORY PRINCIPLES. 233 passing through the eye of an observer, perpendicular to a plumb-line hanging freely ; and the true or rational horizon is a plane passing through the centre of the earth, parallel to the sensible horizon. ; Altitudes observed at sea are measured from the visible horizon. At land, when an astronomical quadrant is used, or when observations are taken with a Hadley's quadrant by the method of reflection, the altitude is measured from the sensible horizon ; and in either case the altitude must be reduced to the true horizon. i The zenith of any given place is the point immediately above that place, and is, therefore, the elevated pole of the horizon. The nadir is the other pole, or point diametrically opposite. i A vertical is a great circle passing through the zenith and nadir ; and therefore intersecting the horizon at right angles. The altitude of any celestial body is that portion of a ver- tical which is contained between its centre and the true hori- zon. The meridian altitude is the distance of the object from the true horizon, when on the meridian of the place of obser- vation. When the observed altitude is corrected for the de- pression of the horizon and the errors arising from the instru- ment, it is called the apparent altitude ; and when reduced to the true horizon, by applying the parallax in altitude, it is called the true altitude. Altitudes are expressed hi degrees and parts of a degree. The zenith distance of any object is its distance from the zenith, or the complement of its altitude. , The decimation of any object is that portion of its meridian which is contained between the equinoctial and the centre of the object ; and is either north or south according as the star is between the equinoctial and the north or south pole. The ecliptic is that great circle in which the annual revolu- tion of the earth round the sun is performed. It is so named because eclipses cannot happen but when the moon is in or near .. that circle. The inclination of the ecliptic and equinoctial is at present about 23 28' ; and by comparing ancient with mod- ern observations, the obliquity of the ecliptic is found to be diminishing which diminution, in the present century, is about half a second yearly. The ecliptic, like all other great circles of the sphere, is di- vided into 360 ; and is further divided into twelve equal parts, called signs : each sign, therefore, contains 30. The names and characters of these signs are as follows ; 234 INTRODUCTORY PRINCIPLES. Aries, Taurus, Gemini, Cancer, ss Leo, i Virgo, UK Libra, ess Scorpio, TT], Sagittarius, Capricornus, Aquarius, Pisces, Since the ecliptic and equinoctial are great circles, they therefore bisect each other in two points, which are called the equinoctial points. The sun is in one of these points in March, and in the other in September ; hence, the first is called the vernal, and the other the autumnal equinox and that sign which begins at the vernal equinox is called Aries. Those points of the ecliptic which are equidistant from the equinoc- tial points are called the solstitial points ; the first the summer, and the second the winter solstice. That great circle which passes through the equinoctial points and the poles of the earth is called the equinoctial colure ; and the great circle which passes through the solstitial points and the poles of the earth is called the solstitial colure. When the sun enters Aries it is in the equinoctial, and therefore has no declination. From thence it moves forward in the ecliptic, according to the order of the signs, and ad- vances towards the north pole, by a kind of retarded motion, till it enters Cancer, and is then most distant from the equinoc- tial ; and moving forward in the ecliptic, the sun apparently recedes from the north pole with an accelerated motion till it enters Libra, and, being again in the 'equinoctial, has no decli- nation ; the sun, moving through the signs Libra, Scorpio, and Sagittarius, enters Capricorn ; and then its south declination is greatest, and is, therefore most distant from the north pole ; and moving forward through the signs Capricorn, Aquarius, and Pisces, agajn enters Aries : hence a period of the seasons is completed, and this period is called a solar year. The signs Aries, Taurus, Gemini, Cancer, Leo, and Virgo are called northern signs, because they are contained in that part of the ecliptic which is between the equinoctial and north pole ; and, therefore, while the sun is in these signs, its decli- nation is north : the other six signs are called southern signs. The signs in the first and fourth quarters of the ecliptic are called ascending signs, because while the sun is in these signs it approaches the north pole ; arid, therefore, in the northern, temperate, and frigid zones, the sun's meridian altitude daily increases ; or, which is the same, the sun ascends to a greater height above the horizon every day. The signs in the second and third quarters of the ecliptic are called descending signs. The tropics are circles parallel to the equinoctial, whos.e distance therefrom is equal to the obliquity of the ecliptic* THE QUADKAJNT. 23S The northern tropic touches the ecliptic at the beginning of Cancer, and is therefore called the tropic of Cancer ; and the southern tropic touches the ecliptic at the beginning of Capri- corn, and is hence called the tropic of Capricorn. Circles about the poles of the equinoctial, and passing through the poles of the ecliptic, are called polar circles ; the distance, therefore, of each polar circle from its respective pole is equal to the inclination of the ecliptic and equinoctial. That circle which circumscribes the north pole is called the arctic or north polar circle ; and that towards the south pole, the ant- arctic or south polar circle. That semicircle which passes through a star, or any given point of the heavens, and the poles of the ecliptic, is called a circle of latitude. The reduced place of a star is that point of the ecliptic which is intersected by the circle of latitude passing through that star. The latitude of a star is that portion of the circle of latitude contained between the star and its reduced place ; and is either north or south, according as the star is between the ecliptic and the north or south pole thereof. The longitude of a star is that portion of the ecliptic con- tained between the vernal equinox and the reduced place of the star. SECTION II. Description of the instruments requisite in astronomical observations THE QUADRANT. IT is generally allowed that we are indebted to John Hadley, Esq. for the invention, or at least for the first public account, of that admirable instrument commonly called Hadley's quad- rant, who in the year 1731 first communicated its principles to the Royal Society, which were by them published soon after in their Philosophical Transactions ; before this period the cross-staff and Davis's quadrant were the only instruments used for measuring altitudes at sea, both very imperfect, and liable to considerable error in rough weather ; the superior ex- cellence, however, of Hadley's quadrant soon obtained its. 236 THE QUADRANT. general use among seamen, and the many improvements this instrument has received from ingenious men at various times have rendered it so correct, that it is now applied, with the greatest success, to the important purposes of ascertaining both the latitude and longitude at sea or land. Figure 2, Frontispiece, represents a quadrant of reflection, the principal parts of which are, the octant or frame ABC (which is generally made of ebony, or other hard wood, and consists of an arch firmly attached to two radii or bars, which are strengthened and bound by the two braces in order to pre- vent it from warping), the graduated arch jBC, the index D, the nonius or vernier scale , the index glass jP, the horizon glasses G and H, the dark glasses or screens /, and the sight vanes K and L. The arch, or limb J5C, although only the eighth part of a circle, is, on account of the double reflection, divided into 90 degrees, numbered 0, 10, 20, 30, &c., from the right towards the left : these are subdivided into three parts, containing each 20 minutes, which are again subdivided into single minutes, by means of a scale at the end of the index. The arch extending from towards the right-hand is called the arch of excess. The index D is a flat brass bar, that turns on the centre of the instrument ; at the lower end of the index there is an ob- long opening ; to one side of this opening a nonius scale is fixed, to subdivide the divisions of the arch ; at the bottom or end of the index there is a piece of brass which bends under the arch, carrying a spring to make the nonius scale lie close to the divisions ; it is also furnished with a screw to fix the index in any desired position. Some instruments have an adjusting or tangent-screw, fitted to the index, that it may be moved more slowly, and with greater regularity and accuracy than by the hand ; it is proper, however, to observe, that the index must be previously fixed near its right position by the above-mentioned screw, before the adjusting screw is put in motion. The nonius is a scale fixed to the end of the index, for the purpose, as before observed, of dividing the subdivisions on the arch into minutes ; it sometimes contains a space of 7 degrees, or 21 subdivisions of the limb, and is divided into 20 equal parts ; hence*each division on the nonius will be one-twentieth part greater, that is, one minute longer, than the divisions on the arch ; consequently, if the first division of the nonius, marked 0, be set precisely opposite to any degree, the relative position of the nonius and the arch must be altered one minute, before the next division on the nonius will coincide THE QUADRANT. 237 with the next division on the arch, the second division will require a change of two minutes, the third of three minutes, and so on, till the 20th stroke on the nonius arrives at the next 20 minutes on the arch ; the on the nonius will then have moved exactly 20 minutes from the division whence it set out, and the intermediate divisions of each minute have been regularly pointed out by the divisions of the nonius. The divisions of the nonius scale are in the above case reckoned from the midflle towards the right, and frorh the left towards the middle; therefore the first 10 minutes are con- tained on the right of the 0, and the other 10 on the left. But this method of reckoning the divisions being found inconvenient, they are more generally counted beginning from the right- hand towards the left ; and then 20 divisions on the nonius are equal to 19 on the limb, consequently one division on the arch will exceed one on the nonius by one-twentieth part, that is, one minute. The on the nonius points out the entire degrees and odd twenty minutes subtended by the objects observed ; and if it coincides with a division on the arch, points out the required angle : thus, suppose the on the nonius stands at 25 degrees, then 25 degrees will be the measure of the angles observed ; if it coincides with the next division on the left-hand, 25 de- grees 20 minutes is the angle ; if with the second division beyond 25 degrees, then the angle will be 25 degrees 40 minutes ; and so on in every instance where the on the no- nius coincides with a division on the arch ; but if it does not coincide, then look for a division on the nonius that stands directly opposite to one on the arch, and that division on the nonius gives the odd minutes to be added to that on the arch nearest the right-hand of the on the nonius ; for example, suppose the index division does not coincide with 25 degrees, but that the next division to it on the nonius is the first coin- cident division, then is the required angle 25 degrees 1 minute ; if it had been the second division the angle would have been 25 degrees 2 minutes, and so on to 20 minutes, when the on the nonius would coincide with the first 20 minutes on the arch from 25 degrees. Again, let us suppose the on the nonius to stand between 50 degrees and 50 degrees 20 minutes, and that the 15th division on the nonius coincides with a division on the arch, then is the angle 50 degrees 15 minutes. Further, let the on the nonius stand between 45 degrees 20 minutes and 45 degrees 40 minutes, and at the same time the 14th division on the nonius stands directly opposite to a 238 THE QUADRANT. division on the arch, then will the angle be 45 degrees 34 minutes. The index glass F is a plane speculum, or mirror of glass quicksilvered, set in a brass frame, and so placed that the face of it is perpendicular to the plane of the instrument, and imme- diately over the centre of motion of the index. This mirror being fixed to the index moves along with it, and has its direc- tion changed by the motion thereof. This glass is designed to reflect the image of the sun, or any other object, upon either of the two horizon glasses, from whence it is reflected to the eye of the observer. The brass frame, with the glass, is fixed to the index by the screw 'Mj the other screw N serves to place it in a perpendicular position, if by any accident it has been put out of order. The horizon glasses G and H are two small speculums on the radius of the octant ; the surface of the upper one is par- allel to the index glass when the on the nonius is at on the arch ; these mirrors receive the rays of the object reflected from the index glass, and transmit them to the observer. The fore horizon glass G is only silvered on its lower half, the upper half being transparent, in order that the direct object may be seen through it. The back horizon glass H is silvered at both ends ; in the middle there is a transparent slit, through which the horizon may be seen. Each of these glasses is set in a brass frame, to which there is an axis ; this axis passes through the wood-work, and is fitted to a lever on the under side of the quadrant, by which the glass may be turned a few de- grees on its axis, in order to set it parallel to the index glass. To set the glasses perpendicular to the plane of the quad- rant there are two sunk screws, one before and one behind each glass : these screws pass through the plate on which the frame is fixed into another plate, so that by loosening one and tightening the other of these screws, the direction of the frame, with its mirror, may be altered, and thus be set perpendicular to the plane of the instrument. The dark glasses, or shades, /, are used to prevent the bright rays of the sun, or the glare of the moon, from hurting the eye at the time of observation ; there are generally three of them, two red, and one green. They are each set in a brass frame which turns on a centre, so that they may be used separately or together, as the brightness of the object may require. The green glass may be used also alone, if the sun be very faint ; it is likewise used in taking observations of the moon ; when these glasses are used for the fore observation, they are set THE QUADRANT. 230 immediately before the fore horizon glass, as in fig. 1, but in front of the other horizon glass at O when a back observation is made. The sight vanes K and L are pieces of brass, standing per- pendicular to the plane of the instrument : the vane K is called the fore sight vane, and L the back sight vane. There are two holes in the fore sight vane, the lower of which and the upper edge of the silvered part of the fore horizon glass are equi- distant from the plane of the instrument, and the other is oppo- site to the middle of the transparent part of that glass ; the back sight vane has only one hole, which is exactly opposite to the middle of the transparent slit in the horizon glass to which it belongs : but as the back observations are liable to many inconveniences and errors, we shall not give any direc- tions for their practice. The adjusting lever (fig. 3), which is fixed on the back of the quadrant, serves to adjust the horizon glass, by placing it, parallel to the index glass ; when this lever is to be used, the screw B must be first loosened, and when by the adjuster 4. Then add together the log. secant of the altitude ) . .. ., - - ^ r i T j ? rejecting their indices, the log. secant of the latitude ) J the log. co-sine of the half-sum, and the log. co-sine of the remainder. 5. Half the sum of these four logarithms will be the sine of an arch, which doubled will be the sun's true azimuth ; to be reckoned from the south in north latitude, and from the north in south latitude ; towards the east in the morning, and towards the west in the afternoon. 6. Then if the true and observed azimuths be both on the east or both on the west side of the meridian, their difference is the variation ; but if one be on the east and the other on the west side of the meridian, their sum is the variation : and to know if it be east or west, suppose the observer looking to- wards that point of the compass representing the magnetic azimuth ; then if the true azimuth be to the right of the mag- netic, the variation is east, but if the true be to the left of the magnetic the variation is west. EXAMPLE. November 2, 1812, in latitude 25 32' N. and longitude 75 W. the altitude of the sun's lower limb was observed to be 15 36', about 4h. 10m. P. M., his magnetic azimuth at that time being S. 58 32' W., and the height of the eye 18 feet ; re- quired the variation of the compass. Sun's dec. Nov. 2, at n. 14 48' S. Obs. alt. sun's lower limb 15 36* Com for long. 75 W. + 4 Semidiameter 16' > , . Co. for ti. 4h. 10m. af. n. -(- 3 Dip 4 J Reduced declination 14 55 90 00 Refraction Polar distance 104 55 True altitude 15 45 Altitude 15 45 - - Secant 0.01662 Latitude 25 32 - - Secant 0.04463 Sum Half 73 6 - - Co-sine 9.46345 Remainder 31 49 - - Co-sine 9.92929 32 14 - - Sine 9.72699 True azimuth S. 64 28 W. Mag. azimuth S, 68 32 W. Variation 5 56 east, because the true azimuth is to the light of the magnetic. VARIATION OF THE COMPASS. 247j To draw a true meridian line to a map, having the variation and mag- netical meridian given. On any magnetical meridian or parallel, upon which the map is pro- tracted, set off an angle from the north towards the east, equal to the de- grees or quantity of variation if it be westerly, or from the north towards the west if it be easterly, and the line which constitutes such an angle with the magnetical meridian will be a true meridian line. For if the variation be westerly, the magnetical meridian will be the quantity of vanation of the west side of the true meridian, but if easterly, on the east side ; therefore the true meridian must be a like quantity on the east side of the magnetical one when the variation is westerly, and on the west side when it is easterly. To lay out a true meridian line by the circumferentor. If the variation be westerly, turn the box about till the north of the needle points as many degrees from the flower-de-luce towards the east of the box, or till the south of the needle points the like number of degrees from the south towards the west, as are the number of degrees contained in the variation, and the index will be then due north and south ; therefore, if a line be struck out in the direction thereof, it will be a true meridian line. If the variation was easterly, let the north of the needle point as many degrees from the flower-de-luce towards the west of the box, or let the south of the needle point as many degrees towards the east, as are the number of degrees contained in the variation, and then the north and south of the box will coincide with the north and south points of the horizon, and consequently a line being laid out by the direction of the index will be a true meridian line. This will be found to be very useful in setting a horizontal dial, for if you lay the edge of the index by the base of the stile of the dial, and keep the angular point of the stile towards the south of the box, and allow the variation as before, the dial will then be due north and soufh, and in its proper situation, provided the plane upon which it is fixed be duly hori- zontal, and the sun be south at noon ; but in places where it is north at noon the angular point of the index must be turned to the north. How maps may be traced by the help of a true meridian line. If all maps had a true meridian line laid out upon them, it would be easy, by producing it, and drawing parallels, to make out field-notes ; and by knowing the variation, and allowing it upon every bearing, and having the distances, you would have notes sufficient for a trace. But a true meridian line is seldom to be met with ; therefore we are obliged to have recourse to the foregoing method. It is therefore advised to lay out a true meridian line upon every map. To find the difference between the present variation, and that at a time when a tract was formerly surveyed, in order to trace or run out the original lines. If the old variation be specified in the map or writings, and the present be known, by calculation or otherwise, then the difference is immediately seen by inspection ; but as it more frequently happens that neither is certainly known, and as the variation of different instruments is not always alike at the same time, the following practical method will be found to answer every purpose. 248 VARIATION OF THE COMPASS. Go to any part of the premises where any two adjacent corners are known ; and if one can be seen from the other, take their bearing ; which, compared with that of the same line in the former survey, shows the dif- ference. But if trees, hills, &c. obstruct the view of the object, run the I line according to the given bearing, and observe the nearest distance be- ,'tween the line so run and the corner, then, As the length of the whole line Is to 57.3 degrees,* So is the said distance To the difference of variation required. EXAMPLE. Suppose it be required to run a line which some years ago bore NE. 45, ^distance 80 perches, and in running this line by the given bearing, the corner is found 20 links to the left-hand ; what allowance must be made on each bearing to trace the old lines, and what is the present bearing of this particular line by the compass 1 P. Deg. L. As 80 : 57.3 : : 20 25 20 21000 1 146.0(0 34 f 60 2)68 [760.0 Answer, 34 minutes, or a little better than half a degree to the left- hand, is the allowance required, and the line in question bears N. 44 26'E. Note. The different variations do not affect the area in the calculation, as they are similar in every part of the survey. * 57.3 is the radius of a circle (nearly) in such parts as the circumference contains 360. THE END Harper's Stereotype Edition., TABLE OF LOGARITHMS, OF LOGARITHMIC SIXES, AND A TRAVERSE TABLE. DESCRIPTION OF THE TABLES. 1. LOGARITHMS of numbers are the indices that denote the different powers to which a given number must be raised to produce those numbers. 2. If a be the given number, whose indices and powers are to be considered, then a* being put equal to n, a, the given number, or root, is called the base of the system of logarithms, n the number whose logarithm is considered, and a?, the loga- rithm of that number. 3. Any number, except 1, may be taken for the base of a system of logarithms. In the system in general use, the base is 10 ; and this system affords the greatest facilities in calcula- tions, because 10 is the base of the common numeration, both in whole numbers and decimal fractions. , > 4. Taking a z =n, we have, a:=log. n ; and putting a^= OT, gives, y=log. m. If the equations, a z =7, and ay=-m, be multiplied together, member by member, we have, a*Xay= nXwi? or a z +y=7iXwi. In this expression, x-{-y is the loga- rithm of nXm (2) ; from which we conclude, that the sum of the logarithms of any two numbers, is equal to the logarithm of their product. 5. If the equations o z =n, c^=wi, be divided, member by member, =-; or a z y=-. In this expression, a? y is the cP m m logarithm of - (2) ; from which we conclude, that the dijfer- m ence of the logarithms of any two numbers^ is equal to t\e logo rithm of their quotient. 4 DESCRIPTION OF 6. If in the equation a*=ra, both members be raised to the m\h power, a mx = n m . Here, mx is the logarithm of n m ; from which it appears, that the logarithm of the power of any number, is equal to the logarithm of that number, multiplied by the index of that power. 7. If the mth root of both members of the equation a x n, "!.. I be taken, then, a m =n m ; but- is the logarithm of n m ; from m which it appears, that the logarithm of the. root of any number, is equal to the logarithm of that number divided by the index of the root. 8.. It is evident, that the results obtained in the last four arti- cles are equally true, whether the logarithms be positive or nega- tive. These results show,~that the addition of logarithms cor- responds to the multiplication of their numbers ; the subtraction of logarithms, to the division of numbers ; their multiplication, to the raising of powers ; and their division, to the extraction of roots. 9. Returning to the equation a x n, in which a?=log. n, and applying it to the common^ system, in which the base is 10, we have, (10) 4 : (10)3 : (10)2 . ( 10 )i : (10) : (10)- 1 (10)~ 2 : (10)- 3 : (10) 10000:1000:100: 10 : 1 : 0.1 4:3 : 2 : 1 : : 1 0.01 : 0.001 : 0.0001 num 2 : 3 : 4 log. Unity being the number which divides the whole numbers from the decimal fractions, we shall begin with it, and explain some properties of the logarithms of whole numbers. The logarithm of 1 is ^ and this is the case in all systems, for whatever be the base, its power is 1 : but the index of the base is the logarithm of the power ; therefore, is the loga- rithm of 1. As the logarithms increase with the numbers from unity upwards, tne logarithms of all numbers, which are greater than 1, and less than 10, are greater than 0, and less than 1 : their values are generally expressed by decimal fractions ; thus, the log. 2=0.301030. The logarithms of numbers greater than 10, and less than 100, lie between 1 and 2, and are gene- rally expressed by unity and a decimal fraction : thus, the log. 50 = 1.698970. The logarithms of numbers greater than 100, but less than 1000, are greater than 2, and less than 3, and are expressed - . THE TABLES. by uniting 2 with a decimal fraction: thus, the log. 126 = 2.100371. The whole number on the left of the decimal point is called the characteristic, or index of the logarithm. The number of units which it contains, is always one less than the number of places of figures in the number whose logarithm is taken. Thus, in the first case, for numbers between 1 and 10, there is but one place of figures, and the characteristic is 0. In the second case, for numbers between 10 and 100, there are two places, and the characteristic is 1. In the third case, for numbers between 100 and 1000, there are three places, and the characteristic is 2 ; and in like manner for any number of places whatsoever. TABLE OF LOGARITHMS. 10. If the logarithms of all the numbers between 1 and any given number, be calculated and arranged in a tabular form, such table is called a table of logarithms. The table annexed shows the logarithms of all numbers between 1 and 10,000. 11. The first column, on the left of each page of the table of logarithms, is the column of numbers, and is designated by the letter N; the logarithms of these numbers are placed directly opposite them, and on the same horizontal line. 12. To find, from the table, the logarithm of any whole number. If the number be less than 100, look on the first page of the table of logarithms, along the columns of numbers under N, until the number is found ; the number directly opposite it, in the column designated Log., is the logarithm sought. 13. When the number is greater than 100, and less than 10,000. Find, in the column of numbers, the first three figures of the given number. Then, pass across the page, in a horizontal line, into the columns marked 0, 1, 2, 3, 4, &c., until you come to the column which is designated by the fourth figure of the given number: to the four figures so found, two figures taken from the column marked 0, are to be prefixed. If the first four figures found stand opposite to a row of six figures in the column marked 0, the two figures from this column, which are to be prefixed to the four before found, are the first two on the 6 x DESCRIPTION OF left hand ; but, if the first four figures are opposite a line of only four figures, you are then 'to ascend the column, till you come to the line of six figures : the two figures at the left hand are to be prefixed, and then the decimal part of the logarithm is obtained ; to which prefix the characteristic (9), and you have the logarithm sought. In several of the column? designated 0, 1, 2, 3, 4, 5, &c., small dots are found. In such cases, a cipher must be written for each of those dots ; and the two figures, from the first column, which are to be prefixed, are found in the horizontal line directly below. Thus, the log. 2188 is 3.340047, the two dots being changed into two ciphers, and the 34 from the column 0, prefixed. The two figures from the column 0, must also be taken from the line below, if any dots shall have been passed over, in passing along the horizontal line : thus, the logarithm of 3098 is 3.491081, the 49 from the column being taken from the line 310. 14. If the number exceeds 10,000, or consists of fve or more places of figures, consider all the figures after the fourth from the left hand, as ciphers. Find, from the table, the logarithm of this number, which will be the same as the logarithm of the first four places, excepting the characteristic. Take from the last column on the right of the page, marked D, the number on the same horizontal line with the logarithm, and multiply this number by the numbers that have been considered as ciphers: then, cut off from the right-hand as many places for decimals as there are figures in the multiplier, and add the product, so obtained, to the first logarithm, for the logarithm sought. Let it be required to find the logarithm of 672887. The log. of 672800 is found, on the llth page of the table, to be 5.827886, by prefixing the characteristic 5. The number cor- responding in the column D is 65, which being multiplied by 87, the figures regarded as ciphers, gives 5655 ; then, pointing off two plaees for decimals, the number to be added is 56.55. This number being added to 5.827886, gives 5.827942 for the logarithm of 672887 ; the decimal part, .55, being omitted. This method of finding the logarithms of numbers from the table, supposes that the logarithms are proportional to their respective numbers, which is not rigorously true. In the example, the logarithm of 672800 is 5.827886 ; of 672900, a number greater by 100, 5.827951 : the difference of the THE TABLES. 7 logarithms is 65. Now, as 100, the difference of the numbers^ is to 65, the difference of their logarithms, so is 87, the differ- ence between the given number and the least of the numbers used, to the difference of their logarithms, which is 56.55 : this difference bfeing added to 5.827886, the logarithm of the less number, gives 5.827942 for the logarithm of 672887. The use of the column of differences is therefore manifest. 15. The logarithm of a fractional number is easily found, from what has already been said. If the fractional number exceeds unity, as y/, its logarithm is equal to the log. 136 log. 25 (5). If it be less than unity, as T y^, its logarithm may be written under two different forms. First, the log. j-/j = log. 15 log. 125 (log. 125 log, 15)= (2.096910 1.176091) = 0.920819; the number 0.920819 being entirely negative. In the equation log. 15 log. 125 = 0.920819, if the log. 125 be transposed to the second member, the log. 15 =log. 1250.920819. Let N' be the number whose loga- rithm is 0.920819, and N the number whose logarithm is -f 0.920819 ; then, the log. 15 log. 125=log. N'. Since the difference of logarithms of the two numbers is equal to the 125 logarithm of their quotient (5), the log. 15=log. -. But if the logarithms are equal, the numbers themselves are equal ; therefore, 15=, or = =N', since is the number N 125 N 125 whose logarithm is 0.920819. As the same reasoning holds true for any numbers whatever, we conclude, that the number answering to a negative logarithm, is the reciprocal of the number answering to this same logarithm regarded as positive. 16. To find the logarithm of a proper fraction under another form. Let the fraction be N = T 1 F 2 2 5 T . Let this fraction be multiplied by 10, 100, 1000, 10,000, or such higher power of 10, as to make it greater than unity. If it be multiplied by 10,000, we shall have, 10,OOON= ! 9 and taking the oo27 logarithms, 4+ log. N= 4 -flog. 125 -log. 5627 =4 -f- 2.096910 3.750277 = 6.096910 3.750277=2.346633: hence the log. N =2.346633 4=2".346633, the minus sign belonging to 8 DESCRIPTION OF *v X the characteristic only, and not to the decimal part of the loga- rithm. In such case, the minus sign is written above the number ; thus, 2. If, then, it be required to express the loga- rithm of a fractional number, under such ^ form that the characteristic only shall be negative, add such a whole number to the logarithm of the numerator, as will make it greater than the logarithm, of the denominator ; from this sum, subtract the logarithm of the denominator, and from the remainder, the whole number which was added to the logarithm of the numerator : the remainder is the logarithm sought. 17. To find the logarithm of a decimal number. If the num- ber be composed of a whole number and a decimal, such as, 36.78, it may be put under the form \-f-log. cotang. 5= log. tang, a +log. cotang. a; or, log. tang, b log. tang. a=log. cotang. b log. cotang. a. 26. Now, if it were required to find the logarithmic sine of an arc expressed in degrees, minutes, and seconds, we have only to find the degrees and minutes as before ; then multiply the corresponding tabular number by the seconds, cut off two places to the right-hand for decimals, and then add the product to the number first found, for the sine of the given arc. Thus, if we wish the sine of 40 26' 28". The sine 40 26' 9.811952 Tabular difference = 247 Number of seconds = 28 Product = 69.16, which being added = 69.16 Gives for the sine of 40 26' 28" = 9.812021.16 The tangent of an arc, in which there are seconds, is found in a manner entirely similar. In regard to the cosine and cotangent, it must be remembered, that they increase while the arcs decrease, and decrease while the arcs are increased ; con- sequently, the proportional numbers found for the seconds must be subtracted, not added. Ex. To find the cosine 3 40' 40". Cosine 3 40' 9.999110 Tabular difference = 13 Number of seconds = 40 Product = 5.20, which being subtracted = 5.80 Gives for the cosine of 3 40' 40" = 9-999104.20 27. To find the degrees, minutes, and seconds answering to any given logarithmic sine, cosine, tangent, or cotangent. THE TABLES* 13 Search in the table, and in the proper column, until the number be found ; the degrees are shown either at the top or bottom of the page, and the minutes in the side columns, either at the left or right. But if the number cannot be exactly found in the table, take the degrees and minutes answering to the nearest less logarithm, the logarithm itself, and also the corres- ponding tabular difference. Subtract the logarithm taken from the table from the 0456 0584 0712 0840 0968' 1096 1223 1351 128 N. 1 1 1 2 3 4 5 | 6 7 8 9 D. A TABLE OF LOGARITHMS FKOM 1 TO 10,000. N. 1 2 | 3 4 | 5 6 | 7 | 8 | 9 | D. 340 531479 1607 1734 1862 1990 2117 2245 2372 2500 2627 128 341 2754 2882 3009 3136 3264 3391 3518 3645 3772 3999 127 342 4026 4153 4280 4407 4534 4661 4787 4914 5041 5167 127 343 5294 5421 5547 5674 5800 5927 6053 6180 6306 6432 126 344 6558 6685 6811 6937 7063 7189 7315 7441 7567 7693 126 345 7819 7945 8071 8197 8322 8448 8574 8699 8825 8951 126 346 9076 9202 9327 9452 9578 9703 9829 9954 ..79 .204 125 347 540329 0455 0580 0705 0830 0955 1080 1205 1330 1454 125 348 1579 1704 1829 1953 2078 2203 2327 2452 2576 2701 125 349 2825 2950 3074 3199 3323 3447 3571 3696 38ro 3944 124 350 544068 4192 4316 4440 4564 4688 4812 4936 5060 5183 124 351 5307 5431 5555 5678 5802 5925 6049 6172 6296 6419 124 352 6543 6666 6789 6913 7036 7159 7282 7405 7529 7652 123 353 7775 7898 8021 8144 8267 8389 8512 8635! 8758 8881 123 354 9003 9126 9249 9371 9494 9616 9739 9861 9984 .106 123 355 550228 0351 0473 6595 0717 0840 0962 1084 1206 1328 122 356 1450 1572 1694 1816 1938 2060 2181 2303 2425 2547 122 357 2668 2790 2911 3033 3155 3276 3398 3519 3640 3762 121 358 3883 4004 4126 4247 4368 4489 4610 4731 4852 4973 121 359 5094 5215 5336 5457 5578 5699 5820 5940 6061 6182 121 360 556303 6423 6544 6664 6785 6905 7026 7146 7267 7387 120 361 7507 7627 7748 7868 7988 8108 8228 8349 8469 8589 120 362 8709 8829 8948 9068 9188 9308 9428 9548 9667 9787 120 363 9907 ..26 .146 .265 .385 .504 .624 .743 .863 .982 119 364 561101 1221 1340 1459 1578 1698 1817 1936 2055 2174 119 365 2293 2412 2531 2650 2769 2887 3006 3125 3244 3362 119 366 3481 3600 3718 3837 3955 4074 4192 4311 4429 4548 119 367 4666 4784 4903 5021 5139 5257 5376 5494 5612 5730 118 368 5848 5966 6084 6202 6320 6437 6555 6673 6791 6909 118 369 7026 7144 7262 7379 7497 7614 7732 7849 7967 8084 118 370 568202 8319 8436 8554 8671 8788 8905 9023 9140 9257 117 371 9374 9491 9608 9725 9842 9959 ..76 .19b .309 .426 117 372 570543 0660 0776 0893 1010 1126 1243 1359 1476 1592 117 373 1709 1825 1942 2058 2174 2291 2407 2523 2639 2755 116 374 2872 2988 3104 3220 3336 3452 3568 3684 3800 3915 116 375 .4031 4147 4263 4379 4494 4610 4726 4841 4957 5072 116 376 5188 5303 5419 5534 5650 5765 5880 5996 6111 6226 115 377 6341 6457 6572 6687 6802 6917 7032 7147 7262 7377 115 378 7492 7607 7722 7836 7951 8066 8181 8295 8410 8525 115 379 8639 8754 8868 8983 9097 9212 9326 9441 9555 9669 114 380 579784 9898 ..12 .126 .241 .355 .469 .583 .697 .811 114 381 580925 1039 1153 1267 1381 1495 1608 1722 1836 1950 114 382 2063 2177 2291 2404 2518 2631 2745 2858 2972 3085 114 383 3199 3312 3426 3539 3652 3765 3879 3992 4105 4218 113 384 4331 4444 4557 4670 4783 4896 5009 5122 5235 5348 113 385 5461 5574 5686 5799 5912 6024 6137 6250 6362 6475 113 386 6587 6700 6812 6925 7037 7149 7262 7374 7486 7599 112 387 7711 7823 7935 8047 8160 8272 8384 8496 8608 8720 112 388 8832 8944 9056 9167 9279 9391 9503 9615 9726 9838 112 389 9950 ..61 .173 .284 .396 .507 .619 .730 .842 .953 112 59l) 591065 1176 1287 1399 1510 1G21 1732 1843 1955 2066 111 391 2177 2288 2399 2510 2621 2732 2843 2954 3064 3175 111 392 3286 3397 3508 3618 3729 3840 3950 4061 4171 4282 111 393 4393 4503 4614 4724 4834 4945 5055 5165 5276 5386 110 394 5496 5606 5717 5827 5937 6047 6157 6267 6377 6487 110 395 6597 6707 6817 6927 7037 7146 7256 7366 7476 7586 110 396 7695 7805 7914 8024 8134 8243 8353 8462 8572 8681 110 397 8791 8900 9009 9119 9228 9337 9446 9556 9665 9774 109 398 9883 9992 .101 .210 .319 .428 .537 .646 . 755 .864 109 399 600973 1082 1191 1299 1408 1517 1625 1734 1843 1951 109 N. 1 2 | 3 I 4 5 i 6 | 7 | 8 ! 9 I D. A TABLE OF LOGARITHMS FROM 1 TO 10,000. N. 1 1 2 3 4 5 | 6 7 ! 8 9 D 400 602060 2169 2277 2386 2494; 2H031 2711 2819 2928 3036' 108 401 3144 3253 3361 3469 3577 3686 3794 3902 4010 41181 108 402 4226 4334 4442 4550 465S 4766 4874 4982 5089 5197 108 403 5305 5413 5521 5628 5736 5844 551 6059 6166 6274 108 404 6381 6489 6596 6704| 68 11 6919 7026 7133 7241 7348 107 405 7455 7562 7669 7777 7884 7991 8098 8205 8312 8419 107 406 8526 8633 8740 8847 8954 9061 9167 9274 9381 9488 107 407 9594' 9701 9808 9914 ..21 .128 .234 .341 .447 .5541 107 408 409 61066010767 1723| 1829 0873 1936 0979J 1086 20421 2148 1192 2254 1298 2360 1405 2466 1511 2572 1617 2678 106 106 410 612/84 28901 2996 3102 3207 3313 3419 3525 3630 3736 106 411 3842 39471 4053 4159 4264 4370 4475 4581 4686 4792 106 412 4897 5003 5108 5213 5319 5424 5529 5634 5740 5845 105 413 5950 60551 6160 6265 6370 6476 6581 6686 6790 6895 105 414 7000 7105! 7210 7315 7420 7525 7629 7734 7839! 7943 105 415 8048 8153 8257 8362 8466 8571 8676 8780 8884 8989 105 416 9093 9198 9302 9406 9511 9615 9719 9824 9928 ..32 104 417 620136 0240 0344 0448 0552 0656 0760 0864 0968 1072 101 418 1176 1280 1384| 1488 1592 1695 1799 1903 2007 2110 104 419) 2214 2318 2421 2525 2628 2732 2835 2939 3042 3146 ir>4 420 I 623249 3353 3456 3559 3663^ 3766 3869 3973 4076 4179 t03 421 4282 4385 4488 4591 4695 4798 4901 5004 5107! 5210 103 422 5312 5415 5518 5621 5724 5827 5929 6032 6135 6238 103 423 6340 64-43 6546 6648 6751 6853 6956 7058 1 7 16 lj 7263 103 424 7366 7468 7571 7673 7775 7878 7980 8082; 8185 8287J 102" 425 8389 8491 8598 8695 8797 8900 9002 9104! 9206 93081 102 426 9410 9512 9613 9715 9817 9919 ..211 .123; .224 .326J 102 127 630428 0530 0631 0733 0835 0936 1038 1139! 1241 1342 102 428 1444 1545 1647 1748 1849 1951 2052 2153 2255" 235G 101 4 l ,!9 2457 2559 2660 2761 2862 2963 3064 3165 3266 3367 101 480 633468 J569 3670 3771 3872 3973 4074 4175 4276 4376 100 431 4477 4578 4679 4779 4880 4981 5081 51821 5283 5383 100 432 5484 5584 5685 5785 5886 5986 6087 6187 6287 6388 100 433 434 6488 7490 6588 7590 6688 7690 6789 7790 6889 7890 6989 7990 7089 8090 7189 8190 7290 8290 7390! 100 8389i 99 435 8489 8589 8689 8789 8888 8988 9088 9188 9287 9387 99 436 9486 9586 9686 9785 9885 9984 ..84 .183 .283 .382 99 437 640481 0581 0680 j 0779 0879 0978 1077 1177 1276 1375 99 438 1474 1573 1672 1771 1871 1970 2069 2168 2267 2366 99 439 2465 2563 2662 2761 2860 2959 3058 3156 3255 3354 99 440 643453 3551 3650 3749 3847 3946 4044J 4143 4242 4340 98 441 4439 4537 4636 4734 4832 4931 5029 5127 5226 5324 98 442 5422 5521 5619 5717 5815 5913 6011 6110 6208 6306 98 443 6404 6502 6600 6698 6796 6894 6992 7089 7187 7285 98 444 7383 7481 7579 7676 7774 7872 7969 8067 8165 8262 98 445 8360 8458 8555 8653 8750 8848 8945 9043 9140 9237 97 446 9335 9432 9530! 9627 9724 9821 9919 ..16 .113 .210 97 447 650308 0405 0502 0599 0696 0793 0890 0987 1084 1181 97 44S 1278 1375 1472 1569 1666 1762 1859 1956 2053 2150 97 449 2246 2343 2440J 2536 2633 2730 2826 2923 3019 3116 97 450 653213 3309 3405 3502 3598! 3695 3791 3888 3984 4080 96 451 4177 4273 4369! 4465 4562 4658 4754 48501 4946 5042 96 452 5138 5235 533 li 5427 5523 5619 5715 5810| 5906 6002 96 453 6098 6194 6290 6386 6482J 6577 6673 6769 6864 6960 96 454 7056 7152 7247 7343 7438i 7534 7629 7725 7820 7916 96 455 8011 8107 B203 8298 8393 j 8488 8584 8679 8774 8870 95 456 8965 9060 9155 9250 9346 9441 9536 9631 9726 9821 95 457 9916 ..11 .1061 .201 .296 .391 .486 .581 .676 .771 95 458 660865 0960 1055 1150 1245 1339 1434 1529 1623 1718 95 459 HI 3 1907 2002 2096 2191 228C 2380 2475 2569 2663 95 N. 1 1234 5 6 7 8 9 D. A TABLE OF LOGAKITHMS FROM 1 TO 10,000. N. o ; i 2 | 3 4 5 6 | 7 | 8 9 | D. 460 662758 2852 2947 3041 3135 3230 3324 3418 3512 3607 94 461 3701 3795 3889 3983 4078 4172 4266 4360 4454 4548 94 462 4642 4736 4830 4924 5018 5112 5200 5299 5393 5487 94 463 5581 5675 5769 862 5956 6050 6143 6237 6331 6424 94 464 6518 6612 6705 6799 6892 6986 7079 7173 7266 7360 94 465 7453 7546 7640 7733 7826 7920 8013 8106 8199 8293 93 466 8386 8479 8572 8665 8759 8852 8945 9038 9131 9224 93 467 9317 9410 9503 9596 9689 9782 9875 9967 ..60 .153 93 468 670241 0339 0431 0524 0617 0710 0802 0895 0988 1080 93 469 1173 1265 1358 1451 1543 1636 1728 1821 1913 2005 93 470 672098 2190 2283 2375 2467 2560 2652 2744 2836 2929 92 471 3021 3113 3205 3297 3390 3482 3574 3666 3758 3850 92 472 3942 4034 4126 4218 4310 4402 4494 4586 4677 4769 92 473 4861 4953 5045 5137 5228 5320 5412 5503 5595 5687 92 474 5778 5870 5962 6053 6145 6236 6328 6419 6511 6602 92 475 6694 6785 6876 6968 7059 7151 7242 7333 7424 7516 91 476 7607 7698 7789 7881 7972 8063 8154 8245 8336 8427 91 477 8518 8609 8700 8791 8882 8973 9064 9155 9246 9337 91 478 9428 9519 9610 9700 9791 9882 9973 ..63 .154 .245 91 479 680336 0426 0517 0607 0698 0789 0879 0970 1060 1151 91 480 681241 1332 1422 1513 1603 1693 1784 1874 1964 2055 90 481 2145 2235 2326 2416 2506 2596 2686 2777 2867 2957 90 482 3047 3137 3227 3317 3407 3497 3587 3677 3767 3857 90 483 3947 4037 4127 4217 4307 4396 4486 4576 4666 4756 90 484 4845 4935 5025 5114 5204 5294 5383 5473 5563 5652 90 485 5742 5831 5921 6010 6100 6189 6279 6368 6458 6547 89 486 6636 6726 6815 6904 6994 7083 7172 7261 7351 7440 89 487 7529 7618 7707 7796 7886 7975 8064 8153 8242 8331 89 488 8420 8509 8598 8687 8776 8865 8953 9042 9131 9220 89 489 9309 9398 9486 9575 9664 9753 9841 9930 .,19 .107 89 490 690196 0285 0373 0462 0550 0639 0728 0816 0905 0993 89 491 1081 1170 1258 1347 1435 1524 1612 1700 1789 1877 88 492 1965 2053 2142 2230 2318 2406 2494 2583 2671 2759 88 493 2847 2935 3023 3111 3199 3287 3375 3463 3551 3639 88 494 3727 3815 3903 3991 4078 4166 4254 4342 4430 4517 88 495 4605 4693 4781 4868 4956 5044 5i31 5219 5307 5394 88 496 5482 5569 5657 5744 5832 5919 6007 6094 6182 6269 87 497 6356 6444 6531 6618 6706 6793 6880 6968 7055 7142 87 498 7229 7317 7404 7491 7578 7665 7752 7839 7926 8014 87 499 8101 8188 8275 8362 8449 8535 8622 8709 8796 8883 87 500 698970 9057 9144 9231 9317 9404 9491 9578 9664 9751 87 501 9838 9924 ..11 ..98 .184 .271 .358 .444 .531 .617 87 502 700704 0790 0877 0963 1050 1136 1222 1309 1395 1482 86 503 1568 1654 1741 1827 1913 1999 2086 2172 2258 2344 86 504 2431 2517 2603 2689 2775 2861 2947 3033 3119 3205 86 505 3291 3377 3463 3549 3635 3721 3807 3895 3979 4065 86 506 4151 4236 4322 4408 4494 4579 4665 4751 4837 4922 86 507 5008 5094 5179 5265 5350 5436 5522 5607 5693 5778 86 508 5864 5949 6035 6120 6206 6291 6376 6462 6547 6632 85 509 6718 6803 6888 6974 7059 7144 2229 7315 7400 7485 85 510 707570 7655 7740 7826 7911 7996 8081 8166 8251 8336 85 511 8421 8506 8591 8676 8761 8846 8931 9015 9100 9185 85 512 9270 9355 9440 9524 9609 9694 9779 9863 9948 ..33 85 513 710117 0202 0287 0371 0456 0540 0625 0710 0794 0879 85 514 0963 1048 1132 1217 1301 1385 1470 1554 1639 1723 84 515 1807 1892 1976 2060 2144 2229 2313 2397 2481 2566 84 516 265C 2734 2815 2902 298fi 3070 3154 3238 3323 3407 84 517 349 3575 365C 3742 3826 3910 3994 4078 4162 4246 84 518 433C 4414 4497 4581 4665 474S 4833 4916 5000 5084 84 519 516- 5251 533 5418 55021 558C 5669 5753 583P 5920 84 N. I 1 2 | 3 ! 4 | 5 6 | 7 | 8 | 9 | D. A TABLE OF LOGARITHMS FROM 1 TO 10,000. N. | 1 2 3 4 5 fi | 7 8 | 9 | D. 520 716003 6087; 6170 6254 6337 6421 6504 H588 6671 6754 83 521 522 6838 7671 6921 7754 1 7004 7837 7088 7920 7171 8003 7254 8086 7338 7421 7504 8169 8253 8336 7587 8419 83 83 523 8502 8585 8668 8751 8834J 8917 9000 9083:9165 9248 83 524 9331 9414 9497 9580 96631 9745 9828 9911 9994 ..77 83 525 720159 0242 0325 0407 0490! 0573 0655 0738 0821 0903 83 526 0986 1068 1151 1233 1316) 1398 1481 1563 1646 1728 82 527 1811 1893 1975 2058 2140 2222 2305 2387 2469 2552 82 528 2634 2716| 2798 2881 2963 3045 3127| 3209, 3291 3374 82 529 3456 3538! 3620 3702 3784 3866 3948 4030 4112 4194 82 530 724276 4358 4440 4522 4604 4685 4767 4849 4931 5013 82 531 5095 5176 5258 5340 5422 5503 5585 5667 5748 5830 82 532 5912 5993 6075 6156 6238 6320 6401 6483 6564 6646 82 533 6727 68091 6890 6972 7053) 7134 7216 7297 7379 7460 81 534 7541 76231 7704 7785 7866 7948 8029 8110 8191 8273 81 535 8354 8435 8516 8597 8678 8759 8841 8922 9003 9084 81 536 9165 9246 9327 9408 9489 9570 9651 9732 9813 9893 81 537 9974 ..55 .136 .217 .298 .378 .459 540 .621 .702 81 538 730782 0863 0944 1024 1105 1186 1266 1347 1428 1508 81 539 1589 1C69 1750 1830 1911 1991 2072 2152 2233 2313 81 540 732394 2474 2555 2635 2715 2796 2876 2956 3037 3117 80 541 3197 3278 3358 3438 3518 3598 3679 3759 3839 3919 80 542 3999 4079 4160 4240 4320 j 4400 4480 4560 4640 4720 80 543 4800 4880 4960 5040 5120| 5200 5279 5359 5439 5519 80 544 5599 5679 5759 5838 5918 5998 6078 6157 6237 6317 80 545 6397 6476 6556 6635 6715 6795 6874 6954 7034 7113 80 546 7193 7272 7352 7431 7511 7590 7670 7749 7829 7908 79 547 7987 8067 8146 8225 8305 8384 8463 8543 8622 8701 79 548 8781 8860 8939 9018 9097 9177 9256 9335 9414 9493 79 549 9572 9651 9731 9810 9889 9968 ..47 .126 .205 .284 79 550 740363 0442 0521 0600 0678 0757 0836 0915 0994 1073 79 551 1152 1230 1309 1388 1467 1546 1624 1703 1782 1860 79 552 1939 2018 2096 2175 2254 2332 2411 2489 2568 2646 79 553 2725 2804 2882 2961 3039 3118 3196 3275 3353 3431 78 554 3510 3588 3667 3745 3823 3902 3980 4058 4136 4215 78 555 4293 4371 4449 4528 4606 4684 4762 4840 4919 4997 78 556 5075 5153 5231 5309 5387 5465 5543 5621 5699 5777 78 557 5855 5933 6011 6089 6167 6245 6323 6401 6479 6556 78 558 6634 6712 6790 6868 6945 7023 7101 7179 7256 7334 78 559 7412 7489 7567 7645 7722 7800 7878 7955 8033 8110 78 560 748188 8266 8343 8421 8498 8576 8653 8731 8808 8885 77 561 8963 9040 9118 9195 9272 9350 9427 9504 9582 9659 77 562 9736 9814 9891 9968 ..45 .123 .200 .277 .354 .431 77 563 750508 0586 0663 0740 0817 0894 0971 1048 1125 1202 77 564 1279 1356 1433 1510 1587 1664 1741 1818 1895 1972 77 565 2048 2125 2202 2279 2356 2433 2509 2586 2663 2740 77 566 2816 2893| 2970 3047 3123 3200 3277 3353 3430 3506 77 567 3583 3660 3736 3813 3889 3966 4042 4119 4195 4272 77 568 4348 4425 4501 4578 4654 4730 4807 4883 4960 5036 76 569 5112 5189 5265 5341 5417 5494 5570 5646 5722 5799 76 570 755875 5951 6027 6103 6180 6256 6332 6408 6484 6560 76 571 6636 6712 6788 6864 6940 7016 7092 7168 7244 7320 76 572 7396 7472 7548 7624 7700 7775 7851 7927 8003 8079 76 573 8155 8230 8306 8382 8458 8533 8609 8685 8761 8836 76 574 8912 8988 9063 9139 9214 9290 9366 9441 9517 9592 76 575 9668 9743 9819 9894 9970 ..45 .121 .196 .272 .347 75 576 760422 0498 0573 0648 0724 0799 0875 0950 10251 1101 75 577 1176 1251 1326 1402 1477 1552 1627 1702 1778| 1853 75 578 1928 2003 2078 2153 2228 2303 2378 2453 2529J 2604 75 579 2679 27541 2829 2904' *v<8l3053 3128 3203 3278' 3353 75 N. | | 1 2 3 | 4 5 6 | 7 8 1 9 D. A TABLE OF LOGARITHMS FKOM 1 TO 10,000. N. I 1 2 3 | 4 | 5 | 6 7 8 9 ! D. 580 76342S 3503 357fc 3653 3727 3802 3877 3952 4027 4101 75 581 4176 4251 4326 4400 4475 4550 4624 4699 4774 4848 75 582 4923 4998 5072 5147 5221 5296 5370 5445 5520 5594 75 583 5669 5743 5818 5892 5966 6041 6115 6190 6264 6338 74 584 6413 6487 6562 6636 6710 6785 6859 6933 7007 7082 74 585 7156 7230 7304 7379 7453 7527 7601 7675 7749 7823 74 586 7898 7972 8046 8120 8194 8268 8342 8416 8490 8564 74 587 8638 8712 8786 8860 8934 9008 9082 9156 9230 9303 74 588 9377 9451 9525 9599 9673 9746 9820 9894 9968 ..42 74 589 770115 0189 0263 0336 0410 0484 0557 0631 0705 0778 74 590 770852 0926 0999 1073 1146 1220 1293 1367 1440 1514 "74 591 1587 1661 1734 1808 1881 1955 2028 2102 2175 2248 73 592 2322 2395 2468 2542 2615 2688 2762 2835 2908 2981 73 593 3055 3128 3201 3274 3348 3421 3494 3567 3640 3713 73 594 3786 3860 3933 4006 4079 4152 4225 4298 4371 4444 73 595 4517 4590 4663 4736 4809 4882 4955 5028 5100 5173 73 596 5246 5319 5392 5465 5538 5610 5683 5756 5829 5902 73 597 5974 6047 6120 6193 6265 6338 6411 6483 6556 6629 73 598 6701 6774 6846 6919 6992 7064 7137 7209 7282 7354 73 599 7427 7499 7572 7644 7717 7789 7862 7934 8006 8079 72 600 778151 8224 8296 8368J 8441 8513 8585 8658 8730 8802 72 601 8874 8947 9019 9091 19163 9236 9308 9380 9452 9524 72 602 9596 9669 9741 9813 9885 9957 ..29 .101 .173 .245 72 603 780317 0389 0461 0533 0605 0677 0749 0821 0893 0965 72 604 1037 1109 '1181 1253 1324 1396 1468 1540 1612 1684 72 605 1755 1827 1899 1971 2042 2114 2136 2258 2329 2401 72 606 2473 2544 2616 2688 2759 2831 2902 2974 3046 3117 72 607 3189 3260 3332 3403 3475 3546 3618 3689 3761 3832 71 608 3904 3975 4046 4118 4189 4261 4332 4403 4475 4546 71 609 4617 4689 4760 4831 4902 4974 5045 5116 5187 5259 71 610 785330 5401 5472 5543 5615 5686 5757 5828 5899 5970 ~71 611 6041 6112 6183 6254 6325 6396 6467 6538 6609 6680 71 612 6751 6822 6893 6964 7035 7106 7177 7248 7319 7390 71 613 7460 7531 7602 7673 7744 7815 7885 7956 8027 8098 71 614 8168 8239 8310 8381 8451 8522 8593 8663 8734 8804 71 615 8875 8946 9016 9087 9157 9228 9299 9369 9440 9510 71 616 9581 9651 9722 9792 9863 9933 ...4 ..74 .144 .215 70 617 790285 0356 0426 0496 0567 0637 0707 0778 0848 0918 70 618 0988 1059 1129 1199 1269 1340 1410 1480 1550 1620 70 619 1691 1761 1831 1901 1971 2041 2111 2181 2252 2322 70 620 792392 2462 2532 2602 2672 2742 2812 2882 2952 3022 70 621 3092 3162 3231 3301 3371 3441 3511 3581 3651 3721 70 622 3790 3860 3930 4000 4070 4139 4209 4279 4349 4418 70 623 4488 4558 4627 4697 4767 4836 4906 4976 5045 5115 70 624 5185 5254 5324 5393 5463 5532 5602 >5672 5741 5811 70 625 5880 5949 6ul9 6088 6158 6227 6297 6366 6436 6505 69 626 6574 6644 6713 6782 6852 6921 6990 7060 7129 7198 69 627 7268 7337 7406 7475 7545 7614 7683 7752 7821 7890 69 628 7960 8029 8098 8167 8236 8305 8374 8443 8513 8582 69 629 8651 8720 8789 8858 8927 8996 9065 9134 9203 9272 69 630 799341 9409 9478 9547 9616 9685 9754 9823 9892 9961 69 631 800029 0098 0167 0236 0305 0373 04421 0511 0580 06481 69 632 0717 0786 0854 0923 0992 1061 1129 1198 1266 1335 69 633 1404 1472 1541 1609 1678 1747 1815 1884 1952 2021 69 634 2089 2158 2226 2295 2363! 2432 2500 2568 2637 2705 69 635 2774 2842 2910 2979. 3047 3116 3184 3252 3321 3389 68 636 3457 3525- 3594 3662 3730 3798 3867 3935 4003 4071 68 637 4139 4208 4276 4344 44121 4480 4548 4616 4685 4753 68 638 4821 4889 4957 5025 50931 5161 5229 52S3 5961 6010 6059 6108 6157 62071 6256 6305 6354 6403 49 884 6452 6501 6551 6600 6649 6698 6747 6796 6845 6894 49 885 6943 69921 7041 7090 7140 7189 7238 7287 7336 7385 49 886 7434 7483 7532 7581 7630 7679 7728 7777 7826 7875 49 887 7924 7973 8022 8070 8119 8168 8217 8266 8315 8364 49 888 8413 8463 8511 8560 8609 8657 8706 8755 8804 8853 49 889 8902 8951 8999 9048 9097 9146 9195 9244 9292 9341 49 890 949390 9439 9488 9536 9585 9634 9683 9731 9780 9829 49 891 9878 9926 9975 ..24 ..73 .121 .170 .219 .267 .316 49 892 950365 0414 0462 0511 0560 0608 OG57 0706 0754 0803 49 893 0851 0900 0949 0997 1046 1095 1143 1192 1240 12*9 49 894 1338 1386 1435 1483 1532 1580 1629 1677 1726 1775 49 8<*5 1823 1872 1920 1969 2017 2066 2114 2163 2211 2260 48 896 2308 2356 2405 2453 2502 2550 2599 2647 2696 1 2744 48 897 2792 2841 2889 2938 2986 3034 3083 3131 3180 3228 48 898 3276 3325 3373 3421 3470 3518 3566 3615 3663 3711 48 899 3760 3808 3856 3905 3953 4001 4049 4098 4146 4194 48 900 954243 4291 4339 4387 4435 4484 4532 4580 4628 4677 48 901 4725 4773 4821 4869 4918 i960 5014 5062 5110 5158i 48 902 5207 5255 5303 5351 5399 5147 5495 5543 5592 56401 48 903 5688 5736 5784 5832 5880 5928 5976 6024 6072 6120 48 904 6168 6216 6265 6313 6361 6409 6457 6505 6553 6601 48 905 6649 6697 6745 6793 6840 6888 6936 69841 7032 7080 48 906 7128 7176 7224 7272 7320 7368 7416 7464! 7512 7559 48 907 7607 7655 7703 7751 7799 7847 7894 7942 7990 8038 48 KM 8086 8134 8181 8229 8277 8325 8373 8421 8468 85] 6! 48 909 8564 8612 8659 8707 8755 8803 8850 88981 8946 8994 48 910 959041 9089 9137 9185 9232 9280 9328 9375 9423 9471 48 911 9518 9566 9614 9661 9709 9757 9804 9852 9900 9947 48 912 9995 ..42 ..90 .138 .185 .233 .280 .328 .376 .423! 48 913 960471 0518 0566 0613 0661 0709 0756 0804 0851 0899 48 914 0946 0994 1041 1089 1136 1184 1231 1279] 1326 1374 47 915 1421 1469 1516 1563 1611 1658 1706 1753 1801 1848 47 916 1895 1943 1990 2038 2085)2132 2180 2227 2275 2322 47 917 2369 2417 2464 2511 2559 2606 2653 270l| 2748 2795 47 918 2843 2890 2937 2985 3032 3079 3126 3174 3221 3268 47 919 3316 3363 3410 3457 3504 3552 3r99 3646 3693 3741 47 920 963788 3835 3882 3929 3977 4024 4071 4118 4165 4212 47 921 4260 4307 4354 4401 4448 4495 4542 4590 4637 4684 47 922 4731 4778 4825 4872 4919 4966 5013 5061 5108 5155 47 923 5202 5249 5296 5343 5390 5437 5484 5531 55781 56251 47 924 5672 5719 5766 5813 5860 5907 5954 6001 6048 6095 47 925 6142 6189 6236 6283 6329 6376 6423 6470 6517 6564^ 47 926 6611 6658 6705 6752 6799 6845 6892 69391 6986 7033 47 927 708a 7127 7173 7220 7267 7314 7361 7408 7454 7501 47 928 7548 7595 7642 7688 77301 7782 7829 7875 7922 7969 47 929 8016 8062 8109 8156 8203! 8249 8296 8343 8390 8436: 47 930 9168483 8530 8576 8623 8670 8716 8763 8810 8856 8903i 47 931 8950 8996 9043 9090 9136! 9183 9229 9276 9323 9369 47 932 9416 9463 9509 9556 9602 9649 9695 9742 9789 9835 47 933 9882 9928 9975 ..21 ..68 .114 .161 .207 .254 .3001 47 934 970347 0393 0440 0486 0533 0579 0626 0*72 0719 1 07651 46 935 0812 0858 0904 0951 0997 1044 1090 113? 1183 1229 46 936 1276 1322 1369 1415 1461 1508 1554 1601 1647 1693| 46 937 174C 1786 1833 1879J 1925 1971 2018 2064 t 2110 21571 46 938 2203 2249 2295 2342,2388 2434 2481 25271 2573 2619' 46 939 266f 2712 1 2758 ! 2804 2851 2897 : 2943 2389'3035 3082 46 N. 1 1 2 3 | 4 5 6 |- 7 | 8 9 D. 16 A TABLE OP LOGARITHMS FROM 1 TO 10,000. N. I 1 2|3|4|5|6|7|8|9|D. 940 973128 317413220 3266 33131 3359 3405 3451 ( 3497 3543 46 941 3590 3636 3682 3728 3774 3820 3866 3913 3959 4005 46 942 4051 4097 4143 4189 4235 4281 4327 4374 4420 4466 46 943 4512 4558 4604 4650 4696 4742 4788 4S34 4880 4926 46 944 4972 5018 5064 5110 5106 5202 5248 5294 5340 5386 46 945 5432 5478 5524 5570 5616 5662 5707 5753 5799 5845 46 946 5891 5937 5983 6029 6075 6121 6167 6212 6258 6304 46 947 6350 6396 6442 6488 6533 6579 6625 6671 6717 6763 46 948 6808 6854 6900 6946 6992 7037 7083 7129 7175 7220 46 949 7266 7312 7358 7403 7449 7495 7541 7586 7632 7678 46 950 977724 7769 7815 7861 7906 7952 7998 8043 8089 8135 46 951 8181 8226 8272 8317 8363 8409 8454 8500 8546 8591 46 952 8637 8683 8728 8774 8819 8865 8911 8956 9002 9047 46 953 9093 9138 9184 9230 9275 9321 9366 9412 9457 9503 46 954 9548 9594 9639 9685 9730 9776 9821 9867 9912 9958 46 955 980003 0049 0094 0140 0185 0231 0276 0322 0367 0412 45 956 0458 0503 0549 0594 0640 0685 0730 0776 0821 0867 45 957 0912 0957 1003 1048 1093 1139 1184 1229 1275 1320 45 958 1366 1411 1456 1501 1547 1592 1637 1683 1728 1773 45 959 1819 1864 1909 1954 2000 2045 2090 2135 2181 2226 45 960 982271 2316 2362 2407 2452 2497 2543 2588 2633 2678 45 961 2723 2769 2814 2859 2904 2949 2994 3040 3085 3130 45 962 3175 3220 3265 3310 3356 3401 3446 3491 3536 3581 45 963 3626 3671 3716 3762 3807 3852 3897 3942 3987 4032 45 964 4077 4122 4167 4212 4257 4302 4347 4392 4437 4482 45 965 4527 4572 4617 4662 4707 4752 4797 4842 4887 4932 45 966 4977 5022 5067 5112 5157 5202 5247 5292 5337 5382 45 967 5426 5471 5516 5561 5606 5651 5696 5741 5786 5830 45 968 5875 5920 5965 6010 6055 6100 6144 6189 6234 6279 45 969 6324 6369 6413 6458 6503 6548 6593 6637 6682 6727 45 970 986772 6817 6861 6906 6951 6996 7040 7085 7130 7175 45 971 7219 7264 7309 7353 7398 7443 7488 7532 7577 7622 45 972 7666 7711 7756 7800 7845 7890 7934 7979 8024 8068 45 973 8113 8157 8202 8247 8291 8336 8381 8425 8470 8514 45 974 8559 8604 8648 8693 8737 8782 8826 8871 8916 8960 45 975 9005 9049 9094 9138 9183 9227 9272 9316 9361 9405 45 976 9450 9494 9539 9583 9628 9672 9717 9761 9806 9850 44 977 9895 9939 9983 ..28 ..72 .117 .161 .206 .250 .294 44 978 990339 0383 0428 0472 0516 0561 0605 0650 0694 0738 44 979 0783 0827 0871 0916 0960 1004 1049 1093 1137 1182 44 980 991226 1270 1315 1359 1403 1448 1492 1536 1580 1625 44 981 1669 1713 1758 1802 1846 1890 1935 1979 2023 2067 44 982 2111 2156 2200 2244 2288 2333 2377 2421 2465 2509 44 983 2554 2598 2642 2686 2730 2774 2819 2863 2907 2951 44 984 2995 3039 3083 3127 3172 3216 3260 3304 3348 3392 44 985 3436 3480 3524 3568 3613 3657 3701 3745 3789 3833 44 986 3877 3921 3965 4009 4053 4097 4141 4185 4229 4273 44 987 4317 4361 4405 4449 4493 4537 4581 4625 4669 4713 44 988 4757 4801 4845 4889 4933 4977 5021 5065 5108 5152 44 989 5196 5240 5284 5328 5372 5416 5460 5504 5547 5591 44 990 995635 5679 5723 5767 5811 5854 5898 5942 5986 6030 44 991 6074 6117 6161 6205 6249 6293 6337 6380 6424 6U68 44 992 6512 6555 6599 6643 6687 6731 6774 6818 6862 6906 44 993 6949 6993 7037 7080 7124 7168 7212 7255 7299 7343 44 994 7386 7430 7474 7517 7561 7605 7648 7692 7736 7779 44 995 7823 7867 7910 7954 7998 8041 8085 8129 8172 8216 44 996 8259 8303 8347 8390 8434 8477 8521 8564 8608 8652 44 997 8695 8739 8782 8826 8869 8913 8956 9000 9043 9087 44 998 9131 9174 9218 9261 9305 9348 9392 9435 9479 9522 44 999 9565 9609 9652 9696 9739 9783 9826 9870 9913 9957 43 N. | | 1 2 3 I 4 | 5 1 6 | 7 8 | 9 D. 4 TABLE OF LOGARITHMIC SINES AND TANGENTS, FOR EVERY DEGREE AND MINUTE OP THE QUADRANT. N.B. The minutes in the left-hand column of each page, increasing downwards, belong to the degrees at the top ; and those increasing upwards, in the right-hand column, belong to the degrees below. 