TABLES or LOGARITHMS OF NUMBERS AND OF SUES AND TAIGENTS FOR EVERT TEN SECONDS OF THE QUADRANT, WITH OTHER USEFUL TABLES. BY ELIAS LOO MIS, LLJX, PKOFESSOE OF NATURAL PHILOSOPHY AND A8TRONOMV IN TALK COLLEGE, AND ATTTHOK OT "COTIESE OP MATHEMATICS." TWENTIETH EDITION. NEW-YORK: HARPER & BROTHERS, PUBLISHERS, 329 & 331 PEARL STREET, FRANKLIN SQUARE. 1862. Entered, according to Act of Congress, in the year one thousand eight hund ed and forty-eight, bj HARPER & BROTHERS, in the Clerk's Office of the District Court of the Southern District of New York. CONTENTS. EXPLANATION i)P THE TABLES Y TABLE OF LOGARITHMS OF NUMBERS 1 LOGARITHMIC SINES AND TANGENTS 21 NATURAL SINES AND TANGENTS . .... 1 16 NATURAL SECANTS 134 LENGTHS OF CIRCULAR ARCS 1 35 TRAVERSE TABLE 136 MERIDIONAL PARTS 142 CORRECTIONS TO MIDDLE LATITUDE 149 LOGARITHMS FOR COMPOUND INTEREST, E^C 1 50 PREFACE. THE accompanying tables were designed to afford the means of per forming trigonometrical computations with facility and precision. The tables chiefly used in this country for purposes of education extend to six decimal places, like those in the present collection; but the pre- cision which they are designed to furnish is only attained by a serious expenditure of labor. In the Table of Logarithms of Numbers they do not furnish the correction for a fifth figure in the natural number, and the labor of computing this correction is such that I always prefer the use of Hutton's Tables, extending to seven places, even in computations to which six-place logarithms are abundantly competent. In the pres ent collection, the correction for a fifth figure of the natural number is introduced at the bottom of each page, and the table is thus rendered nearly as useful as one of the common kind extending to 100,000. The whole has been carefully compared with standard authors, and nearly a dozen errors have thus been detected in the common tables. The principal table in this collection is that of Logarithmic Sines and Tangents. The common tables in this country extend only to minutes, with differences to 100". If, in a trigonometrical computation, angles are only required to the nearest minute, tables to five places are quite sufficient ; but if the computation is to be carried to seconds, these can only be obtained from the common tables by a great expenditure ol time and labor. In the present collection, the sines and tangents are fur- nished to every ten seconds of the quadrant, and at the bottom of each page is given the correction for any number of seconds less than ten, so that the precision of seconds can be obtained with almost the same fa- cility as that of minutes with the tables in common use. Moreover, near the limits of the quadrant, by means of an auxiliary table,<*ines and tangents are readily obtained, even for a fraction of a second. The method of arrangement of the sines and tangents was suggested by a table in Mackay's Longitude ; but the errors of that table, amounting to several thousand, have been corrected by a careful comparison with the work of Ursinus. By comparison with the same standard, more than two hundred errors (chiefly in the final figures) have been detected in the tables in common use. The Table of Natural Sines and Tangents is of less use than the loga- rithmic ; nevertheless, it is often important for reference, particularly in analytical geometry and the calculus ; and it is useful as a stepping stone to assist the beginner in comprehending the nature of logarithmic 339660 REFACE. sines ar.d tangents. The Traverse Table commonly usea in this country furnishes the latitude and departure to every quarter degree of the quad- rant, for distances from 1 to 100, and occupies ninety pages. The accom- panying table occupies but six pages, and yields ten times greater pre- cision. The Table of Meridional Parts extends to tenths of a mile, and grea care has been taken to insure its accuracy. For this purpose, I have compared all the similar tables within my reach, and among them have found two which appeared to have been computed independently. Be- tween them there were detected 674 discrepancies in the final figures. These cases were all recomputed, and 78 errors were detected in the jest copy compared. It is probable. that the numbers in this table are not in every instance true to the nearest tenth of a mile ; but it is be lieved that the remaining -errors are few in number, as well as minute. This table is confidently pronounced more accurate than any similar one with which I have been able to compare it. The Table of Corrections to Middle Latitude was computed entirely anew. The corresponding table in common use, which was originally computed by Workman, contains more than four hundred errors, sev- eral of them amounting to two minutes. On the whole, it is believed that the accompanying tables will be found more convenient to the computer than any tables of six decimal places hitherto published in this country ; and that they will be pro- nounced sufficiently extensive for all purposes of academic and collegri- ite instruction, as well as for practical mechanics and surveyors. EXPLANATION OF THE TABLES. TABLE OF LOGARITHMS OF NUMBERS, pp. 1-20. LOGARITHMS are numbers contrived to diminish the labor of Multiplica- tion and Division by substituting in their stead Addition ancl Subtrac tion. All numbers are regarded as powers of some one number, which is called the base of the system ; and the exponent of that power of the base which is equal to a given number, is called the logarithm of that number. The base of the common system of logarithms (called, from their in- ventor, Briggs' logarithms) is the number 10. Hence all numbers are to be regarded as powers of 10. Thus, since 10= 1, is the logarithm of 1 in Briggs' system ; 10'= 10, 1 " " 10 " " 10 a =100, 2 " " 100 " " 10 3 =1000, 3 " " 1000 " " 10 4 = 10,000, 4 " 10,000 &c., &c., &c. ; whence it appears that, in Briggs' system, the logarithm of every num- ber between 1 and 10 is some number between and 1, i. e., is a prop- er fraction. The logarithm of every number between 10 and 100 is some number between 1 and 2, i. e., is 1 plus a fraction. The loga- rithm of every number between 100 and 1000 is some number between 2 and 3, i. e., is 2 plus a fraction, and so on. The preceding principles may be extended to fractions by means of negative exponents. Thus, since 10^= 0.1, 1 is the logarithm of 0.1 in Briggs' system ; 10~ 2 =0.01, 2 " " 0.01 " " \0~ 3 =0.001, 3 " " 0.001 10~ 4 =0.0001, 4 " " 0.0001 &c., &c., &c. Hence it appears that the logarithm of every number between 1 and 0.1 is some number between and 1, or may be represented by 1 plus a fraction; the logarithm of every number between 0.1 and .01 is some number between 1 and 2, or may be represented by 2 plus v'\ EXPLANATION or THE TABLES. a fraction ; the logarithm of every number between .01 and .001 is some number between 2 and 3, or is equal to 3 plus a fraction, and so on. The logarithms of most numbers, therefore, consist of an integer and a. fraction. The integral part is called the characteristic, and may be known from the following RULE. The characteristic of the logarithm of a number greater than unity, is cue less than the number of integral figures in the given number. Thus the logarithm of 297 is 2 plus a fraction ; that is, the character- istic of the logarithm of 297 is 2, which is one less than the number of integral figures. The characteristic of the logarithm of 5673.29 is 3 ; that of 73254.1 is 4, &c. The characteristic of the logarithm of a decimal fraction is a negative number, and is equal to the number of places by which its first significant figure is removed from the place of units. Thus the logarithm of .0046 is 3 plus a fraction; that is, the char- acteristic of the logarithm is 3, the first significant figure 4 being removed three places from units. The accompanying table contains the logarithms of all numbers from I to 10,000 carried to 6 decimal places. To find the Logarithm of any Number between 1 and 100. Look on the first page of the table, along the column of numbers under N, for the given number, and against it, in the next column, will be found the logarithm, with its characteristic. Thus, opposite 13 is 1.113943, which is the logarithm of 13; " 65 is 1.812913, " " 65. To find ?//* Logarith?n of any Number consisting of three Figures. Look on one of the pages from 2 to 20, along the left-hand column marked N, for the given number, and against it, in the column headed 0, will be found the decimal part of its logarithm. To this the character- istic must be prefixed, according to the rule already given. Thus the logarithm of 347 will be found, from page 8, to be 2.540329 ; " " 871 " " " 18, " 2.940018. As the first two figures of the decimal are the same for several suc- cessive numbers in the table, they are not repeated for each logarithm separately, but are left to be supplied. Thus the decimal part of the logarithm of 339 is .530200. The first two figures of the decimal remain the same up to 347 ; they are therefore omitted in the table, and are to be supplied. To find the Logarithm of any Number consisting of four Figures. Find the three left-hand figures in the column marked N as before EXPLANATION OP THE TABLES. vii jid the fourth figure at the head of one of the other columns. Opposite to the first three figures, and in the column under the fourth figure, will be found four figures of the logarithm, to which two figures from the column headed are to be prefixed, as in the former case. The char- acteristic, must be supplied by the usual rule. Thus the logarithm f 3456 is 3.538574 ; " 8765 is 3.042752. In sever-ai df the columns headed 1, 2, 3, &c., small dots are lound in the place of figures. This is to show that the two figures which are to be prefixed from the first column have changed, and they are to be taken from the horizontal line directly below. The place of the dots is to be supplied with ciphers. Thus the logarithm of 2045 is 3.310693 ; 9777 is 3.990206. The two leading figures from the column must also be taken from the horizontal line below, if any dots have been passed over on the same horizontal line. Thus the logarithm of 1628 is 3.211654. To find the Logarithm of any Number containing more than four Figures. By inspecting the table, we shall find that within certain limits the log- arithms are nearly proportional to their corresponding numbers. Thus the logarithm of 7250 is 3.860338 ; " " 7251 is 3.860398 ; " " 7252 is 3.860458 ; " " 7253 is 3.860518. Here the difference between the successive logarithms, called the tabular difference, is constantly 60, corresponding to a difference of unity in the natural numbers. If, then, we suppose the logarithms to be pro- portional to their corresponding numbers (as they are nearly^, a differ- ence of 0.1 in the numbers should correspond to a difference of 6 in the logarithms ; a difference of 0.2 in the numbers should correspond to a difference of 12 in the logarithms, &c. Hence the logarithm of 7250.1 must be 3.860344 ; " " 7250.2 " 3.860350; " " 7250.3 " 3.860356; &c., &c. In order to facilitate the computation, the tabular difference is insert- ed on page 16 in the column headed D, and the proportional part for the fifth figure of the natural number is given at the bottom of the page. Thus, when the tabular difference is 60, the corrections for .1, .2, .3 &c., are seen to be 6, 12, 18, &c. If the given number was 72501, the characteristic of its logarithm would be 4, but the decimal part would be the same as for Vlll EXPLANATION OF THE TABLES. If it were required to find the correction for a sixth figure in the nat ural number, it is readily obtained from the Proportional Parts in the table. Thus, if the correction for .5 is 30, the correction for .05 is ob viously 3. As the differences change rapidly in me first part of the table, n was found inconvenient to give the proportional parts for each tabular difference ; accordingly, for the first seven pages they are only given for the even differences, but the proportional parts for the odd differences will be readily found by inspection. Required the logarithm of 452789. The logarithm of 452700 is 5.655810 The tabular difference is 96. Accordingly, the correction for the fifth figure, 8, is 77, and for the sixth figure, 9, is 8.6, or 9 nearly. Adding these corrections to the num- ber before found, we obtain 5.655896. The preceding logarithms do not pretend to be perfectly exact, bu only the nearest numbers having but six decimal places. Accordingly when the fraction which is omitted exceeds half a unit in the sixth deH mal place, the last figure must be increased by unity. Required the logarithm of 8765432. The logarithm of 8765000 is 6.942752 Correction for the fifth figure 4, 20 " " sixth figure 3, 1.5 " " seventh figure 2, 0.1 Therefore the logarithm of 8765432 is 6.942774. Required the logarithm of 234567. The logarithm of 234500 is 5.370143 Correction for the fifth figure 6, 111 " sixth figure 7, 13 Therefore the logarithm of 234567 is 5.370267. To find the Logarithm of a Decimal Fraction. The decimal part of the logarithm of any number is the same as that of the number multiplied or divided by 10, 100, 1000, &c. Hence, for a decimal fraction, we find the logarithm as if the figures were integers and prefix the characteristic according to the usual rule. EXAMPLES. The logarithm of 345.6 is 2.538574 ; 87.65 is 1.942752; " 2.345 is 0.370143; " .1234 is 1.091315; 005678 is 3.754195. EXPLANATION OF THE TABLC 3. .x The minus sign is placed over the characteristic to show that this alone is negative, while the decimal part of the logarithm is positive. To find the Logarithm of a Vulgar Fraction. We may reduce the vulgar fraction to a decimal, and find its loga- rithm by the preceding rule ; or, since the value of a fraction is equal to the quotient of the numerator divided by the denominator, we may sub- tract the logarithm of the denominator from that of the numerator ; the difference will be the logarithm of the quotient. Required the logarithm of T 3 g-, or 0.1875. From the logarithm of 3, .0.477121, Subtract the logarithm of 16, 1.204120. Leaves logarithm of T \, or .1875, 1.273001. Tn the same manner we find the logarithm of ^ is 2.861697 ; " }ff is 1.147401. To find the natural Number corresponding to any Logarithm. Look in the table in the column headed for the first two figures of the logarithm, neglecting the characteristic ; the other four figures are to be looked for in the same column, or in one of the nine following col- umns ; and if they are exactly found, the first three figures of the corre- sponding number will be found opposite to them in the column headed N, and the fourth figure will be found at the top of the page. This num- ber must be made to correspond with the characteristic of the given logarithm by pointing off decimals or annexing ciphers. Thus the natural number belonging to the logarithm 4.370143 is 23450 ; 1.538574 is 34.56. If the decimal part of the logarithm can not be exactly found in the table, look for the nearest less logarithm, and take out the four figures of the corresponding natural number as before ; the additional figures may be obtained by means of the Proportional Parts at the bottom of the page. Required the number belonging to the logarithm 4.368399. On page 6, we find the next less logarithm .368287. The four corresponding figures of the natural number are 2335. Their logarithm is less than the one proposed by 112. The tabular difference is 186 ; and, by referring to the bpttom of page 6, we find that, with a difference of 186, the figure corresponding to the Propor- tional Part 112 is 6. Hence the five, figures of the natural number are 23356 ; and, since the characteristic of the proposed logarithm is 4, these five figures are all integral. Required the number belonging to logarithm 5.345678. The next less logarithm in the table is .345570 Their difference 7 's 108. x EXPLANATION OF THE TABLES. The first four figures of the natural number are 2216. With the tabular difference 196, the fifth figure corresponding to 108 >a seen to be 5. with a remainder of 10. which furnishes a sixth figure 5 nearly. Hence the required number is 221' In the same manner we find the number corresponding to logarithm 3 ~ $ ; * T.IV17S17 is .444444. TABLE OF NATURAL SIN TANGENTS, pp. 116-133. This is a table of natural sines and tangents for every degree ana minute of the quadrant, carried to six places of figures. Since the ra- dius of the circle is supposed to be unity, t: less than unity. These sines are expressed in decimal parts of the radius ; and. although the decimal point is not written in the table, it must always be prefixed. The degrees are arranged in order at the top of the page, and the minutes in the left hand vertical column. Directly under the given number of - at the top of the 1 opposite to the minutes on the left, will be found the sine required. The tw--> leading figures are repeated at intervals of ten minutes. Thus the sine of s. 11 2330: " The same number in the table is both the sine of an arc and t! sine of its complement. The degrees for the cosines must be sought at the bottom of the page, and the minutes on the right. Thus the cosine oioJ 2: .4631 .. If a sine is required for an arc consisting of degrees, minuies. and sec ondsj it may be found by means of the line at the bottom of each page. which gives the proportional part corresponding to one second of arc Required the sine of 8 9' 10". The sine of 8 9' is .141: By referring to the bottom of page 116, in the column mui find the correction for 1" is 4.80 ; hence the correction for 10" must be 48, which, added to the number above found, gives for the sine of S c 9' 10", .141813. In the same manner we find the cosine of 56 34' 28" is .550S53. It will be observed, that since the cosines decrease while the arcs m crease, the correction for the 2S ' is to be subtracted from the cosine 34. The arrangement of the table of natural tangents is similar to that of the table of sines. The tangents for arcs less than 45 are all less than radius, and, consist wholly of decimals. For arcs above 45 C . the tan- are all greater than radius and contain both integral and decimal EXPLANATION OF THE T A 111.1:9. xj ngures. The proportional parts at the bottom of each page enable us readily to find the correction for seconds. Thus the natural tangent of 32 29' 18" is .636784 ; " 74 35' 55" is 3.63014. To find the Number of Degrees, Minutes, and Seconds belonging to given Sine or Tangent. If the given sine or tangent is found exactly in the table, the corre- sponding degrees will be found afc the top of the page, and the minutes on the left hand. But when the given number is not found exactly in the table, look for the sine or tangent which is next less than the pro- posed one, and take out the corresponding degrees and minutes. Find, also, the difference between this tabular number and the number pro- posed, and divide it by the proportional part for 1" found at the bottom of the page ; the quotient will be the required number of seconds. Required the arc whose sine is .750000. The next less sine in the table is .749919, the arc corresponding to which is 48 35'. The difference between this sine and that proposed is 81, which, divided by 3.21, gives 25. Hence the required arc is 48 35' 25". In the same manner we find the arc whose tangent is 2.000000, to be 63 26' 6". TABLE OP NATURAL SECANTS, pp. 134-5. This is a table of natural secants for every ten minutes of the quad- rant carried to seven places of figures. The degrees are arranged in order in the first vertical column on the left, and the minutes at the top of the page. Thus the secant of 21 20' is 1.073561 ; " " 81 50' is 7.039622. If a secant is required for a number of minutes not given in the table, the correction for the odd minutes may be found by means of the last vertical column on the right, which shows the proportional part for one minute. Let it be required to find the secant of 30 33'. The secant of 30 30' is 1.160592. The correction for 1' is 198.9, which, multiplied by 3, gives 597 Adding this to the number before found, we obtain 1.161189. For a cosecant, the degrees must be sought in the right-hand vertical column, and the minutes at the bottom of the page. Thus the cosecant of 47 40' is 1.352742. TABLE OF LOGARITHMIC SINES AND TANGENTS, pp. 21-115. This is a table of the logarithms of the sines and tangents for every ten seconds of the quadrant, carried to six places of decimals The de- in EXPLANATION OF THE TABLES. grees and seconds are placed at the top of the page, and the minutes .n the left vertical column. After the first two degrees, the three leading figures in the table of sines are only given in the column headed 0", and are to be prefixed to the numbers in the other columns, as in the table of logarithms of numbers. Also, where the leading figures change, this change is indicated by dots, as in the former table. The correction foi any number of seconds less than 10 is given at the bottom of the page. To find the Logarithmic Sine or Tangent of a given Arc. Look for the degrees at the top of the page, the minutes on the lelt hand, and the next less tenth second at the top ; then, under the seconds, and 'opposite to the minutes, will be found four figures, to which the three leading figures are to be prefixed from the column headed 0" ; to this add the proportional part for the odd seconds from the bottom of the page. Required the logarithmic she of 24 27' 34". The logarithmic sine of 24 27' 30" is 9.617033. Proportional part for 4" is 18. Logarithmic sine of 24 27' 34" is 9.617051. This is the logarithm of .414049 found in the table of natural sines on page 120. The natural sine being less than unity, the characteristic of its logarithm is negative. Tc obviate this inconvenience, the char- acteristics in the table nave all been increased by 10 ; or the logarith- mic sines may be regarded as the logarithms of natural sines computed for a radius of 10,000,000,000. Required the logarithmic tangent of 73 35' 43". The logarithmic tangent of 73 35' 40" is 10.531031. Proportional part for 3" is 23. Logarithmic tangent of 73 35' 43" 10.531054. When a cosine is required, the degrees and seconds must be sought at the bottom of the page, and the minutes on the right, and the correc tion for the odd seconds must be subtracted from the number in the table Required the logarithmic cosine of 59 33' 47". The logarithmic cosine of 59 33' 40" i-s 9.704682. Proportional part for 7" is 25. Logarithmic cosine of 59 33' 47" is 9.704657. So, also, the logarithmic cotangent of 37 27' 14" is found to be 10.115744. The proportional parts given at the bottom of each page correspond to the degrees at the top oi the page increased by 30', and are not strictly applicable to any other number of minutes ; nevertheless, the differences of the sines change so slowly, except near the commence- ment of the quadrant, that the error resulting from using these numbers' for every part of the page will sa Jom exceed a unit in the sixth deci- mal place. For the first two degrees, the differences change so rapidly EXPLANATION OF THE TABLES. xii tuat the proportional part for 1" is given for each minute in the right- hand column of the page. The correction for any number of seconds less than ten will be found by multiplying the proportional part for i" by the given number of seconds. Required the logarithmic sine of 1 17' 33". The logarithmic sine of 1 17' 30" is 8.352991 The correction for 3" is found by multiplying 93.4 by 3, which gives 280. Adding this to the above tabular number, we obtain the sine of 1 IT 33", 8.353271. A similar method may be employed for several of the first degrees of the quadrant, if the proportional parts at the bottom of the page are not thought sufficiently precise. This correction may, however, be ob- tained pretty nearly by inspect : on from comparing the proportional parts for two successive degrees. Thus, on page 26, the correction for 1", corresponding to the sine of 2 30', is 48 ; the correction for 1", cor- responding to the sine of 3 30', is 34. Hence the correction for 1", corresponding to the sine of 3 0', must be about 41 ; and in the same manner we may proceed for any other part of the table. Near the close of the quadrant, the tangents vary so rapidly, that the same arrangement of the table is adopted as for the commencement of the quadrant. For the last as well as the first two degrees of the quad- rant, the proportional part to 1" is given for each minute separately. These proportional parts are computed for the minutes placed opposite to them, increased by 30' , and are not strictly applicable to any other number of seconds ; nevertheless, the differences for the most part change so slowly, that the error resulting from. using these numbers for every part of the same horizontal line is quite small. When great ac- curacy is required, the table on page 114 may be employed for arcs near the limits of the quadrant. This table furnishes the differences be- tween the logarithmic sines and the logarithms of the arcs expressed in seconds. Thus the logarithmic sine of 5' is 7.162696 ; the logarithm of 300" (=5 ; ) is 2.477121 ; the difference is 4.685575. This is the number found on page 114, under the heading log. sine A log. A", opposite 5 min. ; and in a similar manner the other numbers in the same column are obtained. These numbers vary quite slowly for two degrees ; and hence, to find the logarithmic sine of an arc less than two degrees, we have but to add the logarithm of the arc expressed iu seconds to the appropriate number found in this table. Required the logarithmic sine of 7' 22". Tabular number from page 114, 4.685575. The logarithm of 442" is 2.645422. Logarithmic sine of T 22" is 7.330997 xiv EXPLANATION OF THE TABLES. The logarithmic tangent of an arc less than two degrees is found in a similar manner. Required the logarithmic tangent of 27' 36". Tabular number from page 114, 4.685584. The logarithm of 1656" is 3.219060. Logarithmic tangent of 27' 36" is 7.904644. The column headed log. cot. A+log. A" is found by adding -the log- arithmic cotangent to the logarithm of the arc expressed in seconds. Hence, to find the logarithmic cotangent of an arc less than two degrees, we must subtract from the tabular number the logarithm of the arc in seconds. Required the logarithmic cotangent of 27' 36". Tabular number from page 114, 15.314416. The logarithm of 1656" is 3.219060. Logarithmic cotangent of 27' 36" is 12.095356. The same method will, of course, furnish cosines and cotangents ol arcs near 90. The secants and cosecants are omitted in this table, since they are easily derived from the cosines and sines. The logarithmic secant is found by subtracting the logarithmic cosine from 20 ; and the logarithmic cosecant is found by subtracting the loga- rithmic sine from 20. Thus we have found the logarithmic sine of 24 27' 34" to be 9.617051. Hence the logarithmic cosecant of 24 27' 34" is 10.382949. The logarithmic "cosine of 54 12' 40" is 9.767008. Hence the logarithmic secant of 54 12' 40" is 10.232992. To find the Arc corresponding to a given Logarithmic Sine or Tangent If the given number is found exactly in the table the corresponding degrees and seconds will be found at the top of the page, and the min- utes on the left. But when the given number is not found exactly in the table, look for the sine or tangent which is next less than the pro- posed one, and take out the corresponding degrees, minutes, and sec- onds. Find, also, the difference between this tabular number and the number proposed, and, corresponding to this difference, at the bottom of the page will be found a certain number of seconds, which is to be added vO the arc before found. Required the arc corresponding to the logarithmic sine 9.750000. The next less sine in the table is 9.749987. The arc corresponding to which is 34 13' 0". The difference between its sine and the one proposed is 13, corre- sponding to which, at the bottom of the page, we find 4" nearly. Hence the required arc is 34 19' 4-". EXPLANATION OF THE TABLES, xv In the same manner we find the arc corresponding to logarithmic tan gent 10.250000, to be 60 38' 57". When the arc falls within the first two degrees of the quadrant, the odd seconds may be found by dividing the difference between the tab- ular number and the one proposed, by the proportional part for 1". We thus find the arc corresponding to logarithmic sine 8.400000, to be 1 26' 22" nearly. We may employ the same method for the last two degrees of the quadrant when a tangent is given ; but near the limits of the quadrant it is better to employ the auxiliary table on page 114. If we subtract the corresponding tabular number on page 114 from the given logarith- mic sine, the remainder will be the logarithm of the arc expressed in seconds. Required the arc corresponding to logarithmic sine 7.000000. We see, from page 22, that the arc must be nearly 3' ; the correspond ing tabular number on page 114 is 4.685575. The difference is 2.314425; which is the logarithm of 206."265. Hence the required arc is 3' 26."265. In the same manner we find the arc corresponding to logarithmic tangent 8.184008, to be 52' 35 /; . TABLE FOR THE LENGTHS OF CIRCULAR ARCS, p. 135. This table contains the lengths of every single degree up to 60, and at intervals often degrees up to 180 ; also for every minute and second up to 20. The lengths are all expressed in decimal parts of radius. Required the length of an arc of 57 17' 44."8. Take out from their respective columns the lengths answering to each of these numbers singly, and add them all together thus : 57 0.9948377 17' 0049451 40" 0001939 4" 0000194 0."8 . .0000039 The sum is 1.0000000. That is, the length of an arc of 57 17' 44."8 is equal to the radius of the circle. TRAVERSE TABLE, pp. 136-141. This table shows the difference of latitude and the departure to four decimal places for distances from 1 to 10, and for bearings from to 90rat intervals of 15'. If the bearing is less than 45, the angle will be found on the left margin of one of the pages of the table, and the dis *ance at the top or bottom of the page ; the difference of latitude wil A t i EXPLANATION OF THE TABLES be found in the column headed lat. at the top -of the page, and the de parture in the column headed dep. If the bearing is more than 45, the angle will be found on the right margin, and the difference of latitude will be found in the column marked lat. at the bottom of the page, and the departure in the other column. The latitudes and departures for different distances with the same bearing, are proportional to the dis- tances. Therefore the distances may be reckoned as tens, hundreds, or thousands, if the place of the decimal point in each departure and differ- ence of latitude be changed accordingly. Required the latitude and departure for the distance 32.25, and the bearing 10 30'. On page 136, opposite to 10 30', we find the following latitudes and departures, proper attention being paid to the position of the decimal -joints. Distance. Diff. Lat. Dep. 30 29.498 5.467 2 1.966 .364 .2 .197 .036 .05 .049 .009 32.25 31.710 5.876. TABLE OF MERIDIONAL PARTS, pp. 142-148. This table gives the length of the enlarged meridian on Mercators Chart to every minute of latitude expressed in geographical miles and tenths of a mile. The degrees of latitude are arranged in order at the top of the page, and the minutes en both the right and left margins. Under the degrees and opposite to the minutes are placed the merid- ional parts corresponding to any latitude less than 80. Thus the meridional parts for latitude 12 23' are 748.9 ; 57 42' are 4260.5. TABLE OF CORRECTIONS TO MIDDLE LATITUDE, p. 149. This table is used in Navigation for correcting the middle latitude The given middle latitude is to be found either in the first or last verti- cal column, opposite to which, and under the given difference of latitude, is inserted the proper correction in minutes, to be added to the middle latitude to obtain the latitude in which the meridian distance is accu rately equal to the departure. Thus, if the middle latitude is 41, and the difference of latitude 14, the correction will be found to be 25', which, added to the middle latitude, gives the corrected middle latitude 41 25'. A TABLE * OP LOGARITHMS OF lUMBEHS FROM 1 TO 10,000. N. Log. K. Log. N. Log. N. Log. i o.oooooo 26 .4i4973 5i .707570 76 .880814 52 o.3oio3o 27 .43i364 52 .716003 77 .886491 3 0.477121 28 .447i58 53 .724276 78 .892095 '4 0.602060 29 .462398 54 . 