18 (0 Degree.) A TABLE OF LOGARITHMIC M. Sine | D. Cosine D. | Tang. D. Cotang. | 0.000000 10.000000 O.OOOOOOl Ininme. bO 1 6.463726 501 T17 000000 00 6.463726 501717 13.536274 59 2 764756 293485 000000 00 764756 293483 235244 58 3 940847 208231 000000 00 940847 208231 059i53 57 4 7.065786 161517 000000 00 7.065786 161517 12.934214 56 5 162696 131968 000000 00 162696 131969 837304 55 6 241877 111575 9.999999 01 241878 1115-78 758122 54 7 308824 96653 999999 01 308825 99653 691175 53 8 366816 85254 999999 01 366817 85254 633183 52 9 417968 76263 999999 01 417970 76263 582030 51 10 463725 68988 999998 01 463727 68988 5362731 50 11 7.505118 62981 9.999998 01 7.505120 62981 12.494880 49 12 542906 57936 999997 01 542909 57933 457091 48 13 577668 53641 999997 01 577672 53642 422328 47 14 609853 49938 999996 01 609857 49939 390143 46 15 639816 46714 999996 01 639820 46715 360180 45 16 667845 43881 999995 01 667849 43882 332151 44 17 694173 41372 999995 01 694179 41373 305821 43 18 7]8997 39135 999994 01 719003 39136 280997 42 19 742477 37127 999993 01 742484 37128 257516 41 20 764754 35315 999993 01 764761 35136 235239 40 21 7.785943 33672 9.999992 01 7.785951 33673 12.214049 39 22 806146 32175 999991 01 806155 32176 193845 38 23 825451 30805 999990 01 825460 30806 174540 37 24 843934 29547 999989 0-2 843944 29549 156056 36 25 861662 28388 999988 02 861674 28390 138326 35 26 878695 27317 999988 0-2 878708 27318 121292 34 27 895085 26323 999987 0'2 895099 26325 104901 33 28 910879 25399 999986 02 910894 25401 089106 32 29 926119 24538 999985 02 926134 24540 073866 31 30 940842 23733 999983 02 940858 23735 059142 30 31 7.955082 22980 9'. 999982 0-2 7.955100 22981 12.044900 29 32 968870 22273 999981 0-2 968889 22275 031111 28 33 982233 21608 999980 02 982253 21610 017747 27 S4 995198 20981 999979 02 995219 2J983 004781 26 35 8.007787 20390 999977 02 8.007809 2J392 11.992191 25 36 020021 19831 999976 02 020045 19833 979955 24 37 031919 19302 999975 02 031945 19305 968055 23 38 043501 18801 999973 02 043527 18803 956473 22 39 054781 18325 999972 02 054809 18327 945191 21 40 065776 17872 999971 02 065806 17874 934194 20 41 8.076500 17441 9.999969 02 8.076531 17444 11.923469 19 42 086965 17031 999968 02 086997 17034 913003 18 43 097183 16639 999966 02 097217 16642 902783 17 44 107167 16265 999964 03 107202 16268 892797 16 45 116926 15908 999963 03 116963 15910 883037 15 46 126471 15566 999961 03 126510 15568 873490 14 47 135810 15238 999959 03 135851 15241 864149 13 48 144953 14924 999958 03 144996 14927 855004 12 49 153907 14622 999956 03 153952 14627 846048 11 SJ 163681 14333 999954 03 162727 14336 837273 10 51 8.171280 14054 9.999952 03 8.171328 14057 11.828672 9 52 179713 13786 999950 03 179763 13790 820237 8 53 187985 13529 999948 1)3 188036 13532 811964 7 54 196102 13280 999946 03 196156 13284 803844 6 55 204070 13041 999944 ;j 204126 13044 795874 5 56 211895 12810 999942 4 211953 12814 788047 4 57 219581 12587 999940 04 219641 12590 780359 3 58 227134 12372 999938 04 227195 12376 772805 2 59 234557 12164 999936 04 234621 12168 765379 1 60 241855 11963 999934 04 241921 11967 758079 Cosine Sine 1 j Cotang. J Tang. M. Degrees. SINES AND TANGENTS. (1 DeglCC.) M. | Sine | D. Cosine D. Tang;. D. Cotang. | 8.241855 11963 9.999934 04l 8.241921 11967 1 1 . 758079 60 1 249033 11768 999932 04 249102 11772 750898 59 2 256094 1 1580 999929 04 256165 11584 743835 58 3 26304^ 11398 999927 01 263115 11402 736885 57 4 269881 11221 999925 04 269956 11225 730044 56 5 276614 11050 999922 04 276691 11054 723309 55 6 283243 10883 999920 04 283323 10887 716677 54 7 289773 10721 999918 04 289856 10726 710144 53 8 296207 10565 999915 M 296292 10570 703708 52 9 302546 10413 999913 04 302634 10418 697366 51 10 308794 10266 999910 04 308884 10270 691116 50 11 8.314954 10122 9.999907 04 8.315046 10126 11.684954 49 12 321027 9982 999905 04 321122 9987 678878 48 13 327016 9847 999902 04 327114 9851 672886 47 14 332924 9714 999899 05 331025 9719 666975 46 15 338753 9586 999897 Go 33SS56' 9590 661144 45 16 344504 9460 999894 05 344610 9465 655390 44 17 350181 9338 999891 05 350289 9343 649711 43 18 355783 9219 999888 06 355895 9224 644105 42 19 361315 9103 999885 05 361430 9108 638570 41 20 366777 8990 999882 05 366895 8995 633105 40 21 8.372171 8880 9.999879 05 8.372292 8885 11.627708 39 22 377499 8772 999876 05 377622 8777 622378 38 23 382762 8667 999873 06 382889 8672 617111 37 24 387962 8564 999870 05 388092 8570 611908 36 25 393101 8464 999867 05 393234 8470 606766 35 26 398179 8366 999864 05 398315 8371 601685 34 27 403199 8271 999861 05 403338 8276 596662 33 28 408161 8177 999858 05 408304 8182 591696 32 29 413068 8086 999854 05 413213 8091 586787 31 30 417919 7996 999851 06 418068 8002 581932 30 31 8.422717 7909 9.999848 06 8.422869 7914 11.577131 29 32 427462 7823 999844 06 427618 7830 572382 28 33 432156 7740 999841 06 432315 7745 567685 27 34 436800 7657 999838 06 436962 7663 563038 26 35 441394 7577 999834 06 441560 7583 558440 25 36 445941 7499 999831 06 446110 7505 553890 24 37 450440 7422 999827 06 450613 7428 549387 23 38 454893 7346 999823 06 455070 7352 544930 22 39 459301 7273 999820 06 459481 7279 540519 21 40 463665 7200 999816 06 463849 7206 536151 20 41 8.467985 7129 9.999812 06 8.468172 7135 11.531828 19 42 472263 7060 999809 06 472454 7066 527546 18 43 476498 6991 999805 06 476693 6998 523307 17 44 480693 6924 999801 06 480892 6931 519108 16 45 484848 6859 999797 07 485050 6865 514950 15 46 488963 6794 999793 07 489170 6801 510830 14 47 493040 6731 999790 07 493250 6738 506750 13 48 497078 6669 999788 07 497293 6676 502707 12 49 501080 6608 999782 07 501298 6615 498702 11 50 505045 6548 999778 07 505267 6555 494733 10 51 8.508974 6489 9.999774 07 8,509200 6496 11.490800 9 52 512867 6431 999769 07 513098 6439 486902 8 53 516726 6375 999765 07 516961 6382 483039 7 54 520551 6319 999761(07 5207P9 6326 479210 6 55 524343! 6264 999757 07 5245k 5 6272 475414 5 56 528102 6211 999753 07 528349 6218 471651 4 57 531828 6158 999748 or 532080 6165 467920 3 58 535523 6106 999744 or 535779 6113 464221 2 59 539186 6055 999740 or 539447 6062 460553 1 60 542819 6004 99973ft or 543084 6012 456916 Cosine Sine Cotang. Tang ! Al. db Degrees 20 (2 Degrees.) A TABLE OF LOGARITHMIC M. Sine | D. Cosine | I). Tanp. i D. Cnnuv. 8.542819 6004 9.999735 07 8.543084 6012 1 1.4569ibi 00 1 546422 5955 999731 07 54669 1 5962 453309 59 2 549995 5906 999726 07 550268 5914 449732 58 3 553539 5858 999722 08 553817 5866 * 446183 57 4 557054 5811 999717 08 557336 5819 442664 56 5 560540 5765 999713 08 560828 5773 439172 55 6 563999 5719 999708 08 564291 5727 4357091 54 7 567431 5674 999704 08 567727 5682 4322731 53 8 570836 5630 999699 08 571137 5638 428863 52 9 574214 5587 999694 08 574520 5595 425480 51 10 577566 5544 999689 08 577877 5552 422123 50 11 8.580892 5502 9.999085 OS 8.581208 5510 11.418792 49 12 584193 5460 999680 08 584514 5468 415486 48 13 587469 5419 999675 08 587795 5427 412205| 47 14 590721 5379 9^9670 08 591051 5387 408949 46 15 593948 5339 999665 08 594283 5347 405717] 45 *6 597152 5300 999660 08 597492 5308 4025081 44 17 600332 5261 999655 08 600677 5270 3993231 43 18 603489 5223 999650 08 603839 5232 396161 42 19 606623 5186 999645 09 606978 5194 393022 41 20 609734 5149 999640 <>9 610094 5158 389906 40 21 8.612823 5112 9.999035 09 8.613189 5121 11.386811 39 22 615891 5076 999629 09 616262 5085 383738 38 23 618937 5041 999624 09 619313 5050 380687 37 24 621962 5006 999619 09 622343 5015 377657 36 25 624965 4972 999614 OH 625352 4981 374648 35 26 627948 4938 999608 09 628340 4947 371660 34 27 631)911 4904 999603 09 631308 4913 368692 33 28 633854 4871 999597 09 634256 4880 365744 32 29 636776 4839 999592 09 637184 4848 3628 J 6 31 30 639680 4806 999586 09 640093 4816 359907 30 31 8.642563 4775 9.999581 09 8 . 642982 4784 11.357018- 29 32 645428 4743 999575 09 645853 4753 354147 28 33 648274 4712 999570 09 648704 4722 351296 27 34 651102 4682 999564 09 651537 4691 348463 26 35 653911 4652 999558 10 "654352 4661 345648 25 36 656702 4622 999553 10 657149 4631 34285 1 24 37 659475 4592 999547 10 659928 4602 340072 23 38 662230 4563 999541 10 662689 4573 337311 22 39 664968 4535 999535 10 665433 4544 3345671 21 40 667689 4506 999529 10 668160 4526 331 840 j 20 41 8.670393 4479* 9.999524 10 8.670870 4488 11.329130 19 42 673080 4451 999518 10 673563 4461 326437 18 43 675751 4424 999512 10 676239 4434 323761 17 44 678405 4397 999506 10 678900 4417 321100 16 45 681043 4370 999500 10 681544 4380 318456 15 46 683665 4344 999493 10 684172 4354 315828 14 47 686272 4318 999487 10 686784 4328 313216 13 48 688863 4292 999481 10 689381 4303 310619 12 49 691438 4267 999475 10 691963 4277 308037 11 50 693998 % 4242 999469 10 694529 4252 305471 10 51 8.696543 4217 9.999463 11 8.697081 4228 11.302919 9 52 699073 4192 999456 11 699617 4203 300383 8 53 701589 4168 999450 11 702139 4179 297861 7 54 704090 4144 999443 11 704646 4155 295354 6 55 706577 4121 999437 11 707140 4132 292860 5 56 709049 4097 999431 11 709618 4108 290382 4 57 711507 4074 999424 11 712083 4085 287917 3 58 713952 4051 999418 11 714534 4062 285465 2 59 716383 4029 999411 11 716972 4040 283028 1 60 718800 4006 999404 11 719396 4017 280304 Cosine j | Sine I Cotanc. 1 T3nc. M. H7 Degrees. SINES AND TANGENTS. (3 Degrees.) 21 M. Sine | D. Cosine n. Tang. D. CotHne. S. 718800 4006 9.9994U4 ll 8.719396 4017 11.280604 60 1 721204 3984 999398 11 721806 3995 278194 59 2 723595 3962 999391 11 724204 3974 275796 58 3 725972 3941 999384 11 726588 3952 273412 57 4 728337 3919 999378 ll 728959 39JO 271041 56 5 730688 3898 999371 ll 731317 3909 268683 55 6 733027 3877 999364 12 733663 3889 266337 54 7 735354 3857 999357 I '2 735996 3868 264004 53 8 737607 3836 999350 12 738317 3848 261683 52 9 739969 3816 999343 12 740626 3827 259374 51 10 742259 3796 999336 I) 742922 3807 257078 50 11 8.744536 3776 9.999329 12 8.745207 3787 11.254793 49 12 746802 3756 999322 12 747479 3768 252521 48 13 749055 3707 999315 ia 749740 3749 250260 47 14 751297 3717 999308 12 751989 3729 248011 46 15 753528 3698 999301 IS 754227 3710 245773 45 16 755747 3679 999294 14 756453 3692 243547 44 17 757955 3661 999286 12 758668 3673 241332 43 18 760151 3642 999279 12 760872 3655 239128 42 19 762337 3624 999272 12 763065 3636 236935 41 20 764511 3606 999265 12 765246 3618 234754 40 21 8.766675 3588 9.999257 12 8.767417 3600 11.232583 39 22 768828 3570 999250 13 769578 3583 230422 38 23 770970 3553 999242 13 771727 3565 228273 37 24 773101 3535 999235 13 773866 3548 226134 36 25 775223 3518 999227 13 775995 3531 224005 35 26 777333 3501 999220 13 778114 3514 221886 34 27 779434 3484 999212 13 780222 3497 219778 33 28 781524 3467 999205 j ': 782320 3480 217680 32 29 * 783605 3451 999197 13 784408 3464 215592 31 30 785675 3431 999189 ia 786486 3447 213514 30 31 8.787736 3418 9.999181 13 8.788554 3431 11.211446 29 32 789787 3402 999174 ia 790613 3414 209387 28 33 791828 3386 999166 13 792662 3399 207338 27 34 793859 3370 999158 13 794701 3383 205299 26 35 795881 3354 999150 13 796731 3368- 203269 25 36 797894 3339 999142 13 798752 3352 201248 24 37 799897 3323 999134 ia 800763 3337 199237 23 38 801892 3308 999126 ft 802765 3322 197235 22 39 803876 3293 999118 804758 3307 195242 21 40 805852 3278 999110 '. 806742 3292 193258 20 41 8.807819 3263 9.999102 I 8.808717 3278 11.191283 19 42 809777 3249 999094 / 810683 3262 189317 18 43 811726 3234 999086 4 812641 3248 187359 17 44 813667 3219 999077 4 814589 3233 185411 16 45 815599 3205 999069 .: 816529 3219 183471 15 46 817522 3191 999061 .'. 818461 3205 181539 14 47 819436 3177 999053 .'. 820384 3191 179616 13 48 821343 3163 999044 { 822298 3177 177702 12 49 823240 3149 999036 ,'. 824205 3163 175795 11 50 825130 3135 999027 .: 826103 3150 173897 10 51 8.827011 3122 9.999019 14 8.827992 3136 11.172008 9 52 828884 3108 999010 14 829874 3123 170126 8 53 830749 3095 999002 14 831748 3110 168252 7 54 832607 3082 998993 14 833613 3096 166387 6 55 834456 3069 998984 14 835471 3083 164529 5 56 836297 3056 998976 14 837321 3070 162679 4 57 838130 3043 998967 15 839163 3057 160837 3 58 839956 3030 998958 15 840998 3045 159002 2 59 841774 3017 998950 15 842825 3032 157175 1 60 843585 3000 998941 15 844644 3019 155356 Cosine Sine Cotang. Tang. M. 86 Degrees. (4 Degrees.) A TABLE OF LOGARITHMIC M. Sine D. Cosine D. | Tang. D. Cotang. U 8.843585 3005 9.998941 15 8.844644 3019 11.155356 60 1 845387 2992 998932 15 846455 3007 153545 59 2 847183 2980 998923 15 848260 2995 151740 58 3 848971 2P67 998914 15 850057 2982 149943 57 4 850751 2955 998905 15 851846 2970 148154 56 5 852525 2943 998896 15 853628 2958 146372 55 6 854291 2931 998887 15 855403 2946 144597 54 7 856049 2919 998878 15 857171 2935 142829 53 8 857801 2907 998869 15 858932 2923 141068 52 9 859546 2896 998860 15 860686 2911 139314 51 10 861283 2884 998851 15 862433 2900 137567 50 11 .8.863014 2873 9.998841 15 8.864173 2888 11.135827 49 12 864738 2861 998832 15 865906 2877 134094 48 13 666455 2850 998823 16 867632 2868 132368 47 14 868165 2839 998813 16 869351 2854 130649 46 15 869868 2828 998804 16 871064 2843 128936 45 16 871565 2817 998795 16 872770 2832 127230 44 17 873255 2806 998785 16 874469 2821 125531 43 18 874938 2795 998776 16 876162 2811 123838 42 19 876615 2786 998766 16 877849 2800 122151 41 20 878285 2773 998757 16 879529 2789 120471 40 21 8.879949 2763 9.998747 16 8.881202 2779 11.118798 39 22 881607 2752 998738 16 882869 2768 117131 38 23 883258 2742 998728 16 884530 2758 115470 37 24 884903 2731 998718 16 886185 2747 113815 36 25 886542 2721 998708 16 887833 2737 112167 35 26 888174 2711 998699 16 889476 2727 110524 34 27 889801 2700 998689 16 891112 2717 108888 33 28 891421 2690 998679 16 892742 2707 107258 32 29 893035 2680 998669 17 894366 2697 105634 31 30 894643 2670 998659 17 895984 2687 104016 30 31 8.896246 2660 9.998649 17 8.897596 2677 11.102404 29 32 897842 2651 998639 17 899203 2667 100797 28 33 899432 2641 998629 17 900803 2658 099197 27 34 901017 2631 998619 17 902398 2648 097602 26 35 902596 2622 998609 17 903987 2638 096013 25 36 904169 2612 998599 17 905570 2629 094430 24 37 905736 2603 998589 17 907147 2620 092853 23 38 907297 2593 998578 17 908719 2610 091281 22 39 908853 2584 998568 17 910285 2601 089715 21 40 910404 2575 998558 17 911846 2592 088154 20 41 8.911949 2566 9.998548 17 8.913401 2583 11.086599 19 42 913488 2556 998537 17 914951 2574 085049 18 43 915022 2547 998527 17 916495 2565 083505 17 44 916550 2538 . 998516 18 918034 2556 081966 16 45 918073 2529 998506 18 919568 2547 080432 15 46 919591 2520 998495 18 921096 2538 078904 14 47 921103 2512 998485 18 922619 2530 077381 13 48 922610 2503 998474 18 924136 2521 075864 12 49 924112 2494 998464 18 925649 2512 074351 11 50 925609 2486 998453 18 927156 2503 072844 10 51 8.927100 24^7 9.998442 18 8.928658 2495 11.071342 9 52 928587 2469 998431 18 930155 2486 069845 8 53 930068 2460 998421 18 931647 2478 068353 7 54 931544 2452 998410 18 933134 2470 066866 6 55 933015 2443 998399 18 934616 2461 065384 5 56 934481 2435 998388 18 936093 2453 063907 4 57 935942 2427 998377 18 937565 2445 062435 3 58 937398 2419 998366 18 939032 2437 060968 2 59 938850 2411 998355 18 940494 2430 059506 1 60 940296 2403 998344 18 941952 2421 J 058048 Cosine | Sine | Cutang. | Tang. | M. 85 Degrees. SINES AND TANGENTS. (5 Degrees.) M. | Sine | D. Cosine | D. | Tang. D. Ootang. 8.940296 2403 9.99834* 19 8.941952 2421 11.058048 60 1 941738 2394 998333 19 943404 2413 056596 59 2 943174 2387 998322 19 944S52 2405 055148 58 3 944606 2379 998311 19 946295 2397 053705 57 4 946034 2371 998300 19 947734 2390 052266 56 t t 947456 2363 998289 19 949168 2382 050832 55 f. 948874 2355 998277 19 950597 2374 049403 54 V 950287 2348 998266 19 952021 2366 047979 53 | 951696 2340 998255 19 953441 2360 046559 52 C 953100 2332 998243 19 954856 2351 045144 51 10 954499 2325 998232 19 956267 2344 043733 50 11 8 . 955894 2317 9.998220 19 8.957674 2337 11.042326149 15 957284 2310 998209 19 959075 2329 040925 48 IS 958670 2302 998197 19 960473 2323 039527 47 14 960052 2295 998186 19 961866 2314 038134 46 If- 961429 2288 998174 19 963255 2307 036745 45 10 962801 2280 998163 19 964639 2300 035361 44 17 964170 2273 998151 19 966019 2293 033981 43 18 965534 2266 998139 20 967394 2286 032606 42 Ifl 966893 2259 998128 20 968766 2279 031234 41 20 968249 2252 998116 20 970133 2271 029867 40 21 8.969600 2244 9.998104 20 8.971496 2265 11.028504 39 22 970947 2238 998092 20 972855 2257 027145 38 23 972289 2231 998080 20 974209 2251 025791 37 24 973628 2224 998068 20 975560 2244 024440 36 25 974962 2217 998056 20 976906 2237 0230941 35 26 , 976293 2210 998044 20 978248 2230 021752 34 27 977619 2203 998032 20 979586 2223 020414 33 28 978941 2197 998020 20 980921 2217 019079 32 29 980259 2190 998008 20 982251 2210 017749 31 30 981573 2183 997996 20 983577 2204 016423 30 31 8.982883 2177 9.997984 20 8.984899 2197 11.015101 29 32 984189 2170 997972 20 986217 2191 013783 28 33 985491 2163 997959 20 987532 2184 012468 27 34 986789 2157 997947 20 988842 2178 011158 26 35 988083 2150 997935 21 990149 2171 009851 25 36 989374 2144 997922 21 991451 2165 008549 24 37 990660 2138 997910 21 992750 2158 007250 23 :3^ 991943 2131 997897 21 994045 2152 005955 22 39 993222 2125 997885 21 995337 2146 004663 21 40 994497 2119 997872 21 996624 2140 003376 20 41 8.995768 2112 9.997860 21 8.997908 2134 11.002092 19 42 997036 2106 997847 21 999188 2127 000812 18 43 998299 2100 997835 21 9.000465 2121 10.999535 17 44 999560 2094 997822 21 001738 2115 998262 16 45 9.000816 2087 997809 21 003007 2109 996993 15 46 002069 2082 997797 21 004272 2103 995728 14 47 003318 2076 997784 21 005534 2097 994466 13 48 004563 2070 997771 21 006792 2091 993208 12 49 005805 2064 997758 21 008047 2085 991953 11 50 007044 2058 997745 21 009298 2080 990702 51 9.008278 2052 9.997732 21 9.010546 2074 10.989454 9 52 009510 2046 997719 21 011790 2068 988210 8 53 010737 2040 997706 21 013031 2062 986969 7 54 011962 2034 997693 22 014268 2056 985732 6 55 013182 2029 997680 22 015502 2051 984498 5 56 014400 2023 997667 22 016732 2045 983268 4 57 015613) 2017 997654 22 017959 2040 982041 3 58 016824 1 201? 907641 22 019183 2033 980817 2 59 018031: 2006 997628 22 020403 2028 979597 1 60 019235 2000 997614 22 021620 2023 978380 Csine | Sine | j Cotang. j^ Tang. M. 84 Degrees. 24 (6 Degrees.) A TABLE OF LOGARITHMIC M. | Sine D. | Cosine | I). Tang. | D. Cotang. 9.019235) 2000 9.997614 22 9.021620 2023 0.978380 60 1 020435 1 1995 997601 22 022834 2017 977166 59 2 021632 1989 997588 22 024044 2011 975956 58 3 022825 1984 997574 22 025251 2006 974749 57 4 024016 1978 997561 22 026455 2000 973545 56 5 025203 1973 997547 22 027655 1995 972345 55 6 026386 1967 997534 23 028852 1990 971148 54 7 027567 1962 997520 23 030046 1985 969954 53 8 028744 1957 997507 23 031237 1979 968763 52 9 029918 1951 997493 23 032425 1974 67575 51 10 031089 1947 997480 23 033609 1969 966391 50 11 9.032257 1941 9.997466 23 9.034791 1964 10.965209 49 12 033421 1936 997452 23 0359691 1958 964031 48 13 034582 1930 997439 23 037144 1953 962856 47 14 035741 1925 997425 23 038316 1948 961684 46 15 036896 1920 997411 23 039485 1943 960515 45 16 038048 1915 997397 23 040651 1938 959349 44 17 039197 1910 997383 23 041813 1933 958187 43 18 040342 1905 997369 23 042973 1928 957027 42 19 041485 1899 997355 23 044130 1923 955870 41 20 042625 1894 997341 23 045284 1918 954716 40 21 9.043762 1889 9.997327 24 9.046434 1913 10.953566 39 22 044895 1884 997313 24 047582 1908 952418 38 23 046026 1879 997299 24 048727 1903 951273 37 24 047154 1875 997285 24 049869 1898 950131 36 25 048279 1870 997271 24 051008 1893 948992 35 26 049400 1865 997257 24 052144 1889 947856 34 27 050519 1860 997242 24 053277 1884 946723 33 28 051635 1855 997228 24 054407 1879 945593 32 29 052749 1850 997214 24 055535 1874 944465 31 30 053859 1845 997199 24 056659 1870 943341 30 31 054966 1841 9.997185 24 9.057781 1865 10.942219 29 32 0560711 1836 997170 24 058900 1869 941100 28 33 057172 1831 997156 24 060016 1855 939984 27 34 058271 1827 997141 24 061130 1851 938870 26 35 059367 1822 997127 24 062240 1846 937760 25 36 060460 1817 997112 24 063348 1842 936652 24 37 061551 1813 997098 24 064453 1837 935547 23 38 062639! 1808 997083 25 065556 1833 934444 22 39 063724 1 1804 997068 25 066655 1828 933345 21 40 064806 1799 997053 25 067752 1824 932248 20 41 9.065885! 1794 9.997039 25 9.068846 1819 10.931154 19 42 066962 1790 997024 25 069938 1815 930062 18 43 068036 1786 997009 25 071027 1810 928973 17 44 069107 1781 996994 25 072113 1806 927887 16 45 070176! 1777 996979 25 073197 1802 926803 15 46 071242 1772 996964 25 074278 1797 925722 14 47 072306| 1768 996949 25 075356 1793 924644 13 48 073366 1763 996934 25 ' 076432 1789 923568 12 49 074424 ! 1759 996919 25 077505 1784 922495 11 50 075480 1755 996904 25 078576 1780 921424 10 51 9.076533 1750 9.996889 25 9.079644 1776 10.920356 9 52 *. 0775831 1746 996874 25 080710 1772 919290 8 53 078631 1742 996858 25 081773 1767 918227 7 54 079676 1738 996843 25 082833 1763 917167 6 55 080719 1733 996828 25 083891 1759 916109 c 56 081759 1729 996812 26 084947 1755 915053 4 57 082797 1725 996797 26 086000 1751 914000 58 083832 1721 996782 26 087050 1747 912950 c 59 084864 1717 996766 26 08S098 1743 911902 1 60 085894 1713 996751 26 089144 1738 910856 Cosine I Sine 1 Coiang. Tang. M. 83 Degrees. SIXES AND TANGENTS. ^7 Degrees.) 25 M. | Sine D. Cosine | D. | Tang. j D. Cotang. J 9. 085894 1713 9.996751' 26 9.089144 1738 0.910850 60 1 086922 1709 996735 26 090187 1734 909813 59 2 087947 1704 996720 26 091228 1730 908772 58 3 088970 1700 996704 26 092266 1727 907734 57 4 089990 1696 996688 26 093302 1722 906698 56 5 091008 1692 996673: 26 094336 1719 905664 55 6 092024 1688 996657 26 095367 1715 9046^,3 54 7 093037 1684 996641126 096395 1711 903605 53 8 094047 1680 996625 26 097422 1707 902578 52 9 095056 1676 996610 26 098446 1703 901554 51 10 096062 1673 996594 26 099468 1699 900532 50 11 9.097065 1668 9.996578 27 9.100487 1695 10.899513 49 12 098066 1665 996562 27 101504 1691 898496 48 13 099065 1661 996546 27 102519 1687 897481 47 14 100062 1657 996530 27 103532 1684 896468 46 15 101056 1653 996514 27 104542 1680 895458 45 16 102048 1649 996498 27 105550 1676 894450 44 17 103037 1645 996482 27 106556 1672 893444 43 18 104025 1641 996465 27 107559 1669 892441 42 19 105010 1638 996449 27 108560 1665 891440 41 20 105992 1634 996433 27 109559 1661 890441 40 21 9.106973 1630 9.996417 27 9.110556 1658 10.889444 39 22 107951 1627 996400 27 111551 1654 888449 38 23 108927 1623 996384 27 112543 1650 887457 37 24 109901 1619 996368 27 113533 1646 886467 36 25 110873 1616 996351 27 114521 1643 885479 35 26 - 111842 1612 996335 27 115507 1639 884493 34 27 112809 1608 996318 27 116491 1636 883509 33 28 113774 ' 1605 996302 28 117472 1632 882528 32 29 114737 1601 996285 28 118452 1629 881548 31 30 115698 1597 996269 28 119429 1625 880571 30 31 9.116656 1594 9.996252 28 9.120404 1622 10.879596 29 32 117613 1590 996235 28 121377 1618 878623 "28 33 118567 1587 996219 28 122348 1615 877652 27 34 119519 1583 996202 28 123317 1611 876683 26 35 120469 1580 996185 28 124284 1607 875716 25 36 121417 1576 996168 28 125249 1604 874751 24 37 122362 1573 996151 28 126211 1601 873789 23 38 123306 1569 996134 28 127172 1597 872828 22 39 124248 1566 996117 28 128130 1594 871870 21 40 125187 1562 996100 >28 129087 1591 870913 20 41 9.126125 1559 9.996083 29 9.130041 1587 10.869959 19 42 127060 1556 996066 29 130994 1584 869006 18 43 127993 1552 996049 29 131944 1581 868056 17 4-1 128925 1549 996032 29 132893 1577 867107 16 45 129854 1545 996015 29 133839 1574 866161 16 46 130781 1542 995998 29 134784 1571 865216 14 47 131706 1539 995980 29 135726 1567 864274 13 48 132630 1535 995963 29 136667 1564 863333 12 49 133551 1532 995946 29 137605 1561 862395 11 50 134470 1529 995928 29 138542 1558 861458 10 51 9.135387 1525 9.995911 29 9.139476 1555 10.860524 9 52 136303 1522 995894 29 140409 1551 859591 8 53 137216 1519 995876 j 29 141340 1548 858660 54 138128 1516 995859 29 142269 1545 857731 ( 55 139037 1512 995841 29 143196 1542 856804 { 56 139944 1509 995823! 29 144121 1539 855879 t 57 140850 1506 995806 29 145044 1535 854956 ', 58 141754 150S 995788 29 145966 1532 854034 ' 59 142655 1500 995771 29 146885 1529 853115 60 143555 1496 995753 29 147803 1526 852197 1 Cosine Sine (.otcii.i'. J Itti.g M. 82 Degrees. D 20 (8 Degrees.; A TABLE OF LOGARITHMIC M. Sine D. Cosine | D. Tang. | D. | Cotang. | 9.143555 1496 9.995753 30 9.147803 1526 I0.852197i 60 I 144453 1493 995735 30 ' 148718 1523 851282 59 2 145349 1490 995717 30 149632 1520 850368 58 3 146243 1487 * 995699 30 150544 1517 849456 57 4 147136 1484 995681 30 151454 1514 848546 56 5 148026 1481 995664 30 152363 1511 847637 55 c 148915 1478 995646 30 153269 1508 846731 54 7 149802 1475 995628 30 154174 1505 845826 53 8 150686 1472 995610 30 155077 1502 844923 52 9 151569 1469 995591 30 155978 1499 844022 21 10 152451 1466 995573 30 156877 1496 843123 50 11 9 153330 1463 9.995555 30 9.157775 1493 10.842225 49 12 154208 1460 995537 30 158671 1490 841329 48 13 155083 1457 995519 30 159565 1487 840435 47 14 156957 1454 995501 31 160457 1484 839543 46 15 156830 1451 995482 31 161347 1481 838653 45 16 157700 1448 995464 31 162236 1479 837764 44 17 158569 1445 995446 31 163123 1476 836877 43 18 159435 1442 995427 31 164008 1473 835992 42 19 160301 1439 995409 31 164892 1470 835108 41 20 161164 1436 995390 31 165774 1467 834226 40 21 9.162025 1433 9.995372 31 9.166654 1464 10.833346 39 22 162885 1430 995353 31 167532 1461 832468 38 23 163743 1427 995334 31 168409 1458 831591 37 24 164600 1424 995316 31 169284 1455 830716 36 25 165454 1422 995297 31 170157 1453 829843 35 26 166307 1419 995278 31 171029 1450 828971 34 27 167159 1416 995260 31 171899 1447 828101 33 28 168008 1413 995241 32 172767 1444 827233 32 29 168856 1410 995222 32 173634 1442 826366 31 30 169702 1407 995203 32 174499 1439 825501 30 31 9.170547 1405 9.995184 32 9.175362 1436 10.824638 29 32 171389 1402 995165 32 176224 1433 823776 28 33 172230 1399 995146 32 177084 1431 822916 27 34 173070 1396 995127 32 177942 1428 822058 26 35 173908 1394 995108 32 178799 1425 821201 25 36 174744 1391 995089 32 179655 1423 820345 24 37 175578 1388 995070 32 180508 1420 819492 23 38 176411 1386 995051 32 181360 1417 818640 22 39 177242 1383 995032 32 182211 1415 817789 21 40 178072 1380 995013 32 183059 1412 816941 20 41 9.178900 1377 9.994993 32 9.183907 1409 10.816093 19 42 179726 1374 994974 32 184752 1407 815248 18 43 180551 1372 994955 32 185597 1404 814403 17 44 181374 1369 994935 32 186439 1402 813561 16 45 182196 1366 994916 33 187280 1399 812720 15 46 183016 1364 994896 33 188120 1396 811880 14 47 183834 1361 994877 33 188958 1393 811042 13 48 184651 1359 994857 33 . 189794 1391 810206 12 49 185466 1356 994838 33 190629 1389 809371 11 50 186280 1353 994818 33 191462 1386 808538 10 51 9.187092 1351 9.994798 33 9.192294 1384 10.807706 9 52 187903 1348 994779 33 193124 1381 80G876 8 53 188712 1346 994759 33 193953 1379 806047 7 54 189519 1343 994739 33 194780 1376 805220 6 55 190325 1341 994719 33 195606 1374 804394 5 56 191130 1338 994700 33 196430 1371 803570 4 57 191933 1336 994680 33 197253 1369 802747 3 58 192734 1333 994660 33 198074 1366 801926 2 59 193534 1330 994640 33 198894 1364 801106 7 60 194332 1328 994620 33 199713 1361 800287 Cosine J Sine Cotang. 1 Tanir. | M. 81 Degrees. SINES AT^D TANGF-NTS. (9 Degrees.; 27 M. Sine D. Cosine | D. Tang. D. Comng. 9.194332 1328 9.994620 33 9.199713 1361 10.800287 60 195129 1326 994600 33 200529 1359 799471 59 2 195925 1323 994580 33 201345 1356 798655 5S 3 196719 1321 994660 34 202159 1354 797841 57 4 197511 1318 994540 34 202971 1352 797029 56 5 198302 1316 994519 34 203782 1349 796218 55 6 199091 1313 994499 34 204592 1347 795408 54 7 199879 1311 994479 34 205400 1345 794600 53 8 200666 1308 994459 34 206207 1342 793793 52 9 201451 1306 994438 34 207013 1340 792987 51 10 202234 1304 994418 34 207817 1338 792,183 50 11 9.203017 1301 9.994397 34 9.208619 1335 10.791381 49 12 203797 1299 994377 34 209420 1333 790580 48 13 204577 1296 994357 34 210220 1331 78978%| 47 14 205354 1294 994336 34 211018 1328 788982 46 15 206131 1292 994316 34 211815 1326 788185 45 16 206906 1289 994295 34 212611 1324 787389 44 17 207679 1287 994274 35 213405 1321 786595 43 18 208452 1285 994254 35 214198 1319 785802 42 19 209222 1282 994233 35 214989 1317 785011 41 20 209992 1280 994212 35 215780 1315 784220 40 21 9.210760 1278 9.994191 35 9.216568 1312 10.783432 39 22 211526 1275 994171 35 217356 1310 782644 38 23 212291 1273 994150 35 218142 1308 781858 37 24 213055 1271 994129 35 218926 1305 781074 36 25 213818 1268 994108 35 219710 1303 780290 35 26 214579 1266 994087 35 220492 1301 779508 34 27 215338 1264 994066 35 221272 1299 778728 33 28 216097 1261 994045 35 222052 1297 777948 32 29 216854 1259 994024 35 222830 1294 777170 31 30 217609 1257 994003 35 223606 1292 776394 30 31 9.218363 1255 9.993981 35 9.224382 1290 10.775618 29 32 219116 1253 993960 35 225156 1288 774844 28 33 219868 1250 993939 35 225929 1286 774071 27 34 220618 1248 993918 35 226700 1284 7*73300 26 35 221367 1246 993896 36 227471 1281 772529 25 36 222115 1244 993875 36 228239 1279 771761 24 37 222861 1242 993854 36 229007 1277 770993! 23 38 223606 1239 993832 36 219773 1275 770227 22 39 224349 1237 993811 36 230539 1273 769461 21 40 225092 1235 993789 36 231302 1271 768698 20 41 9.225833 1233 9.993768 36 9.232065 1269 10.767935 19 42 226573 1231 993746 36 232826 1267 767174 18 43 227311 1228 993725 36 233586 1265 766414 17 44 228048 122C 993703 36 234345 1262 765655 16 45 228784 1224 993681 36 235103 1260 764897 15 46 229518 1222 993660 36 235859 1258 764141 14 47 230252 1220 993638 36 236614 1256 763386 13 48 230984 1218 993616 36 237368 1254 762632 12 49 231714 1216 993594 37 238120 1252 761880 11 50 232444 1214 993572 37 238872 1250 761128 10 51 9.233172 1212 9.993550 37 9.239622 1248 10.760378 9 52 233899 1209 993528 37 240371 1246 759629 8 53 234625 1207 993506 37 241118 1244 758882 7 54 235349 1205 993484 37 241865 1242 758135 6 55 236073 1203 993462 37 242610 1240 757390 5 56 236795 1201 993440 37 243354 1238 756646 4 57 237515 1199 993418 37 244097 1236 755903 3 58 238235 1197 993396 37 244839 1234 755161 2 59 238953 1195 993374 37 245579 1232 754421 1 60 2396701 1193 993351 37 246319 1230 753681 | Cosine | | Sine | Cotang. Tang. JM. 80 Degrees. 28 (10 Degrees.) A TABLE OF LOGABITHMIC M. Sine | D. Cosine D. Tang. D. Cotansr. [ 9.239670 1193 9.993351 37 9.246319 1230 10.753681 60 1 240386 1191 993329 37 247057 1228 752943 59 2 241101 1189 993307 37 247794 1226 752206 58 3 241814 1187 993285 37 248530 1224 751470 57 4 242526 1185 993262 37 249264 1222 750736 56 5 243237 1183 993240 37 249998 1220 750002 55 6 243947 1181 993217 38 250730 121S 749270 54 7 244656 1179 993195 38 251461 1217 748539 53 8 245363 1177 993172 38 252191 1215 747809 52 9 246069 1175 993149 38 252920 1213 747080 51 10 246775 1173 993127 38 253648 1211 746352 50 11 9 . 247478 1171 9.993104 38 9.254374 1209 10.745626 49 12 248181 1169 993081 38 255100 1207 744900 48 13 * 248883 1167 993059 38 255824 1205 744176 47 14 249583 1165 993036 38 256547 1203 743453 46 15 250282 1163 993013 38 257269 1201 742731 45 16 250980 1161 992990 38 25T990 1200 742010 44 17 251677 1159 992967 38 258710 1198 741290 43 18 252373 1158 992944 38 259429 1196 740571 42 19 253067 1156 992921 38 260146 1194 739854 41 20 253761 1154 992898 38 260863 1192 739137 40 21 9 . 254453 1152 9.992875 38 9.261578 1190 10.738422 39 22 255144 1150 992852 38 262292 1189 737708 38 23 255834 1148 992829 39 263005 1187 736995 37 24 256523 1146 992806 39 263717 1185 736283 36 25 257211 1144 992783 39 264428 1183 735572 35 26 257898 1142 992759 39 265138 1181 734862 34 27 258583 1141 992736 39 265847 1179 734153 33 28 259268 1139 992713 39 266555 1178 733445 32 29 259951 1137 992690 39 267261 1176 732739 31 30 260633 1135 992666 39 267967 1174 732033 30 31 9.261314 1133 9.992643 39 9.268671 1172 10.731329 29 32 261994 1131 992619 39 269375 1170 730625 28 33 262673 1130 992596 39 270077 1169 729923 27 34 263351 1128 992572 39 270779 1167 729221 26 35 264027 1126 992549 39 271479 1165 728521 25 36 264703 1124 992525 39 272178 1164 727822 24 37 265377 1122 992501 39 272876 1162 727124 23 38 266051 1120 992478 40 273573 1160 726427 22 39 266723 1119 992454 40 274269 1158 725731 21 40 267395 1117 992430 40 274964 1157 725036 20 41 9.268065 1115 9.992406 40 9.275658 1155 10.724342 19 42 268734 1113 992382 40 276351 1153 723649 18 43 269402 1111 992359 40 277043 1151 722957 17 44 270069 1110 992335 40 277734 1150 722266 16 45 270735 1108 992311 40 278424 1148 721576 15 46 271400 1106 992287 40 279113 1147 720887 14 47 272064 1105 992263 40 279801 1145 720199 13 48 272726 1103 992239 40 280488 1143 719512 12 49 273388 1101 992214 40 281174 1141 718826 11 50 274049 1099 992190 40 281858 1140 718142 10 51 9.274708 1098 9.992166 40 9.282542 1138 10.717458 9 52 275367 1096 992142 40 283225 1136 716775 8 53 276024 1094 992117 41 283907 1135 716093 7 54 276681 1092 992093 41 284588 1133 715412 6 55 277337 1091 992069 41 285268 1131 714732 5 56 277991 1089 992044 41 285947 1130 714053 4 57 278644 1087 992020 41 286624 1128 713376 3 58 279297 1086 991996 41 287301 1126 712699 2 59 279948 1084 991971 41 287977 1125 712023 1 60 280599 1082 991947 41 288652 1123 711348 Cosine Sine ) Cotang. | Tang. M. 79 Degrees. SINES AND TANGENTS. ( 1 1 Degrees.) 29 >l. Sine P. | Citsii* l>. | Tana. | D. Cota-ia. | 9. 280599 1082 9.991947 41 9.288652 1123 10.711348 60 1 281248 1081 991922 41 289326 1122 710674 59 2 281897 1079 991897 41 289999 1120 710001 58 3 282544 1077 991873 41 290671 1118 709329 57 4 283190 1076 991848 41 291342 1117 708658 56 5 283836 1074 991823 41 292013 1115 707987 55 6 284480 1072 991799 41 292682 1114 707318 54 7 285124 1071 991774 42 293350 1112 706650 53 8 285766 1069 991749 42 294017 1111 705983 52 9 286408 1067 991724 42 294684 1109 705316 51 10 287048 1066 991699 42 295349 1107 704651 50 11 9.287687 1064 9.991674 42 9.296013 1106 10.703987 49 12 288326 1063 991649 42 296677 1104 703323 48 13 238964 1061 991624 42 297339 1103 70266 1 47 14 289600 1059 991599 42 298001 1101 701999 46 15 290236 1058 991574 42 2J8662 1100 701338 45 16 290870 1056 991549 42 299322 1098 700678 44 17 291504 1054 991524 42 299980 1096 700020 43 13 292137 1053 991498 42 300638 1095 699362 42 19 292768 1051 991473 42 301295 1093 698705 41 20 293399 1050 991448 42 301951 1092 698049 40 21 9 . 294029 1043 9.991422 42 9.302607 1090 10.697393 39 22 294658 1046 991397 42 303261 1089 696739 38 23 295286 1045 991372 43 303914 1087 696086 37 24 295913 1043 991346 43 304567 1086 695433 36 25 296539 1042 991321 43 305218 1084 694782 35 26 297164 1040 991295 43 305869 1083 694131 34 27 297788 1039 991270 43 306519 1081 693481 33 23 298412 1037 991244 43 307168 1080 692832 32 23 299034 1036 991218 43 307815 1078 692185 31 30 299655 1034 991193 43 308463 1077 691537 30 31 9.300276 1032 9.991167 43 9.309109 1075 10.690891 29 32 300895 1031 991141 43 309754 1074 690246 28 33 301514 1029 991115 43 310398 1073 689602 27 34 302132 1028 99'1090 43 811042 1071 6889G8 26 35 302748 1026 991064 43 311685 1070 688315 25 36 303364 1025 991038 43 312327 1068 687673 24 37 303979 1023 991012 43 312967 1067 687033 23 33 304593 1022 990986 43 313608 1065 686392 22 39 305207 1020 990960 43 314247 1064 685753 21 40 305819 1019 990934 44 314885 1062 685115 20 41 9.306430 1017 9.990908 44 9.315523 1061 10.684477 19 42 307041 1016 990882 44 316159 1060 683841 18 43 307650 1014 990855 44 316795 1058 683205 17 44 308259 1013 990829 44 317430 1057 682570 16 45 308867 1011 990803 44 318064 1055 681936 15. 46 309474 1010 990777 44 318697 1054 681303 14 47 310080 1008 990750' 44 319329 1053 680671 13 48 310685 1007 990724; 44 319961 1051 680039 12 49 311289 1005 990697 44 320592 1050 679408 11 50 311893 1004 990671 44 321222 1048 678778 10 51 9.312495 1003 19.990644 44 9. 321851 i 1047 10.678149 9 52 313097 1001 990618 44 322479* 1045 677521 8 53 313698 1000 990591 44 323106 1044 676894 7 54 314297 998 990565 44 323733 1043 676267 6 55 314897 997 990538 44 324358 1041 675642 5 56 315495 996 990511 45 324983 1040 675017 4 57 316092 994 9904.S5 45 325607 1039 674393 3 58 316689 993 990458 45 326231 1037 673769 2 59 317284 .191 I 990431 45 326853 1036 673147 1 GO 317879 990 ! ,990404 45 327475 1035 672525 j Cosine 1 Sine | Cotartg. | Tang. ( 78 Degrees. 30 (12 Degrees.) A TABLE OF LOGARITHMIC M. Sine | D. | Conine | D. | Tang. D. Cotanji. | 9.317879 990 9.990404 45 9.327474 1035 10.672526 60 1 318473 988 990378 45 328095 1033 671905 59 2 319066 987 990351 45 328715 1032 671285 58 3 319658 986 990324 45 329334 1030 6706.66 57 4 320249 984 990297 45 329953 1029 670047 56 5 320840 983 990270 45 330570 1028 669430 55 6 321430 982 990243 45 331187 1026 668813 54 7 322019 980 990215 45 331803 1025 668197 53 8 322607 979 990188 45 332418 1024 667582 52 9 323194 977 990161 45 333033 1023 666967 51 10 323780 976 990134 45 333646 1021 666354 50 11 9.324366 975 9.99~0107 46 9.334259 1020 10.665741 49 12 324950 973 990079 46 334871 1019 665129 48 13 325534 972 990052 46 335482 1017 664518 47 14 326117 970 990025 46 336093 1016 663907 46 15 326700 969 981,997 46 336702 1015 663298 45 16 327281 968 9899-70 46 337311 1013 662689 44 17 327862 966 989942 46 337919 1012 662081 43 18 328442 965 989915 46 338527 1011 661473 42 19 329021 964 989837 46 339133 1010 660867 41 20 329599 962 989860 46 339739 1008 660261 40 21 9.330176 961 9.989832 46 9.340344 1007 10.659656 39 22 330753 960 989804 46 340948 1006 659052 38 23 331329 958 989777 46 341552 1004 658448 37 24 331903 957 989749 47 342155 1003 657845 36 25 332478 956 989721 47 342757 1002 657243 35 26 333051 954 989693 47 343358 1000 656642 34 27 333624 953 989665 47 843958 999 656042 33 28 334195 952 989637 47 344558 998 655442 32 29 334766 950 989609 47 345157 997 654843 31 30 335337 949 989582 47 345755 996 654245 30 31 9.335906 948 9 . 989553 47 9.346353 994 10.653647 29 32 336475 946 989525 47 346949 993 653051 28 33 337043 945 989497 47 347.545 992 652455 27 34 337610 944 989469 47 348141 991 651859 26 35 338176 943 989441 47 348735 990 651265 25 36 338742 941 989413 47 349329 988 650671 24 37 339306 940 989384 47 349922 987 650078 23' 38 339871 939 989356 47 350514 986 64948C 22 39 340434 937 989328 47 351106 985 64P894 21 40 340996 936 989300 47 351697 983 648303 20 41 9.341558 935 9.989271 47 9.352287 982 10.647713 19 42 342119 934 989243 47 352876 981 647124 18 43 342679 932 989214 47 353465 980 646535 17 44 343239 931 989186 47 354053 979 645947 16 45 343797 930 989157 47 354640 977 645360 15 46 344355 929 989128 48 355227 976 644773 14 47 344912 927 989100 48 355813 975 644187 13 48 345469 926 989071 48 356398 974 643602 12 49 346024 925 989042 48 356982 973 643018 11 .50 346579 924 989014 48 357566 971 642434 10 51 9.347134 922 9.988985 48 9.358149 970 10.641851 9 52 347687 921 988956 48 358731 969 641269 8 53 348240 920 988927 48 359313 968 640687 7 54 348792 919 988898 48 359893 967 640107 6 55 349343 917 988869 48 360474 966 639526 5 56 349893 916 988840 48 361053 965 638947 4 57 350443 915 988811 49 361632 963 638368 3 58 350992 914 988782 49 362210 962 637790 2 59 351540 913 988753 49 362787 961 637213 ] 60 352088 911 988724 49 363364 960 63663fi Cosine 1 1 Sine I I Colang. II II Tang | M. 77 Degrees. SINES AND TANGENTS. (13 Degrees.) 31 M. | Sine D. Cosine I). Ta-iti. 1>. Oiianii. | 9.352088 911 9 . 988724 49 9.3H33H4 960 10.636630 60 1 352635 910 988695 49 363940 959 636060 59 2 353181 909 983666 49 364515 958 635485 58 3 353726 908 988636 49 365090 957 634910 57 4 354271 907 988607 49 365664 955 6343361 56 5 354815 905 988578 49 366237 954 633763 55 6 355353 904 988548 49 366810 953 633190 54 7 355901 903 988519 49 367382 952 632618 53 8 356443 902 988489 49 367953 951 632047 52 9 356934 901 988460 49 368524 950 631476 51 10 357524 899 983430 49 369094 949 630906 50 11 9.358064 898 9.988401 49 9.369663 948 10.630337 49 12 358603 897 988371 49 370232 946 629768 48 13 359141 896 988342 49 370799 945 629201 47 14 359673 895 988312 50 371367 944 628633 46 15 360215 893 988282 50 371933 943 623067 45 16 360752 892 988252 50 372499 942 627501 44 17 361287 891 988223 50 373064 941 626936 43 18 361822 890 988193 50 373629 940 626371 42 19 362356 889 988163 50 374193 939 625807 41 20 362889 888 988133 50 374756 938 625244 40 21 9.363422 887 9.988103 50 9.375319 937 10762468 1 39 22 363954 885 988073 50 375881 935 624119 38 23 3T>4485 884 988043 50 376442 934 623558 37 24 365016 883 988013 50 377003 933 622997 36 25 365546 8S2 987983 50 377563 932 622437 35 26. 366075 881 987953 50 378122 931 621878 34 27 366604 880 987922 50 378681 930 621319 33 23 367131 879 987892 50 379239 929 620761 32 29 367659 877 987862 50 379797 928 620203 31 30 368185 876 987832 51 380354 927 619646 30 31 9.363711 875 9.987801 51 9.380910 926 10.619090 29 32 369236 874 987771 51 381466 925 618534 28 33 369761 873 987740 51 382020 924 617980 27 34 370285 872 9*87710 51 382575 923 617425 26 35 370808 871 987679 51 383129 922 616871 25 36 371330 870 987649 51 383682 921 616318 24 37 371852 869 987618 51 384234 920 615766 23 38 372373 867 987588 51 384786 919 615214 22 39 372894 866 987557 51 385337 918 614663 581 40 373414 865 987526 51 385888 917 614112 20 41 9.373933 864 9.987496 51 9.386433 915 10.613562 19 42 374452 863 987465 51 386987 914 613013 18 43 374970 862 987434 51 387536 913 612464 17 44 375487 861 987403 52 838084 912 611916 16 45 376003 860 987372 52 388631 911 611369 15 46 376519 859 987341 52 389178 910 610822 14 47 377035 858 997310 52 389724 909 610276 13 43 377549 857 987279 52 390270 908 609730 12 49 3780G3 856 987248 52 390815 907 609185 11 50 378577 854 987217 52 391360 906 603640 10 51 9.379089 853 9.987186 52 9.391903 905 10.608097 9 52 379601 852 987155 52 392447 904 607553 8 53 380113 851 937124 52 392989 903 607011 7 54 380624 850 987092 52 393531 902 606469 6 55 331134 849 987061 52 394073 901 605927 5 56 381643 848 987030 52 394614 900 605386 4 57 382152 847 986998 52 395154 899 604846 3 58 382661 846 986967 52 395694 898 604306 2 59 383168 845 986936 52 396233 897 603767 1 60 383675 844 986904 52 396771 896 603229 j C..si Sine Cot IMC. lanp. M. 76 Degrees. 32 (14 Degrees.) A TABLE or LOGARITHMIC M. Sine I). | Cosine I). | Tang. D. C'otang. 9.383675 844 9.986904 52 9.396771 896 10.603229 60 1 384182 843 986873 53 397309 896 602691 59 2 384687 842 986841 53 397846 895 602154 58 3 385192 841 986809 53 398383 894 601617 57 4 385697 840 986778 53 398919 893 601081 56 5 386201 839 986746 53 399455 892 600545 55 6 386704 838 986714 53 399990 891 600010 54 7 387207 837 986683 53 400524 890 599476 53 8 387709 836 986651 53 401058 889 598942 52 9 388210 835 986619 53 401591 888 598409 51 10 388711 834 986587 53 402124 887 597876 50 11 9.389211 833 9.986555 53 9.402656 886 10.597344 49 12 389711 832 986523 53 403187 885 596813 48 13 390210 831 986491 53 403718 884 596282 47 14 390708 830 986459 53 404249 883 595751 46 15 391206 828 986427 53 404778 882 595222 45 16 391703 827 986396 53 405308 881 594692 44 17 392199 826 986363 54 405836 880 594164 43 18 392695 825 986331 54 406364 8,79 593636 42 19 393191 824 986299 54 406892 878 593108 41 20 393685 823 986266 54 407419 877 592581 40 21 9.394179! 822 9.986234 54 9.407945 876 10.592055 39 22 394673 821 986202 54 408471 875 591529 38 23 395166 820 986169 54 408997 874 591003 37 24 395658 819 986137 54 409521 874 590479 36 S5 396150 816 986104 54 410045 873 589955 35 26 396641 817 986072 54 410569 872 589431 34 27 397132 17 986039 54 411092 871 588908 33 28 397621 816 986007 54 411615 870 588385 32 29 398111 815 985974 54 412137 869 587863 31 30 398600 814 985942 54 412658 868 587342 30 31 9.399088 813 9.985909 55 9.413179 867 10.586821 29 32 399575 812 985876 p c 413699 866 586301 28 33 400062 811 985843 55 414219 865 585781 27 34 400549 810 985811 55 414738 864 585262 26 35 401035 809 9S5778 55 415257 864 584743 25 36 401520 808 985745 55 415775 863 584225 24 37 402005 807 985712 55 416293 862 583707 23 38 402489 806 985679 55 416810 861 583190 22 39 402972 805 985646 55 417326 860 582674 21 40 403455 804 985613 55 417842 859 582158 20 41 9.403938 803 9.985580 55 9.418358 858 10.581642 19 42 404420 802 985547 55 418873 857 581127 18 43 404901 801 985514 55 419387 856 580613 17 44 405382 800 985480 55 419901 855 580099 16 45 405862 799 985447 55 420415 855 579585 15 46 406341 798 985414 56 420927 854 579073 14 47 406820 797 985380 56 421440 853 578560 13 48 407299 796 985347 56 421952 852 578048 12 49 407777 795 985314 56 422463 851 57753? 11 50 408254 794 985280 56 422974 850 577026 10 51 9.408731 794 9.985247 56 9.423484 849 10.576510 9 52 409207 793 985213 56 423993 848 576007 8 53 409682 792 985180 56 424503 848 575497 7 54 4101571 791 985146 56 425011 847 574989 6 55 410632! 790 985113 56 425519 846 574481 5 56 4111061 789 985079 56 426027 845 573973 4 57 411579! 788 985045 56 426534 844 573466 3 58 412052 787 985011 56 427041 843 572959 2 59 412524 786 984978 56 427547 843 572453 1 60 412996' 785 9S4944 56 428052 842 571 94 Cosine Sine | Coung. | Tang [ M. 75 Degrees. SINKS AND TANGENTS. (15DegreeS.) 33 M. Sine D. | Cosine | D. Tarn.'- | D. Cotaiie. | 9.412996 785 9.984944 57 96 64 9.485339 755 10.514661 60 1 466348 688 980558 64 485791 "52 514209 C9 2 466761 687 980519 65 486242 751 513758 58 3 467173 686 980480 65 486693 751 513307 57 4 467585 685 980442 65 487143 750 512857 56 5 467996 685 980403 65 487593 749 512407 55 6 468407 684 980364 65 488043 749 511957 54 7 468817 683 980325 65 488492 748 511508 53 8 469227 683 980286 65 488941 747 511059 52 9 469637 682 980247 65 489390 747 510610 51 10 470046 681 980208 65 489838 746 510162 50 11 9.470455 680 9.980169 65 9.490286 746 10.509714 49 12 470863 680 980130 65 490733 745 509267 48 13 471271 679 980091 65 491180 744 508820 47 14 471679 678 980052 65 491627 744 508373 46 15 472086 678 980012 65 492073 743 507927 45 16 472492 677 979973 65 492519 743 507481 44 17 472898 676 979934 66 492965 742 507035 43 18 473304 676 979895 66 493410 741 506590 42 19 473710 675 979855 66 493854 740 506143 41 20 474115 674 979816 66 494299 740 505701 40 21 9.474519 674 9.979776 66 9.494743 740 10.505257 39 22 474923 673 979737 66 495186 739 504814 38 23 475327 672 979697 66 495630 738 504370 37 24 475730 672 979658 66 496073 737 503927 36 25 476133 671 979618 66 496515 737 503485 35 26 476536 670 979579 66 496957 736 503043 34 27. 476938 669 979539 66 497399 736 502601 33 28 477340 669 979499 66 497841 735 502159 32 29 477741 668 979459 66 498282 734 501718 31 30 478142 667 979420 66 498722 734 501278 30 31 9.478542 667 9.979380 66 9.499163 733 10.500837 29 32 478942 666 979340 66 499603 733 500397 28 33 479312 666 979300 67 500042 732 499958 27 34 479741 665 979260 67 500481 731 499519 26 35 480140 664 979220 67 500920 731 499080 25 36 480539 663 979180 67 501359 730 498641 24 37 480937 663 979140 67 501797 730 498203 A.-O 38 481334 662 979100 67 502235 729 497765 22 39 481731 661 979059 67 502672 728 497328 21 40 482128 661 979019 67 503109 728 496891 20 41 9.482525 660 9.978979 67 9.503546 727 10.496454 19 42 482921 659 978939 67 503982 727 496018 18 43 483316 659 978898 67 504418 726 495582 17 44 483712 658 978858 67 504854 725 495146 16 45 484107 657 978817 67 505289 725 494711 15 46 484501 657 978777 67 505724 724 494276 14 47 484895 656 978736 67 506159 724 493841 13 48 485289 655 978696 68 506593 723 493407 12 49 485682 655 978655 68 507027 722 492973 11 50 486075 654 978615 68 507480 722 492540 10 51 9.486467 653 9.978574 68 9.507893 " 721 10.492107 9 52 486860 653 978533 68 508326 721 491674 8 53 487251 652 78493 68 508759 720 491241 7 54 487643 651 978452 68 509191 719 490809 6 55 488034 651 978411 68 509622 719 490378 5 56 488424 650 978370 68 510054 718 489946 4 57 488814 650 978329 68 510485 718 489515 3 58 489204 649 978288 68 510916 717 489084 2 59 489593 648 978247 68 511346 716 488654 1 60 489982 648 978206 68 5117.76 716 488224 Cosine Sine 1 1 Cotang. 'Jang. M. 72 Degrees. (18 Degrees.) A TABLE or LOGARITHMIC M. Sine D. \ Cosine | 1). Tang. D. [ Cirtaiw. 9.4899821 648 9. 978206' 68 9.5117761 716 10.488224 60 1 490371 648 978165 68 512206 716 487794 59 2 490759 647 978124 68 512635 715 487365 58 3 491147 646 978083 69 513064 714 486936 57 4 4915351 646 978042 69 513493 714 486507 56 5 491922 645 978001 69 513921) 713 486079 55 6 492308 644 977959 69 514349 713 485651 54 7 492695 644 977918 69 514777 712 485223 53 8 493081 643 977877 69 515204 712 484796 52 9 493466 642 977835 69 515631 711 484369 51 10 493851 642 977794 69 516057 710 483943 50 11 9.494236 641 9.977752 69 9.516484 710 10.483516 49 12 494621 641 977711 69 516910J 709 483090 48 13 495005 640 977669 69 517335 709 482665 47 14 495388 639 977628 69 517761 708 482239 46 15 4957721 639 977586 69 518185 708 481815 45 16 496154 638 977544 70 518610 707 481390 44 17 496537 637 977503 70 519034 706 480966 43 18 496919 637 977461 70 519458 706 480542 42 19 497301 636 977419 70 519882 705 480118 41 20 497682 636 977377 70 520305 705 479695 40 21 9.498064 635 9.977335 70 9.520728 704 10.479272 39 22 498444 634 977293 70 521151 703 478849 38 23 498825 634 977251 70 521573 703 478427 37 24 499204 633 977209 70 521995 703 478005 36 25 499584 632 977167 70 522417 702 477583 35 26 499963 632 977125 70 522838 702 477162 34 27 500342 631 977083 70 523259 701 476741 33 28 500721 631 977041 70 523680 701 476320 32 29 501099 630 976999 70 524100 700 475900 31 30 501476 629 976957 70 524520 699 475430 30 31 9.501854 629 9.976914 70 9.524939 699 10.475061 29 32 502231 628 976872 71 525359 698 474641 28 33 502607 628 976830 71 525778 698 474222 27 34 502984 627 976787 71 526197 697 473803 26 35 503360 G26 976745 71 526615 697 473385 25 36 503735 626 976702 71 527033 696 472967 24 37 504110 625 976660 71 527451 696 472549 23 38 504485 625 976617 71 527868 695 472132 22 39 504860 624 976574 71 528285 695 471715 21 40 505234 623 976532 71 528702 694 471298 20 41 9.505608 623 9.976489 71 9.529119 693 0.470881 19 42 505981 622 976446 71 529535 693 470465 18 43 506S54 622 976404 71 529950 693 470050 17 44 506727 621 976361 71 530366 692 469634 16 45 507099 620 976318 71 530781 691 469219 15 46 507471 620 976275 71 531196 691 468804 14 47 507843 619 976232 72 531611 690 468389 13 48 508214 619 976189 72 532025 690 467975 12 49 508585 618 976146 72 532439 689 467561 11 50 508956 618 976103 72 532853 689 467147 10 51 9.509326 617 9.976060 72 9.533266 688 10.466734 9 52 509696 616 976017 72 533679 688 466321 8 53 510065 616 975974 72 534092 687 465908 7 54 510434 615 975930 72 534504 687 465496 6 55 510803 615 975887 72 534916 686 465084 c 56 511172 614 975844 72 535328 686 464672 4 57 511540 613 975800 72 535739 685 464261 3 58 511907 613 975757 72 536150 685 463850 2 59 612275 612 975714 72 536561 684 463439 1 60 512642 512 975670 72 536972 684 463028 Cosine Sine | Cotang. | Tang. M. ^1 Degrees. SINES AND TANGENTS. (19 Degrees.) 37 M. Sine | D. Cosine D. Tang. | D. Cotanp. | 9.512642 612 9.975670 V3 9.536972 684 10.463028 60 1 513009 611 975627 73 537382 683 462618 59 2 513375 611 975583 73 537792 683 462208 58 3 513741 610 975539 73 538202 682 461798 57 4 514107 609 975496 73 538611 682 461389 56 5 514472 609 975452 73 539020 681 460980 55 6 514837 608 9 ^5408 73 539429 681 460571 54 7 515202 608 9T5365 73 539837 680 460163 53 8 515566 607 975321 73 540245 680 459755 52 9 515930 607 975277 73 540653 679 459347 51 10 516294 606 975233 73 541061 679 458939 50 11 9.516657 605 9.975189 73 9.541468 678 10.458532 49 12 517020 605 975145 73 541875 678 458125 48 13 517382 604 975101 73 542281 677 457719 47 14 517745 604 975057 73 542688 677 457312 46 15 518107 603 975013 73 543094 676 456906 45 16 518468 603 974969 74 543499 676 456501 44 17 518829 602 974925 74 543905 675 456095 43 18 519190 601 974880 74 544310 675 455690 42 19 519551 601 974836 74 544715 674 455285 41 20 519911 600 974792 74 545119 674 454881 40 21 9.520271 600 9.974748 74 9.545524 673 10.454476 39 22 520631 599 974703 74 545928 673 454072 38 23 520990 599 974659 74 546331 672 453669 37 24 521349 598 974614 74 546735 672 453265 36 25 521707 598 974570 74 547133 671 452862 35 26 522066 597 974525 74 547540 671 452460 34 27- 522424 596 974481 74 547943 670 452057 33 28 522781 596 974436 74 548345 670 451655 32 29 523138 595 974391 74 548747 669 451253 31 30 523495 595 974347 75 549149 669 450851 30 31 9.523852 594 9.974302 75 9.549550 668 10.450450 29 32 524208 594 974257 75 549951 668 450049 28 33 524564 593 974212 75 550352 667 449648 27 34 524920 593 974167 75 550752 667 449248 26 35 525275 592 974122 75 551152 666 448848 25 36 525630 591 974077 75 551552 666 448448 24 37 525984 591 974032 75 551952 665 448048 23 38 526339 590 973987 75 552351 665 447649 22 39 526693 590 973942 75 552750 665 447250 21 40 527046 589 973897 75 553149 664 446851 20 41 9.527400 589 9.973852 75 9.553548 664 10.446452 19 42 527753 588 973807 75 553946 663 446054 18 43 528105 588 973761 75 554344 663 445656 17 44 528458 587 97.3716 76 554741 662 445259 16 45 528810 587 973671 76 555139 662 444861 15 46 529161 586 973625 76 555536 661 444464 14 47 529513 586 973580 76 555933 661 444067 13 48 529864 585 973535 76 556329 660 443671 12 49 530215 585 973489 76 556725 660 443275 11 50 030565 584 973444 76 557121 659 442879 10 51 9.530915 584 9.973398 76 9.557517 659 10.442483 9 52 531265 583 973352 76 557913 659 442087 6 53 531614 582 973307 76 558308 658 441692 7 54 531963 582 973261 76 558702 658 441298 6 55 532312 581 973215 76 559097 657 440903 56 532661 581 973169 76 559491 657 440509 4 57 533009 580 973124 76 559885 656 440115 r t. 58 533357 580 973078 76 560279 656" 439721 f 59 533704 579 973032 77 560673 655 439327 ] 60 534052 578 972986 77 561066 655 438934 Cosine | | Sine Cotang. Tang. J \L 70 Degrees. 38 (20 Degrees.) A TABLE OF LOGARITHMIC M. Sine D. | Cosine D. Tang. j D. Cotang. 9.634052) 578 9.972986 77 9.56106 655 10.438934 60 1 534399 577 972940 77 56145 654 438541 59 2 534745 577 9728941 77 56185 654 438149 58 3 535092 577 972848 77 562244 653 437756 57 4 535438 576 972802 77 562636 653 437364 56 5 535783 576 9727551 77 563028 653 436972 55 6 536129 575 972709 77 563419 652 436581 54 7 536474 574 972663 77 56381 652 436189 53 8 536818 574 972617 77 564-202 651 435798 52 9 537163 573 972570 77 564592 651 435408 51 10 537507 573 972524 77 564983 650 435017 50 11 9.537851 572 9.972478 77 9.565373 650 10.434627 49 12 538194 572 972431 78 565763 649 434237 48 13 538538 571 972385 78 566153 649 433847 47 14 538880 571 972338 78 566542 649 433458 46 15 539223 570 972291 78 566932 648 433068 45 16 539565 570 972245 78 567320 648 432680 44 17 539907 569 972198 78 567709 647 432291 43 18 540249 569 972151 78 568098 647 431902 42 19 540590 568 972105 79 568486 646 431514 41 20 540931 5-68 972058 78 568873 646 431127 40 21 9.541272 567 9.972011 71 9.569261 645 10.430739 39 22 541613 567 971964 73 569648 645 430352 38 23 541953 566 971917 73 570035 645 429965 37 24 542293 566 971870 78 570422 644 429578 36 25 542632 565 971823 78 570809 644 429191 35 26 542971 565 971776 rs 571195 643 428805 34 27 543310 564 971729 79 571581 643 4284-19 33 28 543649 564 971682 79 571967 642 428033 32 29 543987 563 971635 79 572352 642 427648 31 30 544325 563 971588 79 572738 642 427262 30 31 9.544663 562 9.971540 79 9.573123 641 10.426877 29 32 545000 562 971493 79 573507 641 426493 28 33 545338 561 971446 79 573892 640 426108 27 34 545674 561 971398 79 574276 640 425724 26 35 546011 560 971351 79 574660 639 425340 25 36 546347 560 971303 79 575044 639 424956 24 37 546683 559 971256 79 575427 639 424573 23 38 547019 559 971208 79 575810 638 424190 22 39 547354 558 971161 79 576193 638 423807 21 40 547689 558 971113 79 576576 637 423424 20 41 9.548024 557 9.971066 80 9.576958 637 T07423041 19 42 548359 557 971018 80 577341 636 422659 18 43 548693 556 970970 80 577723 636 422277 17 44 549027 556 970922 80 578104 636 421896 16 45 549360 555 970874 80 578486 635 421514 15 46 549693 555 970827 80 578867 635 421133 14 47 550026 554 970779 80 579248 634 420752 13 48 550359 554 970731 80 579629 634 420371 12 49 550692 553 970683 80 580009 634 419991 11 50 551024 553 970635 80 580389 633 419611 10 51 9.551356 552 9.970586 80 9.580769 633 10.419231 9 52 551687 552 970538 80 581149 632 418851 8 53 552018 552 970490 80 581528 632 418472 7 54 552349 551 970442 80 581907 632 418093 6 55 552680 551 970394 80 582286 631 417714 5 56 553010 550 970345 81 582665 631 417335 4 57 553341 550 970297 81 583043 630 416957 3 58 553670 549 970249 81 583422 630 416578 2 59 554000 549 970200 81 583800 629 416200 1 60 554329 548 970152 81 584177 629 415823 Cosine Sine 1 Cotang. Tang. M. Degrees. SINES AND TANGENTS. (21 Degrees.) M. Sine D. Connf D. f /fang. D. Cntang. | 9.554329 548 I 9.970152 81 9.684177 629 0.415823 60 1 554658 548 970103 81 584555 629 415445 59 2 554987 547. 970055 81 584932 628 415068 58 3 555315 547 970006 81 585309 628 414691 57 4 555643 546 969957 81 585686 627 4143-14 56 5 '555971 546 969909 81 586062 627 413938 55 6 556299 545 969860 81 586439 627 413561 54 7 556626 545 969811 81 586815 626 413185 53 8 556953 544 969762 81 587190 626 412810 52 9 557280 544 969714 81 587566 625 412434 51 10 557606 543 969665 81 587941 625 412059 50 11 9.557932 543 9.969616 82 9.588316 625 0,411684 49 12 558258 543 969567 82 588691 624 411309 48 13 558583 542 969518 82 589066 624 410934 47 14 558909 542 969469 82 589440 623 410560 46 15 559234 541 969420 82 589814 623 410186 45 16 559558 641 969370 82 590188 623 409812 44 17 559883 540 969321 82 590562 622 409438 43 18 560207 540 969272 82 590935 622 409065 42 19 560531 539 969223 82 691308 622 408692 41 20 560855 539 969173 82 591681 621 408319 40 21 9.561178 538 9.969124 82 9.592054 621 10.407946 39 22 561501 538 969075 82 592426 620 407574 38 23 561824 537 969025 82 592798 620 407202 37 24 562146 537 968976 82 593170 619 406829 36 25 562468 536 968926 83 593542 619 406458 35 26 562790 536 968877 83 593914 618 406086 34 27 563112 536 968827 83 594285 618 405715 33 28 563433 535 968777 83 594656 618 405344 32 29 563755 535 968728 83 595027 617 404973 31 30 564075 534 968678 83 595398 617 404602 30 31 9.564396 534 9.968628 83 9.595768 617 10.404232 29 32 564716 533 968578 83 596138 616 403862 28 33 565036 533 968528 83 596508 616 403492 27 34 565356 532 968479 83 596878 616 403122 26 35 565676 532 968429 83 597247 615 402753 25 36 565995 531 968379 83 597616 615 402384 24 37 566314 531 968329 83 597985 615 402015 23 38 566632 531 968278 83 598354 614 401646 22 39 566951 530 968228 84 598722 614 401278 21 40 567269 530 968178 84 599091 613 400909 20 41 9.567587 529 9.968128 84 9.599459 613 10.400541 19 42 567904 529 968078 84 59982~ 613 400173 18 43 568222 528 968037 84 600194 612 399806 17 44 568539 528 967977 84 600562 612 399438 16 45 568856 528 967927 84 60092 611 399071 15 46 569172 527 967876 84 60129 Gil 398704 14 47 569488 527 967826 84 60166 611 398338 13 48 569804 526 96777 84 60202 610 397971 12 49 570120 526 967725 84 60239 610 397605 11 50 570435 525 967674 84 60276 610 397239 10 M 9.570751 525 9.967624 84 9.60312 609 10.396873 52 571066 524 967573 84 60349 609 396507 53 57138(] 524 967522 85 60385 609 396142 54 571 69E 523 967471 85 60422 608 395777 55 57200= 523 967421 85 60458 608 395412 56 57232J 523 96737C 85 60495 607 395047 57 57263C 522 9673 1G 85 60531 607 394683 58 57295( 522 96726S 85 60568 607 394318 59 57326J 521 96721? 