7 323 9 4 79 .897627 5 0.698970 3o .477121 55 74o363 80 .903090 6 0.778151 3i .491362 56 .748188 8 1 .908485 7 0.845098 32 .5o5i5o 5 7 . 7 558 7 5 82 .913814 8 0.903090 33 .5i85i4 58 .763428 83 .919078 9 0.954243 34 .53i479 5 9 .770852 84 .924279 10 i .000000 35 .544o68 60 .778151 85 .929419 ii .041393 36 .5563o3 61 . 7 8533o 86 .934498 12 .079181 37 .568202 62 .792392 87 .939519 i3 .113943 38 .579784 63 .799341 88 . 9 44483 i4 .146128 3 9 .591065 64 .806180 89 .949390 i5 .176091 4o .602060 65 .812913 9 .954243 16 .204120 4i .612784 66 .819544 9 1 .959041 J 7 .23o449 4a .623249 67 .826075 92 .963788 18 .255273 43 .633468 68 .832509 93 . 9 68483 19 .278754 44 .643453 69 .838849 94 .973128 2Q .3ojo3o 45 .653213 70 .845098 9 5 .977724 21 .322219 46 .662758 7 1 .85i258 96 .982271 22 .342423 47 .672098 72 .857332 97 .986772 23 .361728 48 .681241 73 .863323 98 .991226 24 .380211 49 .690196 74 .869232 99 . 99 5635 25 .397940 5o .698970 75 .8 7 5o6i 100 2.OOOOOO N.B. In the following table, the two leading figures in the first column of logarithms are to be prefixed to all the numbexs of the same horizontal line in the next nine columns ; but when a point (.) occurs, its place is to be suppHfed by a cipher, and the two leading figures are to be taken from the next lower line. LOGARITHMS OF NUMBERS. Nj 0. 1 ,- 2 3 .4 5 6 7 8 9 D. 100 oooooo o434 0868 i3oi i 1734 2166 25 9 8 3o2 9 346i 38 9 i 432 IOI 4321 4 7 5i 5x8i 56o 9 6o38 6466 68 9 4 7321 7748 8174 428 IO2 8600 9026 9 45i 9876 .3oo .724 ii4? 1670 i 99 3 2 4i5 424 io3 012837 3269 368o 4ioo 452i 4 9 &> 53Co 5 779 6i 9 7 6616 419 io4 7o33 745i 7868 8284 8700 9116 9 53 2 9947 .36i . 77 5 4x6 io5 021189 i6o3 2016 2428 2841 3252 3664 4o 7 5 4486 4896 419 1 06 53o6 5 7 i5 6i25 6533 6942 7 35o 77 5 7 8i64 85 7 i 8978 4o8 107 9 384 9789 .i 9 5 .600 ioo4 i4o8 1812 2216 26i 9 3021 4o4 108 o33424 | 3826 422 7 4628 $029 543o 583o 623o 662 9 7028 4oo io 9 7426 7825 8223 8620 9017 9 4i4 9811 .207 .602 . 99 8 3 9 6 no 041393 I i 7 8 7 2l82 2676 2969 3362 3 7 55 4i48 454o 4 9 32 3 9 3 III 5323 5 7 i4 6io5 6495 6885 7 2 7 5 7 664 8o53 8442 883o 38 9 112 9218 9 6o6 999 3 .38o .766 ii53 i538 1924 23o 9 26 9 4 386 n3 053078 3463 3846 423o. 46i3 4996 53 7 8 6760 6142 6524 382 n4 6905 7 286 7 666 8o46 % 8426 88o5 9 i85 9563 99 42 .320 379 n5 060698 io 7 5 i452 1829 2206 -2582 2 9 58 3333 3 7 o 9 4o83 3 7 6 116 4458 4832 5206 558o 5953 6326 66 99 7071 7443 7815 3 7 3 117 8186 855 7 8928 9298 9668 ..38 4o 7 .776 ii45 i5i4 36 9 118 071882 2250 261-7 2986 3352 3718 4o85 445 1 48i6 5i8 3 366 ii 9 5547 5 9 I2 6276 664o 7004 736~8 77 3i 8094 845 7 8819 363 120 9181 9 543 9904 .266 ; .625 .987 1 34? 1707 2067 2426 36o 121 082785 3i44 35o3 386i 4219 45 7 6 4 9 34 6291 5647 6o 4 35 7 N. 1 2 3 4 || 5 6 7 8 9 D. 434 43 87 i3o 1 7 4 217 260 3o4 34? 3 9 i 432 43 86 i3o I 7 3 216 269 302 346 38 9 43o 43 86 129 I 7 2 2l5 258 3oi 344 38 7 428 43 86 128 I 7 I 2l4 25 7 3oo 342 385 426 43 85 128 I 7 213 256 298 34i 383 424 42 85 127 I 7 212 254 297 33o 382 422 42 84 127 169 211 253 295 338 38o 420 42 84 126 168 210 252 294 336 3 7 8 4x8 42 84 125 167 209 25l 293 334 376 ! 4i6 42 83 125 1 66 208 25o 291 333 3?4 4x4 4i 83 124 166 207 248 290 33i 3 7 3 412 4i 82 124 i65 206 247 288 33o 3 7 i 4io 4i 82 123 1 64 2O5 246 287 3 2 8 36 9 4o8 4i 82 122 i63 204 245 286 326 36 7 4o6 4i 81 122 162 203 . 244 284 3 2 5 365 4o4 4o Bi 121 162 2O2 242 2 83 323 364 402 a 4o 80 121 161 201 241 281 322 362 (D 4oo ^ 4o 80 120 160 200 240 280 320 36o a 3 9 8 1 4o 80 II 9 i5o 199 23 9 279 3i8 358 J 3 9 6 o 4o 79 II 9 i58 I 9 8 238 277 3i 7 356 ID 5 W ! 3 9 79 118 1 58 I 9 7 236 276 3i5 355 H-i 3 9 2 o 39 78 118 i5 7 I 9 6 235 2 7 4 3x4 353 3 9 o CU 39 78 xi 7 i56 i 9 5 234 273 3l2 35i 388 39 78 116 i55 194 233 272 3io 349 386 39 77 116 1 54 i 9 3 232 270 3o 9 34? 384 38 77 ii5 1 54 192 230 269 307 346 38 2 38 76 iilS i53 191 22 9 267 3o6 344 38o 38 76 n4 152 190 228 266 3o4 342 3 7 8 38 76 Ii3 i5i 189 227 2 65 302 34o 3 7 6 38 75 li3 i5o 1 88 226 263 3oi 338 3 7 4 37 75 112 i5o 187 224 262 2 99 33 7 3 7 2 37 74 112 1 49 186 223 260 2 9 8 335 3 7 o 368 37 37 74 74 III no i48 147 i85 1 84 222 221 2 58 2 9 6 2 9 4 333 t3i 366 37 73 IIO i46 i83 220 256 2 9 3 329 364 36 73 109 i46 182 218 2 55 291 3a8 362 36 72 109 i45 181 217 253 290 326 36o 36 72 108 i44 180 216 Si 288 324 LOGARITHMS OF NUMBERS. N. 1 2 3 4 5 6 7 8 9 D. 122 o8636o 6716 7071 7426 7781 8i36 8490 8845 9198 9662 355 123 9906 .268 .611 .963 i3i5 1667 2018 2370 2 7 2I 3071 35i 124 098422 3 77 2 4l22 447i 4820 6169 55i8 -5866 62l5 6662 349 125 6910 7267 7604 79 5i 8298 8644 8990 9335 9681 ..26 346 126 100371 0716 1069 i4o3 1747 2091 2434 2777 3lI9 3462 343 127 38o4 4i46 448 7 4828 6169 55io 585i 6191 653i 6871 34i 128 7210 7649 7888 8227 8565 8903 9241 9679 9916 .253 338 129 110690 0926 1263 1699 1934 2270 2606 2940 32 7 5 3609 335 i3o 3 9 43 4277 46u 4944 6278 56u 5 9 43 6276 6608 6g4o 333 i3i -7271 7603 79 34 8266 8696 8926 9266 9686 9916 .245 33o 132 120674 0903 I23l 1660 1888 2216 2 544 2871 3198 35 2 5 328 i33 3852 4178 45o4 483o 5i56 548i 58o6 6i3i 6456 6781 325 1 34 7106 7429 77 53 8076- 83 99 8722 9o45 9 368 9690 . . 12 323 i35 i3o334 o655 0977 1298 1619 I 9 3 9 2260 2680 2900 3219 321 i36 3539 3858 4177 4496 48i4 5i3 545i 6769 6086 64o3 3i8 i3 7 6721 7 o3 7 7354 7671 7987 83o3 8618 8 9 34 9249 9564 3x5 i38 9879 .194 .5o8 .822 n36 i45o i 7 63 2076 238 9 2702 3:4 i3 9 i43oi5 3327 3639 3961 4263 45 7 4 4885 6196 55o 7 58i8 3n i4o 6128 6438 6 7 48 7068 7 36 7 7676 7986 8294 86o3 8911 309 i4i 9219 9627 9 835 .142 .449 .766 io63 1370 i6 7 6 1982 3o 7 142 162288 2 5 9 4 2900 3206 35io 38i5 4l20 4424 4 7 28 5o3 2 3o5 i43 5336 564o 5 9 43 6246 6549 6862 7i54 745 7 7769 8061 3o3 i44 8362 8664 8966 9266 9667 9868 .168 46 9 .769 1068 3oi i45 i6i368 1667 1967 2266 2664 2863 3i6i 346o 3 7 58 4o55 299 i46 4353 465o 4947 5244 554i 5838 6i34 643o 6726 7022 2 97 147 7 3i 7 76 1 3 7908 8ao3 8497 8792 9086 9380 9674 9968 296 1 48 170262 o555 o848 n4i i434 1726 2019 23ll 26o3 2896 293 N. 1 2 | 3 4 || 5 6 7 8 9 TT" 358 36 72 .107 i43 179 2l5 261 286 322 356 36 7 1 107 i4a 178 9X4 249 286 320 354 35 7 1 1 06 142 177 212 248 283 319 352 35 7 1 06 i4i 176 211 246 282 3i 7 35o - 35 70 io5 i4o 176 2IO 245 280 3i5 348 35 70 io4 i3g 1 74 209 244 278 3i3 346 35 69 io4 1 38 i 7 3 208 242 277 3n 344 34 69 io3 i38 172 2O6 241 276 3io 342 34 68 io3 i3 7 171 206 239 274 3o8 34o 34 68 102 1 36 170 2O4 238 272 3o6 338 34 68 101 1 35 169 203 23 7 270 3o4 336 ' 34 67 101 1 34 168 202 235 269 302 334 . 33 67 IOO 1 34 167 2OO 234 267 3oi 332 g 33 66 IOO i33 166 I 99 232 266 299 33o - 33 66 99 132 i65 198 23l 264 2 97 328 ~ 33 66 98 i3i 1 64 I 97 230 262 296 H . $^ 266 = 27 53 80 106 i33 1 60 186 213 23 9 | 264 t 26 53 79 1 06 iSa 168 186 211 238 & 262 26 52 79 106 i3i 167 i83 210 236 260 g 26 52 78 io4 i3o i56 182 208 s34 2 58 * 26 52 77 io3 129 i55 181 2O6 232 266 26 5i 77 102 128 1 54 1-79 206 230 264 25 5i 76 IO2 127 162 i 7 8 203 22 9 262 25 5o 76 101 126 161 176 202 22 7 260 26 5o 75 IOO 125 160 176 2OO 225 248 25 5o 74 99 124 149 x?4 I 9 8 223 246 25 49 74 98 123 i48 172 I 9 7 221 a44 24 49 73 98 122 i46 171 i 9 5 22O < 142 24 48 73 97 121 i45 169 i 9 4 218 *4o 24 48 72 96 I2O 1 44 168 I 9 a 216 LOGARITHMS OF NUMBERS. N. 1 2 3 4 1 5 6 7 8 9 D. 182 260071 o3io o548 0787 1025 1263 i5oi 1739 10,76 22l4 2 38 i83 2461 2688 2925 3:62 3399 3636 38 7 3 4109 4346 4582 23 7 1 84 48i8 5o54 5290 55 2 5 5 7 6i 5996 6232 646 7 6702 6 9 3 7 235 i85 7172 7406 7 64i 7 8 7 5 8110 8344 85 7 8 8812 9 o46 9 2 79 234 186 9 5i3 9 7 46 9980 .213 .446 .679 . 9 I2 n44 i3 77 1609 233 187 271842 2074 23o6 2538 2770 3ooi 3233 3464 36 9 6 3 9 2 7 232 188 4i58 438 9 4620 485o 5o8i 53u 5542 5 77 2 6002 6232 230 189 6462 6692 6921 7 i5i 738o 76o 9 7838 8067 8296 8525 2? 9 190 8 7 54 8982 9211 943 9 9667 9 8 9 5 .123 .35i 5 7 8 .8e6 228 191 2 8io33 1261 i488 1715 1942 2i6 9 23 9 6 2622 2849 3o 7 5 227 192 33oi 352 7 3 7 53 3979 42o5 443 1 4656 4882 5107 5332 226 i 9 3 555 7 5782 6007 6232 6456 6681 6 9 o5 7 i3o 7354 7 5 7 8 225 194 7802 8026 8249 8473 8696 8 9 2O 9 i43 9366 9 58 9 9 8l2 223 196 290035 0257 o48o 0702 0925 1147 i36 9 iSgi i8i3 2034 222 196 2266 2478 2699 2920 3i4i 3363 3584 38o4 4o25 4246 221 197 4466 468 7 4907 5127 534 7 556 7 5 7 8 7 6007 6226 6446 22O 198 6665 6884 7104 7. 3 2 3 7542 7761 7979 8198 84:6 8635 2I 9 199 8853 9071 9289 9607 9725 99 43 .161 .378 .5 9 5 .8i3 218 200 3oio3o 1247 i464 1681 1898 2Il4 233i 2547 2764 2 9 8o 217 201 3196 3412 36 2 8 3844 4o5 9 4275 44 9 i 4706 4 9 2I 5i36 216 2O2 535i 5566 5 7 8i 5 99 6 6211 6425 663 9 6854 7068 7282 214 203 7496 7710 7924 8i3 7 835i 8564 8778 8991 9 204 9 4i 7 213 204 963o 9 843 ..56 .268 .481 .6 9 3 . 9 o6 1118 i33o 1 542 212 205 311754 1966 21 77 2389 2600 2812 3d23 3234 3445 3656 211 206 386 7 4o 7 8 4289 44 99 4710 4 9 20 5i3o 534o 555i 5 7 6o 2IO 207 6970 6180 6390 65 99 6809 70l8 7227 7436 7 646 7854 2O 9 208 8o63 8272 848 1 868 9 8898 9 io6 9 3i4 9522 97 3o 99 38 208 209 32oi46 o354 o562 0769 0977 1184 i3 9 i iSgS i8o5 2OI2 207 210 2219 2426 2633 283 9 3o46 3252 3458 3665 38 7 i 40 77 2O6 211 4282 4488. 46 9 4 48 99 5io5 53io 55i6 5 7 2i 5 9 26 6i3i 2O5 212 6336 654i 6 7 45 6950 7 i55 7 35 9 7 563 7767 797 2 8176 2O4 2l3 838o 8583 8787 8991 9194 9 3 9 8 9 6oi 9805 ...8 .211 203 2l4 33o4i4 0617 0819 IO22 .1225 1427 i63o i832 2034 2236 2O2 2l5 2438 2640 2842 3o44 3246 3447 364 9 385o 4o5i 4253 202 216 4454 4655 4856 5o5 7 5 2 5 7 5458 5658 585 9 6o5 9 6260 2OI 217 646o 6660 6860 7060 7260 7 45 9 7 65 9 7 858 8o58 8257 2OO 2I 8 8456 8656 8855 9054 9253 9 45i 9 65o 9849 ..4 7 .246 I 99 219 34o444 0642 0841 io3 9 1237 i435 i632 i83o 2028 2225 I 9 8 220 2423 2620 2817 3oi4 3212 34o 9 36o6 38o2 3 999 4i 9 6 I 97 N. 1 2 3 4 5 6 7 8 9 D. 238 ' 24 48 7i 9 5 ^i 9 i43 167 I 9 O 214 236 24 47 7i 94 118 i4a i65 189 212 234 23 4? 70 94 117 i4o 1 64 187 211 232 23 46 70 9 3 lie i3 9 162 186 20 9 230 23 46 69 9 2 u5 i38 161 1 84 207 228 23 46 68 9 1 n4 i3 7 160 182 205 226 23 45 68 9 n3 i36 i58 181 203 224 22 45 67 9 112 1 34 i5 7 179 2O2 o5 222 e3 22 44 67 89 III i33 i55 178 2OO 8 22O ^ 22 44 66 88 no 132 1 54 176 I 9 8 C "3 CD 3 tS ' 218 < 22 44 65 87 io 9 i3i i53 i 7 4 i 9 6 (g 216 1 22 43 65 86 1 08 i3o i5i I 7 3 i 9 4 214 & 21 43 64 86 107 128 i5o i 7 i I 9 3 212 21 42 64 85 106 127 i48 I 7 O I 9 i 210 21 42 63 84 io5 126 i4 7 1 68 i8 9 208 21 42 62 83 104 125 i46 166 187 206 21 4i 62 82 io3 124 1 44 i65 i85 2O4 2O 4i 61 82 IO2 122 i43 i63 1 84 2O2 20 4o 61 81 IOI 121 i4i 162 182 200 2O 4o 60 80 100 120 i4o 1 60 1 80 198 2O 4o 5 9 79 99 II 9 i3 9 1 58 178 LOGARITHMS OP .NUMBERS. N. 1 2 3 4 5 6 7 8 9 D. 221 344392 458 9 4 7 85 4 9 8i 5178 53 7 4 55 7 o 5766 5962 6i5 7 i 9 6 . 222 6353 654 9 6 7 44 6 9 3 9 7i35 7 33o 7 5 2 5 7720 79 i5 8110 i 9 5 223 83o5 85oo 86 9 4 888 9 9 o83 9278 9 472 9 666 9 86o ..54 1 9 4 224 35o248 0442 o636 o82 9 1023 1216 i4io i6o3 i 79 6 1989 i 9 3 225 2i83 2 3 7 5 2568 2761 2 9 54 3i47 333 9 3532 3 7 24 3 9 i6 226 4io8 43oi 44 9 3 4685 48 7 6 5o68 5260 5452 5643 5834 192 22 7 6026 621-7 64o8 65 99 67 9 o 6981 7172 7363 7 554 7744 191 228 79 35 8i 2 5 83i6 85o6 86 9 6 8886 9 o 7 6 9 266 9 456 9646 I 9 22 9 - 9 835 ..25 .215 4o4 .5 9 3 . 7 83 972 1161 i35o i53 9 189 230 36i 7 28 191-7 2105 22 9 4 2482 2671 285 9 3o48 3236 3424 188 23l 36i2 38oo 3 9 88 4176 4363 455i 4 7 3 9 4 9 26 5u3 53oi 232 5488 56 7 5 5862 6o4 9 6236 6423 6610 67 9 6 6 9 83 7 l6 9 187 233 7 356 7 542 772 9 7 9 i5 8101 8287 8473 865 9 8845 186 234 9216 9401 9 58 7 9772 99 58 .143 .3 2 8 .5i3 .6 9 8 .883 i85 235 3 7 io68 1253 i43 7 1622 1806 1991 2175 236o 2544 2 7 28 1 84 236 2912 3096 3 2 8o 3464 3647 383i 4oi5 4i 9 8 4382 4565 23 7 4748 4932 5u5 5 29 8 548i 5664 5846 6o2 9 6212 63 9 4 i83 238 65 77 6 7 5 9 6 9 42 7124 73o6 7 488 7670 7852 8o34 8216 182 23 9 83 9 8 858o 8761 8 9 43 9 I24 93o6 9 48 7 9 668 9 84 9 ..3o 181 240 38o2ii o3 9 2 o5 7 3 o 7 54 o 9 34 in5 I2 9 6 1476 i656 i83 7 241 201 7 2197 2377 2 55 7 2737 2917 3o 97 3277 3456 3636 180 242 38i5 3 99 5 4i74 4353 4533 4712 48 9 i 5070 524 9 5428 I 79 243 56o6 5 7 85 5 9 64 6142 632i 6499 6677 6856 7 o34 7212 178 344 7 3 9 o 7 568 7746 79 23 -8101 8279 8456 8634 8811 8989 245 9166 9 343 9 520 9 6 9 8 9 8 7 5 .228 .4o5 .582 177 246 390935 III2 1288 i46 i64i 1817 i 99 3 2i6 9 2345 252? i 7 6 24 7 269-7 28 7 3 3o48 3224 34oo 35 7 5 3751 3 9 26 4ioi 42 77 248 4452 462-7 4802 4977 5i5 2 5326 55oi 5676 585o 6o25 i 7 5 24 9 6199 63 7 4 6548 6722 68 9 6 7071 7245 7 4i 9 7 5 9 2 77 66 174 25o 8n4 828-7 846 1 8634 8808 8 9 8i 9 i54 95oi i 7 3 2 5i 96 7 4 9 84 7 ..20 . I 9 2 .365 .538 .711 .883 ?o56 1228 ' 253 4oi4oi i5 7 3 1745 I9Z7 2o8 9 2261 2433 26o5 2777 2949 171 2 53 3l2I 32 9 3 3464 3635 3807 3 97 8 4i4 9 4320 44 9 2 4663 1-71 2 54 48,34 5oo5 5i 7 6 5346 55i 7 5688 5858 6o2 9 6i 99 63 7 o 255 654o 6710 6881 7 o5i 7221 7 3 9I 7 56i 7731 79 oi 80-70 170 256 8240 84io 85 79 8 7 4 9 8 9 i8 9 25 7 0.426 9 5 9 5 97 6 4 i6 9 25 7 99 33 .102 .271 44o .6o 9 777 9 46 in4 1283 i45i 258 411620 1788 i 9 56 2124 22 9 3 2461 262 9 2 79 6 2964 3i32 168 25 9 33oo 3467 3635 38o3 3970 4i3 7 43o5 4472 463 9 48o6 167 260 4 97 3 5i4o 53o 7 5474 564i 58o8 5 97 4 6i4i 63o8 6474 261 664i 680-7 6 97 3 7i3 9 7 3o6 74 7 2 7 638 7804 7970 8i35 1 66 262 83oi 846 7 : 8633 87 9 8 8 9 64 9 I2 9 9 2 9 5 9 46o 9 625 9791 i65 263 9956 .121 j .286 .45i .616 .781 . 9 45 II IO 1275 i43 9 N. G 1 2 3 4 5 6 7 8 9 D. 196 20 3 9 5 9 78 98 118 i3 7 i5 7 176 194 J 9 3 9 58 78 97 116 1 36 i55 i 7 5 192 i 9 38 58 77 96 u5 1 34 1 54 i 7 3 190 i 9 38 57 76 9 5 n4 1 33 1 59 171 188 i 9 38 56 75 94 n3 I 32 i5o 169 186 g 9 37 56 74 93 112 I So 1 49 i6 7 i 1 84 c 18 3 7 55 74 9 2 110 129 i4 7 166 o 182 -3 18 36 55 73 9 1 I0 9 12-7 i46 1 64 I- 180 18 36 54 72 1 08 126 i44 162 I 178 18 36 53 7 1 8 9 I0 7 125 1 49 1 60 s 176 g. 18 35 53 70 88 106 123 i4i 1 58 174 Pk 17 35 52 70 87 io4 122 1 3 9 i5 7 172 X 7 34 52 69 86 io3 I2O 1 38 i55 170 i 7 34 5i 68 85 102 II 9 i36 i53 1 68 1 7 34 5o 67 84 IOI 118 1 34 i5i 1 66 17 33 5o 66 83 IOO 116 i33 i4 9 Ii64 16 33 49 66 82 9 8 n5 i3i 1 48 LOGARITHMS OF NUMBERS. N. 1 2 3 4 5 6 7 8 9 D. 264 421604 1768 1933 2097 2261 2426 25 9 o 2 7 54 2 9 l8 3o82 1 64 265 3246 34io 35 7 4 3 7 3 7 3 9 oi 4o65 4228 43 9 2 4555 4718 266 4882 5o45 5208 53 7 i 5534 56 97 586o 6023 6186 634 9 i63 267 65ii 66 7 4 6836 6999 7161 7 324 7486 7 648 7811 7973 162 268 8i35 8297 845 9 8621 8 7 83 8 9 44 9 io6 0,268 9 42 9 9 5 9 i 269 9752 9914 ..75 .236 .3 9 8 .55 9 .720 .881' 1042* 1203 161 270 43i364 i525 i685 1846 2007 2167 2328 2488 264 9 28o 9 271 2969 3i3o 3290 345o 36io 3 77 o 3 9 3o 4o 9 o 4249 44o 9 1 60 272 4569 .4729 4888 5o48 5207 536 7 5526 5685 5844 6oo4 169 2 7 3 6i63 6322 648 1 664o 6799 6 9 5 7 7116 7 2 7 5 7 433 7 5 9 2 2 7 4 77 5i 7909 8067 8226 8384 8542 8701 885 9 9 oi7 9 J 7 5 1 58 276 9 333 9491 9648 9806 9964 . 122 2 79 .43 7 5 9 4 .752 276 440909 1066 1224 1 38 1 i538 i6 9 5 i852 20O 9 2166 2323 i5 7 277 2^80 263 7 2 79 3 2 9 5o 3io6 3263 34i9 35 7 6 3 7 3 2 388 9 278 4o45 4201 435 7 45i3 466 9 4825 4g8i 5i3 7 52 9 3 544 9 i56 279 56o4 5760 5 9 i5 6o 7 i 6226 6382 653 7 66 9 2 6848 7003 i55 280 7 i58 7 3i3 7 468 7623 7778 79 33 8088 8242 83 97 8552 281 8706 8861 9015 9170 9 324 9 4 7 8 9 633 9787 99 4i .. 9 5 1 54 282 450249 o4o3 o55 7 0711 o865 1018 1172 i326 i4 79 i633 283 1786 1940 2093 2247 2400 2553 2706 285 9 3012 3i65 i53 284 33i8 347i 3624 3 777 3 9 3o 4082 4235 438 7 454o 46 9 2 286 4845 4997 5i5o 5302 5454 56o6 5 7 58 5 9 io 6062 6214 I 52 286 6366 65i8 6670 6821 6 97 3 7 I25 7276 7 428 7 5 79 77 3i 287 7882 8o33 8:84 8336 848 7 8638 8789 8 9 4o 9 o 9 i 9 242 i5i 288 9392 9 543 9694 9 845 999 5 .i46 .296 44 7 .5 9 7 748 289 460898 io48 1198 1 348 1499 i64 9 1799 i 9 48 2O 9 8 2248 i5o 290 2398 2548 2697 2847 2997 3i46 3296 3445 35 9 4 3744 291 38 9 3 4042 4191 434o 4490 463 9 4788 4 9 36 5o85 5 2 34 i4 9 292 5383 5532 568o 5829 5 977 6126 6274 6423 65 7 i 6719 298 6868 7016 7 i64 ?3l2 7 46o 7 6o8 7756 79 o4 8o52 8200 1 48 294 8347 8495 8643 8790 8 9 38 9 o85 9 233 9 38o 9 5 27 9 6 7 5 295 9822 9969 .116 .263 4io .55 7 .704 .85 t 998 n45 i4 7 296 471292 i438 i585 1732 i8 7 8 2O25 2171 23i8 2464 2610 297 2756 2903 3o49 3195 334i 348 7 3633 3779 3 9 25 4071 i46 298 4216 4362 45o8 4653 4 799 4 9 44 Sogo 5235 538i 55 2 6 299 56 7 i 58i6 5962 6107 6252 63 97 6542 6687 6832 6 97 6 i45 3 oo 7121 7266 74 ii 7 555 77 oo 7 844 7989 8i33 8278 8422 3oi 8566 8711 8855 8999 9 i43 9 28 7 943i 9 5 7 5 9719 9 863 1 44 302 480007 oi5i 0294 o438 o582 O 7 25 0869 1012 n56 I2 99 3o3 i443 i586 1729 1872 2016 2i5 9 2302 2445 2588 2 7 3l i43 3o4 2874 3oi6 3i5 9 3302 3445 358 7 3 7 3o 38 7 2 4oi5 4i5 7 3o5 43oo 4442 4585 4727 4869 Son 5i53 52 9 5 5437 55 79 i4a 3o6 5721 5863 6oo5 6i4 7 6289 643o 6572 6 7 i4 6855 6997 3o 7 7 i38 7280 7421 7 563 77 o4 7845 7986 8l2 7 8260. 84io i4i 3o8 855i 8692 8833 8 97 4 9114 9 255 9 3 9 6 9 53 7 9 6 77 9 8i8 SOQ 99 58 99 .239 .38o .520 .661 .801 . 9 4i 1081 1222 i4o 3io 491362 i5o2 1 642 1782 1922 2062 22OI 2 34i 248 1 2621 3u 2760 2900 3o4o 3i 79 33i 9 3458 35 9 7 3 7 3 7 38 7 6 4oi5 i3 9 N. 1 2 3 4 || 5 6 7 8 9 D. 162 r 16 32 49 65 81 97 213 i3o i46 160 16 32 48 64 80 96 112 128 i44 i58 iQ 32 4? 63 79 9 5 III 126 i4a i56 16 3i 4? 62 78 94 IO 9 125 i4o (0 1 54 PH i5 3i 46 62 77 92 108 123 i3 9 I l52 "S i5 3o 46 61 76 9 1 106 122 i3 7 1' I5o| i5 3o 45 60 75 9 io5 I2O x35 P"* 1 48 fc i5 3o 44 5 9 74 8 9 io4 *l8 i33 i46 % i5 29 44 58 73 * 88 102 117 i3i i44 i4 29 43 58 72 86 101 u5 i3o i4a i4 28 43 57 7i 85 99 n4 128 i4o 1 4 28 42 56 70 84 98 112 126 LOGARITHMS OF NUMBERS. N. I 2 3 4 5 6 7 8 9 D. 312 4 9 4i55 42 9 4 4433 45 7 2 4711 485o 4 9 8 9 0128 526 7 54o6 i3 9 3i3 5544 5683 5822 5 9 6o 6o 99 6238 63 7 6 65i5 6653 6 79 i 3i4 6 9 3o -7068 7206 7 344 7483 7621 77 5 9 7 8 97 8o35 8i 7 3 1 38 3i5 83n 8448 8586 8 7 24 8862 8999 9 i3 7 9 2 7 5 9412 9 55o 3i6 9 68 7 9 824 99 62 99 .236 .3 7 4 .5n .648 . 7 85 . 9 22 i3 7 3i 7 5oio5 9 n 9 6 i333 i4 7 o i6o 7 1 7 44 i860 ! 20I 7 2i54 22 9 I 3i8 242 7 2564 2700 283 7 2973 3109 3246 2382 35i8 3655 i36 3i 9 3 79 i 3927 4o63 4199 4335 4471 4607 4743 48 7 8 5oi4 320 5i5o 5 2 86 5421 555 7 56 9 3 58 2 8 5 9 64 6o 99 6234 63 7 o 321 65o5 664o 6776 6 9 n 7 o46 7181 7 3i6 745i 7 586 772i i35 322 7 856 799 1 8126 8260 83 9 5 853o 8664 8799 8 9 34 9 o68 323 9 2o3 9 33 7 9471 9 6o6 97 4o 9874 . . . 9 .i43 2 7 7 .4n 1 34 324 5io545 o6 79 o8i3 o 9 4 7 1081 I2l5 i34 9 1482 1616 i 7 5o 325 i883 2OI 7 2l5l 2284 2418 255i 2684 2818 2 9 5i 3o84 i33 326 32i8 335i 3484 36i 7 3 7 5o 3883 4oi6 4i4 9 4282 44i5 32 7 4548 468 1 48i3 4 9 46 5o 79 5211 5344 5476 56o 9 5 7 4i 328 58 7 4 6006 6i3 9 62 7 I 64o3 6535 6668 6800 6 9 3 3 7 o64 132 32 9 -7196 7 328 7460 7 5 9 2 77 24 7 855 7987 8ii 9 825i 8382 33o 85i4 8646 8777 8 9 o 9 9 o4o 9171 9 3o3 9 434 9566 9 6 97 i3i 33i 9 828 99 5 9 .. 9 o .221 .353 484 .6i5 .745 .8 7 6 I00 7 332 52ii38 I26 9 i4oo i53o 1661 1792 I 9 22 2o53 2i83 23l4 333 2444 2 5 7 5 2 7 o5 2835 2 9 66 3096 3226 3356 3486 36i6 i So 334 3 7 46 38 7 6 4oo6 4:36 4266 43 9 6 4526 4656 4 7 85 4 9 i5 335 5o45 5i 7 4 53o4 5434 5563 56 9 3 5822 5 9 5i 6081 6210 I2 9 336 633 9 646 9 65 9 8 6 7 2 7 6856 6 9 85 7 n4 7243 7 3 7 2 7 5oi 33 7 " 7 63o 77 5 9 7 888 8016 8i45 8274 8402 853i 8660 8 7 88 338 8 9 i 7 9 o45 9 i 7 4 9 3C2 9 43o 9 55 9 9 68 7 98 i 5 9943 .. 7 2 128 33 9 53o2oo o328 o456 o584 7 I2 o84o o 9 68 1096 1223 i35i 34o i4 79 i6o 7 i 7 34 1862 I 99 2117 2245 23 7 2 2500 2627 34i 2754 2882 3oo 9 3i36 3264 33 9 i 35i8 3645 3772 38 99 I2 7 342 4026 4i53 4280 44o 7 4534 466i 4787 4914 5o4i 5i6 7 343 52 9 4 542i 554 7 56 7 4 58oo 5 9 2 7 6o53 6180 63o6 6432 126 344 6558 6685 6811 6 9 3 7 7 o63 7 i8 9 7 3i5 7 44i 7 56 7 7 6 9 3 345 7819 79 45 8o 7 i 8i97 8322 8448 8699 8825 8 9 5i 346 90 7 6 9 2O2 9327 9 45 2 9 5 7 8 97 3 9 82 9 99 54 . .79 .204 125 34 7 54o32 9 o455 o58o o 7 o5 o83o o 9 55 1080 i2o5 i33o 1454 348 i5 79 i 7 o4 i82 9 i 9 53 20 7 8 22O3 232 7 2452 2 5 7 6 2 7 OI 34 9 2825 2 9 5o 3o 7 4 3i 99 3323 344 7 35 7 i 3696 3820 3 9 44 124 35o 4o68 4l 9 2 43i6 444o 4564 4688 4812 4 9 36 5o6o 5i83 35i 53o 7 543 1 5555 56 7 8 58o2 5 9 25 6o4 9 61-72 6296 64i 9 352 353 6543 777 5 6666 7808 6 7 8 9 8021 6 9 i3 8i44 7 o36 826 7 7 i5 9 838 9 -7282 85i2 7 4o5 8635 I'll 7652 8881 123 354 9 oo3 9 I26 9 24 9 9 3 7 i 9 4 9 4 9 6i6 9739 9861 9984 .106 355 550228 o35i o4 7 3 o5 9 5 7 I 7 o84'o O 9 62 io84 1206 i328 122 356 i45o 1572 i6 9 4 1816 i 9 38 2060 2181 2 3o3 2425 254 7 35 7 2668 2 79 2 9 II 3o33 3i55 32 7 6 33 9 8 i 35i 9 364o 3 7 62 121 358 3883 4oo4 4126 424 7 4368 448 9 46io 4 7 3i 4852 4 97 3 35 9 5o 9 4 52i5 5336 545 7 55 7 8 56 99 5820 5 9 4o 6061 6182 36o 63o3 6423 6544 6664 6785 -7026 7 i46 7 26 7 7 38 7 120 36i 7 5o 7 7627 77 48 -7868- 7988 "8108 8228 ' 834 9 846 9 858 9 N. 1 2 3 4 5 6 7 8 9 D. 1 38 i4 28 4i 55 6^ 8.3 97 IIQ 124 i36 oj i4 2 7 4i 54 68 82 9 5 109 122 1 34 S i3 27 4o 54 6 7 80 94 10-7 121 132 PL- i3 26 4o 53 66 79 92 !06 119 c i3o "5 i3 26 39 52 65 78 9 1 io4 l! 7 1 ' 128 |' i3 26 38 Si 64 77 9 1 02 Il5 5 126 o i3 25 38 5o 63 76 88 101 n3 P 124 f 12 25 37 5o 62 74 87 99 112 1122 12 24 37 49 61 73 85 98 110 120 12 24 36 48 60 72 84* 96 1 08 LOGARITHMS OF NUMBERS. . N. 1 2 3 4 5 6 7 8 9 D. ; 362 558 7 o9 8829 8948 9068 9 i88 9 3o8 9 428 9 548 9 66 7 9787 120 363 9907 ..26 .i46 .265 .385 .5o4 .624 . 7 43 .863 . 9 &2 364 56noi 1221 i34o i459 1578 i6 9 8 1817 1936 2o55 2I 7 4 1I 9 365 2293 24l2 253i 265o 2 7 6 9 288 7 3oo6 3i25 3244 3362 366 348i 36oo 3 7 i8 3837 3 9 55 4o 7 4 4l 9 2 43n 442 9 4548 56 7 4666 4784 4903 5O2I 5i3 9 5 2 5 7 53 7 6 5494 56i2 5 7 3o 118 368 5848 5 9 66 6o84 6202 6320 643 7 6555 66 7 3 679,1 6 9 o 9 369 7026 7i44 7262 7 3 79 7497 7 6i4 7732 7 84 9 79 6 7 8084 3 7 o 8202 8319 8436 8554 86 7I 8 7 88 8 9 o5 9023 9 i4o 9 25 7 117 3 7 i 9 3 7 4 9491 9608 9725 9 842 99 5 9 ..76 .193 .3o 9 .426 3 7 2 5 7 o543 0660 0776 o8 9 3 IOIO 1126 1243 1359 1476 l5 9 2 3 7 3 I 79 1825 2o58 2I 7 4 22 9 I 240 7 2523 263 9 2 7 55 116 3 7 4 2872 2988 3io4 3220 3336 3452 3568 3684 38oo 3 9 i5 3 7 5 4o3i 4i47 4263 43 7 9 44 9 4 46io 4 7 26 484i 4 9 5 7 5o 7 2 3 7 6 5i88 53o3 54i9 5534 565o 5 7 65 588o 5 99 6 6m 6226 n5 377 634i 645 7 65 7 2 6687 6802 6 9 i 7 7 o32 7 i4 7 7262 7377 3 7 8 7 4 9 2 7607 77 22 7836 79 5i 8066 8181 82 9 5 84io 8525 379 863 9 8 7 54 8868 8 9 83 997 O2I2 9 3 2 6 9 44i 9 555 9 66 9 n4 38o 9 784 9898 . .12 . 126 .241 .355 46 9 .583 .6 9 7 .811 38i 58o 9 25 1039 u53 1267 i38i i4 9 5 1608 I 7 22 i835 i 9 5o 382 2o63 2I 77 2291 2404 2 5i8 263i 2745 2858 2 9 72 3o85 383 3io 9 33i2 3426 N 353 9 3652 3 7 65 38 79 3 99 2 4io5 4218 n3 384 433i 4444 455 7 4670 4 7 83 48 9 6 5oo 9 5l22 5235 5348 385 546i 55 7 4 5686 5 799 5 9 I2 6024 6i3 7 625o 6362 6475 386 658 7 6700 6812 6 9 25 7 o3 7 7 i4 9 7262 7 3 7 4 7 486 7 5 99 112 38 7 7711 7 8 2 3 7935 8047 8160 82 7 2 8384 84 9 6 8608 8720 388 8832 8944 9 o56 9 l6 7 9 2 79 9 3 9 i 9 5o3 9 6i5 9726 9 838 38 9 99 5o ..61 .I 7 3 .284 .3 9 6 .5o 7 .6i 9 . 7 3o .842 . 9 53 Sgo 5 9 io65 1176 1287 i3 99 i5io 1621 I 7 32 i843 i 9 55 2066 III 391 2177 2288 23 99 25lO 2621 2 7 32 2843 2 9 54 3o64 3i 7 5 392 3286 33 97 " 3 5 08 36i8 3729 384o 3 9 5o 4o6i 4i 7 i 4282 3 9 3 43 9 3 45o3 46i4 4724 4834 4 9 45 5o55 5i65 52 7 6 5386 110 3 9 4 54 9 6 56o6 6717 582 7 5 9 3 7 6047 6i5 7 626 7 63 77 648 7 3 9 5 65 97 6707 6817 6 9 2 7 7 o3 7 7146 7 256 7 366 7 4 7 6 7 586 3 9 6 7 6 9 5 7 8o5 7 9 i4 8024 8i34 8243 8353 846a 85 7 2 8681 3 97 8 79 i 8900 9009 9119- 0.228 9337 9 446 9 556 9 665 9774 100 3 9 8 9 883 9992 .101 .210 .319 .428 .53 7 .646 . 7 55 .864 399 6oo 9 73 1082 1191 I2 99 i4o8 i5i7 1620 1734 i843 i 9 5r 4oo 2060 2169 2277 2386 24 9 4 a6o3 2 7 II 28i 9 2928 3o36 108 4oi 3i4'4 3253 336i 346 9 35 77 3686 3 79 4 3 9 02 4oio 4n8 4O2 4226 4334 4442 455o 4658 4766 48 7 4 4 9 82 5089 5i97 4o3 53o5 54i3 552i 5628 5 7 36 5844 5 9 5i 6o5 9 6166 62 7 4 4o4 638i 648 9 6596 6704 6811 6 9 i 9 7 026 7 i33 7241 7 348 io 7 4o5 7455 7562 7669 7777 7 884 799 1 8o 9 8 82o5 83i2 8419 4o6 8526 8633 8 7 4o 8847 8 9 54 9 o6i 9167 9 274 9 38i 9 488 4o 7 9 5 9 4 9701 9808 99 i4 ..21 .128 .234 .34i 44 7 .554 4o8 610660 0767 0873 o 9 7 9 1086 II 9 2 1298 i4o5 i5n i6i 7 1 06 N. 1 2 3 4 5 6 7 8 9 D. n 9 12 24 36 48 60 7 J 83 9 5 10-7 118 12 24 35 47 5 9 7 1 83 94 1 06 "7 . 12 23 35 47 5 9 70 82 94 io5 "6 fi 12 23 35 46 58 70 81 93 io4 o5 115 1 12 23 35 46 58 69 81 -9 3 io4 s u4 II 23 34 46 5 7 68 80 9 1 io3 i- n3 | . II 23 34 45 57 68 79 9 1 02 5 112 II 22 34 45 56 67 78 90 101 ft III 0, II 22 33 44 56 67 78 89 100 no 2 II 22 33 44 55 66 77 88 99 109 ^ II 22 33 44 55 65 76 87 98 1 08 II 22 32 43 54 65 76 86 97 107 II 21 32 43 54 64' 75 86 96 to LOGARITHMS OP NUMBERS. N. 1 2 3 4 5 6 7 8 9 D. 409 611723 1829 1936 2O42 2i48 2254 236o 2466 2572 2 6 7 8 106 4io 2784 2890 2996 3102 3207 33i3 3419 35 2 5 363o 3 7 36 4n 3842 3 9 4 7 4o53 4i5 9 4264 43 7 o 44?5 458i 4686 479 2 412 48 97 5oo3 5io8 52i3 5319 5424 5529 5634 5 7 4o 5845 io5 4i3 5950 6o55 6160 6265 63 7 o 64 7 6 658i 6686 6790 68 9 5 4U 7000 7io5 7210 7 3i5 7 420 7 5 2 5 7629 77 34 7 83 9 79 43 4i5 8o48 8i53 825 7 8362 8466 85 7 i 8676 8780 8884 8989 4i6 99 3 9198 9302 9406 9 5i i 9 6i5 9719 0.824 9928 ..32 104 4i 7 62oi36 O24o o344 0448 o55 2 o656 0760 o864 0968 1072 4i8 1176 1280 1 384 i486 l5 9 2 i6 9 5 1799 I 9 o3 2007 2110 419 22l4 23i8 2421 2525 2628 2 7 32 2835 2 9 3 9 3o42 3i46 420 3249 3353 3456 355 9 3663 3 7 66 386 9 3 97 3 4076 4179 io3 421 4282 4385 4488 45 9 i 46 9 5. 4 79 8 4901 5oo4 5107 5210 422 53i2 54i5 55i8 562i 5 7 24 582 7 5 9 2 9 6o32 6i35 6238 423 634o 6443 6546 6648 6 7 5i 6853 6 9 56 7 o58 7161 7 263 424 7 366 7 468 7 5 7 i 7 6 7 3 7775 7878 7980 8082 8i85 8287 IO2 426 838 9 8491 85 9 3 8695 8797 8 9 oo 9002 9 io4 9206 93*8 426 9410 9512 9 6i3 9 7 i5 0817 99 i 9 . .2.1 .123 .224 .326 427 63o428 o53o o63i o 7 33 o835 o 9 36 io38 n3 9 1241 1 342 428 1 444 1 545 1647 1748 i84 9 i 9 5i 2062 2i53 2255 2356 101 429 245 7 2 55 9 2660 2761 2862 2 9 63 3o64 3i65 3266 3367 43o 3468 356 9 3670 3 77 i 3872 3 97 3 4074 4i 7 5 4276 43 7 6 43i 4477 45 7 8 4679 4779 488o 4 9 8i 5o8i 5i8 2 5 2 83 5383 IOO 432 5484 5584 5685 5 7 85 5886 5 9 86 6087 6i8 7 6287 6388 433 6488 6588 6688 6789 688 9 6 9 8 9 7089 7 i8 9 7290 7 3 9 o 434 7490 7 5 9 7690 779 7 8 9 o 799 8090 8i 9 o 8290 838 9 435 8489 858 9 8689 8789 8888 8 9 88 9088' 9 i88 9287 9 38 7 99 436 9 486 9 586 9686 9785 9 885 99 84 ..84 .i83 .283 .382 43 7 64o48i o58i 0680 0779 o8 79 o 97 8 1077 1177 1276 i3 7 5 438 i4?4 1573 1672 1771 18-71 i 97 o 2069 2168 2267 2366 439 2465 2563 2662 2761 2860 2 9 5 9 3o58 3i56 3 2 55 3354 44o 3453 355i 365o 3 7 4 9 384 7 3 9 46 4o44 4i43 4242 434o 98 44 1 443 9 453 7 4636 4734 4832 4 9 3i 5029 5127 5226 5324 442 5422 552i 56i 9 5717 58i5 5 9 i3 60 1 1 6110 6208 63o6 443 64o4 65o2 6600 6698 6 79 6 68 9 4 6992 7 o8 9 7187 7 285 444 7383 748 1 7 5 79 7676 7774 7872 7969 8067 8i65 8262 445 836o 8458 8555 8653 8 7 5o 8848 8 9 45 9 o43 9140 9 23 7 97 446 9 335 9 43 2 9 53o 9627 97 2 4 9 82I 99 i 9 ..16 .n3 .210 447 65o3o8 o4o5 o5o2 0599 o6 9 6 o 79 3 o8 9 o o 9 8 7 io84 1181 448 1278 i3 7 5 1472 i56 9 1666 1762 i85 9 I 9 56 2o53 2i5o 449 2246 2343 2440 2536 2633 2730 2826 2 9 23 3019 3n6 45o 32i3 33o 9 34o5 35o2 35 9 8 36 9 5 3 79 i 3888 3 9 84 4o8o 96 45 1 4i77 42 7 3 436 9 4465 4562 4658 4?54 485o 4946 5o42 452 5:38 5235 533i 5427 5523 56i 9 5 7 i5 58io 5906 6002 453 6098 6194 629.0 6386 6482 65 77 66 7 3 6 7 6 9 6864 6 9 6o 454 7 o56 7lf>2 7247 7343 7438 7534 7 62 9 7725 7820 7 9 i6 455 Sou 8107 8202 8298 83 9 3 8488 8584 8679 8774 8870 9 5 456 8965 9060 9 i55 925o 9 346 9 44i 9 536 9 63i 9726 0.821 45 7 9916 . . ii . 106 .201 .2 9 6 .3 9 i .486 .58i .676 .771 N. 1 2 3 4 5 6 7 8 9 1). 1 06 ii 21 32 4a 53 64 74 85 9 b io5 ii 21 32 4a 53 63 74 84 9 5 io4 Z IO 21 3i 42 52 62 73 83 94 d| 103 10 21 3i 4i 52 62 72 82 93 05 g 102 IO 2O 3i 4i 5i 61 7i 82 93 1 101 | , IO 20 3o 4o 5i 61 7i 81 9 1 | loo ' IO t 20 3o 4o 5o 60 70 80 90 5 99 L 10 2O 3o 4o 5o 5 9 69 79 89 9 8 ? IO 2O 29 3 9 49 5 9 78 88 ftj 97 P 10 I9' 29 3 9 49 58 68 78 87 96 10 1 9 29 38 48 58 67 77 86 Lo-GARITHMS OF NUMBERS. N." 1 " 1 2 3 4 ]| 5 6 7 8 9 D 458 66o865 o 9 6o io55 n5o 1245 i33 9 i434 ID2 9 1623 1718 9 5 -45 9 i8i3 I 9 o 7 2O02 2O 9 6 2I 9 I 2286 238o 2475 256 9 2663 46o 2 7 58 2852 2947 3o4i 3 1 35 323o 3324 34i8 35i2 3607 94 46 1 3701 3 79 5 3889 3 9 83 4o 7 8 4l 7 2 4266 436o 4454 4548 462 4642 4 7 36 483o 4 9 24 5oi8 5lI2 5206 52 99 53 9 3 548 7 463 558i 56 7 5 5769 5862 5 9 56 6o5o 6i43 6237 633i 6424 464 65i8 6612 6705 6799 68 9 2 6 9 86 779 7 i 7 3 7266 736o 465 7453 7 546 7640 7733 7826 79 20 8oi3 8106 8i 99 82 9 3 9 3 466 8386 84 79 85 7 2 8665 8 7 5 9 8852 8 9 45 9 o38 9 i3i 9 224 46 7 9 3i 7 9 4io 95o3 9 5 9 6 9 68 9 97 82 9 8 7 5 99 6 7 ..60 ,i53 468 670246 oSSg o43i o524 061-7 7 IO 0802 o8 9 5 o 9 88 1080 46 9 1173 1265 i358 i45i 1 543 i636 1728 1821 I 9 i3 2OO5 4 7 o 2098 2190 2283 2375 246 7 256o 2652 2744 2836 2 9 2 9 92 4 7 i 3021 3n3 32o5 3297 33 9 o 3482 35 7 4 3666 3 7 58 385o 4 7 2 3 9 42 4o34 4126 4218 43io 4402 4494 4586 46 77 4 7 6 9 4 7 3 486i 4953 5o45 5i3 7 5228 5320 54i2 55o3 55 9 5 5687 4 7 4 > 77 8 58 7 o 5962 6o53 6i45 6236 6328 64i 9 65n 6602 4 7 5 66 9 4 6 7 85 6876 6 9 68 7 o5 9 7 i5i 7242 -,333 7424 7 5i6 9 1 7607 7698 7789 7881 7972 8o63 8i54 8245 8336 8427 477 85i8 8609 8700 8 79 i 8882 8973 9064 9 i55 9 246 933 7 478 9 428 9 5i 9 9610 9 7oo 979 1 9 882 9973 ..63 .i54 .245 479 68o336 0426 o5i7 0607 o6 9 8 o 7 8 9 0879 o 9 7O 1060 n5i 48o 1241 i332 l422 i5i3 i6o3 i6 9 3 1784 i8 7 4 i 9 64 2o55 9 48 1 2i45 2235 2326 2416 25o6 2 5 9 6 2686 2777 2867 2 9 5 7 482 3o47 3i3 7 3227 33i7 34o 7 34 9 7 3587 36 7 7 3 7 6 7 385 7 483 3 9 4 7 4o3 7 4l27 4217 43o 7 43 9 6 4486 45 7 6 4666 4756 484 4845 4 9 35 5o25 5n4 52o4 52 9 4 5383 54 7 3 5563 5652 485 5742 583i 5921 6010 6100 6i8 9 6279 6368 6458 6547 8 9 486 6636 6726 68i5 6 9 o4 6 99 4 7 o83 7172 7 26l 735i 744o 487 7 52 9 7618 7707 779 6 7886 797 5 8o64 8i53 8242 833i 488 8420 8509 85 9 8 868 7 8776 8865 8953 9 o42 9 i3i 9 22O 48 9 9 3o 9 9 3 9 8 9486 9 5 7 5 9 664 97 53 9841 99 3o . .19 .107 4 9 o 6 9 oi 9 6 0285 0373 0462 o55o o63 9 0728 0816 ogoS o 99 3 4 9 i 1081 1170 I2 58 i34 7 i435 i524 1612 1700 1789 1877 88 492 i 9 65 2o53 2l42 2230 2 3i8 2406 24 9 4 2583 2671 2 7 5 9 493 284 7 2 9 35 3023 3m 3i 99 328 7 3375 3463 355i 363 9 4 9 4 3 7 2 7 38i5 SgoS 3 99 i 4o 7 8 4i66 4254 4342 443o 45i 7 495 46o5 46 9 3 478l 4868 4 9 56 5o44 5i3i 52I 9 5307 53 9 4 496 5482 556 9 5657 5 7 44 5832 5 9 i 9 6007 6o 9 4 6182 626 9 87 497 6356 6444 653i 6618 6 7 o6 6 79 3 6880 6 9 68 7 o55 7142 498 7 22 9 7 3: 7 74o4 74 9 i 7 5 7 8 7 665 77 5a 7 83 9 7926 8oi4 499 8101 8188 82 7 5 8362 844 9 8535 8622 8 7 o 9 8796 8883 5oo 8 97 o 9067 9i44 9 23l 9 3i 7 9 4o4 9491 9 5 7 8 9664 97 5i 5oi 9 838 9024 . . ii ..08 .184 .271 .358 .444 .53i .617 502 7 oo 7 o4 0790 0877 oo63 io5o n36 1222 i3o 9 iSgS 1482 86 5o3 i568 1 654 1741 1827 I 9 i3 i 999 2086 2I 7 2 2258 2344 5o4 243l 2517 2 6o3 268 9 2 77 5 2861 2947 3o33 3119 32o5 5o5 32 9 I 33 77 3463 354 9 3635 3721 3807 38 9 3 3 979 4o65 5o6 4i5i 4236 4322 44o8 44 9 4 45 79 4665 4 7 5i 483 7 4922 507 5oo8 5094 5 1 79 5 2 65 535o 5436 5522 56o 7 56 9 3 5 77 8 N. 1 2 3 4 || 5 6 7 8 9 D. 9 5 IO 19 2 9 38 48 57 67 76 86 94 a 9 19 28 38 47 56 66 75 85 93 s 9 i 9 28 37 47 56 65 74 84 a 9 2 PU 9 18 28 37 46 55 64 74 83 Q - 91 1- 9 18 27 36 46 55 64 73 82 9 9 18 27 36 45 54 61 72 81 P' 89 I' 9 18 2 7 36 45 53 6? 