85 60604 606 393954 60 57357? 521 96716t 85 60641 606 393590 Cosine Sine Cotang. Tang. M. Go Decrees. 40 (22 Degrees.) A TABLE OF LOGARITHMIC M. | Sine D. Cosine D. Tang. D. Cotang. | 9.573575 521 9.967166 85 9.606410 606 10.393590 60 1 573888 520 967115 85 606773 606 393227 59 2 574200 520 967064 85 607137 605 392863 58 3 574512 519 967013 85 607500 605 392500 57 4 574824 519 966961 85 607863 604 392137 56 5 575136 519 966910 85 608225 604 391775 55 6 575447 518 966859 85 608588 604 391412 54 7 575758 518 966808 85 608950 603 391050 53 8 576069 517 966756 86 609312 603 390688 52 9 576379 51T 966705 86 609674 603 390326 51 10 576689 516 966653 86 610036 602 389964 50 11 9.576999 516 9.966602 86 9.610397 602 10.389603 49 12 577309 516 966550 86 610759 602 389241 48 13 577618 515 966499 86 611120 601 388880 47 14 577927 515 966447 86 611480 601 388520 46 15 578236 514 966395 86 611841 601 388159 45 16 578545 514 966344 86 612201 600 387799 44 17 578853 513 966292 86 612561 600 387439 43 18 579162 513 966240 86 612921 600 387079 42 19 579470 513 966188 86 613281 599 386719 41 20 579777 512 966136 86 613641 599 386359 40 21 9.580085 512 9 966085 87 9.614000 598 10.386000 39 22 580392 511 966033 87 614359 598 385641 38 23 580699 511 965981 87 6U718 598 385282 37 24 581005 511 965928 87 615077 597 384923 36 25 581312 510 965876 87 615435 597 384565 35 26 581618 510 965824 87 615793 597 384207 34 27 581924 509 965772 87 616151 596 383849 33 28 582229 509 965720 87 616509 596 383491 32 29 582535 509 965668 87 616867 596 383133 31 30 582840 508 965615 87 617224 595 382776 30 31 9.583145 508 9.965563 87 9 617582 595 10.382418 29 32 583449 507 965511 87 617939 595 382061 28 33 583754 507 965458 87 618295 594 381705 27 34 584058 506 965406 87 618652 594 381348 26 35 584361 506 965353 88 619008 594 380992 25 36 584665 *06 965301 88 619364 593 380636 24 37 584968 505 965248 88 619721 593 380279 23 38 585272 505 965195 88 620076 593 379924 22 39 585574 504 965143 88 620432 592 379568 21 40 585877 504 965090 88 620787 592 379213 20 41 9.586179 503 9.965037 88 9.621142 592 10.376858 19 42 586482 503 964984 88 621497 591 378503 18 43 586783 503 964931 88 621852 591 378148 17 44 587085 502 964879 88 622207 590 377793 16 45 587386 502 964826 88 622561 590 377439 15 46 587688 501 964773 88 622915 590 377085 14 47 587989 501 964719 88 623269 589 376731 13 48 588289 501 964666 89 623623 589 376377 12 49 588590 500 964613 89 623976 589 376024 11 50 . 588890 500 964560 89 624330 588 375670 10 51 9.589190 499 9.964507 89 9.624683 588 10.375317 9 52 589489 499 964454 89 625036 588 374964 8 53 589789 499 964400 89 625388 587 374612 7 54 590088 498 964347 89 625741 587 374259 6 55 590387 498 964294 89 626093 587 373907 5 56 590686 497 964240 89 626445 586 373555 4 57 590984 497 964187 89 626797 586 373203 3 58 591282 497 964133 89 627149 586 372851 2 59 591580 496 964080 89 627501 585 372499 1 60 591878 496 964026 89 627852 585 372148 Cosine Sine | | Cotang. Tang. j M. 67 Degrees. SINES AND TANGENTS. (23 Degrees.) 41 M. Sine | D. Cosine | D. | Tanir. D. Cotang. j y. 591878 496 9 . 964026 89 9.627852 585 10.372148 60 1 592176 495 963972 89 628203 585 371797 59 2 592473 495 963919 89 628554 585 371446 58 3 596770 495 963865 90 628905 584 371095 57 4 593067 494 963811 90 629255 584 370745 56 5 593363 494 963757 90 629606 583 370394 55 6 593659 493 963704 90 629956 583 370044 54 7 593955 493 963650 90 630306 583 369694 53 8 594251 493 963596 90 630656 583 369344 52 9 594547 492 963542: 90 631005 582 368995 51 10 594842 492 963488 90 631355 582 368645 50 11 9.595137 491 9.963434 90 9.631704 582 10.368296 49 12 595432 491 963379 90 632053 581 367947 48 13 595727 491 963325 90 632401 581 367599 47 14 596021 490 963271 90 632750 581 367250 46 II 596315 490 963217 90 633098 580 366902 45 16 596609 489 963163 90 633447 580 366553 44 17 596903 489 963108 91 633795 580 366205 43 18 597196 489 963054 91 634143 579 365857 42 19 597490 488 962999 91 634490 579 365510 41 20 597783 488 962945 91 634838 579 365162 40 21 9 . 598075 487 9.962890 91 9.635185 578 10.364815 39 22 598368 487 962836 91 635532 578 364468 38 23 598660 487 962781 '91 635879 578 364121 37 24 598952 486 962727 91 638226 577 363774 36 25 599244 486 962672 91 636572 577 363428 35 26 . 599536 485 962617 91 636919 577 363081 34 27 599827 485 962562 91 637265 577 362735 33 28 600118 485 962508 91 637611 576 362389 32 29 600409 484 962453 91 637956 576 362044 31 30 600700 484 962398 92 638302 576 361698 30 31 9.600990 484 9.962343 92 9.638647 575 10.361353 29 32 601280 483 962288 92 638992 575 361008 28 33 601570 483 962233 92 639337 575 360663 27 34 601860 482 962178 92 639682 574 360318 26 35 602150 482 962123 92 640027 574 359973 25 36 602439 482 962067 92 640371 574 359629 24 37 602728 481 962012 92 640716 573 359284 23 38 603017 481 961957 92 641060 573 358940 22 39 603305 481 961902 92 641404 573 358596 21 40 603594 480 961846 92 641747 572 358253 20 41 9.603882 480 9.961791 92 9.642091 572 10.357909 19 42 604170 479 961735 92 642434 572 357566 18 43 604457 479 961680 92 642777 572 357223 17 44 604745 479 961624 93 643120 571 356880 16 45 605032 478 961569 93 643463 571 35653? 15 46 605319 478 961513 93 643806 571 356194 14 47 605606 478 961458 93 644148 570 355852 13 48 605892 477 961402 93 644490 570 355510 12 49 606179 477 961346 93 644832 570 355168 11 50 606465 476 961290 93 645174 569 354826 10 51 9.606751 476 9.961235 93 9.645516 569 107354484 9 52 607036 476 961179 93 645857 569 354143 8 53 607322 475 961123 93 646199 569 353801 7 54 607607 475 961067 93 646540 568 353460 6 55 607892 474 961011 93 646881 568 353119 5 56 608177 474 960955 93 647222 568 352778 4 57 608461 474 960899 93 647562 567 352438 3 53 608745 473 960843 94 647903 567 352097 2 59 609029 473 960786 94 648243 567 351757 1 60 609313 473 960730 94 648583 566 351417 Cosine Sine | Cotang. 1 Tang. M. 66 Degrees. F 42 (4 Degrees.) A TABLE OF LOGARITHMIC M | ^ine D. Cosine | D. Tanp. 1 D. Cotang. | 9.609313 473 9.960730 94 9.648583 566 10.351417 60 1 609597 472 960674 94 648923 566 351077 59 2 609880 472 960618 94 649263 566 350737 58 3 610164 472 960561 94 649602 566 350398 57 4 610447 471 960505 94 649942 565 350058 56 5 610729 471 960448 94 650281 565 349719 55 6 611012 470 960392 94 650020 565 349380 54 7 611294 470 960335 94 650959 564 349041 53 8 611576 470 960279 94 651297 564 348703 52 9 611858 469 960222 94 651636 564 348364 51 10 612140 469 960165 94 651974 563 348026 50 11 9.612421 469 9.960109 95 9.652312 563 10.347688 49 12 612702 468 960052 95 652650 563 347350 48 13 612983 468 959995 95 652988 563 347012 47 14 613264 467 959938 95 653326 562 346674 46 15 613545 467 959882 95 653663 562 346337 45 16 613825 467 959825 95 654000 562 346000 44 17 614105 466 959768 95 654337 561 345663 43 18 614385 466 959711 95 654674 561 345326 42 19 614665 466 959654 95 655011 561 344989 41 20 614944 465 959596 95 655348 561 344652 40 21 9.615223 465 9.959539 95 9.655684 560 10.344316 39 22 615502 465 959482 95 656020 560 343980 38 23 615781 464 959425 95 656356 560 343644 37 24 616060 464 959368 95 656692 559 343308 36 25 616338 464 959310 96 657028 559 342972 35 26 616616 463 959253 96 657364 559 342636 34 27 616894 463 959195 96 657699 559 342301 33 28 617172 462 959138 96 658034 558 341966 32 29 617450 462 959081 96 658369 558 341631 31 30 617727 462 959023 96 658704 558 341296 30 31 9.618004 461 9.958965 96 9 . 659039 558 10.340961 29 32 618281 461 958908 96 659373 557 340627 28 33 618558 461 958850 96 659708 557 340292 27 34 618834 460 95879^ 96 660042 557 339958 26 35 619110 460 958734 96 . 660376 557 339624 25 36 619386 460 958677 96 660710 556 339290 24 37 619662 459 958619 96 661043 556 338957 23 38 619938 459 958561 96 661377 556 338623 22 39 620213 459 958503 97 661710 555 338290 21 40 620488 458 958445 97 662043 555 337957 20 41 9.620763 ' 458 9.958387 97 9.662376 555 10.337624 19 42 621038 457 958329 97 662709 554 337291 18 43 621313 457 958271 97 663042 554 336958 17 44 621587 457 958213 97 663375 554 336625 16 45 621861 456 958154 97 663707 554 336293 15 46 622135 456 958096 97 664039 553 335961 14 47 622409 456 958038 97 664371 553 335629 13 48 622682 455 957979 97 664703 553 335297 12 49 622956 455 957921 97 665035 553 334965 11 50 623229 455 957863 97 665366 552 334634 10 51 9.623502 454 9.957804 9V 9.665697 552 1^7334303 9 52 623774 454 957746 98 666029 552 333971 8 53 624047 454 957687 98 666360 551 333640 7 54 624319 453 957628 98 666691 551 333309 6 55 624591 453 957570 98 667021 551 332979 5 56 624863 453 957511 98 667352 551 332648 4 57 625135 452 957452 98 667682 550 332318 3 58 625406 452 957393 98 668013 550 331987 2 59 625677 452 957335 98 668343 550 331657 60 625948 451 957276 98 668672 550 331328 Cosine I I Sine | Colling Tang. | M. 65 Degrees. SINES AND TANGENTS. (25 Degrees.) M. Sine D. | Cosine | D. Tang. | D. Cotang. j 9 . 625948 451 9.957276 981 9.668673 550 10.331327|60 1 626219 451 957217 98' 669002 549 330998 59 2 626490 451 957158 98 669332 549 330668 58 3 626760 450 957099 98 669661 549 330339 57 4 627030 450 957040 98 669991 548 330009 56 5 627300 450 956981 98 670320 548 329680 55 6 627570 449 956921 99 670649 548 329351 54 7 627840 449 956862 99 670977 548 329023 53 8 628109 449 956803 99 671306 547 328694 52 9 628378 448 956744 99 671634 547 328366 51 10 628647 448 956684 99 .671963 547 328037 50 11 9.628916 447 9.956625 99 9.672291 547 10.327709 49 12 629185 447 956566 99 672619 546 327381 48 13 629453 447 956506 99 672947 546 327053 47 14 629721 446 956447 99 673274 546 326726 46 15 629989 446 956387 99 673602 546 326398 45 16 630257 446 956327 99 673929 545 326071 44 17 630524 446 956268 99 674257 545 325743 43 18 630792 445 956208 100 674584 545 325416 42 19 631059 445 956148 100 674910 544 325090 41 20 631326 445 956089 100 675237 544 324763 40 21 9.631593 444 9.956029 100 9.675564 544 10.324436 39 22 631859 444 955969 100 675890 544 324110 38 23 632125 444 955909 100 676216 543 323784 37 24 632392 443 955849 100 676543 543 323457 36 25 632658 443 955789 100 676869 543 323131 35 26 . 632923 443 955729 100 677194 543 322806 34 27 633189 442 955669 100 677520 542 322480 33 28 633454 442 955609 100 677846 542 322154 32 29 633719 442 955548 100 678171 542 321829 31 30 633984 441 955488 100 678496 542 321504 30 31 9.634249 441 9.955428 101 9.678821 541 10.321179 29 32 634514 440 955368 101 679146 541 320854 28 33 634778 440 955307 101 679471 541 320529 27 34 635042 440 955247 101 679795 541 320205 26 35 635306 439 955186 101 680120 540 319880 25 36 635570 439 955126 101 680444 540 319556 24 37 635834 439 955065 101 680768 540 319232 23 38 636097 438 955005 101 681092 540 318908 22 39 636360 438 954944 101 681416 539 318584 21 40 636623 438 954883 101 681740 5C 318260 20 41 9.636886 437 9 954823 101 9.682063 539 10.317937 19 42 637148 437 954762 101 682387 539 317613 18 43 63741 1 437 954701 101 682710 538 317290 17 44 637673 437 954640 101 683033 538 316967 16 45 637935 436 954579 101 683356 538 316644 15 46 638197 436 954518 102 683679 538 316321 14 47 638458 436 954457 102 684001 537 315999 13 48 638720 435 954396 102 684324 537 315676 12 49 638981 435 954335 102 684646 537 315354 11 50 639242 435 954274 102 684968 537 315032 10 51 9 . 639503 434 9.954213 102 9.685290 536 10.314710 9 52 639764 434 954152 102 685612 536 314388 8 53 640024 434 954090 102 685934 536 314066 7 54 640284 433 954029 102 686255 536 313745 6 55 640544 433 953968 102 686577 C35 313423 5 56 640804 433 953906 102 686898 535 313102 4 57 641064 432 953845 102 687219 535 812781 3 58 641324 432 953783 102 687540 535 312460 t 59 641584 432 953722 103 687861 534 31-2139 ] 60 641842 431 953660 103 688182 534 311818 Cosine | Sine ( Cotang. Tang. | M. 64 Degrees. 44 (26 Degrees.) A TABLE OF LOGARITHMIC M. Sine D. ' Cosine | 1). | T-nr. 1 D Cutaii*. 9.641842 431 9.953660 103 9.688182 534 10.311818 60 1 642101 431 953599 103 688502 534 311498 59 2 642360 431 953537 103 688823 534 311177 58 3 642618 430 953475 103 689143 533 310857 57 4 642877 430 953413 103 689463 533 310537 56 5 643135 430 953352 103 689783 533 310217 55 6 643393 430 953290 103 690103 533 309897 54 7 643650 429 953228 103 690423 533 309577 53 8 643908 429 953166 103 690742 532 309258 52 9 644165 429 953104 103 691062 532 308938 51 10 644423 428 953042 103 691381 532 308619 50 11 9 . 644680 428 9.952980 104 9.691700 531 10.308300 49 12 644936 428 952918 104 692019 531 307981 48 13 645193 427 952855 104 692338 531 307662 47 14 645450 427 952793 104 692656 531 307344 46 15 645706 427 952731 104 692975 531 307025 45 16 645962 426 952669 104 693293 530 306707 44 17 646218 426 952606 104 693612 530 306388 43 18 646474 426 952544 104 693930 530 306070 42 19 646729 425 952481 104 694248 530 305752 41 20 646984 425 952419 104 694566 529 305434 40 21 9.647240 425 9.952356 104 9.694883 529 10.3D5117 39 22 647494 424 952294 104 695201 529 304799 38 23 647749 424 952231 104 695518 529 304482 37 24 648004 424 952168 105 695836 529 304164 36 25 648258 424 952106 105 696153 528 303847 35 26 648512 423 952043 105 696470 528 303530 34 27 648766 423 951980 105 696787 528 303213 33 28 649020 423 951917 105 697103 528 302897 32 29 64J9274 422 951854 105 697420 527 302580 31 30 649527 422 951791 105 697736 527 302264 .30 31 9.649781 422 9.951728 105 JFT698053 527 10.301947 29 32 650034 422 951665 105 698369 527 301631 28 33 650287 421 951602 105 698685 526 301315 27 34 650539 421 951539 105 699001 526 300999 26 35 650792 421 951476 105 699316 526 300684 25 36 651044 420 951412 105 699632 526 300368 24 37 651297 420 951349 106 699947 526 300053 23 38 651549 420 951286 106 700263 525 299737 22 39 651800 419 951222 106 700578 525 299422 21 40 652052 419 951159 106 700893) 525 299107 20 41 9.652304 419 9.951096 106:9.701208 524 10.298792 19 42 652555 418 951032 106 701523 524 298477 18 43 652806 418 950968 106 701837 524 298163 17 44 653057 418 950905 106 702152 524 297848 16 45 653308 418 950841 106 702466 524 297534 15 46 653558 417 950778 106 702780 523 297220 14 47 653808 417 950714 106 703095 523 296905 13 48 654059 417 950650 106 703409 523 296591 12 49 654309 416 950586 106 703723 523 296277 11 50 654558 416 950522 107 704036 522 295964 10 51 9.654808 416 9.950458 107 9.704350 522 10.295650 9 52 655058 416 950394 107 704663 522 295337 8 53 655307 415 950330 107 704977 522 295023 7 54 655556 415 ' 950266 107 705290 522 294710 6 55 655805 415 950202 107 705603 521 294397 5 56 656054 414 950138 107 705916 521 294084 4 57 656302 414 950074 107 706228 521 293772 3 58 656551 414 950010 107 706511 521 293459 2 59 656799 413 940945 107 706854 521 293146 1 60 657047 413 949881 107 707166 520 292834 Cosine j Sine | Cotan ? . |- Tang. j Al. 63 Degrees. SINES AND TANGENTS. (27 Degrees.) 45 M. Sine D. | Cosine D. Tang. ! D. Cotang. . 657047 413 9.949881 107 9,707166 520 10.292834 60 1 657295 413 949816 107 707478 520 292522 59 2 657542 412 949752 107 707790 520 292210 58 3 657790 412 949688 108 708102 520 291898 57 4 658037 412 949623 108 708414 519 291586 56 5 658284 412 949558 108 708726 519 291274 55 6 658531 411 949494 108 709037 519 290963 54 7 658778 411 949429 108 709349 519 290651 53 8 659025 411 949364 108 709660 519 290340 52 9 659271 410 949300 108 709971 518 290029 51 10 659517 410 949235 108 710282 518 289718 50 11 9.659763 410 9.949170 108 9.710593 518 10.289407 49 12 660009 409 949105 108 710904 518 289096 48 13 660255 409 949040 108 711215 518 288785 47 14 660501 409 948975 108 711525 517 288475 46 15 660746 409 948910 108 711836 517 288164 45 16 660991 408 948845 108 712146 517 287854 44 17 661236 408 948780 109 712456 517 287544 43 18 661481 408 948715 109 712766 516 287234 42 19 661726 407 948650 109 713076 516 286924 41 20 661970 407 948584 109 713386 516 286614 40 21 9.662214 407 9.948519 109 9.713696 516 10.286304 39 22 662459 407 948454 109 714005 516 285995 38 23 662703 406 948388 109 714314 515 285686 37 24 662946 406 948323 109 714624 515 285376 36 25 663190 406 948257 109 714933 515 285067 35 26 663433 405 948192 109 715242 515 284758 34 27 663677 405 948126 109 715551 514 284449 33 28 663920 405 948060 109 715860 514 284140 32 29 664163 405 947995 110 716168 514 283832 31 30 664406 404 947929 110 716477 514 283523 30 31 9.664648 404 9.947863 no 9.716785 514 10.283215 29 32 664891 404 947797 110 717093 513 282907 28 33 665133 403 947731 110 717401 513 282599 27 34 665375 403 947665 110 717709 513 282291 26 35 665617 403 947600 110 718017 513 281983 25 36 665859 402 947533 110 718325 513 281675 24 37 666100 402 947467 110 718633 512 281367 23 38 666342 402 947401 110 718940 512 281060 22 39 666583 402 947335 110 719248 512 280752 21 40 666824 401 947269 110 719555 512 280445 20 41 9.667065 401 9.947203 110 9.719862 512 10.280138 19 42 667305 401 947136 111 720169 511 279831 18 43 667546 401 947070 111 720476 511 279524 17 44 667786 400 947004 111 720783 511 279217 16 45 668027 400 946937 111 721089 511 278911 15 46 668267 400 946871 111 721396 511 278604 14 47 668506 399 946804 111 721702 510 278298 13 48 668746 399 946738 111 722009 510 277991 12 49 668986 399 946671 111 722315 510 277685 11 50 669225 399 946604 111 722621 510 277379 10 51 9.669464 398 9.946538 111 9.722927 510 10.277073 9 52 669703 398 946471 111 723232 509 276768 8 53 669942 398 946404 111 723538 509 276462 7 54 670181 397 946337 111 723844 509 276156 6 55 670419 397 946270 112 724149 509 275851 5 56 670658 397 946203 112 724454 509 275546 4 57 670896 397 946136 112 724759 508 275241 a 58 671134 396 946069 112 725065 508 274935 2 59 671372 396 946002 112 725369 508 274631 1 60 671609 396 945935 112 725674 508 274326 j Cosine Sine | Cotang. Tang. | M. Degrees. *.* (28 Degrees.) A TABLE OF LOGARITHMIC M. Sine D. Cosine D T.IMK. 1). Coranat. | 9.67160 396 9.94593. r m 9.72567 508 10.274321 60 1 67184 395 945866 m 72597 508 274021 59 2 67208 395 94580C 112 72628 507 2737H 58 3 67232 395 94573? 112 72658 507 273412 57 4 67255 395 94566fi 112 72689 507 2731 OS 56 5 67279 394 94559$ 112 72719 507 272803 55 6 67303 394 945531 112 72750 507 272499 54 7 67326 394 945464 113 72780 506 272195 53 8 67350 394 945396 113 72810 506 271891 52 9 67374 393 945328 113 72841 506 271588 51 10 67397 393 945261 113 72871 506 271284 50 11 9.67421 393 9.945193 113 9.729020 506 10.270980 49 12 674448 392 945125 113 729323 505 270677 48 13 674684 392 945058 113 729626 505 270374 47 14 674919 392 944990 113 729929 505 270071 46 15 675155 392 944922 113 730233 505 269767 45 16 675390 391 944854 113 730535 505 269465 44 17 675624 391 944786 113 730838 504 269162 43 18 675859 391 944718 113 731141 504 268859 42 19 676094 391 944650 113 731444 504 268556 41 20 676328 390 944582 114 731746 504 268254 40 21 9.676562 390 9.944514 114 9.732048 504 10.267952 39 22 676796 390 944446 114 732351 503 267649 38 23 677030 390 944377 114 732653 503 267347 37 24 677264 389 944309 114 732955 503 267045 36 25 677498 389 944241 114 733257 503 266743 35 26 677731 389 944] 72 114 733558 503 266442 34 27 677964 388 944104 114 733860 502 266140 33 28 678197 388 944036 114 734162 502 265838 32 29 678430 388 943967 114 734463 502 265537 31 30 678683 388 943899 114 734764 502 265236 30 31 9 678895 387 9.943830 114 9.735066 502 10.264931 29 32 679128 387 943761 114 735367 502 264633 28 33 679360 387 943693 115 735668 501 264332 27 34 679592 387 943624 115 735969 501 264031 26 35 679824 386 943555 115 736269 501 263731 25 36 680056 386 943486 115 736570 501 263430 24 37 680288 386 943417 115 736871 501 263129 23 38 680519 385 943348 115 737171 500 262829 22 39 680750 385 943279 115 737471 500 262529 21 40 680982 385 943210 115 737771 500 262229 20 41 9.681213 385 9.943141 115 9.738071 500 10.261929 19 42 681443 384 943072 115 738371 500 261629 18 43 681674 384 943003 115 738671 499 261329 17 44 681905 384 942934 115 738971 499 261029 16 45 682135 384 942864 115 739271 499 260729 15 46 682365 383, 942795! 116 739570 499 260430 14 47 "682595 383 942726 116 739870 499 260130 13 48 682825 383 942656 116 740169 499 259831 12 49 683055 383 942587 116 740468 498 259532 11 50 683284 382 942517 116 740767 498 259233 10 61 9.683514 382 9 . 942448 116 9.741066 498 10.258934 9 c.2 683743 382 942378 116 741365 498 258635 8 53 683972 382 942308 116 741664 498 258336 7 54 684201 381 942239 116 741962 497 258038 6 55 684430 381 942169 116 742261 497 257739 5 56 684658 381 942099 116 742559 497 257441 4 57 684887 380 942029 116 742858 497 257142 3 58 685115 380 941959 116 743156 497 256844 2 59 685343 380 941889 117 743454 497 256546 1 60 ' 6S5571 380 941819 117 743752 496 256248 Cosine Sinr: | | Cotang. Tang. M. 61 Degrees. SINES AM) TANGENTS. ^29 DegfCCS.) M. Sine D. Cosine D. | Tang. D. Cotang. 9.685571 380 9.941819 117 9.743752 496 10.256248 60 1 685799 379 941749 117 744050 496 255950 59 2 686027 379 941679 117 744348 496 255652 58 3 686254 379 941609 117 744645 496 255355 57 4 686482 379 941539 117 744943 496 255057 56 5 686709 378 941469 117 745240 496 254760 55 6 686936 378 941398 117 745538 495 254462 54 7 687163 378 941328 117 745835 495 254165 53 8 687389 378 941258 117 746132 495 253868 52 9 687616 377 941187 117 746429 495 253571 51 10 687843 377 941117 117 746726 495 253274 50 11 9.688069 377 9.941046 118 9.747023 494 10.252977 49 12 688295 377 940975 118 747319 494 252681 48 13 688521 376 940905 118 747616 494 252384 47 14 688747 376 940834 118 747913 494 252087 46 15 688972 376 940763 118 748209 494 251791 45 16 689198 376 940693 118 748505 493 251495 44 17 689423 375 940622 118 748801 493 251199 43 18 689648 375 940551 118 749097 493 250903 42 19 689873 375 940480 118 749393 493 250607 41 20 %690098 375 940409 118 749689 493 250311 40 21 9.690323 374 9.940338 118 9.749985 493 10.250015 39 22 690548 374 940267 118 750281 492 249719 38 23 690772 374 940196 118 750576 492 249424 37 24 690996 374 940125 119 750872 492 249128 36 25 691220 373 940054 119 751167 492 248833 35 26 691444 373 939982 119 751462 492 248538 34 27 691668 373 939911 119 751757 492 248243 33 28 691892 373 939840 119 752052 491 247948 32 29 692115 372 939768 119 752347 491 247653 31 30 6923391 372 939697 119 752642 491 247358 ,30 31 9.692562 372 9.939625 119 9.752937 491 107247063 29 32 692785 371 939554 119 753231 491 246769 28 33 693008 371 939482 119 753526 491 246474 27 34 693231 371 939410 119 753820 490 246180 26 35 693453 371 939339 119 754115 490 245885 25 36 693676 370 939267 120 754409 490 245591 24 37 693898 370 939195 120 754703 490 245297 23 38 694120 370 939123 120 754997 490 245003 22 39 694342 370 939052 120 755291 490 244709 21 40 694564' 369 938980 120 755585 489 244415 20 41 9.694786 369 9.938908 120 9.755878 489 10.244122 19 42 695007 369 938836 120 756172 489 243828 18 43 695229 369 938763 120 756465 489 243535 17 44 695450 368 938691 120 756759 489 243241 16 45 695671 368 938619 120 757052 489 242948 15 46 695892 368 938547 120 757345 488 242655 14 47 696113 368 938475 120 757638 488 242362 13 48 696334 367 ' 938402 121 757931 488 242069 12 49 696554 367 938330 121 758224 488 241776 11 50 696775; 367 938258 121 758517 488 241483 10 51 9.696995: 367 9.938185 121 9.758810 488 10.241190 Q 52 697215 366 938113 121 759102 487 240898 8 53 697435 366 938040J 121 759395 487 240605 7 54 697654 366 9379671 121 759687 487 240313 6 55 697874J 366 937895 121 759979 487 24002 5 56 6980941 365 937822' 121 760272 487 239728 4 57 698313: 365 937749 121 760564 487 239436 3 58 698532 355 937670 121 760856 486 239144 2 59 698751 365 937604J 121 761148 486 238852 1 60 698970 364 9375311 121 761439 486 23856 | Cosine Sine Cotang. Tang. M. Decree*. 48 (30 Degrees.) A TABLE OP LOGARITHMIC M. Sine D. | Cosine | D. j Tans;. D. Cotang. | 9.698970 364 9.937531 121 9.761439 486 10.238561 60 1 699189 364 937458 122 761731 486 238269 59 2 699407 364 937385 122 762023 486 237977 58 3 699626 364 937312 122 762314 486 237686 57 4 699844 363 937238 122 762606 485 237394 56 5 700062 363 937165 122 762897 485 237103 55 6 700280 363 937092 122 763188 485 236812 54 7 700498 363 937019 122 763479 485 236521 53 8 700716 363 936946 122 763770 485 236230 52 9 700933 362 936872 122 764061 485 235939 51 10 701151 362 936799 122 764352 484 235648 50 11 9.701368 362 9.936725 122 9.764643 484 10.235357 49 12 701585 362 936652 123 764933 484 235067 48 13 701802 361 936578 123 765224 484 234776 47 14 702019 361 936505 123 765514 484 234486 46 15 702236 361 936431 123 765805 484 234195 45 16 702452 361 936357 123 766095 484 233905 44 17 702669 360 936284 123 766385 483 233615 43 18 702885 360 936210 123 766675 483 233325 42 19 703101 360 936136 123 766965 483 233035 41 20 703317 360' 93M62 123 767255 483 232745 40 21 9.703533 359 9 . 935988 123 9.767545 483 10.232455 39 22 703749 359 935914 123 767834 483 232166 38 23 703964 359 935840 123 768124 482 231876 37 24 704179 359 935766 124 768413 482 231587 36 25 704395 359 935692 124 768703 482 231297 35 26 704610 358 935618 124 768992 482 231008 34 27 704825 358 935543 124 769281 482 230719 33 28 705040 358 935469 124 769570 482 230430 32 29 705254 358 935395 124 769860 481 230140 31 30 705469 357 935320 124 770148 481 229852 30 31 9.705683 357 9.935246 124 9.770437 481 10.229563 29 32 705898 357 935171 124 770726 481 229274 28 33 706112 357 935097 124 771015 481 228985 27 34 706326 356 935022 124 771303 481 228697 26 35 706539 356 934948 124 771592 481 228408 25 36 706753 356 934873 124 771880 480 228120 24 37 706967 356 934798 125 772168 480 227832 23 38 707180 355 934723 125 772457 480 227543 22 39 707393 355 934649 125 772745 480 227255 21 40 707606 355 934574 125 773033 480 226967 20 41 9.707819 355 9.934499 125 9.773321 480 10.226679 19 42 708032 354 934424 125 773608 479 226392 18 43 708245 354 934349 125 773896 479 226104 17 44 708458 354 934274 125 774184 479 225816 16 45 708670 354 934199 125 774471 479 225529 15 46 708882 353 934123 125 774759 479 225241 14 47 709094 353 934048 125 775046 479 224954 13 48 709306 353 933973 125 775333 479 224667 12 49 709518 353 933898 126 775621 478 224379 11 50 709730 353 933822 126 775908 478 224092 10 51 9.709941 352 9.933747 126 9.776195 478 10.223805 9 52 710153 352 933671 126 776482 478 223518 8 53 710364 352 933596 126 776769 478 223231 7 54 710575 352 933520 126 777055 478 222945 6 55 710786 351 933445 126 777342 478 222658 5 56 71099? 351 933369 126 777628 477 222372 4 57 711208 351 933293 126 777915 477 222085 3 58 711419 351 933217 126 778201 477 221799 2 59 711629 350 933141 126 778487 477 221512 1 60 711839 350 933066 126 778774 477 221226 Cosine 1 Bine | Uotaiig. | Tung. | M. 59 Degrees. SINES AND TANGENTS. (31 Degrees.) 49 If. Sine n. Cosine | D. Tantr. D. Cotang. 9 711839 350 9.933066 126 9.778774 477 10.221226 60 1 712050 350 932990 127 779060 477 220940 59 o 712260 350 932914 127 779346 176 220654 58 3 712469 349 932838 127 779632 476 220368 57 4 712679 849 932762 127 779918 476 220082 56 5 712889 349 932685 127 780203 476 219797 55 6 713098 349 932609 127 780489 476 219511 54 7 713308 349 932533 127 780775J 476 219225 53 8 713517 348 932457 127 781060 476 218940 52 9 713726 348 932380 127 781346 475 218654 51 10 713935 348 932304 127 781631 475 218369 50 11 9.714144 348 9.932228 127 9.781916 475 10.218084 49 12 714352 347 932151 127 782201 475 217799 48 13 714561 347 932075 128 782486 475 217514 47 14 714769 347 931998 128 782771 475 217229 46 15 "714978 347 931921 128 783056 475 216944 45 16 715186 347 931845 128 783341 475 216659 44 17 715394 346 931768 128 783626 474 216374 43 18 715602 346 931691 128 783910 474 216090 -42 19 715809 346 931614 128 784195 474 215805 41 20 716017 346 931537 128 784479 474 215521 40 21 9,716224 345 9.931460 128 9.784764 474 10.215236 39 22 716432 345 931383 128 785048 474 214952 38 23 716639 345 931306 128 785332 473 214668 37 24 716846 345 931229 129 785616 473 214384 36 25 717053 345 931152 129 785900 473 214100 35 26 717259 344 931075 129 786184 473 213S1G 34 27 717466 344 980998 129 786468 473 213532 33 28 717673 344 930921 129 786752 473 213248 32 29 717879 344 930843 129 787036 473 212964 31 30 718085 343 930766 129 787319 472 212681 30 31 9.718291 343 9.930688 129 9.787603 472 1(K2 12397 29 32 718497 343 930611 129 787886 472 212114 28 33 718703 343 930533 129 788170 472 211830 27 34 718909 343 930456 129 788453 472 211547 26 35 719114 342 930378 129 788736 472 211264 25 36 719320 342 930300 130 789019 472 210981 24 37 719525 - 342 930223 130 789302 471 210698 23 38 719730 342 930145 130 789585 471 210415 22 39 719935 341 930067 130 789868 471 210132 21 40 720140 341 929989 130 '790151 471 209849 20 41 9.720345 341 9.929911 130 9 . 790433 471 10.209567 19 42 720549 341 929833 130 790716 471 209284 18 43 720754 340 929755 130 790999 471 209001 17 44 720958 340 929677 130 791281 471 208719 16 45 721162 340 929599 130 791563 470 208437 15 46 721366 340 929521 130 791846 470 208154 14 47 721570 340 929442 130 7921 28 j 470 207872 13 48 721774 339 929364 131 792410 470 207590 12 49 721978 339 929286 131 792692 470 207308 11 50 722181 j 339 929207 131 792974 470. 207026 10 51 9.7223851 339 9.929129 131 9.793256 470 10.206744 9 52 7225881 339 929050 131 793538 469 206462 8 53 722791 338 928972 .131 793819 469 206181 7 54 722994 338 928893 131 794101 469 205899 6 55 723197 338 928815 131 794383 469 205617 5 56 723400 338 928736 131 794664' 469 205336 4 57 723603 337 928657 131 794945 469 205055 3 58 723805 337 928578 131 795227 469 204773 2 59 724007 337 928499 131 795508 468 204492 1 60 724210 337 928420 131 795789; 468 204211 Cosine Sine | Cotarig. Tang. M. 58 Degrees. G 50 (32 Degrees.) A TABLE OF LOGARITHMIC M. Sine D. Cosine | D. Tanjr. D. Ootang. | 9.724210 337 9.928420 132 9 . 795789 468 10.204211 60 1 724412 337 928342 132 796070 468 203930 59 2 724614 336 928263 132 796351 468 203649 58 3 724816 336 928183 132 796632 468 203368 57 4 725017 336 928104 132 796913 468 203087 56 5 725219 336 928025 132 797194 468 202806 55 6 725420 335 927946 132 797475 468 202525 54 7 725622 335 927867 132 797755 468 202245 53 8 725823 335 927787 132 798036 467 201964 52 9 726024 335 927708 132 798316 467 201684 51 10 726225 335 927629 132 798596 467 201404 50 11 9 . 726426 334 9.927549 132 9 . 798877 467 10.201123 49 12 726626 334 927470 133 799157 467 200843 48 13 726827 334 927390 133 799437 467 200563 47 14 727027 334 927310 133 799717 467 200283 46 15 727228 334 927231 133 799997 466 200003 45 16 727428 333 927151 133 800277 466 199723 44 17 727628 333 927071 133 800557 466 199443 43 18 727828 333 926991 133 800836 466 199164 42 19 728027 333 926911 133 801116 466 198884 41 20 728227 333 926831 133 801396 466 198604 40 21 9 . 728427 332 9.926751 133 9.801675 466 10.198325 39 22 728626 332 926671 133 801955 466 198045 38 23 728825 332 926591 133 802234 465 197766 37 24 729024 332 926511 134 802513 465 197487 36 25 729223 331 926431 134 802792 465 197208 35 26 729422 331 926351 134 803072 465 196928 34 27 729621 331 926270 134 803351 465 196649 33 28 729820 331 926190 134 803630 465 196370 32 29 730018 330 926110 134 803908 465 196092 31 30 730216 330 926029 134 804187 465 195813 30 31 9.730415 330 9 . 925949 134 9.804466 464 10.195534 29 32 730613 330 925868 134 804745 464 195255 28 33 730811 330 925788 134 805023 464 194977 27 34 731009 329 925707 134 805302 464 194698 26 35 731206 329 925626 134 805580 464 194420 25 36 731404 329 925545 135 805859 464 194141 24 37 731602 329 925465 135 806137 464 193863 23 38 731799 329 925384 135 806415 463 193585 22 39 731996 328 925303 135 806693 463 193307 21 40 732193 328 925222 135 806971 463' 193029 20 41 9.732390 328 9.925141 135 9.807249 463 10.192751 19 42 732587 328 925060 135 807527 463 192473 18 43 732784 328 924979 135 807805 463 192195 17 44 732980 327 924897 135 808083 463 191917 16 45 733177 327 924816 135 808361 463 191639 15 46 733373 327 924735 136 808638 462 191362 14 47 733569 327 924654 136 808916 462 191084 13 48 733765 327 924572 136 809193 462 190807 12 49 733961 326 924491 136 809471 462 190529 11 50 734157 326 924409 136 809748 462 190252 10 51 9.734353 326 9.924328 136 9.810025 462 10.189975 9 52 734549 326 924246 136 810302 462 189698! 8 53 734744 325 924164 136 810580 462 189420! 7 54 734939 325 924083 136 810857 462 189143 6 55 735135 325 924001 136 81 J 134 461 188866 5 56 735330 325 923919 136 811410 461 188590 4 57 735525 325 923837 136 811687 461 188313 3 58 735719 324 923755 137 811964 461 188036 2 59 735914 324 923673 137 812241 461 187759 1 00 73f> ! 09 324 923591 137 81S517 461 187483 () Cosine | Sine Cotang. Tang. M. 57 Degrees. SINES AND TANGENTS. (33 Degrees.) 51 M.I Sine | D. j Cosine | D. | Tang. D. Cotanx. | 9.7361091 324 9.923591 137 9.812517 461 10.187482|60 1 736303 324 923509 137 812794 461 187206 59 2 736498 324 923427 137 813070 461 186930 58 3 736692 323 923345 137 813347 460 186653 57 4 736886 323 923263 137 813623 460 186377 56 ft 737080 323 923181 137 813899 460 186101 55 6 737274 323 923098 137 814175 460 185825 54 7 737467 323 923016 137 814452 460 185548 53 8 737661 322 922933 137 814728 460 185272 52 9 737855 322 922851 137 815004 460 184996 51 10 738048 322 922768 138 815279 460 184721 50 11 9.738241 322 9.922686 138 9.815555 459 10.184445 49 12 738434 322 922603 138 815831 459 184169 48 13 738627 321 922520 138 816107 459 183893 47 14 738820 321 922438 138 816382 459 183618 46 15 739013 321 922355 138 816658 459 183342 45 16 739206 321 922272 138 816933 459 183067 44 17 739393 321 922189 138 817209 459 182791 43 18 739590 320 922106 138 817484 459 182516 42 19 739783 320 922023 138 817759 459 182241 41 20 739975 320 921940 138 818035 458 181965 40 21 9.740167 320 9.921857 139 9.818310 458 10.181690 39 22 740359 320 921774 139 818585 458 181415 38 23 740550 319 921691 139 818860 458 181140 37 24 740742 319 921607 139 819135 458 180865 36 25 740934 319 921524 139 819410 458 180590 35 26- 741125 319 921441 139 819684 458 180316 34 27 741316 319 921357 139 819959 458 180041 33 28 741508 318 921274 139 820234 458 179766 32 29 741699 318 921190 139 820508 457 179492 31 30 741889 318 921107 139 820783 457 179217 30 31 9.742080 318 9.921023 139 9.821057 457 10.178943 29 32 742271 318 920939 140 821332 457 178668 28 33 742462 317 920856 140 821606 457 178394 27 34 742652 317 920772 140 821880 457 178120 26 35 742842 317 920688 140 822154 457 177846 25 36 743033 317 920604 140 822429 457 177571 24 37 743223 317 920520 140 82270S 457 177297 23 38 743413 316 920436 140 822977 456 177023 22 39 743602 316 920352 140 823250 456 176750 21 40 743792 316 920268 140 823524 456 176476 20 41 9.743982 316 9.920184 140 9.823798 456 10.176202 19 42 744171 316 920099 140 824072 456 175928 18 43 744361 315 920015 140 824345 456 175655 17 44 744550 315 919931 141 824619 456 175381 16 45 744739 315 919846 141 824893 456 175107 15 46 744928 315 919762 141 825166 456 174834 14 47 745117 315 919677 141 825439 455 174561 13 48 745306 314 919593 141 825713 455 174287 12 49 745494 314 919508 141 825986 455 174014 11 50 745683 314 919424 141 826259 455 173741 10 51 9.745871 314 9.919339 141 9.826532 455 1 Q.I 73468 9 52 746059 314 919254 141 826805 455 173195 8 53 746248 313 9191691 141 827078 455 172922 7 54 746436 313 919085 141 827351 455 172649 6 55 746624 313 919000 141 827624 455 172376 5 56 746812 313 918915 142 827897 454 172103 4 57 746999 313 918830 142 828170 454 171830 3 58 747187 312 918745 142 828442 454 171558 2 69 747374 312 918659 142 828715 454 171285 1 60 747562 312 918574 142 828987 454 171013 | Cosine [ Sine Cotang. Tang. | M. 56 Degrees. (34 Degrees.") A TABLE OF LOGARITHMIC M. Sine D. Cosine D. | Tang. \ D. Cotang. j 9.747562 312 9.918574 142 9.828987 454 10.171013 60 1 747749 312 918489 142 829260 454 170740 59 2 747936 312 918404 142 829532 454 170468 58 3 748123 311 918318 142 829805 454 170195 57 4 748310 311 918233 142 830077 454 169923 56 5 748497 311 918147 142 830349 453 169651 55 6 748683 311 918062 142 830621 453 169379 54 7 748870 311 917976 143 830893 453 169107 53 8 749056 310 917891 143 831165 453 168835 52 9 749243 310 917805 143 831437 453 168563 51 10 749429 310 917719 143 831709 453 168291 50 11 9.749615 310 9.917634 143 9.831981 453 10.168019 49 12 749801 310 917548 143 832253 453 167747 48 13 749987 309 917462 143 832525 453 167475 47 14 750172 309 917376 143 832796 453 167^04 46 15 750358 309 917290 143 833068 452 166932 45 16 750543 309. 917204 143 833339 452 166661 44 17 750729 309 917118 144 833611 452 166389 43 18 750914 308 917032 144 833882 452 1661 IS 42 19 751099 308 916946 144 834154 452 165846 41 20 751284 308 916859 144 834425 452 165575 40 21 9.751469 308 9.916773 144 9.834696 452 10.165304 39 22 751654 308 916687 144 834967 452 165033 38 23 751839 308 916600 144 835238 452 164762 37 24 752023 307 916514 144 835509 452 164491 36 25 752208 307 916427 144 835780 451 164220 35 26 752392 307 916341 144 836051 451 163949 34 27 752576 307 916254 144 836322 451 163678 33 28 752760 307 916167 145 836593 451 163407 32 29 752944 306 916081 145 836864 451 16313,6 31 30 753128 306 915994 145 837134 451 162866 30 31 9.753312 306 9.915907 145 9.837405 451 10.162595 29 32 753495 306 915820 145 837675 451 162325 28 33 753679 306 915733 145 837946 451 162054 27 34 753862 305 915646 145 838216 451 161784 26 35 754046 305 915559 145 838487 450 161513 25 36 754229 305 915472 145 838757 450 161243 24 37 754412 305 915385 145 839027 450 160973 23 38 754595 305 915297 145 839297 450 160703 22 39 754778 304 915210 145 839568 450 160432 21 40 754960 304 915123 146 839838 450 160162 20 41 9.755143 304 9.915035 146 9.840108 450 10.159892 19 42 755326 304 914948 146 840378 450 159622 18 43 755508 304 914860 146 840647 450 159353 17 44 755690 304 914773 146 840917 449 159083 16 45 755872 303 914685 146 841187 449 158813 15 46 756054 303 914598 146 841457 449 158543 14 47 756236 303 914510 146 841726 449 158274 13 48 756418 303 914422 146 841996 449 158004 12 49 756600 303 914334 146 842266 449 157734 11 50 756782 302 914246 147 842535 449 157465 10 51 9.756963 302 9.914158 147 9.842805 449 10.157195 9 52 757144 302 914070 147 843074 449 156926 8 53 757326 302 913982 147 843343 449 156657 7 54 757507 302 913894 147 843612 449 156388 6 55 757688 301 913806 147 843882 448 156118 5 56 757869 301 913718 147 844151 448 155849 4 57 758050 301 913630 147 844420 448 155580 3 58 758230 301 913541 147 844689 448 155311 2 59 758411 301 913453 147 844958 448 155042 1 60 758591 301 913365 147 845227 448 154773 'T Cosine Sine j | Cotang. | Tang. j M. 55 Degrees. SINES AND TANGENTS. (35 Degrees.) 53 M. | Sine | D. Cosine P. | Tane | D. Cotaiig. | 9 . 75859 1 301 9.913365 147 9.845227 448 10.154773 60 1 758772 300 913276 147 845496 448 154504 59 2 758952 300 913187 148 845764 448 154236 58 3 759132 300 913099 148 846033 448 153967 57 4 759312 300 913010 148 846302 448 153698 56 5 759492 300 912922 148 846570 447 153430 55 6 759672 299 912833 148 846839 447 153161 54 7 759852 299 912744 148 847107 447 152893 53 8 760031 299 912655 148 847376 447 152624 52 9 760211 299 912566 148 847644 447 152356 51 10 760390 299 912477 14S 847913 447 152087 5.0 11 9.760569 298 19.912388 148 9.848181 447 10.151819 49 12 760748 298 912299 149 848449 447 151551 48 13 760927 298 912210 149 848717 447 151283 47 14 761106 298 912121 149 848986 447 151014 46 15 761285 298 912031 149 849254 447 150746 45 16 761464 298 911942 149 849522 447 150478 44 17 761642 297 911853 149 849790 446 150210 43 18 761821 297 911763 149 850058 446 149942 42 19 761999 297 911674 149 850325 446 149675 41 20 762177 297 911584 149 850593 446 149407 40 21 9.762356 297 9.911495 149 9.850861 446 10.149139 39 22 762534 296 911405 149 851129 446 148871 38 23 762712 296 911315 150 851396 446 148604 37 24 762889 296 911226 150 851664 446 148336 36 25 763067 296 911136 150 851931 446 148069 35 26 763245 296 911046 150 852199 446 147801 34 27 763422 296 910956 150 852466 446 147534 33 28 763600 295 910866 150 852733 445 147267 32 29 763777 295 910776 150 853001 445 146999 31 30 763954 295 910686 150 853268 445 146732 30 31 9.764131 295 9.910596 150 9.853535 445 10.146465 29 32 764308 295 910506 150 853802 445 146198 28 33 764485 294 910415 150 854069 445 145931 27 34 764662 294 910325 151 854336 445 145664 26 35 764838 294 910235 151 '854603 445 145397 25 36 765015 294 910144 151 854870 445 145130 24 37 765191 294 9100,54 151 855137 445 144863 23 38 765367 294 909963 151 855404 445 144596 22 39 765544 293 909873 151 855671 444 144329 21 40 785720 293 909782 151 855938 444 144062 20 41 9.765896 293 9.909691 151 9.856204 444 10.143796 19 42 766072 293 909601 151 856471 444 143529 18 43 766247 293 909510 151 856737 444 143263 17 44 766423 293 909419 151 857004 444 142996 16 45 766598 292 909328 152 857270 444 142730 15 46 766774 292 909237 152 857537 444 142463 14 47 766949 292 909146 152 857803 444 142197 13 48 767124 292 909055 152 858069 444 141931 12 49 767300 292 908964 152 858336 444 141664 11 50 767475 291 908873 152 858602 443 141398 10 51 9.767649 291 9.908781 152 9.858868 443 10.141132 9 52 767824 291 908690 152 859134 443 140866 8 53 767999 291 908599 152 859400 443 140600 7 54 768173 291 908507 152 859666 443 140334 6 55 768348 290 908416 153 859932 443 140068 5 56 768522 290 908324 153 860198 443 139802 4 57 768697 290 908233 153 860464 443 139536 3 58 768871 290 908141 153 860730 443 139270 2 59 769045 290 908049 153 860995 443 139005 1 60 769219! 290 907958 153 861261 443 138739 | Cosine Sine | Uotanj!. | Tang. M. 54 Degrees. 54 (36 Degrees.) A TABLE OF LOGARITHMIC M. Sine D Cosine | 1). | Tang. D. | Colanp. 9. 7692 19 290 9.9079581 153 9.861261 443 "10.138739 60 1 769393 289 907866 153 861527 443 138473 59 2 769566 289 907774 153 861792 442 138208 58 3 769740 289 907682 153 862058 442 137942 57 4 769913 289 907590 153 862323 442 137677 56 5 770087 289 907498 153 862589 442 137411 55 6 770260 288 907406 153 862854 442 137146 54 7 770433 288 907314 154 863119 442 136881 53 8 770606 288 907222 154 863385 442 136615 52 9 770779 288 907129 154 863650 442 136350 51 10 770952 288 907037 154 863915 442 136085 50 11 9.771125 288 9 906945 154 9.864180 442 10.135820 49 12 771298 287 906852 154 864445 442 135555 48 13 771470 287 906760 154 864710 442 135290 47 14 771643 287 906667 154 864975 441 135025 46 15 771815 287 906575 154 865240 441 134760 45 16 771987 287 906482 154 865505 441 134495 44 17 772159 287 906389 155 865770 441 134230 43 18 772331 286 906296 155 866035 441 133965 42 19 772503 286 906204 155 866300 441 133700 41 20 772675 286 906111 155 866561 441 133436 40 21 9.772847 286 9.906018 155 9.866829 441 10.133171 39 22 773018 286 905925 155 867094 441 132906 38 23 773190 286 905832 155 867358 441 132642 37 24 773361 285 905739 155 867623 441 132377 36 25 773533 285 905645 155 867887 441 132113 35 26 773704 285 905552 155 868152 440 131848 34 27 773875 285 905459 155 868416 440 131584 33 28 774046 285 905366 156 868680 440 131320 32 29 774217 285 905272 15H 868945 440 131055 31 30 774388 284 905179 156 869209 440 130791 30 31 9.774558 284 9.905085 156 9.869473 440 10.130527 29 32 774729 284 904992 156 869737 440 130263 28 33 774899 284 904898 156 870001 440 129999 27 34 775070 284 904804 156 870265 440 129735 26 35 775240 284 904711 156 870529 440 129471 25 36 775410 283 904617 156 870793 440 129207 24 37 775580 283 904523 156 871057 440 128943 23 38 775750 283 904429 157 871321 440 128679 22 39 775920 283 904335 157 871585 440 128415 21 40 776090 283 904241 157 871849 439 128151 20 41 9.776259 283 9.904147 157 9.872112 439 10.127888 19 42 776429 282 904053 157 872376 439 127624 18 43 776598 282 903959 157 872640 439 127360 17 44 776768 282 903864 157 872903 439 127097 16 45 776937 282 903770 157 873167 439 126833 15 46 777106 282 903676 157 873430 439 1265YO 14 47 777275 281 903581 157 873694 439 126306 13 48 777444 281 903487 157 873957 439 126043 12 49 777613 281 903392 158 874220 439 125780 11 50 777781 281 903298 1-58 874484 439 '125516 10 51 9.777950 281 9.903203 158 9.874747 439 10.125253 9 52 778119 281 903108 158 875010 439 124990 8 53 778287 280 903014 158 875273 438 124727 7 54 778455 280 902919 158 875536 438 124464 6 55 778624 280 902824 158 875800 438 124200 5 56 778792 280 902729 158 876063 438 123937 4 57 778960 280 902634 158 876326 438 123674 3 58 779128 280 902539 159 876589 438 123411 2 59 779295 279 902444 159 876851 438 123149 1 60 779463 279 902349 159 877114 438 122888 . Cosine I Sine | Cotang. | | Tang. J M. 53 Degrees. SINES AND TANGENTS. (37 Degrees.) 55 M. Sine D. | Cosine I). | T:IM<; [). Cotnnvr. | 9 . 779463 279 9 . 902349 159 9.877114 438 10. 1228^6 60 1 779631 279 902253 159 87737? 438 122623 59 9 779798 279 902158 159 877640 438 122360 58 3 779966 279 902063 159 877903 438 122097 57 4 780133 279 901967 159 878165 438 121835 56 5 780300 278 901872 159 878428 438 121572 55 6 780467 278 901776 159 878691 438 121309 54 7 780634 278 901681 159 878953 437 121047 53 8 780801 278 901585 159 879216 437 120784 52 9 780968 278 901490 159 879478 437 120522 51 10 781134 278 901394 160 879741 437 120259 50 11 9.781301 277 9.901298 160 9.880003 437 10.119997 49 12 781468 277 901202 160 880265 437 119735 48 13 781634 277 901106 160 880528 487 119472 47 14 781800 277 901010 160 880790 437 119210 46 15 781966 277 900914 160 881052 437 118948 45 16 782132 277 900818 160 881314 437 118686 44 17 782298 276 900722 160 881576 437 1 18424 43 18 782464 276 900626 160 881839 437 118161 42 19 782630 276 900529 160 882101 437 117899 41 20 782796 276 900433 161 882363 436 117637 40 21 9.782961 276 9.900337 161 9.882625 436 10.117375 39 22 783127 276 900240 161 882887 436 117113 38 23 783292 275 900144 161 883148 436 116852 37 24 783458 275 900047 161 883410 436 116590 36 26 783623 275 899951 161 883672 436 116328 35 25 783788 275 899854 161 883934 436 116066 34 27 783953 275 899757 161 884196 436 115804 33 28 784118 275 899660 161 884457 436 115543 32 29 784282 274 899564 161 884719 436 115281 31 30 784447 274 899467 162 884980 436 115020 30 31 9.784612 274 9.899370 162 9.885242 436 10.114758 29 32 784776 274 899273 162 885503 436 114497 28 33 784941 274 899176 162 885765 436 1 14235 27 34 785105 274 899078 162 886026 436 113974 26 35 785269 273 898981 1&2 886288 436 113712 25 36 785433 273 898884 162 886549 435 113451 24 37 785597 273 898787 162 886810 435 113190 23 38 785761 273 898689 162 887072 435 112928 22 39 785925 273 898592 162 887333 435 112667 21 40 786089 273 898494 163 887594 435 112406 20 41 9.786252 272 9.898397 163 9.887855 435 10.112145 19 42 786416 272 898299 163 888116 435 111884 18 43 786579 272 898202 163 888377 435 111623 17 44 786742 272 898104 1-63 888639 435 111361 16 45 786906 272 898006 163 888900 435 111100 15 46 787069 272 897908 163 889160 435 110840 14 47 787232 271 897810 163 889421 435 110579 13 48 787395 271 897712 163 889682 435 110318 12 49 787557 271 897614 163 889943 435 110057 11 50 787720 271 897516 163 890204 434 109796 10 51 9.787883 271 9.897418 164 9.890465 434 10.109535 9 52 788045 271 897320 164 890725 434 109275 8 53 788208 271 897222 164 890986 434 109014 7 54 788370 270 897123 164 891247 434 108753 6 55 788532 270 897025 164 891507 434 108493 5 56 788694 270 896926 164 891768 434 ,108232 4 57 788856 270 896828 164 892028 434 107972 3 58 789018 270 890729 164 892289 434 107711 2 59 789180 270 896631 164 892549 434 107451 1. 60 789342 269 896532 164 892810 '434 107190 Cosine | Sine | Cotang. Tang. j 52 Degrees 56 (38 Degrees.) A TABLE OF LOGARITHMIC M. Sine D. Cosine D. Tanj;. D. Cotang. | 9.789342 269 9.89653:2 164 9.892810 434 10. 107190; 60 1 789504 269 896433 165 893070 434 106930 59 2 789665 269 896335 165 893331 434 106669 58 3 789827 269 896236 165 893591 434 106409 57 4 789988 269 896137 165 893851 434 106149 56 5 790149 269 896038 165 894111 434 105889 55 6 790310 268 895939 165 894371 434 105629 54 7 790471 268 895840 165 894632 433 105368 53 8 790632 268 895741 165 894892 433 105108 52 9 790793 268 895641 165 895152 433 104848 51 10 . 790954 268 895542 165 895412 433 104588 50 11 9.791115 268 9.895443 166 9.895672 433 10,104328 49 12 791275 267 895343 166 895932 433 104068 48 13 791436 267 895244 166 896192 433 103808 47 14 791596 267 895145 166 896452 433 103548 46 15 791757 267 895045 166 896712 433 103288 45 16 791917 267 894945 166 896971 433 103029 44 17 792077 267 894846 166 897231 433 102769 43 18 792237 266 894746 166 897491 433 102509 42 19 792397 266 894646 166 897751 433 102249 41 20 792557 266 894546 166 898010 433 101990 40 21 9.792716 266 9.894446 167 9.898270 433 10.101730 39 22 792876 266 894346 lt>7 898530 433 101470 38 23 793035 266 894246 167 898789 433 101211 37 24 793195 265 894146 167 899049 432 100951 36 25 793354 265 894046 167 899308 432 100692 35 26 793514 265 893946 167 899568 432 100432 34 27 793673 265 893846 167 899827 432 100173 33 28 793832 265 893745 167 900086 432 099914 32 29 793991 265 893645 167 900346 432 099654 31 30 794150 264 893544 167 900605 432 099395 30 31 9.794308 264 9.893444 168 9.900864 432 10.099136 29 32 794467 264 893343 168 901124 432 098876 28 33 794626 264 893243 168 901383 432 098617 27 34 794784 264 893142 168 901642 432 098358 26 35 794942 264 893041 168 901901 432 098099 25 36 795101 264 892940 168 902160 432 097840 24 37 795259 263 892839 168 902419 432 097581 23 38 795417 263 892739 168 902679 432 097321 22 39 795575 263 892638 168 902938 432 097062 21 40 795733 263 892536 168 903197 431 096803 20 41 9.795891 263 9.892435 169 9.903455 431 10.096545 19 42 796049 263 892334 169 903714 431 096286 18 43 796206 263 892233 169 903973 431 096027 17 44 796364 262 892132 169 904232 431 095768 16 45 796521 262 892030 169 904491 431 095509 15 46 796679 262 891929 169 904750 431 095250 14 47 796836 262 891827 169 905008 431 094992 43 48 796993 262 891726 169 905267 431 094733 12 49 797150 261 891624 169 905526 431 094474 11 50 797307 261 891523 170 905784 431 094216 10 51 9.797464 261 9.891421 170 9.906043 431 10.093957 9 52 797621 261 891319 170 906302 431 093698 8 53 797777 261 891217 170 906560 431 093440 7 54 797934 261 891115 170 906819 431 093181 6 55 798091 261 891013 170 907077 431 092923 5 56 798247 261 890911 170 907336 431 092664 4 57 798403 260 890809 170 907594 431 092406 3 58 798560 260 890707 170 907852 431 092148 2 59 798716 260 . 890605 170 908111 430 091889 1 60 798872 260 890503 170 908369 430 091631 Cosine Sine Coiang. Tang. 1 M. 51 Decrees. SINES AND TANGENTS. (39 Degrees.) 57 M. | Sine n. C.isine D. Tana. | D. Cotans. 9.798872 200 9.890503 170 9.908369 430 10.091631 60 1 7990281 260 890400 171 908628 430 091372 59 2 799184! 260 890298 171 908886 430 091114 58 3 799339; 259 890195 171 909144 430 090856 57 4 799495 259 890093 171 909402 430 090598 56 5 799651 259 889990 171 909660 430 090340 55 6 799806 259 889888 171 909918 430 090082 54 7 799962 259 88978,5 171 910177 430 089823 53 8 800117 259 889682 171 910435 430 089565 52 9 800272 258 . 889579 171 910693 430 08930? 51 10 800427 258 889477 171 910951 430 089049 50 11 9.800582 258 9.8893/4 172 9.911209; 430 10.088791 49 12 800737 258 889271 172 91U67 430 088533 48 13 800892 258 889168 172 911724 430 088276 47 14 801047 258 889064 172 911982 430 088018 46 15 801201 258 888961 172 912240 430 087760 45 16 801356 257 88888 172 912498 430 087502 44 17 801511 257 888755 172 912756 430 087244 43 18 801665 257 888651 172 913014 429 0869S6 42 19 801819 257 888548 172 913271 429 086729 41 20 801973 257 888444 173 913529 429 086471 40 21 9.802128 257 9.888341 173 9.913787 429 10.086213 39 22 802282 256 888237 173 914044 429 085956 38 23 802436 256 888134 173 914302 429 085698 37 24 802589 256 888030 173 914560 429 085440 36 25 802743 256 887926 173 914817 429 085183 35 26 ' 802897 256 887822 173 915075 429 084925 34 27 803050 256 887718 173 915332 429 084668 33 28 803204 256 887614 173 915590 429 084410 32 29 803357 255 887510 173 915847 429 084153 31 30 803511 255 887406 174 916104 429 083896 30 31 9.803664 255 9.887302 174 9.916362 429 10,083638 29 32 803817 255 887198 174 916619 429 083381 28 33 803970 255 887093 174 9168771 429 083123 M 34 804123 255 886989 174 917134J 429 082866 26 35 804276 254 886885 174 917391 429 082609 25 36. 804428 254 886780 174 917648 429 082352 24 <>v 804581 254 886676 174 917905 429 082095 23 38 804734 254 886571 174 918163 428 081837 22 39 804886 254 886466 174 918420! 428 08^580 21 40 805039 254 886362 175 918677 428 081323 20 41 9.805191 254 9.886257 175 9.918934 428 10.081066 19 42 805343 253 886152 175 919191 428 080809 18 43 805495 253 886047 175 919448 428 080552 17 44 805647 253 885942 175 919705 428 080295 16 45 805799 253 885837 175 919962 428 080038 15 46 805951 253 885732 175 920219 428 079781 14 47 806103 253 885627 175 920476 428 079624 13 48 806254 253 885522 175 920733 428 079267 12 49 806406 252 885416 175 920990 428 079010 11 50 806557 252 885311 176 921247 428 078753 10 51 9.806709 252 9.885205 176 9.921503 428 10.078497 9 52 806860 252 885100 176 921760! 428 078240 8 53 807011 252 884994 176 922017 428 077983 7 54 807163 252 884889 176 9222741 428 077726 6 55 807314 S52 884783 176 922530 428 077470 5 56 807465 251 884677 176 922787 428 077213 4 57 807615 251 884572 176 923044 428 076956 3 58 807766 251 884466 176 923300i 428 076700 2 59 807917 251 884360 176 923557 427 076443 1 60 808067' 251 884254 177 923813! 427 076187 '0 Cosine | Sine Cotansf. | Tan?:. M. 50 Decrees. H 58 (40 Degrees.) A, TABLE OP LOGAKITHMIC M. S-He D. Cosine | D. | Tang. D. Cotang. | 9.808067 251 9.884254 177 9.923813 427 10.076187 60 1 808218 251 884148 177 924070 427 07593U 59 2 808368 251 884042 177 924327 427 075673 58 3 808519 250 883936 177 924583 427 075417 57 4 808669 250 883829 177 924840 427 075160 56 5 . 808819 250 883723 177 925096 427 074904 55 6 808969 250 883617 177 925352 427 074648 54 7 809119 250 883510 177 925609 427 07439 ] 53 8 809269 250 883404 177 925865 427 074135 52 9 809419 249 883297 178 926122 427 073878 51 10 809569 249 883191 178 926378 427 073622 50 11 9.809718 249 9.883084 178 9.926634 427 10.073366 49 12 809868 249 882977 178 926890 427 073110 48 13 810017 249 882871 178 927147 427 072853 47 14 810167 249 882764 178 927403 427 072597 46 15 810316 248 882657 178 927659 427 072341 45 16 810465 248 882550 178 8E7915 427 072085 44 17 .810614 248 882443 178 928171 427 071829 43 18 810763 248 882336 179 928427 427 071573 42 19 810912 248 882229 179 928683 427 071317 41 20 811061 248 882121 179 928940 427 071060 40 21 9.811210 248 9.882014 179 9.929196 427 10.070804 39 22 811358 247 881907 179 929452 427 070548 38 23 811507 247 881799 179 929708 427 070292 37 24 811655 247 881692 179 929964 426 070036 36 25 811804 247 881584 179 930220 426 069780 35 26 811952 247 881477 179 930475 426 069525 34 27 812100 247 881369 179 930731 426 069269 33 28 812248 247 881261 180 930987 426 069013 32 29 812396 246 881153 180 931243 426 068757 31 30 812544 246 881046 180 931499 426 068501 30 3i 9.812692 246 9.880938 180 9.931755 426 10.068245 29 32 812840 246 880830 180 932010 426 067990 28 33 812988 246 880722 180 932266 426 067734 27 34 813135 246 880613 180 932522 426 067478 26 35 813283 246 880505 180 932778 426 067222 25 36 813430 245 880397 180 933033 426 066967 24 37 813578 245 880289 181 933289 426 066711 23 38 813725 245 880180 181 933545 426 066455 22 39 813872 245 880072 181 933800 426 066200 21 40 814019 245 879963 181 934056 426 065944 20 41 9.814166 245 9.879855 181 9.934311 426 10.065689 19 42 814313 245 879746 181 934567 426 065433 18 43 814460 244 879637 181 934823 426 065177 17 44 814607! 244 879529 181 935078 426 064922 16 45 814753 244 879420 181 935333 426 064667 15 46 814900 244 879311 181 935589 426 064411 14 47 815046 244 879202 182 935844 426 064156 13 48 815193 244 879093 182 936100 426 063900 12 49 815339 244 878984 182 936355 426 063645 11 50 815485 243 878875 182 936610 426 063390 10 51 9.815631 243 9.878766 182 9.936866 425 10.063134 & 52 815778 243 878656 182 937121 425 062879 8 53 815924 243 878547 182 937376 425 062624 7 54 816069 243 878438 182 937632 425 062368 6 55 816215 243 878328 182 937887 425 062113 5 56 8163G1 243 878219 183 938142 425 061858 4 57 816507 242 878109 183 938398 425 061602 3 58 816652 242 877999 183 938653 425 061347 2 59 816798 242 877890 183 938908 425 061092 1 60 8169431 242 877780 183 939163 425 060837 Cosinc- Sine | | Cotang. Tang. M. 49 Degrees. SINES AND TANGENTS. (41 Degrees.) N 59 M. Sine D. Cosine | D. Tang. | D. Cotang. 9.816943 242 9.877780 183| 9.939163 425 10.060837 GO 1 817088 242 877670 183 939418 425 060582 59 2 817233 242 877560 183 939673 425 060327 58 3 817379 242 877450 183 939928 425 060072 57 4 817524 241 877340 183 940183 425 059817 56 5 817668 241 877230 184 940438 425 059562 55 6 817813 241 877120 184 940694 425 059306 54 7 817958 241 877010 184 940949 425 059051 53 8 818103 -241 876899 184 941204 425 058796 52 9 818247 241 876789 184 941458 425 058542 51 10 818392 241 876678 184 941714 425 058286 50 11 9.818536 240 9.876568 184 9.941968 425 10.058032 49 12 818681 240 876457 184 942223 425 057777 48 13 818825 240 876347 184 942478 425 057522 47 14 818969 240 876236 185 942733 425 057267 46 15 819113 240 876125 185 942988 425 057012 45 16 819257 240 876014 185 943243 425 056757 44 17 x8!940l 240 875904 185 943498 425 056502 43 18 819545 239 875793 185 943752 425 056248 42 19 819689 239 875682 185 944007 425 055993 41 20 819832 239 875571 185 944262 425 055738 40 21 9.819976 239 9.875459 185 9.944517 ^425 10.055483 39 22 820120 239 875348 185 944771 424 055229 38 23 820263 239 875237 185 945026 424 054974 37 24 820406 239 875126 186 945281 424 054719 36 25 820550 238 875014 186 945535 424 054465 35 26 820693 238 874903 186 945790 424 054210 34 27 820836 238 874791 186 946045 424 053955 33 28 820*79 238 874680 186 946299 424 053701 32 29 821122 238 874568 186 946554 424 053446 31 30 821265 238 874456 186 946808 424 053192 30 31 9.821407 238 9.874344 186 9.947063 424 10.052937 29 32 821550 238 874232 187 947318 424 052682 28 33 821693 237 874121 187 947572 424 052428 27 34 821835 237 874009 187 947826 424 052174 56 35 821977 237 873896 187 948081 424 051919 25 36 822120 237 873784 187 948336 424 051664 24 37 822262 237 873672 187 948590 424 051410 23 38 822404 237 873560 187 948844 424 051156 22 39 822546 237 873448 187 949099 424 050901 21 40 822688 236 873335 187 949353 424 050647 20 41 9.822*30 236 9.87322a 187 9.949607 424 10.050393 19 42 822972 236 873110 188 949862 424 050 13S 18 43 823114 236 872998 188 950116 424 049884 17 44 823255 236 872885 188 950370 424 049630 16 45 823397 236 872772 188 950625 424 049375 15 46 823539 236 872659 188 950879 424 049121 14 47 823680 235 872547 188 951133 424 048867 16 48 823821 235 872434 188 951388 424 048612 12 49 823963 235 872321 188 951642 424 048358 11 50 824104 235 872208 '188 951896 424 048104 10 51 9.824245 235 9.872095 189 9.952150 424 10.047850 9 52 824386 235 871981 189 952405 424 047595 8 53 824527 235 87168 189 952659 424 047341 7 54 824668 234 871755 189 952913 424 047087 6 55 824808 234 871641 189 953107 423 046833 5 56 824949 234 871528 189 953421 423 046579 4 57 825090 234 871414 189 953675 423 046325 3 58 825230 ?,34 871301 189 953929 423 046071 2 59 825371 234 871187 189 954183 423 045817 1 GO 825511! 