80 88 o" g 18 26 35 44 53 62 7 79 8 7 9 17 26 35 44 52 61 70 78 86 9 17 26 34 43 52 60 69 77 LOGARITHMS OF NUMBERS. N. 1 2 3 4 5 6 7 8 9 D. 5o8 7 o5864 5 9 49 6o35 6120 6206 6291 63 7 6 6462 654 7 6632 85 5o 9 6 7 i8 68o3 6888 6974 7 o5 9 7i44 7 22 9 7 3i5 7 4oo 7485 5io 7 5 7 o 7 655 7740 7826 7911 7996 8081 8166 825x 8336 5u 8421 85o6 85 9 i 8676 8761 8846 8 9 3i 9 oi5 9 xoo 9 x85 5l2 9 2 7 o 9 355 9 44o 9524 9609 9694 9779 9 863 9 9 48 ..33 5i3 7 IOII 7 O2O2 0287 0371 o456 o54o 0625 0710 o 79 4 08 79 5i4 o 9 63 io48 Il32 1217 i3oi i385 1470 x554 x63 9 1723 84 5i5 i8o 7 l8 9 2 1976 2060 2i44 2229 2 3i3 2 3 97 248 1 2566 5i6 265o 2 7 34 2818 2902 2986 3070 3i54 3238 3323 34o 7 5i 7 34 9 i 35 7 5 365 9 3 7 42 3826 3910 3 99 4 4078 4x62 4246 5i8 433o 44i4 44 9 7 458i 4665 4749 4833 4 9 x6 5ooo 5o84 5i 9 5i6 7 5 2 5i 5335 54i8 55o2 5586 566 9 5 7 53 5836 5 9 2O 52O 6oo3 6087 6170 6254 633 7 6421 65o4 6588 66 7 x 6 7 54 83 521 6838 6 9 2I 7004 7088 7171 7 254 7338 7421 7 5o4 7 58 7 522 7671 7754 7 83 7 7 9 20 8oo3 8086 8i6 9 8 2 53 8336 84i 9 5 2 3 85o2 8585 8668 8 7 5i 8834 8917 9 ooo 9 o83 9i65 9 248 524 9 33i 9 4i4 9497 9$ So 9 663 9745 9 828 99 xx 9994 77 525 7 20l5 9 0242 o3 2 5 0407 0490 o5 7 3 o655 o 7 38 0821 o 9 o3 5 2 6 o 9 86 1068 u5i 1233 i3i6 i3 9 8 i48i x563 x 646 1728 82 52 7 1811 i8 9 3 i 97 5 2o58 2i4o 2222 2 3o5 2 38 7 2469 2552 5 2 8 2634 2716 2 79 8 2881 2963 3o45 3127 320 9 3291 33 7 4 52 9 3456 3538 3620 3702 3784 3866 3 9 48 4o3o 4lI2 4i 9 4 53o 42 7 6 4358 444o 4522 46o4 4685 4767 484 9 4g3x 5ox3 53i 5o 9 5 5176 5 2 58 534o 5422 55c3 5585 566 7 5 7 48 583o 532 5 9 I2 5 99 3 6o 7 5 6i56 6238 6320 64oi 6483 6564 6646 533 6 7 2 7 68o 9 68 9 o 6 9 72 7 o53 7i34 7216 7 2 97 7379 7460 81 534 7 54i 7623 77 o4 7785 7866 7948 8o2 9 8110 8191 8273 535 8354 8435 85i6 85 97 8678 8 7 5 9 884i 8(,22 9003 9084 536 9 i65 9 246 9 32 7 9 4o8 9489 9 5 7 o 9 65i 97 3'2 9813 9 8 9 3 53 7 9974 ..55 .136 .2I 7 .298 .3 7 8 45 9 .540 .621 .702 538 7 3o 7 82 o863 o 9 44 1024 no5 1186 1266 1 347 1428 i5o8 53 9 1589 i66 9 i 7 5o i83o 1911 i 99 i 2072 2l52 2233 a3i3 54o 2394 2474 2555 2635 2715 2 79 6 2876 2 9 56 3o37 3n 7 80 54i 3i 97 32 7 8 3358 3438 35i8 35 9 8 36 79 3 7 5 9 383 9 3 9 x 9 542 3 999 4o7 9 4x^0 4240 4320 44oo 448o 456o 464o 4 7 20 543 48oo 488o 4 9 6o 5o4o 5l2O 52OO 527 9 535 9 543 9 55x 9 544 55 99 56 7 9 5 7 5 9 5838 5 9 i8 5 99 8 6078 6i5 7 6 2 3 7 63i 7 545 63 97 6476 6556 6635 6715 6 79 5 68 7 4 6 9 54 7o34 7 n3 546 7193 7272 7 352 743 1 7 5n 7 6 7 o 7749 7829 79 o8 79 54 7 79 8 7 8067 8i46 8225 83o5 8384 8463 8543 8622 8 7 ox 548 8 7 8i 8860 8 9 3 9 9 oi8 9097 9 i77 9 256 9 335 9 4i4 9493 54 9 9 5 7 2 9 65i 97 3i 9 8io 9889 99 68 ..47 .126 .2O5 .284 55o 7 4o363 0442 o52I 0600 0678 7 5 7 o836 0915 o 99 4 xo 7 3 55i Il52 1230 1 309 1 388 1467 1 546 1624 I 7 o3 1782 1860 552 i 9 3 9 2018 2096 2175 2254 2332 2411 2489 2568 2 64 7 553 2725 2804 2882 2 9 6i 3o3 9 3n8 3i 9 6 32 7 5 3353 343 1 78 554 35io 3588 366 7 3 7 45 38 2 3 3 9 O2 3 9 8o 4o58 4x36 42i5 555 4293 43 7 i 4449 4528 46o6 4684 4762 484o 4 9 x 9 4997 556 5o 7 5 5i53 5 2 3i 53o 9 538 7 5465 5543 562i 56 99 5 777 55 7 5855 5 9 33 6011 6089 6167 6245 6323 64ox 6479 6556 558 6634 6712 6790 6868 6 9 45 7023 7101 7 x 7 9 7256 7 334 N. 1 2 3 4 5 i 7 8 9 D. 86 9 -7 26 34 43 52 60 6 9 77 85 fi 17 26 34 43 5i 60 68 77 n 84 8 25 34 42 5o 5 9 67 76 I 83 2 8 17 25 33 42 5o 58 6fr 75 I* 82 g, o 8 16 25 33 4i 49 57 66 74 *e 81 'S 8 1 16 24 32 4i 49 5 7 65 73 Q 80 | 8 16 24 32 4o 48 56 64 7 2 79 8 16 24 32 4o 47 55 63 71 78 * 8 16 23 3i 3 9 47 55 62 70 LOGARITHMS OF J\UMBERS. 13 N. 1 2 3 4 5 6 7 8 9 D. 55 9 7 4 7 4i2 7 48 9 7 56 7 7 645 7722 7800 7878 79.55 8o33 8110 7 8 56o 8188 8266 8343 8421 84 9 8 85 7 6 8653 8 7 3i 8808 8885 77 56i 8 9 63 9 o4o 9118 9 i 9 5 9 272 9 35o 9427 9 5o4 9582 9 65 9 562 9736 9 8i4 9891 99 68 ..45 .123 .200 .277 .354 .43i 563 7 5o5o8 o586 o663 o 7 4o 0817 0894 0971 io48 1125 I2O2 564 I2 79 i356 i433 i5io 1587 i664 i 7 4i 1818 1895 I 97 2 565 2048 2125 22O2 22 79 2356 2433 25o 9 2586 2663 2740 566 2816 28 9 3 2 97 3o4 7 3i23 3200 3277 3353 343o 35o6 567 3583 366o 3 7 36 38i3 388 9 3 9 66 4042 4n 9 4ig5 4272 \ $68 4348 4425 45oi 45 7 8 4654 4?3o 4807 4883 4960 5o36 76 56 9 5lI2 5i8 9 5265 534: 54i 7 54 9 4 5570 5646 5722 5 799 570 58 7 5 5 9 5i 602-7 6io3 6180 6256 633 2 64o8 6484 656o 5 7 i 6636 6 7 I2 6 7 88 6864 6 9 4o 7016 70 9 2 7168 7 244 7320 5 7 2 7396 7 4 7 2 7 548 7624 7700 777 5 7 85i 79 2 7 8oo3 8079 5 7 3 8i55 823o 83o6 8382 8458 8533 86o 9 8685 8761 8836 5 7 4 8 9 I2 8 9 88 9 o63 9 i3 9 9 2l4 9 2 9 o 9 366 9 44i 9 5l 7 9 5 9 2 5 7 5 9 668 9743 9 8i 9 9 8 9 4 997 ..45 .121 .196 .272 34 7 75 5 7 6 760422 o4 9 8 o5 7 3 o64 9 0724 799 ogSo IO25 IIOI 5 77 n 7 6 I25l i326 1402 i4 77 i552 1627 1702 1778 i853 5 7 8 I 9 28 2OO3 2O 7 8 2i53 2228 23o3 23 7 8 2453 2529 2604 5 79 26 79 2 7 54 282 9 2 9 04 2 97 8 3o53 3i28 32o3 32 7 8 3353 58o 3428 35o3 35 7 8 3653 3727 38o2 38 77 3 9 5 2 4027 4ioi 58i 4i 7 6 425i 4326 44oo 44 7 5 455o 4624 4699 4 77 4 4848 582 4 9 23 4 99 8 5o 7 2 5i4 7 5221 52 9 6 53 7 o 5445 5520 5594 583 566 9 5743 58i8 58 9 2 5 9 66 6o4i 6n5 6190 6264 6338 74 584 64i3 648 7 6562 6636 6 7 io 6 7 85 685 9 6 9 33 7007 -7082 585 7 i56 723o 7 3o4 7 3 79 7 453 7 52 7 7601 7 6 7 5 7749 7 823 586 7898 7972 8o46 8120 8i 9 4 8268 8342 -84i6 8490 8564 58 7 8638 8712 8 7 86 8860 8 9 34 9008 9 o82 9 i56 9230 93o3 588 9 3 77 945 1 9 5 2 5 9 5 99 9673 9746 9 820 9 8 9 4 9968 ..42 58 9 77 on5 oi8 9 0263 o336 o4io o484 o55 7 o631 0705 0778 5 9 o o852 0926 999 io 7 3 n46 I22O I2 9 3 i36 7 i44o i5i4 5 9 i i58 7 1661 i 7 34 1808 1881 i 9 55 202% 2 1 02 2175 2248 73 2322 2 3 9 5 2468 2542 2 6i5 2688 2 7 62 2835 2908 2081 5 9 3 3o55 3i28 3201 32 7 4 3348 3421 34 9 4 3567 364o 3713 5 9 4 3 7 86 386o 3 9 33 4oo6 4o 79 4i52 4225 4298 437i 4444 5 9 5 45i 7 45 9 o 4663 4 7 36 48o 9 4882 4 9 55 5028 5ioo 5i 7 3 5 9 6 5246 53i 9 53 9 2 5465 5538 56io 5683 5 7 56 5829 5902 5 97 5 97 4 6o4 7 6120 6i 9 3 6265 6338 64n 6483 6556 6629 5 9 8 6701 6774 6846 6 9 i 9 6 99 2 7 o64 7 i3 7 7209 7282 7 354 5 99 7 42 7 7499 7 5 7 2 7 644 77 i 7 7789 7862 7934 8006 8o 7 9 72 600 8i5i 8224 82 9 6 8368 844 1 85i3 8585 8658 8 7 3o 8802 . 601 88 7 4 8 9 4 7 9 OI 9 9 o 9 i 9 i63 9 236 93o8 9380 9452 9624 602 9 5 9 6 9 66 9 974i 9 8i3 9 885 99 5 7 ..29 .101 .i 7 3 .245 6o3 7 8o3i 7 o38 9 o46i o533 o6o5 0677 o 7 4 9 0821 0893 0965 6o4 1037 nog 1181 1253 1324 i3 9 6 i468 i54o 1612 1 684 6o5 I 7 55 1827 i8 99 1971 2042 2Il4 2186 2258 2329 24OI 606 24 7 3 2544 2616 2688 2 7 5 9 283i 2 9 O2 2974 3o46 3n 7 6o 7 3i8 9 3260 3332 34o3 34 7 5 3546 36i8 368 9 3 7 6i 3832 71 608 3 9 o4 3 97 5 4o46 4n8 4i8 9 4261 4332 44o3 44 7 5 4546 6o 9 46i 7 468 9 4760 483i 4902 4974 5o45 5n6 5187 5 2 5 9 610 533o 54oi 54 7 2 543 56i5 5686 5 7 5 7 5828 58 99 5970 611 6o4i 6112 6i83 6254 63 2 5 63 9 6 646 7 6538 6609 6680 N. 1 2 3 4 5 6 7 8 9 D. 77 8 i5 23 3i 39 46 54 62 69 8 7 6 } 8 i5 23 3o 38 46 53 61 68 7 5 8 i5 23 3o 38 45 53 60 68 2 ' 74 ^< 7 i5 23 3o 3 7 44 52 5 9 67 i 7 3 g, 7 i5 22 29 3? 44 5i 58 66 S 72 2 7 i4 22 29 36 43 5o 58 65 7 I PH 7 i4 31 28 36 43 5o 57 64 14 LOGARITHMS OF LUMBERS. N. 1 2 3 4 5 6 7 8 9 D. 612 786751 6822 68 9 3 6964 7 o35 7 io6 7 i 77 7248 7 3i 9 7 3 9 o 7 1 6i3 7460 7 53i 7602 7 6 7 3 7744 7 8i5 7 885 79 56 802-7 8o 9 8 6i4 8168 8239 83io 838i 845i 8522 85 9 3 8663 8 7 34 88o4 6i5 88 7 5 8 9 46 9016 9 o8 7 9 l5 7 9228 9299 9 36 9 9 44o 9 5io 616 9 58i 9 65i 97 22 979 2 9 863 99 33 ...4 .. 7 4 i44 .215 70 6i 7 7 9 0285 o356 O426 0496 0567 06 3 7 0707 o 77 8 o848 o 9 i8 618 o 9 88 1059 1129 1199 1269 i34o i4io i48o i55o 1620 6i 9 i6 9 i i 7 6i i83i 1901 1971 2041 2III 2181 2252 2322 620 23 9 2 2462 2532 2602 2672 2742 >8l2 2882 2 9 52 3022 621 3o 9 2 3i6 2 3 2 3i 33oi 33 7 i 344i 35u 358i 365i 3 7 2I 622 3790 386o 3 9 3o 4ooo 4o 7 o 4i3 9 420 9 42 79 4349 44i8 6 2 3 4488 4558 462 7 4697 4 7 6 7 4836 4 9 o6 4 97 6 5o45 5n5 624 5i85 5 2 54 5324 53 9 3 5463 5532 5602 56 7 2 5 7 4i 58n 6 2 5 588o 5949 6019 6088 6i58 6227 62 97 6366 6436' v65o5 69 626 65 7 4 6644 6 7 i3 6782 6852 6 9 2I 6990 7060 7 I2 9 7 i 9 8 627 7268 7 33 7 7 4o6 7 4 7 5 7 545 7614 7 683 77 '52 -7821 628 79 6o 8029 8098 8167 8236 83o5 _83?4 8443 85i3 8^82 620, 865i 8 7 20 8-789 8858 8927 8 99 6 9 o65 9 i34 9 203 9 2 7 2 63o 9 34i 9409 94 7 8 9 547 9616 9685 97 54 9 823 9 8 9 2 99 6i 63i 8ooo2 9 0098 oi6 7 0236 o3o5 o3 7 3 0442 o5u o58o o648 632 0717 0-786 'o854 O 9 23 0992 1061 II2 9 n 9 8 1266 i335 633 i4o4 l4 7 2 i54i 1609 i6 7 8 i 7 4 7 i8i5 1 88.; I 9 52 2021 634 2o8 9 2i58 2226 22 9 5 2363 2432 25oo 2568 263 7 2 7 o5 635 2774 2842 2910 2979 3o4 7 3u6 3i84 3252 332i 338 9 68 636 345 7 3525 35 9 4 3662 3 7 3o 3798 386 7 3 9 35 4oo3 4o 7 i 63 7 4i3 9 4208 42 7 6 4344 44i2 448o 4548 46i6 4685 4?53 638 4821 488 9 4 9 5 7 5o25 5o 9 3 5i6i 522 9 52 97 5365 5433" 63 9 55oi 556 9 563 7 5 7 o5 5 77 3 584i 5908 5 97 6 6o44 6112 64o 6180 6248 63i6 6384 645 1 65i 9 6587 6655 6 7 23 670.0 64 1 6858 6926 6 99 4 7061 7 I2 9 7197 7264 7 33 2 7 4oo 7 46 7 1 642 7 535 7 6o3* 7 6 7 o 7738 7806 7873 7941 8008 80-76 8i43 I 643 8211 8 2?9 8346 84i4 848 1 8549 8616 8684 8 7 5i 8818 67 644 8886 9 02I 1 9 o88 9i56 9223 9290 9 358 9 425 9 4 9 2 645 9 f>6o 962-7 9 6 9 4 9762 9829 9 8 9 6 9964 . .3i ..98 .i65 646 8io233 o3oo o36 7 o434 o5oi o56 9 o636 o 7 o3 o 77 o o83 7 647 o 9 o4 09-71 io3 9 1 1 06 H 7 3 1240 1307 i3 7 4 i44i i5o8 648 i5 7 5 1642 I 7 o 9 1776 i843 I 9 IO 1977 2044 2III 2178 64 9 2245 23l2 2 3 79 2445 25l2 25 79 2646 2 7 l3 2 7 80 2847 65o 2 9 l3 2980 3o4 7 3n4 3i8i 33i4 338x 3448 35x4 65i 358i 3648 3 7 i4 3 7 8i 3848 3 9 i4 3 9 8i 4o48 4ii4 4i8i 652 4248 43i4 438i 4447 45i4 458 1 4647 4 7 i4 4 7 8o 4847 653 4 9 i3 4980 5o46 5u3 51-79 5246 53i2 53 7 8 5445 55n 66 654 55 7 8 5644 5 7 i i 5777 5843 5 9 io 5 97 6 6042 6io 9 6i 7 5 655 6241 63o8 63 7 4 644o 65o6 65 7 3 663 9 6 7 o5 6 77 i 6838 , 656 6 9 o4 69-70 7 o36 7102 7169 7 235 7 3oi 7 36 7 7 433 7499 65 7 7 565 7 63i 7 6 9 8 7764 7 83o 7 8 9 6 79 62 8028 8o 9 4 8160 658 8226 8292 8358 8424 8490 8556 8622 8688 8 7 54 8820 65 9 8885 8 9 5i 9 oi 7 9083 9149 9 2l5 0281 9 346 9 4l2 9478 660 661 9 544 820201 9 6io 026-7 9676 o333 97 4i o3 99 o464 9873 653o llll ...4 0661 ..70 7 2 7 .i36 0792 662 o858 O 9 24 o 9 8 9 io55 1120 1186 I25l i3i 7 1382 i448 663 i5i4 i5 79 i645 I 7 IO i 77 5 i84i I 9 o6 I 97 2 203 7 2103 65 664 2168 2233 22 99 2364 243o 24 9 5 256o 2626 26 9 I 2 7 56 N. 1 2 3 4 5 6 7 8 9 D. 7 1 7 i4 21 28 36 43 5o 57 64 7 o 7 i4 21 28 35 42 49 56 63 g 69 p. 7 i4 21 28 35 4i 48 55 62 * 68 .. . 7 i4 20 27 34 4i 43 54 61 i 67 . 7 i3 30 27 34 4o 47 54 60 s 66 2 7 i3 20 26 33 4o 46 53 5 9 65 < 7 i3 20 26 33 39 46 52 5 9 LOGARITHMS OF NUMBERS. N. 1 2 3 4 5 6 7 8 9 D. 665 822822 2887 2 9 52 3oi8 3o83 3i48 32i3 3279 3344 3409 65 666 3474 3539 36o5 3670 3 7 35 38oo 3865 3 9 3o 3 99 6 4o6i 667 4126 4191 4256 4321 4386 445 1 45i6 458i 4646 4711 668 4776 484i 4go6 4971 5o36 5ioi 5i66 523i 52 9 6 536i 669 5426 5491 5556 562i 5686 5 7 5i- 58i5 588o 5 9 45 6010 670 6075 6i4o 6204 626 9 6334 63 99 6464 65 2 8 65 9 3 6658 671 6723 6787 6852 6917 6 9 8i 7046 7111 7 i 7 5 7240 7 3o5 672 7 36 9 7434 7499 7 563 7628 76 9 2 77 5 7 7821 7 886 795i 673 8oi5 8o'8o 8i44 8209 82 7 3 8338 8402 846 7 853i 85 9 5 64 674 8660 8724 8789 8853 8 9 i8 8 9 82 9046 9111 9 i 7 5 9 23 9 6 7 5 93o4 9368 9432 9497 9 56i 9 625 9690 9754 9818 9 88 2 676 9947 . .11 .. 7 5 .189 .2O4 .268 .332 .3 9 6 .46o .525 677 83o58 9 o653 0717 0781 0845 o 9 o 9 0973 io3 7 IIO2 1166 678 1230 1294 i358 1422 i486 i55o 1614 i6 7 8 1742 1806 679 1870 1934 1998 2062 2126 2189 2253 23l 7 23~8i 2445 680 2509 2 5 7 3 2637 2700 2 7 64 2828 2892 2956 3020 3o83 68 1 3i47 3211 32 7 5 3338 3402 3466 353o SSgS 365 7 3721 682 3 7 84 3848 3912 3 97 5 4o3 9 4io3 4i66 4*3o 4294 435 7 683 442i 4484 4548 46n 46 7 5 4 7 3 9 4802 4866 4929 4 99 3 684 5o56 5l20 5i83 5 2 47 53io 53 7 3 543 7 55oo 5564 5627 63 685 6691 5754 58i 7 588i 5 9 44 6007 6071 6r34 619-7 -6261 686 6324 638 7 645 1 65i4 65 77 664i 6704 6767 683o 68 9 4 687 6 9 5 7 7 020 7 o83 7i46 7210 7273 7336 7399 7462 7 5 2 5 688 7 588 7 652 771.5 7778 7 84i 7904 7967 8o3o 8093 8i56 689 8219 8282 8345 84o8 84 7 i 8534 8597 8660 8 7 a3 8786 690 8849 8912 8 97 5 9 o38 9 ioi 9164 9227 9289 9 35 2 9 4i5 691 9478 9 54i 9 6o4 9 667 97 2 9 9792 9855 9918 998i ..43 692 84oio6 0169 0232 02 9 4 o35 7 O420 0482 o545 0608 0671 693 0733 o 7 96 o85 9 9 2I 0984 io46 1109 1172 1234 I2 9 7 6 9 4 1359 l422 i485 1 547 1610 1672 I 7 35 1797 1860 I 9 22 6 9 5 1985 204 7 2IIO 2172 2235 2297 2 36o 2422 2484 2547 6a 696 2609 26 7 2 2 7 34 2 79 6 2859 2921 2983 3o46 3io8 3170 697 3233 32 9 5 3357 3420 3482 3544 36o6 3669 3 7 3i 3 79 3 698 3855 3918 3 9 8o 4042 4io4 4i66 4229 4291 4353 44i5 699 4477 453 9 46oi 4664 4-726 4788 485o 4912 4 97 4 5o36 700 5098 5i6o 5222 5284 5346 54o8 5470 5532 55 9 4 5656 701 5 7 i8 5 7 8o 5842 5 9 o4 5966 6028 6090 6i5i 6213 6275 702 6337 63 99 646 1 6523 6585 6646 6708 6770 6832 68 9 4 7 o3 6 9 55 7oi 7 7079 7141 7202 7264 7326 7388 7449 7 5n 704 7 5 7 3 7634 7696 7758 7819 7881 79 43 8oo4 8066 8128 705 8189 825i 83i2 83 7 4 8435 8497 855 9 8620 8682 8 7 43 706 88o5 8866 8928 8 9 8 9 9o5i 9112 9 i 7 4 9235 9297 ^358 61 707 9419 948i 9542 9 6o4 9665 9726 97 88 9849 9911 9972 708 85oo33 0095 oi56 0217 0279 o34o o4oi 0462 o5 2 4 o585 709 o646 070? 0769 o83o 0891 0952 1014 io 7 5 n36 n 97 710 1258 1320 i38i 1442 i5o3 i564 1625 1686 1747 i8o 9 711 1870 1931 1992 2o53 2Il4 2175 2236 229 7 2358 24l 9 712 2480 2 54i 2602 2663 2724 2 7 85 2846 290 7 2968 3o2 9 718 Sogo 3i5o 3211 3272 3333 33 9 4 3455 35i6 35?7 363 7 7 i4 36 9 8 3 7 5 9 3820 388i 3 9 4i 4002 4o63 4124 4i85 4245 7 i5 43o6 436 7 4428 4488 454 9 46io 46 7 o 4 7 3i 479 2 485 2 716 4gi3 4 9 ?4 5o34 5o 9 5 5i56 52i6 5 2?7 533 7 53 9 8 545 9 717 55i 9 558o 564o 5701 5761 5822 5882 5 9 43 6oo3 6o64 718 6124 6i85 6245 63o6 6366 6427 648 7 6548 6608 6668 60 719 6729 6789 685o 6 9 io 6 97 7o3i 7 o 9 i 7 l52 7212 7 2 7 2 N. ' 1 2 3 4 || 5 6 7 8 9 D. 64 og 6 i3 J 9- 26 32 38 45 5i 58 |2 63 S 6 i3 1 9 25. 32 38 44 5o 57 1 62 PH- 6 12 J 9 25 3i 37 43 5o 56 6 61 o 6 12 18 24 3i 3? 43 49 55 . 60 6 12 18 24 3o 36 42 48 54 LOGARITHMS OF NUMBERS. N. 1 2 3 4 5 6 7 8 9 D. 720 85 7 332 7 3 9 3 7 453 7 5i3 7 b 7 4 7 634 7 6 9 4 77 55 7 8i5 7 8 7 5 60 721 79 35 799 5 8o56 8116 8i 7 6 8236 82 97 835 7 84i 7 84 77 722 853 7 85 97 865 7 8 7 i8 8778 8838 8898 8 9 58 9 oi8 9 o 7 8 72 3 9 i38 9198 9 258 9318 9 3 79 9 43 9 9499 9 55 9 9 6i 9 9 6 79 7 24 9739 9799 9 85 9 99 i8 997 s ..38 ..98 .158 .218 .278 726 86o338 0398 o458 o5i8 o5 7 8 o63 7 o69 7 0757 o8i 7 0877 726 o 9 3 7 0996 io56 1116 H 7 6 1236 1295 i355 i4i5 i4 7 5 727 i534 1594 i654 1-714 I 77 3 i833 i8 9 3 I 9 52 2012 2O 7 2 728 2l3l 2191 225l 23lO 23 7 243o 2489 254 9 2608 2668 729 2-728 2 7 8 7 2 84 7 2 9 o6 2966 3o25 3o85 3i44 3-204 3263 7 3o 33 2 3 3382 3442 35oi 356i 3620 368o 3 7 3 9 3 799 3858 5 9 7 3i 3 9 i 7 3 977 4o36 4o 9 6 4i55 42i4 42 7 4 4333 43 9 2 4452 7 32 45n 45 7 o 463o 468 9 4 7 48 48o8 486 7 4 9 26 4 9 85 5o45 7 33 5io4 5i63 5222 5282 534i 54oo 545 9 55i 9 55 7 8 563 7 734 56 9 6 5 7 55 58i4 58 7 4 5 9 33 5 99 2 6o5i 6110 6i6 9 6228 7 35 6287 6346 64o5 6465 6524 6583 6642 6701 6 7 6o 68i 9 736 68 7 8 6 9 3 7 6996 7 o55 7 n4 7 i 7 3 7 232 72 9 i 7 35o 7 4o 9 7 3 7 7 46 7 7 5 2 6 7 585 7 644 77 o3 7762 7 82I 7880 79 3 9 -7998 7 38 8o56 8n5 8i 7 4 8233 82 9 2 835o 8409 8468 85 2? 