234 87 i 073 190 954437 423 045563 Cosine j Sine j Colang | Tang. M. . 48 Degrees. 60 (42 Degrees.) A TABLE OF LOGARITHMIC M. Sine D. Cosine D. | Tanc. I). ColHIlp. | 9.825511 234 9.871073 190 9.954437 423 10.045563 60 1 825651 233 870960 190 954691 423 045309 <59 2 825791 233 870846 J90 954945 423 045055 58 3 825931 233 870732 J90 955200 423 044800 57 4 826071 233 870618 190 955454 423 044546 56 5 826211 233 870504 190 955707 423 044293 55 6 826351 233 870390 190 955961 423 044039 54 7 826491 233 870276 190 956215 423 043785 .53 8 826631 233 870161 190 956469 423 043531 52 9 826770 232 87004? 191 956723 423 043277 51 10 826910 232 869933 191 956977 423 043023 50 11 9.827049 232 9.869818 191 9.957231 423 10.042769 49 12 827189 232 869704 191 957485 423 042515 48 13 827328 232 869589 191 957739 423 042261 47 14 827467 232 869474 191 957993 423 042007 46 15 827606 232 869360 191 958246 423 041754 45 16 827745 232 869245 191 958500 423 041500 44 17 827884 231 869130 191 958754 423 041246 43 18 82&023 231 869015 192 959008 423 040992 42 19 828162 231 868900 192 959262 423 040738 41 20 828301 231 868785 192 959516 423 040484 40 21 9.828439 231 9.868670 192 9.959769 423 10.040231 39 22 828578 231 868555 192 960023 423 039977 38 23 828716 231 868440 192 960277 423 039723 37 24 828855 230 868324 192 960531 423 039469 36 25 828993 230 868209 192 960784 423 039216 35 26 829131 230 868093 192 961038 423 038962 34 27 829269 230 867978 193 961291 423 038709 33 28 829407 230 867862 193 961545 423 038455 32 29 829545 230 867747 193 961799 423 038201 31 30 829683 230 867631 193 962052 423 037948 30 31 9.829821 229 9.867515 193 9.962306 423 10.037694 29 32 829959 229 867399 193 962560 423 037440 28 33 830097 229 867283 193 962813 423 037187 27 34 830234 229 867167 193 963067 423 036933 26 35 830372 229 867051 193 963320 423 036680 25 36 830509 229 866935 194 963574 423 036426 24 37 830646 229 866819 194 963827 423 036173 23 38 830784 229 866703 194 964081 423 035919 22 39 830921 228 866586 194 964335 423 035665 21 40 831058 228 866470 194 964588 422 . 035412 20 41 9.831195 228 9.866353 194 9 . 964842 422 10.035158 19 42 831332 228 866237 194 965095 422 034905 18 43 831469 228 866120 194 965349 422 034651 17 44 831606 228 866004 195 965602 422 034:398 16 45 831742 228 865887 195 965855 422 034145 15 46 831879 228 865770 195 966109 422 033891 14 47 832015 227 865653 195 966362 422 033638 13 48 832152 227 865536 195 966616 422 033384 12 49 832288 227 865419 195 966869 422 033131 11 50 832425 227 865302 195 967123 422 032877 10 51 9.832561 227 9.865185 195 9.967376 422 10.032624 9 52 832697 227 865068 195 967629 422 032371 8 53 832833 227 864950 195 967883 422 032117 7 54 832969 226 864833 196 968136 422 031864 6 55 833105 226 864716 196 968389 422 031611 5 56 833241 226 864598 196 968643 422 031357 4 57 833377 226 864481 196 968896 422 031104 3 58 833512 226 864363 196 969149 422 030851 2 59 833648 226 864245 196 969403 422 030597 1 60 833783 226 864127 196 969656 422 030344 COM! ne ! Sine Cotang. | Tang. M. 47 Degrees. SINES AND TANGENTS. (43 Degrees.) 61 M Sine 1). Cosiiif; | D. T;ui. j D. Cottinp. j 9.833783 226 9.864127 196 9.969656 422 10.030344 60 1 833919 225 864010 196 969909 422 030091 59 2 834054 225 863892 197 970162 422 029838 58 3 834189 225 863774 197 ' 970416 422 029584 57 4 834325 225 863656 1-97 970669 422 029331 56 5 834460 225 863538 197 970922 422 029078 55 6 834595 225 863419 197 971175 422 028825 54 7 834730 225 863301 197 971429 422 028571 53 8 834865 225 863183 197 971682 422 0283 18 1 52 9 834999 224 863064 197 971935 422 028065', 51 10 835134 224 862946 198 972188 422 027812 50 11 9.835269 224 9.862827 198 9.972441 422 10.027559 49 12 835403 224 862709 198 972694 422 027306 48 13 835538 224 862590 198 972948 422 027052 47 14 835672 224 862471 198 973201 422 026799 46 15 835807 224 862353 198 973454 422 026546 45' 16 835941 224 862234 198 973707 422 026293 44 17 836075 223 862115 198 973960 422 026040 43 18 . 836209 223 861996 198 974213 422 025787 42 19 836343 223 861877 198 974466 422 025534 41 20 836477 223 861758 199 974719 422 025281 40 21 9.836611 223 9.861638 199 9.974973 422 10.025027 39 22 836745 223 861519 199 975226 422 024774 38 23 836878 223 861400 199 975479 422 024521 37 24 837012 '222 861280 199 975732 422 - 024268 36 25 837146 222 861161 199 975985 422 024015 35 26 837279 222 861041 199 976238 422 023762 34 27 837412 222 860922 199 976491 422 023509 33 28 837546 222 860802 199 976744 422 023256 32 29 837679 222. 860682 200 976997 422 023003 31 30 837,81-2 222 860562 200 977250 422 022750 30 31 9.837945 222 9.860442 200 9.977503 422 10.022497 29 32 838078 221 860322 200 977756 422 022244 28 33 838211 221 860202 200 978009 422 021991 27 34 838344 221 860082 200 978262 422 021738 26 35 838477 221 859962 200 978515 422 021485 25 36 838610 221 859842 200 978768 422 021232 24 37 838742 221 859721 201 979021 422 020979 23 38 838875 221 859601 201 . 979274 422 020726 22 39 839007 221 859480 201 979527 422 020473 21 40 839140 220 859360 201 979780 422 020220 20 41 9.839272 220 9.859239 201 9.980033 422 10.019967 19 42 839404 220 859119 201 980286 422 019714 18 43 839536 220 858998 201 980538 422 019462 17 44 839668 220 858877 201 980791 421 019209 16 45 839800 220 858756 202 981044 421 018956 15 46 839932 220 858635 202 981297 421 018703 14 47 840064 219 858514 202 981550 421 018450 13 48 840196 219 858393 202 981803 421 018197 12 49 840328 219 858272 202 982056 421 017944 11 50 840459 219 858151 202 982309 421 017691 10 51 9.840591 219 9.858029 202 9.982562 421 10.017438 9 52 840722 219 857908 202 982814 421 017186 8 53 840854 219 857786 202 983067 421 016933 7 54 840985 219 857665 203 983320 421 016680 6 55 841116 218 857543 203 983573 421 016427 5 56 841247 218 857422 203 983826 421 016174 4 57 841378 218 857300 203 984079 421 015921 3 58 841509 218 857178 203 984331 421 015669 2 59 841640 218 857056 203 984584 421 015416| 1 60 841771 218 856934| 203 984837 421 015163' Cosine Sine | j Cotang. 'fang. | M. 46 Degrees. (44 Degrees.) A TABLE OF LOGARITHMIC M. Sine 1). Cosine | 1). Tana. D. Cotang. 9.841771 218 9.856934 203 9.984837 421 10.015163 60 1 841902 218 856812 203 985090 421 0149 It) 59 2 842033 218 856690 204 985343 421 014657 58 3 842163 ' 217 856568 204 985596 421 014404 57 4 842294 217 856446 204 985848 421 014152 56 5 842424 217 856323 204 986101 421 013899 55 6 842555 217 858201 204 986354 421 013646 54 7 842685 217 856078 204 986607 421 013393 53 8 842815 217 855956 204 986860 421 013140 52 9 842946 217 855833 204 987112 421 012888 51 10 843076 217 855711 205 987365 421 012635 50 11 9.843206 216 9.855588 205 9.987618 421 10.012382 49 12 843336 216 855465 205 987871 421 012129 48 13 843466 216 855342 205 988123 421 011877 47 14 #43595 216 855219 205 988376 421 011624 46 15 843725 216 855096 205 988629 421 011371 45 16 843855 216 854973 205 988882 421 011118 44 17 843984 216 854850 205 989134 421 010866 43 18 844114 215 854727 206 989387 421 010613 42 19 844243 215 854603 206 989640 421 010360 41 20 844372 215 854480 206 989893 421 010107 40 21 9.844502 2l5 9.854356 206 9.990145 421 10.009855 39 22 844631 215 854233 206 990398 421 009602 38 23 844760 215 854109 206 990651 421 009349 37 24 844889 215 853986 206 990903 421 009097 36 25 845018 215 853862 206 991156 421 008844 35 26 845147 215 853738 206 991409 421 008591 34 .27 845276* 214 853614 207 991662 421 008338 33 28 845405 214 853490 207 991914 421 008086 32 29 845533 214 853366 207 992167 421 007833 31 30 845662 214 853242 207 992420 421 007580 30 31 9.845790 214 9.853118 207 9.992672 421 10.007328 29 32 845919 214 852994 207 992925 421 007075 28 33 846047 214 852869 207 993178 421 00682'' 27 34 846175 214 852745 207 993430 421 006570 26 35 846304 214 852620 207 993683 421 006317 25 36 846432 213 852496 208 993936 421 006064 24 37 846560 213 852371 208 994189 421 005811 23 38 846688 213 852247 208 994441 421 005559 22 39 846816 213 852122 208 994694 421 005306 21 40 846944 213 851997 208 994947 421 005053 20 41 9.847,071 213 9.851872 208 9.995199 421 10.004801 19 42 847199 213 851747 208 995452 421 004548 18 43 847327 213 851622 208 995705 421 004295 17 44 847454 212 851497 209 995957 421 004043 16 45 847582 212 - 851372 209 996210 421 003790 15 46 847709 212 851246 209 996463 421 003537 14 47 847836 212 851121 209 996715 421 003285 13 48 847964 212 850996 209 996968 421 003032 12 49 848091 212 850870 209 997221 421 002779 11 50 848218 . 212 850745 209 997473 421 002527 10 51 9.848345 212 9.850619 209 9.997726 421 10.002274 9 52 848472 211 850493 210 997979 421 002021 8 53 848599 211 850368 210 998231 421 001769 7 54 848726 211 850242 210 998484 421 001516 6 5>5 848852 211 850116 210 998737 421 001263 5 56 848979 211 849990 210 998989 421 001011 4 57 849106 211 849864 210 999242^ 421 000758 3 58 843232 211 849738 210 999495 421 000505 2 59 849359 211 849611 210 999748 421 000253 1 60 849485 211 849485 210 10.000000 421 000000 Cosine 1 Sine | Co'itang. 1 Tang. | M. 45 Degrees. A TRAVERSE TABLE, SHOWING THE DIFFERENCE OF LATITUDE AND DEPARTURE FOR DISTANCES BETWEEN 1 AND 100, AND FOB ANGLES TO Q^feTER DEGREES BETWEEN 1 AND 90 TRAVERSE TABLE. o 4 Deg. t fDeg. ff 1 o p Dat. Dep. Lat. Dep. Lat. Dep. 1 1 1.00 0.00 1.00 0.01 1.00 0.01 I 2 2.00 0.01 2.00 0.02 2.00 0.03 2 3 3.00 0.01 3.00 0.03 3.00 0.04 3 4 4.00 0.02 4.00 0.03 4.00 0.05 4 5 5.00 '0.02 5.00 0.04 5.00 0.07 5 6 6.00 0.03 6.00 0.05 6.00 0.08 6 7 7.00 0.03 7.00 0.06 7.00 0.09 7 8 8.00 0.03 8.00 0.07 8.00 0.10 8 9 9.00 0.04 9.00 0.08 9.00 0.12 9 10 10.00 0.04 10.00 0.09 10.00 .0.13 10 11 11.00 0.05 11.00 0.10 11.00 0.14 ri 12 12.00 0.05 12.00 0.10 12.00 0.16 12 13 13.00 0.06 13.00 0.11 13.00 0.17 13 14 14.00 0.06 14.00 0.12 14.00 0.18 14 15 15.00 0.07 15.00 0.13 15.00 0.20 15 16 16.00 0.07 16.00 0.14 16.00 0.21 16 17 17.00 0.07 17.00 0.15 17.00 0.22 17 18 18.00 0.08 18.00 0.16 18.00 0.24 18 19 19.00 0.08 19.00 0.17 19.00 0.25 19 20 20.00 0.09 20.00 0.17 20.00 0.26 20 21 21.00 0.09 21.00 0.18 21.00 0.27 21 22 22,00 0.10 22.00 0.19 22.00 0.29 22 23 23.00 0.10 23.00 0.20 23.00 0.30 23 24 24.00 0.10 24.00 0.21 24.00 0.31 24 25 25.00 0.11 25.00 0.22 25.00 0.33 25 26 26.00 0.11 26.00 0.23 26.00 0.34 26 27 27.00 0.12 27.00 0.24 27.00 0.35 27 28 28.00 0.12 28.00 0.24 28.00 0.37 28 29 29.00 0.13 29.00 0.25 29.00 0.38 29 30 30.00 0.13 30.00 0.26 30.00 0.39 30 31 31.00 0.14 31.00 0.27 31.00 0.41 31 32 32.00 0.14 32.00 0.28 32. 0| 0.42 32 33 33.00 0.14 33.00 0.29 33.1" 0.43 33 34 34.00 0.15 34.00 0.30 34.00 0.45 34 35 35.00 0.15 35.00 0.31 35.00 0.46 35 36 36.00 0.16 36.00 0.31 36.00 0.47 36 37 37.00 0.16 37.00 0.32 37.00 0.48 37 38 38.00 0.17 38.00 0.33 38.00 0.50 38 39 39.00 0.17 39.00 0.34 39.00 0.51 39 40 40.00 0.17 40.00 0.35 40.00 0.52 40 41 41.00 0.18 41.00 0.36 41.00 0.54 41 42 42.00 0.18 42.00 0.37 42.00 0.55 42 43 43.00 0.19 43.00 0.38 43.00 0.56 43 44 44.00 0.19 44.00 0.38 44.00 0.58 44 45 45.00 0.20 45.00 0.39 45.00 0.59 45 46 46.00 0.20 46,00 0.40 46.00 0.60 46 47 47.00 0.21 47.00 0.41 47.00 0.62 47 48 48.00 0.21 48.00 0.42 48.00 0.63 48 49 49.00 0.21 49.00 0.43 49.00 0.64 49 50 50.00 0.22 50.00 0.44 50.00 0.65 50 1 Dep. Lat. Dep. Lat. Dep. Lat. oJ o q a 89| Deg. 89^ Deg. 89i Deg. S TRAVERSE TABLE. g iDeg. iDeg. I Deg. B 8 Lat. Dep. Lat. Dep. Lat. Dep. 51 51.00 0.22 51.00 0.45 51.00 0.67~ 51 52 52.00 0.23 52.00 0.45 52.00 0.68 52 53 53.00 0.23 53.00 0.46 53.00 0.60 53 54 54.00 0.24 54.00 0.47 54.00 0.71 54 55 55.00 0.24 55.00 0.48 55.00 0.72 55 56 56.00 0.24 56.00 0.49 56.00 0.73 56 57 57.00 0.25 57.00 0.50 57.00 0.75 57 58 58.00 0.25 58.00 0.51 57.99 0.76 58 59 59.00 0.26 59.00 0.51 58.99 0.77 59 60 60.00 0.26 60.00 0.52 59.99 0.79 60 61 61.00 0.27 61.00 0.53 60.99 0.80 *1 62 62.00 0.27 62.00 0.54 61.99 0.81 t>2 63 63.00 0.27 63.00 0.55 62.99 0.82 63 64 64.00 0.28 64.00 0.56 63.99 0.84 64 65 65.00 0.28 65.00 0.57 64.99 0.85 65 66 66.00 0.29 66.00 0.58 65.99 0.86 66 67 67.00 0.29 67.00 0.58 66.99 0.88 67 63 68.00 0.30 68.00 0.59 67.99 0.89 68 69 69.00 0.30 69.00 0.60 68.99 0.90 69 70 70.00 0.31 70.00 0.61 69.99 0.92 70 71- 71.00 0.31 71.00 0.62 70.99 0.93 71 72 72.00 0.31 72.00 0.63 71.99 0.94 72 73 73.00 0.32 73.00 0.64 72.99 0.96 73 74 74.00 0.32 1 74.00 0.65 73.99 0.97 74 75 75.00 0.33 75.00 0.65 74.99 0,98 75 76 76.00 0.33 76.00 0.66 75.99 0.99 76' 77 77.00 0.34 77.00 0.67 76.99 .01 77 78 78.00 0.34 78.00 0.68 77.99 .02 78 79 79.00 0.34 79.00 0.69 78.99 .03 79 80 80.00 0.35 80.00 0.70 79.99 .05 80 81 81.00 0.35 81.00 0.71 80.99 .06 81 82 82.00 0.36 82.00 0.72 81.99 .07 82 83 83.00 0.36 83.00 0.72 82.99 .09 83 84 84.00 0.37 84.00 0.73 83.99 .10 84 85 85.00 0.37 85.00 0.74 84.99 .11 85 86 86.00 0.38 86.00 0.75 85.99 .13 86 87 87.00 0.38 87.00 0.76 86.99 .14 87 88 88.00 0.38 88.00 0.77 87.99 .15 88 89 89.00 0.39 89.00 0.78 88.99 .16 89 90 90.00 0.39 90.00 0.79 89.99 .18 90 91 91.00 0.40 91.00 0.79 90.99 .19 91 92 92.00 0.40 92.00 0.80 91.99 .20 92 93 93.00 0.41 93.00 0.81 92.99 .22 93 94 94.00 0.41 94.00 0.82 93.99 .23. 94 95 95.00 0.41 95.00 0.83 94.99 .24 95 96 96.00 0.42 96.00 0.84 95.99 .26 96 97 97.00 0.42 97.00 0.85 96.99 .27 97 98 98.00 0.43 98.00 0.86 97.99 .28 98 99 99.00 0.43 99.00 0.86 98.99 .30 99 100 100.00 0.44 100.00 0.87 99.99 .31 100 | Dep. Lat. Dep. Lat. Dep. Lat. | .5 I 5 89| Deg. 89 Deg. 89| Deg. Q TRAVI.RSE TABLE. o IDeg. H Deg. 11 Deg. H Deg. 5 CQ 1 P Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 1 1.00 0.02 1.00 0.02 1.00 ~0703~ 1.00 0.03 i 2 2.00 0.03 2.00 0.04 2.00 0.05 2.00 0.06 2 3 3.00 0.05 3.00 0.07 3.00 0.08 3.00 0.09 3 4 4.00 0.07 4.00 0.09 4.00 0.10 4.00 0.12 4 5 5.00 0.09 5.00 0.11 5.00 0.13 5.00 0.15 5 6 6.00 0.10 6.00 0.13 6.00 0.16 6.00 0.18 6 7 7.00 0.12 7.00 0.15 7.00 0.18 7.00 0.21 7 8 8.00 0.14 8.00 0.17 8.00 0.21 8.00 0.25 8 9 9.00 0.16 9.00 0.20 9.00 0.24 9.00 0.28 9 10 10.00 0.17 10.00 0.22 10.00 0.26 10.00 0.31 10 11 11.00 0.19 11.00 0.24 11.00 0.28 10.99 0.34 11 12 12.00 0.21 12.00 0.26 12.00 0.31 11.99 0.37 12 13 13.00 0.23 13.00 0.28 13.00 0.34 12.99 0.40 13 14 14.00 0.24 14.00 0.31 14.00 0.37 13.99 0.43 14 15 15.00 0.26 15.00 0.33 14.99 0.39 14.99 0.46 15 16 16.00 0.28 16.00 0.35 15.99 0.42 15.99 0.49 16 17 17.00 0.30 17.00 0.37 16.99 0.45 16.99 0.52 17 18 18.00 0.31 18.00 0.39 17.99 0.47 17.99 0.55 18 19 19.00 ^0.33 19.00 0.41 18.99 0.50 18.99 0.58 19 20 20.00 0.35 20.00 0.44 19.99 0.52 19.99 0.61 20 21 21.00 0.37 21.00 0.46 20.99 0.55 j 20.99 0.64 21 22 22.00 0.38 21.99 0.48 21.99 0.58 21.99 0.67 22 23 23.00 0.40 22.99 0.50 22.99 0.60 22.99 0.70 23 24 24.00 0.42 23.99 0.52 23.99 0.63 23.99 0.73 24 25 25.00 0.44 24.99 0.55 24,99 0.65 24.99 0.76 25 26 26.00 0.45 25.99 0.57 25.99 0.68 25.99 0.79 26 27 27.00 0.47 26.99 59 26.99 0.71 26.99 0.83 27 28 28.00 0.49 27.99 0.61 27.99 0.73 27.99 0.86 28 29 29.00 0.51 28.99 0.63 28.99 0.76 28*. 99 0.89 29 30 30.00 0.52 29.99 0.65 29.99 0.79 29.99 0.92 30 31 31.00 0.54 30.99 0.68 30.99 0.81 30.99 0.95 31 32 32.00 0.56 31.99 0.70 31.99 0.84 31.99 0.98 32 33 32.99 0.58 32.99 0.72 32 . 99 0.86 32.98 1.01 33 34 33.99 0.59 33.99 0.74 33.99 0.89 33.98 1.04 34 35 34.99 0.61 34.99 0.76 34.99 0.92 34.98 1.07 35 36 35.99 0.63 35.99 0.79 35.99 0.94 35.98 1.10 36 37 36.99 0.65 36.99 Q.81 36.99 0.97 36.98 1.13 37 38 37.99 0.66 37.99 0.83 37.99 0.99 37.98 1.16 38 39 38.99 0.68 38.99 0.85 38.99 1.02 38.98 1.19 39 40 39.99 0.70 39.99 0.87 39 . 99 1.05 39.98 1.22 40 41 40.99 0.72 40.99 0.89 40.99 1.07 40.98 1.25 '41 42 41.99 0.73 41.99 0.92 41.99 1.10 41.98 1.28 42 43 42.99 0.75 42.99 0.94 42.99 1.13 42.98 1.31 43 44 43.^9 0.77 43.99 0.96 43.99 1.15 43.98 1.34 44 45 44.99 0.79 44.99 0.98 44.99 1.18 44.98 1.37 45 46 45.99 0.80 45.99 1.00 45.99 1.20 45.98 1.40 46 47 46 . 99 0.82 46.99 1.03 46.99 1.23 46.98 1.44 47 48 47.99 0.84 47.99 1.05 47.98 1.26 47.98 1.47 48 49 48.99 0.86 48.99 1.07 48.98 1.28 48.98 1.50 49 50 49.99 0.87 49.99 1.09 49.98 1.31 49.98 1.53 50 0> 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 .2 b 89 Deg. 88| Deg. 881 D e% . 884 Deg. 2 TRAVERSE TABLE. 6 P* IDeg. U Deg. H De s- HDeg. O 1 P Lat Dep. Lat. Dep. Lat. Dep. Lat. Dep. i 51 50.99 0.89 50.99 .11 50.98 1.34 50.98 1.56 51 52 51.99 0.91 51.99 .13 51.98 .36 51.98 1.59 52 53 52.99 0.92 52.99 .10 52.98 .39 52.98 1.62 53 54 53.99 0.94 53.99 .18 53.98 .41 53.97 1.65 54 55 54.99 0.96 54.99 .20 54.98 .44 54.97 1.68 55 56 55.99 0.98 55.99 .22 55.98 .47 55.97 1.71 56 57 56.99 0.99 56.99 .24 56.98 .49 56.97 1.74 57 58 57.99 l.Ql 57.99 1.27 57.98 .52 57.97 1.77 58 59 58.99 1.03 58.99 1.29 58.98 .54 58.97 1.80 59 60 59.99 1.05 59.99 1.31 59.98 .57 59.97 1.83 60 61 60.99 1.06 60.99 .33 60.98 .60 60.97 1.86 61 62 61.99 1.08 61.99 .35 61.98 .62 61.97 1.89 62 63 62.99 1.10 62.99 .37 62.98 .65 62.97 1.92 63 64 63.99 .12 63.98 .40 63.98 .68 63.97 1.95 64 65 64.99 .13 64.98 .42 64.98 .70 64.97 1.99 65 66 65.99 .15 65.98 .44 35.98 .73 65.97 2.02 66 67 66.99 .17 66.98 .46 66.98 .75 66.97 2.05 67 68 67.99 .19 67.98 .48 67.98 .78 67.97 2.08 68 69 68.99 .20 68.98 1.51 68.98 .81 68.97 2.11 69 70 69.99 .22 69.98 1.53 69.98 .83 69.97 2.14 70 71 70.99 .24 70. 9S 1.55 70.98 .86 70.97 2.17 71 72 71.99 .26 71.98 1.57 71.98 .88 71.97 2.20 72 73 72.99 .27 72.98 1.59 72.97 .91 '"2.97 2.23 73 74 73.99 .29 73.98 1.61 73.97 .94! 73.97 2.26 74 75 74.99 .31 74.98 1.64 74.97 .96 74.97 2.29 75 76 75.99 .33 75.98 1.66 75.97 .99 75.96 2.32 76 77 76.99 .34 76.98 1.68 76.97 2.02 76.96 2.35 77 78 77.99 .36 77.98 1.70 77.97 2.04 77.96 2.38 78 79 78.99 .38 78.98 1.72 78.97 2.07 78.96 2.41 79 80 79.99 .40 79.98 1.75 79.97 2,09 79.96 2.44 80 81 80.99 .41 80.98 1.77 80.97 2.12 80.96 2.47 81 82 81.99 .43 81.98 1.79 81.97 2.15 81.96 2.50 82 83 82.99 .45 82.98 1.81 82.97 2.17 82.96 2.53 83 84 83.99 .47 83.98 1.83 83.97 2.20 83.96 2.57 84 85 84.99 .48 84.98 1.85 84.97 2.23 84.96 2.60 85 86 85.99 .50 85.98 1.88 85.97 2.25 85.96 2.63 86 87 86.99 .52 86.98 1.90 86.97 2.28 86.96 2.66 87 88 87.99 .54 87.98 1.92 87.97 2.30 87.96 2.69 88 89 88.99 .55 88.98 1.94 88.97 2.33 88.96 2.72 89 90 89.99 .57 89.98 1.96 89.97 2.36 89.96 2.75 90 91 90.99 .59 90.98 1.99 90.97. ?.38 90.96 2.78 91 92 91.99 .61 91.98 2.01 91.97 2.41 91.96 2.81 92 93 92.99 .62 92.98 2.03 92.97 2.43 92.96 2.84 93 94 93.99 .64 93.98 2.05 93.97 2.46 93.96 2.87 94 95 94.99 .66 94.98 2.07 94.97 2.49 94.96 2.90 95 96 95.99 .68 95.98 2.09 95.97 2.51 95.96 2.94 96 97 96.99 .69 96.98 2.12 96.97 2*54 96.95 2.96 97 98 97.99 .71 97.98 2.14 97.97 2.57 97-. 95 2.99 98 99 98.98 .73 98.98 2.16 98.97 2.59 98.95 3.02 99 100 99.98 .75 99.98 2.18 99.97 2.62 99.95 3.05 100 | Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 5 89 Deg. 88J Deg. 88 Deg. 88} Deg. Q TRAVERSE TABLE. 1 2 Deg. 2k Deg. 2 Deg. 2| Deg. s; P 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 1 1.00 0.03 1.00 0.04 1.00 0.04 1.00 0.05 l 2 2.00 0.07 2.00 0.08 2.00 0.09 2.00 0.10 2 p 3.00 0;10 3.00 0.12 3.00 0.13 3.00 0.14 3 4 4.00 0.14 4.00 0.16 4.00 0.17 4.00 0.19 4 5 5.00 0.17 5.00 0.20 5.00 0.22 4.99 0.24 5 6 6.00 0.21 6.00 0.24 5.99 0.26 5.99 0.29 6 7 7.00 0.24 6.99 0.27 6.99 0.31 6.99 0.34 7 8 7.99 0.28 7.99 0.31 7.99 0.35 7.99 0.38 8 9 8.99 0.31 8.99 0.35 8.99 0.39 8.99 0.43 9 10 9.99 0.35 9.99 0.39 9.99 0.44 9.99 0.48 10 11 10.99 0.38 10.99 0.43 10.99 0.48 10.99 0.53 11 12 11.99 0.42 11.99 0.47 11.99 0.52 11.99 0.58 12 13 12.99 0.45 12.99 0.51 12.99 0.57 12.99 0.62 13 14 13.99 0.49 13.99 0.55 13.99 0.61 13.98 0.67 14 15 14.99 0.52 14.99 0.59 14.99 0.65 14.98 0.72 15 16 15.99 0.56 15.99 0.63 15.99 0.70 15.98 0.77' 16 17 16.99 0.59 16.99 0.67 16.98 0.74 16.98 0.82 17 18 17.99 0.63 17.99 0.71 17.98 0.79 17.98 0.86 18 19 18.99 0.66 18.99 0.75 18.98 0.83 18.98 0.91 19 20 19.99 0.70 19.9? 0.79 19.98 0.87 19.98 0.96 20 21 20.99 0.73 20.98 0.82 20.98 0.92 20.98 .01 21 22 21.99 0.77 21.98 0.86 21.98 0.96 21.97 .06 22 23 22.99 O.bO 22.98 0.90 22.98 1.00 22.97 .10 23 24 23.99 0.84 23.98 0.94 23.98 1.05 23.97 .15 24 25 24.98 0.87 24.98 0.98 24.98 1.09 24.97 .20 25 26 25.98 0.91 25.98 1.02 25.98 1.13 25.97 .25 26 27 26.98 0.94 26.98 1.06 26.97 1.18 26.97 .30 27 28 27.98 0.98 27.98 .10 27.97 1.22 27.97 .34 28 29 28.98 1.01 28.98 .14 28.97 1.26 28.97 .39 29 30 29.98 1.05 29.98 .18 29 . 97 1.31 29 . 97 .44 30 31 30.98 .08 30.98 .22 30.9-7 1.35 30.96 .49 31 32 31.98 .12 31.98 .26 31.97 1.40 31.96 .54 32 33 32.98 .15 32.97 .30 32.97 1.44 32.96 .58 33 34 33.98 .19 33.97 .33 33.97 1.48 33.96 .63 34 35 34.98 .22 34.97 .37 34.97 1 . 53 34.96 .68 35 36 35.98 .26 35.97 .41 35.97 1.57 35 . 96 .73 36 37 36.98 .29 36.97 .45 36.96 1.61 36.96 .78 37 38 37.98 .33 37.97 .49 37.96 1.66 37.96 .82 38 39 38.98 .36 38.97 .53 38.96 1.70 38.96 .87 39 40 39.98 .40 39.97 .57 39.96 1.75 39 . 95 1.92 40 41 40.98 .43 40.97 .61 40.96 1.77 40.95 1.97 41 42 41.97 .47 41.97 .65 41.96 1.83 41.95 2.02 42 43 42.97 .50 42.97 .69 42.96 1.88 42.95 2.06 43 44 43.97 .54 43.97 .73 43.96 1.92 43.95 2.11 44 45 44.97 .57 44.97 .77 44.96 1.96 44.95 2.16 45 46 45.97 .61 45.96 .81 45.96 2.01 45.95 2.21 46 47 46.97 .64 46.96 .85 46.96 2.05 46.95 2.25 47 48 47.97 .68 47.96 .88 47.95 2.09 47.95 2.30 48 49 48.97 1.71 48.96 .92 48.95 2.14 48.94 2.35 49 50 49.97 1.74 49.96 .96 49.95 2.18 49.94 2.40 50 i Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. o 1 88 Peg. 87| Deg. 87^ Deg. 87$ Deg. 'to 3 TRAVERSE TABLE. Q 2 Deg. 2* Deg. 2* Deg. 2J Deg. G stance. f Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 51 50.97 1.78 50.96 2.00 50.95 2.22 50.94 2.45 51 52 51.97 1.81 51.96 2.04 51.95 2.27 51.94 2.50 52 53 52.97 1.85 52.96 2.08 52.95 2.31 52.94 2.54 53 54 53.97 1.88 53.96 2.12 53.95 2.36 53.94 2.59 54 55 54.97 1.92 54.96 2.16 54.95 2.40 54.94 2.64 55 56 55.97 1.95 55.96 2. "20 55.95 2.44 55.94 2.69 56 57 56.97 1.99 56.96 2.24 56.95 2.49 56.93 2.73 57 58 57.96 2.02 57.96 2.28 57.94 2.53 57.93 2.78 58 59 58.96 2.06 58.95 2.32 58.94 2.57 58.93 2.83 59 60 59.96 2.09 59.95 2.36 59.94 2.62 59.93 2.88 60 61 60.96 2.13 60,95 2.39 ~60^4~ 2.66 60.93 2.93 61 62 61.96 2.16 61.95 2.43 61.94 2.70 61.93 2.97 62 63 62.96 2.20 62.95 2.47 62.94 2.75 62.93 3.02 63 64 63.96. 2.23 63.95 2.51 63.94 2.79 63.93 3.07 64 65 64. 96~ 2.27 64.95 2.55 64.94 2; 84 64.93 3.12 65 66 65.96 2.30 65.95 2.59 65.94 2.88 65.92 3.17 66 67 66.96 2.34 66.95 2.63 66.94 2.92 66.92 3.21 67 68 67.96 2.37 67.95 2.67 67.94 2.97 67.92 3.26 68 69 68.96 2.41 68.95 2.71 68.93 3.01 68.92 3.31 69 70 69.96 2.44 69.95 2.75 69.93 3.05 69.92 3.36 70 71 70.96 2.481 70.95 2.79 70.93 3.10 70.92 3.41 71 72 71.96 2.51 71.94 2.83 71.93 3.14 71.92 3.45 72 73 72.96 2.55 72.94 2.87 72.93 3.18 72.92 3.50 73 74 73.95 2.58 73.94 2.91 73.93 3.23 73.91 3.55 74 75 74.95 2.62 74.94 2.94 74.93 3.27 74.91 3.60 75 76 75.95 2.65 75.94 2.98 75.93 3.31 75.91 3.65 76 77 76.95 2.69 76.94 3.02 76.93 3.36 76.91 3.70 77 78 77.95 2.72 77.94 3.06 77.93 3.40 77.91 3.74 78 79 78.95 2.76 78.94 3.10 78.92 3.45 78.91 3.79 79 80 79.95 2.79 79.94 3.14 79.92 3.49 79.91 3.84 80 81 80.95 2.83 80.94 3.18 80.92 3.53 80.91 3.89 81 82 81.95 2.86 81/94 3.22 81.92 3.58 81.91 3.93 82 83 82.95 2.90 82.9>i 3.26 82.92 3.62 82.90 3.98 83 84 83.95 2.93 83.94 3.30 83.92 3.66 83:90 4.03 84 85 84.95 2.97 84.93 3.34 84.92 3.71 84.90 4.08 85 86 85.95 3.00 85.93 3.38 85.92 3.75 85.90 4.13 86 87 86.95 3.04 86.93 3.42 86.92 3.79 86.90 4.17 87 88 87.95 3.07 87.93 3.45 87.92 3.84 87.90 4.22 88 89 88.95 3.11 88.93 3.49 88.92 3.88 88.90 4.27 89 90 89.95 3.14 89.93 3.53 89.91 3.93 89.90 4.32 90 91 90.95 3:18 90.93 3.57 90.91 3.97 90.90 4.37 91 92 91.94 3.21 91.93 3.61 91.91 4.01 91.89 4.41 92 93 92.94 3.25 92.93 3.65 92.91 4.06 92.89 4.46 93 94 93.94 3.28 93.93 3.69 93.91 4.10 93.89 4.51 91 S5 94.94 3.32 94.93 3.73 94.91 4.14 94.89 4.56 95 96 95.94 3.35 95.93 3.77 95.91 4.19 95.89 4.61 96 97 96.94 3.39 96.93 3.81 96.91 4.23 96.89 4.65 97 98 97.94 3.42 97.92 3.85 97.91 4.27 97.89 4.70 98 99 98.94 3.46 98.92 3.89 98.91 4.32 98.89 4.75 99 100 99.94 3.49 99.92 3.93 99.91 4.36 99.88 4.80 100 o> p Dep. Lac. Dep. Lat. Dep. Lat. Dep. Lat. c 1 1 88 Deg. 87| Deg. 87 Deg. 87* Deg. P TRAVERSE TABLE. c 3 Deg. 31 Deg. 3 Deg. 3| Deg. O w" 1 (0 5 a o Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 1.00 0.05 1. 00 0.06 Too" 0.06 1.00 0.06 I 2 2.00 0.10 2.00 0.11 2.00 0.12 2.00 0.13 2 3 3.00 0.16 3.00 0.17 2.99 0.18 2.99 0.20 3 4 3.99 0.21 3.99 0.23 3.99 0.24 3.99 0.26 4 5 4.99 0.26 4.99 0.28 4.99 0.31 4.99 0.33 5 6 5.99 0.31 5.99 0.34 5.99 0.37 5.99 0.39 6 7 6.99 0.37 6.99 0.40 6.99 0.43 6.99 0.46 7 8 7.99 0*42 7.99 0.45 7.99 0.49 7.98 0.52 8 9 8.99 0.47 8.99 0.51 8.98 0.55 8.98 0.59 9 10 9.99 0.52 9.98 0.57 9.98 0.61 9.98 0.65 10 11 10.98 0.58 10.98 0.62 10.98 0.67 10.98 0.72 11 12 11.98 0.63 11.98 0.68 11.98 0.73 11.97 0.78 12 13 12.98 0.68 12.98 0.73 12.98 0.79 12.97 0.85 13 14 13.98 0.73 13.98 0.79 13.97 0.85 13.97 0.92 14 15 14.98 0.79 14.98 0.85 14.97 0.92 14.97 0.98 15 16 15.98 0.84 15.97 0.91 15.97 0.98 15.97 .05 16 17 16.98 0.89 16.97 0.96 16.97 1.04 16.96 .11 17 18 17.98 0.94 17.97 1.02 17.97 1.10 17.96 .18 18 19 18.98 0.99 18.97 1.08 18.96 1.16 18.96 .24 19 20 19.97 1.05 19.97 1 . r.i 19.96 1.22 19.98 .31 20 21 20.97 .10 20.97 .19 20.96 1.28 20.96 .37 21 22 21.97 .15 21.96 .25 21.96 1.34 21.95 .44 22 23 22,97 .20 22.96 .30 22.96 1.40 22.95 .50 23 24 23.97 .26 23.96 .36 23.96 1.47. 23.95 .57 24 25 24.97 .31 24.96 .42 24.95 1.53 24.95 .64 25 26 25.96 .36 25.96 .47 25.95 1.59 25 . 94 .70 26 27 26.96 .41 26.96 .53 26.95 1.65 26.94 .77 27 28 27.96 .47 27.95 .59 27.95 1.71 27.94 .83 28 29 28.96 .52 28.95 .64 28.95 1.77 28.94 1.90 29 30 29.96 .57 29 . 95 . . 70 29.94 1.83 29.94 1.96 30 31 30.96 .62 30.95 .76 30.94 1.89* 30.93 2.03 31 32 31.96 .67 31.95 .81 31.94 1.95 31.93 2.09 32 33 32.95 .73 32.95 .87 32.94 2.0J 32.93 2.16 33 34 33.95 .78 33.95 .93 33.94 !2.08 33.93 2.22 34 35 34.95 .83 34.94 .98 34.93 2.11 34.92 2.29 35 36 35.95 .88 35.94 2.04 35 . 93 2.20 35.92 2.35 36 37 36 . 95 .94 36.94 2.10 36.93 2.26 36.92 2.42 37 38 37.95 .99 37.94 2.15 37.93 2.32 37.92 2.49 38 39 38.95 2.04 38 . 94 2.21 38.93 2.38 38 . 92 2.55 39 40 39.95 209 39.94 2.27 39.93 2.44 39.91 2.62 40 41 40.94 2.15 40 . 93 2.32 40.92 2.50 40.91 2.68 ~41 42 41. &4 2.20 41 . 93 2.38 41.92 2.56 41.91 2.75 42 43 42.94 2.25 42.93 2.44 42.92 2.63 42.91 2.81 43 44 43.94 2.30 43.93 2.49 43 . 92 2.69 43.91 2.88 44 45 44.94 2.36 44.93 2.55 44.92 2.75 44.90 2.94 45 46 45.94 2.41 45.93 2.61 45.91 2.81 45.90 3.01 46 47 46.94 2.46 46 . 92 2.66 46.91 2.87 46.90 3.07 47. 48 47.93 2.51 47.92 2.72 47.91 2.93 47.90 3.14 48 49 48.93 2.56 48.92 2.78 48.91 2.99i 48.90 3.20 49 50 49.93 2.62 49.92 2.83 49.91 3.05! 49.89 3.27 50 OJ o G Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 5 87 Deg. 86J Deg. 86A Deg. 861 Deg. CO .5 Q TRAVERSE TABLE. o 3 Deg. 3i Deg. 3 Deg. 3| Deg. 2 1 S- P Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. I 51 50.93 2.67 50.92 2.89 50.90 3.11 50.89 3.34 51 52 51.93 2.72 51.92 2.95 51.90 3.17 51.89 3.40J 52 53 52.93 2.77 52.91 3.00 52.90 3.24 52.89 3/47 53 54 53.93 2.83 53.91 3.06 53.90 3.30 53.88 3.53 54 55 54.92 2.88 54.91 3.12 54.90 3.36 54.88 3.60 55 56 55.92 2.93 55.91 3.17 55.90 3.42 55.88 3.66 56 57 56.92 2.98 56.'91 3.23 56.89 3.48 56.88 3 73 57 58 57.92 3.04 57.91 3.29 57.89 3.54 57.88 3.79 58 59 58.92 3.09 58.91 3.34 58.89 3.60 58.87 3.86 59 60 59.92 3.14 59.90 3.40 59.89 3.66 59.87 3.92 60 61 60.92 3.19 60.90 3.46 60.89 3.72 60.87 3.99 61 62 61.92 3.24 61.90 3.51 61.88 3.79 61.87 4.05 62 63 62.91 3.30 62.90 3.57 62.88 3.85 62.87 4.12 63 64 63.91 3.35 63.90 3.63 63.88 3.91 63.86 4.19 64 65 64.91 3.40 64.90 3.69 64.88 3.97 64.86 4.25 65 66 65.91 3.45 65.89 3.74 65.88 4.03 65.86 4.32 66 67 66.91 3.51 66.89 3.80 66.88 4 09 66.86 4.38 67 68 67.91 3.56 67.89 3.86 67.87 4.15 67.85 4.45 68 69 68.91 3.61 68.89 3.91 68.87 4.21 68.85 4.51 69 70 69.90 3.66 69.89 3.97 69.87 4.27 69.85 4.58 70 71. 70.90 3.72 70.89 4.03 70.87i 4.33 70.85 4.64 71 72 71.90 3.77 71.88 4.08 71.87 4.40 71.85 4.71 72 73 72.90 3.82 72.88 4.14 72.86 4.46 72.84 4.77 73 74 73.90 3.87 73.88 4.20 73.86 4.52 73.84 4.84 74 75 74.90 3.93 74.88 4.25 74.86 4.58 74.84 4.91 75 76 75.90 3.98 75.88 4.31 75-86 4.64 75.84 4.97 76 77 76.89 4.03 76.88 4.37 76.86 4.70 76.84 5.04 77 78 77.89 4.08 77.87 4.42 77.85 4.76 77.83 5.10 78 79 78.89 4.13 78.87 4.48 78.85 4.82 78.83 5.17 79 80 79.89 4.19 79.87 4.54 79.85 4.88 79.83 5.23 80 81 80.89 4.24 80.87 4.59 80.85* 4.94 80.83 5.30 81 82 81.89 4.29 81.87 4.65 81.85 5.01 81.82 5.38 82 83 82.89 4.34 82.87 4.71 82.85 5.07 82.82 5.43 83 84 83.88 4.40 83.86 4.76 83.84 5.13 83.82 5.49 84 85 84.88 4.45 84.86 4.82 84.84 5.19 84.82 5.56 85 86 85.88 4.50 85.86 4.88 85.84 5.25 85.82 5.62 86 87 86.88 4.55 86.86 4.93 86.84 5.31 86.81 5.69 87 88 87.88 .4.61 87.86 4.99 87.84 5.37 87.81 5.7Q 88 89 88.88 4.66 88.86 5.05 88.83 5.43 88.81 5.82 89 90 89.88 4.71 89.86 5.10 89.83 5.49 89.81 5.89 90 91 90.88 4.76 90.85 '5.16 90.83 5.56 90.81 5.95 91 92 91.87 4.81 91.85 5.22 91.83 5.62 91.80 6.02 92 93 92.87 4.87 92.85 5.27 92.83 5.68 92.80 6.08 93 94 93.87 4.92 93.85 5.33 93.82 5.74 93.80 6.15 94 95 94.87 4.97 94.85 5.39 94.82 5.80 94.80 6.21 95 96 95.87 5.02 95.85 5. '44 95.82 5.86 95.79 6.28 96 97 96.87 5.08 96.84 5.50 96.82 5.92 96.79 6.34 97 98 97.87 5.13 97.84 5.56 97.82 5.98 97.79 6.41 98 99 98.86 5.18 98.84 5.61 98.82 6.04 98.79 6.47 99 100 99.86 5.23 99.84 5.67 99.81 6.10 99.79 6.54 100 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 C 87 Deg. 86| Deg. 8G| Deg. 86i Deg. H 1 10 TRAVERSE TABLE. b 4 Deg. 4| Deg. 4-' Deg. 4| Deg. O 5 i ? a 5 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. a P i 1.00 0.07 1.00 0.07 1.00 0..08 1.00 0.08 1 2 2.00 0.14 1.99 0.15 1.99 0.16 1.99 0.17 2 3 2.99 0.21 2.99 0.22 2.99 0.24 2.99 0.25 3 4 3.99 0.28 3.99 0.30 3.99 0.31 3.98 0.33 4 5 4.99 0.35 4.99 0.37 4.98 0.39 4.98 0.41 5 6 5.99 0.42 5.98 0.44 5.98 0.47 5.98 0.50 6 7 6.98 0.49 6.98 0.52 6.98 0.55 6.97 0.58 7 8 7.98 0.56 7.98 0.59 7.98 0.63 7.97 0.66 8 9 8.98 0.63 8.98 0.67 8.97 0.7J 8.97 0.75 9 10 9.98 0.70 9.97 0.74 9.97 0.78 9.97 0.83 10 11 10.97 0.77 10.97 6.82 i 10.97 0.86 10.96 O.S1 11 12 11.97 0.84 11.97 0.89 11.96 0.94 11.96 0.99 12 13 12.97 0.91 12.96 0.96 12.96 1.02 12.96 .08 13 14 13.97 0.98 13.96 1.C4 13.96 1.10 3.95 .16 14 15 14.96 1.05 14.96 1.11 14.95 l.lg 14.95 .24 15 16 15.96 1.12 15.96 1.19 15.95 1.26 15.95 .32 16 17 16.96 1.19 16.95 1.26 16.95 1.33 16.94 .41 17 18 17.96 1.26 17.95 1.33 17.94 1.41 17.94 .49 18 19 18.95 1.33 18.95 1.40 18.94 1.49 18.93 1.57 19 20 19.95 1.40 19.95 1.48 19.94 1.57 19.93 1.66 20 21 20.95 1.46 20.94 1.56 20.94 1.651 20.93 1.74 21 22 21.95 1.53 21.94 1.63 21.93 1.73 21.92 1.82 22 23 22.94 1.60 22.94 1.70 22.93 1.80 22.92 1.90 23 24 23.94 1.67 23.93 1.78 23.93 1.88 23.92 1.99 24 25 24.94 1.74 24.93 1.85 24.92 1.96 24.91 2.07 25 26 25.94 1.81 25.93 1.93 25.92 2.04 25.91 2.15 26 27 26.93 1.88 20.93 2.00 26.92 2.12 26.91 2.24 27 28 27.93 1.95 27.92 2.08 27.91 2.20 27.90 2.32 28 29 28.93 2.02 28.92 2.15 28.91 2.28 28.90 2.40 29 .30 29.93 2.09 29.92 2.22 29.91 2.35 29.90 2.48 30 31 30.92 2.16 30.91 *2.30 30.90 2.43 30.89 2.57 31 32 31.92 2.23 31.91 2.37 31.90 2;51 31.89 2.65 32 33 32.92 2.30 32.91 2.45 32.90 2.59 32.89 2.73 33 34 3-3.92 2.37 33.91 2.52 33.90 2.67 33.88 2.82 34 35 34.91 2.44 34.90 2.59 34.89 2.75 34.88 2.90 35 36 35.91 2.51 35.90 2.67 35.89 2.82 35.88 2.98 36 37 36.91 2.58 36.90 2.74 36.89 2.90 36.87 3.06 37 38 ^7. 91 2.65 37.90 2.82 37.88 2.98 37.87 3.15 38 39 38.90 2.72 38.89 2.89 38.88 3.06 38.87 3.23 39 40 39.90 2.79 39.89 2.96 39.88 3.14 39.86 3.31 40 41 40.90 2.86 40.89 3.04 40.87 3.22 40.86 3.40 41 42 41.90 2.93 41.88 3.11 41.87 3.30 41.86 3.4S 42 43 42.90 3.00 42.88 3.19 42.87 3.37 42.85 8.56 43 44 43.89 3.07 43.88 3.26 43.86 3.45 43.85 3.64 44 45 41.89 3.14 44.88 3.33 44.86 3.53 44.85 3.73 45 46 45.89 3.21 45.87 3.41 45.86 3.61 45.84 3.81 46 47 46.89 3.28 46.87 3.48 46.86 3.69 46.84 3.89 47 48 47.88 3.35 47.87 3.56 47.85 3.77 47.84 3.97 48 49 48.88 3.42 48.87 3.63 48.85 3.84 48.83 4.06 49 50 49.881 3.49 49.86 3.71 49.85 3.92 49.83 4.14 50 Q> O c Dep. | Lat. Dep. Lat. Dep. Lat. Dep. Lat. CJ O S3 1C 3 86 Deg. 85| Deg. 85 Deg. 85J Deg. rt Q TBAVERSE TABLE. 11 o 53' ? 4 Deg. 4i Deg. 4^ Deg. 4JDeg. g a n P Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. P 51 50.88 3.56 50.86 3.78 50.84 4.00 50.82 4.22 51 52 51.87 3.63 51.86 3.85 51.84 4.08 51.82 4.31 52 53 52.87 3.70 52.85 3.93 52.84 4.16 52.82 4.39 53 ' 54 53.87 3.77 53.85 4.00 53.83 4.24 53.81 4.47 54 55 54.87 3.84 54.85 4.08 54.83 4.32 54.81 4.55 55 56 55.86 3.91 55.85 4.15 55.83 4.39 55.81 4.64 56 57 56.86 3.98 56.84 4.22 56.82 4.47 56.80 4.72 57 58 57.86 4.05 57.84 4.30 57.82 4.55 57.80 4.80 58 59 58.86 4.12 58.84 4.37 58.82 4.63 58.80 4.89 59 60 59.85 4.19 59.84 4.45 59.82 4.71 59.79 4.97 60 61 60.85 4.26 60.83 4.52 60.81 4.79 60.79 5.05 61 62 61.85 4.32 61.83 4.59 61.81 4.86 61.79 5.13 62 63 62.85 4.39 62.83 4.67 62.81 4.94 62.78 5.22 63 64 63.84 4.46 63.82 4.74 63.80 5.02 63.78 5.30 64 65 64.84 4.53 64.82 4.82 64.80 5.10 64.78 5.38 65 66 65.84 4.60 65.82 4.89 65.80 5.18 65.77 5.47 66 67 66.84 4.67 66.82 4.97 66.79 5.26 66.77 5.55 67 68 67.83 4. ,74 67.81 5.04 67.79 5.34 67.77 5.63 68 69 68.83 4.81 68.81 5.11 68.79 5.41 68.76 5.71 69 70 69.83 4.88 69.81 5.19 69.78 5.49 69,76 5.80 70 71 70.83 4.95 70.80 5.26 70.78 5.57 70.76 5.88 71 72 71.82 5.02 71.80 5.34 71.78 5.65 71.75 5.96 72 73 72.82 5.09 72.80 5.41 72.77 5.73 72.75 6.04 73 74 73.82 5.16 73.80 5.48 73.77 5.81 73.75 6.13 74 75 74.82 5.23 74.79 5.56 74.77 5.88 74.74 6.21 75 76 75.81 5.30 75.79 5.63 75.77 5.96 75.74 6.29 76 77 76.81 5.37 76.79 5.71 76.76 6.04 76.74 6.38 77 78 77.81 5.44 77.79 5.78 77.76 6.12 77.73 6.46 78 79 78.81 5.51 78.78 5.85 78.76 6.20 78.73 6.54 79 80 79.81 5.58 79.78 5.93 79.75 6.28 79.73 6.62 80 81 80.80 5.65 80.78 6.00 80.75 6.36 80.72 6.71 81 82 81.80 5.72 81.78 6.08 81.75 6.43 81.72 6.79 82 83 82.80 5.79 82.77 6.15 82.74 6.51 82.71 6.87 83 84 83.80 5.86 83.77 6.23 83.74 6.59 83.71 6.96 84 85 84.79 5.93 84.77 6.30 84.74 6.67 84.71 7.04 85 86 85.79 6.00 85.76 6.3? 85.73 6.75 85.70 7.12 86 87 86.79 6.07 86.76 6.45 86.73 6.83 86.70 7.20 87 88 87.79 6.14 87.76 6.52 87.73 6.90 87.70 7.29 83 89 88.78 6.21 88.76 6.60 88.73 6.98 88.70 7.37 89 90 89.78 6.28 89.75 6.67 89.72 7.06 89.69 7.45 90 91 90.78 6.35 90.75 6.74! 90.72 7.14 90.69 7.54 91 92 91.78 6.42 91.75 6.82 91.72 7.22 91.68 7.62 92 93 92.77 6.49 92.74 6.89 92.71 7.30 92.68 7.70 93 94 93.77 6.56 93.74 6.97 93.71 7.38 93.68 7.78 94 95 94.77 6.63 94.74 7.04 94.71 7.45 94.67 7.87 95 96 95.77 6.70 95.74 7.11 95.70 7.53 95.67 7.95 96 97 96.76 6.77 96.73 7.19 96.70 7.61 96.67 8.03 97 98 97.76 6.84 97.73 7.26 97.70 7.69 97.66 8.12 98- 99 98.76 6.91 98.73 7.34 98.69 7.77 98.66 8.20 99 100 99.76 6.98 99.73 7.41 99.69 7.85 99.66 8.28 100 u c Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. C c3 3 86 Deg. 85| Deg. 85 Deg. 85i Deg. c3 .3 b K 12 TRAVERSE TABLE. g en* P 5 Deg. 5} Deg, 51 Deg. 6J Deg. 5 w* 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 i 1.00 0.09 1.00 0.09 1.00 0.10 0.99 0.10 1 2 1.99 0.17 1.99 0.18 1.99 0.19 1.99 0.20 2 3 2.99 0.26 2.99 0.27 2.99 0.29 2.98 0.30 3 4 3.98 0.35 3.98 0.37 3.98 0.38 3.98 0.40 4 5 4.98 0.44 4.98 0.46 4.98 0.48 4.97 0.50 5 6 5.98 0.52 5.97 0.55 5.97 0.58 5.97 0.60 6 7 6.97 0.61 6.97 0.64 6.97 0.67 6.96 0.70 7 8 7.97 0.70 7.97 0.73 7.96 0.76 7.96 0.80 8 9 8.97 0.78 8,96 0.82 8 96 0.86 8.95 0.90 9 10 9.96 0.87 9.96 0.92 9.95 0:96 9.95 1.00 10 11 10.96 0.96 10.95 .01 10.95 .05 10.94 1.10 11 12 11.95 1.05 11.95 .10 11.94 .15 11.94 1.20 12 13 12.95 1.13 12.95 .19 12.94 .25 12.93 1.30 13 14 13.95 1.22 13.94 .28 13.94 .34 13.93 1.40 14 15 14.94 1.31 14.94 .37 14.93 .44 14.92 1.50 15 16 15.94 1.39 15.93 .46 15.93 .53 15.92 1.60 16 17 16.94 1.48 16.93 .56 16.92 .63 16.91 1.70 17 13 17.93 1.57 17.92 .65 17.92 .73 17.91 1.80 18 19 18.93 1.66 18.92 .74 18.91 .82 18.90 1.90 19 20 19.92 1.74 19.92 .83 19.91 1.92 19.90 2.00 20 21 20.92 1.83J 20.91 1.92 20.90 2.01 1 20.89 2.10 21 22 21.92 1.92 21.91 2.01 21.90 2.11 21.89 2.20 22 23 22.91 2.00 22.90 2.10 22.89 2.20 22.88 2.30 23 24 23.91 2.09 23.90 2.20 23.89 2.30 23.88 2.40 24 25 24.90 2.18 24.90 2.29 24.88 2.40 24.87 2.50 25 26 25.90 2.27 25.89 2.38 25.88 2.49 25.87 2.60 26 27 26.90 2.35 26.89 2.47 26.88 2.59 26.86 2.71 27 28 27.89 2.44 27.88 2.56 27.87 2.68 27.86 2.81 28 29 28.89 2.53 28.88 2.65 28.87 2.78 28.85 2.91 29 30 29.89 2.61 29.87 2.75 29.86 2.88 29.85 3.01 30 31 30.88 2.70 30.87 2.84 30.86 2.97 30.84 3.11 31 32 31.88 2.79 31.87 2.93 31.85 3.07 31.84 3. -21 32 33 32.87 2.88 32.86 3.02 32.85 3.16 32.83 3.31 33 34 33.87 2.96 33.86 3.11 33.84 3.26 33.83 3.41 34 35 34.87 3.05 34.85 3.20 34.84 3.35 34.82 3.51 35 36 35.86 3.14 35.85 3.29 35.83 3.45 35.82 3.61 36 37 36.86 3.22 36.84 3.39 36.83 3.55 36.81 3.71 37 38 37.86 3.31 37.84 3.48 37.83 3.64 37.81 3.81 38 39 38.85 3.40 38.84 3.57 38.82 3.74 38.80 3.91 39 40 39.85 3.49 39.83 3.66 39.82 3.83 39.80 4.01 40 41 40.84 3.57 40.83 3.75 40.81 3.93 40.79 4.J.1 41 42 41.84 3.66 41.82 3.84 41.81 4.03 41.79 4.21 42 43 42.84 3.75 42.82 3.93 42.80 4.12 42.78 4.31 43 44 43.83 3.83 43.82 4.03 43.80 4.22 43.78 4.41 44 45 44.83 3.92 44.81 4.12 44.79 4.31 44.77 4.51 45 46 45.82 4.01 45.81 4.21 45.79 4.41 45.77 4.61 46 47 46.82 4.10 46.80 4.30 46.78 4.50 46.76 4.71 47 48 47.82 4.18 47.80 4.39 47.78 4.60 47.76 4.81 48 49 48.81 4.27 48.79 4.48 48.77 4.70 48.75 4.91 49 50 49,81 4.36 49,79 4.58 49.77 4.79 49.75 5.01 50 I Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 09 O c a c3 00 s 85 Deg. 84J Deg. 841 Deg. 84i Deg. .a b TRAVERSE TABLE. 13 G 5 Deg. 5i Deg. H De - 5| Deg. D ' p 1' 3 n ? Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 51 50.81 4.44 50.79 4.67 50.77 4.89 50.74 5.11 51 52 51.80 4.53 51.78 4.76 51.76 4.98 51.74 5.21 52 53 52.80 4.62 52.78 4.85 62.76 5.08 52.73 5.31 53 54 53.79 4.71 53.77 4.94 53.75 5.18 53.73 5.41 54 55 54.79 4.79 54.77 5.03 54.75 5.27 54.72 5.51 55 56 55.79 4.88 55.77 5.12 55.74 5.37 55.72 5.61 56 57 56.78 4.97 56.76 5.22 56.74 5.46 56.71 5.71 57 58 57.78 5.06 57.76 5.31 57.73 5.56 57.71 5.81 58 59 58.78 5.14 58.75 5.40 58.73 5.65 58.70 5.91 59 60 59.77 5.23 59.75 5.49 59.72 5.75 59.70 6.01 60 61 60.77 5.32 60.74 5.58 60.72 5.85 60.69 6.11 61 62 61.76 5.40 61.74 5.67 61.71 5.94 61.69 6.21 62 63 62.76 5.49 62.74 5.76 62.71 6.04 62.68 6.31 63 64 63.76 5.58 63.73 5.86 63.71 6.13 63.68 6.41 64 65 64.75 5.67 64.73 5.95 64.70 6.23 64.67 6.51 65 66 65.75 5.75 65.72 6.04 65.70 6.33 65.67 6.61 66 67 66.75 5.84 66.72 6.13 66.69 6.42 66.66 6.71 67 63 67.74 5.93 67.71 6.22 67.69 6.52 67.66 6.81 68 69 68.74 6.01 68.71 6.31 68.68 6.61 68.65 6.91 69 70 69.73 6.10 69.71 6.41 69.68 6.71 69.65 7,01 70 71 70.73 6.19 70.70 6.50 70.67 6.81 70.64 7.11 71 72 71.73 6.28 71.70 6.59 71.67 6.90 71.64 7.21 72 73 72.72 6.36 72.69 6.68 72.66 7.00 72.63 7.31 73 74 73.72 6.45 73.69 6.77 73.66 7.09 73.63 7.41 74 75 74.71 6.54 74.69 6.86 74.65 7.19 74.62 7.51 75 76 75.71 6.62 75.68 6.95 75.65 7.28 75.62 7.61 76 77 76.71 6.71 76.68 7.05 76.65 7.38 76.61 7.71 77 78 77.70 6.80 77.67 7.14 77.64 7.48 77.61 7.81 78 79 78.70 6.89 78.67 7.23 78.64 7.57 78.60 7.91 79 80 79.70 6.97 79.66 7.32 79.63 7.67 79.60 8.02 80 81 80.69 7.06 80.66 7.41 80.63 7.76 80.59 8.12 81 82 81.69 7.15 81.66 7.50 81.62 7.86 81.59 8.22 82 83 82.68 7.23 82.65 7.59 82.62 7.96 82.58 8.32 83 84 83.68 7.32 83.65 7.69 83.61 8.05 83.58 8.42 84 85 84.68 7.41 84.64 7.78 84.61 8.15 84.57 8.52 85 86 85.67 7.50 85.64 7.87 85.60 8.24 85.57 8.62 86 87 86.67 7.58 86.64 7.96 86.60 8.34 86.56 8.72 87 88 87.67 7.67 87.63 8.05 87.59 8.43 87.56 8.82 88 89 as. 66 7.76 88.63 8.14 88.59 8.53 88.55 8.92 89 90 80.66 7.84 89.62 8.24 89.59 8.63 89.55 9.02 90 91 90.65 7.93 90.62 8.33 90.58 8.72 90.54 9.12 91 92 91.65 8.02 91.61 8.42 91.58 8.82 91.54 9.22 92 93 92.65 8.11 92.61 8.51 92.57 8.91 92.53 9.32 93 94 93.64 8.19 93.61 8.60 93.57 9.01 93.53 9.42 94 95 94.64 8.28 94.60 8.69 94.56 9.11 94.52 9.52 95 96 95.63 8.37 95.60 8.78 95.56 9.20 95.52 9.62 96 97 96.63 8.45 96.59 8.88 96.55 9.30 96.51 9.72 97 98 97.63 8.54 97.59 8.97 97.55 9.39 97.51 9.82 98 99 98.62 8.63 98.59 9.06 98.54 9.49 98.50 9.92 99 100 99.62 8.72 99.58 9.15 99.54 9.58 99.50 10.02 100 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. I 85 Deg. 84J Deg. 84 Deg. 84* Deg. 5 14 TRAVERSE TABLE. o 6 I )eg. m )eg. 6^1 )eg. 6| I )eg. O I P* I Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 5 n CD 1 0.99 0.10 0.99 0.11 0.99 0.11 0.99 ~"07l2~ 1 2 1.99 0.21 1.99 0.22 1.99 0.23 1.99 0.24 2 3 2.98 0.31 2.98 0.33 2.98 0.34 2.98 0.35 3 4 3.98 0.41 3.98 0.44 3.97 0.45 3.97 0.47 4 5 4.97 0.52 4.97 0.54 4.97 0.57 4.97 0.59 5 6 5.97 0.63 5.96 0.65 5.96 0.68 5.96 0.71 6 7 6.96 0.73 6.96 0.76 6.96 0.79 6.95 0.82 7 8 7.96 0.84 7.95 0.87 7.95 0.91 7.94 0.94 8 9 8.95 0.94 8.95 0.98 8.94 .02 8.94 1.06 9 10 9.95 1.05 9.94 1.09 9.94 .13 9.93 1.18 10 11 10.94 1.15 10.93 .20 10.93 .25 10.92 1.29 11 12 11.93 1.25 11.93 .31 11.92 .36 11.92 1.41 12 13 12.93 1.36 12.92 .42 12.92 .47 12.91 1.53 13 14 13.92 1.46 13.92 .52 13.91 .59 13.90 1.65 14 15 14.92 1.57 14.91 .63 14.90 .70 14.90 1.76 15 16 15.91 1.67 15.90 .74 15.90 1.81 15.89 1.88 16 17 16.91 1.78 16.90 .85 16.89 1.92 16.88 2.00 17 18 17.90 1.88 17.89 1.96 17.88 2.04 17.88 2.12 18 19 18.90 1.99 18.89 2.07 18.88 2.15 18.87 2.23 19 20 19.89 2.09 19.88 2.18 19.87 2.26 19.86 2.35 20 21 20.88 2.20 20.88 2.29 20.87 2.38 20.85 2.47 21 22 21.88 2.30 21.87 2.40 21.86 2.49 21.85 2.59 22 23 22.87 2.40 22.86 2.50 22.85 2.60 22.84 2.70 23 24 23.87 2.51 23.86 2.61 23.85 2.72 23.83 2.82 24 25 24.86 2.61 24.85 2.72 24.84 2.83 24.83 2.94 25 26 25.86 2.72 25.85 2.83 25.83 2.94 25.82 3.06 26 27 26.85 2.82 26.84 2.94 26.83 3.06 26.81 3.17 27 28 27.85 2.93 27.83 3.05 27.82 3.17 27.81 3.29 28 29 28.84 3.03 28.83 3.16 28.81 3.28 28.80 3.41 29 30 29.84 3.14 29.82 3.27 29.81 3.40 29.79 3.53 30 31~ 30.83 3.24 30.82 3.37 30.80 3.51 30.79 3.64 31 32 31.82 3.34 31.81 3.48 31.79 3.62 31.78 3.76 32 33 32.82 3.45 32.80 3.59 32.79 3.74 32.77 3.88 33 34 33.81 3.55 33.80 3.70 33.78 3.85 33.76 4.00 34 35 34.81 3.66 34.79 3.81 34.78 3.96 34.76 4.11 35 36 35.80 3.76 35.79 3.92 35.77 4.08 35,75 4.23 36 37 36.80 3.87 36.78 4.03 36.76 4.19 36.75 4.35 37 38 37.79 3.97 37.77 4.14 37.76 4.30 37.74 4.47 38 39 38.79 4.08 38.77 4.25 38.75 4.41 38.73 4.58 39 40 39.78 4.18 39.76 4.35 39.74 4.53 39.72 4.70 40 41 40.78 4.29 40.76 4.46 40.74 4.64 40.72 4.82 41 42 41.77 4.39 41.75 4.5? 41.73 4.76 41.71 4.94 42 43 42.76 4.49 42.74 4.68 42.72 4.87 42.70 5.05 43 44 43.76 4.60 43.74 4.79 43.72 4.98 43.70 5.17 44 45 44.75 4.70 44.73 4.90 44.71 5.09 44.69 5.29 45 46 45.75 4.81 45.73 5.01 45.70 5.21 45.68 5.41 46 47 46.74 4.91 46.72 5.12 46.70 5.32 46.67 5.52 47 48 47.74 5.02 47.71 5.23 47.69 5.43 47.67 5.64 48 49 48.73 5.12 48.71 5.34 48.69 5.55 48.66 5.76 49 50 49.73 5.23 49.70 5.44 49.68 5.66 49.65 5.88 50 1 Dep.^ Lat. Dep. Lat. Dep. Lat. Dep. Lat. QJ U c 1 G 841 Deg. 83| Deg. 831 Deg. Deg. I TRAVERSE TABLF.. 15 g 6Deg x 6i Deg. 6i Deg 6| Deg. 2 So" 1 3 o p Lat. Dep. Lat. Dep. Lat. Dep. 1 Lat. Dep. 3 n 51 50.72 5.33 50.70 5.55 50.67 5.77 50.65 5.99 ~51 52 51.72 5.44 51.69 5.66 51.67 5-89 51.64 6.11 52 53 52.71 5.54 52.68 5.77 52.66 6.00 52.63 6.23 53 54 53.70 5.64 53.68 5.88 53.65 6-11 53.63 6.35 54 55 54.70 5.75 54.67 5.99 54.65 6-23 54.62 6.46 55 56 55.69 5.85 55.67 6.10 55.64 6-34 55.61 6.58 56 57 56.69 5.96 56.66 6.21 56.63 6-45 56.60 6.70 57 58 57.68 6.06 57.66 6.31 57.63 6-57 57.60 6.82 58 59 58.68 6.17 58.65 6.42 58.62 6.68 58.59 6.93 59 60 59.67 6.27 59.64 6.53 59.61 6.79 59.58 7.05 60 61 60.67 6.38 60.64 6.64 60.61 6. 91 ll 60. 58 7.17 61 62 81.66 6.48 61.63 6.75 61.60 V. 02 61.57 7.29 62 63 62.65 6.59 62.63 6.86 62.60 7.131 62.56 7.40 63 64 63.65 6.69 63.62 6.97 63.59 7.25 163.56 7.52 64 65 64.64 6.79 64.61 7.08 64.58 7.36 64.55 7.64 65 66 65.64 6.90 65.61 7.19 65.58 7.47 65.54 7.76 66 67 66.63 7.00 66.60 7.29 66.57 7 58 66.54 7.88 67 68 67.63 7.11 67.60 7.40 67.56 7.70 67.53 7.99 68 69 68.62 7.21 68.59 7.51 68.56 7.81 68.52 8.11 69 70 (69.62 7.32 69.58 7.62 69.55 7.92 69.51 8.23 70 71. 70.61 7.42 70.58 7.73 70.54 8.04 170.51 8.35 71 72 71.61 7.53 71.57 7.84 71.54 8.15 71.50 8.46 72 73 72.60 7.63 72.57 7.95 72.53 8.26 (72.49 8.58 73 74 73.59 7.74 73.56 8.06 73.52 8.38 '73.49 8.70 74 75 74.59 7.84 74.55 8.17 74.52 8.49 74.48 8.82 75 76 75.58 7.94 75.55 8.27 75.51 8.60 i75.47 8.93 76 77 7U.58 8.05 76.54 8.38 76.51 8.72 176.47 9.05 77 78 77.57 8.15 77.54 8.49 77.50 8.83 ,77.46 9.17 78 79 78.57 8.26 78.53 8.60 78.49 8.94 i78.45 9.29 79 80 79.56 8.36 79.53 8.71 79.49 9.06 79.45 9.40 80 81 80.56 8.47 80.52 8.82 80.48 ~~9~. 17 J80.44 9.52 81 82 81.55 8.57 81.51 8.93 81.47 9! 28 81.43 9.64 82 83 82.55 8.68 82.51 9.04 82.47 0.40 '82.42 9.76 83 84 83.54 8.78 83.50 9.14 S3. 46 9.51 183.42 9.87 84 85 84.53 8.88 84.50 9.25 84.45 9.62 ; 84.41 9.99 85 86 85.53 8.99 85.49 9.36 85.45 9.74 85.40 10.11 86 87 86.52 9.09 86.48 9.47 86.44 9.85 186.40 10.23 87 88 87.52 9.20 87.48 9.58 87.43 9.96 87.39 10.34 88 89 88.51 9.30 88.47 9.69 88.43 10.08 188.38 10.46 89 90(89.51 9.41J 89.47 9.80 89.42 10.19 189.38 10.58 90 91 J90.50 9.51 | 90.46 9.91 90.42 10.30 190.37 10.70 91 92 191.50 9.62 91.45 10.02 91.41 10.41 i91.36 10.81 92 93 92.49 9.72 92.45 10.12 92.40 10.53 i 92.36 10.93 93 94 93.49 9.83 93.44 10.23 93.40 10.64 93.35 11.05 94 95 94.48 9.93 94.44 10.34 94.39 10.75 94.34 11.17 95 96 95.47 10.03 95.43 10.45 95.38 10.87 95.33 11.28 96 97 196.47 10.14 96.42 10.56 96.38 10.98 !!96.33 11.40 97 98 97.46 10.24 97.42 10.67 97.3V 11.09 97.32 11.52 98 991 98.46 10.35 98.41 10.78 98.36 11.21 98.31 11.64 99 100 99.45 10.. 45 99.41 10.89 99.36 11. 33 || 99.31 11.75 100 1 Dep. Lat. Dep. Lat. Dep. Lat. 1 Dep. Lat. 1 P 84 Deg. 83| Deg. 83| Deg. 83i Deg. rt 3- 16 TRAVERSE TABLE- o 7 Deg. 1\ Deg. 7^Deg. 71 Deg. C 5' P Lat. Dep. Lat. Dep. Lat Dep. Lat. Dep. P i 0.99 0.12 0.99 0.13 0.99 0.13 0.99 O.J3 1 2 1.99 0.24 1.98 0.25 1.98 0.26 1.98 0.27 2 3 2.98 0.37 2.98 0.38 2.97 0.39 2.97 0.40 3 4 3.97 0.49 3.97 0.50 3.97 0.52 3.96 0.54 4 5 4.96 0.61 4.96 0.63 4.96 0.65 4.95 0.67 5 6 5.96 0.73 5.95 0.76 5.95 0.78 5.95 0.81 6 7 6.95 0.85 6.94 0.88 6.94 0.91 6.94 0.94 7 8 7.94 0.97 7.94 1.01 7.93 1.04 7.93 .08 8 9 8.93 1.10 8.93 1.14 8.92 1.17 8.92 .21 9 10 9.93 1.22 9.92 1.26 9.91 1.31 9.91 .35 10 11 10.92 1.34 10.91 1.39 10.91 1.44 10.90 .48 11 12 11.91 .46 11.90 1.51 11.90 1.57 11.89 .62 12 13 12.90 .58 12.90 1.64 12.89 1.70 12.88 .75 13 14 13.90 .71 13.89 1.77 13.88 1.83 13.87 .89 14 15 14.89 .83 14.88 1.89 14.87 1.96 14.86 2.02 15 16 15.88 .95 15.87 2.02 15.86 2.09 15.85 2.16 16 17 16.87 2.07 16.86 2.15 16.85 2.22 16.84 2.29 17 18 17.87 2.19 17.86 2.27 17.85 2.35 17.84 2.43 18 19 18.86 2.32 18.85 2.40 18.84 2.48 18.83 2.56 19 20 19.85 2.44 19.84 2.52 19.83 2.61 I 19.82 2.70 20 21 20.84 2.56 20.83 2.65 20.82 2.74 20.81 2.83 21 22 21.84 2.68 21.82 2.78 21.81 2.87 21.80 2.97 22 23 22.83 2.80 22.82 2.90 22.80 3.00 22.79 3.10 23 24 23.82 2.92 23.81 3.03 23.79 3.13 23.78 3.24 24 25 24.81 3.05 24.80 3.15 24.79 3.26 24.77 3.37 25 26 25.81 3.17 25.79 3.28 25.78 3.39 25.76 3.51 26 27 26.80 3.29 26.78 3.41 26.77 3.52 26.75 3.64 27 28 27.79 3.41 27.78 3.53 27.76 3.65 27.74 3.78 28 29 28.78 3.53 28 . 77 3.66 28.75 3.79 28.74 3.91 29 30 29.78 3.66 29.76 3.79 29.74 3.92 29.73 4.05 30 31 30.77 3.78 30.75 3.91 30.73 4.05 30.72 4.18 31 32 31.76 3.90 31.74 4.04 31.73 4.18 31.71 4.32 32 33 32.75 4.02 32.74 4.16 32.72 4.31 32.70 4.45 33 34 33.75 4.14 33.73 4.29 33.71 4.44 33.69 4.58 34 35 34.74 4.27 34.72 4.42 34.70 4.57 34.68 4.72 35 36 35.73 4.39 35.71 4.54 35.69 4.70 35.67 4.85 36 37 36.72 4.51 36.70 4.67 36.68 4.83 36.66 4.99 37 38 37.72 4.63 37.70 4.80 37.67 4.96 37.65 5.12 38 39 38.71 4.75 38.69 4.92 38.67 5.09 38.64 5.26 39 40 39.70 4.87 39.68 5.05 39.66 5.22 39.63 5.39 40 41 40.70 5.00 40.67 5.17 40.65 5.35 40.63 5.53 41 42 41.69 5.12 41.66 5.30 41.64 5.48 41.62 5.66 42 43 42.68 5.24 42.66 5.43 42.63 5.61 42.61 5.80 43 44 43.67 5.36 43.65 5.55 43.62 5.74 43.60 5.93 44 45 44.67 5.48 44.64 5.68 44.62 5.87 44.59 6.0' 45 46 45.66 5.61 45.63 5.81 45.61 6.00 45 58 6.20 46 47 46.65 5.73 46.62 5.93 46.60 6.13 46.57 6.34 47 48 47.64 5.85 47.62 6.06 47.59 6.27 47.56 6.47 48 49 48.63 5.97 48.61 6.18 4S.58 6.40 48.55 6.61 49 50 49.63 6.09 49.60 6.31 49.57 6.53 49.54 6.74 50 8 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 6 CJ c W "K 3 83 Deg. 82| Deg. 82| Deg. 82i Deg. 3 TRAVERSE TABLE. 17 2 7 Deg. 7 Deg. 7* Deg. a sr I Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. i 51 50.62 6.22 50.59 6.44 50.56 6.66i 50.53 6.88 51 52 51.61 6.34 51.58 6.56 51.56 6.79 51.53 7.01 52 53 52.60 6.46 52.58 6.69 52.55 6.92 52 . 52 7.15 53 54 53.60 6.58 53.57 6.81 53.54 7.05 53.51 7.28 54 55 54.59 6.70 54.56 6.94 54.53 7.18 54 . 50 7.42 55 56 55.58 6.82 55.55 7.07 55.52 7.31 55.49 7.55 56 57 56.58 6.95 56.54 7.19 56.51 7.44 56.48 7.69 57 58 57.57 7.07 57.54 7.32 57.50 7.57 57.47 7.82 58 59 53.56 7.19 58.53 7.45 58.50 7.70 58.46 7.96 59 60 59.55 7.31 59.52 7.57 59.49 7.83 59.45 8.09 60 61 60.551 7.43 60.51 7.70 60.48 7.96 69.44 8.23 "H 62 61.54 7.56 61.50 7.82 61.47 8.09 61.43 8.36 62 63 62.53 7.68 62.50 7.95 62.46 8.22 62.42 8.50 63 64 63 . 52 7.80 63.49 8.08 63.45 8.35 63.42 8.63 64 65 64.52 7.92 64.48 8.20 64.44 8.48 64.41 8.77 65 66 65.51 8.04 65.47 8.33 65.44 8.61 65.40 8.90 66 67 66 50 8.17 66.46 8.46 66.43 8.75 66.39 9.04 67 68 67.49 8.29 67.46 8.58 67.42 8.88 67.38 9.17 68 69 68.49 8.41 68.45 8.71 68.41 9.01 68.37 9.30 69 70 69.48 8.53 69.44 8.83 69.40 9.14 69.36 9.44 70 71 70.47 8.65 70.43 8.96 70,30 9.27 70.35 9.57 71 72 71.46 8.77 71.42 9.09 71.38 9.40 71.34 9.71 72 73 72.46 8.90 72.42 9.21 72 38 9.53 72.33 9.84 73 74 73.45 9.02 73.41 9.34 73.37 9.66 73.32 9.98 74 75 74.44 9.14 74.40 9.46 74.36 9.79 74.31 10.11 75 76 75.43 9.26 75.39 9.59 75.35 9.92 75.31 10.25 76 77 76.43 9.38 76.38 9.72 76.34 10.05 76.30 10.38 77 78 77.42 9.51 77.38 9.84 77.33 10.18 77.29 10.52 78 79 78.41 9.63 78.37 9.97 78.32 10.31 78.28 10.65 79 80 79.40 9.75 79>.36 10.10 79.32 10.44 79.27 10.79 80 81 80.40 9.87 80.35 10.22 80.31 10.57 80.26 10.92 81 82 81.39 9.99 81.34 10.35 81.30 10.70 81.25 11.06 82 83 82.38 10.12 82.34 10.47 82.29 10.83 82.24 11.19 83 84 83.37 10.24 83.33 10.60 83.28 10.96 83.23 11.33 84 85 84.37 10.36 84.32 10.73 84.27 11.09 84.22 11.46 85 86 85.36 10.48 85.31 10.85 85.26 11.23 85.21 11.60 86 87 86.35 10.60 86.30 10.98 86.26 11.36 86.21 11.73 87 88 87.34 10.72 87.30 11.11 87.25 11.49 87.20 11.87 88 89 88.34 10.85 88.29 11.23 88.24 11.62 88.19 12.00 89 90 89.33 10 97 89.28 11.36 89.23 11.75 89.18 12.14 90 91 90.32 11.09 90.27 11.48 90.22 11.88 90U7 12.27 91 92 91.31 11.21 91.26 11.61 91.21 12. Oi 91.16 12.41 92 93 92.31 11.33 92.26 11.74 92.20 12.14 92.15 12.54 93 94 93.30 11.46 93.25 11.86 93.20 12.27 93.14 12.68 94 95 94.29 11.58 94.24 11.99 94.19 12.40 94.13 12.81 95 96 95.28 11.70 95.23 12.12 95.18 12.53 95.12 12.95 96 97 96.28 11.82 96.22 12.24 96.17 12.66 96.11 13.08 97 98 97.27 11.94 97,22 12.37 97.16 12.79 97.10 13.22 98 99 93.26 12.07 98.21 12.49 98.15 12.92 98.10 13.35 99 100 99.25 12.19 99.20 12.62 99.14 13.05 99.09 13.49 100 i Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 ~ .-i 83 Deg. 821 Deg. 82ADeg. 82J Degr. Q 18 TRAVERSE TABLE. o 8 Deg. 8* Deg. 8 Deg. 8| Deg. 3 stance. stance.! Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 0.99 0.14 0.99 0.14| 0.99 0.15 0.99 0.15 1 2 1.98 0.28 1.98 0.29 1.98 0.30 1.98 0.30 2 3 2.97 0.42 2.97 0.43 2.97 0.44 2.97 0.46 3 4 3.96 0.56 3.96 0.57 3.96 0.59 3.95 0.61 4 5 4.95 0.70 4.95 0.72 4.95 0.74 4.94 0.76 5 6 5.94 0.84 5.94 0.86 5.93 0.89 5.93 0.91 6 7 6.93 0.97 6.93 1.00 6.92 1.03 6.92 1.06 7 8 7.92 1.11 7.92 1.15 7.91 1.18 7.91 1.22 8 9 8.91 1.25 8.91 1.29 8.90 1.33 8.90 1.37 9 10 9.90 1.39 9.90 1.43 9.89 1.48 9.88 1.52 10 11 10.89 1.53 ;0.89 1.58 10.88 1.63 10.87 "l.67 11 12 11.88 1.67 11.88 1.72 11.87 1.77 11.86 1.83 12 13 12.87 1.81 12.87 1.87 12.86 1.92 12.85 1.98 13 14 13.86 1.95 13.86 2.01 13.85 2.07 13.84 2.13 14 15 14.85 2.09 14.85 2.15 14.84 2.22 14.83 2.28 15 16 15.84 2.23 15.84 2.30 15.82 2.36 15.81 2.43 16 17 16.83 2.37 16.83 2.44 16.81 2.51 16.80 2.59 17 IS 17.82 2.51 17.81 2.58 17.80 2.66 17.79 2.74 18 19 18.82 2.64 18.80 2.73 18.79 2.81 18.78 2.89 19 20 19.81 2.78 19.79 2.87 19.78 2.96 19.77 3.04 20 21 20.80 2.92 20.78 3.01 20.77 3.10 20.76 3.19 21 22 21.79 3.06 21.77 3.16 21.76 3.25 21.74 3.35 22 23 22.78 3.20 22.76 3.30 22.75 3.40 22.73 3.50 23 .24 23.77 3.34 23.75 3.44 23.74 3.55 23.72 3.65 24 25 24.76 3.48 24.74 3.59 24.73 3.70 24.71 3.80 25 26 25.75 3.62 25.73 3.73 25.71 3.84 25.70 3.96 26 27 26.74 3.76 26.72 3.87 26.70 3.99 26.69 4.11 27 28 27.73 3.90 27.71 4.02 27.69 4.14 27.67 4.26 28 29 28.72 4.04 28.70 4.16 28.68 4.29 28.66 4.41 29 30 2,9.71 4.18 29.69 4.30 29.67 4.43 29.65 4.56 30 31 30.70 4.31 | 30.68 4.45 30.66 4.58 30.64 4.72 31 32 31.69 4.45 31.67 4.59 31.65 4 - . 73 31.63 4.87 32 33 32.68 4.59 32.66 4.74 32.64 4.88 32 . 62 5.02 33 34 33.67 4.73 33.65 4.88 33.63 5.03 33.60 5.17 34 35 34.66 4.87 34.64 5.02 34.62 5.17 34.59 5.32 35 36 35.65 5.01 35.63 5.17 35.60 5.32 35.58 5.48 36 37 36.64 5.15 36.62 5.31 36.59 5:47 36.57 5.63 37 38 37.63 5.29 37.61 5.45 37.58 5.62 37.56 5.78 38 39 38.62 5.43 38.60 5.60 38.57 5:76 38.55 5.93 39 40 39.61 5.57 39 . 59 5.74 39.56 5.91 39.53 6.08 40 "41 40.60 5.71 40.58 5.88 40 . 55 6.06 40.52 6.24 41 42 41.59 5.85 41.57 6.03 41.54 6.21 41.51 6.39 42 43 42.58 5.98 42.56 6.17 42.53 6.36 42.50 6.54 43 44 43.57 6.12 43.54 6.31 43.52 6.50 43.49 6.69 44 45 44.56 6.26 44.53 6.46 44.51 6.65 44.48 6.85 45 46 45.55 6.40 45.52 6.60 45.49 6.80 45.46 7.00 46 47 46.54 6.54 46.51 6.74 46.48 6.95 46.45 7.15 47 48 47.53 6.68 47.50 6.89 47.47 7.09 47.44 7.30 48 49 48.52 6.82 48.49 7.03 48.46 7.24 48.43 7.45 49 50 49.51 6.96 49.48 7.17 49.45 7.39 49.42 7.61 50 i Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. i s 82 Deg. 81J Deg. - 8t Deg. 81i Deg. P TRAVERSE TABLE. 19 c 8 Deg. i Deg. 8* Deg. S| Deg. g CO 1 1' p Lat. Dep. Lat. Dep. Lat. Dep. Lat Dep. 1 51 50.50 7.10 50.47 7.32 50.44 7.54 50.41 7.76 51 52 51.49 7.24 51.46 7.46 51.43 7.69 51.39 7.91 52 53 52.48 7.38 52.45 7.61 52.42 7.83 52.38 8.06 53 54 53.47 7.52 53.44 7.75 53.41 7.98 53.37 8.21 54 55 54.46 7.65 54.43 7.89 54.40 8.13 54.36 8.37 55 56 55.46 7.79 55.42 8.04 55.38 8.28 55.35 8.52 56 57 56.45 7.93 56.41 8.18 56.37 8.43 56.34 8.67 57 58 57.44 8.07 57.40 8.32 57.36 8.57 57.32 8.82 58 59 58.43 8.21 58.39 8.47 58.35 8.72 58.31 8.98 59 60 59.42 8.35 59.38 8.61 59.34 8.87 59.30 9.13 60 61 60.41 8.49 60.37 8.75 60.33 9.02 60.29 " 9.28 61 62 61.40 8.63 61.36 8.90 61.32 9.16 61.28 9.43 62 63 62.39 8.77 62.35 9.04 62.31 r 9.31 62.27 9.58 63 64 63.38 8.91 63.34 9.18 63.30 9.46 63.26 9.74 64 65 64.37 9.05 64.33 9.33 64.29 9.61 64.24 9.89 65 66 65.36 9.19 65.32 9.47 65.28 9.76 65.23 10.04 66 67 66.35 9.32 66.31 9.61 66.26 9.90 66.22 10.19 67 68 67.34 9.46 67.30 9.76 67.25 10.05 67.21 10.34 68 69 68.33 9.60 68.29 9.90 68.24 10.20 68.20 10.50 69 70 69.32 9.74 69.28 10.04 69.23 10.35 69.19 10.65 70 71 70.31 9.88. 70.27 10.19 70.22 10.49 70.17 10.80 71 72 71.30 10.02 71.25 10.33 71.21 10.64 71.16 10.95 72 73 72.29 10.16 72.24 10.47 72.20 10.79 72.15 11.10 73 74 73.28 10.30 73.23 10.62 73.19 10.94 73.14 11.26 74 75 74.27 10.44 74.23 10.76 74.18 11.09 74.13 11.41 75 78 75.26 10.58 75.21 10.91 75.17 11.23 75.12 11.56 76 77 76.25 10.72 76.20 11.05 76.15 11.38 76.10 11.71 77 78 77.24 10.86 77.19 11.19 77.14 11.53 77.09 11.87 78 79 78.23 10.99 78.18 11.34 78.13 11.68 73.08 12.02 79 80 79.22 11.13 79.17 11.48 79.12 11.82 79.07 12.17 80 81 80.21 11.27 80.16 11.62 80.11 11.97 80.06 12.32 81 82 81.20 11.41 81.15 11.77 81.10 12.12 81.05 12.47 82 83 82.19 11.55 82.14 11.91 82.09 12.27 82.03 12.63 83 84 83.18 11.69 83.13 12.05 83.08 12.42 83.02 12.78 84 85 84.17 11.83 84.12 12.20 84.07 12.56 84.01 12.93 85 86 85.16 11.97 85.11 12.34 85.06 12.71 85.00 13.08 86 87 86.15 12.11 86.10 12.48 86.04 12.86 85.99 13.23 87 88 87.14 12.25 87.09 12.63 87.03 13.01 86.98 13.39 88 89 88.13 12.39 88.08 12.77 88.02 13.16 87.96 13.54 89 90 89.12 12.53 89.07 12.91 89.01 13. 88.95 13.69 90 31 90.11 12.66 90.06 13.06 90.00 13.45 89.94 13.84 91 92 91.10 12.80 91.05 13.20 90.99 13.60 90.93 14.00 92 93 92.09 12.94 92.04 13.34 91.98 13.75 91.92 14.15 93 94 93.09 13.08 93.03 13.49 92.97 13.89 92.91 14.30 94 95 94.08 13.22 94.02 13.63 93.96 14.04 93.89 14.45 95 96 95.07 13.36 95.01 13.78 94.95 14.19 94.88 14.60 96 97 96.06 13.50 96.00 13.92 95.93 14.34 95.87 14.76 97 98 97.05 13.64 96.99 14.06 96.92 14.49 96.86 14.91 98 99 98.04 13.78 97.98 14.21 97.91 14.63 97.85 15.06 99 100 99.03 13.92 98.97 14.35 98.90 14.78 98.84 15.21 100 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 1 Q 82 Deg. C1J Deg. Sl^Deg. 814 Deg. J .2 Q TRAVERSE TABLE. g 9 Deg. 9} Deg. 9i Deg. 9| Deg. C 1 CD stance.l Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 0.99 0.16 0.99 0.16 0.99 0.17 0.99 0.17 1 2 1.98 0.31 1.97 0.32 1.97 0.33 1.97 0.34 2 3 2.96 0.47 2.96 0.48 2.96 0.50 2.96 0.51 3 4 3.95 0.63 3.95 0.64 3.95 0.66 3.94 0.68 4 5 4.94 0.78 4.93 0.80 4.93 0.83 4.93 0.85 5 6 5.93 0.94 5.92 0.96 5.92 0.99 5.91 1.02 6 7 6.91 1.10 6.91 1.13 6.90 1.16 6.90 1.19 7 8 7.90 1.25 7.90 1.29 7.89 1.32 7.88 1.35 8 9 8.89 1.41 8.88 1.45 8.88 1.49 8.87 1.52 9 10 9.88 1.56 9.87 1.61 , 9.86 1.65 9.86 1.69 10 11 10.86 1.72 10.86 1.77 10.85 1.82 10.84 1.86 11 12 11.85 1.88 11.84 1.93 11.84 1.98 11.83 2,03 12 13 12.84 2.03 12.83 2.09 12.82 2.15 12.81 2.20 13 14 13.83 2.19 13.82 2.25 13.81 2.31 13.80 2.37 14 15 14.82 2.35 14.80 2.41 14.79 2.48 14.78 2.54 15 16 15.80 2.50 15.79 2.57 15.78 2.64 15.77 2.71 16 17 16.79 2.66 16.78 2.73 16.77 2.81 16.75 2.88 17 18 17.78 2.82 17.77 2.89 17.75 2.97 17.74 3.05 13 19 18.77 2.97 18.75 3.05 18.74 3.14 IS. 73 3.22 19 20 19.75 3.13 19.74 3.21 19.73 3.30 j 19.71 3.39 20' 21 20.74 3.29 20.73 3.38 20.71 3.47 20.70 3.56 21 22 21.73 3.44 21.71 3.54 21.70 3.63 21.68 3.73 22 23 22.72 3.60 22.70 3.70 22.68 3.80 22.67 3.90 23 24 23.70 3.75 23.69 3.86 23.67 3.96 23.65 4.06 24 25 24.69 3.91 24.67 4.02 24.66 4.13 24.64 4.23 25 26 25.68 4.07 25.66 4.18 25.64 4.29 25.62 4.40 26 27 26.67 4.22 26.65 4.34 26.63 4.46 26.61 4.57 27 28 27.66 4.38 27.64 4.50 27.62 4.62 27.60 4.74 28 29 28 , 64 4.54 28.62 4.66 28.60 4.79 28.58" 4.91 29 30 29.63 4.69 29.61 4.82 29.59 4.95 29.57 5.08 30 31 30.62 4.85 30.60 4.98 30.57 5.12 30.55 5.25 31 32 31.61 5.01 31.58 5.14 31.56 5.28 31.54 5.42 32 33 32.59 5.16 32.57 5.30 32.55 5.45 32.52 5.59 33 34 33.58 5.32 33.56 5.47 33.53 5.61 33.51 5.76 34 35 34.57 5.48 34.54 5.63 34.52 5.78 34.49 5.93 35 36 35.56 5.63 35.53 5.79 35.51 5.94 35.48 6.10 36 37 36.54 5.79 36.52 5.95 36.49 6.11 36.47 6.27 37 38 37.53 5.94 37.51 6.11 37.48 6.27 37.45 6.44 38 39 38.52 6.10 38.49 6.27 38.47 6.44 38.44 6.60 39 40 39.51 6.26 39.48 6.43 39.45 6.60 39.42 6.77 40 11 40.50 6.41 40.47 6.59 40.44 6.77 40.41 6.94 41 42 41.48 6.57 41.45 6.75 41.42 6.92 41.39 7.11 42 43 42.47 6.73 42.44 6.91 42.41 7.10 42.38 7.28 43 44 43.46 6.88 43.43 7.07 43.40 7.26 43.36 7,45 44 45 44.45 7.04 44.41 7.23 44.38 7.43 44.35 7.62 45 46 45.43 7.20 45.40 7.39 45.37 7.59 45.34 7.79 46 47 46.42 7.35 46.39 7.55 46.36 7.76 46.32 7.96 47 48 47.41 7.51 47.38 7.72 47.34 7.92 47.31 8.13 48 49 48.40 7.67 48.36 7.88 48.33 8.09 48.29 8.30 49 50 49.38 7.82 49.35 8.04 49.32 8.25 49.28 8.47 50 ' 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 .2 Q 81 Deg. 80| Deg. 801 Deg. 80i Deg. 1 3 TRAVERSE TABLE. 1 9 5 6 9 Deg. 94 Deg. 9^ Deg. 9| Deg. q P ? I a Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 51 50.37 7.98 50.34 8.20 50.30 8.42 50.26 8.64 51 52 51.36 8.13 51.32 8.36 51.29 8.58 51.25 8.81 52 53 52.35 8.29 52.31 8.52 52.27 8.75 52.23 8.98 53 54 53.34 8.45 53.30 8.68 53.26 8.91 53.22 9.14 54 55 54.32 8.60 54.28 8.84 54.25 9.08 54.21 9.31 55 56 55.31 8.76 55.27 9.00 55.23 9.24 55.19 9.48 56 57 56.30 8.92 56.26 9.16 56.22 9.41 56.18 9.65 57 58 57.29 9.07 57.25 9.32 57.20 9.57 57.16 9.82 58 59 58.27 9.23 58.23 9.48 58.19 9.74 58.15 9.99 59 60 59.26 9.39 59.22 9.64 59.18 9.90 59.13 10.16 60 61 60.25 9.54 60.21 9.81 60.16 10.07 60.12 10.33 6] 62 61.24 9.70 61.19 9.97 61.15 10.23 61.10 10.50 62 63 62.22 9.86 62.18 10.13 62.14 10.40 62.09 10.67 63 64 63.21 10.01 63.17 10.29 63.12 10.56 63.08 10.84 64 65 64.20 10.17 64.15 10.40 64.11 10.73 64.06 11.01 65 66 65.19 10.32 65.14 10.61 65.09 10.89 65.05 11.18 66 67 66.18 10.48 66.13 10.77 66.08 11.06 66.03 11.35 67 68 67.16 10.64 67.12 10.93 67.07 11.22 67.02 11.52 68 69 68.15 10.79 68.10 11.09 68.05 11.39 68.00 11.69 69 70 69.14 10.95 69.09 11.25 69.04 11.55 68.99 11.85 70 71 70.13 11.11 70.08 11.41 70.03 11.72 69.97 12.02 71 72 71.11 11.26 71.06 11.57 71.01 11.88 70.96 12.19 72 73 72.10 11.42 72.05 11.73 72.00 12.05 71.95 12.36 73 74 73.09 11.58 73.04 11.89 72.99 12.21 72.93 12.53 74 75 74.08 11.73 74.02 12.06 73.97 12.38 73.92 12.70 75 76 75.06 11.89 75.01 12.22 74.96 12.54 74.90 12.87 76 77 76.05 12.05 76.00 12.38 75.94 12.71 75.89 13.04 77 78 77.04 12.20 76.99 12.54 76.93 12.87 76.87 13.21 78 79 78.03 12.36 77.97 12.70 77.92 13.04 77.86 13.38 79 80 79.02 12.51 78.96 12.86 78.90 13.20 78.84 13.55 80 81 80.00 12.67 79.95 13.02 79.89 13.37 79.83 13.72 81 82 80.99 12.83 80.93 13.18 80.88 13.53 80.82 13.89 82 83 81.98 12.98 81.92 13.34 81.86 13.70 81.80 14.06 83 84 82.97 13.14 82.91 13.50 82.85 13.86 82.79 14.23 84 85 83.95 13.30 83.89 13.66 83.83 14.03 83.77 14.39 85 86 84.94 13.45 84.88 13.82 84.82 14.19 84.76 14.56 86 87 85.93 13.61 85.87 13.98 85.81 14.36 85.74 14.73 87 88 86.92 13.77 86.86 14.15 86.79 14.52 86.73 14.90 88 89 87.90 13.92 87.84 14.31 87.78 14.69 87.71 15.07 89 90 88.89 14.08 88.83 14.47 88.77 14.85 88.70 15.24 90 91 89.88 14.24 89.82 14.63 89.75 15.02 89.69 15.41 91 92 90.87 14.39 90.80 14.79 90.74 15.18 90.67 15.58 92 93 91.86 14.55 91.79 14.95 91.72 15.35 91.66 15.75 93 94 92.84 14.70 92.78 15.11 92.71 15.51 92.64 15.92 94 95 93.83 14.86 93.76 15.27 93.70 15.68 93.63 16.09 95 96 94.82 15.02 94.75 15.43 94.68 15.84 94.61 16.26 96 97 95.81 15.17 95.74 15.59 95.67 16.01 95.60 16.43 97 98 96.79 15.33 96.73 15.75 96.66 16.17 96.58 16.60 98 99 97.78 15.49 97.71 15.91 97.64 16.34 97.57 16.77 99 100 98.77 15.64 98.70 16.07 98.63 16.50 98.56 16.93 100 | Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. I Q 81 Deg. 80| Deg. 80f Deg. 804 Deg. -"; s . *. t. *#*" TEA VERSE TABLE. o 10 Deg. 10i Deg. 10| De S- 10| Deg. g r 3 D o o Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. P E o CO 1 0.98 0.17 0.98 0.18 0.98 0.18 0.98 0.19 1 2 1.97 0.35 1.97 0.36 1.97 0.36 1.96 0.37 3 2.95 0.52 2.95 0.53 2.95 0.55 2.95 0.56 3 4 3.94 0.69 3.94 0.71 3.93 0.73 3.93 0.75 4 5 4.92 0.87 4.92 0.89 4.92 0.91 4.91 0.93 5 6 5.91 1.04 5.90 1.07 5.90 1.09 5.89 1 12 6 7 6.89 1.22 6.89 1.25 6.88 1.28 6.88 1.31 7 8 7.88 1.39 7.87 1.42 7.87 1.46 7.86 1.49 8 9 8.86 1.56 8.86 1.60 8.85 1.64 8.84 1.68 9 10 9.85 1.74 9.84 1.78 9.83 1.82 9.82 1.87 10 11 10.83 1.91 10.82 1.96 10.82 2.00 10.81 2.05 11 12 11.82 2.08 11.81 2.14 11.80 2.19 11.79 2.24 12 13 12.80 2.26 12.79 2.31 12.78 2.37 12.77 2.42 13 14 13.79 2.43 13.78 2.49 13.77 2.55 13.75 2.61 14 15 14.77 2.60 14.76 2.67 14.75 2.73 14.74 2.80 15 16 15.76 2.78 15.74 2.85 15.73 2.92 15.72 2.98 16 17 16.74 2.95 16.73 3.03 16.72 3.10 16.70 3.J7 17 18 17.73 3.13 17.71 3.20 17.70 3.28 17.68 3.36 18 19 18.71 3.30 18.70 3.38 18.68 3.46 18.67 3.54 19 20 19.70 3.47 19.68 3.56 19.67 3.64 19.65 3.73 20 21 20.68 3.65 20.66 3.74 20.65 3.83" 20.63 3.92 21 22 21.67 3.82 21.65 3.91 21.63 4.01 21.61 4.10 22 23 22.65 3.99 22.63 4.09 22.61 4.19 22.60 4.29 23 24 23.64 4.17 23 . 62 4.27 23.60 4.37 23 . 58 4.48 24 25 24.62 4-34 24.60 4.45 24.58 4.56 24.56 4.66 25 26 25.61 4.51 25.59 4.63 25.56 4.74 25.54 4.85 26 27 26.59 4.69 26.57 4.80 26.55 4.92 26 . 53 5.04 27 28 27.57 4.86 27.55 4.98 27.53 5.10 27.51 5.22 28 29 28.56 5.04 28.54 5.16 28.51 5.28 28.49 5.41 29 30 29.54 5.21 29.52 5.34 29.50 5.47 29.47 5.60 30 31 30.53 5.38 30.51 5.52 30.48 5.65 30.46 5.78 31 : 32 31.51 5.56 31.49 5.69 31.46 5.83 31.44 5.97 32 33 32.50 5.73 32.47 5.87 32.45 6.01 32.42 6.16 33 34 33.48 5.90 33.46 6.05 33.43 6.20 33.40 6.34 34 35 34.47 6.08 34.44 6.23 34.41 6.38 34.39 6.53 35 36 35.45 6.25 35.43 6.41 35.40 6.56 35.37 6.71 35 37 36.44 6.42 36.41 6.58 36.38 6.74 36.35 6.90 37 38 37.42 6.60 37.39 6.76 37.36 6.92 37.33 7.09 38 39 38.41 6.77 38.38 6.94 38.35 7.11 38.32 7.27 39 40 39.39 6.95 39.36 7.12 39.33 7.29 39.30 7.46 40 41 40.38 7.12 40.35 7.30 40.31 ~7.47 40.28 7.65 41 42 41.36 7.29 41.33 7.47 41.30 7.65 41.26 7.83 42 43 42.35 7.47 42.31 7.65 42.28 7.84 42.25 8.02 43 44 43.33 7.64 43.30 7.83 43.26 8.02 43.23 8.21 44 45 44.32 7.81 44.28 8.01 44.25 8.20 44.21 8.39 45 46 45.30 7.69 45.27 8.19 45.23 8.38 45.19 8.58 46 47 46.29 8.16 46.25 8.36 46.21 8.57 46.18 8.77 47 48 47.27 8.34 47.23 8.54 47.20 8.75 47.16 8.95 48 49 48.26 8.51 48.22 8.72 48.18 8.93 48.14 9.14 49 50 49.24 8.68 49.20 8.90 49.16 9.11 49.12 9.33 50 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. c s 80 Deg. 79| Deg. 79| Deg. 79} Deg. s TRAVERSE TABLE. 23 p 1' 10 Deg. 10J Deg. 101 Deg. | 10| Deg. O S" 2 O Q Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. P ~5l 50.23 8.86 50.19 9.08 50.15 9 .-29 50.10 9.51 51 52 51.21 9.03 51.17 9.25 51.13 9.48 51.09 9.70 52 53 52.19 9.20 52.15 9.43 52 . 1 1 9.66 52.07 9.89 53 54 53.18 9.38 53.14 9.61 53.10 9.84 53.05 10.07 54 55 54.16 9.55 54.12 9.79 54.08 10.02 04.03 10.26 55 56 55.15 9.72J 55.11 9.96 55.06 10.21 55.02 10.45 56 57 56.13 9.90, 56.09 10.14 56.05 10.39 56.00 10.63 57 58 57.12 10.07 57.07 10.32 57.03 10.57 56.98 10.82 58 59 58.10 10.25 58.06 10.50 58.01 10.75 57.96 11.00 59 60 59.09 10.42 59.04 10.68 59.00 10.93 58.95 11.19 60 61 ^60.07 10.59 60.Q3 10.85 59.98 11.12 59.93 11.38 61 62 61.06 10.77 61.01 11.03 60.96 11.30 60.91 11.56 62 63 62.04 10.94 61.99 11.21 61.95 11.48 61.89 1*.75 63 64 63.03 11.11 62.98 11.39 62.93 11.66 62.88 11.94 64 65 64.01 11.29 63.96 11.57 63.91 11.85 63.86 12.12 65 66 65.00 11.46 64.95 11.74 64.89 12.03 64.84 12.31 66 67 65.98 11.63 65.93 11.92 65.88 12.21 65.82 12.50 67 68 66.97 11.81 66.91 12.10 66.88 12.39 66.81 12.68 68 69 67.95 11.98 67.90 12.28 67.84 12.57 67.79 12. S7 69 70 88.94 12.16 68.88 12.46 68.83 12.76 68.77 13.06 70 71 69.92 12.33 69.87 12.63 69.81 12.94 69.75 13.24 7] 72. 70.91 12.50 70.85 12.81 70.79 13.12 70.74 13.43 72 73 71.89 12.68 71.83 12.99 71.78 13.30 71.72 13.62 73 74 72.88 12.85 72.82 13.17 72.76 13.49 72.70 13.80 74 75 73.86 13.02 73.80 13.35 73.74 13.67 73.68 13.99 75 76 74.85 13.20 74.79 13.52 74.73 13.85 74.67 14.18 76 77 75.83 13.37 75.77 13.70 75.71 14.03 75.65 14.36 77 78 76.82 13.54 76.76 13.88 76.69 14.21 76.63 14.55 78 79 77.80 13.72 77.74 14.06 77.68 14.40 77.61 14.74 79 80 78.78 13.89 78.72 14.24 78.66 14.58 78.60 14.92 80 81 79.77 14.07 79.71 14.41 79.64 14.76 79.58 15.11 81 82 80.75 14.24 80.69 14.59 80.63 14.94 80.56 15.29 82 83 81.74 14.41 81.68 14.77 81.61 15.13 81.54 15.48 83 84 82.72 14.59 82.66 14.95 82.59 15.31 82.53 15.67 84 85 83.71 14.76 83.64 15.13 83.58 15.49 83.51 15.85 85 86 84.69 14.93 84.63 15.30 84.56 15.67 84.49 16.04 86 87 85.68 15.11 85.61 15.48 85.54 15.85 85.47 16.23 87 88 86.66 15.28 86.60 15.66 86.53 16.04 85.46 16.41 88 89 87.65 15.45 87.58 15.84 87.51 16.22 87.44 16.60 89 90 88.63 15.63 88.56 16.01 88.49 16.40 88.42 16.79 90 91 89.62 15.80 89.55 16.19 89.48 16.53 89.40 16.97 91 92 90.60 15.98 90.53 16.37 90.46 16.77 90.39 17-16 92 93 91.59 16.15 91.52 16.55 91.44 16.95 91.37 17.35 93 94 92.57 16.32 92.50 16.73 92.43 17.13 92.35 17.53 94 95 93.56 16.50 93.48 16.90 93.41 17.31 93.33 17.72 95 96 94.54 16.67 94.47 17.08 94.39 17.49 94.32 17.91 96 97 95.53 16.84 95.45 17.26 95.38 17.68 95.30 18.09 97 98 96.51 17.02 96.44 17.44 96.36 17.86 96.28 18.28 1 98 99 97.50 17.19 97.42 17.62 97.34 18.04 97.26 18.47 99 100 98.48 17.36 98.40 17.79 98.33 18.22 98.25 18.65 100 d Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. i I 80 Deg. 79J Deg. 791 Deg. 79i Deg. CD- s TRAVERSE TABLE. o 5' 11 Deg. Hi Deg. ' 11 Deg. Ill Deg. O ? 1 & P Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. p 1 0.98 0.19 0.98 0.20 0.98 0.20 0.98 0.20 1 2 1.96 0.38 1.96 0.39 1.96 0.40 1.96 0.41 2 3 2.94 0.57 2.94 0.59 2.94 0.60 2.94 0.61 3 4 3.93 0.76 3.92 0.78 3.92 0.80 3.92 0.82 4 5 4.91 0.95 4.90 0.98 4.90 .00 4.90 1.02 5 6 5.89 1.14 5.88 1.17 5.88 .20 5.87 1.22 6 7 6.87 1.34 6.87 1.37 6.86 .40 6.85 1.43 7 8 7.85 1.53 7.85 1.56 7.84 .59 7.83 1.63 8 9 8.83 1.72 8.83 1.76 8.82 .79 8.81 1.83 9 10 9.82 1.91 9.81 1.95 9.80 .99 9.79 2.04 10 11 10.80 2.10 10.79 2.15 10.78 2.19 10.77 2.24 11 12 11.78 2.29 11.77 2.34 11.76 2.39 11.75 2.44 12 13 12. f6 2.48 12.75 2.54 12.74 2.59 12.73 2.65 13 14 13.74 2.67 13.73 2.73 13.72 2.79 13.71 2.85 14 15 14.72 2.86 14.71 2.93 14.70 2.99 14.69 3.06 15 16 15.71 3.05 15.69 3.12 15.68 3.19 15.66 3.26 16 17 16.69 3.24 16.67 3.32 16.66 3.39 16.64 3.46 17 18 17.67 3.43 17.65 3.51 17.64 3.59 17.62 3.66 18 19 18.65 3.63 18.63 3.71 18.62 3.79 18.60 3.87 19 20 19.63 3.82 19.62 3.90 19.60 3.99 19.58 4.07 20 21 20.61 4.01 20.60 4.10 20.58 4.19 20.56 4.28 21 22 21.60 4.20 21.58 4.29 21.56 4.39 21.54 4.48 22 23 22.58 4.39 22.56 4.49 22.54 4.59 22.52 4.68 23 24 23.56 4.58 23.54 4.68 23.52 4.78 23.50 4.89 24 25 24.54 4.77 24.52 4.88 24.50 4.98 24.48 5.09 25 26 25.52 4.96 25.50 5.07 25.48 5.18 25.46 5.30 26 27 26.50 5.15 26.48 5.27 26.46 5.38 26.43 5.50 27 28 27.49 5.34 27.46 5.46 27.44 5.58 27.41 5.70 28 29 28.47 5.53 28.44 5.66 28.42 5.78 28.39 5.91 29 30 29.45 5.72 29.42 5.85 29.40 5.98 29.37 6.11 30 31 30.43 5.92 30.40 6.05 30.38 6.18 30.35 6.31 31 32 31.41 6.11 31.39 6.24 31.36 6.38 31.33 6.52 32 33 32.39 6 30 32.37 6.44 32.34 6.58 32.31 6.72 33 34 33.38 6.49 33.35 6.63 33.32 6.78 33.29 6.92 34 35 34.36 6.68 34.33 6.83 34.30 6.98 34.27 7.13 35 36 35.34 6.87 35.31 7.02 35.28 7.18 35.25 7.33 36 37 36.32 7.06 36.29 7.22 36.26 7.38 36.22 7.53 37 38 37.30 7.25 37.27 7.41 37.24 7.58 37.20 7.74 38 39 38.28 7.44 38.25 7.61 38.22 7.78 38.18 7.94 39 40 39.27 7.63 39.23 7.80 39.20 7.97 39.16 8.15 40 41 40.25 7.82 40.21 8.00 40.18 8.17 40.14 8.35 41 42 41.23 8.01 41.19 8.19 41.16 8.37 41.12 8.55 42 43 42.21 8.20 42.17 8.39 42.14 8.57 42.10 8.76 43 44 43.19 8.40 43.15 8.58 43.12 8.77 43.08 8.96 44 45 44.17 8.59 44.14 8.78 44.10 8.97 44.06 9.16 45 46 45.15 8.78 45.12 8.97 45.08 9.17 45.04 9.37 46 47 46.14 8.97 46.10 9.17 46.06 9.37 46.02 9.57 47 48 47.12 9.16 47.08 9.36 47.04 9.57 46.99 9.78 48 49 48.10 9.35 48.06 9.56 48.02 9.77 47.97 9.98 49 50 49.08 9.54 49.04 9.75 49.00 9.97 48.95 10.18 50 49 o a Dep. Lai, Dep. Lat. Dep. Lat. Dep. Lat. o o a ei .a Q 79 Deg. 78| Deg. 78 Deg. 78i Deg, cA s TRAVERSE TABLE. 25 3 11 Deg. Hi Deg, 11 Deg. 11| Deg, s So" 3 n Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. ~sT 50.06 9.73 50.02 9.95 49.98 10.17 49.93 10.39 51 52 51.04 9.92 51.00 10.14 50.96 10.37 50.91 10.59 52 53 52.03 10.11 51.98 10.34 51.94 10.57 51.89 10.79 53 54 53.01 10.30 52.96 10.53 52.92 10.77 52.87 11.00 54 55 53.99 10.49 53.94 10.73 53.90 10.97 53.85 11.20 55 56 54.97 10.69 54.92 10.93 54.88 11.16 54.83 11.40 56 57 55.95 10.88 55.90 11.12 55.86 11.36 55.81 11.61 57 53 56.93 11.07 56.89 11.32 56.84 11.56 56.78 11.81 58 59 57.92 11.26 57.87 11.51 57.82 11.76 57.76 12.01 59 60 58.90 11.45 58.85 11.71 58.80 11.96 58.74 12.22 60 61 59.88 11.64 59.83 11.90 59.78 12.16 59.72 12.42 61 62 60,86 11.83 60.81 12.10 60.76 12.36 60.70 12.63 62 63 61,84 12.02 61.79 12.29 61.74 '12.56 61.68 12.83 63 64 62.82 12.21 62.77 12.49 62.72 12.76 62.66 13.03 64 65 63.81 12.40 63.75 12.68 63.70 12.96 63.64 13.24 65 66 64,79 12.59 64.73 12.88 64.68 13.16 64.62 13.44 66 67 65,77 12.78 65.71 13.07 65.66 13.36 65.60 13.64 67 63 66.75 12.98 66.69 13.27 66.63 13.56 66.58 13.85 68 69 67.73 13.17 67.67 13.46 67.61 13.76 67.55 14.05 69 70 68.71 13.36 68.66 13.66 68.59 13.96 68.53 14.25 70 71 69.70 13.55 69.64 13.85 69.57 14.16 69.51 14.46 71 72 70.68 13.74 70.62 14.05 70.55 14.35 70.49 14.66 72 73 71.66 13.93 71.60 14.24 71.53 ,'4.55 71.47 14.87 73 74 72.64 14.12 72.58 14.44 72.51 14,75 72.45 15.07 74 75 73.62 14.31 73.56 14.63 73.49 14.95 73.43 15.27 75 76 74.60 14.50 74.54 14.83 74.47 15.15 74.41 15.48 76 77 75.59 14.69 75.52 15.02 75.45 15.. 35 75.39 15.68 77 78 76.57 14.83 76.50 15.22 76.43 15". 55 76.37 15.88 78 79 77.55 15.07 77.48 15.41 77.41 15.75 77.34 16.09 79 _80 78 . 53 15.26 78.46 15.61 78.39 15.95 78.32 16.29 80 81 79.51 15.46 79.44 15.80 79.37 16.15 79.30 16.49 81 82 80.49 15.65 80,42 16.00 80.35 16.35 80.28 16.70 82 83 81.48 15.84 81.41 16.191 81.33 16.55 81.26 16.90. 83 84 82.46 16.03 82.39 16.39 82.31 16.75 82.24 17.11 84 85 83.44 16.22 83.37 16.53 83.29 16.95 83.22 17.31 85 86 84.42 16.41 84.35 16.78 84.27 17.. 15 84.20 17.51 86 87 85.40 16.60 85.33 16.97 85.25 17.35 85.18 17.72 87 88 86.38 16.79 86.31 17.17 86.23 17.54 86.16 17.92 88 89 87.36 16,98 87.29 17.36 87.21 17.74 87.14 18.12 89 90 88,35 17.17 88.27 17.56 88.19 17.94 88.11 18.33 90 91 89.33 17.36 89.25 17.75 89.17 18.14 89.09 18.53 91 92 90,31 17.55 90.23 17.95 90.15 18.34 90.07 18.74 92 93 91.29 17.75 91.21 18.14 91.13 18.54 91.05 18.94 93 94 92,27 17.94 92.19 18.34 92.11 18.74 92.03 19-. 14 94 95 93.25 18.13 93.17 18.53 93.09 18.94 93.01 19.35 95 96 94.24 18.32 94.16 18.73 94.07 19.14 93.99 19.55 96 97 95.22 18.51 95.14 18.92 95.05 19.34 94.97 19.75 97 98 96.20 18.70 96.12 19.12 96.03 19.54 95.95 19.96 98 99 97.18 18.89 97.10 19.31 97.01 19.74 96.93 20.1-6 99 100. 93.16 19.03 98.08 19.51 97.99 19.94 97.90 20.36 jOO I Dep. Lat. Dep. Lat. I Dep. Lat. Dep. Lat. 1 5 1 Q 79 Deg. 78| Deg. l 78Deg. II 78* Deg. Q TRAVERSE TABLE. s 12 Deg. 12k Deg. m Deg. 12| Deg. O 00 1 I* 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 r 0.98 0.21 0.98 0.21 0.98 0.22 0.98 0.22 1 2 1.96 0.42 1.95 0.42 1.95 0.43 1.95 0.44 2 3 2,93 0.62 2.93 0.64 2.93 0.65 2.93 0.66 3 4 3.91 0.83 3.91 0.85 3.91 0.87 3.90 0.88 4 5 4.89 1.04 4.89 1.06 4.88 1.08 4.88 1.10 5 6 5.87 1.25 5.86 1.27 5.86 1.30 5.85 1.32 6 7 6.85 1.46 6.84 1.49 6.83 1.52 6.83 1.54 7 8 7.83 1.66 7.82 1.70 7.81 1.73 7.80 1.77 8 9 8.80 1.87 8.80 1.91 8.79 1.95 8.78 1.99 9 10 9.78 2.08 9.77 2.12 9.76 2.16 9.75 2.21 10 11 10.76 2.29 10.75 2.33 10.74 2.38 10.73 2.43 11 12 11.74 2.49 11.73 2.55 11.72 2.60 11.70 2.65 12 13 12.72 2.70 12.70 2.76 12.69 2.81 12.68 2.87 13 14 13.69 2.91 13.68 2.97 13.67 3.03 13.65 3.09 14 15 14.67 3.12 14.66 3.18 14.64 3.25 14.63 3.31 15 16 15.65 3.33 15.64 3.39 15.62 3.46 15.61 3.53 16 17 16.63 3.53 16.61 3.61 16.60 3.68 16.58 3.75 17 18 17.61 3.74 17.59 3.82 17.57 3.90 17. C6 3.97 18 19 18.58 3.95 18.57 4.03 18.55 4.11 18.53 4.19 19 20 19.56 4.16 19.54 4.24 19.53 4.33 19.51 4.41 20 21 20.54 4.37 20.52 4.46 20.50 4.55 20.48 4.63 21 22 21.52 4.57 21.50 4.67 21.48 4.76 21.46 4.86 22 23 22.50 4.78 22.48 4.88 22.45 4.98 22.43 5.08 23 24 23.48 4.99 23.45 5.09 23.43 5.19 23.41 5.30 24 25 24.45 5.20 24.43 5.30 24.41 5.41 24.38 5.52 25 26 25.43 5.41 25.41 5.52 25.38 5.63 25.36 5.74 26 27 26.41 5.61 26.39 5.73 26.36 5.84 26.33 5.96 27 28 27.39 5.82 27.36 5.94 27.34 6.06 27.31 6.18 28 29 28.37 6.03 28.34 6.15 28.31 6.28 28.28 6.40 29 30 29.34 6.24 29.32 6.37 29.29 6.49 29.26 6.62 30 31 30 . 32 6.45 30.29 6.58 30.27 6.71 30.24 6.84 31 32 31.30 6.65 31.27 6.79 31.24 6.93 31.21 7.06 32 33 32.28 6.86 32.25 7.00 32.22 7.14 32.19 7.28 33 34 33.26 7.07 33.23 7.21 33.19 7.36 33.16 7.50 34 35 34.24 7.28 34.20 7.43 34.17 7.58 34.14 7.72 35 36 35.21 7.48 35.18 7.64 35.15 7.79 35.11 7.95 36 37 36.19 7.69 36.16 7.85 36.12 8.01 36.09 8.17 37 38 37.17 7.90 37.13 8.06 37.10 8.22 37.06 8.39 38 39 38.15 8.11 38.11 8.27 38.08 8.44 38.04 8.61 39 40 39.13 8.32 39.09 8.49 39.05 8.66 39.01 8.83 40 41 40.10 8.52 40.07 8.70 40.03 8.87 39.99 9.05 41 42 41.08 8.73 41.04 8.91 41.00 9.09 40.96 9.27 42 43 42.06 8.94 4?. 02 9.12 41.98 9.31 41.94 9.49 43 44 43.04 9.15 43.00 9.34 42.96 9.52 42.92 9.71 44 45 44.02 9.36 43.98 9.55 43.93 9.74 43.89 9.93 45 46 44.99 9.56 44.95 9.76 44.91 9.96 44.87 10.15 46 47 45.97 9.77 45.93 9.97 45.89 10.17 45.84 10.37 47 48 46.95 9.98 46.91 10.18 46.86 10.39 46.82 10.59 48 49 47.93 10.19 47.88 10.40 47.84 10.61 47.79 10.81 49 50 48.91 10.40 48.86 10.61 48.81 10.82 48 . 77 11.03 50 i Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Q 78 Deg. 77| Deg. 771 Deg. 774 Deg. rf s TRAVERSE TABLE. 27 e 12 Deg. 12i Deg. 12 Deg. 12J Deg. S 1 I Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 5i 49.89 10.00 49.84 10.82 49.79 11.04 49.74 11.26 51 52 50.86 10.81 50.82 11.03 50.77 11.25 50.72 11.48 52 53 51.84 11.02 51.79 11.25 51.74 11.47 51.69 11.70 53 54 52.82 11.23 52.77 11.46 J52.72 11.69 52.67 11.02 54 55 53.80 11.44 53.75 11.67 153.70 11.90 53.64 12.14 55 56 54.78 11.64 54.72 11.88 J54.67 12.12 54.62 12.36 56 57 55.75 11.85 55.70 12.09 55.65 12.34 55.59 12.58 57 58 56.73 12.06 56.68 12.31 56.63 12.55 56.57 12.80 58 59 57.71 12.27 57.66 12.52 57.60 12.77 57.55 13.02 59 60 58.69 12.47 58.63 12.73 58.58 12.99 58.52 13.24 60 61 59.67 12.68 59.61 12.94 159.55 13.20 59.50 13.46 61 62 60.65 12.89 60.59 13.16 60.53 13.42 60.47 13.68 62 63 61.62 13.10 61.57 13.37 61 51 13.64 61.45 13.90 63 64 62.60 13.31 62.54 13.58 62 .'48 13.85 62.42 14.12 64 65 63.58 13.51 63.52 13.79 i63.46 14.07 63.40 14.35 65 66 64.56 13.72 64.50 14.00 J64.44 14.29 64.37 14.57 06 67 65.54 13.93 65.47 14.22 165.41 14.50 65.35 14.79 67 68 66.51 14.14 66.45 14.43 66.39 14.72 66.32 15.01 68, 69 67.49 14.35 67.43 14.64 67.36 14.93 67.30 15.23 69 70 68.47 14.55 68.41 14.85 68.34 15.15 68.27 15.45 70 71 69.45 14.76 69.38 15.06 69.32 15.37 69.25 15.67 71 72 70.43 14.97; 70.36 15.28 70.29 15.58 70.22 15.89 72 73 71.40 15.18! 71.34 15.49 71.27 15.80 71.20 16.11 73 74 72.38 15.39 72.32 15.70 72.25 16.02 72.18 16.33 74 75 73.36 15.59 73.29 15.91 73.22 16.23 73.15 16.55 75 76 74.34 15.80 74.27 16.13 74.20 16.45 74.13 16.77 76 77 75.32 16.01 75.25 16.34 75.17 16.67 75.10 16.99 77 78 76.30 16.22 76.22 16.55 76.15 16.88 76.08 17.21 78 79 77.27 16.43 77.20 16.76 77.13 17.10 77.05 17.44 79 80 78.25 16.63 78.18 16.97 78.10 17.32 78.03 17.66 80 81; 79.23 16.84 79.16 17.19 79.08 17.53 79.00 17.88 81 82 80.21 17.05 80.13 17.40 80.06 17.75 79.98 18.10 82 83 81.19 17.26 81.11 17.61 81.03 17.96 80.95 18.32 83 84 82.16 17.46 82.09 17.82 82.01 18.18 81.93 18.54 84 85 83.14 17.67 83.06 18.04 82.99 18.40 82.90 18.76 85 86 84.12 17. 8S 84.04 18.25 83.96 18.61 83.88 18.98 86 87 85.10 18.09 85.02- 18.46 84.94 18.83 84.85 19.20 87 88 86.08 18.30 86.00 18.67 85.91 19.05 85.83 19.42 88 89 87.06 18.50 86.97 18.88 86.89 19.26 86.81 19.64 89 90 88.03 18..71 87.95 19.10 87.87 19.48 87.78 19.86 90 91 89.01 18.92 88.93 19.31 88.84 19.70 88.76 20.08 PI 92 89.99 19.13 89.91 19.52 89.82 19.91 89.73 20.30 92 93 90.97 19.34 90.88 19.73 90.80 20.13 90.71 20.52 9? 94 91.95 19.54 91.86 19.94 91.77 20.35 91.68 20.75 94 95 92.92 19.75 92.84 20.16 92.75 20.56 92.66 20.97 95 96 93.90 19.96 93.81 20.37 93 . 72 20.78 93.63 21.19 96 97 94.88 20.17 94.79 20.08 94.70 20.99! 94.61 21.41 97 98 195. 86 20.38 95.77 20.79 95.68 21.21 95.58 21.63 98 99 96. >4 20.58 96.75 21.01 96.65 21.43 96.56 21.85 99 100 97.81 20.79 97.72 21.22 97.63 21.64 97.53 22.07 100 o o c Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 6 c rt 1 5 78 Deg. 77J Deg 771 Deg. 77* Deg. 3 M 26 TRAVERSE TABLE. G 13 Deg. 13* Deg. 131 Deg. 13J Deg. C 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 1 0.97 0.23 0.97 0.23 0.97 0.23 0.97 0.24 1 2 1.95 0.45 1.95 0.46 1.95 0.47 1.94 0.48 2 3 2.92 0.67 2.92 0.69 2.92 0.70 2.91 0.71 3 4 3.90 0.90 3.89 0.92 3.89 0.93 3.89 0.95 4 6 4.87 1.12 4.87 1.15 4.86 1.'17 4.86 1.19 5 6 5.85 1.35 5.84 1.38 5.83 1.40 5.83 1.43 6 7 6.82 1.57 6.81 1.60 6.81 1.63 6.80 1.66 7 8 7.80 1.80 7.79 1.83 7.78 1.87 7.77 1.90 8 9 8.77 2.02 8.76 2.06 8.75 2.10 8.74 2.14 9 10 9.74 2.25 9.73 2.29 9.72 2.33 9.71 2.38 10 11 10.72 2.47 10.71 2.52 10.70 2.57 10.68 2.61 11 12 11.69 2.70 11.68 2.75 11.67 2.80 11.66 2.85 12 13 12.67 2.92 12.65 2.98 12.64 3.03 12.63 3.09 13 14 13.64 3.io 13.63 3.21 13.61 3.27 13.60 3.33 14 15 14.62 3.37 14.60 3.44 14.59 3.50 14.57 3.57 15 16 15.59 3.60 15.57 3.67 15.56 3.74 15.54 3.80 16 17 16.57 3.82 16.55 8.90 16.53 3.97 16.51 4.04 17 18 17.54 4.05 17.52 4.13 17.50 4.20 17.48 4.28 18 19 18.51 4.27 18.49 4.35 18.48 4.44 18.46 4.52 19 20 19.43 4.50 19.47 4.58 19.45 4.67 19.43 4.75 20 21 20.46 4.72 20.44 4.81 20.42 4.90 20.40 4.99 21 22 21.44 4.95 21.41 5.04 21.39 5.14 21.37 5.23 22 23 22.41 5.17 22.39 5.27 22.36 5.37 22.34 5.47 23 24 23.38 5.40 23.36 5.50 23.34 5.60 23.31 5.70 24 25 24.36 5.62 24.33 5.73 24.31 5.84 24.28 5.94 25 26 25.33 5.85 25.31 5.96 25.28 6.07 25.25 6.18 26 27 26.31 6.07 26.28 6.19 26.25 6.3-0 26.23 6.42 27 28 27.28 6.30 27.25 6.42 27.23 6.54 27.20 6.66 28 29 28.26 6.52 28.23 6.65 28.20 6.77 28.17 6.89 29 30 29.23 6.75 29.20 6.88 29.17 7.00 29.14 7.13 30 31 30.21 6.97 30.17 7.11 30.14 7.24 30.11 7.37 31 32 31.18 7.20 31.15 7.33 31.12 7.47 31.08 7.61 32 33 32.15 7.42 32.12 7.56 32.09 7.70 32.05 7.84 33 34 33.13 7.65 33.09 7.79 33.06 7.94 33.03 8.08 34 35 34.10 7.87 34.07 8.02 34.03 8.17 34 00 8.32 35 36 35.08 8.10 35.04 8.25 35.01 8.40 34.97 8.56 36 37 36.05 8.32 36.02 8.48 35.98 8.64 35.94 8.79 37 38 37.03 8.55 36.99 8.71 36.95 8.87 36.91 9.03 38 39 38.00 8.77 37.96 8.94 37.92 9.10 37.88 9.27 39 40 38.97 9.00 38.94 9.17 38.89 9.34 38.85 9.51 40 41 39.95 9.22 39.91 9.40 39.87 9.57 39.83 9.75 41 42 40.92 9.45 40.88 9.63 40.84 9.80 40.80 9.98 42 43 41.90 9 67 41.86 9.86 41.81 10.04 41.77 10.22 43 44 42.87 9.90 42.83 19.08 42. 73 10.27 42.74 10.46 44 45 43.85 10.12 43.80 10.31 43.76 10.51 43.71 10.70 45 46 44.82 10.35 44.78 10.54 44.73 10.74 44.68 10.93 46 47 45.80 10.57 45.75 10.77 45.70 10.97 45.65 11.17 47 48 46.77 10.80 46.72 11.00 46.67 11.21 46.62 11.41 48 49 47.74 11.02 47.70 11.23 47.65 11.44 47.60 11.65 49 50 48.72 11.25 48.67 11.46 48.62 11.67 48.57 11.88 50 B o JS Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 ctf I 5 77 Deg. 76| Deg. 76] Deg. 76* Deg. ri .2 b UNIVERSITY TRAVERSE TABLE. 29 c ' 13 Deg. 134 Deg. 13* Deg. 13| Deg. O Lance.l o ? Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 51 49.69 11.47 49.64 11.69 49.59 11.91 49.54 12.12 "51 52 50.67 11.70 50.62 11.92 50.56 12.14 50.51 12.36 52 53 51.64 11.92 51.59 12.15 51.54 12.37 51.48 12.60 53 54 52.62 12.15 52.56 12.38 52.51 12.61 52.45 12.84 54 55 53.59 12.37 53.54 12.61 53.48 12.84 53.42 13.07 55 56 54.56 12.60 54.51 12.84 54.45 13.07 54.40 13.01 56 57 55.54 12.82 55.48 13.06 55.43 13.31 55.37 13.55 57 58 56.51 13.05 56.46 13.29 56.40 13.54 56 34 13.79 58 59 57.49 13.27 57.43 13.52 57.37 13.77 57.31 14.02 59 60 58.46 13.50 58.40 13.75 58.34 14.01 58.28 14.26 60 61 59.44 13.72 59.38 13.98 59.31 14.24 59.25 14.50 61 62 60.41 13.95 60.35 14.21 60.29 14.47 60.22 14.74 62 63 61.39 14.17 61.32 14.44 61.26 14.71 61.19 14.97 63 64 62.36 14.40 62.30 14.67 62.23 14.94 62.17 15.21 64 65 63.33 14.62 63.27 14.90 63.20 15.17 63.14 15.45 65 66 64.31 14.85 64.24 15.13 64.18 15.41 64.11 15.69 66 67 65.28 15.07 65.22 15.36 65.15 15.64 65.08 15.93 67 68 66.26 15.30 66.19 15.59 66.12 15.87 66.05 16.16 68 69 67.23 15.52 67.16 15.81 67.09 16.11 67.02 16.40 69 70 68.21 15.75 68.14 16.04 68.07 16.34 67.99 16.64 70 71' 69.18 15.97! 69.11 16.27 69.04 16.57 68.97 16.88 71 72 70.15 16.20 70.08 16.50 70.01 16.81 69.94 17.11 72 73 71.13 16.42 71.06 16.73 70.98 17.04 70.91 17.35 73 74 72.10 16.65 72.03 16.96 71.96 17.28 71.88 17.59 74 75 73.08 16.87 73.00 17.19 72.93 17.50 72.85 17.83 75 76 74.05 17.10 73.98 17.42 73.90 17.74 73.82 18.06 76 77 75.03 17.32 74.95 17.65 74.87 17.98 74.79 18.30 77 78 76.00 17.55 75.92 17.88 75.84 18.21 75.76 18.54 78 79 76.98 17.77 76.90 18.11 76.82 18.44 76.74 18.78 79 80 77.95 18.00 77.87 18.34 77.79 18.68 77.71 19.01 80 81 78.92 18.22 78.84 18.57 78.76 18.91- 78.68 19.25 81 82 79.90 18.45 79.82 18.79 79.73 19.14 79.65 19.49 82 83 80.87 18.67 80.79 19.02 80.71 19.38 80.62 19.73 83 84 81.85 18.90 81.76 19.25 81.68 19.61 81.59 19.97 & 85 82.82 19.12 82.74 19.48 82.65 19.84 82.56 20.20 85 86 83.80 19.35 83.71 19.71 83.62 20/08 83.54 20.44 86 87 84.77 19.57 84.68 19.94 84.60 20.31 84.51 20.68 87 88 85.74 19.80 85.66 20.17 85.57 20.54 85.48 20.92 88 89 86.72 20.02 86.63 20.40 86.54 20.78 86.45 21.15 89 90 87.69 20 . 25 87.60 20.63 187.51 21.01 87.42 21.39 90 91 88.67" 20.47 88.58 20.86 88.49 21.24 88.39 21.63 91 92 89.64 20.70 89.55 21.09 89.46 21.48 89.36 21.87 92 93 90.62 20.92 90.52 21.32 190.43 21.71 90.33 22.10 93 94 91.59 21.15 91.50 21.54 91.40 21.94 91.31 22.34 94 95 92.57 21.37 92.47 21.77 92.38 22.18 92.28 22.58 95 96 93.54 21.60 93.44 22.00 93.35 22.41 93.25 22.82 96 97 94.51 21.82 94.42 22.23 94.32 22.64 94.22 23.06 97 98 95.49 22.05 95.39 22.46 95.29 22-88 95.19 23.29 98 99 96.46 22.27 96.36 22.69 96.26 23.11 96.16 23.53 99 100 97.44 22.50 97.34 22.92 97.24 23.34 97.13 23.77 100 o c Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 rt 5 77 Deg. 76J Deg. 76^ Deg. 76* Deg. cd 51 30 TRAVERSE TABLE. O sr 14 Deg. 14i Deg. 14 Deg. 14| Deg. O P P Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. P i 0.97 0.24 0.97 0.25 0.97 0.25 0.97 0.25 1 2 1.94 0.48 1.94 0.49 1.94 0.50 1.93 6.51 2 3 2.91 0.73 2.91 0.74 2. -90 0.75 2.90 0.76 3 4 3.88 0.97 3.88 0.98 3.87 1.00 3.87 1.02 4 5 4.S5 1.21 4.85 1.23 4.84 1.25 4.84 1.27 5 6 5.82 1.45 5.82 1.48 5.81 1.50 5.80 1.53 6 7 6.79 1.69 6.78 1.72 6.78 1.75 6.77 1.78 7 8 7.76 1.94 7.75 1.97 7.75 2.00 7.74 2.04 8 9 8.73 2.18 8.72 2.22 8.71 2.25 8.70 2.29 9 10 9.70 2.42 9.69 2.46 9.63 2.50 9.67 2.55 10 11 10.67 2.66 10.66 2.71 10.65 2.75 10.64 2.80 11 12 11.64 2.90 11.63 2.95 11.62 3.00 11.60 3.06 12 13 12.61 3.15 12.60 3.20 12.59 3.25 12.57 3.31 13 14 13.58 3.39 13.57 3.45 13.55 3.51 13.54 3.56 14 15 14.55 3.63 14.54 3.69 1 14.52 3.76 14.51 3.82 15 16 15.52 3.87, 15.51 3.94 15.49 4.01 15.47 4.07 16 17 16.50 4.11 16.43 4.18 ! 16.46 4.26 16.44 4.33 17 18 17.47 4.35 17.45 4.43. 17.43 4.51 17.41 4.58 18 19 18.44 4.60 18.42 4.68 ' 18.39 4.76 18.37 4.84 19 20 19.41 4.84 19.38 4.92 1 19.36 5.01 19.34 5.09 20 21 20.38 5.08 20.35 5.17 20.33 5.26 20.31 5.35 21 22 21.35 5.32 21.32 5.42 21.30 5.51 21.28 5.00 22 23 22.32 5.56 22.29 5.66 22.27 5.76 22.24 5.86 23 24 23.99 5.81 23.26 5.91 23.24 6.01 23.21 6.11 24 25 24.26 6.05 24.23 6.15 24.20 6.26 24.18 6.37 25 26 25.23 6.29 25.20 6.40 25.17 6.51 25.14 6.62 26 27 26.20 6.53 26.17 6.65 26.14 6.76 26.11 6.87 27 28 27.17 6.77 27.14 6.89 27.11 7.01 27.08 7.13 28 29 23.14 7.02 28.11 7.14 28.08 7.26 28.04 7.38 29 30 29.11 7.26 29.08 7.38 29.04 7.51 29.01 7.64 30 31 30.08 7.50 30.05 7.63 30.01 7.76 29.93 7.89 31 32 31.05 7.74 31.02 7.88 30.98 8.01 30.95 8.15 32 33 32.02 7.98 31.98 8.12 31.95 8.26 31.91 8.40 33 34 32.99 8.23 32,95 8.37 32.92 8.51 32.88 8.66 34 35 33.96 8.47 33.92 8.62 33.89 8.76 33.85 8.91 35 36 34.93 8.71 34.89 8.86 34.85 9.01 34.81 9.17 36 37 35.90 8.95 35.86 9.11 35.82 9.26 35.78 9.42 37 38 36.87 9.19 36.83 9.35 36.79 9.51 36.75 9.67 38 39 37 . 84 9.44 37.80 9.60 37.76 9.76 37.71 9.93 39 40 38.81 9.68 38.77 9.85 38.73 10.02 38.68 10.18 40 41 39.78 9.92 39.74 10.09 39.69 10.27 39.65 10.44 41 42 40.75 10.16 40.71 10.34 40.66 10.52 40.62 10.69 42 43 41.72 10.40 41.68 10.58 41.63 10.77 41.58 10.95 43 44 42.69 10.64 42.65 10.83 42.60 11.02 42 . 55 11.20 44 4n 43.66 10.89 43.62 11.08 43.57 11.27 43.52 11.46 45 46 44.63 11.13 44.58 11.32 44.53 11.52 44.48 11.71 46 47 45.60 11.37 45.55 11.57 45.50 11.77 45.45 11.97 47 48 46.57 11.61 46.52 11.82 46.47 12.02 46.42 12.22 48 49 47.54 11.85 47.49 12.06 47.44 12.27 47.39 12.48 49 50 48.51 12.10 48.46 12.31 48.41 12.52 48.35 12.73 50 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. s 1 1 1C CO |5 76 Deg. 75| Deg. 7fii Deg. 75i Deg. 3 TRAVERSE TABLE. 31 b E 14 Deg. 144 Deg. 14A Deg. 14| Deg. ? 1 9 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 3 51 49.49 12.34 49.43 12.55 J49. 38 12.77 49.32 12.98 51 52 50.46 12.58 50.40 12.80 50.34 13.02 50.29 13.24 52 53 51.43 12.82 51.37 13.05 51.31 13.27 51.25 13.49 53 54 52.40 13.06 52.34 13.29 52.28 13.52 52.22 13.75 54 55 53.37 13.31 53.31 13.54 53.25 13.77 53.19 14.00 55 56 54.34 13.55 54.28 13.78 54.22 14.02 54.15 14.26 56 57 55.31 13.79 55.25 14.03 65.18 14.27 55.12 14.51 57 58 56.28 14.03 56.22 14.28 56.15 14.52 56.09 14.77 58 59 57.25 14.27 57.18 14.52 57.12 14.77 57.06 15.02 59 60 58.22 14.52 58.15 14.77 58.09 15.02 58 . 02 15.28 60 61 59.19 14.76 59.12 15.02 59.06 15.27 58.99 15.53 61 62 60.16 15.00 60.09 15.26 60.03 15.52 59.96 15.79 62 63 61.13 15.24 61.06 15.51 60.99 15.77 60.92 16.04 63 64 62.10 15.48 62.03 15.75 61.96 16.02 61.89 16.29 64 65 63.07 15.72 63.00 16.00 62.93 16.27 62.86 16.55 65 66 64.04 15.97 63.97 16.25 63.90 16.53 63.83 16.80 66 67 65.01 16.21 '64.94 16.49 64.87 16.78 64.79 17.06 67 68 65.98 16.45 65.91 16.74 65.83 17.03 65.76 17.31 68 69 66.95 16.69 66.88 16.98 66.80 17.28 66.73 17.57 69 70 67.92 16.93 67.85 17.23 67.77 17.53 67.69 17.82 70 71 68.89 17.18 68 . 82 17.48 68.74 17.78 68.66 18.08 71 72 69.86 17.42 69.78 17.72 69.71 18.03 69.63 18.33 72 73 70.83 17.66 70.75 17.97 70.67 18.28 70.59 18.59 73 74 71.80 17.90 71.72 18.22 71.64 18.53 71.56 18.84 74 75 72.77 18.14 72.69 18.46 72.61 18.78 72.53 19.10 75 76 73.74 18.39 73.66 18.71 73.58 19.03 73.50 19.35 76 77 74.71 18.63 74.63 18.95 74.55 19.28 74.46 19.60 77 78 75.68 18.87 75.60 19.20 75.52 19.53 75.43 19.86 78 79 76.65 19.11 76.57 19.45 76.48 19.78 76.40 20.11 79 80 77.62 19.35 77.54 19.69 77.45 20.03 77.36 20.37 80 81 78.59" 19.60 78.51 19.94 78.42 20.28 78.33 20.62 81 82 79.56 19.84 79.48 20.18 79.39 20.53 79.30 20.88 82 83 80.53 20.08 80.45 20.43 80.36 20.78 80.26 21.13 83 84 81.50 20.32 81.42 20.68 81.32 21.03 81.23 21.39 84 85 82.48 20.56 82.38 20.92 82.29 21.28 82.20 21.64 85 86 83.45 20.81 83.35 21.17 83.26 21.53 83,17 21.90 86 87 84.42 21.05 84.32 21.42 84.23 21.78 84.13 22.15 87 88 85.39 21.29 85.5:9 21.66 85.20 22.03 85.10 22.41 88 89 86.36 21.53 86.26 21.91 86.17 22.28 86.07 22.66 89 90 87.33 21.77 87.23 22.15 87.13 22.53 87.03 22.91 90 91 88.30 22.01 88 .20 22.40 88.10 22.78 88.00 23.17 91 92 89.27 22.26 89.17 22.65 89.07 23.04 88.97 23.42 92 93 90.24 22.50 90.14 22.89 90.04 23.29 89.94 23.68 93 94 I 91. 21 22.74 91.11 23.14 91.01 23.54 90.90 23.93 94 95192.18 22.98 92.08 23.38 91.97 23.79 91.87 24.19 95 96 93.15 23.22 93.05 23.63 92.94 24.04 92.84 24.44 96 97 ' 94.12 23.47 94.02 23.88; 93.91 24.29 93.80 24.70 97 98 95.09 23.71 94.98 24.12! 94.88 24.54 94.77 24.95 98 99 96.06 23 9i, 95.95 24.37! 95.85 24.79 95.74 25.21 99 100 97.03 24.19 96.92 24.62 , 96.81 25.04 96.70 25.46 100 I Dep. Lat. Dcp. Lat. | Dep. Lat. Dep. Lat. 1 P 76 Deg. II 75jDeg. I 75^ Deg. S 75* Deg. 5- TRAVERSE TABLE. 2 15 Deg. 15i Deg. 15 Deg. 15| Deg. O " T i Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. P i 0.97 0.26 0.96 0.26 0.96 0.27 0.96 0.27 1 2 1.93 0.52 1.93 0.53 1.93 0.53 1.92 0.54 2 3 2.90 0.78 2.89 0.79 2.89 0.80 2.89 0.81 3 4 3.86 1.04 3.86 1.05 3.85 1.07 3.85 1.09 4 5 4.83 1.29 4.82 1.32 4.82 1.34 4.81 1.36 5 6 5.80 1.55 5.79 1.58 5.78 1.60 5.77 1.63 6 7 6.76 1.81 6.75 1.84 6.75 1.87 6.74 1.90 7 8 7.73 2.07 7.72 2.10 7.71 2.14 7:70 2.17 8 9 8.69 2.33 8.68 2.37 8.67 2.41 8.66 2.44 9 10 9.66 2.59 9.65 2.63 9.64 2.67 9.62 2.71 10 11 10.63 2.85 10.61 2.89 10.60 2.94 10.59 2.99 11 12 11.59 3.11 11.58 3.16 11.56 3.21 11.55 3.26 12 13 12.56 3.36 12.54 3.42 12.53 3.47 12.51 3.53 13 14 13.52 3.62 13.51 3.68 13.49 3.74 13.47 3.80 14 15 14.49 3.88 14.47 3.95 14.45 4.01 14.44 4.07 15 16 15.45 4.14 15.44 4.21 15.42 4.28 15.40 4.34 16 17 16.42 4.40 16.40 4.47 16.38 4.54 16.36 4.61 17 18 17.39 4.66 17.37 4.73 17.35 4.81 17.32 4.89 18 19 18.35 4.92 18.33 5.00 18.31 5.08 18.29 5.16 19 20 19.32 5.18 19.30 5.26 19.27 5.34 19.25 5.43 20 21 20.28 5.44 20.26 5.52 20.24 5.61 20.21 5.70 21 22 21.25 5.69 21.23 5.79 21.20 5.88 21.17 5.97 22 23 22.22 5.95 22.19 6.05 22.16 6.15 22.14 6.24 23 24 23.18 6.21 23.15 6.31 23.13 6.41 23.10 6.51 24 25 24.15 6.47 24.12 6.58 24.09 6.68 24.06 6.79 25 26 25.11 6.73 25.08 6.84 25.05 6.95 25.02 7.06 26 27 26.08 6.99 26.05 7.10 26.02 7.22 25.99 7.33 27 28 27.05 7.25 27.01 7.36 26.98 7.48 26.95 7.60 28 29 28.01 7.51 27.98 7.63 27.95 7.75 27.91 7.87 29 30 28.98 7.76 28.94 7.89 28.91 8.02 28.87 8.14 30 31 '29.94 8.02 29.91 8.15 29.87 8.28 29.84 8.41 31 32 30.91 8.28 30.87 8.42 30.84 8.55 30.80 8.69 32 33 31.88 8.54 31.84 8.68 31.80 8.82 31.76 8.96 33 34 32.84 8.80 32 , 80 8.94 32.76 9.09 32.72 9.23 34 35 33.81 9.06 33.77 9.21 33.73 9.35 33.69 9.50 35 36 34.77 9.32 34.73 9.47 34.69 9.62 34.65 9.77 36 37 35.74 9.58 35.70 9.73 35.65 9.89 35.61 10.04 37 38 36.71 9.84 36.66 10.00 36 . 62 10.16 36.57 10.31 38 39 37.67 10.09 37.63 10.26 37.58 10.42 37.54 10.59 39 40 38.64 10.35 38.59 10.52 38.55 10.69 38.50 10.86 40 41 39.60 10.61 39.56 10.78 39.51 10.96 39.46 11.13 41 42 40.57 10.87 40.52 11.05 .40.47 11.22 40.42 11.40 42 43 41.53 11.13 41.49 11.31 41.44 11.49 41.39 11.67 43 44 42.50 11.39 42.45 11.57 42.40 11.76 42.35 11.94 44 45 43.47 11.65 43.42 11.84 43.36 12.03 43.31 12.21 45 46 44.43 11.91 44.38 12.10 44.33 12.29 44.27 12.49 46 47 45.40 12.16 45.35 12.36 45.29 12.56 45.24 12.76 47 48 46.36 12.42 46.31 12.63 46.25 12.83 46.20 13.03 48 49 47.33 12.68 47.27 12.89 47.22 13.09 47.16 13.30 49 50 48.30 12.94 48.24 13.15 48.18 13.36 48.12 13.57 50 8 C Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 9 O c 1 rt w i 75 Deg. 74} I>eg. 74>- Deg. 74i Deg. s Tfi AVERSE TABLE. c 1 P 15 Deg. 15* Deg. Deg. 15| Deg. 5 P Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 51 52 53 54 ii 57 58 59 60 61 62 63 64 65 66 67 68 69 70 49.26 50.23 51.19 52.16 53.13 54.09 55.06 56.02 56.99 57.96 I3.20l 13.46 13.72 13.98 14.24 14.49 14.75i 15.01 15.27 15.53 49.20 50.17 51.13 52.10 53.06 54.03 54.99 55.96 56.92 57.89 13.41 13.68 13.94 14.20 14.47 14.73 14.99 15.26 15.52 15.78 49,15 50.11 51.07 52.04 53.00 53.96 54.93 55.89 56.85 57.82 58.78 59.75 60.71 61.67 62.64 63.60 64.56 65.53 66.49 67.45 13.63 13.90 14.16 14.43 14.70 14.97 15.23 15.50 15.77 16.03 49.09 50.05 51.01 51.97 52.94 53.90 54.86 55.82 56.78 57.75 13.84 14.11 14.39 14.66 14.93 15.20 15.47 15.74 16.01 16.29 51 52 53 54 55 56 57 58 59 60 58.92 59.89 60.85 61.82 62.79 63.76 64.72 65.68 66.65 67.61 15.79 16.05 16.31 16.56 16.82 17.08 17.34 17.60 17.86 18.12 58.85 59.82 60.78 61.75 62.71 63.68 64.64 65.61 66.57 67.54 16.04 16.31 16.57 16.83 17.10 17.36 17.62 17.89 18.15 18.41 16.30 16.57 16.84 17.10 17.37 17.64 17.90 18.17 18.44 18.71 58.71 59.67 60.63 61.60 62.56 63.52 64.48 65.45 66.41 67.37 16.56 16.83 17.10 17.37 17.64 17.92 18.19 18.46 18.73 19.00 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76_ 68.58 69.55 70.51 71 48 18.38 18.63 18.89 19.15 19.41 19.67 68.50 69.46 70.43 71.39 72.36 73.JJ2- 74.29 75.25 76.22 77.18 18.68 18.94 19.20 19.46 19.73 19.99 20.25 20.52 20.78 21.04 68.42 69.38 70.35 71.31 72.27 73.24 74.20 75.16 76.13 77.09 18.97 19.24 19.51 19.78 20.04 20.31 20.58 20.84 21.11 21.38 68.33 69.30 70.26 71.22 72.18 73.15 74.11 75.07 76.03 77.00 19.27 19.54 19.82 20.09 20.36 20.63 20.90 21.17 21.44 21.72 71 72 73 74 75 76 77 78 79 80 Jf 78 79 80 74.38 75.34' 76.31 77.27 19.93 20.19 20.45 20.71 81 82 83 84 85 86 87 88 89 90 78.24 79.21 80.17 81.14 82'. 10 83.07 84.04 85.00 85-. 97 86.93 20.96 21.22 21.48 21.74 22.00 22.26 22.52 22.78 23.03 23.29 78.15 79.11 80.08 81.04 82.01 82.97 83.94 84.90 85.87 86.83 21.31 21.57 21.83 22.09 22.36 22.62 22.88 23.15 23.41 23.67 78.05 79.02 79.98 80.94 81.91 82.87 83.84 84.80 85.76 86.73 21.65 21.91 22.18 22.45 22.72 22?98 23.25 23.52 23.78 24.05 77.96 78.92 79.88 80.85 81.81 82.77 83.73 84.70 85.66 86.62 21.99 22.26 22.53 22.80 23.07 23.34 23.62 23.89 24.16* 24.43 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 G 87.90 88.87 89.83 90.80 91.76 92.73 93.69 94.66 95.63 96.59 23.55 23.81 24.07 24.33 24.59 24.85 25.11 25.36 25.62 25.88 87.80 88.76 89.73 90.69 91.65 92.62 93.58 94.55 95.51 96.48 23.94 24.20 24.46 24.72 24.99- 25.25 25.51 25.78 26.04 26.30 87.69 88.65 89.62 90.58 91.54 92.51 93.47 94.44 95.40 96.36 24.32 24.59 24.85 25.12 25.39 25.65 25.92 26.19 26.46 26.72 87.58 88.55 89.51 90.47 91.43 92.40 93.36 94.32 95.28 96.25 24.70 24.97 25.24 25.52 25.79 26.06 26.33 26.60 26.87 27.14 91 92 93 94 95 96 97 98 99 100 to w To 3 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 75 Deg. 74* Deg. 741 Deg. 744 Deg. 34 TRAVERSE TABLE. g 16 Deg. 16i Deg, 161 Deg. 16| Deg. C CO ! Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. ft CD 'i 1)796" 0.28 0.96 0.28 0.96 0.28 0.96 0.29 ~T 2 1 92 0,55 1.92 0.56 1.92 0.57 1.92 0.58 2 3 2.88 0.83 2.88 0.84 2.88 0.85. 2.87 0.86 3 4 3.85 1.10 3.84 1.12 3.84 1.14 3:83 1 . 15 4 5 4.81 1.38 4.80 1.40 4.79 1.42 4.79 1.44 5 6 5.77 1.65 5.76 1.68 5.75" 1.70 5.75 1.73 6 7 6.73 1.93 6.72 1.96 6.71 1.99 6.70 2.02 7 8 7.69 2.21 7.68 2.24 7.67 2.27 7.66 2.31 8 9 8.65 2.48 8.64 2.52 8.63 2.56 8.62 2.59 9 10 9.61 2.76 9.60 2.80 9.59 2.84 9.58 2.88 10 11 10.57 3.031 10.56 3.08 10.55 3.12 10.53 3.17 11 12 11.54 3.31 11.52 3.36 11.51 3.41 11.49 3.46 12 13 12.50 3.58 12.48 3.64 12.46 3.69 12.45 3.75 13 14' 13.46 3.86 13.44 3.92 13.42 3.98 13.41 4.03 14 15 14.42 4.13 14.40 4.20 14.38 4.26 14.36 4.32 15 16 15.38 4.41 15.36 4.48 15.34 4.54 15.32 4.61 16 17 16.34 4.69 16.32 4.76 16.30 4.83 16.28 4.90 17 18 17.30 4.96 17.28 5.04 17.26 5.11 17.24 5.19 18 19 18.26 5.24 18.24 5.32 18.22 5.40 18.19 5.48 19 20 19.23 5.51 19.20 5.60 19.18 5.68 19.15 5.76 20 21 20.19 5.79! 20.16 5.88 20.14 5.96 20.11 6.05 21 22 21.15 6.06 21.12 6.16 21.09 6.25 21.07 6.34 22 23 22.11 6.34 22.08 6.44 22.05 6.53 22.02 6.63 23 24 23.07 6.62 23.04 6.72 23.01 6.82 22.98 6.92 24 25 24.03 6.89 24.00 7.00 23.97 7.10 23.94 7.20 25 26 24.99 7.17 24.96 7.28 24.93 .7.38 24.90 7.49 26 27 25.95 7.44 25 . 92 .7.56 25.89 r.tt 25.85 7.78 '27 28 26.92 7.72 26.88 7.84 26.85 7.95 26.81 8.07 28 29 27.88 7.99 27.84 8.11 27.81 8.24 27.77 8.36 29 30 28.84 8.27 28.80 8.39 28.76 8.52 28.73 8.65 30 31 29.80 8.54 29 . 76 8.67 29 . 72 8.80 29.68 8.93 31 32 30.76 8.82 30.72 8.95 30.68 9.09 30.64 9.22 32 33 31.72 9.10 31.68 9.23 31.64 9.37 31.60 9.51 33 34 32.68 9.37 32.64 9.51 32.60 9.66 32.56 9.80 34 35 33.64 9.65 33.60 9.79 33.56 9.94 33.51 10.09 35 36 34.61 9.92 34.56 10.07 34.52 10.22 34.47 10.38 36 37 35.57 10.20 35.52 10.35 35.48 10.51 35.43 10.66 37 38 35.53 10.47 36.48 10.63 36.44 10.79 36.39 10.95 38 39 67.49 10.75 37.44 10.91 37.39 11.08 37.35 11. -24 39 40 38.45 11.03 38.40 11.19 38.35 11.36 38.30 11.53 40 41 39.41 11.30 39.36 11.47 39.31 11.64 39.26 11.82 41 42 40.37 11.58 40.32 11.75 40.27 11.93 40.22 12.10 42 43 41.33 11.85 41.28 12.03 41.23 12.21 41.18 12.39 43 44 42.30 12.13 42.24 12.31 42.19 12.50 42.13 12.68 44 45 43.26 12.40 43.20 12.59 43.15 12.78 43.09 12.97 45 46 44.22 12.68 44.16 12.87 ^4.11 13.06 44.05 13.26 46 47 45.18 12.95 45.12 13.15 45.08 13.35 45.01 13.55 47 48 46.14 13.23 46.08 13.43 46.02 13.63 45 . 96 13.83 48 49 47.10 13.51 47.04 13.71 46.98 13.92 46.92 14.12 49 50 43.06 13.78 48.00 13.99 47.94 14.20 47.88 14.41 50 Dep. Lat. Dep. Lat Pep. Lat. Dep. Lat. V o c 5 74 Beg. 73| Deg. 731 Deg. 734 Deg. rf ^ Q TRAVERSE TABLE 35 d 16 Deg. 16} Deg. 16^ Deg. 16| Deg. - 1 ? s a Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. s n 51 49.02 \ 14.06 48.96 14.27 48.90 14.48 48.84 14.70 ~5~I 52 49.99 14.33 49.92 14.55 49.86 14.77 49.79 14.99 52 53 50.95 14.61 50.88 14.83 50.82 15.05 50.75 15.27 53 54 51.91 14.88 51.84 15.11 51.78 15.34 51.71 15.56 54 55 52.87 15.16 52.80 15.39 52.74 15.62 52.67 15.86 55 56 53.83 15.44 53.76 15.67 53.69 15.90 53.62 16.14 56 57 54.79 15.71 54.72 15.95 54.65 16.19 54.58 16.43 57 58 55 . 75 15.99! 55.68 16.23 55.61 16.47 55.54 16.72 58 59 56.71 16.J6 56.64 16.51 56.57 16.76 56.50 17.00 59 60 57.68 16.54 57.60 16.79 57.53 17.04 57.45 17.29 60 61 58.64 16.81 58.56 17.07 58.49 17.32 58.41 17.58 61 62 59.60 17.09 59.52 17.35 59.45 17.61 59.37 17.87 62 63 60.56 17.37 60.48 17.63 60.41 17.89 60.33 18.16 63 64 61.52 17.64 61.44 17.91 61.36 18.18 61.28 18.44 64 65 62.48 17.92 62.40 18.19 62.32 18.46 62.24 18.73 65 66 63.44 18.19 63.36 18.47 63.28 18.74 63.20 19.02 66 67 64.40 18.47 64.32 18.75 64.24 19.03; 64.16 19.31 67 68 65.37 18.74 65.28 19.03 65.20 19.31 65.11 19.60 68 69 66.33 19.02 66.24 19.31 66.16 19.60 66.07 19.89 69 70 67.29 19.29 67.20 19.59 67.12 19.88 67.03 20.17 70 71 68.25 19.57 68.16 19.87 68.08 20.17! 67.99 20.46 71 72 69.21 19.85 69.12 20.15 69.03 20.45 68.95 20.75 72 73 70.17 20.12 70.08 20.43 69.99 20.73 69.90 21.04 73 74 71.13 20.40 71.04 20.71 70.95 21.02 70.86 21.33 74 75 72.09 20.67 72.00 20.99 71.91 21.30 71.82 21.61 75 76 73.06 20.95 72.96 21.27 72.87 21.59 72.78 21.90 76 77 74.02 21.22 73.92 21.55 73.83 21.87 73.73 22.19 77 78 74.98 21.50 74.88 21.83 74.79 22.15 74.69 22.48 78 79 75.94 21.78 75.84 22.11 75.75 22.44 7.5.65 22.77 79 80 76.90 22.05 76.80 22.39 76.71 22.72 76.61 23.06 80 81 77.86 22.33 77.76 22.67 77.66 23.01 77.56 23.34 81 82 78.82 22.60 78.72 22.95 78.62 23.29 78.52 23.63 82 83 79.78 22.88 79.68 23.23 79.58 23.57 79.48 23.92 83 84 80.75 23.15 80.64 23.51 80.54 23.86 80.44 24.21 84 85 81.71 23.43 81.60 23.79 81.50 24.14 81.39 24.50 85 86 82.67 23.70 82.56 24.07 82.46 24.43 82.35 24.78 86 91 83.63 23.98 83.52 24.35 83.42 24,71 83.31 25.07 87 88 84.59 24.26 84.48 24.62 84.38 24.99 184.27 25.36 88 89 85.55 24.53 85.44 24.90 85.33 25.28 85.22 25.65 89 90 8G.51 24.81 86.40 25.18 86.29 25.56 ;86.18 25.94 90 91 87.47 25.08 87.36 25.46 87.25 25.85 |87.14 26.23 91 92 88.44 25.36 88.32 25.74 88.21 26.13 88.10 26.51 92 93 89.40 25.63 89.28 26.02 89.17 26.41 :89.05 26.80 93 94 90.36 25.91 90.24 26.30 90.13 26.70 90.01 27.09 94 95 91.32 26.19 91.20 26.58 91.09 26.98 90.97 27.38 95 96 92.28 26.46 92.16 26.86 92.05 27.27 91.93 27.67 96 97 93.24 26.74 93.12 27.14 93.01 27.55 92.88 27.95 97 98 94.20 27.01 94.08 27.42 93.96 27.83 93.84 28.24 98 99 95.16 27.29 95.04 27.70 94.92 28.12 94.80 28.53 99 100 96.13 27.56 96.00 27.98 95.88 28.40 95.76 28.82 100 jj | Dep. Lat. Dep. Xat. Dep. Lat. Dep. Lat. g 5 1 P 74 Deg. 73 Deg. 73iDe S . 73i Deg. Q N 36 TRAVERSE TABLE. o t* 17 Deg. 174 Deg. 17^ Deg. 17| Deg. o 5- p V 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. D C5 ? 1 0.96 0.29 0.95 0.30 0.95 0.30 0.95 0.30 I 2 1.91 0.58 1.91 0.59 1.91 0.60 1.90 0.61 2 3 2.87 0,88 2.87 0.89 2.86 0.90 2.86 0.91 3 4 3.83 1,17 3.82 1.19 3.81 1.20 3.81 1.22 4 5 4.78 1.46 4.78 1.48 4.77 1.50 4.76 1.52 5 6 5.74 1.75 5.73 1.78 5.72 1.80 5.71 1.83 6 7 6.69 2,05 6.69 2.08 6.68 2.10 6.67 2.13 7 8 7.65 2.34 7.64 2.37 7.63 2.41 7.62 2.44 8 9 8.61 2,63 8.60 2.67 8.58 2.71 8.57 2.74 9 10 9.56 2.92 9.55 2.97 9.54 3.01 9.52 3.05 10 11 10.52 3.22 10.51 3.26 10.49 3.31 10.48 3.35 11 12 U.48 3.51 11.45 3.56 11.44 3.61 11.43 3.66 12 13 12.43 3.80 12.42 3.85 12.40 3.91 12.38 3.96 13 14 13.39 4.09 13.37 4.15 13.35 4.21 13.33 4.27 14 15 14.34 4.39 14,33 4.45 14.31 4.51 14.29 4.57 15 16 15.30 4.68 15.28 4.74 15.26 4.81 15.24 4.88 16 17 16.26 4.97 16.24 5.04 16.21 5.11 16.19 5.18 17 18 17.21 5.26 17.19 5.34 17.17 5.41 17.14 5.49 18 19 18.17 5.56 18.15 5.63 18.12 5.71 18.10 5.79 19 20 19.13 5.85 19.10 5.93 19.07 6.01 19.05 6.10 20 21 20.08 6.14 20.06 6.23 20.03 6.31 20.00 6.40 21 22 21.04 6.43 21.01 6.52 20.98 6.62 20.95 6.71 22 23 21.99 6.72 21.97 6.82 21.94 6.92 21.91 7.01 23 24 22.95 7.02 1 22.92 7.12 22.89 7.22 22.86 7.32 24 25 23.91 7.31 23.88 7.41 23.84 7.52 23.81 7.62 25 26 24.86 7.60 24.83 7.71 24.80 7.82 24.76 7.93 26 27 25.82 7.89 25.79 8.01 25.75 8.12 25.71 8.23 27 28 26.78 8.19 26.74 8.30 26.70 8.42 26.67 8.54 28 29 27.73 8.48 27.70 8.60 27.66 8.72 27.62 8.84 29 30 28.69 8.77 28.65 8.90 28.61 9.02 28.57 9.15 30 31 29.65 9.06 29.61 9.19 29.57 9.32 29.52 9.45 31 32 30.60 9.36 30.56 9.49 30.52 9.62 30.48 9.76 32 33 31.56 9.65 31.52 9.79 31.47 9.92 31.43 10.06 33 34 32.51 9.94 32.47 10.08 32.43 10.22 32.38 10.37 34 35 33.47 10.23 33.43 10.38 33.38 10.52 33.33 10.67 35 36 34.43 10.53 34.38 10.68 34.33 10.83 34.29 tO. 98 36 37 35.38 10.82 35.34 10.97 35.29 11.13 35 24 11.28 37 38 36.34 .11.11 36 . 29 11,27 36.24 11.43 36.19 11.58 38 39 37.30 11.40 37.25 11.57 37.19 11.73 37.14 11.89 39 40 38.25* 11.69 38.20 11.86 38.15 12.03 38.10 12.19 40 41 39.21 11.99 39.16 12.16 39.110 12.33 39.05 12.50 41 42 40.16 12.28 40 . 1 1 12.45 40.06 12.63 40.00 12.80 42 43 41.12 12.57 41.07 12.75 41.01 12.93 40.95 13.11 43 44 42.08 12.86 42.02 13.05 41.96 13.23 41.91 1341 44 45 | 43.03 13.16 42.98 13.34 42.92 13.53 42.86 13.72 45 46 43.99 13.45 43.93 13.64 43.87 13.83 43.81 14,02 46 47 44.95 13.74 44.89 13.94 44.82 14.13 44.76 14.33 47 48 45.90 14.03 45.84 14.23 45.78 14.43 45.71 14.63 48 49 46.86 14.33 46.80 14.53 46.73 14.73 46.67 14.94 49 50 47.82 14.62 47.75 14.83 47.69 15.04 47.62 15.24 50 1 3 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. V o c Q 73 Deg. 72| Deg. 721 Deg. 72i Deg. rf Q TRAVERSE TABLE. 37 o 17 Deg. 17* Deg. 171 Deg. 17| De r. O EC" p i 1 p Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. ~5*i 48.77 11.91 48.71 15.12 48.64 15.34 48.57 15.55 TT 62 49.73 15.20 49.66 15.42 49.59 15.64 49.52 15.85 52 53 50.68 15.50 50.62 15.72 50.55 15.94 50.48 16.16 53 54 51.64 15.79 51.57 16.01 51.50 16.24 51.43 16.46 54 55 52.60 16.08 52.53 16.31 52.45 16.54 52.38 16.77 55 56 53.55 16.37 53.48 16.61 53.41 16.84 53.33 17.07 56 57 54.51 16.67 54.44 16.90 54.36 17.14 54.29 17.38 57 58 55.47 16.96 55.39 17.20 55.32 17.44 55.24 17.68 58 59 56.42 17.25 66.35 17.50 56.27 17.74 56.10 17.99 59 60 57.38 17.54 57.30 17.79 57.22 18.04 57.14 18.29 60 61 58.33 17.83 58.26 18.09 58.18 18.34 58.10 18.60 61 62 59.29 18.13 59.21 18.39 59.13 18.64 59.05 18.90 62 63 60.25 18.42 60.17 18.68 60.08 18.94 0.00 19.21 63 64 61.20 18.71 61.12 18.98 61.04 19.25 60.95 19.51 64 65 62,16 19.00 62.08 19.28 61.99 19.55 61.91 19.82 65 66 63.12 19.30 63.03 19.57 62.95 19.85 62.86 20.12 66 67 64.07 19.59 63.99 19.87 63.90 20.15 63.81 20.43 67 68 65.03 19.88 64.94 20.16 64.85 20.45 64.76 20.73 68 69 65.99 20.17; 65.90 20.46 65.81 20.75 65.72 21.04 69 70 6ft. 94 20.47! 66.85 20.76 66.76 21.05 66.67 21.34 70 71 67.90 20.76 67.81 21.05 67.71 21.35 67.62 21.65 71 72 68.85 21.05 68.76 21.35 68.67 2L.66 68.57 21.95 72 73 69.81 21.34 69.72 21.65 69.62 21.95 69.52 22.26 73 74 70.77 21.64 70.67 21.94 70.58 22.25 70.48 22.56 74 75 71.72 21.93 71.63 22.24 71.53 22.55 71.43 22.86 75 76 72.68 22.22 72.58 22.54 72.48 22.85 72.38 23.17 76 77 73.64 22.51 73.54 22.83 73.44 23.15 73.33 23.47 77 78 74.59 22.80 74.49 23.13 1,74.39 23.46 74.29 23.78 78 79 75.55 23.10 75.45 23.43 I 75.34 23.76 75.24 24.08 79 80 76.50 23.39 76.40 23.72 ' 76.30 24.06 76.19 24.39 80 81 77.46 23.68 77.36 24.02 77.25 24.36 77.14 24.69 81 82 78.42 23.97 78.31 24.32:178.20 24.66 78.10 25.00 82 83 79.37 24.27 79.27 24.61 i 79.16 25.96 79.05 25.30 83 84 80.33 24.56 80.22 24.91 i 80.11 25.26 80.00 25.61 84 85 81.29 24.85 81.18 25.21 ' 81.07 25.56 80.95 25.91 85 86 82.24 25.14 82.13 25.50 : 82.02 25.86 81.91 26.22 86 87 S3. 20 25.44 83.09 25.80 82.97 26.16 82.86 26.52 87 88 84.15 25.73 84.04 26.10- 83.93 26.46 83.81 26.83 88 89 85.11 26.02 85.00 26.39 j 84.88 26.76 84.76 27.13 89 90 86.07 26.31 85.95 26.69 85.83 27.06 85 . 7-2 27.44 90 91 87.02 26.61 86. 9i 26.99 86.79 27.36 86.67 27.74 91 92 87.98 26.90 87.86 27.28 87. ^4 27.66 87.62 28.05 92 93 88.94 27.19 88.82 27.58 88.70 27.97 88.57 28.35 93 94 S9.89 27.48 89.77 27.87 J89.65 28.27 89.53 28.66 94 9o 90.85 27.78 90.73 28.17 190.60 28.57 90.48 28.96 95 9!') 91.81 28.07 91.68 28.47 'J91.56 28.87 91.43 29.27 96 97 92.76 28.36 92.64 28.76 92.51 29.17 92.38 29.57 97 98 93.72 28.65 93.59 29.06 93.46 29.47 93.33 29.88 98 99 94.67 28.94 94.55 29.36 94.42 29.77 94.29 30.18 99 100 95.63 29.24 .95.50 29.65 95.37 30.07 95.24 30.49 100 8 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 8 rt Q 73 Deg. 72| Deg. 72j Deg. 72* Deg. 3 38 TRAVERSE TABLE. 18 Deg. 184 Deg. 18| Deg. 18| Deg. O I Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. B I 1 0.95 0.31 0.95 0.31 0.95 0.32 0.95 0.32 1 2 1.90 0.62 1.90 0.63 1.90 0.63 1.89 0.64 2 3 2.85 0.93 2.85 0.94 2.84 0.95 2.84 0.96 3 4 3.80 1.24 3.80 1.25 3.79 1.27 3.79 1.29 4 5 4.76 1.55 4.75 1.57 4.74 1.59 4.73 1.61 5 6 5.71 1.85 5.70 1.88 5.69 1.90 5.68 1.93 6 7 6.66 2.16 6.65 2.19 6.64 2.22 6.63 2.25 7 8 7.61 2.47 7.60 2.51 7.59 2.54 7.58 2.57 8 9 8.56 2.78 8.55 2.82 8.53 2.86 8.52 2.89 9 10 9.51 3.09 9.50 3.13 9.48 3.17 9.47 3.21 10 11 10.46 3.40 10.45 3.44 10.43 3.49 10.42 3.54 11 12 11.41 3.71 11.40 3.76 11.38 3.81 11.36 3.86 12 13 12.36 4.02 12.35 4.07 12.33 4.12 12.31 4.18 13 14 13.31 4.33 13.30 4.38 13.28 4.44 13.26 4.50 14 15 14.27 4.64 14.25 4.70 14.22 4.76 14.20 4.82 15 16 15.22 4.94 15.20 5.01 15.17 5.08 15.15 5.14 16 17 16.17 5.25 16.14 5.32 id. 12 5.39 16.10 5.46 17 18 17.12 5.56 17.09 5.64 17.07 5.71 17.04 5.79 18 19 18.07 5.87 18.04 5.95 18.02 6.03 17.99 6.11 19 20 19.02 6.18 18.99 6.26 18.97 6.35 18.94 6.43 20 21 19.97 6.49 19.94 6.58 19.91 6.66 19.89 6.75 21 22 20.92 6.80 20.89 6.89 20.86 6.98 20.83 7.07 23 23 21.87 7.11 21.84 7.20 21.81 7.30 21.78 7.39 23 24 22.83 7.42 22.79 7.52 22.76 7.62 22.73 7.71 24 25 23.78 7.73 23.74 7.83 23.71 7.93 23.67 8.04 25 26 24.73 8.03 24.69 8.14 24.66 8.25 24.62 8.36 26 27 25.68 8.34 25.64 8.46 25.60 8.57 25.57 8.68 27 28 26.63 8.65 26.59 8.77 26.55 8.88 26.51 9.00 28 29 27.58 8.96 27.54 9.08 27.50 9.20 27.46 9.32 29 30 28.53 9.27 28.49 9.39 28.45 9.52 28.41 9.64 30 31 29.48 9.58 29.44 9.71 29.40 9.84 29.35 9.96 31 32 30.43 9.89 30.39 10.02 30.35 10.15 30.30 10.29 32 33 31.38 10.20 31.34 10.33 31.29 10.47 31.25 10.61 33 34 32.34 JO. 51 32.29 10.65 32.24 10.79 32.20 10.93 34 35 33.29 10.82 33.24 10.96 33.19 11.11 33.14 11.25 35 36 34.24 11.12 34.19 11.27 34.14 11.42 34.09 11.57 36 37 35.19 11.43 35.14 11.59 35.09 11.74 35.04 11.89 37 38 36.14 11.74 36.09 11.90 36,04 12.00 35.98 12.21 3S 39 37.09 12.05 37.04 12.21 36.98 12.37 36.93 12.54 39 40 38.04 12.36 37.99 12.53 37.93 12.69 37.88 12.86 40 41 38.99 12.67 38.94 12.84 38.88 13.01 38.82 13.18 41 42 39.94 12.98 39.89 13.15 39.83 13.33 39.77 13.50 42 43 40.90 13.29 40.84 13.47 40.78 13.64 40.72 13.82 43 44 41.85 13.60 41.79 13.78 41.73 13.96 41.66 14.14 44 45 42.80 13.91 42.74 14.09 42.67 14.28 42.61 14.46 45 46 43.75 14.21 43.69 14.41 43.62 14.60 43.56 14.79 46 47 44.70 14.52 44.64 14.72 44.57 14.91 44.51 15.11 47 48 45.65 14.83 45.59 15.03 45.52 15.23 45.45 15.43 48 49 46.60 15.14 46.54 15.35 46.47 15.55 46.40 F5.75 49 50 47.55 15.4,6 47.48 15.66 47.42 15.87 47.35 16.07 50 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 8) I 72 Deg. 71| Deg. HD* 71 i Deg. OB 5 TRAVERSE TABLE. 39 1 18 Deg. 18i Deg. 18 Deg. 18| Deg. O p Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 51 18.50 15.76 48.43 15.97 48.36 16.18 48.29 16.39 51 52 49.45 16.07 49.38 16.28 49.31 16.50 49.24 16.71 52 53 50.41 16.38 50.33 16.60 50.26 16.82 50.19 17.04 53 54 51.36 16.69 51.28 16.91 51.21 17.13 51.13 17.36 54 55 52.31 17.00 52.23 17.22 52.16 17.45 52.08 17.68 55 56 53.26 17.30 53.18 17.54 53.11 17.77 53.03 18.00 56 57 54.21 17.61 54.13 17.85 54.05 18.09 53.98 18.32 57 58 55.16 17.92 55.08 18.16 55.00 18.40 54.92 18.64 58 59 56.11 18.23 56.03 18.48 55.95 18.72 55.87 18.96 59 60 57.06 18.54 56. 9$ 18.79 56.90 19.04 56.82 19.29 60 61 58.01 18 85 57.93 19.10 57.85 19.36 57.76 19.61 61 62 58.97 19.16 58.88 19.42 58.80 19.67 58.71 19.93 62 63 59.92 19.47 59.83 19.73 59.74 19.99 59 . 66 20.25 63 64 60.87 19.78 60.78 20.04 60.69 20.31 60.60 20.57 64 65 61.82 20.09 61.73 20.36 61.64 20.62 61.55 20.89 65 66 62.77 20.40 62.68 20.67 62.59 20.94 62.50 21.22 66 67 63.72 20.70 63.63 20.98 63.54 21.26 63.44 21.54 67 68 64.67 21.01 64.58 21.30 64.49 21.58 64.39 21.86 68 69 65.62 21.32 65.53 21.61 65.43 21.89 65 . 34 22.18 69 70 66.57 21.63 66.48 21.92 66.38 22.21 66.29 22.50 70 71 67.53 21.94 67.43 22.23 67.33 22 . 53 67.23 22.82 71 72 68.48 22.25 68.38 22.55 68.28 22.85 68.18 23.14 72 73 69.43 22.56 69.33 22.86 69.23 23.16 69.13 23.47 73 74 70.38 22.87 70.28 23.17 70.18 23.48 70.07 23.79 74 75 71.33 23.18 71.23 23.49 71.12 23.80 71.02 24.11 75 76 72.28 23.49 72.18 23.80 72.07 24.12 71.97 24.43 76 77 73.23 23.79 73.13 24.11 73.02 24.43 72.91 24.75 77 78 74.18 24.10 74.08 24.43 73.97 24.75 73.86 25.07 78 79 75.13 24.41 75.03 24.74 74.92 25.07 74.81 25.39 79 80 76.08 24.72 75.98 25.05 75.87 25.38 75.75 25.72 80 81 77.04 25.03 76.93 25.37 76.81 25.70 76.70 26.04 81 82 77.99 25.34 77.88 25.68 77.76 26.02 77.65 26.36 82 83 78.94 25.65 78.83 25.99 78.71 26.34 78.60 26.68 83 84 79.89 25.96 79 . 77 26.31 79.66 26.65 79.54 27.00 84 85 80.84 26.27 80.72 26.62 80.61 26.97 80.49 27.32 85 86 81.79 26.58 81.67 26.93 81.56 27.29 81.44 27.64 86 87 82.74 2&.S8 82.62 27.25 82.50 27.61 82.38 27.97 87 88 83.69 27.19 83.57 27.56 83.45 27.92 83.33 28.29 88 89 84.64 27.50 84.52 27.87 84.40 28.24 84.28 28.61 89 90 85.60 27.81 85.47 28.18 85.35 28.56 85.22 28.93 90 91 6.55 28.12 86.42 28.50 86.30 28.37 86.17 29.25 91 92 87.50 28.43 87.37 28.81 87.25 29.19 87.12 29.57 92 93 88.45 28.74 88.32 29.12 88.19 29.51 88.06 29.89 93 94 89.40 29.05 89.27 29.44 89.14 29.83 89.01 30.22 94 95 90.35 29.36 90.22 29.75 90.09 30.14 89.96 30.54 95 96 91.30 29.67 91.17 30.06 91.04 30.46 90.91 30/86 96 97 92.25 29.97 92.12 30.38 91.99 30.78 91.85 31.18 97 98 93.20 30.28 93.07! 30.69 92.94 31.10 92.80 31.50 98 99 94.15 30.59 94.02 31.00 93.88 31.41 93.75 31.82 99 100 95.11 30.90 94.97 31.32 94.83 31.73 94.69 32.14 100 i Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 cd .2 72 Deg. 71J Deg. 71 Deg. 7H Deg. " Q 40 TRAVERSE TABLE. o 5' 19 Deg. 19i Deg. 19 Deg. 19| Deg. s P ta P Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 0.95 0.33 0.94 0.33 0.94 0.33 0.94 0.34 1 2 1.89 0.65 1.89 0.66 1.89 0.67 1.88 0.68 2 3 2.84 0.98 2.83 0.99 2.83 1.00 2.82 1.01 3 4 3.78 1.30 3.78 1.32 3.77 1.34 3.76 1.35 4 5 4.73 1.63 4.72 1.65 4.71 1.67 4.71 1.69 5 6 5.67 1.95 5.66 1.98 5.66 2.00 5.65 2.03 6 7 6.62 2.28 6.61 2.31 6.60 2.34 6.59 2.37 7 8 7.56 2.60 7.55 2.64 7.54 2.67 7.53 2.70 8 9 8.51 2.93 8.50 2.97 8.48 3.00 8.47 3.04 9 10 9.46 3.26 9.44 3.30 9.43 G.34 , 9.41 3.38 10 11 10.40 3.58 10.38 3.63 10.37 3.67 10.35 3.72 11 12 11.35 3.91 11.33 3.96 11.31 4.01 11.29 4.06 12 13 12.29 4.23 12.27 4.29 12.25 4.34 12.24 4.39 13 14 13.24 4.56 13.22 4.62 13.20 4.67 13.18 4.73 14 15 14.18 4.88 14.16 4.95 14.14 5.01 14.12 5.07 15 16 15.13 5.21 15.11 5.28 15.08 5.34 15.06 5.41 16 17 16.07 5.53 16.05 5.60 16.02 5.67 16.00 5.74 17 18 17.02 5.86 16.99 5.93 16.97 6.01 16.94 6.08 18 19 17.96 6.19 17.94 6.26 17.91 6.34 17.88 6.42 19 20 18.91 6.51 18.88 6.59 18.85 6.68 18.82 6.76 20 21 19.86 6.84 19.83 6.92 19.80 7.01 19.76 7.10 21 22 20.80 7.16 20.77 7.25 20.74 7.34 20.71 7.43 22 23 21.75 7.49 21.71 7.58 21.68 7.68 21.65 7.77 23 24 22.69 7.81 22.66 7.91 22.62 8.01 22.59 8.11 24 25 23.64 8.14 23.60 8.24 23.57 8.35 23.53 8.45 25 26 24.58 8.46 24.55 8.57 24.51 8.68 24.47 8.79 26 27 25.53 8.79 25.49 8.90 25.45 9.01 25.41 9.12 27 28 26.47 9.12 26.43 9.23 26.39 9.35 26.35 9.46 28 29 27.42 9.44 27.38 9.56 27.34 9.68 27.29 9.80 29 30 28.37 9.77 28.32 9.89 28.28 10.01 28.24 10.14 30 31 29.31 10.09 29.27 10.22 29.22 10.35 29.18 10.48 31 32 30.26 10.42 30.21 10.55 30.16 10.68 30.12 10.81 32 33 31.20 10.74 31.15 10.88 31.11 11.02 31.06 11.15 33 34 32.15 11.07 32.10 11.21 32.05 11.35 32.00 11.49 34 35 33.09 11.39 33.04 11.54 32.99 11.68 32.94 11.83 35 36 34.04 11.72 33.99 11.87 33.94 12.02 33.88 12.17 36 37 34.98 12.05 34.93 12.20 34.88 12.35 34.82 12.50 37 38 35.93 12.37 35.88 12.53 35.82 12.68 35.76 12.84 38 39 36.88 12.70 36.82 12.86 36.76 13.02 36.71 13.18 39 40 37.82 13.02 37.76 13.19 37.71 13.35 37.65 13.52 40 41 38.77 13.35 38.71 13.52 38.65 13.69" 38.59 13.85 41 42 39.71 13.67 39.65 13.85. 39.59 14.02 39.53 14.19 42 43 40.66 14.00 40.60 14.18 40.53 14.35 40.47 14.53 43 44 41.60 14.32 41.54 14.51 41.48 14.69 41.41 14.87 44 45 42.55 14.65 42.48 14.84 42,42 15.02 42.35 15.21 45 46 43.49 14.98 43.43 15.17 43.36 15.36 43.29 15.54 46 47 44.44 15.30 44.37 15.50 44.30 15.69 44.24 15.88 47 48 45.38 15.63 45.32 15.83 45.25 16.02 45.18 16.22 48 49 46.33 15.95 46.26 16.15 46.19 16.36 46.12 16.56 49 50 47.28 16.28 47.20 16.48 47.13 16.69 47.06 16.90 no 8 A Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. o o c d i 5 71 Deg. 70} Deg. 70 Deg. 70} Deg. s TRAVERSE TABLE. 41 b 19 Deg. 19$ Deg. 191 Dog. 19| Deg. o f Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. i 51 48.22 16.60 48.15 16.81 48.07 17.02 48.00 17.23 51 52 49.17 16.93 49.09 17.14 49.02 17.36 48.94 17.57 52 53 50.11 17.26 50.04 17.47 49.96 .17.69 49.88 17.91 53 54 51.06 17.58 50.98 17.80 50.90 18.03 50.82 18.25 54 55 52.00 17.91 51.92 18.13 51.85 18.36 51.76 18.59 55 56 52.95 18.23 52.87 18.46 52.79 18.69 52.71 18.92 56 57 53.89 18.56 53.81 18.79 53.73 19.03 53.65 19.26 57 58 54.84 18.88 54.76 19.12 54.67 19.36 54.59 19.60 58 59 55.79 19.21 55.70 19.45 55.62 19.69 55.53 19.94 59 60 56.73 19.53 56.65 19.78 56.56 20.03 56.47 20.27 60 61 57.68 19.86 57.59 20.11 57.50 20.36 57.41 20.61 61 62 58.62 20.19 58.53 20.44 58.44 20.70 58.35 20,95 62 63 59.57 20.51 59.48 20.77 59.39 21.03 59.29 21.29 63 64 60.51 20.84 60.42 21.10 60.33 21.36 60.24 21.63 64 65 61.46 21.16 61.37 21.43 61.27 21.70 61.18 21.96 65 66 62.40 21.49 62.31 21.76 62.21 22.03 62.12 22.30 66 67 63.35 1-21.81 63.25 22.09 63.16 22.37 63.06 22.64 67 68 64. 30 122.14 64.20 22.42 64.10 22.70 64.00 22.98 68 69 65.24 22.40 65.14 22.75 65.04 23.03 64.94 23.32 69 70 66.19 22.79 66.09 23.08 65.98 23.37 65.88 23.65 70 71 67.13 23.12 67.03 23.41 66.93 23.70 66.82 23.99 71 72 68.03 23.44 67.97 23.74 67.87 24.03 67.76 24.33 72 73 69.02 23.77 68.92 24.07 68.81 24.37 68.71 24.67 73 74 69.97 24.09 69.86 24.40 69.76 24.70 69.65 25.01 74 75 70.91 24.42 70.81 24.73 70.70 25.04 70.59 25.34 75 76 71.86 24.74 71.75 25.06 71.64 25.37 71.53 25.68 76 77 72.80 25.07 72.69 25.39 72.58 25.70 72.47 26.02 77 78 73.75 25 . 39 73.64 25.72 73.53 26.04 73.41 26.36 78 79 74.70 J25.72 74.58 26.05 74.47 26.37 74.35 26.70 79 80 75. 64 1 26. 05 75.53 26.38 75.41 26.70 75.29 27.03 80 81 73.59 26.37 76.47 26.70 76.35 27.04 76.24 27.37 81 82 77.53 26.70 77.42 27.03 77.30 27.37 77.18 27.71 82 83 78.48 27.02 78.36 27.36 78.24 27.71 78.12 28.05 83 84 79.42 27.35 79.30 27.69 79.18 28.04 79.06 28.39 84 85 80.37 27.67 80.25 28.02 80.12 28.37 80.00 28.72 85 86 81.31 28.00 81.19 28.35 81.07 28.71 80.94 29.06 86 87 82.26 28.32 82.14 28.68 82.01 29.04 81.88 29.40 87 88 83.21 28.65 83.08 29.01 92.95 29.37 82.82 29.74 88 89 84.15 28.98 84.02 29.34 83.90 29.71 |83.76 30.07 89 90 85.10 29.30 84.97 29.67 84.84 30.04 84.71 30.41 90 91 86.04 29.63 85.91 30.00 85.78 30.38 85.65 30.75 91 92 86.99 29.95 86.86 30.33 86.72 30.71 86.59 31.09 92 93 87.93 30.28 87.80 30.66 87.67 31.04 87.53 31.43 93 94 88.88 30.60 88.74 30.99 88.61 31.38 88.47 31.76 94 95 89.82 0.93 89.69 31.32 89.55 31.71 89.41 32.10 95 96 90.77 31.25 90.63 31.65 90.49 32.05 90.35 32.44 96 97 91.72 31.58 91.58 31.98 91.44 32.38 91.29 32.78 97 93 92.66 31.91 92.52 32.31 92.38 32.71 92.24 33.12 98 99 93.61 32.23 93.46 32.64 93.32 33.05 93.18 33.45 99 100 94.55 32.56 94.41 32.97 94.26 33.38 94.12 33.79 100 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. u c 1 71 Deg. 70| Deg. 701 Deg. 70J Deg. "OT S i TRAVERSE TABLE. i 20 Deg. 204 Deg. 20| Deg. 20| Deg. O s P itance. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. i 0.94 0.34 0.94 0.35 0.94 0.35 0.94 0.35 1 2 1.88 0.68 1.88 0.69 1.87 0.70 1.87 0.71 2 3 2.82 1.03 2.81 1.04 2.81 1.05 2.81 1.06 3 4 3.76 1.37 3.75 1.38 3.75 1.40 3.74 1.42 4 5 4.70 1.71 4.69 1.73 4.68 1.75 4. 