8586 7 3 9 8644 8 7 o3 8 7 6 2 8821 88 79 8 9 38 8997 9 o56 9 ii4 9 i 7 3 ?4o 9232 9 2 9 9349 9 4o8 9 466 9 5 2 5 9 584 9 642 97 oi 9 7 6o 7 4i 9818 9 8 77 9935 9994 ..53 .in .1-70 .228 .28-7 .345 742 8 7 o4o4 0462 0521 o5 79 o638 o6 9 6 o 7 55 o8i3 08-72 0930 58 743 0989 1047 1106 n64 1223 1281 1339 i3 9 8 i456 i5i5 744 i5 7 3 i63i 1690 i 7 48 1806 1 865 1923 i 9 8i 2040 2098 745 2i56 22l5 22 7 3 2 33i 2 38 9 2448 25o6 2564 2622 2681 746 2 7 3 9 2797 2855 2913 2 97 2 3o3o 3o88 3i46 3204 3262 74 7 332i 3379 343 7 3495 3553 36ii 366 9 3727 3 7 85 3844 748 3902 3960 4oi8 4o 7 6 4i34 4192 425o 43o8 4366 4424 7^9 4482 4540 45 9 8 4656 4 7 i4 4772 483o 4888 4 9 45 5oo3 7 5o 5o6i 5119 5i 77 5 2 35 52 9 3 535i 54o 9 5466 5524 5582 7 5i 564o 56 9 8 5 7 56 58i3 58 7I 5929 5 9 8 7 6o45 6102 6160 762 6218 62-76 6333 63 9 i 644 9 65o7 6564 6622 6680 6 7 3 7 7 53 6795 6853 6 9 io 6968 -7026 7083 7 i4i 7i 99 7 256 7 3i4 7 54 7 3 7 i 7 42 9 7 48 7 7544 -7602 7 65 9 77i7 7774 7 832 7889 7 55 7947 8oo4 8062 8119 8177 8234 8292 834 9 84o 7 8464 57 7 56 8522 85 79 863 7 86 9 4 8 7 5 2 8809 8866 8 9 24 8 9 8i 9 o3 9 7 5 7 9096 9 i53 9 2II 9268 9 325 9383 944o 9497 9 555 9612 7 58 9669 97 26 97 84 984i 9898 9956 ..i3 ..70 .I2 7 .i85 7 5 9 880242 0299 o356 o4i3 o4 7 i o5 2 8 o585 0642 o6 99 o 7 56 7 6o o8i4' 08-71 0928 0985 io4a 1099 n56 I2l3 I2 7 I i3 2 8 761 1 385 1 442 1499 i556 i6i3 i6 7 o I 7 2 7 1784 1841 1898 762 1955 2OI2 2069 2126 2i83 2240 229-7 2354 2411 2468 763 2525 258l 2638 2695 2 7 52 2809 2866 2 9 23 2 9 8o 3o3 7 764 SogS 3i5o 32O 7 3 2 64 3321 33 77 3434 34 9 i 3548 36o5 7 65 366i 3 7 i8 3 77 5 3832 3888 3 9 45 4OO2 4o5 9 4n5 4l 7 2 766 4229 4285 4342 43 99 4455 45i2 456 9 4625 4682 4 7 3 9 767 4 79 5 485 2 4909 4 9 65 5O22 5o 7 8 5i35 5l 9 2 5248 53o5 768 536i 54i8 54 7 4 553i 558 7 5644 5 7 oo 5 7 5 7 58i3 58 7 o 769 5926 6983 6039 6096 6i5 2 6209 6a65 632i 63 7 8 6434 56 770' 6491 654 7 6604 6660 6 7 i6 6 77 3 6829 6885 6 9 42 6998 771 7o54 7111 7 i6 7 7223 7280 7 336 7 3 9 2 7 44 9 7 5o5 7 56i 772 7 6i 7 76 7 4 77 3o 7786 7 842 7 8 9 8 79 55 8011 8o6 7 8i23 773 8i79 8236 8292 8348 84o4 846o 85i6 85 7 3 862 9 8685 774 8741 8 797 8853 8909 8 9 65 9021 977 9 i34 9 i 9 o 9246 N. 1 2 3 4 5 6 7 8 9 D. 60 a 6 12 18 24 3o 36 42 48 54 5 9 S 6 12 18 24 3o 35 4i 47 53 | 58 PH . 6 12 17 23 29 35 4i 46 52 ft 5 7 o 6 II J 7 23 29 34 4o 46 5i 56 6 II 17 23 28 34 3 9 45 5o LOGARITHMS OF NUMBERS. 17 N. 1 2 3 4 5 6 7 8 9 D. 7?5 889302 9 358 94i4 9 4 7 o 9 526 9582 9 638 9 6 9 4 97 5o 9 8o6 56 776 9862 9918 9974 ..3o ..86 ,x4x .197 .253 .3o 9 .365 111 890421 o4 77 o533 o58 9 o645 o 7 oo o 7 56 0812 0868 9 24 778 0980 io35 1091 n4? 1203 I25 9 i3i4 i3 7 o 1426 1482 779 i53 7 i5 9 3 1649 1705 I 7 6o 1816 l8 7 2 I 9 28 I 9 83 2o3 9 780 2096 2i5o 2206 2262 23l 7 23 7 3 2429 2484 254o 2 5 9 5 781 2661 2 7 7 2762 2818 28 7 3 2929 2 9 85 3o4o 3o 9 6 3i5i 782 3207 3262 33i8 3373 3429 3484 354o 35 9 5 365i 3 7 o6 7 83 3 7 62 38i 7 38 7 3 3 9 28 3 9 84 4o3 9 4og4 4i5o 42o5 4261 55 784 43i6 43 7 i 4427 4482 4538 45 9 3 4648 4 7 o4 4 7 5 9 48i4 7 85 4870 4925 4980 5o36 5o 9 i 5i46 5201 5 2 5 7 53i2 536 7 786 5423 54 7 8 5533 5588 5644 5699 5 7 54 58o 9 5864 5 9 20 787 5 97 5 6o3o 6o85 6i4o 6i 9 5 6 2 5i 63o6 636i 64i6 64 7 i 788 6626 658i 6636 6692 6 7 4 7 6802 685 7 6 9 I2 6 9 6 7 7022 789 7077 7 l32 7187 7242 7 2 97 7 352 7 4o 7 7 462 7 5i 7 7 5 7 2 79 7627 -7682 7737 7792 7 84 7 7902 79 5 7 8012 8o6 7 8122 791 8176 823i 8286 834i 83 9 6 845 1 85o6 856i 86i5 86 7 o 792 8726 8 7 8o 8835 8890 8 9 44 8999 9o54 9 io 9 9 i64 9 2l8 793 0273 9828 9383 943 7 9 4 9 2 9 54 7 9602 9 656 9711 97 66 794 9821 9 8 7 5 9930 99 85 ..3 9 .. 9 4 .149 .203 .258 .312 79 5 900367 0422 0476 o53i o586 o64o 0695 o 7 4 9 o8o4 o85 9 796 0913 0968 1022 1077 n3i 1186 1240 I2 9 5 i34 9 i4o4 797 i458 i5i3 i56 7 1622 i6 7 6 I 7 3i i 7 85 i84o i8 9 4 i 9 48 54 798 2003 2057 2112 2166 2221 22 7 5 2329 2384 2438 24 9 2 799 2647 2601 2655 2710 2 7 64 28l8 28 7 3 2 9 2 7 2981 3o36 800 3090 3i44 3i 99 3253 33o 7 336i 34i6 3470 3524 35.78 801 3633 368 7 374i 3 79 5 384 9 3904 SgSS 4OI2 4o66 4l2O 802 4i74 4229 4283 433 7 43 9 i 4445 4499 4553 4607 466i 8o3 4716 477<> 4824 48 7 8 4 9 32 4986 5o4o 5o 9 4 5i48 52O2 8o4 6266 53io 5364 54i8 54 7 2 5526 558o 5634 5688 5 7 42 8o5 6796 585o 5 9 o4 5 9 58 6012 6066 6119 6173 6227 6281 806 6335 6389 6443 6497 655i 6604 6658 6712 6766 6820 807 68 7 4 6927 6981 7o35 7 o8 9 7 i43 7 i 9 6 725o ?3o4 7 358 808 7 4n 7465 7519 7 5 7 3 7626 7 68o 7734 7787 784i 7895 809 7949 8002 8o56 8110 8i63 82I 7 82 7 8324 83 7 8 843 1 810 8485 853 9 8592 8646 86 99 8 7 53 88o 7 8860 8 9 i4 8 9 6 7 8n 9021 9074 9128 9181 9 235 9289, 9 342 9 3 9 6 9 44 9 9 5o3 812 9 556 9610 9663 9 7 i6 $77 98,33 9877 99 3o 99 84 ..3 7 53 8i3 910091 oi44 0197 025l o3o4 o358 o4n o464 o5i8 o5 7 i 8x4 062^ o6 7 8 0731 0784 o838 0891 o 9 44 o 99 8 io5i no4 8i5 n58 I2II 1264 1317 i3 7 i i424 1477 i53o 1 584 i63 7 8x6 1690 i 7 43 1797 i85o I 9 o3 1956 2OO 9 2o63 2116 2l6 9 817 2222 22 7 5 23 2 8 238i 2435 2488 254l 25 9 4 2647 2 7 OO 8x8 2 7 53 2806 2859 2913 2 9 66 3019 3o 7 2 3i25 3i 7 8 323i 819 3284 333 7 SSgo 3443 34 9 6 354 9 36o2 3655 3 7 o8 3 7 6i 820 38i4 386 7 3920 3 97 3 4026 4o 7 9 4l32 4i84 423 7 42 9 O 821 4343 43 9 6 4449 45o2 4555 46o8 466o 47i3 4 7 66 48i 9 822 48 7 2 4925 4977 5o3o 5o83 5i36 5i8 9 5 2 4i 52 9 4 534 7 828 54oo 5453 55o5 5558 56n 5664 5 7 i6 5 7 6 9 5822 58 7 5 824 5 9 2 7 5980 6o33 6o85 6i38 6191 6243 62 9 6 634 9 64oi 826 6454 65o7 655 9 6612 6664 6 7 i 7 6 77 o 6822 68 7 5 6 9 2 7 826 6980 7o33 7 o85 7 i38 7 i 9 o 7 243 7 2 9 5 7 348 7 4oo 7 453 827 7 5o6 7 558 7 6n 7 663 77 i6 7768 7820 7873 79 25 7978 52 828 8o3o 8o83 8i35 8188 8240 8293 8345 83 97 845o 85o2 829 8555 8607 865 9 8 7 I2 8 7 64 8816 886 9 8 9 2I 8 97 3 9 O26 83o 90 7 8 9i3o 9183 9 235 9 28 7 9340 9 3 9 2 9 444 9 4 9 6 9 54 9 N, | | 1 2 3 4 5 6 7 8 9 D. . f 55 o5 f 6 ii J 7 22 28 33 3 9 44 5o jiJ-w-SJ 5 ii 16 22 27 32 38 43 49 5 53 P;j 5 ii 16 21 27 32 37 42 48 Q I 62 I 5 10 16 21 26 3i 36 4a 47 B 18 LOGARITHMS OF NUMB E RS. N. VI i 2 3 4 5 6 7 8 9 D. 83i 919601 ( g653 9706 97 58 9 8io 9862 99*4 99 6 7 ..i 9 ..71 52 832 920123 0176 0228 0280 o332 o384 o436 o48 9 o54i o5 9 3 833 o645 0697 0749 0801 o853 0906 o 9 58 IOIO 1062 i u4 834 ii 66 I2i8 1270 l322 i3 7 4 1426 i4 7 8 i53o i58 2 1 634 835 1686 1733 1790 1842 i8 9 4 I 9 46 i 99 8 2o5o 2IO2 2i54 836 2206 2258 s3io 2362 24i4 2466 2 5i8 2570 2622 2674 83 7 2725 2777 2829 2881 2 9 33 2 9 85 3o3 7 3o8 9 3i4o 3i 9 2 838 3244 3296 3348 33 99 345 1 35o3 3555 36o 7 3658 3710 83 9 3762 38i4 3865 3 9 i 7 3 9 6 9 4021 4o 7 2 4i2A 4176 4228 84o 4279 433i 4383 4434 4486 4538 458 9 464? 4693 4744 84i 479 6 4848 4899 4 9 5i 5oo3 5o54 5io6 5i5 7 52O 9 5261 842 53i2 5364 54i5 546 7 55i8 55 7 o 562i 56 7 3 5 7 25 5 77 6 843 58 2 8 58 79 5 9 3i 5 9 82 6o34 6o85 6i3 7 6188 6240 62 9 I 5i 844 6342 63 9 4 6445 64 97 6548 6600 665i 6702 6 7 54 68o5 845 685 7 6908 6 9 5 9 7 OII 7062 7 n4 7 i65 7216 7268 7 3i 9 846 7 3 7 7422 7 4 7 3 7 5 2 4 7576 7 62 7 7678 7 7 3o 77 8i 7 832 84? 7883 79 35 7986 8o3 7 8088 8i4o 8191 8 2 4 82 9 3 8345 848 83 9 6 8447 8498 854 9 8601 8652 8 7 o3 8 7 54 88o5 8857 849 8908 8 9 5 9 9010 9 o6i 9 I 12 1 9163 9 2l5 9 266 9 3l 7 9 368 85o 9419 947 9 52I 9 5 7 2 9 623 96 7 4 97 s5 9776 9 82 7 9 8 79 85i 99 3o 99 8i ..32 ..83 .134 .i85 .236 .287 .338 .38 9 85 2 9 3o44o o4 9 i o542 o5 9 2 o643 0694 0745 o 79 6 o84 7 o8 9 8 853 0949 IOOO io5i 1102 u53 I2O4 1254 i3o5 i356 1407 854 i458 i5o 9 i56o 1610 166! I 7 I2 1763 1814 i865 I 9 i5 855 1966 2017 2068 2118 2i6 9 222O 2271 2322 23 7 2 2423 856 2474 2524 2 5 7 5 2626 2677 2 7 2 7 2778 282 9 a8 79 2 9 3o 85 7 2981 3o3i 3o82 3i33 3i83 3234 3285 3335 3386 3437 858 348 7 3538 358 9 363 9 36 9 o 3 7 4o 3 79 i 384i 38 9 2 3 9 43 85 9 3 99 3 4o44 4094 4i45 4i 9 5 4246 42 9 6 4347 43 97 4448 860 44 9 8 4549 4599 465o 4700 4 7 5i 48oi 4852 4 9 02 4 9 53 5o 86 1 5oo3 5o54 5io4 5i54 52o5 5 2 55 53o6 5356 5406 545 7 862 55o 7 5558 56o8 5658 5709 5 7 5 9 58o 9 586o 5 9 io 5 9 6o i 863 6011 6061 6m 6162 6212 6262 63i3 6363 64i3 6463 864 65i4 6564 66i4 6665 6 7 i5 6 7 65 68i5 6865 6 9 i6 6 9 66 865 7016 7066 7117 7 i6 7 7217 7 26 7 7 3i 7 7 36 7 7 4i8 7 468 866 75i8 7 5B8 7618 7668 7718 77 6 9 7819 7869 79 i 9 79 6 9 867 8019 8069 8119 8i6 9 8219 826 9 8320 8^0 8420 84 7 o 868 8520 85 7 o 8620 86 7 o 8720 8 77 o 8820 88 7 o 8 9 20 8 97 o 869 9020 9070 9120 9 i 7 o 9220 9 2 7 9 320 9 36 9 9 4i 9 9 46 9 870 9 5i 9 9569 9619 9 66 9 9719 9769 9 8i 9 9 86 9 99 i8 99 68 871 9 4ooi8 0068 0118 0168 0218 026 7 o3i 7 o36 7 o4i 7 o46 7 872 o5i6 o566 0616 0666 0716 o 7 65 o8i5 o865 o 9 i5 o 9 64 8 7 3 1014 io64 in4 n63 I2l3 1263 i3i3 i36 2 1412 1462 874 i5n 1661 1611 1660 1710 I 7 6o i8o 9 i85 9 I 9 9 i 9 58 8 7 5 2008 2o58 2107 2l5 7 2207 2256 2 3o6 2355 24o5 2455 876 25o4 2554 26o3 2653 2702 2 7 52 2801 285i 2 9 OI 2 9 5o 877 3ooo 3o4g 3o 99 3i48 3i 9 8 324 7 32 97 3346 33 9 6 3445 49 878 34 9 5 3544 35 9 3 3643 36 9 2 3 7 4a 3 79 i 384i 38 9 o 3 9 3 9 879 3 9 8 9 4o38 4o88 4i3 7 4i86 4236 4285 4335 4384 4433 880 4483 4532 458i 463i 468o 4 7 2 9 4779 4828 48 77 4 9 2 7 Hi 4976 5o 2 5 5074 5i24 5i 7 3 5222 5272 532i 53 7 o 54i 9 882 546 9 55i8 556 7 56i6 5665 5 7 i5 5764 58i3 5862 5 9 I2 883 5 9 6i 6010 6059 6108 6157 62O 7 6256 63o5 6354 64o3 884 6452 65oi 655i 6600 6649 6698 6 7 4 7 6 79 6 6845 68 9 4 885 6 9 43 6992 704 1 7 o 9 o 7140 7 i8 9 7238 728-7 7 336 7 385 886 7434 7483 7 532 7 58i 763o 7 6 79 7728 7777 7826 7 8 7 5 N. | 1 2 3 4 5 6 7 8 9 D. . f 52 a f 5 10 16 21 26 3i 36 42 47 fe 5i SI 5 10 16 2O 26 3i 36 4i 46 fe 5o M S IO i5 20 25 3o 35 4o 45 q I 4 9 * { 5 10 i5 2O 25 29 34 3 9 44 LOGARITHMS OF NUMBERS. N. 1 2 3 4 | 5 6 7 8 9 D. 887 947924 7978 8022 8070 8lI 9 8168 8217 8266 83i5 8364 4 9 888 84i3 8462 85u 856o 860 9 865 7 8706 8 7 55 88o4 8853 889 8902 8 9 5i 8999 9048 997 9 i46 9 i 9 5 9244 9292 9 34i 890 9890 9489 9 488 9 536 9 585 9 634 9688 9781 9780 9 82 9 891 9878 9926 9975 ..24 ..78 .121 . 170 .219 .267 .816 892 9 5o365 o4i4 0462 o5n o56o 0608 0657 0706 o 7 54 0808 8 9 3 0861 0900 0949 0997 io46 lOgS u43 1192 1240 1289 894 1888 1886 i435 i483 i53 2 i58o 1629 1677 1726 i 77 5 8 9 5 1828 1872 1920 1969 2017 2066 2Il4 2168 2211 2260 48 896 2808 2356 24o5 2453 2502 255o 2 5 99 2647 2696 2744 897 2792 2841 2889 2988 2986 3o34 3o83 8181 3i8o 8228 898 8276 3325 33 7 3 3421 3470 35i8 3566 36i5 3663 3 7 n 899 8760 8808 3856 8905 3 9 53 4ooi 4o4g 4o 9 8 4i46 4i 9 4 900 4243 4291 433 9 438 7 4435 4484 4532 458o 4628 46 77 901 4726 4??3 4821 4869 4918 4966 5oi4 5o6 2 5no 5i58 902 6207 5 2 55 53o3 535i 53 99 544 7 5495 5543 55 9 2 564o 908 5688 5 7 36 5784 5832 588o 5928 5976 6024 6072 6120 904 6168 6216 6265 6818 636i 6409 645 7 65o5 6553 6601 906 6649 6697 6 7 45 6 79 3 684o 6888 6986 6984 7082 7080 906 7128 7176 7224 7272 7820 7 368 7416 7464 7512 7 55 9 997 7607 7655 7708 775 1 7799 7 84 7 7894 7942 799 8088 908 8086 8i34 8181 8229 8277 8325 8878 8421 8468 85i6 909 8564 8612 865 9 8707 8 7 55 8808 885o 8898 8 9 46 8994 910 9041 9089 9 i3 7 9i85 9 232 9 28o 9828 9 3 7 5 9 423 9471 911 95i8 9566 9614 9661 -979 97 5 7 9804 9852 99 9947 912 9995 ..42 ..90 .188 .i85 .288 .280 .828 .876 .428 9 i3 960471 o5i8 o566 o6i3 0661 070 9 0756 0804 o85i 0899 914 0946 0994 io4i 1089 n36 n84 1281 1279 1826 i3 7 4 47 916 1421 1469 i5i6 i563 1611 i658 1706 i 7 53 1801 1 848 916 i8 9 5 1943 1990 2088 2o85 2182 2180 2227 2275 2822 917 2869 2417 2464 25ll 255 9 2606 2653 2701 2748 2795 918 2843 2800 2 9 3 7 2985 '8082 8079 8126 8174 8221 8268 919 33i6 3363 34io 345 7 35o4 3552 35 99 3646 36 9 3 3 7 4i 920 8788 3835 8882 8929 8977 4024 4071 4n8 4i65 4212 921 4a6o 43o 7 4354 44oi 4448 44 9 5 4542 4590 463 7 4684 922 4?3i 4778 4825 4872 4919 4 9 66 5oi3 5o6i 5io8 5i55 928 6202 5249 52 9 6 5343 5390 5437 5484 553i 5578 5625 924 5672 5719 5766 58i3 586o 5 9 o 7 5 9 54 6001 6o48 6oo5 925 6142 6189 6286 6288 6829 6376 64s3 6470 65 1 7 6564 926 66u 6658 6705 6752 6799 6845 68 9 2 6989 6986 7o33 927 7080 7127 7 i 7 3 7220 7267 73i4 736i 7408 7454 75oi 928 7548 7 5 9 5 7642 7688 7735 7782 7820. 7 8 7 5 7922 7969 929 8016 8062 8109 8i56 8208 824 9 82 9 6 8343 8890 8436 980 8483 853o 8576 8628 8670 8716 8768 8810 8856 8908 9 3! 8 9 5o 8996 9o43 9090 9186 9 i83 9 22 9 9276 9828 9869 982 9416 9 463 9 5o 9 9 556 9602 9 64 9 9 6 9 5 9742 9789 9 835 988 9882 9928 9975 . .21 ..68 .n4 .161 .207 .254 .800 934 970347 0893 o44o o486 o533 o57 9 0626 0672 0719 0765 46 935 0812 o858 0904 ogSi 0997 io44 io 9 o 1187 1188 1229 986 1276 1822 1869 i4i5 i46i i5o8 i554 1601 1 647 1698 987 1740 1786 i832 1879 1925 1971 2018 2064 2110 2157 988 2^208 2249 2295 2842 2888 2434 2481 2527 2 5 7 3 2619 989 21666 2712 2 7 58 2804 285i 2897 2 9 43 2989 3o35 8082 940 8128 3i74 8220 8266 33i3 SSSg 34o5 345 1 34 9 7 3543 94 1 35 9 o 3636 3682 8728 3 77 4 8820 3866 8918 3 9 5 9 4oo5 942 4o5i 4097 4i43 4i8 9 4235 4281 4827 43 7 4 4420 4466 943 45i2 4558 46o4 465o 46 9 6 4742 4 7 88 4834 488o 4926 N. 1 2 3 4 5 6 7 8 9 D. u 48 f 5 10 i4 19 . 24 2 9 34 38 43 . 4 7 M 5 9 i4 *9 24 28 33 38 42 . 46 * I 5 9 r4 18 28 28 32 37 4i LOGARITHMS OF NUMBERS. N. 1 2 3 4 5 6 7 8 9 D. 944 97497 2 6018 5o64 5no 5i56 52O2 5248 5 29 4 534o 5386 46 945 5432 5478 5524 55 7 o 56i6 5662 5 7 o 7 5 7 53 5 799 5845 946 58 9 i 5 9 3 7 5 9 83 6029 6o 7 5 6121 6i6 7 6212 6258 63o4 94? 