08 1.77 5 6 5.64 2.05 5.63 2.08 5.62 2.10 5.61 2.13 6 7 6.58 2.39 6.57 2.42 6.56 2.45 6.55 2.48 7 8 7.52 2.74 7.51 2.77 7.49 2.80 7.48 2.83 8 9 8.46 3.08 8.44 3.12 8.43 3.15 8.42 3.19 9 10 9.40 3.42 9.38 3.46 9.37 3.50 9.35 3.54 10 11 10.34 3.76 10.32 3.81 10.30 3.85 10.29 3.90 11 12 11.28 4.10 11.26 4.15 11.24 4.20 11.22 4.25 12 13 12.22 4.45 12.20 4.50 12.18 4.55 12.16 4.61 13 14 13.16 4.79 13.13 4.85 13.11 4.90 13.09 4.96 14 15 14.10 5.13 14.07 5.19 14.05 5.25 14.03 5.31 15 16 15.04 5.47 15.01 5.54 14.99 5.60 14.96 5.67 16 17 15.97 5.81 15.95 5.88 15.92 5.95 15.90 6.02 17 18 16.91 6.16 16.89 6.23 16.86 6.30 16.83 6.38 18 19 17.85 6.50 17.83 6.58 17.80 6.65 17.77 6.73 19 20 18.79 6.84 18.76 6.92 18.73 7.00 18.70 7.09 20 21 19.73 7.18 19.70 7.27 19.67 7.35 19.64 7.44 21 22 20.67 7.52 20.64 7.61 20.61 7.70 20.57 7.79 22 23 21.01 7.87 21.58 7.96 21.54 8.05 21.51 8.15 23 24 22.55 8.21 22.52 8.31 22.48 8.40 22.44 8.50 24 25 23.49 8.55 23.45 8.65 23.42 8.76 23.38 8.86 25 26 24.43 8.89 24.39 9.00 24.35 9.11 24.31 9.21 26 27 25.37 9.23 25.33 9.35 25.29 9.46 25.25 9.57 27 28 26.31 9.58 26.27 9.69 26.23 9.81 26.18 9.92 28 29 27.25 9.92 27.21 10.04 27.16 10.16 27.12 10.27 29 30 28.191 10.26 28.15 10.38 28.10 10.51 28.05 10.63 30 31 29.13 10.60 29.08 10.73 29.04 10.86 28.99 10.98 31 32 30.07 10.94 30.02 11.08 29.97 11.21 29.92 11.34 32 33 31.01 11.29 30.96 11.42 30.91 11.56 30.86 11.69 33 34 31.95 11.63 31.90 11.77 31.85 11.91 31.79 12.05 34 35 32.89 11.97 32.84 12.11 32.78 12.26 32.73 12.40 35 36 33.83 12.31 33.77 12.46 33.72 12.61 33.66 12.75 36 37 34.77 12.65 34.71 12.81 34.66 12.96 34.60 13.11 37 38 35.71 13.00 35.65 13.15 35.59 13.31 35.54 13.46 38 39 36.65 13.34 36 . 59 13.50 30.53 13.66 36.47 13.82 39 40 37.59 13.68 37.53 13.84 37.47 14.01 37.41 14.17 40 41 38.53 14.02 38.47 14.19 38.40 14.36 38.34 14.53 41 42 39.47 14.36 39.40 14.54 39.34 14.71 39.28 14.88 42 43 40.41 14.71 40.34 14.88 40.28 15.06 40.21 15.23 43 44 41.35 15.05 41 .28 15.23 41.21 15.41 41.15 15.59 44 45 42.29 15.39 42.22 15.58 42.15 15.76 42.0 15.94 45 46 43.23 15.73 43.16 15.92 43.09 16.11 43.02 16.30 46 47 44.17 16.07 44.09 16.27 44.02 16.46 43.95 16.65 47 48 45.11 16.42 45.03 16.61 44.96 16.81 44.89 17.01 48 49 46.04 16.76 45.97 16.96 45.90 17.16 45.82 17.36 49 50 46.98 17.10 46.91 17.31 46.83 17.51 46.76 17.71 50 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. O) J s 70 Deg. 69| Deg. 69$ Deg. 69i Deg. d 73 3 TBAVERSE TABLE. d 20 Deg. 204 Deg. 20 Deg. 20| Deg. c. p S- 3 n Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. i 51 47.92 17.44| r.ss 17.65 47.77 17.86! 47.69 18.07 51 52 43.86 17.79 48.79 18.00 48.71 18.21 48.63 18.42 52 53 49.80 18.13; 49.72 18.34 49.64 18.56 49.56 18.78 53 54 50.74 18.47 50.66 18.69 50.58 18.91 50.50 19.13 54 55 51.68 18.81 51.60 19.04 51.52 19.26! 51.43 19.49 55 56 52.62 19.15 52.54 19.38 52.45 19.611 52.37 19.84 56 57 53.56 19.50 i 53.48 19.73 53.39 19.96; 53.30 20.19 57 58 54.50 19.84 54.42 20.07 54.33 20.31 54.24 20.55 58 59 55.44 20.13 ! 55.35 20.42 55.26 20.66; 55.17 20.90 59 60 56.38 20.52 56.29 20.77 56.20 21.01 56.11 21.26 60 61 57.32 20.86 57.23 21.11 57.14 21.36 57.04 21.61 61 62 58.26 21.21 58.17 21.46 58.07 21.71 57.98 21.97 62 63 59.20 21.55 59.11 21.81 59.01 22.06 58.91 22.32 63 64 60.14 21.89 60.04 22.15 59.95 22.41 59.85 22.67 64 65 61.08 22.23 1 60.93 22.50 60.88 22.76 60.73 23.03 65 66 62.02 22.57 61.92 22.84 61.82 23.11 61.72 23.38 66 67 62.96 22.92 62.86 23.19 62.76 23.46 62.65 23.74 67 68 63.90 23.26 63.80 23.54 63.69 23.81 63.59 24.09 68 69 64.84 23.60 64.74 23.88 64.63 24.16 64.52 24.45 69 70 65 . 78 23.94 65.67 24.23 65.57 24.51 65.46 24.80 70 71 66.72 24.28 66.61 24.57 66.50 24.86 66.39 25.15 71 72 67.66 24.63 67.55 24.92 67.44 25.21 67.33 25.51 72 73 68.60 24.97 68.49 25.27 68.38 25.57 68.26 25.86 73 74 69.54 25.31 69.43 25.61 69.31 25.92 69.20 26.22 74 75 70.48 25.65 70.36 25.96 70.25 26.27 70.14 26.57 75 76 71.42 25.99 71.30 26.30 71.19 26.62 71.07 26.93 76 77 72.36 26.34 72.24 26.65 72.12 26.97 72.01 27.28 77 78 73.30 26.68 73.18 27.00 73.06 27.32 72.94 27.63 78 79 74.24 27.02 74.12 27.34 74.00 27.67 73.88 27.99 79 80 75.18 27.36 : 75.06 27.69 74.93 28.02 74.81 28.34 80 81 76.12 27.70: 75.99 28.04 75.87 28.37 75.75 28.70 81 82 77.05 28.05| 76.93 23.38 76.81 28.72 76.68 29.05 82 83 77.99 28.39 77.87 28.73 77.74 29.07 77.62 29.41 83 84 78.93 28 . 73 ! 78.81 29.07 78.68 29.42 78.55 29.76 84 85 79.87 29.07! 79.75 29.42 79.62 29.77 79.49 30.11 85 86 80.81 29.41 i 80.68 29.77 80.55 30.12 '80.42 30.47 86 87 81.75 29.76^ 81.62 30.11 81.49 30.47 81.36 30.82 87 88 82.69 30.10; 82.56 30.46 82.43 30.82 182.29 31.18 88 89 83.63 30.44! 83.50 30.80 83.36 31.17 183.23 31.53 89 90 84.57 30.78 84.44 31.15 84.30 31.52 i84.!6 31.89 90 91 85.51 31.12 85.38 31.50 85.24 31.87 J85.10 32.24 91 92 86.45 31.47 86.31 31.84* 86.17 32.22 86.03 32.59 92 93 87.39 31.81 87.25 32.19 87.11 32.57 86.97 32.90 93 94 88.33 32.15 88.19 32.54 88.05 32.92 87.90 33.30 94 95 89.27 32.49 89.13 32.88 88.98 33.27 88.84 33.66 95 96 90.21 32.83 90.07 33.23 89.92 33.62 89.77 34.01 96 97 91.15 33.18 91.00 33.57 90.86 33.97 90.71 34.37 97 98 92.09 33.52 91.94 33.92 91.79 34.32 91.64 34.72 98 99 93.03 33.86 92.88 34.27 92.73 34.67 92.58 35.07 99 100 93.97 34.20 93.82 34.61 93.67 35.02 93.51 35.43 100 o c Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 33 70 Deg. 89| Deg. 69 Deg. 69i Deg. 5 44 TRAVERSE TABLE. o 5' 21 Deg. 21^ Deg. * 21 1 Deg. 21| Deg. C en" 3 (5 ffl Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 3 O a 1 0.93 0.36 0.93 0.36 0.93 O.oT 0.93 0.37 F 2 1.87 0.72 1.86 0.72 ' 1.86 0.73 1.86 0.74 2 3 2.80 1.08 2.80 1.09 2.79 1.10 2.79 1.11 3 4 3.73 1.43 3.73 1.45 3.72 1.47 3.72 1.48 4 5 4.67 1.79 4.66 1.81 4.65 1.83 4.64 1.85 5 6 5.60 2.15 5.59 2.17 5.58 2.20 5.57 2.22 6 7 6.54 2.51 6.52 2.54 6.51 2.57 6.50 2.59 7 8 7.47 2.87 7.46 2.90 7.44 2.93 7.43 2.96 8 9 8.40 3.23 8.39 3.26 8.37 3.30 8.36 3.34 9 10 9.34 3.58 9.32 3.62 9.30 3.67 9.29 3.71 10 11 10.27 3.94 10.25 3.99 10.23 4.03 10.22 4.08 11 12 11.20 4.30 11.18 4.35 11.17 4.40 11.15 4.45 12 13 12.14 4.66 12.12 4.71 12.10 4.76 12.07 4.82 13 14 13.07 5.02 13.05 5.07 13.03 5.13 13.00 5.19 14 15 14.00 5.39 13.98 5.44 13.96 5.50 13.93 5.56 15 16 14.94 5.73 14.91 5.80 14.89 5.86 14.86 5.93 16 17 15.87 6.09 15.84 6.16 15.82 6.23 15.79 6.30 17 18 16.80 6.45 16.78 6.52 16.75 6.60 16.72 6.67 18 19 17.74 6.81 17.71 6.89 17.68 6.96 17.65 7.04 19 20 18.67 7.17 18.64 7.25 18.61 7.33 18.58 7.41 20 21 19.61 7.53 19.57 7.61 19.54 7.70 19.50 7.78 21 22 20.54 7.88 20.50 7.97 20.47 8.06 20.43 8.15 22 23 21.47 8.24 21.44 8.34 21.40 8.43 21.36 8.52 23 24 22.41 8.60 22.37 8.70 22.33 8.80 22.29 8.89 24 25 23.34 8.96 23.30 9.06 23.26 9.16 23.22 9.26 25 26 24.27 9.32 24.23 9.42 24.19 9.53 24.15 9.63 26 25.21 9.68 25.16 9.79 25.12 9.90 25.08 10.01 27 28 26.14 10.03 26.10 10.15 26.05 10.26 26.01 10.38 28 29 27.07 10.39 27.03 10.51 26.98 10.63 26.94 10.75 29 30 28.01 10.75 27.96 10.87 27.91 11.00 27.86 1U12 30 31 28.94 11.11 28.89 11.24 28.84 11.36 28.79 11.49 31 32 29.87 11.47 29.82 11.60 29.77 11.73 29.72 11.86 32 33 30.81 11.83 30.76 11.96 30.70 12.09 30.65 12.23 33 34 31.74 12.18 31.69 12.32 31.63 12.46 31.58 12.60 34 35 32.68 12.54 32.62 12.69 32.56 12.83 32.51 12.97 35 36 33.61 12.90 33.55 13.05 33.50 13.19 33.44 13.34 36 37 34.54 13.26 34.48 13.41 34.43 13.56 .34.37 13.71 37 38 35.48 13.62 35.42 13.77 35.36 13.93 35.29 14.08 38 39 '36.41 J3.98 36.35 14.14 36.29 14.29 36.22 14.45 39 40 37.34 14.33 37.28 14.50 37.22 14.66 37.15 14.82 40 41 38.28 14.69 38.21 14.86 38.15 15.03 38.08 15.19 41 42 39.21 15.05 39.14 15.22 39.08 15.39 39.01 15.56 42 43 40.14 15.41 40.08 15.58 40.01 15.76 39.94 15.93 43 44 41.08 15.77 41.01 15.95 40.94 16.13 40.87 16.30 44 45 42.01 16.13 41.94 16.31 41.87 16.49 41.80 16.68 45 46 42.94 16.48 42.87 16.67 42.80 16.86 42.73 17.05 46 47 43.88 16.84 43.80 17.03 43.73 17.23 43.65 17.42 47 48 44.81 17.20 44.74 17.40 44.66 17.59 44.58 17.79 48 49 45.75 17.56 45.67 17.76 45.59 17.96 45.51 18.16 49 50 46.68 17.92 46.60 18.12 46.52 18.33 46.44 18.53 50 1 Dep. Lat. Dep. Lat. Dep. , Lat. Dep. Lat. i .a Q 69 Deg. 68| Deg. 681 Deg. 684 Deg. .2 Q | TRAVERSE TABLE. 45 c 21 Deg. 21} Deg. 21i Deg. 21 1 Deg. O 55 ? 5" 9 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. n 9 51 47.61 18.28 47.53 18.48 47.45 18.69 47.37 18.90 51 52 48.55 18.64 48.46 18.85 48.38 19.06 48.30 19.27 52 53 49.48 18.99 49.40 19,21 49.31 19.42 49.23 19.64 53 54 50.41 19.35 50.33 19.57 50.24 19.79 50.16 20.01 54 55 51.35 19.71 51.26 19.93 51.17 20.16 51.08 20.38 55 56 52 28 20.07 52.19 20.30 52.10 20.52 52.01 20.75 56 57 53 21 20.43 53.12 20.66 53.03 20.89 52.94 21.12 57 58 54.15 20.79 54.06 21.02 53.96 21.26 53.87 21.49 58 59 55.08 21.14 54.99 21.38 54.89 21.62 54.80 21.86 59 60 56.01 21.50 55.92 21.75 55.83 21.99 55.73 22.23 60 61 56 . 95 21.86 56.85 22.11 56.76 22.36 56.66 22.60 61 62 57.88 22.22 57.78 22.47 57.69 22.72 57.59 22.97 62 63 58.82 22.58 58.72 22.83 58.62 23.09 58.52 23.35 63 64 59.75 22.94 59.65 23.20 59.55 23.46 59.44 23.72 64 65 60.68 23.29 60.58 23.56 60.48 23.82 60.37 24.09 65 66 61.62 23.65 61:. 51 23.92 61.41 24.19 61.30 24.46 66 67 62.55 24.01 62.44 24.28 62.34 24.56 62.23 24.83 67 68 63.48 24.37 63.38 24.65 63.27 24.92 63.16 25.20 68 69 64.42 24.73 64.31 25.01 64.20 25.29 64.09 25.57 69 70 65.35 25.09 65.24 25.37 65.13 25.66 65.02 25.94 70 71 66.38 25.44 66.17 25.73 66.06 26.02 65.95 26.31 71 72 67.22 25.80 67.10 26.10 66.99 26.39 66.87 26.68 72 73 68.15 26.16 68.04 26.46 67.92 26.75 67.80 27.05 73 74 69.08 26.5211 68.97 26.82 68.85 27.12 68.73 27.42 74 75 70.02 26.88 ! 69.90 27.18 69.78 27.49 69.66 27.79 75 76 70.95 27.24 70.83 27.55 70.71 27.85 70.59 28.16 76 77 71.89 27.59 71.76 27.91 71.64 28.22 71.52 28.53 77 78 72.82 27.95 72.70 28.27 72.57 28.59 72.45 28.90 78 79 73.75 28.31 73.63 28.63 73.50 28.95 73.38 29.27 7y 80 74.69 28.67 74.56 29.00 74.43 29.32 74.30 29.64 80 81 75.62 29.03 75.49 29.36 75.36 29.69 75.23 30.02 81 82 76.55 29.39 76.42 29.72 76.29 30.05 76.16 30.39 82 83 77.49 29.74 77.36 30.08 77.22 30.42 77.09 30.76 83 84 78.42 30.10 78.29 30.44 78.16 30.79 78.02 31.13 84 85 79.35 30.46 79.22 30.81 79.09 31.15 78.95 31.50 85 86 80.29 30.82 80.15 31.17 80.02 31.52 79.88 31.87 86 87 81.22 31.18 81.08 31.53 80.95 31.89 80.81 32'. 24 87 88 82.16 31.54 82.02 31.89 81.88 32.25 81.74 32.61 88 89 83.09 31.89 82.95 32.26 82.81 32.62 82.66 32.98 39 90 84.02 32.25 83.88 32.62 83.74 32.99 83.59 33.35 90 91 84.96 32.61 84.81 32.98 84. 6T 33.35 84.52 33.72 91 92 85.89 32.97 85.74 33.34 85.60 33.72 85.45 34.09 92 93 86. 82 33.33 86.68 33.71 86.53 34.08 86.38 34.46 93 94 87.76 33.69 87.61 34.07 87.46 34.45 87.31 34.83 94 95 88.69 34.04 88.54 34.43 88.39 34.82 88.24 35.20 95 96 89.62 34.40 89.47 34.79 89.32 35.18 89.17 35.57 96 97 90.56 34.76 90.40 35.16 90.25 35.55 90.09 35.94 97 98 91.49 35.12 91.34 35.52 91.18 35.92 91.02 36.31 98 99 92.42 35.48 92.27 35.88 92.11 36.28 91.95 36.69 99 100 93.36 35.84 93.20 36.24 93.04 36.65 92.88 37.06 100 I Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. o' g 1 fl 9 Deg. 68.| Deg. 68 Deg. 68i Deg. cd In S 40 TRAVERSE TABLE. o QQ" 22 Deg. 22| Deg. 22^ Deg. 22| Deg. B I' 1 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. a P 1 0.93 0.37 0.93 0.38 0.92 0.38 0.92 0.39 1 2 1.85 0.75 1.85 0.76 1.85 0.77 1.84 0.77 2 i 3 2.78 1.12 2.78 1.14 2.77 1.15 2.77 1.16 3 4 3.71 1.50 3.70 1.51 3.70 1.53 3.69 1.55 4 ; 5 4.64 1.87 4.63 1.89 4.62 1.91 4.61 1.93 5 i 6 5.56 2.25 5.55 2.27 5.54 2.30 5.53 2.32 6 i 7 6.49 2.62 6.48 2.65 6.4V 2.68 6.46 2.71 7 8 7.42 3.00 7.40 3.03 7.39 3.06 7.38 3.09 8 9 8.34 3.37 8.33 3.41 8.31 3.44 8.30 3.48 9 10 9.27 3.75 9.26 3.79 9.24 3.83 9.22 3.87 10 11 10.20 4.12 10.18 4.17 10.16 4.21 10.14 4.25 11 : 12 11.13 4.50 11.11 4.54 11.09 4.59 11.07 4.64 12 13 12.05 4.87 12.03 4.92 12.01 4.97 11.99 5.03 13 14 12.98 5.24 12.96 5.30 12.33 5.36 12.91 5.41 14 15 13.91 5.62 13.88 5.68 13.86 5.74 13.83 5.80 15 i 16 14.83 5,99 14.81 6.06 14.78 6.12 14.76 6.19 16 ' 17 15.76 6.37 15.73 6.44 15.71 6.51 15.68 6.57 17 : is 16.69 6.74 16.66 6.82 16.63 6.89 16.60 6.96 18 19 17.62 7.12 17.59 7.19 17.55 7.27 17.52 7.35 19 20 18.54 7.49 18.51 7.57 18.48 7.65 18.44 7.73 20 21 19.47 7.87 19.44 7.95 19.40 8.04 19.37 8.12 21 ' 22 20.40 8.24 20.36 8.33 20.33 8.42 20.29 8.51 22 1 23 21.33 8.62 21.29 8.71 21.25 8.80 21.21 8.89 23 24 22.25 8.99 22.21 9.09 22.17 9.18 22.13 9.28 24 25 23.18 9.37 23.14 9.47 23.10 9.57 23.05 9.67 25 26 24.11 9.74 24.06 9.84 24.02 9.95 23.98 10.05 26 , 27 25.03 10.11 24.99 10.22 24.94 10.33 24.90 10.44 27 28 25 . 96 10.49 25.92 10.60 25.87 10.72 25.82 10.83 28 29 26.89 10.86 26.84 10.98 26.79 11.10 26.74 11.21 29 30 27.82 11.24 27.77 11.36 27.72 11.48 27.67 11.60 30 31 28.74 11.61 28.69 11.74 28.64 11.86 28.59 11.99 31 32 29.67 11.99 29.62 12.12 29.56 12.25 29.51 12.37 32 33 30.60 12.36 30.54 12.50 30.49 12.63 30.43 12.76 33 34 31.52 12.74 31.47 12.87 31.41 13.01 31.35 13.15 34 35 32.45 13.11 32.39 13.25 32.34 13.39 32.28 13.53 35 36 33.38 13.49 33.32 13.63 33.26 13.78 33.20 13.92 36 37 34.31 13.86 34.24 14.01 34.18 14.16 34.12 14.31 37 38 35.23 14.24 35.17 14.39 35.11 14.54 35.04 14.70 38 39 36.16 14.61 36.10 14.77 36.03 14.92 35.97 15.08 39 40 37.09 14.98 37.02 15.15 36.96 15.31 36.89 15.47 40 41 38.01 15.36 37 . 95 15.52 37.88 15.69 37.81 15.86 41 42 38.94 15.73 38.87 15.90 38.80 16.07 38.73 16.24 42 43 39.87 16.11 39.80 16.28 39.73 16.46 39.65 16.63 43 44 40,. 80 16.48 40.72 16.66 40.65 16.84 40.58 17.02 44 45 41.72 16.86 41.65 17.04 41.57 17.22 41.50 17.40 45 46 42.65 17.23 42.57 17.42 42.50 17.60 42.42 17.79 46 47 43.58 17.61 43.50 17.80 43.42 17.99 43.34 18.18 47 48 44.50 17.98 44.43 18.18 44.35 18.37 44.27 18.56 48 49 45.43 18.36 45'. 35 18.55 45.27 18.75 45.19 18.95 49 ; 50 46.36 18.73 46.28 18.93 46.19 19.13 46.11 19.34 50 i Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. o o a ': .3 68 Deg. 67| Deg. 67A Deg. 67i Deg. 3 Til A VERSE TABLE. 47 c So* 22 Deg. 22* Deg. 22 Deg. 22| Deg. O 5' p ? 3 n a Lat. | Dep. Lat. Dep. Lat. Dep. Lat. Dep. P 51 47.29 19.10 47.20 19.31 47.12 19.52 47.03 19.72 51 52 4S.21 19.48 48.13 19;69 48.04 19.90 47.95 20.11 52 53 49.14 19.85 49.05 20.07 48.97 20.28 48.88 20.50 53 54 50.07 20.23 49.98 20.45 49.89 20.66 49.80 20.88 54 55 51.00 20.60 50.90 20.83 50.81 21.05 50.72 21.27 55 56 51.92 20.98 51.83 21.20 51.74 21.43 51.64 21.66 56 57 52.85 21.35, 52.76 21.58 52.66 21.81 52.57 22.04 57 58 53.78 21.73 53.68 21.96 53.59 22.20 53.49 22.43 58 59 54.70 22.10 54.61 22.34 54.51 22.58 54.41 22.82 59 60 55.63 22.48 55.53 22.72 55.43 22.96 55.33 23.20 60 61 56 . 56 22.85 56.47 23.10 56.36 23.34 56.25 23.59 61 62 57.49 23.23 57.38 23.48 57.28 23.73 57.18 23.98 62 63 58.41 23.60 58.31 23.85 58.20 24.11 58.10 24.38 63 64 59.34 23.97 59.23 .24.23 59.13 24.49 59.02 24.75 64 65 60.27 24.35 60.16 24.61 60.05 24.87 59.94 25.14 65 66 61.19 24.72 61.09 24.99 60.98 25.26 60.87 25.52 66 67 62.12 25.10 62.01 25.37 61.90 25.64 61.79 25.91 67 68 63.05 25.47 62.94 25.75 62.82 26.02 62.71 26.30 68 69 63.98 25.85 63.86 26.13 63.75 26.41 63.63 26.68 69 70 64.90 26.22 64.79 26.51 64.67 26.79 64.55 27.07 70 71 65.83 26.60 65.7! 26.88 65.60 27.17 65.48 27.46 71 72 66.76 26.97 66.64 27.26 66.52 27.55 66.40 27.84 72 73 67.68 27.35 67.56 27.64 67.44 27.94 67.32 28.23 73 74 68.61 27.72 68.49 28.02 68.37 28.32 68.24 28.62 74 75 69.54 28.10 69.42 28.40 69.29 28.70 69.17 29.00 75 76 70.47 23.47 70.34 28.78 70.2JL 29.08 70.09 29.39 76 77 71.39 28.84 71.27 29.16 71. R 29.47 71.01 29.78 77 78 72.32 29.22 72.19 29.53 72.06 29.85 71.93 30.16 78 79 73.25 29.59 73.12 29.91 72.99 30.23 72.85 30.55 79 80 74.17 29.97 74.04 30.29 73.91 30.61 73.78 30.94 80 81 75.10 30.34 74.97 30.67 74.83 31.00 74.70 31.32 81 82 76.03 30.72 75.89 31.05 75.76 31.38 75.62 31.71 82 83 76.96 31.09 76.82 31.43 76.68 31.76 76.54 32.10 83 84 77.88 31.47 77.75 31.81 77.61 32.15 77.46 32.48 84 85 78.81 31.84 78.67 32.19 78.53 32.53 78.39 32.87 85 86 79.74 32.22 79.60 32.56 79.45 32.91 79.31 33.26 86 87 80.66 32.59 80.52 32.94 80.38 33.29 80.23 33.64 87 83 81.59 32.97 81.45 33.32 81.30 33.68 81.15 34.03 88 89 82.52 33.34 82.37 33.70 82.23 34.06 82.08 34.42 89 90 83.45 33.71 83.30 34.08 83.15 34.44 83.00 34.80 90 91 84.37 34.09 84'.22 34.46 84.07 34.82 83.92 35.19 91 92 85.30 34.46 85.15 34.84 85.00 35.21 84.84 35.58 92 93 86.23 34.84 86.08 35.21 85.92 35.59 85.76 35.96 93 94 87.16 35.21 87.00 35.59 86.84 35.97 86.69 36.35 94 95 88.08 35.59 87.93135.97 87.77 36.35 87.61 36.74 95 96 89.01 35.96 88.85 36.35 88.69 36.74 88.53 37.12 96 97189.94 36.34 89.78; 36.73 80.62 37.12 8.45 37.51 97 98 90.86 36.71 90.70 37.11 90.54 37.50 90.38 37.90 98 99 91.79 37.09 91.63 37.49 91.46 37.89 91.30 38.28 99 100 92.72 37.46 92.55! 37.86 92.39 38.27 92.22 38.67 100 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 8 a X 3 68 Deg. 67| Deg. 67 Deg. - 67i Deg. Q TRAVERSE TABLE. O r 23 Deg. 23J Deg. 23| Deg. 23| Deg. i 1 1 P Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. i 0.92 0.39 0.92 0.39 0.92 0.40 0.92 0.40 i 2 1.84 0.78 1.84 0.79 1.83 0.80 1.83 0.81 2 3 2.76 1.17 2.76 1.18 2.75 1.20 2.75 1.21 3 4 3.68 1.56 3.68 1.58 3.67 1.59 3.66 1.61 4 5 4.60 1.95 4.59 1.97 4.59 1.99 4.58 2.01 5 6 5.52 2.34 5.51 2.37 5.50 2.39 5.49 2.42 6 7 6. '14 2.74 6.43 2.76 6.42 2.79 6.41 2.82 7 8 7.36 3.13 7.35 3.16 7.34 3.19 7.32 3.22 8 9 8.28 3.52 8.27 3.55 8.25 3.59 8.24 3.62 9 10 9.20 3.91 9.19 3.95 9.17 3.99 9.15 4.03 10 11 10.13 4.30 10.11 4.34 10.09 4.39 10.07 4.43 11 12 11.05 4.69 11.03 4.74 11.00 4.78 10.98 4.83 12 13 11.97 6.08 11.94 5.13 11.92 5.18 11.90 5.24 13 14 12.89 6.47 12.86 5.53 12.84 5.58 12.81 5.64 14 15 13.81 5.86 13.78 5.92 13.76 5.98 13.73 6.04 15 16 14.73 6.25 14.70 6.32 14.67 6,38 14.64 6.44 16 17 15.65 6.64 15.62 6.71 15.59 6.78 15.56 6.85 17 18 16., 57 7.03 16.54 7.11 16.51 7.18 16.48 7.25 18 19 17.49 7.42 17.46 7.50 17.42 7.58 17.39 7.65 19 20 18.41 7.81 18.38 7.89 18.34 7.97 18.31 8.05 20 21 19.33 8.21 19.29 8.29 19.26 8.37 19.22 8.46 21 22 20.25 8.60 20.21 8.68 20.18 8.77 20.14 8.86 22 23 21.17 8.99 21.13 9. -08 21.09 9.17 21.05 9.26 23 24 22.09 9.28 22.05 9.47 22.01 9.57 21.97 9.67 24 25 23.01 9.77 22.97 9.87 22.93 9.97 22.88 10.07 25 26 23.93 10.16 23.89 10.26 23.84 10.37 23.80 10.47 26 27 24.85 10.55 24.81 10.66 24.76 10.77 24.71 10.87 27 28 25.77 10.94 25.73 11.05 25.68 11.16 25.63 1) .28 28 29 26.69 11.33 26.64 11.45 26.59 11.56 26.54 11.68 29 30 27.62 11.72 27.56 11.84 27.51 11.96 27.46 12.08 30 31 28.54 12.11 28.48 12.24 28.43 12.36 28.37 12.49 31 32 29.46 12.50 29.40 12.63 29.35 12.76 29.29 12.89 3,2 33 30.38 12.89 30.32 13.03 30.26 13.16 30.21 13.29 33 34 31.30 13.28 31.24 13.42 31.18 13.56 31.12 13.69 34 35 32.22 13.68 32.16 13.82 32.10 13.96 32.04 14.10 35 36 33, 14 14.07 33.08 14.21 33.01 14.35 32.95 14.50 36 37 34.06 14.46 34.00 14.61 33 . 93 14.75 33.87 14.90 37 38 34.98 14.85 34.91 15.00 34.85 15.15 34.78 15.30 38 39 35.90 15.24 35.83 15.39 35.77 15.55 35.70 15.71 39 40 36.82 15.63 36.75 15.79 36.68 15.95 36.61 16.11 40 41 37.74 16.02 37.67 16.18 37 . 60 16.35 37.53 16.51 41 42 38.66 16.41 38.59 16.58 38.52 16.75 38.44 16.92 42 43 39.58 16.80 39.51 16.97 39.43 17.15 39.36 17.32 43 44 40.50 17.19 40.43 17.37 40.35 17.54 40.27 17.72 44 45 41.42 17.58 41.35 17.76 41.27 17.94 41.19 18.12 45 46 42.34 17.97 42.26 18.16 42.18 18.34 42.10 18.53 46 47 43.26 18.36 43.18 18.56 43.10 18.74 43.02 18.93 47 48 44.18 18.76 44.10 18.95 44.02 19.14 43 . 93 19.33 48 49 45.10 19.15 45.02 19.34 44.94 19.54 44.85 19.73 49 50 46.03 19.54 45.94 19.74 45.85 19.94 45.77 20.14 50 Dep. 2 i Lat. Dep. Lat. Dep. Lat. Dep. Lat. B ' 1 I Q 67 Deg. 66| Deg. 66^ Deg. 66$ Deg. Q TRAVERSE TABLE. 49 - 23 Deg. 234 Deg. 23 Deg. 23| Deg. D 3 O O Lat. Dep. Lat. Dep. Lat. Dep. Lat. | Dep. 3 o 51 46.95 19.93 46.86 20. 13 46.77 20.34 46.68 20.54 51 52 47.87 20 . 32 47.78 20 . 53 47.69 20.73 47.60 20.94 52 53 43.79 20.71 48.70 20.92 48.60 21.13 48.51 21.35 53 54 49.71 21.10 49.61 21.32 49.52 21.53 49.43 21.75 54 55 50 . 63 21.49 50.53 21.71 50.44 21.93 50.34 22.15 55 56 51.55 21.88 51.45 22 . 1 1 51.36 22.33 51.26 22.55 56 57 52.47 22.27 52.37 22.50 52.27 22.73 52.17 22.96 57 53 53.39 22.66 53.29 22.90 53.19 23.13 53.09 23.36 58 59 54.31 23.05 54.21 23.29 54.11 23.53 54.00 23.76 59 60 55.23 23.44 55.13 23.68 55.02 23.92 54.92 24.16 60 61 56 . 1-5 23.83 56.05 24.08 55.94 24.32 55.83 24.57 61 62 57.07 24.23 56.97 24.47' 56.86 24.72 56.75 24.97 62 63 57.99 24.62 57.88 24.87 57.77 25.12 57.66 25.37 63 64 5.3.91 25.01 58.80 25.26 58.69 25.52 58.58 25.78 64 65 59.83 25.40 59.72 25.66 59.61 25.92 59.50 26.18 65 66 60.75 2-5.79 60.64 26.05 60.53 26 . 32 60.41 26.58 66 67 61.67 26.18 61.56 25.45 61.44 26.72 61.33 26.98 67 68 62.59 26.57 62.48 26.84 62.36 27.11 62.24 27.39 68 69 63.51 26.96 63.40 27.24 63.28 27.51 63.16 27.79 69 70 64.44 27.35 64.32 27.63 64.19 27.91 64.07 28.19 70 71- 65.36 27.74 65.23 28.03 65.11 28.31 64.99 23.59 71 72 66.28 28.13 66.15 28.42 66.03 28.71 65.90 29.00 72 73 67.20 28.52 67.07 28.82 66.95 29.11 66.82 29.40 73 74 68.12 28.91 67.99 29.21 67.86 29.51 67.73 29.80 74 75 69.04 29.30 68.91 29.61 68.78 29.91 68.65 30.21 75 76 69.96 29.70 69.83 30.00 69.70 30.30 69.56 30.61 76 77 70.88 30.09 70.75 30.40 70.61 30.70 70.48 31.01 77 73 71.30 30.48 71.67 30.79 71.53 31.10 71.39 31.41 73 79 72.72 30.87 72.58 31.18 72.45 31.50 72.31 31.82 79 80 73.64 31.26 73.50 31.58 73.36 31.90 73.22 32.22 80 81 74.56 31.65 74.42 31.97 74.23 32.30 74.14 32.62 81 8-4 75.48 32.04 75.34 32.37 75.20 32.70 75.06 33.03 82 83 76.40 32.43 76.26 32.76 76.12 33.10 75.97 33.43 83 S4 77.32 32.82 77.18 33.16 77.03 33.49 76.89 33.83 84 85 78.24 33.21 78.10 33 . 55 77.95 33.89 77.80 34.23 85 fifi 79.16 33.60 79.02 33.95 78.87 34.29 78.72 34.64 86 87 80.08 33.99 79.93 34.34 79.78 34.69 79.63 35.04 87 83 81.00 34-. 38 80.85 34.74 80.70 35.09 80.55 35.44 88 89 81.92 34.78 81.77 35.13 81.62 35.49 81.46 35.84 89 JO 82.85 35.17 32.69 35.53 82.54 35.89 82.38 36.25 90 91 83.77 35.56 83.61 35.92! 83.451 36.29 83.29 36.65 91 92 84.69 35.95 84.53 36.32 84.37 36.68 84.21 37.05 92 93 85.61 36.34 85.45 36.71 85.29 37.08 85.12 37.46 93 94 186.53 36.73 86.37 37.11 86.20 37.48 86.04 37.86 94 95 i 87. 45 37.12 37.29 37.501 87.12 37.88| 86.95 38.26 95 96 88.37 37.51 88.20 37.901 88.04 38.28 j 87.87 38.66 96 97 89.29 37.90 89.12 38.29 88.95 38.68 88.79 39.07 97 98190.21 38.29 90.04 33.68 89.87 39.08 89.70 39.47 98 99 91.13 38.68 90.96 39.08! 90.79 39.48 90.62 39.87 99 100 92.05 39.07 91.88 39.47i 91.71 39.87 91.50 40.27 100 | Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. o> q a 3 67 Deg. 66| Deg. 661 Deg. 66* Deg. q TRAVERSE TABLE. B' 24 Deg. 244 Deg. 24^ Deg. 24| Deg. G 05* 1 I P Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. E 8 1 0.91 0.41 0.91 0.41 0.91 0.41 0.91 0.42 1 2 1.83 0.81 1.82 0.82 1.82 0.83 1.82 0.84 2 3 2,74 1.22 2.74 1.23 2.73 1.24 2.72 1.26 4 3.65 1.63 3.65 1.64 3.64 1.66 3.63 1.67 4 5 4.57 2.03 4.56 2.05 4.55 2.07 4.54 2.09 5 J6 5.48 2.44 5.47 2.46 5.46 2.49 5.45 2.51 6 7 6.39 2.85 6.38 2.87 6.37 . 2.90 6.36 2.93 7 8 7.31 3.25 7.29 3.29 7.28 3.32 7.27 3.35 8 9 8.22 3.66 8.21 3.70 8.19 3.73 8.17 G.77 9 10 9.14 4.07 9.12 4.11 9.10 4.15 9.08 4.19 10 11 10.05 4.47 10.03 4.52 10.01 4.56 9.99 4.61 11 12 10.96 4.88 10.94 4.93 10.92 4.98 10.90 5.02 12 13 11.88 5.29 11.85 5.34 11.83 5.39 11.81 5.44 13 14 12.79 5.69 12.76 5.75 12.74 5.81 12.71 5.86 14 15 13.70 6.10 13.68 6.16 13.65 6.22 13.62 6.28 15 16 14*. 62 6.51 14.59 6.57 14.56 6.64 14.53 6.70 16 17 15.53 6. 92 15.50 6.98 15.47 7.05 15.44 7.12 17 18 16.44 7.32 16.41 7.39 16.38 7.46 K6.35 7.54 18 19 17.36 7.73 17.32 7.80 17.29 7.88 17.25 7.95 19 20 18.27 8.13 18.24 8.21 18.20 8.29 18.16 8.37 20 2i 19.18 8.54 19.15 8.63 19.11 8.71 19.07 8.79 21 22 20.10 8.95 20.06 9.04 20.02 9.12 19.98 9.21 22 23 21.01 9.35 20.97 9.45 20.93 9.54 20.89 9.63 23 24 21.93 9.76 21.88 9.86 21.84 9.95 21.80 10.05 24 25 22.84 10.17 22.79 10.27 22.75 10.37 22.70 10.47 25 26 23.75 10.58 23.71 10.68 23.66 10.78 23.61 10.89 26 27 24.67 10.98 24.62 11.09 24.57 11.20 24.52 11.30 27 28 25.58 11.39 25.53 11.50 25.48 11.61 25.43 11.72 28 29 26.49 11.80 26.44 11.91 26.39 12.03 26.34 12.14 29 30 27.41 12.20 27.35 12.32 27.30 12.44 27.24 12.56 30 31 28.32 12.61 28.26 12.73 28.21 12.86 28.15 12.98 31 32 29.23 13.02 29.18 13.14 29.12 13.27 29.06 13.40 32 33 30.15 13.42 30.09 13.55 30.03 13.68 29.97 13.82 33 34 31.06 13.83 31.00 13.96 30.94 14.10 30.88 14.23 34 35 31.97 14.24 31.91 14.38 31.85 14.51 31.78 14.65 35 36 32.89 14.64 32.82 14.79 32.76 14.93 32.69 15.07 36 37 33.80 15.05 33.74 15.20 33.67 15.34 33.60 15.49 37 38 34.71 15.46 34.65 15.61 34.58 15.76 34.51 15.91 38 39 35.63 15.86 35.56 16.02 35.49 16.17 35.42 16.33 39 40 36.54 16.27 36.47' 16.43 36.40 16.59 36.33 16.75 40 41 37.46 16.68 37.38 16.84 37.31 17.00 37.23 17cl6 * 41 42 38.37 17.08 38 . 29 17.25 38.22 17.42 38.14 17.58 42 43 39.28 17.49 39.21 17.66 39.13 17.83 39.05 18.00 43 44 40.20 17.90 40.12 18.07 40.04 18.25 39.96 18.42 44 45 41.11 18.30 41.03 18.48 40.95 18.66 40.87 18.84 45 46 42.02 18.71 41.94 18.89 41.86 19.08 41.77 19.26 46 47 42 . 94 19.12 42.85 19.30 42.77 19.49 42.68 19.68 47 48 43.85 19.52 43.76 19.71 43.68 19.91 43.59 20.10 48 49 44.76 19.93 44.68 20.13 44.59 20.32 44.50 20.51 49 50 45 . 68 20.34 45.59 20.54 45.50 20.73 45.41 20.93 50 8 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 10 o "oi d d to 5 66 Deg. 65| Deg. 65| Deg. 654 I>eg. s TRAVERSE TABLE. 51 o 24 Deg. 24i Deg. 24* Deg. 24| Deg. O P 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 3 ? 51 46.59 20.74 46.50 20.95 46.41 21.15 46.32 21.35 51 52 47.50 21.15 47.41 21.36 47.32 21.56 47.22 21.77 52 53 48.42 21.56 48.32 21.77 48.23 21.98 4*. 13 22.19 53 54 49.33 21.96 49.24 22.18 49.14 22.39 49.04 22.61 54 55 50.24 22.37 50.15 22.59 50.05 22.81 49.95 23.03 55 56 51.16 22.78 51.06 23.00 50.96 23.22 50.86 23.44 56 57 52.07 23.18 51.97 23.41 51.87 23.64 51.76 23.86 57 58 52.99 23.59 52.88 23.82 52.78 24.05 52.67 24.28 58 59 53.90 24.00 53.79 24.23 53.69 24.47 53.58 24.70 59 60 54.81 24.40 54.71 24 . 64 54.60 24.88 54.49 25.12 60 61 55.73 24.81 55.62 25.05 55.51 25.30 55.40 25.54 61 62 56.64 25.22 56.53 25.46 56.42 25.71 56.30 25.96 62 63 57.55 25.62 57.44 25.88 57.33 26.13 57.21 26.38 63 64 58.47 26.03 58.35 26.29 58.24 26.54 58.12 26.79 64 65 59.38 26.44 59.26 26.70 59.15 26.96 59.03 27.21 65 66 60.29 26.84 60.18 27.11 60.06 27.37 59.94 27.63 66 67 61.21 27.25 61.09 27.52 60.97 27.78 60.85 28.05 67 68 62.12 27.66 62.00 27.93 61.88 28.20 61.75 28.47 68 69 63.03 28.06 62.91 28.34 62.79 28.61 62.66 28.89 69 70 63.95 28.47 63.82 28.75 63.70 29.03 63.57 29.31 70 71 64.86 28.88 64.74 29.16 64.61 29.44 64.48 29.72 71 72 65.78 29.28 65.65 29.57 65.52 29.86 65.39 30.14 72 73 66.69 29.69 66.56 29.98 66.43 30.27 66.29 30.56 73 74 67.60 30.10 67.47 30.39 67.34 30.69 67.20 30.98 74 75 68.52 30.51 68.38 30.80 68.25 31.10 68.11 31.40 75 76 69.43 30.91 69.29 31.21 69.16 31.52 69.02 31.82 76 77 70.34 31.32 70.21 31.63 70.07 31.93 69.93 32.24 77 78 71.26 31.73 71.12 32.04 70.98 32.35 70.84 32.66 78 79 72.17 32.13 72.03 32.45 71.89 32.76 71.74 33.07 79 80 73.08 32.54 72.94 32.86 72.80 33.18 72.65 33.49 80 81 74.00 32.95 73.85 33.27 73.71 33.59 73.56 33.91 81 82 74.91 33.35 74.76 33.68 74.62 34.00 74.47 34.33 82 83 75.82 33.76 75.68 34.09 75.53 34.42 75.38 34.75 83 84 76.74 34.17 76.59 34.50 76.44 34.83 76.28 35.17 84 85 77.65 34.57 77.50 34.91 77.35 35.25 77.19 35.59 85 86 78.56 34.98 78.41 35.32 78 26 35.66 78.10 36.00 86 87 79.48 35.39 79.32 35.73 79.17 36.08 79.01 36.42 87 88 80.39 35.79 80.24 36.14 80.08 36.49 79.92 36.84 88 89 81.31 36.20 81.15 36.55 80.99 36.91 80.82 37.26 89 90 82.22 36.61 82.06 36.96 81.90 37.32 81.73 37.68 90 91 83.13 37.01! 82.97 37.38 82.81 37.74 82.64 33.10 91 92 84.05 37.42 83.88 37.79 83.72 38.15 83.55 38.52 92 93 84.96 37.83 84.79 38.20 84.63 38.57 84.46 38.94 93 94 85.87 38.23 85.71 38.61 85.54 38.98 85.37 39.35 94 95 86.79 38.64 86.62 39.02 86.4,5 39.40 86.27 39.77 95 96 87.70 39.051 87.53 39.43 87.36 39.81 87.18 40.19 96 97 88.61 39.45 88.44 39.84 88.27 40.23 88.09 40.61 97 98 89.53 39.86 89.35 40.25 89.18 40.64 89.00 41.03 98 99 ! 90.44 40.27 90.26 40.66 90.09 41.05 89.91 41.45 99 100 91.35 40.67i 91.18 41.07 91.00 41.47 90.81 41.87 100 | Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. ~i Q 66 Deg. 65| Deg. 65i Deg. 654 Deg. rt 7c Q TRAVERSE TABLE. c 25 Deg. 25} Deg. 25^ Deg. 25| Deg. | 1 B o Lat. Dep. Lat, Dep. Lat. Dep. Lat. Dep. i ~1 0.91 0.42 O.CO 0.43 0.90 0.43 0.90 0.43 i 2 1.81 0.85 1.81 0.85 1.81 0.86 1.80 0.87 2 3 2.72 1.27 2.71 1.28 2.71 1.29 2.70 1.30 3 4 3.63 1.69 3.62 1.71 3.61 1.72 3.60 1.74 4 5 4.53 2.11 4.52 2.13 4.51 2.15 4.50 2.17 5 6 5.44 2.54 5.43 2.56 5.42 2.58 5.40 2.61 6 7 6.34 2.96 6.33 2.99 6.32 3.01 6.30 3.04 7 8 7.25 3.38 7.24 3.41 7.22 3.44 7.21 3.48 8 9 8.16 3.80 .8.14 3.84 8.12 3.87 8.11 3.91 9 10 9.06 4.23 9.04 4.27 9.03 4.31 9.01 4.34 10 11 9.97 4.65 9.95 4.69 9.93 4.74 9.91 4.78 11 12 10.88 5.07 10.85 5.12 10.83 5.17 10.81 5.21 12 13 11.78 5.49 11.76 5.55 11.73 5.60 11.71 5.65 13 14 12.69 5.92 12.66 5.97 1^.64 6.03 12.61 6.08 14 15 13.59 6.34 13.57 6.40 13.54 6.46 13.51 6.52 15 16 14.50 6.76 14.47 6.83 14.44 6.89 14.41 6.95 16 17 15.41 7.18 15.38 7.25 15.34 7.32 15.31 7.39 17 18 16.31 7.61 16.28 7.68 16.25 7.75 16.21 7.82 18 19 17.22 8.03 17.18 8.10 17.15 8.18 17.11 8.25 19 20 18.13 8.45 18.09 8.53 18.05 8.61 18.01 8.69 20 21 19.03 8.87 18.99 8.96 18.95 9.04 18.91 9.12 21 22 19.94 9.30 19.90 9.38 19.86 9.47 19.82 9.56 22 23 20.85 9.72 20.80 9.81 20.76 9.90 20.72 9.99 23 24 2J.75 10.14 21.71 10.24 21.66 10.33 21.62 10.43 24 25 22.66 10.57 22.61 10.66 22.56 10.76 22.52 10.86 25 26 23.56 10.99 23.52 11.09 23.47 11.19 23.42 11.30 26 27 24.47 11.41 24.42 11.52 24.37 11.62 24.32 11.73 27 28 25.38 11.83 25.32 11.94 25.27 12.05 25.22 12.16 28 29 26.28 12.26 26.23 12.37 26.17 12.48 26.12 12.60 29 30 27.19 12.68 27.13 12.80 27.08 12.92 27.03 13.03 30 31 28.10 13.10 28.04 13.22 27.98 13.35 27.92 13.47 31 32 29.00 13.52' 28.94 13.65 28.88 13.78 28.82 13.90 32 33 29.91 13.95 29.85 14.08 29.79 14.21 29.72 14.34 33 34 30.81 14.37 30 .75 14.50 30.69 14.64 30.62 14.77 34 35 31.72 14.79 31.66 14.93 31.59 15.07 31.52 15.21 35 36 32.63 15.21 32.56 15.36 32.49 15.50 32.43 15.64 37 33.53 15.64 33.46 15.78 33.40 15.93 33.33 16.07 f 38 34.44 16.06 34.37 16.21 34.30 16.36 34.23 16.51 39 35.35 16.48 35.27 16.64 35.20 16.79 35.13 16.94 * 40 36.25 16.90 36.18 17.06 36.10 17.22 36.03 17.38 4 41 37.16 17.33 37.08 17.49 37.01 17.65 36.93 17.81 42 38.06 17.75 37.99 17.92 37.91 18.08 37.83 18.25 / 43 38.97 18.17 38.89 18.34 38.81 18.51 38.73 18.68 44 39.88 18.60 39.80 18.77 39.71 18.94 39.63 19.12 45 40.78 19.02 40.70 19.20 40.62 19.37 40.53 19.55 46 41.69 19.44 41.60 19.62' 41.52 19.80 41.43 19.98 ^ 47 42.60 19.86 42.51 20.05 42.42 20.23 42.83 20.42 48 43.50 20.29 43.41 20.48 43.32 20.66 43,23 20.85 L 49 44.41 20.71 44.32 20.90 44.23 21.10 44.13 21.29 i 50 45.32 21.13 45.22 21.33 45.13 21.53 45.03 21.72 5 I Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Is 1 65 Deg. 64J Deg. 64i Deg. 644 Deg. TKAVERSE TABLE. 53 c ' 25 Deg. 25i Deg. 254 Deg. 25 1 Deg. D lance. 1 Lat. stance. Lat. Dep. Lat. Dep. Lat. Dep. Dep. 51 46.22 21.55 46.13 21.75 46.03 21.96 45.94 22.16 51 52 47.13 21.98 47.03 22.18 46.93 22.39 46.84 22.*>9 52 53 48.03 22.40 47.94 22.61 47.84 22.82 47.74 23.03 53 54 48.94 22.82 48.84 23.03 48.74 23.25 48.64 23.46 54 55 49.85 23.24 49.74 23.46 49.64 23.68 49.54 23.89 55 56 50.75 23.67 50.65 23.89 50.54 24.11 50.44 24.33 56 57 51.66 24.09 51.55 24.31 51.45 24.54 51.34 24.76 57 58 52.57 24.51 52.46 24.74 52.35 24.97 52.24 25.20 58 59 53.47 24.93 53,36 25.17 53.25 25.40 53.14 25 . 63 59 60 54.38 25.36 54.27 25.59 54.16 25.83 54.04 26.07 60 61 55.28 25.78 55.17 26.02 55.06 26.26 54.9-1 26.50 61 62 56.19 26.20 56.08 26.45 55.96 26.69 55.84 26.94 62 63 57.10 26.62 56 . 98 26.87 56.86 27.12 56 . 74 27.37 63 64 58.00 27.05 57.89 27.30 57.77 27.55 57.64 27.80 64 65 58.91 27.47 58.79 27.73 58.67 27.98 58.55 28.24 65 66 59.82 27.89 59 . 69 28.15 59 . 57 28.41 59.40 28.67 66 67 60.72 28.32 60.60 28.58 60.47 28.84 60.35 29.11 67 68 61.63 28.74 61.50 29.01 61.38 29.27 61.25 29.54 68 69 62.54 29.16 62.41 29.43 62.28 29.71 62.15 29.98 69 70 63.44 29.58 63.31 29.86 63.18 30.14 63.05 30.41 70 71 64.35 30.01 i 64.22 30.29 64.08 30.57 63.95 30.85 71 72 65.25 30.43 65.12 30.71 64.99 31.00 64.85 31.28 72 73 66.16 30.85 j 66.03 31.14 65.89 31.43 65.75 31.71 73 74 67.07 31.27 66.93 31.57 66.79 31.86 66.65 32.15 74 75 67.97 31.70 67.83 31.99 67.69 32.29 67.55 32.58 75 76 68.88 32.12 68.74 32.42 68.60 32.72 68.45 33.02 76 77 69.79 32.54 69.64 32.85 69.50 33.15 69.35 33.45 77 78 70.69 32.96 70.55 33.27 70.40 33.58 70.25 33.89 78 79 71.60 33.39 71.45 33.70 71.30 34.01 71.16 34.32 79 80 72.50 33.81 72.36 34,13 72.21 34.44 72 06 34.76 80 81 73.41 34.23 73.26 34.55 73.11 34.87 72.96 35.19 81 82 74.32 34.65 74.17 34.98 74.01 35 . 30 73.86 35.62 82 83 75.22 35.08 75.07 35.41 74.91 35.73 74.76 38.06 83 84 76.13 35 . 50 75.97 35.83 75.82 36.16 75.66 36.49 84 85 77.04 35.92 76.88 36.26 76.72 36.59 76.56 36.93 85 86 77.94 36.35 77.78 36.68 77.62 37.02 77.46 37.36 86 87 78.85 36.77 78.69 37.11 78.52 37.45 78.36 37.80 87 88 79.76 37.19 79.59 37.54 79.43 37.88 79.26 38.23 88 89 80.66 37.61 80; 50 37.96 80.33 38.32 80.16 38.67 89 90 81.57 38.04 81.40 38.39 81.23 38.75 81.06 39.10 90 91 82.47 38.46 82.31 38.82 82.14 39.18 81.96 39.53 91 92 83.38 38.88 83.21 39.24 83.04 39.61 82.86 39.97 92 93 84.29 39.30 84.11 39.67 83.94 40.04 83.76 40.40 93 94 So. 19 39 . 73 85.02 40.10 84.84- 40.47 84.67 40.84 94 95 86.10 40.15 85.92 40.52 85.75 40.90 85.57 41.27 95 96 87.01 40.57 86.83 40.95 186.65 41.33 86.47 41.71 96 97 87.91 40.99 87.73 41.38 87.55 41.76 87.37 42.14 97 98 88.82 41.42 88.64 41.80 88.45 42.19 88.27 42.58 98 99 89.72 41.84 89.54 42.23 89.36 42.62 89.17 43.01 99 100 90.63 42.26 90.45 42.66 ;90.26 43.05 90.07 43.44 100 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. <' o c I a 65 Deg. 641 Deg. 64i Deg. 64J Deg. J2 .2 3 i 54 TRAVERSE TABLE. o 5 26 Deg. 264 Deg. 26 Deg. 26| Deg. O K- p Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 1 0.90 0.44 0.90 0.44 0.89 0.45 0.89 0.45 1 2 1.80 0.88 1.79 0.88 1.79 0.89 1.79 0.90 2 3 2.70 1.32 2.69 1.33 2.68 1.34 2.68 1.35 3 4 3.60 1.75 3.59 1.77 3.58 1.78 3.57 1.80 4 5 4.49 2.19 4.48 2.21 4.47 2.23 4.46 2.25 5 6 5.39 2.63 5.38 2.65 5.37 2.68 5.36 2.70 6 7 6.29 3.07 6.28 3.10 6.26 3.12 6.25 3.15 7 8 7.19 3.51 7.17 3.54 7.16 3.57 7.14 3.60 8 9 8.09 3.95 8.07. 3.98 8.05 4.02 8.04 4.05 9 10 8.99 4.38 8.97 4.42 8.95 4.46 8.93 4.50 10 11 9.89 4.82 9.87 4.87 9.84 4.91 9.82 4.95 11 12 10.79 5.26 10.76 5.31 10.74 5.35 10.72 5.40 12 13 11.68 5.70 11.66 5.75 11.63 5.80 11.61 5.85 13 14 12.58 6.14 12.58 6.19 12.53 6.25 12.50 6.30 14 15 13.48 6.58 13.45 6.63 13.42 6.69 13.39 6.75 15 16 14.38 7.01 14.35 7.08 14.32 7.14 14.29 7.20 16 17 15.28 7.45 15.25 7.52 15.21 7.59 15.18 7.65 17 18 16.18 7.89 16.14 7.96 16.11 8.03 16.07 8.10 18 19 17.08 8.33 17.04 8.40 17.00 8.48 16.97 8.55 19 20 17.98 8.77 17.94 8.85 17.90 8.92 17.86 9. GO 20 21 18.87 9.21 18.83 9.29 18.79 9.37 18.75 9.45 21 22 19.77 9.64 19.73 9.73 19.69 9.82 19.65 9.90 22 23 20.67 10.08 20.63 10.17 20.58 10.26 20.54 10.35 23 24 21.57 10.52 21.52 10.61 21.48 10.71 21.43 10.80 24 25 22.47 10.96 22.42 11.06 22.37 11.15 22.32 11.25 25 26 23.37 11.40 23.32 11,50 23.27 1 1 . 60 23.22 11.70 26 27 24.27 11.84 24.22 11.94 24.16 12.05 24.11 12.15 27 28 25.17 12.27 25.11 12.38 25.06 12.49 25.00 12.60 28 29 {26.06 12.71 26.01 12.83 25 . 95 12.94 25.90 13.05 29 30 126.96 13.15 26.91 13.27 26.85 13.39 26.79 13.50 30 31 27.86 13.59 27.80 13.71 27.74 13.83 27.68 13.95 31 32 28.76 14.03 28.70 14.15 28.64 14.28 28.58 14.40 32 33 29.66 14.47 29.60 14.60 29.53 14.72 29.47 14.85 33 34 30.56 14.90 30.49 15.04 30.43 15.17 30.36 15.30 34 35 31.46 15.34 31.39 15.48 31.32 15.62 31.25 15.75 35 36 32.36 15.78 32.29 15.92 32.22 16.06 32.15 16.20 36 37 33.26 16.22 33.18 16.36 33.11 16.51 33.04 16.65 37 38 34.15 16.66 34.08 16.81 34.01 16.96 33.93 17.10 38 39 35.05 17.10 34.98 17.25 34.90 17.40 34.83 17.55 39 40 35.95 17.53 35 . 87 17.69 35.80 17.85 35.72 18.00 40 41 36.85 17.97 36.77 18.13 36.69 18.29 36.61 18.45 41 42 37.75 18.41 37.67 18.58 37.59 18.74 37.51 18.90 42 43 38.65 18.85 38.57 19.02 38.48 19.19 38.40 19.35 43 44 39.55 19.29 39.46 .19.46 39.38 19.63 39.29 19.80 44 45 40.45 19.73 40.36 19.90 40.27 20.08 40.18 20.25 45 46 41.34 20.17 41.26 20.35 41.17 20.53 41.08 20.70 46 47 42.24 20.60 42.15 20.79 42.06 20.97 41.97 21.15 47 48 43.14 21.04 43.05 21.23 42.96 21.42 42.86 21.60 48 49 44.04 21.48 43.95 21.67 43.85 21.86 43.76 22.05 49 50 44.94 21.92 44.84 22.11 44.75 22.31 44.65 22.50 50 | Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 8 W .2 Q 64 Deg. 63| Deg. 63i Deg. 634 Deg. on 3 TRAVERSE TABLE. 55 g a. P 26 Deg. 26* Deg. 26| Deg. 26* Deg. D 8 Lat Dep. Lat. Dep. Lat. Dep. Lmt Dep. i 51 45.84 22.36! 45.74 22756" 45.64 22.76 45.54 22.9V 51 52 46.74 22.80 46.64 23.00 46.54 23.20 46.43 23.41 52 53 47.64 23.23 47.53 23.44 47.43 23.65 47.33 23.86 53 54 48.53 23.67 48.43 23.88 48.33 24.09 48 22 24.31 54 55 49.43 24.11 49.33 24.33 49.22 24.54 49.11 24.76 55 56 50.33 24.55 50.22 24.77 50.12 24.99 50.01 25.21 56 57 51.23 24.99 51.12 25.21 51.01 25-43 50.00 25.66 57 58 52.13 25.43 52.02 25.65 51.91 25 88 51.79 26.11 58 59 53.03 25.86 52.92 26.09 52.80 26.33 52.69 26.56 59 60 53.93 26.30 53.81 26.54 53.70 26 77 53.58 27.01 60 61 54.83 26.74 54.71 26.98 54.59 27.22 54.47 27.46 61 62 55.73 27.18 55.61 27.42 55.49 27.66 55.36 27.91 62 63 56.62 27.62 56.50 27.86 56.33 28.11 56.26 28.36 63 64 57.52 23.06 57.40 28.31 57.28 28.56 57.15 28.81 64 65 58.42 28.49 58.30 28.75 58.17 29.00 58.04 29.26 65 66 59.32 28.93 59.19 29.19 59.07 29.45 58.94 29.71 66 67 60.22 29.37 60.09 29.63 59.96 29.90 59.83 30.16 67 68 81.12 29.81 60.99 30.08 60.86 30.34 60.72 30.61 68 69 62.02 30.25 61.88 30.52 61.75 30.79 61.62 31.06 69 70 62.92 30.69 62.78 30.96 62.65 31.23 62.51 31.51 70 71 63.81 31.12 63.68 31.40 63.54 31.68 jj 63.40 31.96 71 72 64.71 31.56 64.57 31.84 64.44 32.13 1 64. 29 32.41 72 73 65.61 32.00 65.47 32.29 65.33 32.57 1 65.19 32.86 73 74 66.51 32.44 66.37 32.73 66.23 33.02 66.08 33.31 74 75 67.41 32.88 67.27 33.17 67.12 33.46 66.97 33.76 75 76 68.31 33.32 68.16 33.61 68.01 33.91 67.87 34.21 76 77 69.21 33.75 69.06 34.06 68.91 34.36 68.76 34.66 77 78 70.11 34.19 69.96 34.50 69.80 34.80 69.65 35.11 78 79 71.00 34.63 70.85 34.94 70.70 35.25 70.55 35.56 79 80 71.90 35.07 71.75 3.5. 33 71.59 35.70 71.44 36.01 80 81 72.80 35.51 72.65 35 . 83 72.49 36.14 72.33 36.46 81 82 73.70 35.95 73.54 36.27 73.38 36.59 73.22 36.91 82 83 74.60 36.38 74.44 36.71 74.28 37.03 74.12 37.36 83 84 75.50 36.82 75.34 37.15 75.17 37.48 75.01 37.81 84 85 76.40 37.26 76.23 37.59 76.07 37.93 75.90 38.26 85 86 77.30 37.70 77.13 38.04 76.96 38.37 76.80 38.71 86 87 78.20 88.14 78.03 38.48 77.86 38.82 77.69 39.16 87 88 79.09 38.58 78.92 33.92 78.75 39.27 78.58 39.61 88 89 79.99 39.01 79.82 39.36 79.65 39.71 79.48 40.06 89 90 80.89 39.45 80.72 39.81 80.54 40.16 80.37 40.51 90 91 81.79 39.89 81.62 40.25 81.44 40.60 81.26 40.96 91 92 82.69 40.33 82.51 40.69 82.33 41.05 82.15 41.41 92 93 83.59 40.77 83.41 41.13 83.23 41.50 83.05 41.86 93 94 84.49 41.21 84.31 41.58 84.12 41.94 83.94 42.31 94 95 85.39 41.65 85.20 42.02 85.02 42.39 84.83 42.76 95 96 186.28 42.08 86.10 42.46 85.91 42.83 85.73 43.21 96 97 87.18 42.52 87.00 42.90 86.81 43.28 86.62 43.66 97 98 88.08 42.96 87.89 43.34 87.70 43.73 87.51 44.11 98 99 88.98 43.40 88.79 43.79 88.60 44.17 88.40 44.56 99 100 89.88 43.84 89.69 44.23 89.49 44.62 89.30 45.01 100 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 1 64 Deg. 63| Deg. 63| Deg. 63J Deg. 1 TRAVERSE TABLE. o 55' 27 Deg. 274 Deg. 27| Deg. 27| Deg. 5 jlT P | 9 Lat. Dep. Lat. Dep. Lat. Dep. Lat, Dep. P 1 0.89 0.45 0.89 "~O6~ 0.89 0.46 0.88 0.47 1 2 1.78 0.91 1.78 0.92 1.77 0.92 1.77 0.93 2 3 2.67 1.36 2.67 1.37 2.66 1.39 2.65 1.40 3 4 3.56 1.82 3.56 1.83 3.55 1.85 3.54 1.86 4 5 4.45 2.27 4.45 2,29 4.44 2.31 '4.42 2.33 5 6 5.35 2.72 5.33 2.75 5.32 2.77 5.31 2.79 6 7 6.24 3.18 6.22 3.21 6.21 3.23 6.19 3.26 7 8 7.13 3.63 7.11 3.66 7.10 3.69 7.08 3.72 8 9 8.02 4.09 8.00 4.12 7.98 4.16 7.96 4.19 9 10 8.91 4.54 8.89 4.58 8.87 4.62 8.85 4.66 10 11 9.80 4.99 9.78 5.04 9.76 5.08 9.73 5.12 11 12 10.69 5.45 10.67 5.49 10.64 5.54 10.62 5.59 12 13 11.58 5.90 11.56 5.95 11.53 6.00 11.50 6.05 13 14 12.47 6.36 12.45 6.41 12.42 6.46 12.39 6.52 14 15 13.37 6.81 13.34 6.87 13.31 6.93 13.27 6.98 15 16 14.26 7.26 14.22 7.33 14.19 7.39 14.16 7.45 16 17 15.15 7.72 15.11 7.78 15.08 7.85 15.04 7.92 17 18 16.04 8.17 16.00 8.24 15.97 8.31 15.93 8.38 18 19 16.93 8.63 16. 89^ 8.70 16.85 8.77 16.81 8.85 19 20 17.82 9.08 17.78 9.16 17.74 9.23 17.70 9.31 20 21 18.71 9.53 18.67 9.62 18.63 9.70 18.58 9.78 21 22 19. 6D 9.99 19.56 10.07 19.51 10.16 19.47 10.24 22 23 20.49 10.44 20.45 10.53 20.40 10.62 20.35 10.71 23 24 21.38 10.90 21.34 10.99 21.29 11.08 21.24 11.17 24 25 22.28 11.35 22.23 11.45 22.18 11.54 22.12 11.64 25 26 23.17 11.80 23 . 1 1 11.90 23.06 12.01 23.01 12.11 26 27 24.06 12.26 24.00 12.36 23.95 12.47 23.89 12.57 27 28 24.95 12.71 24.89 12.82 24.84 12.93 24.78 13.04 28 29 25.84 13.17 25.78 13.28 25 .* 2 13.39 25.66 13.50 29 30 26.73 13.62 26.67 13.74 26.61 13.85 26.55 13.97 30 31 27.62 14.07 27.56 14.19 27.50 14.31 27.43 14.43 31 32 28.51 14.53 28.45 14.65 28.38 14.78 28.32 14.90 32 33 29.40 14.98 29.34 15.11 29.27 15.24 29.20 15.37 33 34 30.29 15.44 30.23 15.57 30.16 15.70 30.09 15.83 34 35 31.19 15.89 31.12 16.03 31.05 16.16 30.97 16.30 35 36 32.08 16.34 32.00 16.48 31,93 16.62 31.86 16.76 36 37 32.97 16.80 32.89 16.94 32.82 17.08 32.74 17.23 37 38 33.86 17.25 33.78 17.40 33.71 17.55 33.63 17.69 38 39 34.75 17.71 34.67 17.86 34.59 18.01 34.51 18.16 39 40 35.64 18.16 35 . 56 18.31 35.48 18.47 35.40 18.62 40 41 36.53 18.61 36.45 18.77 36.37 18.93 36.28 19.09 41 42 37.42 19.07 37.34 19.23 37.25 19.39 37.17 19.56 42 43 38.31 19.52 38.23 19.69 38.14 19.86 38.05 20.02 43 44 39.20 19.98 39.12 20.15 39.03 20.32 38.94 20.49 44 45 40.10 20.43 40.01 20.60 39.92 20.78 39.82 20.95 45 46 40.99 20.88 40.89 21.06 40.80 21.24 40.71 21.42 46 47 41.88 21.34 41.78 21.52 41.69 21.70 41.59 21.88 47 48 42.77 21.79 42.67 21.98 42.58 22.16 42.48 22.35 48 49 43.66 22.25 43.56 22.44 43.46 22.63 43.36 '22.82 49 50 44.55 22.70 44.45 22.89 44.35 23.09 44.25 23.28 50 I Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 Q 63 Deg. 62| Deg. 62| Deg. 62* Deg. 5 TRAVERSE TABLE. o 5T 27-Deg. 274 Deg. 271 Deg. 27| Deg. O 3 o o Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 "61 45.44 23.15 45.34 23.35 45.24 23.55 45.13 23.75 ~51 52 46.33 23.61 46.23 23.81 46.12 24.01 46.02 24.21 52 53 47.22 24.06 47.12 24.27 47.01 24.47 46.90 24.68 53 54 48.11 24.52 43.01 24.73 47.90 24.93 47.79 25.14 54 55 49.01 24.97 48.90 25.18 48.79 25.40 48.67 25.61 55 56 49.90 25.42 49.78 25.64 49.67 25.86 49.56 26.07 56 57 50.79 25.88 50.67 26.10 50.56 26.32 50.44 26.54 57 58 51.68 26.33 51.56 26.56 51.45 26.78 51.33 27.01 58 59 52.57 26.79 52.45 27.01 52.33 27.24 52.21 27.47 59 60 53.46 27.24 53.34 27.47 53.22 27.70 '53.10 27.94 60 61 54.35 27.69 54.23 27.93 54.11 28.17 53.98 28.40 61 62 55.24 28.15 55.12 28.39 54.99 28.63 54.87 28.87 62 63 56.13 28.60 56.01 28.85 55.88 29.09 55.75 29.33 63 64 57.02 29.06 66.90 29.30 56.77 29.55 56.64 29.80 64 65 57.92 29.51 57.79 29.76 57.66 30.01 57.52 30.26 65 66 58.81 29.96 58.68 30.22 58.54 30.48 58.41 30.73 66 67 59.70 30.42 59.56 30.68 59.43 30.94 59.29 31.20 67 68 60.59 30.87 60.45 31.14 60.32 31.40 60.18 31.66 68 69 61.48 31.33 61.34 31.59 61.20 31.86 61.06 32.13 69 70 62.37 31.78 62.23 32.05 62.09 32.32 61.95 32.59 70 71 63.26 32.23 63.1* 32.51 62.98 32.78 62.83 33.06 71 72 64.15 32.69 64.01 32.97 63.86 33.25 63.72 33.52 72 73 65.04 33.14 64.90 33.42 64.75 33.71 64.60 33.99 73 74 65.93 33.60 65.79 33.88 65.64 34.17 65.49 34.46 74 75 66.83 34.05 66.68 34.34 66.53 34.63 66.37 34.92 75 76 67.72 34.50 67.57 34.80 67.41 35.09 67.26 35.39 76 77 68.61 34.96 68.45 35.26 68.30 35.55 68.14 35.85 77 78 69.60 35.41 69.34 35.71 69.19 36.02 69.03 36.32 78 79 70.39 35.87 70.23 36.17 70.07 36.48 69.91 36.78 79 80 71.28 36.32 71-12 36.63 70.96 36.94 70.80 37.25 80 81 72.17 36.77 72.01 37.09 71.85 37.40 71.68 37.71 81 82 73.06 37.23 72.90 37.55 72.73 37.86 72.57 38.18 82 83 73.95 37.68 73.79 38.00 73.62 38.33 73.45 38.65 83 84 74.84 38.14 74.68 38.46 74.51 38.79 74.34 39.11 84 85 75.74 38.59 75.57 38.92 75.40 39.25 75.22 39.58 85 86 76.63 39.04 76.46 39.38 76.28 39.71 76.11 40.04 86 87 77.52 39.50 77.34 39.83 77.17 40.17 76.99 40.51 87 88 78.41 39.95 78.23 40.29 78.06 40.63 77.88 40.97 88 89 79.30 40.41 79.12 40.75 78.94 41.10 78.76 41.44 89 90 80.19 40.86 80.01 41.21 79.83 41.56 79.65 41.91 90 91 81.08 41.31 80.90 41.67 80.72 42.02 80.53 42.37 91 92 81.97 41.77 81.79 42.12 81.60 42.48 81.42 42.84 92 93 82.86 42.22 82.63 42.58 82.49 42.94 82.30 43.30 93 94 83.75 42.68 83.57 43.04 83.38 43.40 83.19 43.77 94 95 84.65 43.13 84.46 43.50 84.27 43.87 84.07 44.23 95 96 85.54 43.58 85.35 43.96 85.15 44.33 84.96 44.70 96 97 86.43 44.04 86.23 44.41 86.04 44.79 85.84 45.16 97 98 87.32 44.49 87.12 44.87 86.93 45.25 86.73 45.63 98 99 88.21 44.95 88.01 45.33 87.81 45.71 87.61 46.10 99 100 89.10 45.40 88.90 45.79 88.70 46.17 88.50 46.56 100 T Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 J3 1 g 63 Deg. 62| Deg. 62 Deg. 62} Deg. s TRAVERSE TABLE. ] 28 Deg. 284 Deg. 28f Deg. 28| Deg! t? * ? 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. P 1 0.88 0.47 0.88 0.47 0.88 0.48 0.88 0.48 1 2 1.77 0.94 1.76 0.95 1.76 0.95 1.75 0.96 2 3 2.65 1.41 2.64 1.42 2.64 1.43 2.63 1.44 3 4 3.53 1.88 3.52 1.89 3.52 1.91 3.51 1.92 4 5 4.41 2.35 4.40 2.37 4.39 2.39 4.38 2.40 5 6 5.30 2.82 5.29 2.84 5.27 2.86 5.26 2.89 6 7 6.18 3.29 6.17 3.31 6.15 3.34 6.14 3.37 7 8 7.06 3.76 7.05 3.79 7.03 3.82 7.01 3.85 8 9 7:95 4.23 7.93 4.26 7.91 4.29 7.89 4.33 9 10 8.83 4.69 8.81 4.73 8.79 4.77 8.77 4.81 10 11 9.71 5.16 9.69 5.21 9.67 5.25 9.64 5.29 11 12 10.60 5.63 10.57 5.68 10.55 5.73 JO. 52 5.77 12 13 11.48 6.10 11.45 6.15 11.42 6.20 11.40 6.25 13 14 12.36 6.57 12.33 6.63 12.30 6.68 12.27 6.73 14 15 13.24 7.04 13.21 7.10 13.18 7.16 13.15 7.21 15 16 14.13 7.51 14.09 7.57 14.06 7.63 14.03 7.70 16 17 15.01 7.98 14.98 8.05 14.94 8.11 14.90 8.18 17 18 15.89 8.45 15.86 8.52 15.82 8.59 15.78 8.66 18 19 16.78 8.92 16.74 8.99 16.70 9.07 16,66 9.14 19 20 17.66 9.39 17.62 9.47 17.58 ft} 9 ' 54 17.53 9.62 20 21 18.54 9.86 18.50 9.94 18.46 TO. 02 18.41 10.10 21 22 19.42 10.33 19.38 10.41 19.33 10.50 19.29 10.58 22 23 20.31 10.80 20.26 10.89 20.21 10.97 20.16 11.06 23 24 21.19 11.27 21.14 11.36 21.09 11.45 21.04 11.54 24 25 22.07 11.74 22.02 11.83 21.97 11.931 21.92 12.02 25 26 22.96 12.21 22.90 12,31 22.85 12.41 22.79 12.51 26 27 23.84 12.68 23 . 78 12.78 23.73 12.88 23.67 12.99 27 28 24.72 13.15 24.66 13.25 24.61 13.36 24.55 13.47 28 29 25.61 13.61 25.55 13.73 25.49 13.84 25.43 13.95 29 30 26.49 14.08 26.43 14.20 26.36 14.31 26.30 14.43 30 31 27.37 14.55 27.31 14.67 27.24 14.79 27.18 14.91 31 32 28.25 15.02 28.19 15.15 28.12 15.27 28.06 15.39 32 33 29 .44 15.49 29.07 15.62 29.00 15.75 28.93 15.87 33 34 30.02 15.96 29.95 16.09 29.88 16.22 29.81 16.35 34 35 30.90 16.43 30.83 16.57 30.76 16.70 30.69 16.83 35 36 31.79 16.90 31.71 17.04 31.64 17.18 31.56 17.32 36 37 32.67 17.37 32.59 17.51 32.52 17.65 32.44 17.80 37 38 33.55 17.84 33.47 17.99 33.39 18.13 33.32 18.28 38 39 34.43 18.31 34.35 18.46 34.27 18.61 34.19 18.76 39 40 35.32 18.78 35.24 18.93 35.15 19.09 35.07 19.24 40 41 36.20 19.25 36.12 19.41 36.03 19.56 35.95 19.72 41 42 37.08 19.72 37.00 19.88 36.91 20.04 36.82 20.20 42 43 37.97 20.19 37.88 20.35 37.79 20.52 37.70 20.68 43 44 38.85 20.66 38.76 20.83 38.67 20.99 38.58 21.16 44 45 39.73 21.13 39.64 21.30 39.55 21.47 39.45 21.64 45 46 40.62 21.60 40.52 21.77 40.43 21.95 40.33 22.13 46 47 41.50 22.07 41.40 22.25 41.30 22.43 41.21 22.61 47 48 42.38 22.53 42.28 22.72 42.18 22.90 42.08 23.09 48 49 43.26 23.00 43.16 23.19 43.06 23.38 42.96 23.57 49 50 44.15 23.47 44.04 23.67 43.94 23.86 43.84 24.05 50 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. to p 62 Deg. 61| Deg. 61^ Deg. 6H Deg. Q r TRAVERSE TABLE. 59 G 28 Deg. 28i Deg. 28iDeg. 28! Deg. d 35' 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. o ? 51 45.03 23.94 44.93 24.14 44.82 24.34j 44.71 24.53 ~5~1 52 45.91 24.41 45.81 24.61 45.70 24,81 45.59 25.01 52 53 46.80 24.88 46.69 25.09 46.58 25.29 46.47 25.49 53 54 47.68 25.35 47.57 25.56 47.46 25.77 47.34 25.97 54 55 48.56 25.82 48.45 26.03 48.33 26.24 48.22 26.45 55 56 49.45 26.29 49.33 26.51 49.21 26.72 49.10 26.94 56 57 50.33 26.76 50.21 26.98 50.09 27.20 49.97 27.42 57 58 51.21 27.23 51.09 27.45 50.97 27.68 50.85 27.90 58 59 52.09 27.70 51.97 27.93 51.85 28.15 51.73 28.38 59 60 52.98 28.17 52.85 28,40 52.73 28.63 52.60 28,86 60 61 53.86 28.64 53.73 28.87 53.61 29.11 53.48 29.34 61 62 54.74 29.11 54.62 29.35 54.49 29.58 54.36 29.82 62 63 55.63 29.58 55.50 29.82 55.37 30.06 55.23 30.30 63 64 56.51 30.05 56.38 30.29 56.24 30.54 56.11 30.78 64 65 57.39 30.52 57.26 30.77 57.12 31.02 56.99 31.26 65 66 58.27 30.99 58.14 31.24 58.00 31.49 57.86 31.75 66 67 59.16 31.45 59.02 31.71 58.88 31.97 58.74 32.23 67 68 60.04 31.92 59.90 32.19 59.76 32.45 59.62 32.71 68 69 60.92 32.39 60.78 32.66 60.64 32.92 60.49 33.19 69 70 61.81 32.86 61.66 33.13 61.52 33.40 61.37 33.67 70 71 62.69 33.33 62.54 33.61 62.40 33.88 62.25 34.15 71 72 63.57 33.80 63.42 34.08 ;63.27 34.36 63.12 34.63 72 73 64.46 34.27 64.30 34.55 164.15 34.83 64.00 35.11 73 74 65.34 34.74 65.19 35.03 65.03 35.31 '64.88 35.59 74 75 66.22 35.21 66.07 35.50 65.91 35.79 65.75 36.07 75 76 67.10 35.68 66.95 35.97 66.79 36.26 ,66.63 36.56 76 77 67.99 36.15 67.83 36.45 67.67 36.74 167.51 37.04 77 78 68.87 36.62 68.71 36.92 68.55 37.22 68.38 37.52 78 79 69.75 37.09 69.59 37.39 69.43 37.70 !69.26 38.00 79 80 70:64 37,56 70.47 37.87 70.31 38.17 170.14 38.48 80 81 71.52 38.03 71.35 38.34 71.18 38.65 71 .01 38.96 81 82 72.40 38.50 72.23 38.81 72.06 39.13 71.89 39.44 82 83 73.28 38.97 73.11 39.29 72.94 39.60 J72.77 39.92 83 84 74.17 39.44 73.99 39.76 73.82 40.08 73.64 40.40 84 85 75.05 39.91 74.88 40.23 74.70 40.56 74.52 40.88 85 86 75 . 93 40.37 75.76 40.71 75 58 41.04 75.40 41.36 86 87 76.82 40.84 76.64 41.18 76.46 41.51 76.28 41.85 87 88 77.70 41.31 77.52 41.65 77.34 41.99 77.15 42.33 88 89 78.58 41.78 78.40 42.13 78.21 42.47 78.03 42.81 89 90 79.47 42.25 79.28 42.60 79.09 42.94 78.91 43.29 90 91 80.35 42.72 80.16 43.07 79.97 43.42 79.78 43.77 91 92 81.23 43.19 81.04 43.55 80.85 43.90 80.66 44.25 92 93 82.11 43.66 81.92 44.02 81.73 44.38 81.54 44.73 93 94 83.00 44.13 82.80 44.49 82.61 44.85 82.41 45.21 94 95 83.88 44.60 83.68 44.97 83.49 45.33 83.29 45.69 95 96 84.76 45.07 84.57 45.44 84.37 45.81 84.17 46.17 96 97 85.65 45.54 85.45 45.91 85.25 46.28 J85.04 46.66 97 98 86.53 46.01 86.33 46.39 86.12 46.76 85.92 47.14 98 99 87.41 46.48 87.21 46.86 87.00 47.24 86.80 47.62 99 100 88.29 46.95 88.09 47.33 87.88 47.72 87.67 48.10 100 8 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 6 Q 62 Deg. 61} Deg. 61i Deg. 6H Deg. s 60 TRAVERSE TABLE. o 5T 29 Deg. 294 Deg. 29i Deg. 29| Deg. C 5' Jtf 9> P Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. V o 0> 1 0.87 0.48 0.87 0.49 0.87 0.49 1 0.87 0.50 1~ 2 1.75 0.97 1.74 0.98 1.74 0.98 1.74 0.99 2 3 2.62 1.45 2.62 1.47 2.61 1.48 2.60 1.49 3 4 3.50 1.94 3.49 1.95 3.48 1.97 3.47 1.98 4 5 4.37 2.42 4.36 2.44 4.35 2.46 4.34 2.48 5 6 5.25 2.91 5.23 2.93 5.22 2.95 5.21 2.98 6 7 6.12 3.39 6.11 3.42 6.09 3.45 6.08 3.47 7 8 7.00 3.88 6.98 3.91 6.96 3.94 6.95 3.97 8 9 7.87 4.36 7.85 4.40 7.83 4.43 7.81 4.47 9 10 8.75 4.85 8.72 4.89 8.70 4.92 8.68 4.96 10 11 9.62 5.33 9.60 5.37 9.57 5.42 9.55 5.46 11 12 10.50 5.82 10.47 5.86 10.44 5.91 10.42 5.95 12 13 11.37 6.30 11.34 6.35 11.31 6.40 11.29 6.45 13 14 12.24 6.79 12.21 6.84 12.18 6.89 12.15 6.95 14 15 13.12 7.27 13.09 7.33 13.06 7.39 13.02 7.44 15 16 13.99 7.76 13.96 7.8t 13.93 7.88 13.89 7.94 16 17 14.87 8.24 14.83 8.31 14.80 8.37 14.76 8.44 17 18 15.74 8.73 15.70 8.80 15.67 8.86 15.63 8.93 18 19 16.62 9.21 16.58 9.28 16.54 9.36 16.50 9.43 19 20 17.49 9.70 17.45 9.77 17.41 9.85 17.36 9.92 20 21 18.31 10.18 18.32 10.26 18.28 10.34 18.23 10.42 21 22 19.24 10.67 19.19 10.75 19.15 10.83 19.10 10.92 22 23 20.12 11.15 20.07 11.24 20.02 11.33 19.97 11.41 23 24 20.99 11.64 20.94 11.73 20.89 11.82 20.84 11.91 24 25 21.87 12.12 21.81 12.22 21.76 12.31 21.70 12.41 25 26 22.74 12.60 22.68 12.70 22.63 12.80 22.57 12.90 26 27 23.61 13.09 23.56 13.19 23.50 13.30 23.44 13.40 27 28 24.49 13.57 24.43 13.68 24/37 13.79 24.31 13.89 28 29 25.36 14.06 25.30 14.17 25.24 14.28 25.18 14.39 29 30 26.24 14.54 26.17 14.66 26.11 14.77 26.05 14.89 30 31 27.11 15.03 27.05 15.15 26.98 15.27 26.91 15.38 31 32 27.99 15.51 27.92 15.64 27.85 15.76 27.78 15.88 32 33 28.86 16.00 28.79 16.12 28.72 16.25 28.65 16.38 33 34 29.74 16.48 29.66 16.61 29.59 16.74 29.52 16.87 34 35 30.61 16.97 30.54 17.10 30.46 17.23 30.39 17.37 35 36 31.49 17.45 31.41 17.59 31.33 17.73 31.26 17.86 36 37 32.36 17.94 32.28 18.08 32.20 18.22 32.12 18.36 37 38 33.24 18.42 33.15 18.57 33.07 18.71 32.99 18.86 38 39 34.11 18.91 34.03 19.06 33.94 19.20 33.86 19.35 39 40 34.98 19.39 34.90 19.54 34.81 19.70 34.73 19.85 40 41 35.86 19.88 35 . 77 20.03 35.68 20.19 35.60 20.34 41 42 36.73 20.36 36.64 20.52 36.55 20.68 36.46 20.84 42 43 37.61 20.85 37.52 21.01 37.43 21.17 37.33 21.34 43 44 38.48 21.33 38.39 21.50 38.30 21.67 38.20 21.83 44 45 39.36 21.82 39.26 21.99 39.17 22.16' 39.07 22.33 45 46 40.23 22.30 40.13 22.48 40.04 22.65 39.94 22.83 46 47 41.11 22.79 41.01 22.97 40.91 23.14 40.81 23.32 47 48 41.98 23.27 41.88 23.45 41.78 23.63 41.67 23.82 48 49 42.86 23.76 42.75 23.94 42.65 24.13 42.54 24.31 49 50 43.73 24.24 43.62 24.43 43.52 24.62 43.41 24.81 50 | Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 8 3 61 Deg. 1 60| Deg. 60i Deg. 60J Deg. ri y; 3 TRAVERSE TABLE, Q 29 Deg. 29* Deg. 29 Deg. 29} Deg. s P 1 f5 CO Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. P 51 44.61 24.73 44.50 24.92 44.39 25.11 44.28 25.31 51 52 45.48 25.21 45.37 ^5.41 45.26 25.61 45.15 25.80 52 53 46.35 25.69 46.24 25.90 46.13 26.10 46.01 26.30 53 54 47.23 26.18 47.11 26.39 47.00 26.59 46.88 26,80 54 55 48.10 26.66 47.99 26,87 47.87 27.08 47.75 27.29 55 56 48.98 27.15 48.86 27.36 48.74 27.58 48.62 27.79 56 57 49.85 27.63 49.73 27. 8 49.61 28.07 49.49 28.28 57 58 50.73 28.12 50.60 28'.34 50.48 28 V 56 50.36 28.78 58 59 51.60 28.60 51.48 28.83 51.35 29.05 51.22 29.28 59 60 52.48 29.09 52.35 29.32 52.22 29.55 52.09 29.77 60 61 53.35 29.57 53. *2 29.81 53.09 30.04 52.96 30.27. 61 62 54.23 30.06 54.09 30.29 53.96 30.53 53.83 30.77 62 63 55.10 30.54 54.97 30.78 54.83 31.02 54.70 31.26 63 64 55.98 31.03 55.84 31.27 55.70 31.52 55.56 31.76 64 65 56.85 31.5-1 56.71 31.76 56.57 32.01 56.43 32.25 65 66 57.72 32.00 57.58 32.25 57.44 32.50 57.30 32.75 66 67 58.60 32.48 58.46 32.74 58.31 32.99 58.17 33.25 67 68 59.47 32.97 59.33 33.23 59.18 33.48 59.04 33.74 68 69 60.35 33.45 60.20 33.71 60.05 33.98 59.91 34.24 69 70 61.22 33.94 61.07 34.20 60.92 34.47 60.77 34.74 70 71 62.10 34.42 61.95 34.69 61.80 34.96 61.64 35.23 71 72 62.97 34.91 62.82 35.18 62.67 35.45 62.51 35.73 72 73 63.85 35.39 63.69 35.67 63.54 35.95 63.38 36.22 73 74 64.72 35.88 64.56 36.16 64.41 36.44 64.25 36.72 74 75 65.60 36.36 65.44 36.65 65.28 36.93 65.11 37.22 75 76 66.47 36.85 66.31 37.14 66.15 37.42 65.98 37.71 76 Z7 67.35 37.33 67.18 37.62 67.02 37.92 66.80 38.21 77 78 68.22 37.82 68.05 38.11 67.89 38.41 67.72 38.70 78 79 69.09 38.30 68.93 38.60 68.76 38.90 68.59 39.20 79 80 69.97 38.78 69.80 39.09 69.63 39.39 69.46 39.70 80 81 70.84 39.27 70.67 39.58 70.50 39.89 70.32 40.19 81 82 71.72 39.75 71.54 40.07 71.37 40.38 71.19 40.69 82 83 72.59 40.24 72.42 40.56 72.24 40.87 72.06 41.19 83 84 73.47 40.72 73.29 41.04 73.11 41.36 72.93 41.68 84 85 74.34 41.21 74.16 41.53 73.98 41.86 73.80 42.18 85 86 75.22 41.69 75.03 42.02 74.85 42.35 74.67 42.67 86 87 76.09 42.18 75.91 42.51 75.72 42.84 75.53 43.17 87 88 76.97 42.65 76.78 43.00 76.59 43.33 76.40 43.67 88 89 77. 4 43.15 77.65 43.49 77.46 43.83 77.27 44.16 89 90 78.72 43.63 78.52 43.98 78,33 44.32 78.14 44.66 90 91 79.59 44.12 79.40 44.46 79.20 44.81 79.01 45.16 91 92 80.46 44.60 80.27 44.95 80.07 45.30 79.87 45.65 92 93 81.34 45.09 81.14 45.44 80.94 45.80 80.74 46.15 93 94 82.21 45.57 82.01 45.93 81.81 46.29 81.61 46.6-1 94 95 83.09 46.06 82.89 46.42 82.68 46.78 82.48 47.14 95 96 83.96 46.54 83.76 46.91 83.55 47.27 83.35 47.64 96 97 84.84 47.03 84.63 47.40 84.42 47.77 84.22 48.13 97 98 85.71 47.51 85.50 47.88 85. 2B 48.26 85.08 48.63 98 99 86.59 48.00 86.38 48.37 86.17 48.75 85.95 49.13 99 100 87.46 48.48 87.25 48,86 87.04 49.24 86.82 49.62 100 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. o> o c 5 .2 s 61 Deg. 60| Deg. 60i Deg. 60* Deg. 3 62 TRAVERSE TABLE, o 30 Deg. 30i Deg. 30 Deg. 30| Deg. O CO 5' P I Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. P 1 0.87 0.50 0.86 0.50 0.86 0.51 0.86 0.51 i 2 1.73 1.00 1.73 1.01 1.72 1.02 1.72 1.02 2 3 2.60 1.50 2.59 1.51 2.58 1,52 2.58 1.53 3 4 3.46 2.00 3.46 2.02 3.45 2.03 3.44 2.05 4 5 4.33 2.50 4.32 2.52 4.31 2.54 4.30 2.56 5 6 5.20 3.00 5.18 3.02 5.17 3.05 5.16 3.07 6 7 6.06 3.50 6.05 3.53 6.03 3.55 6.02 3.58 7 8 6.93 4.00 6.91 4.03 6.89 4.06 6.88 4.09 8 9 7.79 4.50 7.77 4.53 7.75 4.57 7.73 4.60 9 10 8.66 5.00 8.64 5.04 8.62 5.08 8.59 5.11 10 11 9.53 5.50 9.50 5.54 9.48 5.58 9.45 5.62 11 12 10.39 6.00 10.37 6.05 10.34 6.09 10.31 6.14 12 13 11.26 6.50 11.23 6.55 11.20 6.60 11.17 6 -.65 13 14 12.12 7.00 12.09 7.05 12.06 7.11 12.03 7.16 14 15 12.99 7.50 12.96 7.56 12.92 7.61 12.89 7.67 15 16 13.86 8.00 13.82 8.06 13.79 8.12 13.75 8.18 16 17 14.72 8.50 14.69 8.56 14.65 8.63 14.61 8.69 17 18 15.59 9.00 15.55 9.07 15.51 9.14 15.47 9.20 18 19 16.45 9.50 16.41 9.57 16.37 9.64 16.33 9.71 19 20 17.32 10.00 17.28 10.08 17.23 10.15 17.19 10.23 20 21 18.19 10.50 18.14 10.58 18.09 10.66 18.05 10.74 21 22 19.05 11.00 19.00 11.08 18.96 11.17 18.91 11.25 22 23 19.92 11.50 19.87 11.59 19.82 11.67 19.77 11.76 23 24 20.78 12.00 20.73 12.09 20 . 68 12.18 20.63 12.27 24 25 21.65 12.50 21.60 12.59 21.54 12.69 21.49 12.78 25 26 22.52 13.00 22.46 13.10 22.40 13.20 22.34 13.29 26 27 23.38 13.50 23.32 13.60 23.26 13.70 23.20 13.80 27 28 24.25 14.00 24.19 14.11 24.13 14.21 24.06 14.32 28 29 25.11 14.50 25.05 14.61 24.99 14.72 24.92 14.83 29 30 29.98 15.00 25.92 15.11 25.85 15.23 25.78 15.34 30 31 26.85 15.50 26.78 15.62 26.71 15.73 26.64 15.85 31 32 27.71 16.00 27.64 16.12 27.57 16.24 27.50 16.36 32 33 28 . 58 16.50 28.51 16.62 28.43 16.75 28.36 16.87 33 34 29.44 17.00 29.37 17.13 29.30 17.26 29.22 17.38 34 35 30.31 17.50 30.23 17.63 30.16 17.76 30.08 17.90 35 36 31.18 18.00 31.10 18.14 31.02 18.27 30.94 18.41 36 37 32.04 18.50 31.96 18.64 31.88 18.78 31.80 18.92 37 38 32.91 19.00 32.83 19.14 32.74 19.29 32.66 19.43 38 39 33.77 19.50 33.69 19.65 33.60 19.79 33.52 19.94 39 40 34.64 20.00 34.55 20.15 34.47 20.30 34.38 20.45 40 41 35.51 20.50 35.42 20.65 35.33 20.81 35.24 20.96 41 42 36.37 21.00 36.28 21.16 36.19 21.32 36.10 21.47 42 43 37.24 21.50 37.14 21.66 37.05 21.82 36.95 21.99 43 44 38.11 22.00 38.01 22.17 37.91 22.33 37.81 22.50 44 45 38.97 22.50 38.87 22.67 38 . 77 22.84 38.67 23.01 45 46 39.84 23.00 39.74 23.17 39.63 23.35 39.53 23.52 46 47 40.70 23.50 40.60 23.68 40.50 23.85 40.39 24.03 47 48 41.57 24.00 41.46 24.18 41.36 24.36 41 .'25 24.54 48 49 42.44 24.50 42.33 24.68 42.22 24.87 42.11 25.05 49 50 43.30 25.00 43.19 25.19 43.08 25.38 42.97 25.56 50 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. a! o a .2 q 60 Deg. 59| Dog. 59| Deg. ' 59i Deg. "to Q TRAVERSE TABLE. g 30 Deg. 30$ Deg. 30* Deg. 30, Deg. O QQ S 1' n o Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. I ~51 44.17 25.50 44.06 25.69 43.94 25.88 43.83 26.08 51 52 45.03 26.00 44.92 26.20 44.80 26.39 44.69 26.59 52 53 45.90 26.50 45.78 26 70 45.67 26.90 45.55 27.10 53 54 46.77 27.00 46.65 27.20 46.53 27.41 46.41 27.61 54 55 47.63 27.50 47.51 27.71 47.39 27.91 47.27 28.12 55 56 48.50 28.00 48.37 28.21 48.25 28.42 43.13 28.63 56 57 49.36 28.50 4-9.24 28.72 49.11 28.93 48.99 29.14 57 58 50.23 29.00 50.10 29.22 49.97 29.44 49.85 29.65 58 59 51.10 29.50 50.97 29.72 50.84 29.94 50.70 30.17 59 60 51.96 3U.OO 51.83 30.23 51.70 30.45 51.56 30.68 60 61 52.83 30.50 52.69 30.73 52.56 30.96 52.42 31.19 61 62 53.69 31.00 53.56 31.23 53.42 31.47 53.28 31.70 62 63 54.56 31.50 54.42 31.74 54.28 31.97 54.14 32.21 63 64 55.43 32.00 55.29 32.24 55.14 32.48 55.00 32.72 04 65 56.29 32.50 56.15 32.75 56.01 32.99 55.86 33.23 65 66 57.16 33.00 57.01 33.25 56.87 33.50 56 . 