635o 63 9 6 6442 6488 6533 65 79 6625 6671 6717 6 7 63 948 6808 6854 6900 6 9 46 6992 73 7 7 o83 7 I2 9 7 i 7 5 7 22O 949 7266 7312 7 358 7 4o3 7449 7 4 9 5 7 54i 7 586 7632 7 6 7 8 9 5o 7724 7769 7 8i5 7861 7906 79 52 799 s 8o43 8o8 9 8i35 9 5i 8181 8226 82 7 2 8317 8363 84o 9 8454 85oo 8546 85 9 i o5'2 8637 8683 8 7 28 8774 8810 8865 8 9 n 8 9 56 9 OO2 9 o4 7 953 9 o 9 3 9 i38 9184 9 23o 9275 9 32I 9 366 9 4i2 9 45 7 9 5o3 954 9 548 9^94 9 63 9 9 685 97 3o 9776 9 82I 9 86 7 99 I2 99 58 9 55 9 8ooo3 oo4 9 oo 9 4 oi4o oi85 023l 02 7 6 0322 o36 7 O4l2 45 966 o458 o5o3 o54 9 o5 9 4 o64o o685 o 7 3o o 77 6 0821 o86 7 967 O 9 I2 9 5 7 ioo3 1048 io 9 3 n3 9 n84 I22 9 I2 7 5 1320 968 i366 i4n i456 i5oi i54 7 l5 9 2 i63 7 i683 I 7 28 i 77 3 9 5 9 i8i 9 1 864 i 9 o 9 i 9 54 20OO 2o45 20 9 2i35 2181 2226 960 2271 2 3i6 2362 2407 2452 24 97 2543 2588 2633 2 6 7 8 961 2723 276 9 2814 2 85 9 2 9 04 2 9 4 9 2 99 4 3o4o 3o85 3i3o 962 3175 3220 3265 33io 3356 34oi 3446 34 9 i 3536 358i 9 63 3626 36 7 i 3 7 i6 3762 38o 7 3852 38 9 7 3 9 42 3987 4o32 964 4077 4l22 4i6 7 4212 425 7 4302 434 7 43 9 2 443 7 4482 9 65 4627 45 7 2 46i 7 4662 4 7 o 7 4 7 52 4797 4842 488 7 4 9 32 966 4 9 77 5022 5o6 7 5lI2 5i5 7 52O2 5 2 4 7 5292 533 7 5382 967 5426 9*71 55i6 556i 56o6 565i 56 9 6 5 7 4i 5 7 86 583o 968 6876 5 9 2O 5 9 65 6010 6o55 6100 6:44 6i8 9 6234 62 79 969 6324 636 9 64i3 6458 65o3 6548 65 9 3 663 7 6682 6 7 2 7 97 6772 6817 6861 6 9 o6 6 9 5i 6 99 6 7 o4o 7 o85 7 i3o 7 i 7 5 971 7 2I 9 7264 7 3o 9 7 353 7398 7 443 7 488 7 532 7 5 77 7622 972 7666 7711 77 56 7800 7 845 7 8 9 o 79 34 7979 8024 8068 973 8n3 8i5 7 8202 8247 8291 8336 838i 8425 84 7 o 85i4 974 855 9 86o4 8648 86 9 3 8 7 3 7 878,2 8826 8871 8 9 i6 8 9 6o 976 9 oo5 9 o4 9 9 o 9 4 9 i38 9 i83 9 22 7 9272 9 3i6 9 36i 9 4o5 976 9 45o 9 4 9 4 9 53 9 9 583 9 628 9 6 7 2 9717 976i 9 8o6 9 85o 44 977 9 8 9 5 99 3 9 99 83 ..28 ..72 .II 7 .161 .206 .250 .2 9 4 978 99 o33 9 o383 0428 0472 o5i6 o56i o6o5 o65o o6 9 4 o 7 38 979 o 7 83 0827 o8 7 i o 9 i6 o 9 6o ioo4 1049 io 9 3 n3 7 1182 980 1226 1270 i3i5 i35 9 i4o3 1 448 l4 9 2 i536 i58o i6 2 5 981 i66 9 I 7 i3 i 7 58 1802 1 846 i8 9 o i 9 35 i 979 2023 2O6 7 982 2III 2i56 2200 2244 2288 2333 2377 2421 2465 25o 9 9 83 2554 25 9 8 2642 2686 2 7 3o 2774 28l 9 2863 2 9 7 2 9 5i 984 2 99 5 3o3 9 3o83 3l2 7 3l 7 2 32i6 3260 33o4 3348 33 9 2 986 3436 348o 3524 3568 36r3 365 7 3701 3 7 45 3 7 8 9 3833 986 38 7 7 3 9 2I 3 9 65 4oo 9 4o53 4o 97 4i4i 4i85 4229 42 7 3 987 43i 7 436i 44o5 444 9 44 9 3 453 7 458i 4625 4669 4 7 i3 988 4 7 5 7 48oi 4845 488 9 4 9 33 4 9 77 5021 5o65 5io8 5i5 2 989 5i 9 6 524o 5284 5328 53 7 2 54i6 546o 55o4 554 7 55 9 i 99 5635 567 9 5723 5 7 6 7 58n 5854 58 9 8 5 9 4a 5986 6o3o 991 6074 6117 6161 62o5 624 9 62 9 3 633 7 638o 6424 6468 992 65i2 6555 65 99 6643 668 7 6731 6774 6818 6862 6 9 o6 99 3 6 9 4 9 6 99 3 7 o3 7 7080 7124 7168 7212 7 255 7299 7 343 99 4 7 386 743o 7474 7 5i 7 7 56i 7 6o5 7 648 7 6 9 2 7736 7779 99 5 7823 7867 7 9 io 7954 7998 8o4i 8o85 8l2 9 8l 7 2 8216 99 6 825 9 83o3 8347 83 9 o 8434 84 77 852i 8564 8608 8652 997 86 9 5 8 7 3 9 8782 8826 8869 8 9 i3 8 9 56 9 ooo 9043 9 o8 7 99 8 9 i3i 9 i 7 4 9 2l8 9261 9 3o5 9 348 9 3 9 2 9 435 9479 9 522 999 9 565 9609 9 652 9696 97 3 9 9783 9 826 9 870 99 i3 99 5 7 43 N. | 1 2 3 4 5 6 7 8 9 D. . f 46 * f 5 9 i4 18 23 28 32 37 4i JS j 45 Si 5 9 i4 18 23 2 7 32 36 4i I 44- 1 4 9 i3 18 22 26 3i 35 4o p I 43 { 4 9 i3 i? 22 26 3o 34 3 9 TABLE OF LOGARITHMIC SINES AID TANGENTS FOR EVERY TEN SECONDS OF THE QUADRANT. LOGARITHMIC SINES. Min. Sine of Degree. P. Prt 0" 10" 20" 30" 40" 50" to 1". Inf. Neg. 5.685575 5.9866o5 6.162696 6.287635 6.384545 5 9 1 6.463726 6.53o6 7 3 6.588665 639817 6855 7 5 726968 58 2 764756 799518 83i7o3 861666 889695 916024 5 7 3 940847 964328 9 866o5 7.007794 7.027997 7-o473o3 56 4 7.065786 7.o835i5 7.ioo548 116939 i32 7 33 i4797 3 55 5 162696 176936 190725 204089 217054 229643 54 6 241877 253 77 6 265358 276639 287635 2 9 8358 53 7 3o8824 319043 329027 338 7 8 7 348332 357672 52 8 3668r6 3 7 5 77 i 384544 3 9 3i45 401578 409850 5i 9 417968 425 9 3 7 433762 44i449 449002 456426 5o 10 463726 470904 477966 4849i5 491754 498488 49 68 9 .4 ii 5o5n8 5n64 9 5i8o83 524423 530672 536832 48 62 9 .4 12 542906 548897 5548o6 56o635 56638 7 572065 47 579. i i3 5 77 668 583201 588664 594059 599388 6o4652 46 536.2 i4 6o 9 853 614993 620072 625093 63oo56 634964 45 499.2 i5 63 9 8i6 6446 i 5 649361 654o56 658701 663297 44 467.0 16 667845 672345 676799 681208 6855 7 3 689895 43 438. 7 J 7 694173 698410 702606 706762 710879 714957 te 4i3.6 18 718997 722999 726965 730896 734791 7 3865i 4i 391.3 J 9 742478 746270 75oo3i 753758 7 5 7 455 761119 4o 371.2 20 764754 7 68358 771932 775477 778994 782482 3 9 353.1 21 7 85 9 43 7 8 9 3 7 6 792782 796162 7995i5 802843 38 336.7 22 806146 809423 812677 815906 819111 822292 37 321.7 23 8 2 545i 828586 831700 834791 83 7 86o 840907 36 3o8.o 24 843 9 34 846 9 3 9 849924 85 2 88 9 855833 858 7 5 7 35 2 9 5.4 25 861662 864548 86 7 4i5 870262 873092 875902 34 283.8 26 878695 881470 884228 886968 889690 892396 33 273.1 27 895085 8 977 58 900414 9o3o54 905678 908287 32 263.2 28 910879 9 i345 7 916019 9i8566 921098 923616 3i 254.0 29 926119 928608 931082 933543 935989 938422 3o 245.4 3o 940842 943248 94564i 948020 950387 952741 29 237.3 3i 955082 957411 959727 962031 964322 966602 28 229.8 32 968870 971126 97 33 7 o 9756o3 977824 980034 27 222.7 33 982233 984421 986598 988764 1 990919 993064 26 2:6.1 34 995198 997322 999435 8.ooi538 3.oo363i 8.005714 25 209.8 35 8.007787 8.009850 8.011903 013947 015981 oi8oo5 24 203.9 36 O20O2I 032027 024023 026011 027989 029959 23 198.3 3 7 03I9I9 o338 7 i o358i4 037749 039675 041592 22 193.0 38 o435oi o454oi 047294 049178 o5io54 052922 21 188.0 3 9 054781 o56633 o58477 o6o3i4 062142 o63 9 63 20 183.2 4o 065776 067582 069380 071171 072955 074731 '9 178.7 4i 076500 078261 080016 081764 o835o4 o85238 id 174.4 42 086965 088684 090398 092104 093804 095497 J 7 170.3 43 097183 o 9 8863 ioo537 102204 io3864 io55i9 16 166.4 44 107167 108809 no444 112074 113697 n53i5 i5 162.6 45 116926 ii853 2 I2Ol3l 121725 I233i3 124895 i4 iSg. i 46 126471 128042 129607 i3n66 132720 134268 i3 155.6 47 i358io i3 7 348 138879 i4o4o6 ] 141927 143443 12 i52.4 48 144953 146458 147959 149453 i 50943 152428 II 149.2 49 153907 155382 156852 ~ i 583x6 159776 i6i23i IO i46.a 5o 162681 164126 165566 167002 168433 169859 9 i43.3 5i 171280 172697 174109 175517 176920 178319 8 i4o.5 52 179713 i8uo3 182488 183869 185245 186617 7 i37.9 53 187985 189348 190707 192062 I 9 34i3 194760 6 i35.3 54 196102 I9744o 198774 200104 2oi43o 202752 5 i32.8 55 204070 205384 206694 2O8OOO 209302 210601 4 i3o.4 56 211895 2i3i85 214472 2l5755 217034 218309 3 128.1 57 219581 220849 2221 l3 223374 22463i 225884 2 125. 9 58 227134 228380 229622 23o86i 232096 233328 I 123.7 5 9 234557 235782 237003 238221 239436 240647 O 121. 6 OOP 50" 40" 30" 20" 10" 1 Co-sine of S9 Degrees. Min. LOGARITHMIC TANGENTS. Min. Tangent of Degree. P. Part 0" 10" 20" 30" 40" | 50" to 1 . Inf. Neg. 5.6855 7 5 5. 9 866o5 6. 162696 6.28 7 635 6.384545 5 9 I 6.463 7 26 6.53o6 7 3 6.588665 639817 6855 7 5 726968 58 2 7 64 7 56 799 5i8 83i 7 o3 861666 889695 916024 57 3 9 4o84 7 964329 9 866o5 7.007794 7 O2 799 8 7 .o4 7 3o3 56 4 7 .o65 7 86 7 .o835i5 7.ioo548 116939 i32 7 33 147973 55 5 162696 I 7 6 9 3 7 I 9 O725 204089 2i 7 o54 229643 54 6 24i8 7 8 253 777 26535 9 276640 28 7 635 298359 53 7 3o8825 319044 32 9 028 338 7 88 348333 357673 52 8 366817 3 7 5 77 2 384546 393146 4oi5 79 409852 5i 9 4i 797 o 425939 433 7 64 44i45i 449004 456428 5o 10 463 7 2 7 4-70906 477968 484917 4 9 i 7 56 498490 49 68 9 .4 ii 5o5i2o 5n65i 5i8o85 524426 53o6 7 5 536835 48 620.. 4 12 542 9 o 9 548900 5548o8 56o638 5663 9 o 5-72068 47 5 79 .i i3 577672 583204 588667 5g4o62 699391 6o4655 46 536.2 i4 609857 614996 620076 625097 63oo6o 634968 45 499.2 i5 639820 644619 649366 654o6i 658706 663302 44 46 7 .o 16 66 7 849 6 7 235o 676804 681213 6855 7 8 689900 43 438. 7 1-7 6941-79 698416 702612 7 o6 7 68 7 io885 714963 42 4i3.6 18 719003 7 23oo5 726972 730902 7 34 7 9 7 7 38658 4i 3 9 i.3 *9 742484 7 462 77 750037 7 53 7 65 7 5 7 462 76112-7 4o 371.3 20 7 64 7 6i 7 68365 771940 77 5485 7-79002 782490 3 9 353.1 21 7 85 9 5i 7 8 9 384 792790 7 96i 7 o 799524 802852 38 336.7 22 8o6i55 809433 812686 8i5 9 i5 819120 822302 37 321.7 23 825460 828596 831710 8348oi 83 7 8 7 o 840918 36 3o8.o 24 843944 846950 849935 852900 855844 858 7 69 35 2 9 5.4 25 861674 86456o 867426 8 7 O2 7 4 8 7 3io4 8 7 5 9 i5 34 283.9 26 8-78708 88i483 884240 886981 889-704 892410 33 2 7 3.2 27 895099 8 9777 2 900428 9o3o68 905692 9o83oi 32 263.2 28 910894 913471 9 i6o34 9i858i 921113 92363i 3! 254.0 29 926134 928623 931098 933559 986006 9 3843 9 3o 245.4 3o 94o858 943265 9 45658 948o3 7 95o4o4 952 7 58 29 23 7 .3 3i gSSioo 9 5 7 428 959745 962049 964341 966621 28 22 9 .8 32 968889 97 ii45 97 338 9 9 7 5622 977844 980054 2 7 222.7 33 982253 984441 986618 988-785 990940 99 3o85 26 216.2 34 995219 997343 999457 8.ooi56o 8.oo3653 3.oo5 7 36 25 20 9 .8 35 8.007809 8.009872 8.011926 0139-70 016004 oi8o2 9 24 2o3. 9 36 O20044 O22o5l 024048 026o35 028014 029984 23 i 9 8.3 37 031945 o338 9 7 o3584o o3 777 5 039-701 041618 22 i 9 3.o 38 043527 045428 047321 049205 o5io8i 052949 21 188.0 3 9 054809 o56662 o585o6 o6o342 0621-71 063992 2O i83.3 4o o658o6 067612 069410 O 7 I2OI 0-72985 o 7 4 7 6i I 9 178.7 4i 076531 0782 9 3 080047 O8l 7 95 o83536 o852 7 o 18 i 7 4.4 42 086997 088717 090431 092l3 7 o 9 383 7 095530 i 7 170.3 43 097217 098897 100571 IO2239 108900 io5554 16 166.4 44 107203 io8845 no48i II2IIO n3 7 34 n535 2 15 162.7 45 116963 n856 9 120169 I2i 7 63 i2335i 124933 i4 i5 9 .i 46 i265io 128081 129646 i3i2o6 i32 7 6o i343o8 i3 i55. 7 47 i3585i i3 7 38 9 138921 i4o44 7 ' 141969 143485 12 i5 2 .4 48 144996 i465oi i48ooi i4949 7 15098-7 l524 7 2 II i4 9 .3 49 153952 i55426 156896 i5836i 159821 i6i2 7 6 IO 146.2 5o 162727 164172 i656i3 16-7049 168480 i6 99 o6 9 i43.4 5i 171328 172745 I74i58 I 7 5566 1-76969 i 7 8368 8 i4o.6 52 I 797 63 i8n53 182538 183919 185296 186668 7 137.9 53 i88o36 189400 190760 192115 193466 I 9 48i3 6 135.3 54 196156 197494 198829 200159 2oi485 202808 5 i3 2 .8 55 204126 ao544o 206750 2o8o5 7 209359 2io658 4 i3o.4 56 211953' 213243 2i453o 2i58i4 21-7093 2i836 9 3 128.1 57 219641 220909 222174 223434 224692 225945 2 I25. 9 58 227195 228442 229685 230924 232160 2333 9 2 I 123.8 5 9 234621 235846 237068 238286 339502 24o 7 i3 o 121 .7 60" 50" i 40" 30" 20" 10" Co-tangent of 89 Degrees. Min. LOGARITHMIC SINES. Mia. Sine of 1 Degree. P. Part 0" 10" 20" 30" 40" 50" to 1". O 8.24i855 8. 243o6o 8.244261 8.245459 8.246654 8.24 7 845 5 9 119.6 I 249033 250218 25i4oo 2525 7 8 253 7 53 254925 58 117 7 2 256094 257260 258423 2 5 9 58 2 26o 7 39 261892 5? iiS.S 3 263042 264190 265334 2664 7 5 267613 268 7 49 56 114.0 4 269881 271010 272137 2 7 3260 2 7 438i 275499 55 112. 2 5 276614 277726 2 7 8835 2 7 994i 28io45 282145 54 1*0.5 6 283243 284339 28543i 286521 28 7 6o8 288692 53 IOS.8 7 289773 290852 291928 298002 294073 j 295141 52 IO7.2 8 296207 297270 298330 299388 3oo443 | 301496 5i 105.7 9 3o2546 3o3594 3o4639 3o568i 3o6 7 2i 307759 5o 104.1 10 8.308794 8.309827 8.3io857 8.3n885 8.312910 8.3i3 9 33 4 9 IO2.6 ii 3i4 9 54 315972 316987 3i8ooi 319012 320021 48 IOI .2 12 321027 322031 323o33 324o32 325029 326024 47 99.8 i3 327016 328007 328995 329980 330964 33i 9 45 46 98.5 i4 332924 333 9 oi 334876 335848 3368i 9 33 77 8 7 45 97.1 i5 338 7 53 339717 340679 34i638 342596 34355i 44 9 5.8 16 3445o4 345456 3464o5 34 7 35 3482 97 349240 43 94.6 17 35oi8i 351119 352056 352991 353924 354855 42 93.4 18 355 7 83 356 7 io 35 7 635 358558 35 9 4 79 36o3 9 8 4i 92.2 X 9 36i3i5 36223o 363i43 364o55 364 9 64 3658 7 i 4o 91.0 20 8.366777 8.36 7 68i 8.368582 8.369482 8.370380 8. 3 7 i2 77 3 9 89.9 21 372171 3 7 3o63 3 7 3 9 54 3 7 4843 3 7 5 7 3o 3 7 66i5 38 88.8 22 377499 3 7 838o 379260 38oi38 38ioi5 381889 3? 87.7 23 382762 383633 384502 3853 7 o 386236 387100 36 86.7 24 387962 388823 389682 3oo53 9 SgiSgS 392249 35 85.6 25 3 9 3ioi 393951 394800 3 9 564 7 396493 3 97 33 7 34 84.6 26 3 9 8 I79 399020 399859 4oo6 9 6 4oi532 402366 33 83. 7 27 403199 4o4o3o 4o4859 4o568 7 4o65i4 4o 7 338 32 82.7 28 408161 408983 409803 410621 4n438 412254 3i 81.8 29 4i3o68 4i388o 414691 4i55oo 4i63o8 417114 3o 80.8 3o 8.417919 8.418722 8.419524 8.42o325 8.42II23 8.421921 29 80.0 3i 422717 4235ii 4243o4 425o 9 6 425886 426675 28 79..! 32 427462 428248 429032 429815 43o59 7 43i3 77 27 78.2 33 432i56 432 9 34 433 7 io 434484 43525 7 436029 26 77-4 34 4368oo 437569 43833 7 439103 43 9 868 44o632 25 76.6 35 44i3 9 4 442i56 442915 4436 7 4 44443i 445i86 24 7 5.8 36 445 9 4i 4466 9 4 44 7 446 448196 448 9 46 449694 23 7 5.o 3? 45o44o 45u86 451930 45 2 6 7 3 4534i4 454i54 22 74.2 38 454893 45563i 456368 45 7 io3 45 7 83 7 458570 21 7 3.5 3 9 45 9 3oi 46oo32 46o 7 6i 461489 462215 462941 2O 7 2 -7 4o 8.463665 8.464388 8.465no 8.46583o 8.46655o 8.467268 J 9 7 2.O 4i 467985 468701 469416 4 7 oi29 470841 4 7 i553 18 7 1.3 42 472263 472971 4 7 36 79 4 7 4386 475091 475795 *7 70.6 43 476498 477200 4 779 oi 478601 4 79 2 99 479997 16 69.9 44 48o6 9 3 ! 48 i 388 482083 482776 48346 7 484i58 i5 69.2 45 484848 485536 486224 486910 48 7 5 9 6 488280 i4 68.6 46 488 9 63 489645 490326 491006 4 9 i685 492363 i3 67.9 4? 498040 493715 494390 495o64 495 7 36 496408 12 67.3 48 497078 497748 498416 499084 499 7 5o 5oo4i6 II 66.7 49 5oio8o 501743 5o24o5 5o3o67 5o3 7 2 7 5o4386 IO 66.1 5o 8.5o5o45 8.5o57O2 8.5o6358 8. 507014 8.5o 7 668 8.5o83 2 i 9 65.5 5i 508974 509625 5io2 7 5 510925 5ii5 7 3 5l222I 8 64. 9 52 512867 5i35i3 5i4i5 7 5i48oi 5 i5444 5i6o86 7 64.3 53 516726 5i7366 5i8oo5 5i8643 519280 519916 6 63. 7 54 52o55i 521186 521819 52245i 523o83 523 7 i3 5 63.2 55 524343 524972 525599 526226 526852 527477 4 62.6 56 528102 528725 52934 7 529969 j 53o59o 531209 3 62.1 5? 531828 532446 533o63 5336 79 534295 534909 2 61.6 58 5355 2 3 536i36 536 7 4 7 53 7 358 53 79 6 9 5385 7 8 I 61.1 5 9 539186 : 539794 54o4oi 54ioo 7 54i6i2 542216 O 6o.5 60" 50" 40" 30" 20" 10" Co-sine of 88 Degrees. Min. LOGARITHMIC TANGENTS. Min. Tangent of 1 Degree. P. Part 0" 10" 20" 30" 40" 50" to 1". 8.241921 8.243126 8.244328 8.245526 8.246721 8.247913 5 9 II9-7 I 249102 250287 251469 252648 253823 254996 58 117.7 2 256i65 25 7 33i 258494 25 9 654 260811 261965 57 n5,8 3 263n5 264263 2654o8 266549 267688 268824 56 n4.o 4 269956 271086 272213 273337 274458 275576 55 112. 2 5 276691 277804 278913 280020 281124 282225 54 no. 5 6 2833 2 3 284419 2 855i2 286602 287689 288774 53 io8. 9 7 289856 290935 292012 293086 294157 295226 52 107.2 8 296292 2 97 355 298416 299474 3oo53o 3oi583 5i 105.7 9 3o 2 634 3o3682 304727 305770 3o68u 307849 5o 104.2 10 8.3o8884 8.309917 8.310948 8.311976 8.3i3oo2 8.3i4o25 49 102.7 ii 3i5o46 3i6o65 317081 3i8o 9 5 319106 32on5 48 loi.S 12 32II22 322127 323129 324l2 9 325i26 326121 47 99-8 i3 327II4 328io5 329093 33oo8o | 33io64 332045 46 9 8>5 U 333025 334oo2 334 9 77 335 9 5o ! 336921 337890 45 97-2 i5 338856 339821 340783 34i 7 43 342701 343657 44 9 5. 9 16 3446io 345562 3465i2 347459 3484o5 349348 43 9 4.6 J 7 350289 351229 352i66 353ioi 354o35 354966 42 93.4 18 3558 9 5 3568 2 3 35 77 48 3586 7 i SSgSgS 36o5i2 4i 9 2.2 *9 36i43o 362345 363259 364171 365o8i 365 9 88 4o 9 I.I 20 8.866895 8.36 7799 8.368701 8.369601 8.37o5oo 8.371397 3 9 8 9 . 9 ^ 21 372292 3 7 3i85 374076 3 7 4965 3 7 5853 376738 38 88.8 22 377622 3 7 85o4 3 79 385 380263 38n4o 382oi5 37 87.8 23 382889 383760 38463o 385498 386364 387229 36 86.7 24 388092 388 9 53 389813 390670 391526 392381 35 85. 7 25 393234 3 9 4o85 394934 395782 396628 397472 34 84.7 26 3 9 83i5 399156 399996 4oo834 401670 4o25o5 33 83.7 27 4o3338 404.170 4o5ooo 4o5828 4o6655 407480 32 82.8 28 4o83o4 409126 409946 410765 4n583 412399 3i 81.8 29 4i32i3 414026 4i483 7 4i5647 4i6456 417263 3o 80. 9 3o 8.4i8o68 8.418872 8.419674 8.420475 8.421274 8.422072 2 9 80.0 3i 422869 423664 424458 42525o 426041 42683o 28 7 9 .i 32 427618 428404 4a 9 i8 9 42 99 73 43o 7 55 43i536 27 7 8.3 33 4323i5 433093 433870 434645 4354i9 436191 26 77.5 34 436962 43 77 3 2 4385oo 43 9 267 44oo33 440797 25 76.6 ?5 44i56o 442322 443082 44384i 444599 445355 24 7 5.8 36 446no 446864 447616 448368 449117 449866 23 7 5.o 37 45o6i3 45i35 9 452io4 452847 45358 9 45433o 22 74,3 38 455070 4558o8 456545 457281 458oi6 458749 21 7 3.5 3 9 459481 460212 46o 9 42 461670 462398 463i24 2O 72.8 4o 8.463849 8.464572 8.465 29 5 8. 466016 8.466 7 36 8. 46 7 455 *9 72.1 4i 468172 46888 9 46 9 6o4 47o3i8 47io3i 471743 18 7 i.3 42 472454 473i63 473872 4745 79 475285 475990 J 7 70.7 43 476693 477396 478o 9 7 478798 479497 480195 16 70.0 44 480892 48 i 588 482283 482976 483669 48436o i5 69.3 45 485o5o 48574o 486428 487115 487801 488486 i4 68.6 46 489170 489852 4 9 o534 491215 491894 492573 i3 68.0 4? 4 9 325o 493927 4 9 46o2 495276 495949 496622 12 67.4 48 497293 497963 4 9 8632 499300 499967 5oo633 II 66.8 49 501298 501962 5o2625 503287 5o3948 5o46o8 IO 66.1 5o 8. 505267 8.5o5925 8.5o658 2 8. 507238 8.507893 8.5o8547 9 65.5 5i 509200 509852 5io5o3 5m53 5n8o2 5i245i 8 65.o 62 5 i 3098 5i3 7 44 5i438 9 5i5o34 5i56 7 7 5i632o 7 64.4 53 516961 517602 518241 5i888o 5i 9 5i8 52oi54 6 63.8 54 520790 52i425 522O5 9 522692 523324 523956 5 63.3 55 5a4586 5252i5 525844 526472 527098 527724 4 62.7 56 528349 528973 52 9 5 9 6 53o2i8 53o84o 53i46o 3 62.2 5 7 532o8o 532698 5333i6 533 9 33 534549 535i64 2 61.6 58 535 779 5363 9 2 537oo5 53 7 6i 7 538227 538837 I 61.1 5 9 53 9 447 54oo55 540662 541269 54i8 7 5 54248o O 60.6 fiO 50" | 40" 30" 20" 10" Co-tangent of 88 Degrees. Min. 26 LOGARITHM c SINES. i Sine of 2 Degrees. d Sine of 3 Degrees. 8 0" 10" 20" 30' 40" 50" 9 0" 10" 20" 30" 40" 50" 8.542819 3422 4023 4624 5224 58 2 3 5 9 o 8. 7 i88oo 9 2O2 9 6o3 ...4 4o4 .8o4 5 9 1 6422 7 oi 9 7616 8212 8807 9 4oi 58 I 8. 