72 33.75 66 67 58.02 33.50 57.88 33.75 07.73 34.01 57.58 34.26 67 68 5S.89 34.00 58.74 34.26 58.59 34.51 58.44 34.77 68 * 69 59.76 34.50 59.60 34.76 59.45 35.02 59.30 35.28 69 70 60.62 35.00 60.47 35.26 60.31 35.53 60.16 35.79 70 71 61.49 35.50 1 61.33 35.77 61.18 36.04 61.02 36.30 71 72 62.35 36.00 62.20 36.27 62.04 36.54 61.88 36.81 72 73 63.22 36.50 63.06 36.78 62.90 37.05 62.74 37.32 73 74 64.09 37.00 63.92 37.28 63.76 37.56 63.60 37.84 74 75 64.95 37.50 64.79 37.78 64.62 38.07 64.46 38.35 75 76 65.82 38.00 65.65 38.29 65.48 38.57 65.31 38.86 76 77 66.68 38.50 66.52 38 . 79 66.35 39.08 66.17 39.37 77 78 67.55 39.00 67.38 39.29 67.21 39.59 67.03 39.88 78 79 68.42 39.50. 68.24 39.80 68.07 40.10 67.89 40.39 79 80 69.28 40.00 69.11 40.30 68.93 40.60 68.75 40.90 80 81 70.15 40.50 69.97" 40.81 69.79 41.11 69.61 41.41 81 82 71.01 41.00 70.83 41.31 70.65 41.62 70.47 41.93 82 83 71.88 41.50 71.70 41.81 71.52 42.13 71.33 42.44 83 84 72.75 42.00 72.56 42.32 72.38 42.63 72.19 42.95 84 85 73.61 42.50 73.43 42.82 73.24 43.14 73.05 43.46 85 86 74.48 43.00 74.29 43*. 32 74.10 43.65 73.91 43.97 86 87 75.34 43.50 75.15 43.83 74.96 44.16 74.77 44.48 87 88 76.21 44.00 76.02 44.33 75.82 44.66 75.63 44. S9 88 89 77.08 44.50 76.88 44.84 76.68 45.17 76.49 45.51 89 90 77.94 45.00 77.75 45.34 77.55 45.68 77.35 46.02 90 91 78.81 45.50 78.61 45.84 78.41 46.19 78.21 46.53 91 92 79.67 46.00 79.47 46.35 79.27 46.69 79.07 47.04 92 93 80.54 46.50 80.34 46.85 80.13 47.20 79.92 47.55 93 94 81.41 47.00 81.20 47.35 80.99 47.71 80.78 48.06 94 95 82.27 47.50 82.06 47.86 81. 85 j 48. 22 81.64 48.57 95 96 83.14 48.00 82.93 48.36 82.72 48.72 82.50 49.08 96 97 84.00 48.50 83.79 48.87 83.58 49.23 83.36 49.60 97 98 84.87 49.00 84.66 49.37 84.44 49.74 84.22 50.11 98 99 85.74 49.50 85.52 49.87 85.30 50.25 85.08 50.62 99 100 86.60 50.00 86.38 50.38 86.16 50.75 85.94 51.13 100 a s Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 rt J "x Q 60 Deg. 59| Deg. 59* Deg. 59i Deg. 75 Q 64 TRAVERSE TABLE. p ' P 31 Deg. 314 Deg. 314 Deg. 31 Deg. 5' .1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. I 1 0.86 0.51 0.85 0.52 0.85 0.52 0.85 0.53 1 2 1.71 1.03 1.71 1.04 1.71 1.04 1.70 1.05 2 3 2.57 1.55 2.56 1.56 2.56 1.57 2.55 1.58 3 4 3.43 2.06 3.42 2.08 3.41 2.09 3.40 2.10 4 5 4.29 2.58 4.27 2.59 4.26 2.61 4.25 2.63 5 6 5.14 3.09 5.13 3.11 5.12 3.13 5.10 3.16 6 7 6.00 3.61 5.98 3.63 5.97 3.66 5.95 3.68 7 8 6.86 4.12 6.84 4.15 6.82 4.18 6.80 4.21 8 9 7.71 4.64 7.69 4.67 7.67 4.70 7.65 4.74 9 10 8.57 5.15 8.55 5.19 8.53 5.22 8.50 5.26 10 11 9.43 5.67 9.40 5.71 9.38 5.75 9.35 5.79 11 12 10.29 6.18 10.26 6.23 10.23 &. 27 10.20 6.31 12 13 11.14 6.70 11.11 6.74 11.08 6.79 11.05 6.84 13 14 12.00 7.21 11.97 7.26 11.94 7.31 11.90 7.37 14 15 12.86 7.73 12.82 7.78 12.79 7.84 12.76 7.89 15 16 13.71 8.24 13.68 8.30 13.64 8.36 13.61 8.42 16 17 14.57 8.76 14.53 8.82 14.49 8.88 14.46 8.95 17 18 15.43 9.27 15.39 9.34 15.35 9.40 15.31 9.47 18 19 16.29 9.79 16.24 9.86 16.20 9.93 16.16 10.00 19 20 17.14 10.30 17.10 10.38 17.05 10.45 17.01 10.52 20 21 18.00 10.82 17.95 10.89 17.91 10.97 17.86 11.05 21 22 18.86 11.33 18.81 11.41 18.76 11.49 18.71 11.58 22 23 19.71 11.85 19.66 11.93 19.61 12.02 19.56 12.10 23 24 20.57 12.36 20.52 12.45 20.46 12.54 20.41 12.63 24 25 21.43 12.88 21.37 12.97 21.32 13.06 21.26 13.16 25 26 22.29 13.39 22.23 13.49 22.17 13.58 22.11 13.68 26 27 23.14 13.91 23.08 14.01 23.02 14.11 22.96 14.21 27 28 24.00 J4.42 23.94 14.53 23.87 14.63 23.81 14.73 28 29 24.86 14.94 24.79 15.04 24.73 15.15 24.66 15.26 29 30 25.71 15.45 25.65 15.56 25.58 15.67 25.51 15.79 30 31 26.57 15.97 26.50 16.08 26.43 16.20 26.36 16.31 31 32 27.43 16.48 27.36 16.60 27.28 16.72 27.21 16.84 32 33 28.29 17.00 28.21 17.12 28.14 17.24 28.06 17.37 33 34 29.14 17.51 29.07 17.64 28.99 17.76 28.91 17.89 35 30.00 18.03 29.92 18.16 29.84 18.29 29.76 18.42 35 36 30.86 18.54 30.78 18.68 30:70 18.81 30.61 18.94 36 37 31.72 19.06 31.63 19.19 31.55 19.33 31.46 19.47 37 38 32.57 19.57 32.49 19.71 32.40 19.85 32.31 20.00 38 39 33.43 20.09 33.34 20.23 33.25 20.38 33.16 20.52 39 40 34.29 20.60 34.20 20.75 34.11 20.90 34.01 21.05 40 41 35.14 21.12 35.05 21.27 34.96 21.42 34.86 21.57 41 42 36.00 21.63 35.91 21.79 35.81 21.94 35.71 22.10 42 43 36.86 22.15 36.76 22.31 36.66 22.47 36.57 22.63 43 44 37.72 22.66 37.62 22.83 37.52 22.99 37.42 23.15 44 45 38.57 23.18 38.47 23.34 38.37 23.51 38.27 23.68 45 46 39.43 23.69 39.33 23.86 39.22 24.03 39.12 24.21 46 47 40.29 24.21 40.18 24.38 40.07 24.56 39.97 24.73 47 48 41.14 24.72 41.04 24.90 40.93 25.08 40.82 25.26 48 49 42.00 25.24 41.89 25.42 41.78 25.60 41.67 25 . 78 49 50 42.86 25.75 42.75 25.94 42.63 26.12 42.52 26.31 50 8 c Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. D o Q 59 Deg. 58| Deg. 584 Deg. 58i Deg. 1 TRAVERSE TABLE. o 31 Deg. 3H Deg. 34 Deg. 31$ Deg. G 5T 55' tancc. P Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 51 43.72 26.27 43.60 26.46 43.48 26.65 43.37 26.84 51 52 44.57 26.78 44.46 26.98 44.34 27.17 44.22 27.36 52 53 45.43 27.30 45.31 27.49 45.19 27.69 45.07 27.89 53 54 46.29 27.81 46.17 28.01 46.04 28.21 45.92 28.42 54 55 47.14 28.33 47.02 28.53 46.90 28.74 46.77 28.94 55 56 48.00 28.84 47.88 29.05 47.75 29.26 47.62 29.47 56 57 48.86 29.36 48.73 29.57 48.60 29.78 48.47 29.99 57 58 49.72 29.87 49.58 30.09 49.45 30.30 49.32 30.52 58 59 50.57 30.39 50.44 30.61 50.31 30.83 50.17 31.05 59 60 51.43 30.90 51.29 31.13 51.16 31.35 51.02 31.57 60 61 52.29 31.42 5'2.15 31.65 52.01 31.87 51.87 32.10 61 62 53.14 31.93 53.00 32.16 52.86 32.39 52.72 32 . 63 62 63 54.00 32.45 53.86 32.68 53.72 32.92 53.57 33.15 63 64 54.86 32.96 54.71 33.20 54.57 33.44 54.42 33.68 64 65 55.72 33.48 55.57 33.72 55.42 33.96 55.27 34.20 65 66 56.57 33.99 56.42 34.24 56.27 34.48 56.12 34.73 66 67 57.43 34.51 57.28 34.76 57.13 35.01 56.98 35.26 67 68 58.29 35.02 58.13 35.28 57.98 35.53 57.82 35.78 68 69 59.14 35.54 58.99 35.80 58.83 36.05 58.67 36.31 69 70 60.00 36.05 59.84 36.31 59.68 36.57 59.52 36.83 70 71. 60.86 36.57 60.70 36.83 60.54 37.10 60.37 37.36 71 72 61.72 37.08 61.55 37.35 61.39 37.62 61.23 37.89 72 73 62.57 37.60 62.41 37.87 02.24 38.14 62.08 38.41 73 74 63.43 38.11 63.26 38.39 63.10 38.66 62.93 38.94 74 75 64.29 38.63 64.12 38.91 63.95. 39.19 63.78 39.47 75 76 65.14 39.14 64.97 39.43 64.80 39.71 64.63 39.99 76 77 66.00 39.66 65.83 39.95 65.65 40.23 65.48 40.52 77 78 66.86 40.17 66.68 40.46 66.51 40.75 66.33 41.04 78 79 67.72 40.69 67.54 40.98 67.36 41.28 67.18 41.57 79 80 68.57 41.20 68.39 41.50 68.21 41.80 38.03 42,. 10 80 81 69.43 41.72 69.25 42.02 69.06 42.32 68.88 42.62 81 82 70.29 42.23 70.10 42.54 69.92 42.84 69.73 43.15 82 83 71.14 42.75 70.96 43.06 70.77 43.37 70.58 43.68 83 84 72.00 43.26 71.81 43.58 71.62 43.39 71.43 44.20 84 85 72.86 43.78 72.67 44.10 72.47 44.41 72.28 44.73 85 86 73.72 44.29 73.52 44.61 73.33 44.93 73.13 45.25 86 87 74.57 44.81 74.38 45.13 74.18 45.46 73.98 45.78 87 88 75.43 45.32 75.23 45.65 75.03 45.98 74.83 46.31 88 89 76.29 45.84 76.09 46.17 75.88 46.50 75.68 46.83 89 90 77.15 46.35 76.94 46.69 76.74 47.02 76.53 47.36 90 91 78.00 46.87 77.80 47.21 77.59 47.55 77.38 47.89 91 92 78.86 47.38 78.65 47.73 78.44 48.07 78.23 48.41 92 93 79.72 47,90 79.51 48.25 79.30 48.59 79.08 48.94 93 94 80.57, 48.41 80.36 48,76 80.15 49.11 79.93 49.47 94 95 81.43 48.93 81.22 49.28 81.00 49.64 80.78 49.99 95 96 82.29 49.44 82.07 49.80 81.85 50.16 81.63 50.52 96 97 33.15 49.96 82.93 50.32 82.71 50.68 82.48 51.04 97 98 84.00 50.47 83.78 50.84 83.56 51.20 83.33 51.57 98 99 84.86 50,99 84.64 51.36 84.41 51.73 84.18 52.10 99 100 85.72 51.50 85.49 51.88 85.26 52.25 85.04 52.62 100 i* Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. I ^ cd to 5 59 Detr. 58} Deg. 581 Deg. 58i Deg. 5 66 TRAVERSE TABLE. o 32 Deg. 32i Deg. 32| Deg. 32| Deg. B 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. E 1 0.85 0.53 0.85 0.53 0.84 0.54 0.84 0.54 T 2 1.70 1.06 1.69 1.07 1.69 1.07 1.68 1.08 2 3 2.54 K59 2.54 1.60 2.53 1.61 2.52 1.62 3 4 3.39 2.12 3.38 2.13 3.3~ 2.15 3.36 2.16 4 5 4.24 2.65 4.23 2.67 4.22 2.69 4.21 2.70 5 6 5.09 3.18 5.07 3.20 5.06 3.22 5.05 3.25 6 7 5.94 3.71 5.92 3.74 5.90 3.76 5.89 3.79 7 8 6.78 4.24 6.77 4.27 6.75 4.30 6.73 4.33 8 9 7.63 4.77 7.61 4.80 7.59 4.84 7.57 4.87 9 10 8.48 5.30 8.46 5.34 8.43 5.37 8.41 5.41 10 11 9.33 5.83 9.30 5.87 9.28 5.91 9.25 5.95 11 12 10.18 6.36 10.15 6.40 10.12 6.45 10.09 6.49 12 13 11.02 6.89 10.99 6.94 10.96 6.98 10.93 7.03 13 14 11.87 7.42 11.84 7.47 11.81 7.52 11.77 7.57 14 15 12.72 7.95 12.69 8.00 12.65 8.06 12.62 8.11 15 16 13.57 8.48 13.53 8.54 13.49 8.60 13.46 8.66 16 17 14.42 9.01 14.38 9.07 14.34 9.13 14.30 9.20 17 18 15.26 9.54 15.22 9.61 15.18 9.67 15.14 9.74 18 19 16.11 10.07 16.07 10.14 16.02 10.21 15.98 10.28 19 20 16.96 10.60 16.91 10.67 16.87 10.75 16.82 10.82 20 21 17.81 11.13 17.76 11.21 17.71 11.28 17.66 11.36 21 552 18.66 11.66 18.61 11.74 18.55 11.82 18.50 11.90 22 23 19.51 12.19 19.45 12.27 19.40 12.36 19.34 12.44 23 24 20.35 12.72 20.30 12.81 20.24 12.90 20.18 12.98 24 25 21.20 13.25 21.14 13.34 21.08 13.43 21.03 13.52 25 26 22.05 13.78 21.99 13.87 21.93 13.97 21.87 14.07 26 27 22.90 14.31 22.83 14.41 22.77 14.51 22.71 14.61 27 28 23.75 14.84 23.68 14.94 23.61 15.04 23.55 15.15 28 29 24.59 15.37 24.53 15.47 24.46 15.58 24.39 15.69 29 30 25.44 15.90 25.37 16.01 25.30 16.12 25.23 16.23 30 31 26.29 16.43 26.22 16.54 26.15 16.66 26.07 16.77 31 32 27.14 16.96 27.06 17.08 26.99 17.19 26.91 17.31 32 33 27.99 17.49 27.91 17.61 27.83 17.73 27.75 17.85 33 34 28.83 18.02 28 . 75 18.14 28.68 18.27 28.60 18.39 34 35 29.68 18.55 29.60 18.68 29.52 18.81 29.44 18.93 35 36 30.53 19.08 30.45 19.21 30.36 19.34 30.28 19.48 36 37 31.38 19.61 31.29 19.74 31.21 19.88 31.12 20.02 37 38 32.23 20.14 32.14 20.28 32.05 20.42 31.96 20.56 38 39 33.07 20.67 32.98 20.81 32.89 20.95 32.80 21.10 39 40 33.92 21.20 33.83 21.34 33.74 21.49 33.64 21.64 40 41 34.77 21.73 34.67 21.88 34.58 22.03 34.48 22.18 41 42 35.62 22.26 35.52 22.41 35.42 22.57 35.32 22 . 72 42 43 36.47 22.79 36.37 22.95 36.27 23.10 36.16 23.26 43 44 37.31 23.32 37.21 23.48 37.11 23.64 37.01 23.80 44 45 38.16 23.85 38.06 24.01 37.95 24.18 37.85 24.34 45 46 39.01 24.38 38.90 24.55 38.80 24.72 38.69 24.88 46 47 39.86 24.91 39.75 25.08 39.64 25.25 39.53 25.43 47 48 40.71 25.44 40.59 25.61 40.48 25.79 40.37 25.97 48 49 41.55 25.97 41.44 26.15 41.33 26 .'33 41.21 26.51 49 50 42.40 26.50 42.29 26.68 42.17 26.86 42.05 27.05 50 8 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. j ' 5 Q 58 Deg. 57| Deg. 57 Deg. 57* Deg. 5 TRAVERSE TABLE. 67 o ' . i ~51 52 53 54 55 56 57 58 59 60 32 Deg. 32* Deg. 32* Deg. 32} Deg. 1 a o 9 ~51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 43.25 44.10 4-1.95 45.79 46.64 47.49 48.34 49.19 50.03 50.88 27.03 27.56! 28.09 i 28.62 29.15 29.68 30.21 30.74 31.27 31.80 43.13 43.98 44.82 45.67 46.51 47.36 48.21 49.00 49.90 50.74 27.21, 27.75 28.28 28.82 29,35 29.88 30.42 30.95 31.48 32.02 43.01 43.86 44.70 45.54 46.39 47.23 48.07 48.92 49.76 50.60 27.40 ; 27.94 28.48: 29.01 ! 29.55 30.09 30.63 31.16 31.70 32.24 42.89 43.73 44.58 45.42 46.26 47.10 47.94 48.78 49.62 50.46 27.59 28.13 28.67 29.21 29.75 30.29 30.84 31.38 31.92 32.46 61 62 63 64 65 66 67 68 69 70 51.73 52.58 53.43 54.28 55.12 55.97 56.82 57.67 58.52 59.36 32.33] 32.85 33.38 i 33.91 ! 34.441 34.97. 35.50: 36.03 | 36.56, 37.091 51.59 52.44 53.28 54.13 54.97 55.82 56.66 57.51 58.36 59.20 32.55 33.08 33.62 34.15 34.68 35.22 35.75 36.29 36.82 37.35 51.45 52.29 53.13 53.98 54.82 55.66 56.51 57.35 58.19 59.04 32.78 33.31 33.85 34.39 34.92 35.46 36.00 36.54 37.07 37.61 51.30 52.14 52.99 53.83 54.67 55.51 56.35 57.19 58.03 58.87 33.00 33.54 34.08 34.62 35.16 35.70 36.25 36.79 37.33 37.87 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 60.21 61.06 61.91 62.76 63.60 64.45 65.30 66.15 67.00 67.84 37.62 ; 38.15 38.68: 39.21 I, 39 . 74 40.27 40.80 41.33 41.86 42.39 60.05 60.89 61.74 62.58 63.43 64.28 65.12 65.97 66.81 67.66 37.89 38.42 38.95 39.49 40:02 40.55 41.09 41.62 42.16 42.69 59.88 60.72 61.57 62.41 63.25 64.10 64.94 65.78 66.63 67.47 38.15 38.69 39.22 39.76 40.30 40.83 41.37 41.91 42.45 42.98 59.71 60.55 61.40 62.24 ,63.08 63.92 '64.76 '65.60 '66.44 i67.28 38.41 38.95 39.49 40.03 40.57 41.11 41.65 42.20 42.74 43.28 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 68,69 69.54 70.39 71.24 72.08 72.93 73.78 74.63 75.48 76.32 42.92 43.45 43.98 44.51 45.04 45.57 46.10 46.63 47.16 47.69 68.50 69.35 70.20 71.04 71.89 72.73 73.58 74.42 75.27 76.12 43.22 43.76 44.29 44.82 45.36 45.89 46.42 46.96 47.49 48.03 68.31 69.16 70.00 70.84 71.69 72.53 73.38 74.22 75.06 75.91 43.521 68.12 44.06 ! 68.97 44.60 169.81 45.13 70.65 45.67 71.49 46.21 72.33 46.75 73.17 47.28 : 74. 01 47.82 74.85 48.36 75.09 43.82 44.36 44.90 45.44 45.98 46.52 47.06 47.61 48.15 48.69 77.17 78.02 78.87 79.72 80.56 81.41 82.26 83.11 83.96 84.80 48.221 48.75 49.28 49.81 50.34 50.87 51.40 51.93 52.46 52.99 76.96 77.81 78.65 79.50 80.34 81.19 82.04 82.88 83.73 84.57 48.56 49.09 49.63 50.16 50.69 51.23 51.76 52.29 52.83 53.36 76.75 77.59 78.44 79.28 80.12 80.97 81.81 82.65 83.50 84.34 48.89 76.53 49.43 .77.38 49.97 178.22 50.51 79.06 51.04 179.90 51.58 80.74 52.12 181.58 52.66 1 82. 42 53.19 i 83. 26 53.73 84.10 49.23 49 77 50.31 50.85 51.39 51.93 52.47 53.02 53.56 54.10 Distance. Dep. Lat. Dep. Lat. Dep. Lat. I! Dep. Lat. jj 1 58 Deg. 57J Deg. 57* Deg. 57* Deg. II R 68 TRAVERSE TABLE. d 33 Deg. 33} Deg. 33i Deg. 33| Deg. C 5' 1' P Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. P 1 0.84 0.54 0.84 0.55 0.83 0.55 0.83 0.56 1 2 1.68 1.09 1.67 1. 10 1.67 1.10 1.66 1.11 2 3 2.52 1.63 2.51 1.64 2.50 1.66 2.49 1.67 3 4 3.35 2.18 3.35 2.19 3.34 2.21 3.33 2.22 4 5 4.19 2.72 4.18 2.74 4.17 2.76 4.16 2.78 5 6 5.03 3.27 5.02 3.29 5.00 3.31 4.99 3.33 6 7 5.87 3.81 5.85 3.84 5.84 3.86 5.82 3.89 7 8 6.71 4.36 6.69 4.39 6.67 4.42 6.65 4.44 8 9 7.55 4.90 7.53 4.93 7.50 4.97 7.48 5.00 9 10 8.39 5.45 8.36 5.48 8.34 5.52 8.3L 5.56 10 11 9.23 5.99 9.20 6.03 " 9.17 6.07 9.15 6.11 11 12 10.06 6.54 10.04 6.58 10.01 6.62 9.98 6.67 12 13 10.90 7.08 10.87 7.13 10.84 7.18 10.81 7.22 13 14 11.74 7.62 11.71 7.68 11.67 7.73 11.64 7.78 14 15 12.58 8.17 12.54 8.22 12.51 8.28 12.47 8.33 15 16 13.42 13.38 8.77 13.34 8.83 13.30 8.89 16 17 14.26 9! 26 14.22 9.32 14.18 9.38 14.13 9.44 17 18 15.10 9.80 15.05 9.87 15.01 9.93 14.97 10.00 18 19 15.93 10.35 15.89 10.42 15.84 10.49 15.80 10.56 19 20 16.77 10.89 16.73 10.97 16.68 11.04 16.63 11.11 20 21 17.61 11.44 17.56 11.51 17.51 11.59 17.46 11.6? 21 22 18.45 11.98 18.40 12.06 18.35 12.14 18.29 12.22 22 23 19.29 12.53 19.23 12.61 19.18 12.69 19.12 12.78 23 24 20.13 13.07 20.07 13.16 20.01 13.25 19.96 13.33 24 25 20.97 13.62 20.91 13.71 20.85 13.80 20.79 13.89 25 26 21.81 14.16 21.74 14.26 21:68 14.35 2\. 62 14.44 26 27 22.64 14.71 22.58 14.80 22.51 14.90 22.45 15.00 27 28 23.48 15.25 23.42 15.35 23.35 15.45 23.28 15.56 28 29 24.32 15.79 24.25 15.90 24.18 16.01 24.11 16.11 29 30 25.16 16.34 25.09 16.45 25.02 16.56 24.94 16.67 30 31 26.00 16.88 25.92 17,00 25.85 17.11 25.78 17.22 31 32 26.84 17.43 26.76 17.55 26.68 17.66 26.61 17.78 32 33 27.68 17.97 27.60 18.09 27.52 18.21 27.44 18.33 33 34 28.51 18.52 28.43 18.64 28.35 18.77 28. 2# 13.89 34 35 29.35 19.06 29.27 19.19 29.19 19.32 29.10 19.44 35 36 30.19 19.61 30.11 19.74 30.02 19.87 29.93 20.00 36 37 31.03 20.15 30.94 20.29 30.85 20.42 30.76 20.56 37 38 31.87 2,0.70 31.78 20.84 >31.69 20.97 31.60 21.11 38 39 32 71 21.24 32.62 21.38 32.52 21.53 32.43 21.67 39 40 33.55 21.79 33.45 21.93 33.36 22.08 33.26 22.22 40 41 34.39 22.33 34.29 22.48 34'. 19 22.63 34.09 22.78 41 42 35.22 22.87 35.12 23.03 35.02 23.18 34.92 23.33 42 43 36.06 23.42 35.96 23.58 35.86 23.73 35.75 23.89 43 44 36.90 23.96 36.80 24.12 36.69 24.29 36.58 24.45 44 45 37.74 24.51 37.63 24.67 37.52 24.84 37.42 25.00 45 46 38.58 25.05 38.47 25.22 38.36 25.39 38.25 25.56 46 47 39.42 25.60 39.31 25.77 39.19 25.94 39.08 26.11 47 48 40.26 26.14 40.14 26.32 40.03 26.49 39.91 26.67 48 49 41.09 26.69 40.98 26.87 40.86 27.04 40.74 27.22 49 50 41.93 27.23 41.81 27.41 41.69 27.60 41.57 27.78 50 D O Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. d o d d ci 3 "w b 57 Deg. 56J Deg. 56i Deg. 56J Deg. 3 TRAVERSE TABLE. 69 g 33 Deg. 33i Deg. 33 Deg. 33| Deg. a nance. stance. Lat. Dep. Lat. Dep. Lat. Dep Lat. Dep. 51 42.77 27.78 42.65 27.96 42.53 28.1J> 42.40 28.33 51 52 43.61 28.32 43.49 28.51 43.36 28.70 43.24 28.89 52 53 44.45 28.87 44.32 29.06 44.20 29.25 44.07 29.45 53 54 45.29 29.41 45.16 29.61 45.03 29.80 44.90 30.00 54 55 46.13 29.96 46.00 30.16 45.86 30.36 45.73 30.56 55 56 46.97 30.50 46.83 30.70 46.70 30.91 46.56 31.11 56 57 47.80 31.04 47.67 31.25 47.53 31.46 47.39 31.67 57 58 48.64 31.59 48.50 31.80 48.37 32.01 48.23 32.22 58 59 49.48 32.13 49.34 32.35 49.20 32.56 49.06 32.78 59 60 50.32 32.68 50.18 32.90 50.03 33.12 49.89 33.33 60 61 51.16 33.22 51.01 33.45 50.87 33.67 50.72 33.89 61 62 52.00 33.77 51.85 33.99 51.70 34.22 51.55 34.45 62 63 52.84 34.31 52.69 34.54 52.53 34.77 52.38 35.00 63 64 53.67 34.86 53.52 35.09 53.37 35.32 53.21 35.56 64 65 54.51 35.40 54.36 35.64 54.20 35.88 54.05 36.11 65 66 55.35 35.95 55.19 36.19 55.04 36.43 54.88 36.67 66 67 56.19 36.49 56.03 36.74 55.87 36.98 55.71 37.22 67 68 57.03 37.04 56.87 37.28 56.70 37.53 56.54 37.78 68 69 57.87 37.58 57.70 37.83 57.54 38.08 57.37 3.8.33 69 70 58.71 38.12 58.54 38.38 58.37 38.64 58.20 38.89 70 71 59.55 38.67 59.38 38.93 59.21 39.19 59.03 39.45 71 72 60.38 39.21 60.21 39.48 60.04 39.74 59.87 40.00 72 73 61.22 39.76 61.05 40.03 60.87 40.29 60.70 40.56 73 74 62.06 40.30 61.89 40.57 61.71 40.84 61.53 41.11 74 75 62.90 40.85 62.72 41.12 62.54 41.40 62.36 41.67 75 76 63.74 41.39 63.56 41.67 63.38 41.95 63.19 42.22 76 77 64.58 41.94 64.39 42.22 64.21 42.50 64.02 42.78 77 78 65.42 42.48 65.23 42.77 65.04 43.05 64.85 43.33 78 79 66.25 43.03 66.07 43.32 65.88 43.60 65.69 43.89 79 80 67.09 43.57 66.90 ,43.86 66.71 44.15 66.52 44.45 80 81 67.93 44.12 67.74 44.41 67.54 44.71 67.35 45.00 81 82 68.77 44.66 68.58 44.96 68.38 45.26 68.18 45.56 82 83 69.61 45.20 69.41 45.51 69.21 45.81 69.01 46.11 83 84 70.45 45.75 70.25 46.06 70.05 46.36 69.84 46.67 84 85 71.29 46.29 71.08 46.60 70.88 46.91 70.67 47.22 85 86 72.13 46.84 71.92 47.15 71.71 47.47 71.51 47.78 86 87 72.96 47.38 72.76 47.70. 72.55 48.02 72.34 48.33 87 88 73.80 47.93 73.59 48/.25< 73.38 48.57 73.17 48.89 88 89 74.64 48.47 74.43 48.80 74.22 49.12 74.00 49.45 89 90 75.48 49.02 75.27 49.35 75.05 49.67 74.83 50.00 90 91 76.32 49.56 76.10 49.89 75.88 50.23 75.66 50.56 91 92 77.16 50.11 76.94 50.44 76.72 50.78 76.50 51.11 92 93 78.00 50.65 77.77 50.99 77.55 51.33 77.33 51.67 93 94 78.83 51.20 78.61 51.54 78.39 51.88 78.16 52.22 94 95 79.67 51.74 79.45 52.09 79.22 52.43 78.99 52.78 95 96 80.51 52.29 80.28 52.64 80.05 52.99 79.82 53.33 96 97 81.35 52.83 81.12 53.18 80.89 53.54 80.65 53.89 97 98 82.19 53 . 37 81.96 53.73 81.72 54.09 81.48 54.45 98 99 83.03 53.92 82.79 54.28 82.55 54.64 82.32 55.00 99 100 83.87 54.46 83.63 54.83 83.39 55.19 83.15 55.56 100 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 .2 a 57 Deg. 56| Deg. 56 Deg. 56i Deg. 70 TBAVERSE TABLE. 34 Deg. 344 Deg. 34| Deg. 34| Deg. O g. a* P 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. P 1 0.83 0.56 0.83 0.56 0.82 0.57 0.82 0.57 i 2 1.66 1.12 1.65 1.13 1.65 1.13 1.64 1.14 2 3 2.49 1.68 2.48 1.69 2.47 1.70 2.46 1.71 3 4 3.32 2.24 3.31 2.25 3.30 2.27 3.29 2.28 4 5 4.15 2.80 4.13 2.81 4.12 2.83 4.11 2.85 5 6 4.97 3.36 4.96 3.38 4.94 3.40 4.93 3.42 6 7 5.80 3.91 5.79 3.94 5.77 3.96 5.75 3.99 7 8 6.63 4.47 6.61 4.50 6.59 4.53 6.57 4.56 8 9 7.46 5.03 7.44 5.07 7.42 5.10 7.39 5.13 9 10 8.29 5.59 8.27 5.63 8.24 5.66 8.22 5.70 10 11 9.12 6.15 9.09 6.19 9.07 6.23 9.04 6.27 11 12 9.95 6.71 9.92 6.75 9.89 6.80 9.86 6.84 12 13 10.78 7.27 10.75 7.32 10.71 7.36 10.68 7.41 13 14 11.61 7.83 11.57 7.88 11.54 7.93 11.50 7.98 14 15 12.44 8.39 12.40 8.44 12.36 8.50 12.32 8 . 55 15 16 13.26 8.95 13.23 9.00 13.19 9.06 13.15 9.12 16 17 14.09 9.51 14.05 9.57 14.01 9.63 13.97 9.69 17 18 14.92 10.07 14.88 10.13 14.83 10.20 14.79 10.26 18 19 15.75 10.62 15.71 10.69 15.66 10.76 15.61 10.83 19 20 16.58 11.18 16.53 11.26 16.48 11.33 16.43 11.40 20 21 17.41 11.74 17.36 11.82 17.31 11.89 17.25 11.97 21 22 18.24 12.30 18.18 12.38 18.13 12.46 18.08 12.54 22 23 19.07 12.86 19.01 12.94 18.95 13.03 18.90 13.11 23 24 19.90 13.42 19.84 13.51 19.78 13.59 19.72 13.68 24 25 20.73 13.98 20.66 14.07 20.60 14.16 20.54 14.25 25 26 21.55 14.54 21.49 14.63 21.43 14.73 21.36 14.82 26 27 22.38- 15.10 22.32 15.20 22.25 15.29 22.18 15.39 27 28 23.21 15 66 23.14 15.76 23.08 15.86 23.01 15.96 28 29 24.04 16.22 23.97 16.32 23.90 16.43 23.83 16.53 29 30 24.87 16.78 24.80 16.88 24.72 16.99 24.65 17.10 30 31 25.70 17.33 25 . 62 17.45 25 . 55 17.56 25.47 17.67 31 32 26.53 17.89 26.45 18.01 26 . 37 18.12 26.29 18.24 32 33 27.36 18.45 27.28 18.57 27.20 18.69 27.11 18.81 33 34 28.19 19.01 28.10 19.14 28.02 19.26 27.94 19.38 34 35 29.02 19.57 28.93 19.70 28.84 19.82 28.76 19.95 33 36 29.85' 20.13 29.76 20.26 29.67 20.39 29.58 20.52 36 37 30 . 67 20.69 30.58 20.82 ^0.49 20.96 30.40 21.09 37 38 31.50 21.25 31.41 21.39 il.88 21.52 31.22 21.66 38 39 32.33 21.81 32.24 21.95 32.14 22.09 32.04 22.23 39 40 33.16 22.37 33.06 22.51 32.97 22.66 32.87 22 . 80 40 41 33.99 22.93 33.89 23.07 33.79 23.22 33.69 23.37 41 42 34.82 23.49 34.72 23.64 34.61 23.79 34.51 23.94 42 43 35.65 24.05 35.54 24.20 35.44 24.36 35.33 24.51 43 44 36.48 24.60 36.37 24.76 36.26 24.92 36.15 25 . 08 44 45 37.31 35.16 37.20 25.33 37.09 25.49 36.97 25.65 45 46 38.14 25.72 38.02 25.89 37.91 26.05 37.80 26.22 46 47 38 . 96 26.28 38.85 26.45 38.73 26.62 38.62 26.79 47 48 39.79 26.84 39.68 27.01 39.56 27.19 39.44 27.36 48 49 40.62 27.40 40.50 27.58 40.38 27.75 40.26 27.93 49 50 41 .45 27.96 41.33 28.14 41.21 28.32 41.08 28 . 50 50 1 De| Lat. Dep. Lat. Dep. Lat. Dep. Lat.. i .3 Q 66 Deg. 55| Deg. 55Deg. 554 Deg. cd 3 TRAVERSE TABLE. 71 2 34Deg. 34* Deg. 34A Deg. 34| Deg. b 5' i I' a n ? Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. i 51 42.28 28.52; 42.16 28.70 42.03 28.89 41.90 29.07 51 52 43.11 29.08 42.98 29.27 42.85 29.45 42.73 29.64 52 53 43.94 29.64 43.81 29.83 43.68 30.02 43.55 30.21 53 54 44.77 30.20 44.64 30.39 44.50 30.59 44.37 30.78 54 55 45.60 30.76 45.46 30.95 45.33 31.15 45.19 31.35 55 56 46.43 31.31 46.29 31.52 46.15 31.72 46.01 31.92 56 57 47.26 31.87. 47.12 32.08 46.98 32.29 46.83 32.49 57 58 48.08 32.43 47.94 32.64 47.80 32.85 47.66 33.06 58 59 48.91 32.99 48.77 33.21 48.62 33.42 48.48 33.63 59 60 49.74 33.55 49.60 33.77 49.45 33.98 49.30 34.20 60 61 50.57 34.11 50.42 34.33 50.27 34.55 50.12 34.77 61 62 51.40 34.67 51.25 34.89 51.10 35.12 50.94 35.34 62 63 52.23 35.23 52.08 35.46 51.92 35.68 51.76 35.91 63 64 53.06 35.79 52.90 36.02 52 . 74 36.25 52.59 36.48 64 65 53.89 36.35 53.73 36.58 53.57 36.82 53.41 37.05 65 66 54.72 36.91 54.55 37.15 54.39 37.38 54.23 37.62 66 67 55.55 37.46 55.38 37.71 55.22 37.95 55.05 38.19 67 68 56.37 38.03 56.21 38.27 56.04 38.52 55.87 38.76 68 69 57.20 38.58 57.03 38.83 56.86 39.08 56.69 39.33 69 70 158.03 39.14 57.86 39.40 57.69 39.65 57.52 39.90 70 71 58.86 39.70 58.69 39.96 58.51 40.21 58.34 40.47 71 72 59.69 40.26 59.51 40.52 59.34 40.78 59.16 41.04 72 73 60.52 40.82 60.34 41.08 60.16 41.35 59.98 41.61 73 74 61.35 41.38 61.17 41.65 60.99 41.91 60.80 42.18 74 75 62.18 41.94 61.99 42.21 61.81 42.48 61.62 42.75 75 76 63.01 42.50 63.82 42.77 62.63 43.05 62.45 43.32 76 77 63.84 43.06 63.65 43.34 63.46 43.61 63.27 43.89 77 78 64.66 43 . 62 64.47 43.90 64.28 44.18 64.09 44.46 78 79 65.49 44.18 65.30 44.46 65 . 1 1 44.75 64.91 45.03 79 80 66.32 44.74 66.13 45.02 65.93 45.31 65.73 45.60 80 81 67.15 45.29 66.95 45.59 66. ?o 45.88 66.55 46.17 81 82 67.98 45.85 67.78 46.15 67.58 46.45 67.37 46.74 82 83 68.81 46.41 68.61 46.71 68.40 47.01 68.20 47.31 83 84 69.64 46.97 69.43 47.28 69,23 47.58 69.02 47.88 84 85 70.47 47.53 70.26 47.84 70.05 48.14 69.84 48.45 85 86 71.30 48.09 71.09 48.40 70.87 48.71 70.66 49.02 86 87 72.13 48.65 71.91 48.96 71.70 49.28 71.48 49.59 87 88 72.96 49.21 72.74 49.53 72.52 49.84 72.30 50.16 88 89 73.78 49.77 73.57 50.09 73.35 50.41 73.13 50.73 89 90 74.61 50.33 74.39 50.65 74.17 50.98 73.95 51.30 90 91 75.44 50.89 75.22 51.22 75.00 51.54 74.77 51.87 91 92 76.27 51.45 76.05 51.78 75.82 52.11 75.59 52.44 92 93 77.10 52.00 76.87 52.34 76.64 52.68 76.41 53.01 93 94 77.93 52.56 77.70 52.90 77.47 53.24 77.23 53.58 94 95 78.76 53.12 78.53 53.47 78.29 53.81 78.06 54.15 95 96 79.59 53.68 79.35 54.03 79.12 54.37 78.88 54.72 96 97 80.42 54.24 80.18 54.59 79.94 54.94 79.70 55.29 97 98 81.25 54.80 81.01 55.15 80.76 55.51 80.52 55.86 98 99 82.07 55.36 81.83 55.72 81.59 56.07 81.34 56.43 99 100 82.90 55.92 82.66 56.28 82.41 56.64 82.16 57.00 100 \ Dep. Lat/ Dep. Lat. Dep. Lat. Dep. Lat. o o c a 56 Deg. 55| Deg. 551 Deg. 55i Deg. Cd 'jo 3 72 TRAVERSE TABllE. s 35 Deg. 35* Deg. 35i Deg. 35| Deg. 2 1 s Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. p 1 0.82 0.57 0.82 0.58 0.81 0.58 0.81 0.58 f 2 1.64 1.15 1.63 1.15 1.63 1.16 1.62 1.17 2 3 2.46 1.72 2.45 1.73 2.44 1.74 2.43 1.75 3 4 3.28 2.29 3.27 2.31 3.26 2.32 3.25 2.34 4 5 4.10 2.87 4.08 2.89 4.07 2.90 4.06 2.92 5 6 4.91 "3.44 4.90 3.46 4.88 3.48 4.87 3.51 6 7 5.73 4.01 5.72 4.04 5.70 4.06 5.68 4.09 7 8 6.55 4.59 6.53 4.62 6.51 4.65 6.49 4.67 8 9 7.37 5.16 7.35 5.19 7.33 5.23 7.30 5.26 9 10 8.19 5.74 8.17 5.77 8.14 5.81 8.12 5.84 10 " 11 9.01 0.31 8.98 6.35 8.96 6.39 8.93 6.43 11 12 9.83 6.88 9.80 6.93 9.77 6.97 9.74 7.01 12 13 10.65 7.46 10.62 7.50 10.58 7.55 10.55 7.60 13 14 11.47 8.03 11.43 8.08 11.40 8.13 11.36 8.18 14 15 12.29 8.60 12.25 8.66 12.21 8.71 12.17 8.76 15 16 13.11 9.18 13.07 9.23 13.03 9.29 12.99 9.35 16 17 13.93 9.75 13.88 9.81 13.84 9.87 13.80 9.93 17 18 14.74 10.32 14.70 10.39 14.65 10.45 14.61 10.52 18 19 15.56 10.90 15.52 10.97 15.47 11.03 15.42 11.10 19 20 16.38 11.47 16.33 11.54 16.28 11.61 16.23 11.68 20 21 17.20 12.05 17.15 12.12 17.10 12.19 17.04 12.27 21 22 18.02 12.62 17.97 12.70 17.91 12.78 17.85 12.85 22 23 18.84 13.19 18.78 13.27 18.72 13.36 18.67 13.44 23 24 19.66 13.77 19.60 13.85 19.54 13.94 19.48 14.02 24 25 20.48 14.34 20.42 14.43 20.35 14.52 20.29 14.61 25 26 21.30 14.91 21.23 15.01 21.17 15.10 21.10 15.19 26 27 22.12 15.49 22.05 15.58 21.98 15.68 21.91 15.77 27 28 22.94 16.06 22.87 16.16 22.80 16.26 22.72 16.36 28 29 23.76 16.63 23.68 16.74 23.61 16.84 23.54 16.94 29 30 24.57 17.21 24.50 17.31 24.42 17.42 24.35 17.53 30 31 25.39 17.78 25.32 17.89 25.24 18.00 25.16 18.11 31 32 26.21 18.35 26.13 18.47 26.05 18.58 25.97 18.70 32 33 27.03 18.93 26.95 19.05 26.87 19.16 26.78 19.28 33 34 27.85 19.50 27.77 1 9 . 62 27.68 19.74 27.59 19.86 34 35 28.67 20.08 28.58 20.20 28.49 20.32 28.41 20.45 35 36 29.49 20.65 29.40 20.78 29.31 20.91 29.22 21.03 36 37 30.31 21.22 30.22 21.35 30.12 21.49 30.03 21.62 37 38 31.13 21.80 31.03 21.93 30.94 22.07 30.84 22.20 38 39 31.95 22.37 31.85 22.51 31.75 22.65 31.65 22.79 39 40 32.77 22.94 32.67 23.09 32.56 23.23 32.46 23.37 40 41 33.59 23.52 33.48 23.66 33. 3S 23.81 33.27 23.95 41 42 34.40 24.09 34.30 24.24 34.19 24.39 34.09 24.54 42 43 35.22 24.66 35.12 24.82, 35.01 21.97 34.90 25.12 43 44 36.04 25 . 24 35.93 25.39 35.82 25.55 35.7? 25.71 44 ' 45 36.86 25.81 36.75 25.97 36.64 26.13 36.52 26.29 45 46 37.68 26.38 37.57 26.55 37.45 26.71 37.33 26.88 46 47 38.50 26.96 38.38 27.13 38.26 27.29 38.14 27.46 47 48 39.32 27.53 39.20 27.70 39.08 27.87 38.96 28.04 48 49 40.14 28.11 40.02 28.28 39.89 28.45 39.77 28.63 49 50 40.96 28.68 40.83 28.86 40.71 29.04 40.58 29.21 50 6 o Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. d o SM S B 3 55 Deg. 54| Deg. 54^ Deg. 54i Deg. *2 3 THAVERSE TABLE. o 35Deg. 35i Deg. 35i Deg. 35| Deg. C ft p 5 8 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. i 51 41.78 29.25 41.65 29.43 41.52 29.62 41.39 29.80 51 52 42.60 29.83 42.47 30.01 42.33 30.20 42.20 30.38 52 53 43.42 30.40 43.28 30.59 43.15 30.78 43.01 30.97 53 54 44.23 30.97 44.10 31.17 43.96 31.36 43.82 31.55 54 55 45.05 31.55 44.92 31.74 44.78 31.94 44.64 32.13 55 56 45.87 32.12 45.73 32.32 45.59 32.52 45.45 32.72 56 57 46.69 32.69 46.55 32.90 46.40 33.10 46.26 33.30 57 58 47.51 33.27 47.37 33.47 47.22 33.68 47.07 33.89 58 59 48.33 33.84 48.18 34.05 48.03 34.26 47.88 34.47 59 60 49.15 34.41 49.00 34.63 48.85 34.84 48.69 35.05 60 61 49.97 34.99 49.82 35.21 49.66 35.42 49.51 35.64" 61 62 50.79 35.56 50.63 35.78 50.48 36.00 50.32 36.22 62 63 51.61 36.14 51.45 36.36 51.^29 36.58 51.13 36.81 63 64 52.43 36.71 52.27 36.94 52.10 37.16 51.94 37.39 64 65 53.24 37.28 53.08 37.51 52.92 37.75 52.75 37.98 65 66 54.06 37.86 53.90 38.09 53.73 38.33 53.56 38.56 66 67 54.88 38.43 54.71 38.67 54.55 38.91 54.38 39.14 67 68 55.70 39.00 55.53 39. .25 55.36 39.49 55.19 39.73 68 69 56.52 39.58 56.35 39.82 56.17 40.07 56.00 40.31 69 70 57.34 40.15 57.16 40 40 56.99 40.65 56.81 40.90 70 71 58.16 40.72 57.98 40.98 57.80 41.23 57.62 41.48 71 72 58.98 41.30 58.80 41.55 58 . 62 41.81 58.43 42.07 72 73 59.80 41.87 59.61 42.13 59.43 42.39 59.24 42.65 73 74 60. 62 42.44 60.43 42.71 60.24 42.97 60.06 43.23 74 75 6T.44 43.02 61.25 43.29 61.06 43.55 60.87 43.82 75 76 62.26 43.59 62.06 43.86 61.87 44.13 61.68 44.40 76 77 63.07 44.17 62.88 44.44 62.69 44.71 62.49 44.99 77 78 63.89 44.74 63.70 45.02 63.50 45.29 63.30 45.57 78 79 64.71 45.31 64.51 45.59 64.32 45.88 64.11 46.16 79 80 65.53 45.89 65.33 46.17 65.13 46.46 64.93 46.74 8Q 81 66.35 46.46 66.15 46.75 65.94 47.04 65.74 47.32 81 82 67.17 47.03 66.96 47.33 66.76 47.62 66.55 47.91 82 83 67.99 47.61 67.78 47.90 67.57 48.20 67.36 48.49 83 84 68.81 48.18 68.60 48.48! 68.39 48.78 68.17 49.08 84 85 69.63 48.75 69.41 49. 06'; 69. 20 49. 3& 68.98 49.66 85 86 70.45 49.33 70.23 49.63 i 70. 01 49.94 69.80 50.25 86 87 71.27 49.90 71.05 50.21 I 70.83 50.52 70.61 50.83 87 88 72.09 50 47 71.86 50.79 71.64 51.10 71.42 51.41 88 89 72.90 51.05 72.68 51.37 72.46 51.68 72.23 52.00 89 90 73.72 51.62 73.50 51.94 73.27 52.26 ! 73.04 52.58 90 91 74.54 52.20 74.31 52.52 74.08 52.84 73.85 53.17 91 92 75.36 52.77 75.13 53.10 74.90 53.42 74.66 53.75 92 93 76.18 53.34 75.95 53.67 75.71 54.01 75.48 54.34 93 94 77.00 53.92 76.76 54.25 76.53 54.59 76.29 54.92 94 95 77.82 54.49 77.58 54.83 77.34 55.17 77.10 55.50 95 96 78.64 55.06 78.40 55.41 78.16 55.75 77.91 56.09 96 97 79.46 55.64 79.21 55.98 78.97 56.33 78.72 56.67 97 98 80.28 56.21 80.03 56.56 79.78 56.91 79.53 57.26 98 99 81.10 56.78 80.85 57.14 80.60 57.49 80.35 57.84 99 100 81.92 57.36 81.66 57.71 81.41 58.07 81.16 58.42 100 Q e Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. OJ CJ c 3 d s 55 Deg. 54| Deg. 54iDeg. 544 Deg. 5 74 TRAVERSE TABLE. G 1 36 Deg. cc* 1 36i Deg. 36| Deg. 36| Deg. 5' 1 I? I 1 L/at. Dep. Lat. Dep. Lat. Dep. Lat. Dep. P 1 0.81 0.59 0.81 0.59 0.80 0.59 0.80 0.60 1 2 1.62 1.18 1.61 1.18 1.61 1.19 1.60 1.20 2 3 2.43 1.76 2.42 1.77 ' 2.41 1.78 2.40 1.79 3 4 3.24 2.35 3.23 2.37 3.22 2.38 3.20 2.39 4 5 4.05 2.94 4.03 2.96 4.02 2.97 4.01 2.99 5 6 4.85 3.53 4.84 3.55 4.82 3.57 4.81 3.59 6 7 5.66 4.11 5.65 4.14 5.63 4.16 5.61 4.19 7 8 6.47 4.70 6.45 4.73 6.43 4.76 6.41 4.79 8 9 7.28 5.29 7.26 5.32 7.23 5.35 7.21 5.3S 9 10 8.09 5.88 8.06 5.91 8.04 5.95 8.01 5.98 10 1] 8.90 6.47 8.87 6.50 8.84 6.54 8.81 6.58 11 12 9.71 7.05 9.68 7.10 9.65 7.14 9.61 7.18 12 13 10.52 7.64 10.48 7.69 10.45 7.73 -10.42 7.78 13 14 11.33 8.23 11.29 8.28 11.25 8.33 11.22 8.38 14 15 12.14 8.82* 12.10 8.87 12.06 8.92 12.02 8.97 15 16 12.94 9.40 12.90 9.46 12.86 9.52 12.82 9.57 16 17 13.75 9.99 13.71 10.05 13.67 10.11 13.62 10.17 17 18 14.56 10.58 14.52 10.64 14.47 10.71 14.42 10.77 18 19 15.37 11.17 15.32 11.23 15.27 11.30 15.22 11.37 19 20. 16.18 11.76 16.13 11.83 16.08 11.90 16.03 11.97 20 21 16.99 12.34 16.94 12.42 16.88 12.49 16.83 12.56 21 22 17.80 12.93 17.74 13.01 17.68 13.09 17.63 13.16 22 23 18.61 13.52 18.55 13.60 18.49 13.68 18.43 13.76 23 24 19.42 14.11 19.35 14.19 19.29 14. 28 .19.23 14.36 24 25 20.23 14.69 20.16 14.78 20.10 .14.87 20.03 14.96 25 26 21.03 15.28 20.97 15.37 20.90 15.47 20.83 15.56 26 27 21.84 15.87 21.77 15.97 21.70 16.06 21.63 16.15 27 28 22 . 65 16.46 22.58 16.56 22.51 16.65 22.44 16.75 28 29 23.46 17.05 23.39 17.15 23.31 17.25 23.24 17.35 29 30 24.27 17.63 24.19 17.74 24.12 17.84 24.04 17.95 30 31 25.08 18.22 25.00 18.33 24.92 18.44 24.84 18.55 31 S2 25.89 18.81 25.81 18.92 25.72 19.03 25.64 19.15 32 33 26.70 19.40 26.61 19.51 26.53 19.63 26.44 19.74 33 34 27.51 19.98 27.42 20.10 27.33 20.22 27.24 20.34 34 35 28.32 20.57 28.23 20.70 28.13 20.82 28.04 20.94 35 36 29.12 21.16 29.03 21,29 28.94 21.41 28.85 21.54 36 37 29.93 21.75 29.84 21.88 29.74 22.01 29 . 65 22.14 37 38 30.74 22.34 30.64 22.47 30.55 22.60 30.45 22.74 38 39 31.55 22.92 31.45 23.06 31.35 23.20 31.25 23.33 39 40 32.36 23.51 32.26 23.65 32.15 23 . 79 32.05 23.93 40 41 33.17 24.10 33.06 24.24 32.96 24.39 32.85 24.53 41 42 33.98 24.69 33.87 24.83 33 . 76 24.98 33.65 25.13 42 43 34.79 25.27 34.68 25.43 34.57 25.58 34 .'45 25.73 43 44 35.60 25.86 35.48 26.02 35.37 26.17 35.26 26.33 44 45 36.41 26.45 36.29 26.61 36.17 26.77 36.06 26.92 45 46 37.21 27.04 37.10 27.20 36.98 27.36 36.86 27.52 46 47 38.02 27.63 37.90 27.79 37.78 27.96 37.66 28.12 47 48 38.83 28.21 38.71 28.38 38.59 28 . 55 38,46 28.72 48 49 39.64 28.80 39.52 28.97 39.39 29.15 39.26 29 . 32 49 50 40.45 29.39 40.32 29.57 40.19 29.74 40.06 29.92 50 a u c Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. i 1 CO b 54 Deg. 53| Deg. 53i Deg. 53i Deg. 3 TRAVERSE TABLE. 75 e 36Deg. 36i Deg. 36$ Deg. 36| Deg. O 5.' P 5' a g o Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 ~51 41.26 29.98 4l7l3~ 30.16 41.00 30.34 40.86 30.51 51 52 42.07 30.56 41.94 30.75 141.80 30.93 41.67 31.11 52 53 42.88 31.15 42.74 31.34 42.60 31.53 42.47 31.71 53 54 43.69 31.74 43.55 31.93 43.41 32.12 43.27 32.31 54 55 44.50 32.33 44.35 32.52 44.21 32.72 44.07 32.91 55 56 45.30 32.92 45.16 33.11 45.02 33.31 44.87 33.51 56 57 46.11 33.50 45.97 33.70 145.82 33.90 45.67 34.10 57 58 46.92 34.09 46.77 34.30 46.62 34.50 46.47 34.70 58 59 47.73 34.68 47.58 34.89 47.43 35 09 47.27 35.30 53 60 48.54 35.27 48.39 35.48 48.23 35.69 48.08 35.90 60 61 49.35 35.85 49.19 36.07 49.04 36.28 48.88 36.50 61 62 50.16 36.44 50.00 36.66 49.84 36.88 49.68 37.10 62 63 50.97 37.03 50.81 37.25 50.64 37.47 50.48 37.69 63 64 51.78 37.62 51.61 37.84 51.45 38.07 51.28 38.29 64 65 52.59 38,21 52.42 38.44 52.25 38.66 52.08 38.89 65 66 53.40 38.79 53.23 39.03 53.05 39.26 52.88 39.49 66 67 54.20 39.38 54.03 39.62 53.86 39.85 53.68 40.09 67 68 55.01 39.97 54.84 40.21 54.66 40.45 54.49 40.69 68 69 55.82 40.56 55.64 40.80 55.47 41.04 55.29 41.28 69 70 56.63 41.14 56.45 41.39 56.27 41.64 56.09 41.88 70 71 57.44 41.73 57.26 41.98 57.07 42.23 56.89 42.48 71 72 58.25 42.32 58.06 42.57 57.88 42.83 57.69 43.08 72 73 59.06 42.91 58.87 43.17 58.68 43.42 58.49 43.68 73 74 59.87 43.50j 59.68 43.76 59.49 44.02 59.29 44.28 74 75 60.68 44.08 60.48 44.35 60.29 44.61 60.09 44.87 75 76 61.49 44.67 61.29 44.94 61.09 45.21 60.90 45.47 76 77 62 . 29 45.26 62.10 45.53 61.90 45.80 61.70 46.07 77 78 63.10 45.85 62.90 46.12 62.70 46.40 62.50 46.67 78 79 63.91 46.43 63.71 46.71 63.50 46.99 63.30 47.27 79 80 64.72 47.02! 64.52 47.30 64.31 47.59 64.10 47.87 80 81 65.53 47.61 65.32 47.90 65.11 48.18 64.90 48.46 81 82 66.34 48.20 66.13 48.49 65.92 48.78 65.70 49-06 82 83 67.15 48.79 66.93 49.08 66.72 49.37 66.50 49.66 83 84 67.96 49.37 67.74 49.67 67.52 49.97 67.31 50.26 84 85 68.77 49.96 68.55 50.26 68.33 50.56 68.11 50.86 85 86 69.58 50.55 69.35 50.85 69.13 51.15 68.91 51.46 86 87 70.38 51.14 70.16 51.44 69.94 51.75 69.71 52.05 87 88 71.19 51.73 70.97 52.04 70.74 52.34 70.51 52.65 88 89 72.00 52.31 71.77 52.63 71.54 52.94 71.31 53.25 89 90 72.81 52.90 72.58 53.22 72.35 53.53 72.11 53.85 90 91 73.62 53.49! 73.39 53.81 73.15 54.13 72.91 54.45 91 92 174.43 54.08 74.19 54.40 73.95 54.72 73.72 55.05 92 93 i 75.24 54.66 75.00 54.99 74.76 55.32 74.52 55.64 93 94 76.05 55.25 75.81 55.58 75.56 55.91 75.32 50.24 94 95 76.86 55.84 76.61 56.17 76.37' 56.51 76.12 56.84 95 96 77.67 56.43 77.42 56.77 77.17 57.10 76.92 57.44 96 97 78.47 57.02 78.23 57.36 77.97 57.70 77.72 58.04 97 98 79.28 57.60 79.03 57.95 78.78 58.29 78.52 58.64 98 99 80.09 58.19 79.84 58.54 79.58 58.89 79.32 59.23 ,99 100 ,80.90 58.78 80.64 59.13 80.39 59.48 80.13 59.83 100 1 Dep. Lat. Dep. Lat. Dep. Lat. D*. Lat. od 5 54 Deg. 53| Deg. 53i Deg. 53* Deg. - 76 TRAVERSE TABLE. o 37 Deg. 37* Deg. 37* Deg. 37| Deg. C en" ^ 3 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. f> S o 1 0.80 0.601 6.80 0.61 0.79 0.61 0.79 0.61 I 2 1.60 1.20 1.59 1.21 1.59 1.22 1.58 1.22 2 3 2.40 1.81 2.39 1.82 2.38 1.83 2.37 1.84 3 4 3.19 2.41 3.18 2.42 3.17 2.43 3.16 2.45 4 5 3.99 3.01 3.98 3.03 3.97 3.04 3.95 3.06 5 6 4.79 3.61 4.78 3.63 4.76 3.65 4.74 3.67 6 7 5.59 4.21 5.57 4.24 5.55 4.26 5.53 4.29 7 8 6.39 4.81 6.37 4.84 6.35 4.87 6.33 4.90 8 9 7.19 5.42 7.16 5.45 7.14 5.48 7.12 5.51 9 10 7.99 6.02 7.96 6.05 7.93 6.09 7.91 6.12 10 .11 8.78 6.62 8.76 6.66 8.73 6.70 8.70 6.73 11 12 9.58 7.22 9.55 7.26 9.52 7.31 9.49 7.35 12 13 10.38 7.82 10.35 7.87 10.31 7.91 10.28 7.96 13 14 11.18 8.43 11.14 8.47 11.11 8.52 11.07 8.57 14 15 11.98 9.03 11.94 9.08 11.90 9.13 11.86 9.18 15 16 12.78 9.63 12.74 9.68 12.69 9.74 12.65 9.80 16 17 13.58 10.23 13.53 10.29 13.49 10.35 13.44 10.41 17 18 14.38 10.83 14.33 10.90 14.28 10.96 14.23 11.02 18 19 15.17 11.43 15.12 11.50 15.07 11.57 15.02 11.63 19 20 15.97 12.04 15.92 12.11 15.87 12.48 15.81 12.24 20 21 16.77 12.64 16.72 12.71 16.66 12.78 16.60 12.80 21 22 17.57 13.24 17.51 13.32 17.45 13.39 17.40 13.47 22 OO 18.37 13.84 18.31 13.92 18.25 14.00 18.19 14.08 23 24 19.17 14.44 19.10 14.53 19.04 14.61 18.98 14.69 24 25 19.97 15.05 19.90 15.13 19.83 15.22 19.77 15.31 25 26 20.76 15.65 20.70 15.74 20.63 15.83 20.56 15.92 26 27 21.56 16.25 21.49 16.34 21.42 16.44 21.35 16.53 27 28 22.36 16.85 '22.29 16.95 22.21 17.05 22.14 17.14 28 29 23.16 17.45 23.08 17.55 23.01 17.65 22.93 17.75 29 30 23.96 18.05 23.88 18.16 23.80 18.26 23.72 18.37 30 31 24.76 18.66 24.68 18.76 24.59 18.87 24.51 18.98 31 32 25.56 19.26 25.47 19.37 25.39 19.48 25.30 19.59 32 33 26.35 19. 8G 26.27 19.97 26.18 20.09 26.09 20.20 33 34 27.15 20.46 27.06 20.58 26.97 20.70 26.88 20.82 34 35 27.95 21.06 27.86 21.19 27.77 21.31 27.67 21.43 35 36 28.75 21.67 28.66 21.79 28.56 21.92 28.46 22.04 36 37 29.55 22.27 29.45 22.40 29.35 22.52 29.26 22.65 37 38 30.35 22.87 30.25 23.00 30.15 23.13 30.05 23.26 38 39 31.15 23.47 31.04 23.61 30.94 23.74 30.84 23.88 39 40 31.95 24.07 31.84 24.21 31.73 24,35 31.63 24.49 40 41 32.74 24.67 32.64 24.82 32.53 24.96 32.42 25.10 41 42 33.54 25.28 33.43 25.42 33.32 25.57 33.21 25.71 4-2 43 34.34 25.88 34.23 26.03 34.11 26.18 34.00 26.33 43 44 35.14 2C.48 35.02 26.63 34.91 26.79 34.79 26.94 44 45 35.94 27.08 35.82 27.24 35.70 27.39 35.58 27.55 45 46 36.74 27.68 36.62 27.84 36.49 28.00 36.37 28.16 46 47 37.54 28.29 37.41 28.45 37.29 28.61 37.16 28.77 47 48 38.33 28.89 38.21 29.05 38.08 29.22 37.95 29.39 48 49 39.13 29.49 39.00 29.66 38.87 29.83 38.74 30.00 49 50 39.93 30.09 39.80 30.26 39.67 30.44 39.53 30.61 50 g> 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. o 1 53 Deg. 52| Deg. 52i Deg. 52* Deg. I TRAVERSE TABLE. 77 o f 37 Deg. 37* Deg. 37 i Deg. 37| Deg. C 5- ? p Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 5 P 51 40.73 30.69 40.60 30.87 40.46 31.05 40.33 31.22 51 52 41.53 31.29 41.39 31.48 41.25 31.66 41.12 31.84 52 53 42.33 31.90 42.19 32.08 42.05 32.26 41.91 32.45 53 54 43.13 32.50 42.98 32.69 42.84 32.87 42.70 33.06 54 55 43.92 33.10 43.78 33.29 43.63 33.48 43.49 33.67 55 56 44.72 33.70 44.58 33.90 44.43 34.09 44.28 34.28 56 57 45.52 34.30 45.37 34.50 45.22 34.70 45.07 34.90 57 58 46.32 34.91 46.17 35.11 46.01 35.31 45.86 35.51 58 59 47.12 35.51 46.96 35.71 46.81 35.92 46.65 36.12 59 60 47.92 36.11 47.76 36.32 47.60 36.53 47.44 36.73 60 61 48.72 36.71 48.56 36.92 48.39 37.13 48.23 37.35 61 62 49.52 37.31 49.35 37.53 49.19 37.74 49.02 37.96 62 63 50.31 37.91 50.15 38.13 49.98 38.35 49.81 38.57 63 64 51.11 38.52 50.94 38.74 50.77 38.96 50.60 39.18 64 65 51.91 39.12 51.74 39.34 51.57 39.57 51.39 39.79 65 66 52.71 39.72 52.54 39.95 52.36 40.18 52.19 40.41 66 67 53.51 40.32 53.33 40.55 53.15 40.79 52.98 41.02 67 68 54.31 40.92 54.13 41.16 53.95 41.40 53.77 41.63 68 69 55.11 41.53 54.92 41.77 54.74 42.00 54.56 42.24 69 70 55.90 42.13 55.72 42.37 55.53 42.61 55.35 42 86 70 71 56.70 42.73 56.52 42.98 56.33 43.22 56.14 43.47 71 72 57.50 43.33 57.31 43.58 57.12 43.83 56.93 44.08 72 73 58.30 43.93 58 . 1 1 44.19 57.91 44.44 57.72 44.69 73 74 59.10 44.53 58.90 44.79 58.71 45.05 58.51 45.30 74 75 59.90 45.141 59.70 45.40 59.50 45.66 59.30 45.92 75 76 60.70 45.74 60.50 46.00 60.29 46.27 60.09 46.53 76 77 61.49 46.34 61.29 46.61 61.09 46.87 60.88 47.14 77 78 62.29 46.94 62.09 47.21 61.88 47.48 61.67 47.75 78 79 63.09 47.54 62.88 47.82 62.67 48.09 62.46 48.37 79 80 63.89 48.15 63.68 48.42 63.47 48.70 63.20 48.98 80 81 64.69 48.75 64.48 49.03 64.26 49.31 64.05 49.59 81 82 65.49 49.35 65.27 49.63 65.05 49.92 64.84 50.20 82 83 66.29 49.95 66.07 50.24 6^.85 50.53 65.63 50.81 83 84 67.09 50.55 66.86 50.84 66.64 51.14 66.42 51.43 84 85 67.88 51.15 67.66 51.45 67.43 51.74 67.21 52.04 85 86 68.68 51.76 68.46 52.06 68.23 52.35 68.00 52.65 86 87 69.48 52.36 69.25 52.66 69.02 52.96 68.79 53.26 87 88 70.28 52.96 70.05 53.27 69.82 53.57 69.58 53.88 88 89 71.08 53.56 70.84 53.87 70.61 54.18 70.37 54.49 89 90 71.88 54.16 71.64 54.48 71.40 54.79 71.16 55.10 90 91 72.68 54.77 72.44 55.08 72.20 55.40 71.95 55. 71 91 92 73.47 55.37 73.23 55.69 72.99 56.01 72.74 56.32 92 93 74.27 55.97 74.03 56.29 73.78 56.61 73.53 56.94 93 94 75.07 56.57 74.82 56.90 74.58 57.22 74.32 57.55 94 95 75.87 57.17 75.62 57.50 75.37 57.83 75.12 58.16 95 96 76.67 57.77 76.42 58.11 76.16 58.44 75.91 58.77 96 97 77.47 58.38 77.21 58.71 76.96 59.05 76.70 59.39 97 98 78.27 58,98 78.01 59.32 77.75 59.66 77.49 60.00 98 99 79.06 59.58 78.80 59.92 78.54 60.27 78.28 60.61 99 100 i 79. 86 60.18 79.60 60.53 79.34 60.88 79.07 61.22 100 i Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. | 3 5 Q 53 Deg. 52| Deg. 52* Deg. 52| Deg. 5 78 TRAVJ1RSE TABLE. .0 38 Deg. 38i Deg. 38i Deg. 381 Deg. O 5* E 55 go" P Lat. Dep. Lat. Dep. Lat. I Dpp. Lat. Dep. 3 P i 0.79 0.62 0.79 0.62 0.78 0.62 0.78 0.63 1 2 1.58 1.23 1.57 1.24 1.57 1.24 1.56 1.25 2 3 2.36 1.85 2.36 1.86 2.35 1.87 2.34 1.88 3 4 3.15 2.46 3.14 2.48 3.13 2.49 3.12 2.50 4 5 3.94 3.08 3.93 3.10 3.91 3.11 3.90 3.13 5 6 4.73 3.69 4.71 3.71 4.70 3.74 4.68 3.76 6 7 5.52 4.31 5.50 4.33 5.48 4.36 5.46 4.38 7 8 6.30 4.93 6.28 4.95 6.26 4.98 6.24 5.01 8 9 tf.09 5.54 7.07 5.57 7.04 5,60 7.02 5.63 9 10 7.88 6tl6 7.85 6.19 7.83 6.23 7.80 6.26 10 11 8.67 6.77 8.64 6.81 8.61 6.85 8.58 6.89 11 12 9.46 7.39 9.42 7.43 9.39 7.47 9.36 7.51 12 13 10.24 8.00 10.21 8.05 10.17 8.09 10.14 8.14 13 14 11.03 8.62 10.99 8.67 10.96 8.72 10.92 8.76 14 15 11.82 9.23 11.78 9.29 11.74 9.34 1 1 . 70 9.39 15 16 12.61 9.85 12.57 9.91 12.52 9.96 12.48 10.01 16 17 13.40 10.47 13.35 10.52 13.30 10.58 13.26 10.64 17 18 14.18 11.08 14.14 11.14 14.09 11.21 14.04 11127 18 19 14.97 11.70 14.92 11.76 14.87 11.83 14.82 11.89 19 20 15.76 12.31 15.71 12.38 15.65 12.45 15.60 12.52 20 21. 16.55 12.93 16.49 13.00 16.43 13.07 16.38 13.14 21 22 17.34 13.54 17.28 13.62 17.22 13.70 17.16 13.77 22 23 18.12 14.16 18.06 14.24 18.00 14.32 17.94 14.40 23 24 18.91 14.78 18.85 14.86 18.78 14.94 18.72 15.02 24 25 19.70 15.39 19.63 15.48 19.57 15.56 19.50 15.65 25 26 20.49 16.01 20.42 16.10 20.35 16.19 20.28 16.27 26 27 21.28 16.62 21.20 16.72 21.13 16.81 21.06 16.90 27 28 22.06 17.24 21.99 17.33 21.91 17.43 21.84 17.53 28 29 22.85 17.85 22.77 17.95 22.70 18.05 22.62 18.15 29 30 23.64 18.47 23.56 18.57 23.48 18.68 23.40 18.78 30 31 24.43 19.09 24.34 19.19 24.26 19.30 24.18 19.40 31 32 25.22 19.70 25.13 19.81 25.04 19.92 24.96 20.03 32 33 26.00 20.32 25.92 20.43 25.83 20.54 25.74 20.66 33 34 26.79 20.93 26.70 21.05 26.61 21.17 26.52 21.28 34 35 27.58 21.55 27.49 21.67 27.39 21.79 27.30 21.91 35 36 28.37 22.16 28.27 22 . 29 28.17 22.41 28.08 22.53 36 37 29.16 22.78 29.06 22.91 28.96 23.03 28.86 23.16 37 38 29.94 23.40 29.84 23 . 53 29.74 23.66 29.64 23.79 38 39 30.73 24.01 30.63 24.14 30.52 24.28 30.42 24.41 39 40 31.52 24.63 31.41 24.76 31.30 24.90 31.20 25.04 40 41 32.31 25.24 32.20 25.38 32.09 25 . 52 31.98 25.66 41 42 33.10 25.86 32.98 26.00 32.87 26.15 32.76 26.29 42 43 33.88 26.47 33.77 26.62 33.65 26.77 33.53 26.91 4-3 44 34.67 27.09 34.55 27.24 34.43 27.39 34.31 27.54 44 45 35.46 27.70 35.34 27.86 35.22 28.01 35.09 28.17 45 46 36.25 28.32 36.12 28.48 36.00 28.64 35.87 28.79 46 47 37.04 28.94 36.91 29.10 36.78 29.26 36.65 29.42 47 48 37.82 29.55 37.70 29.72 37.57 29.88 37.43 30.04 48 49 38.61 30.17 38.48 30.34 38.35 30.50 38.21 30.67 49 50 39.40 30.78 39.27 30.95 39.13 31.13 38.99 31.30 50 B O a Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. I "co 5 52 Deg. 51| Deg. 51i Deg. 51i Deg. CO Q TRAVERSE TABLE. 70 G 38 Deg. 38J Deg. 38i Deg. 38f Deg. O P Lat. Dep. L^at. Dep. Lat. Dep. Lat. Dep. 1 51 40.19 31.40 40.05 31.57 39.91 31.75 39.77 31.92 TT 52 40.98 32.01 40.84 32.19 40.70 32.37 40.55 32,55 52 53 41.76 32.63 41.62 32.81 41.48 32.99 41.33 33.17 53 54 42.55 33.25 42.41 33.43 42.26 33.62 42.11 33.80 54 55 43.34 33.86 43.19 34.05 43.04 34.24 42.89 34.43 55 56 44.13 34.48 43.98 34.67 43.83 34.86 43.67 35.05 56 57 44.92 35,09 44.76 35.29 4-4.61 35.48 44.45 35.68 57 58 45 . 70 3*^.71 45.55 35.91 45.39 36.11 45.23 36.30 58 59 46.49 36 .32 46.33 36.53 46.17 36 . 73 46.01 36.93 59 60 47.28 36.94 47*12 37.15 46.96 37.35 46.79 37.56 60 61 48.07 37.56 47.90 37.76 47.74 37.97 47.57 38.18 61 62 48.86 38.17 48.69 38.38 48.52 38.60 48.35 38.81 62 63 49.64 38.79 49.47 39.00 49.30 39.22 .49.13 39.43 63 64 50.43 39.40 50.26 39.62 50.09 39.84 49.91 40.06 64 65 51.22 40.02 51.05 40.24 50.87 40.46 50.69 40.68 65 66 52.01 40.63 51.83 40.86 51.65 41.09 51.47 41.31 66 67 52.80 41.25 52.62 41.48 52.43 41.71 52.25 41.94 67 68 53.58 41.86 53.40 42.10 53.22 42.33 53.03 42.56 68 69 54.37 42.48 54.19 42.72 54.00 42.95 53.81 43. 19 69 70 55.16 43.10 54.97 43.34 54.78 43.58 54.59 43.81 70 71 55.95 43.71 55.76 43.96 55.57 44.20 55.37 44.44 71 72 56.74 44.33 56.54 44.57 56.35 44.82 56.15 45.07 72 73 57.52 44.94 57.33 45.19 57.13 45.44 56.93 45.69 73 74 58.31 45.56 58.11 45.81 57.91 46.07 57.71 46.32 74 75 59.10 46.17 58.90 46.43 58.70 46.69 58.49 46.94 75 76 59.89 46.79 59.68 47.05 59.48 47,31 59.27 47.57 76 77 60.68 47.41 60.47 47.67 60.26 47,93 60.05 48.20 77 78 61.46 48.02 61.25 48.29 61.04 48.56 60.83 48.82 78 79 62.25 48.64 62.04 48.91 61.83 49.18 61.61 49.45 79 80 63.04 49.25 62.83 49.53 62.61 49.80 62.39 50.07 80 81 63.83 49.87 63.61 50.15 63.39 50.42 63.17 50.70 81 82 64.62 50.48 64.40 50.77 64.17 51.05 63.95 51.33 82 83 65.40 51.10 65.18 51.38 64.96 51.67 64.73 51.95 83 84 66.19 51.72 65.97 52.00 65.74 52.29 65.51 52.58 84 85 66.98 52.33 66.75 52.62 i 66.52 52.91 66.29 53.20 85 86 67.77 52.95 67.54 53.^4! 67.30 53.54 67.07 53.83 86 87 68.56 53.56 68.32 53.86 ! 68.09 54.16 67.85 54.46 87 88 69.34 54.18 69.11 54.48 i 68.87 54.78 68.63 55.08 88 89 70.13 54.79 69.89 55.10 ; 69.65 55.40 69.41 55.71 89 90 70.92 55.41 70.68 55 . 72 70.43 56.03 70.19 56.33 90 91 71.71 56.03 71.46 56.34 71.22 56.65 70.97 56.96 91 92 72.50 56.64 72.25 56.96 72.00 57.27 71.75 57.58 92 93 73.28 57.26 73.03 57.58 ; 72.78 57.89 72.53 58.21 93 94 74.07 57.87 73.82 58.19 73.57 58.52 73.31 58.84 94 95 74.86 58.49 74.61 58.81 74.35 59.14 74.09 59.46 95 96 75.65 59.10 75.39 59.43 75.13 59.76 74.87 60.09 96 97 76.44 59.72 76.18 60.05 75.91 60. 3S 75.65 60.71 97 98 77.22 60.33 76.96 60.67 ,76.70 61.01 76.43 61.34 98 99 78.01 60.95 77.75 61.29 77.48 61.63 77.21 61.97 99 100 78.80 61.57 78.53 61.91 J78.26 62.25 77.99 62.59 100 i Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. I a 52 Deg. \ 51J Deg. 51fDeg. 5U Deg. 1 5 1 TRAVERSE TABLE. o ? 39 Deg. 39* Deg. 39 Deg. 39| Deg. O ' CJ Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 1 0.78 0.63 0.77 0.63 0.77 0.64 0.77 0.64 ] 2 1.55 1.26 1.55 1.27 1.54 1.27 1.54 1.28 f 3 2.33 1.89 2.32 1.90 2.31 1.91 2.31 1,92 f. 4 3.11 2.52 3.10 2.53 3.09 2.54 3.08 2.56 i 5 3.89 3.15 3.87 3.16 3.86 3.18 3.84 3.20 5 6 4.66 3.78 4.65 3.80 4.63 3.82 4.61 3.84 6 7 5.44 4.41 5.42 4.43 5.40 4.45 5.38 4.48 7 8 6.22 5.03 6.20 5.06 6.17 5.09 6.1'5 5.12 8 9 6.99 5.66 6.97 5.69 6.94 5.72 6.92 5.75 9 10 7.77 6.29 7.74 6.33 7.72 6.36 7.69 6.39 10 11 8.55 6.92 8.52 6.96 8.49 7.00 8.46 7.03 11 12 9.33 7.55 9.29 7.59 9.26 7.63 9.23 7.67 12 13 10.10 8.18 10.07 8.23 10.03 8.27 9.99 8.31 13 14 10.88 8.81 10.84 8.86 10.80 8.91 10.76 8.95 14 15 11.66 9.44 11.62 9.49 11.57 9.54 11.53 9.59 15 16 12.43 10.07 12.39 10.12 12.35 10.18 12.30 10.23 16 17 13.21 10.70 13.16 10.76 13.12 10.81 13.07 10.87 17 18 13.99 11.33 13.94 11.39 13.89 11.45 13.84 11.51 18 19 14.77 11.96 14.71 12.02 14.66 12.09 14.61 12.15 19 20 15.54 12.59 15.49 12.65 15.43 12.72 15.38 12.79 20 21 16.32 13.22 16.26 13.29 16.20 13.36 16.15 13.43 21 22 17.10 13.84 17.04 13.92 16.98 13.99 16.91 14.07 22 23 17.87 14.47 17.81 14.55 17.75 14.63 17.68 14.71 23 24 18.65 15.10 18.59 15.18 18.52 15.27 18.45 15.35 24 25 19.43 15.73 19.36 15.82 19.29 15.90 19.22 15.99 25 28 20.21 16.36 20.13 16.45 20.06 16.54 19.99 16.63 26 27 20.98 16.99 20.91 17.08 20.83 17.17 20.76 17.26 27 29 21.76 17.62 21.68 17.72 21.61 17.81 21.53 17.90 28 29 22.54 18.25 22.46 18.35 22.38 18.45 22; 30 18.54 29 30 23.31 18.88 23.23 18.98 23.15 19.08 23.07 19.18 30 31 24.09 19.51 24.01 19.61 23.92 19.72 23.83 19.82 31 32 24.87 20.14 24.78 20.25 24.69 20.35 24.60 20.46 32 33 25.65 20.77 25.55 20.88 25.46 20.99 25.37 21.10 33 34 26.42 21.40 26.33 21.51 26.24 21.63 26.14 21.74 34 35 27.20 22.03 27.10 22.14 27.01 22.26 26.91 22 . 38 35 36 27.98 22.66 27.88 22.78 27.78 22.90 27.68 23.02 36 37 28.75 23.28 28.65 23.41 28.55 23.53 28.45 23.66 37 38 29.53 23.91 29.43 24.04 29.32 24.17 29.22 24.30 38 39 30.31 24.54 30.20 24.68 30.09 24.81 29.98 24.94 39 40 31.09 25.17 30.98 25.31 30.86 25.44 30 . 75 25.58 40 41 31.86 25,80 31.75 25.94 31.64 26.08 31.52 26.22 41 42 32.64 26.43 32.52 26.57 32.41 26.72 32.29 26.86 42 43 33.42 27.06 33.30 27.21 33.18 27.35 33.06 27.50 43 44 34.19 27.69 34.07 27.84 33.95 27.99 33.83 28.14 44 45 34.97 28.32 34.85 28.47 34.72 28.62 34.60 28.77 45 46 35.75 28.95 35.62 29.10 35.49 29.26 35.37 29.41 46 47 36.53 29.58 36.40 29.74 36.27 29.90 36.14 30.05 47 48 37.30 B021 37.17 30 . 37 37.04 30.53 36.90 30.69 48 49 38.08 30.84 37.95 31.00 37.81 31.17 37.67 31.33 49 50 38.86 31.47 38.72 31.64 38.58 31.80 38.44 31.97 50 8 c Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. to $ . Q 51 Deg. 50| Deg. 50i Dog. 50i Deg. s TRAVERSE TABLE. G 59 Deg. .39* Deg. 39* Deg. 39} Deg. g 1 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 3 8 51 39.63 32.10 39.49 32.27 39.35 32.44 39.21 32.61 51 52 40.41 32.72 40.27 32.90 40.12 33.08 39.98 33.25 52 53 41.19 33.35 41.04 33.53 40.90 33.71 40.75 33.89 53 54 41.97 33.98 41.82 34.17 41.67 34.35 41.52 34.53 54 60 42.74 34.61 42.59 34.80 42.44 34.98 42.29 35.17 55 56 43.52 35.24 43.37 35.43 43.21 35.62 43.06 35.81 56 57 44.30 35.87 44.14 36.06 43.98 36.26 43.82 36.45 57 58 45.07 36.50 44.91 36.70 44.75 36.89 44.59 37.09 58 59 45.85 37.13 45.69 P7.33 45.53 37.53 45.36 37.73 59 60 46.63 37.76 46.46 37.96 46.30 38.16 46.13 38.37 60 61 47.41 38.39 47.24 38.60 47.07 38.80 46.90 39.01 61 62 48.18 39.02 48.01 39.23 47.84 39.44 47.67 39.65 62 63 48.96 39.65 48.79 39.86 48.61 40.07 48.44 40.28 63 64 49.74 40.28 49.56 40.49 49.38 40.71 49.21 40.92 64 65 50.51 40.91 50.34 ,41.13 50.16 41.35 49.97 41.56 65 66 51.29 41.54 51.11 41.76 50.93 41.98 50.74 42.20 66 67 52.07 42. re 51.88 42.39 51.70 42.62 51.51 42.84 67 68 52.85 42.79 52.66 43.02 52.47 43.25 52.28 43.48 68 69 53.52 43.42 53.43 43.66 53.24 43.89 53.05 44.12 69 70 54.40 44.05 54.21 44.29 54.01 44.53 53.82 44.76 70 71 55.18 44.68 54.98 44.92 54.79 45.16 54.59 45.40 71 72 55.95 45.31 55.76 45.55 55.56 45.80 55.36 46.04 72 73 56.73 45.94 56.53 46.19 56.33 46.43 56.13 46.68 73 74 57.51 46.57 57.31 46.82 57.10 47.07 56.89 47.32 74 75 58.29 47.20 58.08 47.45 57.87 47.71 57.66 47.96 75 76 59.06 47.83 58.85 48.09 58.64 48.34 58.43 48.60 76 77 59.84 48.46 59.63 48.72 59.42 48.98 59.20 49.24 77 78 60.62 49.09 60.40 49.35 60.19 49.61 59.97 49.88 78 79 61.39 49.72 61.18 49.98 60.96 50.25 60.74 50.52 79 80 62.17 50.35 61.95 50.62 61.73 50.89 61.51 51.16 80 81 62.95 50.97 62.73 51.25 62.50 51.52 62.28 51.79 81 82 63.73 51.60 63.50 51.88 63.27 52.16 63.04 52.43 82 83 64.50 52.23 64.27 52.51 64.04 52.79 63.81 53.07 83 84 65.28 52.86 65.05 53.15 64.82 53.43 64.58 53.71 84 85 66.06 53.49 65.82 53.78 65.59 54.07 65.35 54.35 85 86 66.83 54.12 66.60 54.41 66.36 54.70 66.12 54.99 86 87 67.61 54.75 er.37 55.05 67.13 55.34 66.89 55.63 87 88 68.39 55.38 68.15 55.68 67.90 55.97 67.66 56.27 88 89 69.17 56.01 68.92 56.32 68.67 56.61 68.43 56.91 89 90 69.94 56.64 69.70 56.94 69.45 57.25 69.20 57.55 90 91 70.72 57.27 70.47 57.58 70.22 57.88 69.96 58.19 91 92 71.50 57.90 71.24 58.21 70.99 58.52 70.73 58.83 92 93 72.27 58.53 72.02 58.84 71.76 59.16 71.50 59.47 93 94 73.05 59.16 72.79 59.47 72.53 59.79 72.27 60.11 94 95 73.83 59.79 73.57 60.11 73.30 60.43 73.04 60.75 95 96 74.61 60.41 74.34 60.74 74.08 61.06 73.81 61.39 96 97 75.38 61.04 75.12 61.37 74.85 61.70 74.58 62.03 97 98 76.16 61.67 75.89 62.01 75.62 62.34 75.35 62.66 98 99 76.94 62.30 76.66 62.64 76.39 62.97 76.12 63.30 99 100 77.71 62.93 77.44 63.27 77.16 63.61 76.88 63.94 100 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. I 1 51 Deg. 50} Deg. 50i Deg. 50i Deg. 5 TRAVEftSE TABLE. o 40 Deg. 40} Deg. 40i Deg. 40| Deg. 5 B P Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. i 1 0.77 0.64 0.76 0,65 0.76 0.65 0.76 0.65 i 2 1.53 1.29 1.53 1.29 1.52 1.30 1.52 1.31 2 3 2.30 1.93 2.29 1.94 2.28 1.95 2.27 1.96 3 4 3\06 2.57 3.05 2.58 3.04 2.60 3.03 8.61 4 5 3.83 3.21 3.82 3.23 3.80 3.25 3.79 3.26 5 6 4.60 3.86 4.58 3.88 4.56 3.90 4.55 3.92 6 7 5.36 4.50 5.34 4.52 5.32 4.55 5.30 4.57 7 8 6.13 6.14 6.11 5.17 6.08 5.20 6.06 5.22 8 9 6.89 5.79 6.87 5.82 6.84 5.84 6.82 5.87 9 10 7.66 6.43 7.63 6.46 7.60 6.49 7.58 6.53 10 11 8.43 7.07 8.40 7.11 8.36 7.14 8.33 7.18 11 12 9.19 7.71 9.16 7.75 9.12 7.79 9.09 7.83 12 13 9.96 8.36 9.92 8.40 9.89 8.44 9.85 8.49 13 14 10.72 9.00 10.69 9.05 10.65 9.09 10.61 9.14 14 15 11.49 9.64 11.45 9.69 11.41 9.74 11.36 9.79 15 16 12.26 10.28 12.21 10.34 12.17 10.39 12.12 10.44 16 17 13.02 10.93 12.97 10.98 12.93 11.04 12.88 11.10 17 18 13.79 11.57 13.74 11.63 13.69 11.69 13.64 11.75 18 19 14.55 12.21 14.50 12.28 14.45 12.34 14.39 12.40 19 20 15.32 12.86 15.26 12.92 15.21 12.99 15.15 13.06 20 21 16.09 13.50 16.03 13.57 15.97 13.64 15.91 13.71 21 22 16.85 14.14 16.79 14.21 16.73 14.29 16.67 14.36 22 23 17.62 14.78 17.55 14.86 17.49 14.94 17.42 15.01 23 24 18.39 15.43 18.32 15.51 18.25 15.59 18.18 15,67 24 25 19.15 16.07 19.08 16.15 19.01 16.24 18.94 16.32 25 26 19.92 16.71 19.84 16.80 19.77 16.89 19.70 16.97 26 27 20.68 17.36 20.61 17.45 20.53 17.54 20.45 17.62 27 28 21.45 18.00 21.37 18.09 21.29 18.18 21.21 18.28 28 29 22.22 18.64 22.13 18.74 22.05 18.83 21.97 18.93 29 30 22.98 19.28 22.90 19.38 22.81 19.48 22.73 19.58 30 31 23.75 19.93 23.66 20.03 23.57 20.13 23.48 20.24 31 32 24.51 20.57 24.42 20.68 24.33 20.78 24.24 20.89 32 33 25.28 21.21 25.19 21.32 25.09 21.43 25.00 21.54 33 34 26.05 21.85 25.95 21.97 25.85 22.08 25.76 22.19 34 35 26.81 22.50 26.71 22.61 26.61 22.73 26.51 22.85 35 36 27.58 23.14 27.48 23.26 27.37 23.38 27.27 23.50 36 37 28.34 23.78 28.24 23.91 28.13 24.03 28.03 24.15 37 38 29.11 24.43 29.00 24.55 28.90 24.68 28.79 24.80 38 39 29.88 25.07 29.77 25 . 20 29.66 25.33 29.54 25.46 39 40 30.64 25.71 30.53 25.84 30.42 25.98 30,30 26.11 40 41 31.41 26.35 31.29 26.49 31.18 26.03 3i;oe 26.76 41 42 32.17 27.00 32.06 27.14 31.94 27.28 31.82 27.42 42 43 32.94 27.64 32.82 27.78 32.70 27.93 32.58 28.07 43 44 33.71 28.28 33.58 28.43 33.46 28.58 33.33 28.72 44 45 34.47 28.93 34.35 29.08 34.22 29.23 34.09 29.37 45 46 35.24 29.57 35.11 29.72 34.98 29.87 34.85 30.03 46 47 36.00 30.21 35.87 30.37 35.74 30.52 35.61 30.68 47 48 36.77 30.85 36.64 31.01 36.50 31.17 36.36 31.33 48 49 37.54 31.50 37.40 31.66 37.26 31.82 37.12 31.99 49 50 38.30 32.14 38.16 32.31 38.02 32.47 37.88 32.64 50 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. i 5 ^ 2 o 50 Deg. 49| Deg. 49i Deg. * 49i Deg. Q TRAVERSE TABLE. 03 Cj 40 Deg. 401 Deg. 404 Deg. 40| Deg. 5 3 O Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 51 39.07 32.78 38.92 32.95 38 . 78 33.12 38.64 33.29 51 52 39.83 33.42 |39.69 33.60 39.54 33.77 39.39 33.94 52 53 40.60 34.07 40.45 34.34 40.30 34.42 40.15 34.60 53 54 41.37 84.71 41.21 34.89 41.06 35.07 40.91 35.25 54 55 42.13 35.35 41.98 35 . 54 41.82 35.72 41.67 35.90 55 56 42 . 90 36.00 42.74 36.18 42.58 36.37 42.42 36.55 56 57 43 . 66 36.64 43 . 50 36.83 43.34 37.02 43.18 37.21 57 58 44.43 37.28 44.27 37.48 44.10 37.67 43.94 37.86 58 59 45.20 37.92 45.03 38.12 44.86 38.32 44.70 38.51 59 60 45.96 38.57 45 . 79 38.77 45.62 38.97 45.45 39.17 60 61 46.73 39.21 46.56 39.41 46.38 39.62 46.21 39.82 61 62 47.49 39.85 47.32 40.06 47.15 40.27 46.97 40.47 62 63 48.26 40.50 48.08 40.71 47.91 40.92 47.73 41.12 63 64 49.03 41.14 48.85 41.35 48.67 41.56 48.48 41.78 64 60 49 . 79 41.78 49.61 42.00 49.43 42.21 49.24 42.43 65 66 50.56 42.42 50.37 42.64 50.19 42.86 50.00 43.08 66 67 51.32 43.07 51.14 43.29 50.95 43.51 50.76' 43.73 67 63 52.09 43.71 51.90 43.94 51.71 44.16 51.51 44.39 68 69 52.86 44.35 52 . 66 44.58 52.47 44.81 52.27 45.04 69 70 53.62 45.00 53.43 45.23 53.23 45.46 53.03 45.69 70 71 54.39 45.64 54.19 45.87 53.99 46.11 53.79 46.35 71 72 55.16 46.28 54.95 46.52 54.75 46.76 54.54 47.00 72 73 55 . 92 46.92 55.72 47.17 55.51 47.41 55.30 47.65 73 T4 56.69 47.57 56.48 47.81 56.27 48.06 56.06 48.30 74 75 57.45 48.21 57.24 48.46: 57.03 48.71 ! 56.82 48.96 75 76 58.22 48.85 58.01 49.11 1 57.79 49.36 i 57.57 49.61 76 77 58 . 99 49.49 58.77 49.75 58.55 50.01 1 58 . 33 50.26 77 78 59 . 75 50.14 59,53 50.40 59.31 50.66 i 59.09 50.92 78 79 60.52 50.78 60.30 51.04 60.07 51.31 59.85 51.57 79 80 61.28 51.42 61.06 51.69 60.83 51.96 60.61 52.22 80 81 62.05 52.07 -61.82 52.341 61.59 52.61 61.36 52.87 81 82 62.82 52.71 62.59 52.98 62.35 53.25 62.12 53 . 53 82 83 63.58 53.35 63.35 53.63 63.11 53.90 62.88 54.18 83 84 64.35 53.99 64.11 54.27 63.87 54.55 63.64 54.83 84 85 65.11 54.64 64.87 54.92 64.63 55.20 64.39 55.48 85 86 65.88 55.28 65.64 55.57 65.39 55.85 65.15 56.14 86 87 66.65 55.92 66.40 56.21 66.16 56.50 65.91 56.79 87 88 67.41 56.57 67.16 56.86 66.92 57.15 66.67 57.44 88 89 68.18 57.21 67.93 57.50 67.68 57.80 67.42 58.10 89 90 68.94 57.85 68.69' 58.15 68.44 58.45 68.18 58 . 75 90 91 69.71 58.49 69.45 58.80 j 69.20 59.10 68.94 59.40 91 92 70.48 59.14 70.22 59.44 69.96 59.75 69.70 60.05 92 93 71.24 59 . 78 70.98 60.09; 70.72 60.40 70.45 60.71 93 94 72.01 60.42 71.74 60.74: 71.48 61.05 71.21 61.36 94 95 72.77 61.06 72.51 61.38 72.24 6,1.70 71.97 62.01 95 96 73.54 61.71 73.27 62.03 73.00 62.35! 72.73 62.66 96 97 74.31 62.35 74.03 62.67 73.76 63.00 73.48 63.32 97 98 75.07 62.99 74.80 63.32 74.52 63.65 74.24 63.97 98 99 75.84 63.64 75.56 63.97 75.28 64.30 75.00 64.62 99 100 76.60 64.28 76.32 64.61 76.04 64.94 75.76 65.28 100 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. s a Q 50 Deg. 49f Deg. 494 Deg. 49i Deg. P 84 TRAVERSE TABLE. 5" 41 Deg. 4U Deg. 41| Deg. 4,| D* p Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. o 0> 1 0.75 0.66 0.75 O.C6 0.75 0.66 0.75 0.67 J 2 1.51 1.31 1.50 1.32 1.50 1.33 1.49 1.33 2 3 2.26 1.97 2.26 1.98 2.25 1.99 2.24 2.00 3 4 3.02 2.62 3.01 2.64 3.00 2.65 2.98 2.66 4 5 3.77 3.28 3.76 3.30 3.74 3.31 3.73 3.33 5 6 4.53 3.94 4.51 3.96 4.49 3.98 4.48 4.00 6 7 5.28 4.59 5.26 4.62 5.24 4.64 5.22 4.66 7 8 6.04 5.25 6.01 5.27 5.99 5.30 5.97 5.33 8 9 6.79 5.90 6.77 5.93 6.74 5.96 6.71 5.99 9 10 7.55 6.56 7.52 6.59 7.49 6.63 7.46 6.66 10 11 8.30 7.22 8.27 7.25 8.24 7.29 8.21 7.32 11 12 9.06 7.87 9.02 7.91 8.99 7.95 8.95 7.99 12 13 9.81 8.53 9.77 8.57 9.74 8.61 9.70 8.66 13 14 10.57 9.18 10.53 9.23 10.49 9.28 10.44 9.32 14 15 11.32 9.84 11.28 9.89 11.23 9.94 11.19 9.99 15 16 12.08 10.50 12.03 10.55 11.98 10.60 11.94 10.65 16 17 12.83 11.15 12.78 11.21 12.73 11.26 12.68 11.32 17 18 13.58 11.81 13.53 11.87 13.48 11.93 13.43 11.99 18 19 14.34 12.47 14.28 12.53 14.23 12.59 14.18 12.65 19 20 15.09 13.12 15.04 13.19 14.98 13.25 14.92 13.32 20 21 15.85 13.78 15.79 13.85 15.73 13.91 15.67 13.98 21 22 16.60 14.43 16.54 14.51 16.48 14.58 16.41 14.65 22 23 17.36 15.09 17.29 15.16 17.23 15.24 17.16 15.32 23 24 18.11 15.75 18.04 15.82 17.97 15.90 17.91 15.98 24 25 18.87 16.40 18.80 16.48 18.72 16.57 18.65 16.65 25 26 19.62 17.06 19.55 17.14 19.47 17.23 19.40 17.31 26 27 20.38 17.71 20.30 17.80 20.22 17.89 20.14 17.98 27 28 21.13 18.37 21.05 18.46 20.97 18.55 20.89 18.64 28 29 21.89 19.03 21.80 19.12 21.72 19.22 21.64 19.31 29 30 22.64 19.68 22.56 19.78 22.47 19.88 22.38 19.98 30 31 23.40 120.34 23.31 20.44 23.22 20.54 23.13 20.64 31 32 24.15 120.99 24.06 21.10 23.97 21.20 23.87 21.31 32 33 24.91 21.65 24.81 21.76 24.72 21.87 24.62 21.97 33 34 25.66 22.31 25.56 22.42 25.46 22.53 25.37 22.64 34 35 26.41 22.96 26.31 23.08 26.21 23.19 26.11 23.31 35 36 27.17 23.62 27.07 23.74 26.96 23.85 26.86 23.97 36 37 27.92 24.27 27.82 24.40 27.71 24.52 27.60 24.64 37 38 28.68 24.93 28.57 25.06 28.46 25.18 28 . 35 25.30 38 39 29.43 25.59 29.32 25.71 29.21 25.84 29.10 25.97 39 40 30.19 26.24 30.07 26.37 29.96 26.50 29.84 26 . 64 40 41 30.94 26.90 30.83 27.03 30.71 27.17 30.59 27.30 41 42 31.70 27.55 31.58 27.69 31.46 27.83 31.33 27.97 42 43 32.45 28.21 32.33 28.35 32.21 28.49 32.08 28.63 43 44 33.21 28.87 33.08 29.01 32.95 29.16 32.83 29.30 44 45 33.96 29.52 33.83 29.67 33.70 29.82 33.57 29.97 45 46 34.72 30.18 34.58 30.33 34.45 30.48 34.32 30.63 46 47 35.47 30.83 35.34 30.99 35.20 31.14 35.06 31.30 47 48 36.23 31.49 36.09 31.65 35.95 31.81 35.81 31.96 48 49 36.98 32.15 36.84 32.31 36.70 32.47 36.56 32.63 49 50 37.74 32.80 37.59 32.97 37.45 33.13 37.30 33.29 50 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. cJ o e. 5 49 Deg. 48| Deg. 48 Deg. 484 Deg. n s TRAVERSE TABLE. 85 5 41 Deg. 4H Deg. 41* Deg. 41| Deg. s s g. I Lat. Dep. Lat. | Dep, Lat. Dep. Lat. Dep. i 51 38.49 33.46 38.34 33.63 38.20 33.79 38.05 33.96 51 52 39.24 34.12 39,10 34.29 38.95 34.46 38.79 34.63 S3 53 40.00 34.77 39.85 34.95 39.69 35.12 39.54 35.29 53 54 40.75 35.43 40.60 35.60 40.44 35.78 40.29 35.96 54 55 41.51 36.08 41.35 36.26 41.19 36.44 41.03 36.62 55 56 42.26 36.74 42.10 36.92 41.94 37.11 41.78 37.29 56 57 13.02 37.40 42.85 37.58 42.69 37.77 42.53 37.96 57 58 43.77 38.05 43.61 38.24 43.44 38.43 43.27 38.62 58 59 44.53 38.71 44.36 38.90 44.19 39.09 44.02 39.29 59 60 45.28 39.36 45.11 39.56 44.94 39.76 44.76 39.95 60 61 46.04 40.02 45.86 40.22 45 . 69 40.42 45.51 40.62 61 62 4f,.79 40.68 46.61 40.88 46.44 41.08 46.26 41.28 62 63 47.55 41.33 47.37 41.54 47.18 41.75 47.00 41.95 63 64 48.30 41.99 48.12 42.20 47.93 42.41 47.75 42.62 64 65 49.06 42.64 48.87 42.86 48.68 43.07 48.49 43.28 65 66 49.81 43.30 49.62 43.52 49.43 43.73 49.24 43.95 66 67 50.57 43.96 50.37 44.18 50.18 44.40 49.99 44.61 67 68 51.32 44.61 51.13 44.84 50 . 93 45.06 50.73 45.28 68 69 52.07 45.27 51.88 45.49 51.68 45.72 51.48 45.95 69 70 52.83 45.92 52.63 46.15 52.43 46.38 52.22 46.61 70 71 53.58 46.58 53.38 46.81 53.18 47.05 52.97 47.28 71 72 54.34 47.24 54.13 47.47 53.92 47.71 53.72 47.94 72 73 55.09 47.89 54.88 148.13 54.67 48.37 54.46 48.61 73 74 55.85 48.55 55.64 48.79 55.42 49.03 55.21 49.28 74 75 56.60 49.20 56.39 49.45 56.17 49.70 55.95 49.94 75 76 57.36 49.86 57.14 50.11 56.92 50.36 56.70 50.61 76 77 58.1! 50.52 57.89 50.77 57.67 51.02 57.45 51.27 77 78 58.87 51.17 58.64 51.43 58.42 51.68 58.19 51.94 78 79 59.62 51.83 59.40 52.09 59.17 52.35 58.94 52.60 79 80 60.38 52.48 60.15 52.75 59.92 53.01 59.68 53.27 80 81 61.13 53.14 60.90 53.41 60.67 53.67 60.43 53.94 81 82 61.89 53.80 61.65 54.07 61. 4J 54.33 61.18 54.60 82 83 62.64 54.45 62.40 54.73 62.16 55.00 61.92 55.27 83 84 63.40 55.11 63.15 55.38 62.91 55.66 62.67 55.93 84 85 64.15 55.76 63.91 56.04 63.66 56.32 63.41 56.60 85 86 64.90 56.42 64.66 56.70 64.41 56.99 64.16 57.27 86 87 65.66 57.08 65.41 57.36 65.16 57.65 64.91 57.93 87 88 66.41 57.73 66.16 58.02 65.91 58.31 65.65 58.60 88 89 67.17 58.39 66.91 58.68 66.66 58.97 66.40 59.26 89 90 67.92 59.05 67.67 59.34 67.41 59.64 67.15 59.93 90 91 68.68| 59.70 68.42 60.00 68.15 60.30 67.89 60.60 91 92 69.43 60.36 69.17 6-0.66 68.90 60.96 68.64 61.26 92 93 70.19 61.01 69.92 61.32 69.65 61.62 69.38 61.93 93 94 70.94 61.67 70.67 61.98 70.40 62.29 70.13 62.59 94 95 71.70 62.33 71.43 62.64 71.15 62.95 70.88 63.26 95 96 72.45 62.98 72.18 63.30 71.90 63.61 71.62 63.92 96 97 73.21 63.64 72.93 63.96 72.65 64.27 72.37 64.59 97 98 73.96 64.29 73.68 64.62 73.40 64.94 73.11 65.26 98 99 74.72 64.95 74.43 65.28 74.15 65.60 73.86 60. 92 99 100 75.47 65.61 75.18 65.93 74.90 66.26 74.61 66.59 100 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. o V a I 5 3 49 Deg. 48| Deg. 48 Deg. 48* Deg. P TBAVERSE TABLE. d 42 Deg. 424 Deg. 42i Deg. 42| Deg. O B* P 1 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. g 1 0.74 0.67 0.74 0.67 0.74 0.68 0.73 0.68 1 2 1.49 1.34 1.48 1.34 1.47 1.35 1.47 1.36 2 3 2.23 2.01 2.22 2.02 2.21 2.03 2.20 2.04 3 4 2.97 2.68 2.96 2.69 2.95 2.70 2.94 2.72 4 5 3.72 3.35 3.70 3.36 3.69 3.38 3.67 3.39 5 6 4.46 4.01 4.44 4.03 4.42 4.05 4.41 4.07 6 7 5.20 4.68 5.18 4.71 5.16 4.73 5.14 4.75 7 8 5.95 5.35 5.92 5.38 5.90 5.40 5.87 5.43 8 9 6.69 6.02 6.66 6.05 6.64 6.08 6.61 6.11 9 10 7.43 6.69 7.40 6.72 7.37 6.76 7.34 6.79 10 11 8.17 7.36 8.14 7.40 8.11 7.43 8.08 7.47 11 12 8.92 8.03 8.88 8.07 8.85 8.11 8.81 8.15 . 12 13 9.66 8.70 9.62 8.74 9.58 8.78 &.55 8.82 13 14 10.40 9.37 10.36 9.41 10.32 9.46 10.28 9.50 14 15 11.15 10.04 11.10 10.09 11.06 10.13 11.01 10.18 15 16 11.89 10.71 11.84 10.76 11.80 10.81 11.75 10.86 16 17 12.63 11.38 12.58 11.43 12.53 11.48 12.48 11.54 17 18 13.38 12.04 13.32 12.10 13.27 12.16 13.22 12.22 18 19 14.12 12.71 14.06 12.77 14.01 12.84 13.95 12.90 19 20 14.86 13.38 14.80 13.45 14.75 13.51 14.69 13.58 20 21 15.61 14.05 15.54 14.12 15.48 14.19 15.42 14.25 21 22 16.35 14.72 16.28 14.79 16.22 14.86 16.16 14.93 22 23 17.09 15.39 17.02 15.46 16.96 15.54 16.89 15.61 23 24 17.84 16.06 17.77 16.14 17.69 16.21 17.62 16.29 24 25 18.58 16.73 18.51 16.81 18.43 16.89 18.36 16.97 25 26 19.32 17.40 19.25 17.48 19.17 17.57 19.09 17.65 26 27 20.06 18.07 19.99 18.15 19.91 18.24 19.83 18.33 27 28 20.81 18.74 20.73 18.83 20.64 18.92 20 . 56 19.01 28 29 21.55 19.40 21.47 19.50 21.38 19.59 21.30 19.69 29 30 22.29 20.07 22.21 20.17 22.12 20.27 22.03 20.36 30 31 23.04 20.74 22.95 20.84 22.86 20.94 22.76 21.04 31 32 23.78 21.41 23.69 21.52 23.59 21.62 23.50 21.72 32 33 24.52 22.08 24.43 22.19 24.33 22.29 24.23 22.40 33 34 25 . 27 22.75 25.17 22.86 25.07 22.97 24.97 23.08 34 35 26.01 23.42 25.91 23.53 25.80 23 . 65 25.70 23.76 35 36 26.75 24.09 26 . 65 24.21 26.54 24.32 26.44 24.44 36 37 27 50 24.76 27.39 24.88 27 . 28 25.00 27.17 25.12 37 38 28.24 25 .43 28.13 2o.55 28.02 25.67 27.90 25.79 38 39 28.98 26.10 28.87 26.22 28.75 26.35 28 . 64 26.47 39 40 29.731 26.77 29.61 26.81* 29.49 27.02 29.37 27.15 40 41 30.47 27.43 30.35 27.57 30 . 23 27.70 30.11 27.83 41 31.21 28.10 31.09 28.24 30.97 28.37 30.84 28 . 5 1 42 43 31.96 28.77 31.83 28.91 31.70 29.05 31.58 29.19 43 44 32.70 29.44 32.57 29.58 32.44 29.73 32.31 29.87 44 45 33.44 30.11 33.31 30.26 33.18 30.40 33.04 30.55 45 46 34.18 30.78 34.05 30.93 33.91 31.08 33.78 31.22 46 47 34.93 31.45 34.79 31.60 34.65 31.75 34.51 31.90 47 48 35.67 32.12 35.53 32:27 35.39 32.43 35 . 25 32.58 48 49 36.41 32.79 36.27 32 . 95 36.13 33.10 35.98 33 . 26 49 50 37.16 33.46 37.01 33.62 36.86 33.78 36 . 72 33.94 50 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. c c c *> cd ce 3 48 Deg. 47| Deg. 47 i Deg. 474 Deg. 5 TRAVERSE TABLE. 87 D 42 Deg. 424 Deg. 424 Deg. 42} Deg. q O^ P Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. i 51 37.90 34.13 37.75 34.29 37.60 34.46 37.45 34.62 51 52 38.64 34.79 38.49 34.96 38.34 35.13 38.18 35.30 52 53 39.39 35.46 39.23 35.64 39.08 35.81 38.92 35.98 53 54 40.13 36.13 39.97 36.31 39.81 36.48 39.65 36.66 54 55 40.87 36.80 40.71 36.98 40.55 37.16 40.39 37.33 55 56 41.62 37.47 41.45 37.65 41.29 37.83 41.12 38.01 56 57 42.36 38.14 42.19 38.32 42.02 38.51 41.86 38.69 57 58 43.10 38.81 42.93 39.00 42.76 39.18 42.59 39.37 58 59 43.85 39.48 43.67 39.67 43.50 39.86 43.32 40.05 59 60 44.59 40.15 44.41 40.34 44.24 40.54 44.06 40.73 60 61 45.33 40.82 45.15 41.01 44.97 41.21 44.79 41.41 61 62 46.07 41.49 45.89 41.69 45.71 41.89 45.53 42.09 62 63 46.82 42.16 46.63 42.36 46.45 42.56 46.26 42.76 63 64 47.56 42.82 47.37 43.03 47.19 43.24 47.00 43.44 64 65 48.30 43.49 48.11 43.70 47.92 43.91 47.73 44.12 65 66 49.05 44.16 48.85 44.38 48.66 44.59 48.47 44.80 66 67 49.79 44.83 49.59 45.05 49.40 45.26 49.20 45.48 67 68 50.53 45.50 50.33 45.72 50.13 45.94 49.93 46.16 68 69 51.28 46.17 51.07 46.39 50.87 46.62 50.67 46 ..84 69 70 52.02 46.84 51.82 47.07 J51.61 47.29 51.40 47.52 70 71 52.76 47.51 52.56 47.74 |52.35 47.97 52.14 48.19 71 72 53.51 48.18 53.30 48.41 53.08 48.64 52.87 48.87 72 73 54.25 48.85 54.04 49.08 53.82 49.32 53.61 49.55 73 74 54.99 49.52 54.78 49.76 54.56 49.99 54.34 60.23 74 75 55.74 50.18 55.52 50.43 55.30 50.67 55.07 50.91 75 76 56.48 50.85 56.26 51.10 56.03 51.34 55.81 51.59 76 77 57.22 51.52 57.00 51.77 56.77 52.02 56.54 52.27 77 78 57.97 52.19 57.74 52.44 57.51 52.70 157.28 52.95 78 79 58.71 52.86 58.48 53.12 58.24 53.37 58.01 53.63 79 80 59.45 53.53 59.22 53.79 58.98 54.05 58.75 54.30 80 81 00.19 54.20 59.96 54.46 59.72 54.72 i 59.48 54.98 81 82 60.94 54.87 60.70 55.13 60.46 55.40 60.21 55.66 82 83 61.68 55.54 61.44 55.81 61.19 56.07 60.95 56.34 83 84 62.42 56.21 62.18 56.48 61.93 56.75 161.68 57.02 84 85 63.17 56.88 62.92 57.15 62.67 57.43 62.42 57.70 85 86 63.91 57.55 63.66 57.82 63.41 58.10 163.15 58.38 86 87 64.65 58.21 64.40 58.50 64.14 58.78 63.89 59.06 87 88 65.40 58.88 65.14 59.17 64.88 59.45 164.62 59.73 88 89 66.14 59.55 65.88 59.84 65.62 60.13 65.35 60.41 89 90 66.88 60.22 66.62 60.51 66.35 60.80 J66.09 61.09 90 91 67.63 60.89 67.36 61.19 67.09 61.48 ;66.82 61.77 91 92 68.37 61.56 6S.10 61.86 67.83 62.15 1 67.56 62.45 92 93 69.11 62.23 68.84 62.53 68.57 62.83 68.29 63.13 93 94 69.86 62.90 69.58 63.20 69.30 63.51 69.03 63. 8J 94 95 70.60 63.57 70.32 63.87 70.04 64.18 69.76 64.49 95 96 71.34 64.24 71.06 64.55 70.78 64.86 70.49 65.16 96 97 72.08 64.91 71.80 65.22 71.52 65.53 71.23 65.84 97 98 72.83 65.57 72.54 65.89 72.25 66.21 71.96 66.52 98 99 73.57 66.24 73.28 66.56 72.99 66.88 72.70 67.20 99 100 74.31 66.91 74.02 67.24 73.73 67.56 73.43 67.88 100 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 8 H i 00 5 48 Deg. 47} Deg. 474 Deg. 47* Deg. .1 TRAVERSE TABLE. o 43 Deg. 434 Deg. 43i Deg. 43J Deg. C 1' ft po 1 CO Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. p 1 0.73 0.68 0.73 0.69 0.73 0.69 0.72 0.69 1 2 1.46 1.36 1.46 1.37 1.45 1.38 1.44 1.38 2 3 2.19 2.05 2.19 2.06 2.18 2.07 2.17 2.07 3 4 2.93 2.73 2.91 2.74 2.90 2.75 2.89 2.77 4 5 3.66 3.41 3.64 3.43 3.63 3.44 3.61 3.46 5 6 4.39 4.09 4.37 4.11 4.35 4.13 4.33 4.15 6 7 6.12 4.77 5.10 4.80 5.08 4.82 5.06 4.84 7 8 5.85 5.46 5.83 5.48 5.80 5.51 5.78 5.53 8 9 6.58 6.14 6.56 6.17 6.53 6.20 6.50 6.22 9 10 7.31 6.82 7.28 6.85 7.25 6.88 7.22 6 92 10 11 8.04 7.50 8.01 7.54 7.98 7.57 7.95 7.01 11 12 8,78 8.18 8.74 8.22 8.70 8.26 8.67 8.30 12 13 9.51 8.87 9.47 8.91 9.43 8.95 9.39 8.99 13 14 10.24 9.55 10.20 9.59 10.16 9.64 10.11 9.68 14 15 10.97 10.23 10.93 10.28 10.88 10.33 10.84 10.37 15 16 11.70 10.91 11.65 10.96 11.61 11.01 11.56 11.06 16 17 12.43 11.59 12.38 11.65 12.33 11.70 12.28 11.76 17 18 13.16 12.38- 13.11 12.33 13.06 12.39 13.00 12.45 18 19 13.90 12.96 13.84 13.02 13.78 13.08 13.72 13.14 19 20 14.63 13.64 14.57 13.70 14.51 J3.77 14.45 13.83 20 21 15.36 14.32 15.30 14.39 15.23 14.46 15.17 14.52 21 22 16.09 15.00 13.02 15.07 15.96 15.14 15.89 15.21 22 23 16.82 15.69 16.75 15.76 16.68 15.83 16.61 15.90 23 24 17.55 16.37 17.48 16.44 17.41 16.52 17.34 16.60 24 2f> 18.28 17.05 18.21 17.13 18.13 17.21 18.06 17.29 25 26 19.02 17.73 18.94 17.81 18.86 17.90 18.78 17.98 26 27 19.75 18.41 19.67 18 50 19.59 18.59 19.50 18.67 27 28 20.48 19.10 20. 3y 19.19 20.31 19.27 20.23 19.36 28 29 21.21 19. 78 21.12 19.87 21.04 19.96 20.95 20.05 29 30 21.94 20.46 21.85 20.56 21.76 20.65 21.67 20.75 30 31 22.67 21.14 22.58 21.24 22.49 21.34 22.39 21.44 31 32 23.40 21.82 23.31 21. 9a 23.21 22.03 23.12 22.13 32 33 24.13 22.51 24.04 22.61 23.94 22.72 23.84 22.82 33 34 24.87 23.19 24.76 23.30 24.66 23.40 24.56 23.51 34 35 25.60 23.87 25.49 23.98 25.39 24.09 25 . 28 24.20 35 36 26.33 24.55 26.22 24 ..67 26.11 24.78 26.01 24.89 36 37 27.06 25.23 26.95 25.35 26.84 25.47 26.73 25. 5a 37 38 27.79 25.92 27.68 26.04 27.56 26.16 27.45 26.28 38 39 28.52 26.60 28.41 26.72 28.29 26.86 28.17 26.97 39 40 29.25 27.28 29.13 27.41 29.01 27.53 28.89 27.66 40 41 29.99 27.96 29.86 28.09 29.74 28.22 29 . 62 28.35 "41 42 30.72 28.64 30.59 28.78 30.47 28.91 30.34 29.04 42 43 31.45 29.33 31.32 29.46 31.19 29.60 31.06 29 . 74 43 44 32.18 30.01 32.05 30.15 31.92 30.29 31.78 30.43 44 45 32.91 30.69 32.78 30.83 32.64 30.98 32.51 31.12 45 46 33.64 31.37 33.51 31.52 33.37 31.66 33.23 31.81 46 47 34.37 32.05 34.23 32.20 34.09 32. 35 33.95 32 . 50 47 48 35.10 32.74 34.96 32.89 34.82 33.04 34.67 33.19 48 49 35.84 33.42 35.69 33.57 35.54 33.73 35.40 33.88 49 50 36 . 57 34.10 36.42 34.26 36.27 34.42 36.12 34.58 50 Dep. Lat. Dep. Lat. Dep. Lat. Dep.. Lat. 1 1 47 Deg. 46| Deg. 46J I>*g- 46i Deg. I b TB AVERSE TABLE. 89 D 43 Deg. 43| Deg. 43 Deg. 43| Deg. O P Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 3 , 51 37.30 34.78 37.15 34.94 36.99 35.11 36.84 35.27 51 52 38.03 35.46 37.88 35.63 ,37.72 35.79 37.56 35.96 52 53 38.76 36.15 38.60 36.31 38.44 36.48 38.29 36.65 53 54 39.49 36.83 39.33 37.00 39.17 37.17 39.01 37.34 54 55 40.22 37.51 40.06 37.69 39.90 37.86 39.73 38.03 55 56 40.96 38.19 40.79 38.37 40.62 38.55 40.45 38.72 56 57 41.69 38.87 41.52 39.06 41.35 39.24 41.17 39.42 57 58 42.42 39.56 42.25 39.74 42.07 39.92 41.90 40.11 58 59 43.15 40.24 42.97 40.43 42.80 40.61 42.62 40.80 59 60 43.88 40.92 43.70 41.11 43.52 41.30 43.34 41.49 60 61 44.61 41.60 44.43 41.80 44.25 41.99 44.06 42.18 61 62 45.34 42.28 45.16 42.48 44.97 42.68 44.79 42.87 62 63 46.08 42.97 45.89 |43.17 45.70 43.37 45.51 43.57 63 64 46.81 43.65 46.62 43.85 46.42 44.05 46.23 44.26 64 65 47.54 44.33 47.34 44.54 47.15 44.74 46.95 44.95 65 66 48.27 45.01 43.07 45.22 47.87 45.43 47.68 45.64 66 67 49.00 45.69 48.80 45.91 48.60 46.1:* 48.40 46.33 67 68 49.73 46.38 49.53 46.59 49.33 46.81 49.12 47.02 68 69 50.46 47.06 50.26 47.28 50.05 47.50 49.84 47.71 69 70 51.19 47.74 50.99 47.96 50.78 48.18 50.57 48.41 70 71 51.93 48.42 51.71 4S.65 51.50 48.87 51.29 49.10 71 72 52.66 49.10 52.44 49.33 52 . 23 49.56 52.01 49.79 72 73 53.39 49.79 53.17 50.02 52 . 95 50.25 52.73 50.48 73 74 54.12 50.47 53 . 90 50.70 53.68 50.94 53.45 51.17 74 75 54.85 51.15 54.63 51.39 54.40 51.63 54.18 51.86 75 76 55 . 58 51.83 55.36 52.07 55.13 52.31 54.90 52.55 76 77 56.31 52.51 56.08 52.76 55.85 53.00 55.62 53.25 77 78 57.05 53.20 56.81 53.44 56.58 53.69 56.34 53.94 78 79 57.78 53.88 57.54 54.13 57.30 54.38 57.07 54.63 79 80 58.51 54.56 58.27 54.81 58.03 55.07 57.79 55.32 80 81 59.24 55.24 59.00 55.50 58.76 55.76 58.51 56.01 81 82 59.97 55.92 59.73 56.18 59.48 56.45 59.23 56.70 82 83 60.70 56.61 60.45 56.87 60.21 57.13 59.96 57.40 83 84 61.43 57.29 61.18 57.56 60.93 57.82 60.68 58.09 84 85 62.17 57.97 61.91 58.24 61.66 58.51 61.40 58.76 85 86 62.90 58.65 62.64 58 . 93 62.38 59.20 62.12 59.47 86 87 63.63 59.33 63.37 59.61 63.11 59.89 62.85 60.16 87 88 64.36 60.02 64.10 60.30 63.83 60.58 63.57 60.85 88 89 65.09 60.70 64.82 60.98 64.56 61.26 64.29 61.54 89 90 65.82 61.38 65.55 61.67 65.28 61.95 65.01 62,24 90 91 66.55 62.06 66.28 62.35 66.01 62.64 65.74 62.93 91 92 67.28 62.74 67.01 60 . 04 66.73 63.33 66.46 63.62 92 93 68.02 63.43 67.74 63.72 67.46 64.02 67.18 64.31 93 94 68.75 64.11 68.47 64.41 68.19 64.71 67.90 65.00 94 95 69.48 64.79 69.20 65.09 68.91 65.39 68.62 65.69 95 96 70.21 65.47 69.92 65.78 69.64 66.08 69.35 66.39 96 97 70.94 66.15 70.65 66.46 70.36 66.77 70.07 67.08 97 98 71.67 66.84 71.37 67.15 71.09 67.46 70.79 67.77 98 99 72.40 67.52 72.11 67.83 71.81 68.15 71.51 68.46 99 100 73.14 68.20 72.84 68.52 72.54 68.84 72.24 69.15 100 8 c Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. c. e c 1 a cc $ 47 Deg. 46| Deg. 46 Deg. 46$ Deg. 5 TRAVERSE TABLE. g ST 44 Deg. 444 Deg. 44 Deg. 44| Deg. 45 Deg. G B' P 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 3 8 1 0.72 0.69 0.73 0.70 0.71 0.70 0.71 0.71 0.71 ~OT71 i 2 1.44 1.39 1.43 1.40 1.43 1.40 1.42 1.41 1.41 1.41 2 3 2.16 2.08 2.15 2.09 2.14 2.10 2.13 2.11 2.12 2.12 3 4 2.88 2.78 2.87 2.79 2.85 2.80 2.84 2.82 2.83 2.83 4 5 3.60 3.47 3.58 3.49 3.5? 3.50 3.55 3.52 3.54 3.54 5 6 4.32 4.17 4.30 4.19 4.28 4.21 4.26 4.22 4.24 4.24 6 7 5.04 4.86 5.01 4.88 4.99 4.91 4.97 4.93 4.95 4.95 7 8 5.75 5.56 5.73 5.58 5.71 5.61 5.68 5.63 5.66 5.66 8 9 6.47 6.25 6.45 6.28 6.42 6.31 6.39 6.34 6.36 6.36 9 10 7.19 6.95 7.16 6.98 7.13 7.01 7.10 7.04 7.07 7.07 10 11 7.91 7.64 7.88 7.68 7.85 7.71 7.81 7.74 7.78 7.78 11 12 8.63 8.34 8.60 8.37 8.56 8.41 8.52 8.45 8.49 8.49 12 13 9.35 9.03 9.31 9.07 9.27 9.11 9.23 9.15 9.19 9.19 13 14 10.07 9.73 10.03 9.77 9.99 9.81 9.94 9.86 9.90 9.90 14 15 10.79 10.42 10.74 10.47 10.70 10.51 10.65 10.56 10.61 10.61 15 16 11.51 11.11 11.46 11.16 11.41 11.21 11.36 11.26 11.31 11.31 16 17 12.23 11.81 12.18 11.86 12.13 11.92 12.07 11.97 12.02 12.02 17 18 12.95 12.50 12.89 12.56 12.84 12.62 12.78 12.67 12.73 12.73 18 19 13.67 13.20 13.61 13.26 13.55 13.32 13.49 13.38 13.43 13.43 19 20 14.39 13.89 14.33 13.96 14.26 14.02 14.20 14.08 14.14 14.14 20 21 15.11 14.59 15.04 14.65 14.98 14.72 14.91 14.78 14.85 14.85 21 22 15.83 15.28 15.76 15.35 15.69 15.42 15.62 15.49 15.56 15.56 22 23 16.54 15.98 16.47 16.05 16.40 16.12 16.33 16.19 16.26 16.26 23 24 17.26 16.67 17.19 16.75 17.12 16.82 17.04 16.90 16.97 16.97 24 25 17.98 17.37 17.91 17.44 17.83 17.52 17.75 17.60 17.68 17.68 25 26 18.70 18.06 18.62 18.14 18.54 18.22 18.46 18.30 18.38 18.38 26 27 19.42 18.76 19.34 18.84 19.26 18.92 19.17 19.01 19.09 19.09 27 28 20.14 19.45 20.06 19.54 19.97 19.63 19.89 19.71 19.80 19.80 28 29 20.86 20.15 20.77 20.24 20.68 20.33 20.60 20.42 20.51 20.51 29 30 21.58 20.84 21.49 20.93 21.40 21.03 21.31 21.12 21.21 21.21 30 31 22.30 21.53 22.21 21.63 22.11 21.73 22.02 21.82 21.92 21.92S31 32 23.02 22.23 22.92 22.33 22.82 22.43 22.73 22.53 22.63 22.63 32 33 23.74 22.92 23.64 23.03 23.54 23.13 23.44 23.23 23.33 23.33 33 34 24.46 23.62 24.35 23.72 24.25 23.83 24.15 23.94 24.04 24.04 34 3525.18 24.31 25.07 24.42 24.96 24.53 24.86 24.64 24.75 24.7535 36125.90 25.01 25.79 25.12 25 . 68 25 . 23 |25.57 25.34 25.46 25.46136 37 26.62 25.70 26.50 25.82 26.39 25.93 26.28 26.05 26.16 26.16 37 38 27.33 26.40 27.22 26.52 27.10 26.63 |26.99 26.75 26.87 26.87 38 39 28.05 27.09 27.94 27.21 27.82 27.34 ,27.70 27.46 27.58 27.58 39 40 28.77 27.79 28.65 27.91 28 . 53 28.04 ,28.41 28.16 28.28 28.28 40 41 29.49 28.48 29.37 28.61 29.24 28.74 29.12 28.86 28.99 28.99 41 42 30.21 29.18 30.08 29.31 29.96 29.44 29.83 29.57 29.70 29.70 42 43 30.93 29.87 30.80 30.00 30.67 30.14 30.54 30.27 30.41 30.41 43 44 31.65 30.56 31.52 30.70 31.38 30.84 31.25 30.98 31.11 31.11 44 45 32.37 31.26 32.23 31.40 32.10 31.54 31.96 31.68 31.82 31.82 45 46 33.09 31.95 32.95 32.10 32.81 32.24 32.67 32.38 32.53 32.5346 47 33.81 32.65 33.67 32.80 33.52 32.94 33.38 33.09 33.23 33.23 47 48 34.53 33.34 34.38 33.49 34.24 33.64 34.09 33.79 33.94 33.94 48 49 35 . 25 34.04 35.10 34.19 34.95 34.34 34.80 34.50 34.65 34.65 49 50 35.97 34.73 35.82 34.89 35.66 35.05 35.51 35.20 35.36 35.36 50 I Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. I OB Q 46 Deg. 45| Deg. 45 Deg. 45| Deg. 45 Deg. d "02 Q TRAVERSE TABLE. 9i y 44 Deg. ST 444 Deg. 44i Deg. 44| Deg. 45 Deg. D 1' Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 3 o CD 51 36.69 35.43 36.53 35.59 36.3835.75 36.22 35.90:36.06 36.06 51 52 37.41 36.12 37.25 36.29 37.09 36.45 36.93 36.61 36.77 36.77 52 5333.12 36.82 37.96 36.98 37.8037.15 37.64 37.31 37.48 37.48 53 54 38.84 37.51 38.68 37.68 38.5237.85 38.35 38.02 38.18 38.18 54 5539.56 38.21 39.40 38.38 39.2338.55 39.06 38.72 38.89 38.89 55 56 40 . 28 38.90 40.11 39.08 39.94'39.25 39.77 39.42 39.60 39.60 56 5741.0039.60 40.83 39.77 40.6639.95 40.48 40.13 40.31 40.31 57 58,11.72 40.29 41.55 40.47 41.3740.65 41.19 40.83 41.01 41.01 58 5942.44 40.98 42.26 41.17 42.0841.35 41.90 41.54 41.72 41.72 59 6043.16 41.68 42.98 41.87 42.7942.05 42.61 42.24 42.43 42.43 60 61 43.8842.37 43.69 42.57 43 51 42.76 43.32 42.94J43.13 43.13 61 62 44.6043.07 44.41 43.26 44 22 43.46 44.03 43.65 43.84 43.84 62 6345.32J43.76 45.13 43.96 44 9344.16 44.74 44.35 44.55 44.55 63 6446.04 44.46 45.84 44.66 45 6544.86 45.45 45.06 45.25 45.25 64 65146. 76 ! 45. 15 46.56 45.36 46.3645.56 46.16 45.76 45.96 45.96 65 66 47.48 45.85 47.28 46.05 47.07i46.26 46.87 46.46 46.67 46.67 66 8748.20 46.54 47.9946.75 47.79 46.96 47.58 47.17 47.38 47.38 67 6848.9? 47.24 48.71 47.45 48.50 47.66 48.29 47.87 48.08 48.08 68 6949.6347.93 49. 42148. 15 49.21 48.36 49.00 48.58 48.79 48.79 69 70J50.35 48.63 50. H 48.85' 49. 93 49.06 49.71 49.28 49.50 49.50 70 71i51.0749.32 50.86J49.54l50.64 49.761,50.42 49.98 50.20150.20 71 72 51.79 50.02 51.57 50.34851.85 50. 47 151.13 50. 69 50.91 50.91 72 7352.51 50.71 52.29 50.94 52.07 51.17 51.8451.39 51. 62151. 62 73 7453.23 51.40 53.01 51.64J52.78 51.87 ! , I 52.55 ! 52.10 52.33J52.33 74 7553.95 52.10 53.72 52.33j|53.49 52.57i53.26|52.80 53.0353.03 75 7654.67 52.79 54.44 53.03 54.21 53. 27)53. 97 53. 51 53.7453.74 76 77|55.39 53.49 55.16 53. 73.54.92 53.97 54.6854.21 54.45154.45 77 78)56.11 54.18 55.87 54.43J 55.63 54.67155.3954.91 55.1555.15 78 79 56.83 54.88 56.59 55.13 56.35 55.37 56.10 55.62 55.86 55.86 79 8057.55 55.57 57 . 30 55.82 57.06 56.07 56.81 56.32 56.5756.57 80 81 58.27 56.27 58.02 56.52 57.77 56 . 77 57.5257.03 57.2857.28 81 8258.99 56.96 58.74 57.22 58.49 57.47 58. 24|57.73 57.9857.98 82 8359.71 57.66 59.45 57.92 59.20 58.18 58.9558.43 58.6958.69 83 8160.42 58.35 60.17 58.61 59.91 58.88 59.66 59.14 59.4059.40 84 8561.14 59.05 60.89 59.31 60.63 59.58 60.37 59.84 60.1060.10 85 86'61.86 59 . 74 61.60 60.01 61.34 60.28 61.0860.55 60. 81160. 81 86 87162.53 60.44 62.32 60.71 62.05 60.98 61.79:61.25 61.5261.52 87 88163.30 61.13 63.03 61.41 62.77 61.68 62.50i61.95 62.2362.23 88 89:64.0261.82 63.7562.10 63.48 62.38 63.21 62.66 62.93 62.93 89 90.64.7462.52 64.4762.80 64.19 63.08 63.92 63. 36: ; 63. 64:63. 64 90 9L65.46 63.21 65.18 63.50 64.91 63.78 64.63 64.07 64.35 64.35 91 92 66.18 63.91 65.90 64.20 65.62 64.48 65.34 64.77 65.0565.05 92 93 66.90 64.60 66.62 64.89 66.33 65.18 66.0565.47 65.76 65.76 93 94:67.62 65.30 67.33 65.59 67.05 65.89 66.7666.1866.47:66.47 94 9o 68. 34 65. 99 63.0566.29! 67.76 66.59 67. 47)66. 88:67. 18i67. 18 95 9ri 69.0666.69 68.76 66.99 68.47 67.29 68. 18167.59 |67.88 67. 88 96 97;69.78 67.38 69.48 67.69 69.19 67.99 168.89 68.29, 68.59 68.59 97 93 70.50 68.08 70.20 68.38 69.90 68.69 69.60 68.99 69.30 69.30 98 99 71.21 68.77 70.91 69.08 70.61 69.39 70.31 69.70 70.00 70.00 99 100 71.93 69.47 71.63 69.78 71.33 70.09 71.02 70.40 70.71 70.71 100 | Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 6 c 7> 1 2 46 Deg. 45? Deg. 45 i Deg. 45* Deg. 45 Deg. ~ A TABLE OF NATURAL SIXES. JDeg. 1 Deg. 2 L)eg. 3 Deg. 4 Deg. .Nut. N. Co- "ssn V. Co- Nat. V Co- Nat. ] V. Co- Nat. V. Co- M Sine Sii.e Sine Sine Sine Sine Sine Sine Sine Sine M 00000 Unil. 01745J99985 03490 9939 05234 )9863 06976 J9756 t iO 1 00029 00000 01774 99984 03519 9938 05263:99861 07005 59754 i >9 2 3 00058 00087 00000 00000 01803 01832 99984 99983 03548 03577 9937 9936 05292 99860 0532ll99858 07034 07063 ^9752 { 99750 1 >8 37 4 00116 00000 01862 99983 03606 99935 05350*99857 07092 99748 . 36 5 0014.0 00000 01891 99982 03635 99934 05379 99855 07121 99746 , 35 6 00175 00000 01920 99982 03664 99933 05408199854 07150 99744 34 7 00204 00000 01949 99981 03693 99932 05437 99852 07179 99742 33 8 00233 00000 01978 99980 03723 99931 05466 99851 07208 99740 32 9 00262 00000 02007 99980 03752 99930 05495 99849 07237 99738 31 10 00291 00000 02036 99979, 03781 09929 05524 99847 07266 99736 11 0032099999 02065 99979 03810 99927 05553^99846 07295 99734 19 12 00349 99999 02094 99978 03839 99926 05582 99844 07324 99731 48 13 00378 99999 02123 99977 03868 99925 05611 99842 07353 99729 17 14 00407 99999 02152 99977 03897 49924 05640 99841 07382 99727 46 15 Gu436 99999 02181 99976 03926 J9923 05669 99839 07411 99725 45 16 00465 9999 ' 022 1 1 99976 03955 99922 05698 99838 07440 99723 44 17 00495 99999 02240 99975 03984 99921 05727 99836 07469 99721 43 18J00524 99999 02269 99974 04013 J9919 05756 99834 07498 99719 42 19 00553 99998 02298 99974 04042 99918 05785 99833 07527 99716 41 20 00582 99998 02327 99973 04071 99917 05814 99831 07556 99714 40 21 006 1 1 99998 02356 99972 04100 99916 05844 99829 07585 99712 39 22 00640 99998 02385 99972 04129 9991* 05873 99827 07614 99710 38 23 00669 99998 02414 99971 04159 99913 05902 99826 07643 99708 37 24 00698 99998 02443 99970 04188 99912 05931 99824 07672 99705 36 2500727 99997 02472 99969 04217 J9911 05960 99822 07701 99703 35 26t007f'6 99997 02501 99969 04246 99910 05989 9982 07730 99701 34 27(00785 99997 02530 99968 04275 99909 06018 99819 07759 99699 33 28i008l4 ! 99997 02560 9996*7 04304 99907 06047 99817 07788 99696 32 29 00844 99996 02589 99966 04333 99906 06076 99815 07817 99694 31 30 00873 99996 02618 99966 04362 J9905 06105 99813! 07846 99692 30 3L00902 99996 02647 99965| 04391 99L04 06134 99812 1 07875 99689 29 32! 00931 99996 02676 099 64 04420 99902 06163 99810 07904 99687 28 33100960 99995 02705 99963 04449 99901 06192 99808- 07933 99685 27 34100989 99995 02734 99963 04478 99900 06221 99806 07962 99683 26 35 !0 JO 18 999.95 02763 99962 04507 99898 06250 99804 07991 99680 25 36 01047 99995 02792 99961 04536 99897 06279 99803 08020 99678 2* 37 01076 99994 32821 99960 04565 99896 06308 99801 08049 99676 23 38 01105199994 02-! 50 99959 04594 99894 06337 99799 08078 99673 22 39 01131 99994 02879 99959 04623 99893 06366 99797 08107 99671 21 40 01164 99993 02908 09958 04653 99892 06395 99795 08136 99668 20 41 01193 42101222 99993 99993 02938 02967 99957 04682 99956:04711 99890 99889 06424 06453 99793 99792 .08165 08194 99666 99664 19 18 43 : 01251 99992 02996 9965 04740 99888 06482 99790 08223 99661 17 44101280 99992 03025 99954 104769 99886 06511 99788 08252 99659 16 45 01309 99991 03054 99953.0479S 99885 06540 99786 08281 99657 15 46iO 1338|99991 03083 09952 ': 04827 99883 06569 99784 08310 99654 14 4701367 99991 03112 09952 04856 99882 06598 99782 08339 99652 13 48iOl39 99990 03141 99951:04885 99881 06627 99780 08368 99649 12 49 01425 99990 03170 99950 04914 99879 06656 99778 08397 99647 11 50 01454 99989 03199 99949 S04943 99878 06685 99776 08426 99644 1 51 01483 99989 03228 99948 04972 ! 99876 06714 99774 08455 99642 52 01513 99989 03257 99947 05001 99875 06743 99772 08484 99639 53 01542 99988 03286 99946 05030 99873 06773.99770 08513 99637 54 01571 99988 03316 99945 05059 99872 i|06802 .99768 08542 99635 55 01600 99987 03345 99944 05088 99870 06831 99766 08571 99632 5f 01629 99987 03374 99943 0511799869 06860 99764 08600 99630 I 5701658 99986 03403 99942 05146 99867 06889 99762 9862S 99627 5801687 99986 03432 99941 0517f 99866 06918 99760 0865? 99625 * $ 59J01716 99985 03461 99940 0520 99864 06947 99758 08687 99622 M N. Co- Nat. N. Co- Nat. N. Co- Nat. N. Co- Nat. \. Co- Nat. M Sine Sine Sine Sine Sine Sine Sine Sine Sine Sine 89 Deff. 88 He?. 87 Dee. 86 Dejr. 85 Deg. A TABLE OF WATTTRAl S1WES. o L)eg. 7 Deg. I 8 Deg. 9 Deg. M N. 8. N. CS. N.S. N.CS. N.S. N. CS. N.S. N.CS. N.S. N.C8. M 08716 99619 10453 99452 12187 99255 13917 99027; 15643 98769 "0 1 08745 99617 10482 99449 12216 99251 13946 99023 15672 98764 9 2 08774 99614 10511 99446 12245 99248 13975 9P019: 15701 98760 8 3 0880399612 10540 99443 12274 99244J:i4004!990i5 ! 15730 98755 7 4 5 08831 '99609 1056999440 0886(>!99607l 10597 99437 12302 12331 99240 99237 1403399011 14061 99006 15758 15787 98751 98746 6 5 6 0888999604 10626 99434 12360199233 14090 99002i 15816 98741 4 7 08918'99602 8(0894799599 10655 10684 99431 99428 12389 99230 12418199226 141i9 14148 98998 98994 15845 15873 98737 98732 3 2 910897699596 10713 99424 12447199222 14177 98990 15902 98728 1 10 09005 99594 10742 99421 12476 99219 14205 98986 15931 98723 11 09034 99591 10771 99418 12504 99215 ,14234 9S9S2 15959 98718 9 12 09063 99588 10800 99415 12533 99211 14263 98978 15988 98714 48 13 09092 99586 10829 99412 12562 99208 14292 98973 16017 98709 47 1409121 99533 10858 99409 12591 99204 14320 98969 16046 98704 46 15 09150 99580 10887 99406 12620 99200 14349 98965 16074 98700 45 16 09179 99578 10916 99402 12649 99197 14378 98961 16103 98695 44 17 09208 99575 10945 99399 12678 99193 14407 98957 16132 98690 43 18 09237' 99572 10973 99396 12706 99189114436 98953 16160 9*6*6 42 19 09266199570 20!09295I99567 11002 11031 99393 99390 12735 12764 99186 99182 J14464 98948 16189 98681 14493 98944 1 ! 162 IS 28676 41 40 21 09324i99564 ' 11060 99386 12793 99178 14522 98940 16246 98671 39 22|09353!99562 11089 99383 1282^ 99175 14551 98936 16275 98667 38 23 '09382! 99559 11118 99380 12851 99171 14580 98931 16304 98662 37 24'0941 1)99556 25 09440:99553 ill 147 99377 11176199374 12880 12908 99167 99163 14608 14637 98927 98923 16333 98657 16361198652 36 35 26 09469 99551 ,11205 99370 12937 99160! 14666J98919 16390 98648 34 27 09498 J99548 11234 99367 12966 99156 14695198914 16419 9SR43 33 28 09527 99545:11263 99364 12995 99152 1472398910 16447198638 32 29!09556l99542 111291 99360 13024 99148 1475298906 16476 98633 31 30 09585 99540, 11320 99357 13053 99144 14781 98902 16505198629 30 31 09614 99537 1134999354 13081 99141 1481098897 16533 9?* 6 24 29 32 09642 99534 11378 99351 13110 99137 '14838 98893 16562 98619 28 33 0967] 99531 11407 99347 13139 99133 114867 98889 16591 '98614 27 34 09700 995281 1143699344 13168 99129 ; 14896 98884 16620 '98609 26 35 09729 99526 1146599341 1319799125 14925 98880 16648 98604 25 36 09758 99523 : 1149499337 13226 99122 1495498876 16677 98600 24 37 0978799520; 11523 99334113254 99118 '14982 98871 16706 98595 23 38 09816 99517 11552 99331113283 99114 15011198867 16734 ,98590 22 39 09845 995141 11580 99327 13312 99110I15040J98863 16763 '98585 21 40 09874 9951 ij 11609 99324 13341 991061 15069'98858 16792 98580 20 41 09903 995081 11638 99320 13370 99102115097198854 16820 98575 19 42 09932 995061 11667 99317 13399 99098 15126 98849 '16849 98570 18 43 09961 'J95U3 11696 99314 13427199094 15155:98845 1 16878 98565 17 44109990 99500 11725 99310j|13456i99091 i 15184|98841 16906 98561 16 45 10019 99497 11754 99307|| 13485 99087J 15212 98836 16935198556 15 46 10048 99494111783 99303 13514 990S3i 15241 98832 |16964|98551 14 47 48 10077 10106 99491 99488 ;11812 99300 '13543 99079! 15270198827 11840 992971' 13572199075! 15292 98823 1699298546 17021 98541 13 12 49 50 10135199485 10164199482 11869 99293 1 13600 99071 15327:98818 17050 98536 ,11898 99290 13629 99067 15356 ! 98814 17078 98531 11 10 51 10192 99479 11927 99286 13658199063 15385 98809|!17107 ; 98526 9 52 53 10221 10250 99476J 11956 99473 11985 99283 jl 3687 99279 13716 99059 99055 15414 98805 17136 90521 15442 1 98800| 17164 98516 8 7 54 10279199470 12014 99276 : 13744 99051 15471 98796 17193:98511 6 56 10308 99467 12043 99272 113773 99047 15500 98791 17222 98506 5 56 1033799464 12071 99269 13802 99043115529 98787 1 7250 9850 4 57 10366J 99461 12100 99265 13*31 99039:15557 98782 17279 98496 3 58 10395 99458 12129 99262': 13860 99035(15586 98778 17308 9849 2 59 104241 99455 :12158 99258; 1388S 99031115615 98773 17336 '98486 1 M N. CS. N. S. 1 N. CS. N.S. X.cs. \.S. N.CS. N.S. N. CS N.S. M 84 Deff. 83 Dee. 11 2 Deg. | 81 Deg. 80 Ucg. 04 A TABLE OP NATtHAL SINES. 10 Deg. I 1 1 Deg.. 12 Deg. 13 Deg. 14 Deg. M N.S. N. CS. I N.S. N. CS. N.S. N. CS. N.S. N. CS. N.S. N.CS. M 'o 17365 98481 ;19081 98163 20701 97815 22495 97437 24192 97030 60 1 17393 98476 ,19109 98167 20820 97809 22523 97430 24220 97023 59 2 17422 98471 19138 98152 20848 97803 22552 97424 24249 97015 58 3 17451 98466 19167 98146 20877 97797 22580 97417 24277J97008 57 4 17479 98461 :19195 98140 20905 97791 22608 97411 24305197001 56 5 17508 98465 119224 98135 20933 97784 22637 97404 24333 96994 55 6 17537 98450 19252 98129 20962 97778 22665 97398 24362 96987 54 7 17565 98445 19281 98124 20990 97772 22693 97391 24390 96930 53 8 17594 98440 19309 98118 21019 97766122722 97384 24418 96973 52 9 17623 98435 19338 98112 21047 97760 j 22750 97378 24446 96966 51 10 17651 98430 19366 98107 21076 97754 22778 97371 24474 96959 50 11 17680 98425 19395 98101 21104 97748 22807 97365 24503 96952 49 12 17708 98420 19423 98096 21132 97742 22835 97358 24531 96945 48 13 17737 98414 19452 98090 21161 97735 22863 97351 24559 96937 47 14 17766 98409 19481 98084 21189 97729 22892 97345 24587 96930 46 15 15794 98404 19509 98079 21218 97723 22920 97338 24615 96923 45 16 17823 98399 19538 98073 21246 97717 22948 97331 24644 ' 969 16 44 17 17852 98S&4 19566 98067 21275 97711 22977 97325 24672 96909 43 18 17880 98389 19595 98061 21303 97705 23005 97318 24700 96902 42 19 17909 98383 19623 98056 21331 97698 23033 97311 24728 96894 41 20 17937 y8378 19652 98050 21360 97692 23062 97304 24756 96887 40 21 17966 98373 19680 98044 21388 97686 23090 97298 24784 96880 39 22 17995 98368 19709 98039 21417 97680 23118 97291 24813 96873 38 23 18023 98362 19737 98033 21445 97673 23146 97284 24841 96866 37 24 18052 98357 19766 98027 21474 97667 23175 97278 24869 96858 36 25 18081 98352 19794 98021 21502 97661 23203)97271 24897 96851 35 26 18109 98347 19823 98016 21530 97655 2323 1 97264 24925 96844 34 27 18138 98341 19851 98010 21559 97648 23260 97257 24953 96837 33 28 18166 98336 19880 98004 21587 97642- 23288 97251 24982 96829 32 29 18195 98331 19908 97998 21616 97636 23316 97244 25010 96822 31 30 18224 98325 19937 97992 21644 97630 23345 97237 25038 96815 30 31 18252 98320 19965 979S7 21672 97623 23373 97230 25066 96807 29 32 18281 98315 19994 97981 21701 97617 23401 97223 25094 96800 28 33 18309 98310 20022 97975 21729 97611 23429 97217 25122 96793 27 34 18338 98304 20051 97969 21758 97604 23458 97210 25151 96786 26 35 18367 98299 20079 97963 21786 97598 23486 97203 25179 96778 25 iJti 18395 98294 20108 97958 21814 97592 23514 97196 25207 96771 24 37 18424 98288 20136 97952 21843 97585 23542 97189 25235 96764 23 38 18452 98283 20165 97946 21871 97579 23571 97182 25263 96756 22 39 18481 98277 20193 97940 21899 97573 23599 97176 25291 96749 21 40 18509 98272 20222 97934 21928 97566 23627 97169 25320 96742 20 41 18538 98267 20250 97928 21956 97560 23656J971C2 25348 96734 19 42 18567 98261 20279 97922 21985 97553 23684197155 25376 96727 18 43 18595 98256 20307 97916 22013 97547 23712 97148 25404 96719 17 44 18624 98250 20336 97910 22041 97541 23740 97141 25432 96712 16 45 18652 98245 20-364 97905 22070 97534 23769 97134 25460 96705 15 46 18681 98240 20393 97899 22098 97528 23797 97127 25488 96697 14 47 18710 98234 20421 97893 22126 97521 23825 97120 25516 96690 13 48 18738 98229 20450 97887 22155 97515 23853 97113 25545 96682 12 49 18767 98223 20478 97881 22183 97508 23882 97106 25573 96675 11 50 18795 98218 20507 97875 22212 97502 23910 97100 25601 96667 10 51 18824 98212 20535 97869 22240 97496 23938 97093 25629 96660 9 52 18852 98207 20563 97863 22268 97489 23966 97086 25657 96653 8 53 18881 98201 20592 97857 22297 97483 23995 97079 25685196645 7 54 18910 98196 20620 97851 22325 97476 24023 97072 25713 96638 6 55 18938 98190 20649 97845 22353 97470 24051 97065 25741 96630 5 56 18967 98185 20677 97839 22382 97463 24079 97058 25769 96623 4 57 18995 98179 20706; 97833 22410 97457 24108 97051 25798 96615 3 58 19024 98174 20734 97827 22438 97450 24136 97044 25826 96608 2 59 19052 98168 20763 97821 22467 97444 24164 97037 25854 9660P 1 M N. CS. | N. S. N.CS. N.S. N. CM. N.S. N.CS. N.S. N.CS. N.S. M 79 Deg. 78 Deg. 77 Deg. 76 Deg. | 75 Deg. A TABLE OF NATURAL SINES. 15 Dej/. 16 Deg. , J7 i>eg. 18 Deg. 19 Deg. M X. 6. N. CS. N. 3. N. CS. X. S. i\. CS. N.S. N.CS. N.S. N CS H ~0 25882 96593 27564 96126 29237 95630 30902 95106 32557 94552 60 1 25910 96585 27592 96118 29265 95622 30929 95097 325S4 94542 59 2 26938 96578 27620 96110' 29293 95613 30957 95088 32612 9453368 3 25966 96570 27648 96102 2932 1 95605 30985 95079J32639 94523 57 4 25994 96562 27676 96094 29348195596 31012 95070..32667 9451456 5 26022,96555 27704 96086 29376 95588 31040 9 506 ill 32694 94504 55 6 26050196547 27731 96078 29404(95579 31068 95052! i 32722 94495 54 7 26079 96540 27759 96070 29432,95571 31095 96043132749 94485 53 8 26107 96532 27787 96062 2946095562 31123 95033' 32777 94476152 9 26135 96524 27*15 96054 29487 95554 31151 95024 32804 94466 51 10 26163 96517 27843 96046 29515 95545 31178 95015 32832 94457 50 il :>6191 96509 2787-1 96037 29543 95536 31206 95006 32859 94447 49 1226219 96502 27899 96029 29571 95528 31233 94997 32887 94433 48 13 26247 96494 27927 96021 29599 95519 31261 94988 32914 94428 47 14 26275 96486 27955 96013 2962695511 31289 94979 32942 94418 46 15)26303 96479 27983 96005 29654 95502 31316 94970 32969 94409 45 16 26331 9647] 280 1 1 95997 29682 95493 3134494961 32997 94399 44 17 26359 96463 28039 95989 29710 95485 31372194952 33024 94390 43 18 26337 96456 28067 95981 29737 95476 31399 94943 33051 94380 42 19 26415 96448 1 28095 95972 29765 95467 31427 94933 33079 94370 41 20 26443 96440 28123 95964 29793j95459 31454 94924 33106 94361 40 21 2647 lj 96433 28150 95956 29821 95450 31482 94915 33134 94351 39 22 2650096425 28178 95948 29849 95441 31510 94906 33161 94342 38 23 26528 96417 28206 95940 29876 95433 31537 94897 33189 94332 37 24 2655696410 28234 95931 29904 95424 31565 94888 33216 94322 36 25 26584196402 28262 95923 29932 95415 31593 94878 33244 94313 35 262661296394 28290 95915 29960 95407 31620 94869 33271 94303 34 2726640 96386 28318 95907 29987 95398 31648 94860 33298 94293 33 28 26668 96379 28346 95898 30015 95389 31675 94851 33326 94284 32 29 26696 96371 28374 95890 30043 953SO 31703 94842 33353 94274 31 30 26724 96363 28402 95882 30071 95372 31730 94832 33381 94264 30 31 26752 96355 28429 95874 30098 95363 31758 94823 3340S 94254 29 32 26780 96347 28457 95865:30126 95354 31786 94814 33436 94245 28 33:26808 96340 28485 95857 30154 95345 31813 94805 33463 94235 27 34 26836 96332 28513 95849 30182 95337 31841 94795 33490 94225 26 35 26864 96324 28541 95841 30209 9532* 31868 94786 33518J94215 25 36 26892 96316 28569 95832130237 95319 31896 94777 33545 94206 24 37 26920 96308 28597 95824JI30265 95310 31923 94768 33573 94196 23 38 26948)96301 28625 95816 30292 95301 31951 94758 33600 94186 22 39 26976 96293 28652 95807 30320 95293 31979 94749 33627 94176 21 40 27004 96285 41 2703296277 28680 28708 95799 30348 95791 30376 95284 95275 32006 32034 94740 94730 33655 33682 94167 94157 20 19 42 27060:96269 28736 95782 30403 95266 32061 94721 33710 94147 18 43i27088i96261 28764 95774 30431 95257 32089 94712 33737 94137 17 44 27116 96253 28792 95766 30459 95248 32116 94702 33764 94127 16 45 27144 96246 28820 95757)30486 95240 32144 94693 33792 94118 15 4627172 96238 28847 95749 30514 95231 32171 94684 33819 94108 14 47 27200 96230 28875 95740: 30542 95222 32199 94674 33846 194098 13 48 27228)96222 28903 95732 i ; 30570 95213 32227 94665 33874 J94088 12 49 1 27256i96214 28931 95724ii30597 95204 32254 94656 33901 194078 11 50, 27284 1 96206 28959 95715 : 30625 95195 32282 94646 13392994068 10 51 27312 96198 28987 95707 \\ 30653 95186 32309 946371.3395694058 9 52 27340 96190 29015 95698 30680 95177 32337 94627 33983 94049 8 53 27368 96182 29042 95690; 30708 95168 32364 94618 34011 94039 7 5427396 5527424 96174 96166 29070 29098 95681 |!30736|95159ii32392 94609 95673 ! 30763!95150l 32419 194599 34038 94029 34065 94019 6 5 56/^7452 57.27480 96158 96150 29126}95664| 30791 95142IJ32447 29154 95656i'30819 95133 32474 94590 94580 34093 94009 34120 93999 4 3 58 27508 96142 29182 95647i|30846 95124 132502 94571 34147 93989 2 59i2753fi 96134 29209 95639! 30874 96116 32529 94561 34175 93979 I .M N. CS. N. S. N. CS. 1 N. S. j N. C8. N. S. IN.CS. N.S. N. CS. sfis 74 Deg. 73 Deg. 1 72 Deg. 1 71 Dei?, il 70 De ? . | 96 A TABLE OF NATUBAL SINES. 20 Ueg. 21 Deg. 22 Deg. 23 Deg. 24 Deg. M N. S. N. CS. N.S. N.CS. N.S. N.CS. N.S. N.CS. N.S. N.CS. M 34202 93969 35837 93358 37461 92718 39073 92050 40674 91355 60 1 34229 93959135864 93348 37488 92707 139100 92039 40700 91343 59 2 34257 93949 35891 93337 37515 92697 39127 92028 40727 91331 58 3 34284 93939 35918 93327 37542 92686 39153 92016 40753 91319 57 4 34311 93929 35945 93316 37569 92675 J39180 92005 40780 91307 56 5 34339 93919 35973 93306 37595 92664 !39207 91994 40806 91295 55 6 34366 93909 36000 93295 37622 92653 39234 91982 40833 91283 54 7 34393 93899 36027 93285 37649 92642 39260 91971 40860 91272 53 8 34421 93889 36054 93274 37676 92631 39287 91959 40886 91260 52 9 34448 93879 36081 93264 37703 92620 39314 91948 40913 91248 51 10 34475 j 93869 36108 93253 37730 92609 39341 91936 40939 91236 50 11 34503 93859 36135 93243 37757 92598 39367 91925 40966 91224 49 12 34530 93849 36162 93232 37784 92587 39394 91914 40992 91212 48 13 34557 93839 36190 93222 37811 92576 39421 91902 41019 91200 47 14 34584 93829 36217 93211 37838 92565 39448 91891 41045 91188 46 15 34612 93819 36244 93201 37865 92554 39474 91879 41072 91176 45 16 34639 93809 36271 93190 37892 92543 39501 91868 4~1098 91164 44 17 34666193799 36298 93180 37919 92532 39528 91856 41125 91152 43 18 34694193789 36325 93169 37946 92521 39555 91845 41151 91140 42 19 34721 93779 36352 93159 37973 92510 39581 91833 41178 91128 41 20 34748 93768 36379 93148 37999 92499 39608 91822 41204 91116 40 21 34775 93759 36406 93137 38026 92488 39635 91810 41231 91104 39 22 34803 93748 36434 93127 38053 92477 39661 91799 41257 91092 38 23 34830 93738 36461 93116 38080 92466 39688 91787 41284 91080 37 24 34857 93728 36488 93106 38107 92455 39715 91775 41310 91068 36 25 34884 93718 36515 93095 38134 92444 39741 91764' 41337 91056 35 26 34912 93708 36542 93084 38161 92432 39768 91752 41363 91044 34 27 34939 93698 36569 93074 38188 92421 39795 91741 41390 91032 33 28 34966 93688 36596 93063 38215 92410 39822 91729 41416 91020 32 29 34993 93677 36623 93052 38241 92399 39848 91718 41443 91008 31 30 35021 93667 36650 93042 38268 92388 39875 91706 41469 90996 30 31 35048 93657 36677 93031 38295 92377 39902 91694 41496 90984 29 32 35075 93647 36704 93020 38322 92366 39928 91683 41522 90972 28 33 35102 93637 36731 93010 38349 92355 39955 91671 41549 90960 27 34 35 35130 35157 93626 36758 93616 36785 92999 92988 38376 38403 92343 92332 39982 91660 40008 91648 41575 41602 90948 90936 26 25 36 35183 93606 36812 92978 38430 92321 40035 91636 41628 90924 24 37 35211 93596 36839 92967 38456 92310 40062 91625 41655 90911 23 38 35239 93585 36867 92956 38483 92299 40088 91613 41681 90899 22 39 35266 93575 36894 92945 38510 92287 40115 91601 41707 90887 21 40 35293 93565 36921 92935 38537 92276 40141 91590 41734 90875 20 41 35320 93555 36948 92924 38564 92265 40168 91578 41760 90863 19 42 35347 93544 36975 92913 38591 92254 40195 91566 41787 90851 18 43 35375 93534 37002 92902 38617 92243 40221 91555 41813 90839 17 44 35402 93524 37029 92892 38644 92231 40248 91543 41840 90826 16 45 35429 93514 37056 92881 38671 92220 40275 91531 41866 90814 15 46 35456 93503 37083 92870 38698 92209 40301 91519 41892 90802 14 47 35484 93493 37110 92859 38725 92198 40328 91508 41919 90790 13 48 35511 93483 37137 92849 38752 92186 40355 91496 41945 90778 12 49 35538 93472 37164 92838 38778 92175 40381 91484 41972 90766 11 50 35565 93462 37191 92827 38805 92164 40408 91472 41998 90753 10 51 35592 93452 37218 92816 38832 92152 40434 91461 42024 90741 9 52 35619 93441 37245 92805 38859 92141 40461 91449 42051 90729 8 53 35647 93431 37272 92794 38886 92130 40488 91437 42077 90717 7 54 35674 93420 37299 92784 38912 92119 40514 91425 42104 90704 6 55 35701 93410 37326 92773 38939 92107 40541 91414 42130 90692 5 56 35728 93400 37353 92762 38966 92096 40567 91402 42156 J90680 4 57 35755 93389 37380 92751 38993 92085 40594 91390 42183 90668 3 58 35782 93379 37407 92740 39020 92073 40621 91378 42209 90655 2 59 35810 93368 37434 92729 39046 92062 40647 91366 42235 90643 1 Mf N. OS. | N. S. N.CS. N.S". N. CS7 N.S. NTcs: N.S. N. CS. N.S. M 69 Deg. 68 Deg. 67 Deg. 66 Deg. 65 Deg, A TABLE OP NATURAL SINES. 25 Deg. 26 Deg. | 27 Leg. 2ii Deg. 29 Deg. M N.S. N. 6 46149 88715 47690 87896 49217 87050 31 30 43051 90259 44620 89493 46175 88701 47716 87882 49242 87036 30 31 430?7 90246 44646 39480 46201 88688 47741 87868 49268 87021 29 32 43104 90233 44672 39467 46226 88674 47767 87854 49293 87007 28 33 43130 90221 44698 39454 46252 88661 47793 87840 49318 86993 27 34 43156 90208 44724 89441 46278 88647 478 18 87826 49344 86978 26 3o 431GQ OfilQfi A 4. 760 (394*8 40304 88O34 47844 8/812 49369 86964 25 36 43209 90183 44776 89415 46330 88620 47869 87798 49394 86949 24 374323590171 44802 89402 J46355 88607 47895 87784 49419 86935 23 38i4326l!90158 44828 89389 1!46381 88593 47920 87770 49445 86921 22 39 43287 90146 44854 89376 46407 88580 47946 87756 49470 86906 21 4043313 90433 44880 89363 46433 88566 47971 87743 49495 86892 20 4 1 143340 90120 44906 893oO ,46458 88553 47997 87729 49521 86878 19 42 43366 901G8 44932 89337146484 88539 48022 87715 49546 86863 18 43143292 90095 44958 89324 46510 88526 48048 87701 49571 86849 17 44'43418i90082 44984 89311 46536 88512 48073 87687 49596 86834 16 45 43445 j 90070 45010 89298 46561 88499 48099 87673 49622 86820 15 46 43471 90057 45036 89285 46587 88485 48124 87659 49647 86805 14 47 43497 90045 45062 89272 46613 88472 48150 87645 49672 86791 13 48 43523 90032 45088 89259 46639 88458 48175 87631 49697J86777 12 40 43549 90019 45114 89245, 46664 88445 4820] 8761? 49723186762 11 50 43575 90007 45140 89232 146690 88431 48226 87603 49748 86748 10 51143602 89994 45166 89219 46716 88417 48252 87589 49773 86733 9 52143628 89981 45192 89206 46742 88404 48277 187575 49798 86719 8 53 43654 89968 45218 89193 46767 88390 48303 '87561 49824 86704 7 54|43680 89956 45243 89180 46793 88377 48328187546 4984986690 6 55143706 89943 45269 89l67i468l9J88363 48354187532 49874 86675 5 56|43733 89930 45295 89153 4684488349 48379 37518 49899 86661 4 57J43759 89918 45321 * 56040 82822 55 6 7 50151(86515 50176186501 51653 51678 85627 85612 5314084712 5316484697 54610 54635 83772 83756 56064 56088 82306 82790 54 53 8 50201 86486 51703 85597 53189 84681 54659 83740 56112 82773 52 9 50227 86471 51728 85582 53214 84666 54683 83724 56138 82757 51 10 50252)86457 51753 85567 53238 84650 54708 83708 56160 82741 50 11 5027786442 51778 8555 1 53263)84635 54732 83692 56184 82724 49 12 50302)86427 51803 85536 53288 84619 54756 83676 56208 8270S 48 13 50327 86413 51828 85521 53312184604 54781 83660 56232 82692 47 14 50352 86398 51852 85506 53337 84588 54805 33645 56256 82675 46 15 50377 86384 51877 85491 53361)84573 54829 83629 56280 82659 45 16 50403 86369 51902 85476 53386 84557 54854 83613 56305 82643 44 17 50428 86354 51927 85461 53411 84-542 54878 83597 56329 82626 43 18 50453 86340 51952 85446 53435,84526 54902 83581 56353182610 42 19 50478 86325 51977 85431 5346018451 1 54927 83565 56377J82593 41 20 50503 86310 52002 85416 53484)84495 54951 83549 5640182577 40 21 50528 i 86295 5202G 85401 53509 84480 54975 83533 56425 '82561 39 22 5055386281 52051 85385 53534 84464 54999 83517 56449 82544 38 23 50578 86266 52076 85370 53558 84448 55024 83501 56473 82528 37 24 50603 86251 52101 85355 53583 84433 55048 83485 56497 82511 36 25 26 50628 50654 86237 86222 52126 52151 85340 85325 53(M)7 53632 84417 84402 55072 55097 83469 83453 56521 82495 56545 82478 35 34 27 50679 86207 52175 85310 53656 84386 55121 83437 56569 82462 33 28 50704 86192 52200 85294 53631 84370 55145 83421 56593 82446 32 29 50729 86178 52225 85279 53705 S4355 5M69 83405 56617 82429 31 30 50754 86163 52250 85264 53730 84339 55194 83389 56641 82413 30 31 50779 86148 52275 85249 53754 84324 55218 83373 56665 82396 29 32 50804 86133 52299 85234 53779 84308 55242 83356 56689 82380 28 33 50829 86119 52324 85218 53804 84292 55266 83340 56713 82363 27 34 50854 86104 52349 85203 53828 84277 55291 83324 56736 82347 23 35 50879 86089 52374 aoiss oasc>3 S4Z01 OO310 833O8 567O 62330 25 36 50904 86074 52399 85173 53877 84245 55339 83292 56784 82314 24 37 50929 86059 52423 85157 53902 84230 55363 83276 56808 82297 23 38 50954 86045 52448 85142 53926 84214 55388 83260 568312)82281 22 39 50979 86030 52473 R5127 53951 84198 55412 83244 56856)82264 21 40 51004 86015 52498 85112 53975 84182 55436 83228 56880)82248 20 41 51029 86000 52522 85096 54000 84167 55460 83212 56904 82231 19 42 51054 85985 52547 85081 54024 84151 55484 83195 56928 82214 18 43 51079 85970 52572 85066 54049 84135 55509 83179 56952 82198 17 44 51104 85956 52597 85051 54073 84120 55533 83163 56976 82181 16 45 51129 85941 52621 85035 54097 84104 55557 83147 5700082165 15 46 51154 85926 52646 85020 54122 84088 5558 1 83131 57024182148 14 47 51179 859111152671 85005 54 1 40 84072 55605 83115 5704788132 13 48 49 51204 51229 85896)52696 85881 52720 84989 84974 54171 54195 84057 84041 55630 55654 83098 83082 5707 1)82115 57095^82098 12 11 50 51254 85866 52745 84959 54220 84025 55678 83066 57119*82082 10 51 51279 85851 52770 84943 54244 84009 55702 83050 5714382065 9 52 51304 85836 52794 84928 1:5426983994 55726 83034 571671820-8 8 53 51329 85821 52819 84913 i54293|83978 55750 83017 57191 82032 7 54 51354 85806 152844 84897 i54317 83962 55775 83001 57215^82015 6 55 51379 85792 52869 84882 i54342 83946 56799 82985 57238 81999 5 56 51404 85777 52893 84866 54366 83930 55823 82969 57262 81982 4 57 51429 85762 52918 84851 154391(83915 55847182953 57286181965 3 58 51454 85747 52943 84836 15441583399 5587i}82936 573 10 i8 1949 2 59 51479 85732 52967 84S20i; 54440 83883 j 55895 82920 57334 81932 1 M N. CS. N. S. N. CS. N. S. N. OS. N.S. N. CS. N.S. IN.CS. N.S. M 59 Deg. 58 Deg. ii 57 Dceg. 'M Deg. 39 Deg. M N.S. N. CS. N.S. jN.O. N.S. IN.CS. N.S. N. CS. N.S. N. CS. M 57358 81915 58779[80902 60182 79864 61566 7~880l 62932 77715 60 1 57381 81899 58802(80885 60205 79846 61589 78783 62955 ! 77696 59 2 57405 81882 58826 80867 60228 79829 61612 78765 62977177678 58 3 57429 4 57453 81865 81848 58849 58873 80850 80833 60251 60274 7G811 79793 61635 61658 78747 78729 63000 63022 77660 77641 57 56 5 57477 81832 58896 80816 60298 79776 61681 78711 63045 77623 55 6 57501 81815 58920 80799 60321 79758 61704 78694 63068 77605 54 7 57524 81798 58943 80782 60344 79741 61726 786761:63090 77586 53 8 57548 81782 58967 807C5 60367 79723 61749 78668 63113 77568 52 9 57572 81765 58990 80748 60390 79706 61772 78640 63135 77550 51 10 57596 81748 59014 80730 60414 79688 61795 78622 63158 77531 50 11 57619 81731 59037 80713 60137 79671 61818 78604 63180 77513 49 12 57643 81714 59061 80C96 60460 79G53 61841 78536 63203 77494 48 13157667 81698 59084 80679 69483 79635 61864 78568 63225 77475 47 1457691 81681 59108 80662 60506 79618 61887 78550 63248 77458 46 15157715 81664 59131 80S44 60529 79600 61909 78532 63271 77439 45 1657738 81647 59154 30627 60553 79583 61932 78514 63293 77421 44 17|57762 81631 59178 80610 6057G 79565 61955 78496 63316 77402 43 18J57786 81614 59201 80593 60599 79547 61978 78478 63338 77384 42 19 57810 81597 59225 80576 60622 79530 62001 78460 63361 77366 41 20 57833 81580 59248 80558 60645 79512 62024 78442 63383 77347 40 21 57857 81563 59272 80541 60668 79494 62046 78424 63406 77329 39 22 57*i496 77255 35 26 57976 81479 59389 80455 60784 79406 62160 73333 63518 77236 34 27 57999|81462 59412 80438 60807 79338 62183 78315 63540 77218 33 28 5802381445 59436 80420j 60830 79371 62206 78297 63563 77199 32 29*58047 814281159459 80403i 60853 79353 62229 78279 63585 77181 31 30158070 81412 |59482 80386. 60876 79235 62251 78261 63608 77162 30 31 58094 81395 59506 80368 60399 79318 62274 78243 63630 77144 29 3258118 81378 59529 80351 60922 79300 62297 78225 63653 77125 28 3358141 81361 59552 80334 60945 79282 62320 782061 63675 77107 27 34158165 81344 159576 80316 60968 79264 62342 78188 63698 77088 26 35(58189 81327 59599 80299 60991 79247 62365 78170 63720 77070 25 36 58212 81310 59622 80282 61015 79229 62388 78152 63742 77051 24 3758236 81293 59646 80264 61038 79211 82411 78134 33765 77033 23 38|58260 81276 59669 80247 61061 79193 62433 78116 63787 77014 22 39 58283 81259 159693 80230 j 61084 79176 62456 78098 63810 76996 21 40;58307 81242 159716 80212 61107 79158 62479 78079 63832 76977 20 41 58330 81225 59739 S0195 61130 79140 62502 78061 63854 76959 19 42 .->S3.->1. 81208 59763 80178 61153 79122 62524 78043 63877176940 18 43 58378 81191 59786 S0160 61176 79105 62547 78025 63899 76921 17 44 58401 81174 59809 80143 61199 79087 62570 78007 63922 76903 16 45 58425 81157 59832 80125 61222 79069 62592 77988 63944 76884 15 46 58449 81140j5!H58 80108 61245 79051 62615 77970 63966176866 14 47158472 81123 59879 80091 61268 79033 62638 77952 63989|76847 13 48 .53496 49 58519 81106 81089 59902 59926 80073 61291 80056 61314 79015 78998 62660 62683 77934 77916 64011 76823 64033 76810 12 11 50 58543 81072 81055 59949 80038 J61337 59972 8002 1,| 6 1360 78980 78962 62706 62728 77897 77879 6405676791 64078176772 10 9 52 5S590 53 5^614 81038 81021 5999580003 01 383 60019 799861J61406 78944 78926 62751 62774 77861 77843 6410076754 64123 76735 8 7 81004 60042 79968 61429 78908 62796 '77824 64145 76717 6 55|58661 80987 60065 j 79951 16 1451 78891 62819J77806 64167 76698 5 56)58684 80970 60089 79934 'G 1474 7S873 62842 77788 164190 76679 4 57 58708 80953 60112 79916 ,61497 7SS55 B28G4 77769(642 12.76661 3 58 58731 80936 60135 79S99 61520 73837 62887 77751 164234 76642 2 59 58755 80919 60158 79881161543 78819 62909 77733 1|64256 76623 1 M N. CS. N. S. N. CS. I N. S. J N. CS. I N. S. N. CSf N.8. RN.ca N.S. M 54 Deg. 53 Deg. 1 52 Deg. 51 Deg. (I 50 De*. 100 A TABLE OF NATUKAL SINES. 40 IVf . 41 Deg. 42 Ueg. i 43 Deg. 44 Deg. M N. S. N. CTJ N.S: N. CS. N.S. N. CS. N.S. N. CS. N.S. N. CS. M 64279 76604 65606 75471 66913 74314 68200 73135 69466 71934 60 1 64-301 76586 65628 75452 66935 74295 68221 73116 69487 71914 50 2 64323 76567 65650 75433 66956 74276 68242 73096 69508 71894 58 3 64346 76548 65672 75414 66978 74256 68264 73076 69529 71873 57 4 64368 76530 65694 75395 66999 74237 68285 73056 69549171853 56 5 64390 76511 65716 75375 67021 74217 68306 73036 69570 71833 55 6 64412 76492 5738 75356 67043 74198 68327 73016 69591 71813 54 7 64435 76473 65759 75337 67064 74178 68349 72996 69612 71792 53 8 64457 76455 65781 75318 67086 74159 68370 72976 69633 71772 52 9 64479 76436 65803 75299 67107 74139 68391 72957 69654 71752 51 10 64501 76417 65825 75280 67129 74120 68412 72937 69675 71732 50 11 64524 76398 65847 75261 67151 74100 68433 72917 69696 71711 49 12 64546 76380 65869 75241 67172 74080 68455 72897 69717 71691 48 13 04568 76361 65891 75222 67194 740G1 68476 72877 69737 71671 47 14 15 64590 76342 64612 76323 65913 65935 75203 75184 67215 67237 74041 74022 68497 68518 72857 72837 69758 69779 71650 71630 46 45 16 64635 76304 65956 75165 67258 74002 68539 72817 69800 71610 44 17 64657 76286 65978 -5146 67280 73983 68561 72797 69821 71590 43 18 54C79 ^6267 66000 75126 6730] 73963 68582 72777 69842 71569 42 19 64701 76248 66022 75107 67323 73944 68603 72757 69862 71549 41 20 54723 76229 66044 75088 67344 73924 68624 72737 69883 71529 40 21 64746 76210 66066 75069 67366 73904 68645 72717 69904 71508 39 22 54768 76192 66088 75050 67387 73885 68666 72697 69925 71488 38 23 64790 re 173 66109 75030 67409 73865 G'3688 72677 69946 71468 37 24 64812 76154 66131 75011 67430 73S46 68709 72657 69966 71447 36 25 64834 76135 66153 74992 67452 73826 68730 72637 69987 71427 35 26 64856 76116 66175 ~4973 67473 73806 68751 72617 70008 71407 34 27 64878 76097 66197 74953 67495 73787 68772 72597 70029 71386 33 28 64901 76078 66218 74934 7516 73767 68793 72577 70049 71366 32 29 64923 76059 66240 74915 7538 73747 68814 ^2557 70070 71345 31 30 64945 76041 66262 74896 7559 73728 8835 72537 70091 71325 30 31 64967 76022 66284 -4876 7580 737081 8857 72517 /0112 71305 29 32 64989 76003 66306 4857 67602 73688 8878 72497 70132 71284 28 33 65011 75984 66327 74838 67623 73669 68899 72477 70153 71264 27 34 65033 75965 66349 74818 67645 73649 68920 72457 70174 71243 26 35 65055 75946)66371 74799 67666 73629 68941 72437 70195 71223 25 36 65077 75927 66393 74780 67688 73610 68962 72417 70215 71203 24 37 65099 75908 66414 74760 67709 73590 68983 72397 70236 71182 23 38 65122 75889 66436 74741 67730173570 69004 72377 70257 7LI62 22 39 65144 75870 66458 74722 67752 rasu 69C25 72357 70277 71141 21 40 65166 75851 66460 74703 67773 73531 69046 72337 70298 71121 20 41 65188 75832 66501 74683 67795 73511 69067 72317 70319 71100 19 42 65210 75813J66523 74664 67816 73491 69088 72297 70339171080 18 43 65232 75794 66545 74644 67837 73472 69109 72277 70360171059 17 44 65254 75775 66566 74625 67859 73452 69130 72257 70381 71039 16 45 65276 75756 66588 74606 67880 73432 69151 72236 70401 71019 15 46 47 65298 65320 75738 75719 66610 66632 74586 74567 67901 67923 73412 73393 69172 72216 09193 72196 70422 70443 70998 70978 14 13 48 65342 75699 66653 74548 67944 73373 69214 72176 70463 70957 12 49 65364 75680 66675 74528 67965 73353 69235 72156 70484 70937 11 50 65386 75661 166697 74509 67987 73333 69256 72136 70505! 7091 6 10 51 65408 75642 i66718 74489 68008 73314 69277 72116 70525 70896 9 52 65430 75623 1 66740 74470 68029 73294 69298 72095 70546 70875 8 53 G5452 75604 66762 74451 68051 73274 69319 72075 70567 70855 7 54 65474 75585,66783 74431 68072 73254 69340 72055 70587:70834 6 55 6549f 75566 66805 74412 68093 73234 69361 72035 70608 17081 3 5 56 65518 75547 66827 74392 68111 73215 69382 72015 70628 70793 4 57 6554C 75528 66848 74373 68136 73195 69403 71995 70649 70772 3 58 65562 75509 66870 74353 6815? 73175 69424 71974 70670 70752 2 59 65584 75490 66891 74334 6817S 73155 69445 71954 70690 70731 1 60 65606(75471 66913 74314 68200 .73135 69466 71934 70711 70711 M TTcs. ! N. S. N. CS. N.S. N.CS.I N.S. NTcs: N.S. N.CS. N.S Mf I 49 Deg. 48 Deg. 47 Deg. 46 Deg. 45 Deg. j RETURN TO the circulation desk of any University of California Library or to the NORTHERN REGIONAL LIBRARY FACILITY Bldg. 400, Richmond Field Station University of California Richmond, CA 94804-4698 ALL BOOKS MAY BE RECALLED AFTER 7 DAYS 2-month loans may be renewed by calling (510)642-6753 1-year loans may be recharged by bringing books to NRLF Renewals and recharges may be made 4 days prior to due date DUE AS STAMPED BELOW Received in tnteriibrary Loan \V.- SEP -'3 1992 21 1993 AUTODSCCIRC ^ 2^93 , YC 13531 U.C.BERKELEY LIBRARIES CDM5Mbl3Dfl r^<^