7 2I204 i6o3 20O2 2401 2799 3i 97 58 2 999 5 .58 7 1179 I 77 236! 2 9 5o 57 2 35 9 5 3 99 2 438 9 4785 5i8i 55 77 57 3 8 55353 9 4126 4?i3 53oo 5885 64 7 o 56 3 5 97 2 636 7 6762 7 i56 7 55o 7943 56 4 7054 7 63 7 8219 8801 9 38i 99 6i 55 4 8337 872 9 9 I22 9 5i4 9906 2 97 55 5 8.56o54o 1119 1696 2273 284 9 3425 54 5 8. 7 3o688 io 79 i46 9 i85 9 224 9 2638 54 6 3999 45 7 3 5i46 5719 62 9 o 6861 53 6 3027 34i6 38o4 4l 9 2 45 7 9 4 9 6 7 53 7 743 1 8000 856 9 9 i3 7 9 7o4 .2 7 O 52 7 5354 5 7 4o 6126 65i2 68 9 8 72 83 52 8 8.570836 i4oi 1965 2528 3o 9 i 3653 5i 8 7667 8o52 8436 8820 9 2o3 9 586 5i 9 4214 4 77 4 5334 58 9 3 645 1 7 oo 9 5o 9 99 6 9 .352 7 34 in5 i4 9 7 i8 7 8 5o 10 7 566 8122 8678 9 232 97 86 .34o 49 10 8. 7 4225 9 2 63 9 3oi 9 33 99 3 77 8 4i5 7 49 ii 8. 58o8 9 2 1 444 i 99 5 2546 3o 9 6 3645 48 ii 4536 4 9 i4 52 9 3 5670 6o48 6425 48 12 4i 9 3 474i 5 2 88 5834 638o 6 9 25 47 12 6802 7178 7 554 79 3o 83o5 8680 47 i3 7 46 9 8oi3 8556 9098 9 64o .181 46 i3 9 o55 9 43o 9 8o4 .178 .55i .924 46 i4 8.590721 1260 1799 2338 2 8 7 5 34i2 45 i4 8.751297 i6 7 o 2042 24i4 2786 3i5 7 45 i5 3 9 48 4484 5oi 9 !5553 6087 66i 9 44 i5 3528 38 9 8 426 9 463 9 5oo8 53 7 8 44 16 7152 7 683 8214 8 7 45 9 2 7 4 9 8o3 43 16 5 7 4 7 6116 6484 6852 7220 7 58 7 43 J 7 8.6oo332 0859 i38 7 I 9 i3 243 9 2 9 64 42 l l 79 55 832i 8688 9 o54 9 42O 9786 42 18 348 9 4012 4536 5o58 558o6io2 4i 18 8.760151 o5i6 0881 1245 1609 i 97 3 4i X 9 6623 7143 76628181 86 99 9 2I 7 4o J 9 2337 2 7 OO 3o63 3425 3 7 8 7 4i49 4o 20 97 34 . 2 5i .766 1282 i 79 6 23lO 3 9 20 45ii 48 7 2 5 2 34 55 9 4 5 9 55 63i5 39 21 8.612823 3336 3848 436o 48 7 i 538i 38 21 6675 7 o34 7 3 9 4 77 52 8111 846 9 38 22 5891 64oo 69097417 79 24 843 1 37 22 8828 9 i85 9 543 99 . 2 5 7 .6i3 37 23 8 9 3 7 9 442 9947 .452 . 9 56 i45 9 36 23 8. 77 o 97 o i326 1681 2o3 7 2392 2747 36 24 8.621962 2464 2 9 65 3466 3 9 66 4466 35 24 3ioi 3456 38io 4i63 45i 7 48 7 o 35 25 4 9 65 5464 5962 6459 6 9 56 7 453 34 25 5223 55 7 5 5 9 2 7 62 79 663 1 6 9 82 34 26 7948 8444 8938^432 99 26 .419 33 26 7 333 7 684 8o35 8385 8 7 35 9 o85 33 27 8.630911 i4o3 i8 9 42385 28 7 5 3365 32 2 7 9 434 9783 .132 .48o .829 "77 32 28 3854 4342 483o53i 7 58o4 6291 3i 28 8. 7 8i524 1872 22I 9 2566 2912 325 9 3i 29 6776 7262 77468230 8714 9 i 97 3o 2 9 36o5 3 9 5i 42 9 6 464i 4986 533i 3o 3o 9680 .162 .643 1124 i6o4 2084 29 3o 56 7 5 6oi 9 6363 6 77 7o5o 7 3 9 3 29 3i 8.642563 3o42 3520 3998 44 7 5 4 9 52 28 3i 7736 8078 8421 8762 9104 9 446 28 32 5428 5 9 o4 63 79 6854 7328 7801 27 32 97 8 7 .128 .468 .808 1149 i486 27 33 8274 8 7 4 7 9219 9690 .161 .632 26 33 8. 79 i828 2167 25o6 2845 3i83 352i 26 34|8.65iio2 i5 7 i 2040 25o8 2 97 6 3444 25 34 385 9 4i97 4534 4872 52o8 5545 25 351 3 9 n 43 77 484353o8 5 77 3 6238 24 35 588i 6218 6553 688 9 7224 7 55 9 24 36 6702 7 i65 7628 8090 8552 9014 23 36 7 8 9 4 822 9 8563 8897 9231 9 564 23 3?| 94? 5 99 35 .3 9 5 .855 :3i4 1772 22 37 9 8 97 .230 .563 .896 1228 i56o 22 38J8.662230 2688 3i4536o2 4o58 45i3 21 38 8.801892 2223 2554 2885 32i6 3546 21 3 9 4968 5423 58 7 7633i 6 7 84 72 3 7 2O 3 9 38 7 6 42O6 4536 4866 5i 9 5 5524 20 4o 7689 8i4i 8592 943 9 4 9 4 9944 19 4o 5852 6181 65o 9 6837 7 i65 7 4 9 2 '9 4i 8.670393 0842 1291 1739 2187 2634 18 4i 7819 8i46 8473 8799 9126 9 45i 18 42 3o8o 35 27 3 97 2 i 44r8 4863 53o 7 17 42 9777 .io3 .428 . 7 53 1078 1402 17 43 5 7 5i 6i 9 4 6638 7 o8o 7522 7964 16 43 8.811726 2o5o 23 7 4 2698 3021 3344 16 44 84o5 8846 9286!9 7 26 .166 .6o5 i5 44 366 7 3 9 8 9 43i2 4634 4956 5277 i5 45 8. 68io43 i48i 19192356 2 79 3 323o i4 45 55 99 5 9 20 6241 656i 6882 7202' i4 46 3665 4ioi 45364971 54o5 5838 i3 46 7522 7841 8161 848o 8799 9ii8i3 4? 6272 6 7 o5 71377569 8001 8432 12 47 9 436 97 55 .. 7 3 .390 . 7 o8 I025|I2 48 8863 9 a 9 3 97 23 .152 .58i 1010 II 48 8.821343 i65 9 i 97 6 2292 2609 2 9 25 II 49 8.691438 1866 2293 2720 3i46 35 7 2 IO 49 324o 3556 38 7 i 4i86 45oi 48i6 IO 5o 3 99 8 4423 4848 5272 56 9 6 6120 9 5o 5i3o 5444 5 7 58 6072 6385 66 9 8 9 Si 6543 6966 7 388 7810 8232 8653 8 5i 7011 7 324 7 63 7 7949 8261 85 7 3 8 52 97 3 9494 99 i3 .333 . 7 52 1171 7 52 8884 9 i 9 6 9 5 7 9818 . 129 .43 9 7 53 8.7oi58 9 2OO 7 2424 2841 3258 36 7 4 6 53 8.83o74 9 1060 i36 9 1679 1988 22 9 8 6 54 4o 9 o 45o5 4 9 20 5335 5 7 4 9 6i63 5 54 2607 2 9 i5 3224 3532 384o 4i48 5 55 65 7 7 6990 7402 7 8i5 8226 8638 4 55 4456 4 7 63 5070 53 77 5684 5 99 i 4 56 9 o4 9 9460 9870 .280 .6 9 o 1099 3 56 6297 66o3 6 9 o 9 7 2l5 7 520 7825 3 5? 8.711507 1916 2324 2 7 3l 3i3 9 3546 2 57 8i3o 8435 8 7 4o 9044 9348 9 652 2 58 3 9 52 4358 4764 5i6 9 55 7 4 5 979 I 58 99 56 .260 .563 .866 1169 1472 I 5 9 6383 6787 7I 9 7 5 9 3 799 6 83 9 8 O 5 9 8.841774 2O 7 6 23 7 8 2680J2 9 82 3 2 83 O 60" 50" 40" 30" 20" 10" a 60" 50" 40" 30" | 20" 10" g Co-sine of 87 Degrees. s Co-sine of 86 Degrees. S .< 1" 2'' 3" 4" 5" 6" 7" 8" 9" ( I" 2" 3" 4" 5" 6" 7" 8" 9" irt } 48 96 145 192 241 289 33$ 386 434 Lrt } 34 69 103 138 172 207 241 275 310 LOGARITHMIC TANGENTS. 27 B Tangent of 2 Degrees. - a Tangent of 3 Degrees. 9 0" 10" 20" 30" | 40 50" & 0" 10" 20" 30" 40" 50" o 8.543o84 3687 4289 4891 5492 6o 9 2 5 9 o 8.719396 9798 .2OI .6o3 ioo4 i4o5 59 I 6691 7289 7 88 7 8483 9079 9674 58 I 8.721806 220 7 2607 3oo 7 34o6 38o5 58 2 8. 55o268 0862 i454 2046 2 63 7 3227 57 2 4204 i6o2 5ooo 53 97 5-794 6191 57 3 3817 44o5 4993 558o 6166 6752 56 3 6588 6984 7380 777 5 8i 7 o 8565 56 4 7336 7920 85o3 9 o85 9 66 7 248 55 4 8 9 5 9 9353 9746 533 925 55 5 8.56o828 i4o 7 i 9 85 2 563 3i4o (716 54 5 8. 7 3i3i 7 79 2IOI 2492 2883 32 7 3 54 6 4291 4866 544o 6oi3 6585 7 i5 7 53 6 3663 4o53 4442 483i 5220 56o8 53 7 7727 8298 886 7 9 435 ...3 5 7 o 52 7 5 99 6 6384 6771 7 i58 7 545 79 3i 52 8 8.5 7 n37 1702 226 7 2832 3395 3 9 58 5i 8 83i 7 8 7 o3 9088 9 4 7 3 9 858 242 5i 9 452O 5o8i 5642 6201 6760 7319 5o 9 8.740626 1009 i3 9 3 1776 2i58 254o 5o 10 7877 8434 8990 9 545 . IOO .654 J9 10 2922 33o4 3685 4o66 4447 4827 49 ii 8.58i2o8 1760 2312 2864 34i4 3 9 64 ii 5207 5586 5g66 6344 6 72 3 7101 48 -12 45i4 5o62 56io 6i5 7 6 7 o4 7249 i? 12 7479 7 85 7 8234 8611 8988 9 364 47 i3 7795 833 9 8883 9 426 9968 .5io 46 i3 9740 .116 .491 .866 1241 i6i5 46 i4 i5 9 x 2l3l 26-70 3208 3746 45 i4 8.751989 2363 2 7 36 3109 3482 3855 45 i5 4283 4820 5355 58 9 o 6425 6959 44 i5 4227 4599 4970 534i 5712 6o83 44 16 7492 8024 8556 9 o8 7 9618 .147 43 16 6453 6823 7 i 9 3 7562 7931 83oo 43 l l 8.600677 1205 i 7 33 2260 2 7 8 7 33i3 42 l l 8668 9036 9404 9771 .i3 9 .5o5 42 18 3839 4363 488 7 54n 5 9 34 6456 4i 18 8.760872 1238 1604 1970 2335 2700 4i 19 6978 7499 8019 853 9 9 o58 9 5 7 6 4o 19 3o65 3429 3 79 3 4i5 7 452O 4884 4o 20 8.610094 0612 1128 1 644 2160 26 7 5 3 9 20 5246 56og 5 97 i 6333 66 9 5 7 o56 3 9 21 3i8 9 3702 42 1 5 4 7 28 524o 5 7 5i 38 21 7417 7778 8i3 9 8499 885 9 9218 38 22 6262 6772 -7281 779 82 9 8 8806 3? 22 9 5 7 8 99 3 7 .295 .654 IOI2 1370 3 7 23 93i3 9819 .325 .83o i335 1839 36 23 8. 77 i 7 2 7 2o85 2442 2798 3i55 35n 36 24 8.622343 2846 3348 385o 435i 4852 35 24 3866 4222 45 77 4932 5287 564i 35 25 5352 585i 635o 6849 7 346 7 844 34 25 5 99 5 634 9 6702 7 o56 74o 9 7761 34 26 834o 8836 9332 9 82 7 .321 .8x5 33 26 8n4 8466 8817 9169 9 520 9871 33 27 8.63i3o8 1801 2293 2 7 85 32 7 6 3 7 66 32 2 7 8.780222 o5 7 2 0922 1272 1622 1971 32 28 4256 4746 5235 5 7 23 6211 6698 3i 28 2320 2669 3017 3365 3 7 i3 4o6i 3i 29 7i84 7671 8i56 864i 9 I26 9610 3o 2 9 44o8 4755 5 1 02 5448 5 79 4 6i4o 3o 3o 8.640093 o5 7 6 io58 i54o 2O2I 25O2 29 3o 6486 683i 7177 7 52I 7866 8210 29 3i 2982 3462 3 9 4i 4420 48 9 8 53 7 6 28 3i 8554 8898 9242 9585 99 28 .271 28 32 5853 6329 68o5 7 28l 77 56 823o 27 32 8.790613 o 9 55 1297 i63 9 1980 2321 27 33 8 7 o4 91-78 965i . 123 .5 9 5 1067 26 33 2662 3oo3 3343 3683 4023 4362 26 34 8.65i537 2008 24-78 2 9 4 7 34i6 3884 25 34 4 7 oi 5o4o 53 79 5 7 i8 6o56 63 9 4 25 35 4352 4820 5286 5 7 53 62I 9 6684 24 35 6 7 3i 7069 7 4o6 7743 8o 79 84i6 24 36 7149 7 6i3 8o 77 854i 9 oo4 9 466 23 36 8752 9088 g423 97 5 9 .. 9 4 .429 23 3? 9928 .38 9 .85o i3n 1771 2230 22 37 8.800763 1098 1432 i 7 65 2099 2432 22 38 8.662689 3i48 36o6 4o63 4520 4977 21 38 2 7 65 3o 9 8 343 1 3 7 63 4095 4427 21 3 9 5433 588 9 6344 6 799 72 53 7707 2O 3 9 4 7 58 Sogo 5421 5 7 5i 6082 6412 20 4o 8160 86i3 9065 9 5i 7 9968 19 4o 6742 7072 7/J02 77 3i 8060 8389 19 4i 8.670870 1320 I 7 6 9 2218 2667 3ii5 18 4i 8717 9 o46 9 3 7 4 97 oi ..29 .356 18 42 3563 4oio 445 7 4903 5349 5 79 4 17 42 8.8io683 IOIO i33 7 i663 1989 23i5 17 43 6 2 3 9 6684 7 I28 7 5 7 2 8oi5 845 7 16 43 2641 2966 3291 36i6 4265 16 44 8900 9341 9783 .222 .664 1104 i5 44 4589 4913 5 2 3 7 556o 5884 6207 i5 45 8.68i544 i 9 83 2422 2860 3298 3 7 35 i4 45 6529 6852 7174 ?4 23 7 8i8 8i4o i4 46 4172 46o8 5o44 5480 5gi5 635o i3 46 846i 8782 910: 9 7 44 ..64 i3 47 6784 -7218 7 65 2 8o85 85i 7 8 9 5o 12 47 8.820382 0703 102: 1 342 1661 1980 12 48 9381 9 8i3 .244 .6 7 4 1104 i534 II 48 229^ 2617 2935 3253 35 7 o 3888 II 49 8.691963 23 9 2 2820 3248 3675 4io3 10 49 42o5 4522 4838 5i55 54 7 i 5 7 8 7 10 5o 4529 4 9 56 538i 58o 7 6232 6656 9 5o 6io3 64i8 6 7 33 7049 7 363 7678 9 Si 7081 7 5o2 79 28 835i 8773 9 i 9 5 8 5i 799 2 83o 7 8621 8 9 34 924^ 956i 8 52 9617 ..38 .880 i3oo 1720 7 52 9 8 7 4 .187 .5oo .812 1 1 22 i436 7 53 8.702139 2558 29-76 33g5 38i2 4230 6 53 8.83i 7 48 2059 23 7 I 2682 2992 33o3 6 54 4646 5o63 54 7 9 5895 63io 6725 5 54 36i3 3 9 24 4234 4543 4853 5i6 2 5 55 7 i4o 7 554 79 6 7 838i 8 79 4 9206 4 55 54 7 i 5 7 8o 6089 63 97 6 7 o5 701^ 4 56 9618 ..3o .442 .853 1263 1672 3 56 7 32I 7629 7936 8243 855o 885 7 3 5 7 8. 7 i2o83 24 9 3 2902 33xi 3 7 i 9 4127 2 57 9 i63 9470 9776 ..81 .38 7 .692 2 58 4534 4942 5348 5 7 55 6161 6567 I 58 8.840998 i3o3 160-7 1912 2216 2521 I 5 9 69-72 7377 7781 8186 858 9 8 99 3 O 5 9 2825 3i28 3432 3 7 35 4o38 434i O 60" 50" 40" 30" 20" 10" rt 60" 50" 40" 30" 20" 10" d Co-tangent of 87 Degrees. 1 Co-tangent of 86 Degrees. 9 , .5 I" 2" 3" 4" 5" 6" 7" 8" 9" C 1" 2" 3" 4" 5" 6" 7" 8" 9" lrl } 48 97 145 193 242 290 338 387 435 drt { 35 69 104 138 173 207 242 276 311 LOGARITHMIC SINES. 1 Sine of 4 Degrees. Sine of 5 Degrees. H 0" 10" 20" 30" 40" 50" 0" 10" 20" 30" 40" 50" o 8.843585 3886 4i86 448 7 4?7 6087 5 9 o 8.940296 o53 7 0777 IOI 7 1258 1498 59 i 538 7 5687 5 9 8 7 6286 6585 6884 58 I 173? 1977 2217 245 7 2696 2 9 35 58 2 7i83 748 1 7780 80-78 83 7 6 86 7 3 57 2 8174 34x3 3652 3891 4129 4368 5 7 3 8971 9268 9 565 9862 .i5 9 .455 56 3 46o6 4844 5o83 532i 5558 5 79 6 56 4 8.85o75i io4 7 1 343 i63 9 i 9 34 2229 55 4 6o34 6271 65o8 6 7 45 6982 7219 55 5 2525 2819 3n4 34o8 3 7 o3 3 997 54 5 7456 7 6 9 3 7929 8166 8402 8638 54 6 4291 4584 48 7 8 5i 7 i 5464 5 7 5 7 53 6 88 7 4 9110 9 345 9 58i 9817 ..52 53 7 6049 6342 6634 6926 7218 52 7 8.950287 O522 7 5 7 0992 1227 i46i 5a 8 7801 8092 8383 86 7 4 8 9 65 9255 5i 8 1696 1930 2164 23 9 8 2632 2866 5i 9 9 546 9 836 .126 .4i5 .705 994 5o 9 3ioo 3333 356 7 38oo 4o33 4266 5o 10 8.861283 I5 7 2 1861 2149 2438 2726 49 10 4499 4732 4965 5197 5429 5662 49 ii 3oi4 3302 358 9 38 77 4i64 445 1 48 ii 58 9 4 6126 6358 65go 6821 7 o53 48 12 4738 5o24 53n 55 97 5883 6169 47 12 7284 7 5i6 7 7 4 7 7978 8209 844o 47 i3 6455 6 7 4o 7025 7 3io 7 5 9 5 7880 46 i3 8670 8901 9i3i 9362 9592 9822 46 i4 8i65 844 9 8733 901-7 9 3oi 9585 45 i4 8.960052 0282 o5n 0741 0970 I2OO 45 i5 9868 . i5i .434 717 IOOO 1282 44 i5 1429 i658 188-7 2116 2344 2 5 7 3 44 16 8.87i565 i84 7 2129 2410 26 9 2 2973 43 16 2801 3o3o 3258 3486 3714 3 9 42 43 17 3 2 55 3536 38i 7 409-7 4378 4658 42 17 4170 4397 46 2 5 4852 5o8o 53o 7 42 18 4938 5 2 i8 5498 5 777 6o5 7 6336 4i 18 5534 5 7 6i 5 9 8 7 6214 644i 6667 4i 19 66i5 68 9 4 7172 7 45i 7729 8007 4o 19 6893 7120 7 346 75-72 7797 8o23 4o 20 8 2 85 8563 884i 9118 9 3 9 5 9672 3 9 20 8249 8474 8700 8 9 25 9i5o 9 3 7 5 3 9 21 9949 .226 .5o3 779 io55 i33i 38 21 9600 9825 ..49 .274 .498 . 7 23 38 22 8.881607 i883 2i58 2433 2708 2 9 83 37 22 8.970947 1171 1395 1619 1842 2066 37 23 3258 3533 3807 4o8i 4355 462 9 36 23 2289 2 5i3 2 7 36 2959 3182 34o5 36 24 4903 5i 77 545o 5 7 23 5 99 6 626 9 35 24 3628 385i 4o 7 3 4296 45i8 474o 35 25 6542 68i4 7087 7 35 9 763i 79 3 34 25 4962 5i84 54o6 5628 585o 6071 34 26 8i 7 4 8446 8717 8 9 88 9 25 9 9 53o 33 26 6293 65i4 6 7 35 6956 7177 7 3 9 8 33 27 9801 ..71 .34i .612 .882 n5i 32 2 7 7619 7839:8060 8280 85oi 8-721 3a 28 8.891421 i6 9 o 1960 222 9 2498 2767 3i 28 8941 9161 938i 9600 9820 ..3 9 3i 29 3o35 33o4 3572 384o 4io8 43 7 6 3o 2 9 8.980259 o4 7 8 0697 0916 n35 1 354 3o 3o 4643 4 9 n 5i 7 85445 5712 5 979 29 3o i5 7 3 1791 2OIO 2228 2447 2665 29 3i 6246 65i2 6 77 8j 7 o44 73io 7 5 7 6 28 3i 2883 3ioi 33i 9 3536 3 7 54 3 97 2 28 32 7842 8107 83 7 3 8638 8 9 o3 9 i68 27 32 4189 44o6 4623 484o 5007 52 7 4 27 33 9 432 9 6 97 9961 .225 .48 9 . 7 53 26 33 54 9 i 5 7 o8 5924 6i4i 635 7 65 7 3 26 34 8.901017 1280 1 544 180-7 2070 2333 25 34 6789 7oo5 7221 743 7 7 65 2 7868 25 35 2596 2858 3l2I 3383 3645 39<>7 24 35 8o83 8299 85i4 8729 8944 9 l5 9 24 36 4169 443o 4692 4 9 53 52i4 5475 23 36 9 3 7 4 9 588 9 8o3 ..17 .232 .446 23 37 5 7 36 5 997 62576517 6778 7038 22 37 8.990660 o8 7 4 1088 1302 i5i6 I 7 2 9 22 38 7297 7 55 7 7817 8076 8335 85 9 5 21 38 1943 2i56 2370 2583 2796 30O9 21 39 8853 9 II2 9371 9 62 9 9888 .146 20 39 3222 3435 3647 386o 4072 4285 2O 4o 8.910404 0662 0919 1177 i434 1692 19 4o 4497 470 9 4921 5i33 5345 5556 19 4i 1949 22O6 2462 2719 2976 3232 18 4i 5 7 68 5 9 8o 6191 6402 66i4 6825 18 42 3488 3 7 44 4ooo 4256 45n 4767 1-7 42 7 o36 724? 745 7 7668 7879 8089 17 43 5O22 52 77 5532 5 7 8 7 6o4i 62 9 6 16 43 8299 85io 8720 8 9 3o 9140 9 35o 16 44 655o 68o5 7 5 9 7 3i3 7 566 7820 i5 44 9 56o 97 6 9 9979 .188 .398 .607 i5 45 8o 7 3 832 7 858o 8833 9086 9 338 i4 45 9.000816 IO25 1234 i443 i652 1860 i4 46 9 5 9 i 9 843 ..96 .348 .600 .852 i3 46 2069 2277 2486 2694 2902 3no i3 47 8.921103 i355 1606 i858 2109 236o 12 47 33i8 3526 3 7 33 3 9 4i 4i49 4356 12 48 2610 2861 3lI2 3362 36i2 3862 II 48 4563 4771 4978 5i85 5392 55 99 II 49 4112 4362 46l2 486 1 5m 536o IO 49 58o5 6012 6218 6425 663i 683 7 10 5o 5609 5858 6107 6355 66o4 6852 9 5o 7 o44 725o 7456 7661 7 86 7 8o 7 3 9 5i 7100 7348 7 5 9 6 7844 8092 833 9 8 5i 8278 8484 8689 88 9 4 9100 9 3o5 8 52 858 7 8834 9081 9 328 9 5 7 5 9 82I 7 52 gSio 9715 9919 .124 .329 .533 7 53 8.930068 o3i4 o56o 0806 1052 I2 9 8 6 53 9.010737 0942 n46 i35o i554 i 7 58 6 54 1 544 i 7 8 9 2o35 2280 2525 2770 5 54 1962 2i65 2369 25 7 3 2776 2979 5 55 3oi5 3260 35o4 3 7 4 9 3 99 3 423 7 4 55 3182 3385 3588 3 79 I 3 99 4 419-7 4 56 448 1 4725 4969 5212 5456 56 99 3 56 44oo 4602 48o5 5007 5209 54n 3 $7 5942 6i85 6428 6671 6914 7 i56 2 57 56i3 58i5 6017 6219 6421 6622 2 58 7398 7641 7 883 8i25 8366 8608 I 58 6824 7025 722-7 7428 7629 7 83o I 5 9 885o 9 o 9 i 9 332 9 5 7 3 9814 ..55 5 9 8o3i 8232 8433 8633 8834 qoSt 60" 50" 40" 30" 20" 10" ^ 60" 50" 40" 30" 20" 10" d Co-sine of 85 Degrees. 3 Co-sine of 84 Degrees. fl s, / 1 // nil o// 411 K.II ell fll oil nil P PortJ l7 5l22 21 3 9 8. 910285 o546 0806 1066 i3 2 6 1 586 2O 3 9 5337 5552 5 7 66 5981 6196 64io 20 4o 1 846 2106 2365 2624 2883 3l42 19 4o 662^ 683 9 7 o53 7267 748i 7694 9 4i 34oi 366o 3 9 i8 4i77 4435 46 9 3 18 4i 7 9 o8 8122 8335 8549 8762 8 97 5 18 42 4g5i 5209 5466 5724 5 9 8i 6238 *7 42 9 i88 9401 9614 9827 ..4o .252 7 43 64g5 6762 700 9 7 265 7522 7778 16 43 9 .ooo465 0677 0889 1102 i3i4 i5 2 6 16 44 8o34 8290 8546 8801 9 o5 7 9312 16 44 i 7 38 1949 2161 23 7 3 2584 2 79 5 i5 45 9 568 9823 ..78 .332 .58 7 .84i i4 45 3007 32i8 3429 364o 385! 4o6i i4 46 8.921096 i35o 1604 i858 2112 2365 x3 46 4272 4483 46 9 3 4904 5n4 5324 i3 47 2619 2872 3i25 33 7 8 363i 3884 12 47 5534 5744 5 9 54 6i64 63 7 3 6583 12 48 4i36 438 9 464i 48 9 3 5!45 53 97 II 48 6702 7002 7211 7420 7629 7 838 II 49 5649 5900 6i5 2 64o3 6654 6905 IO 49 8047 8256 8465 86 7 3 8882 9090 IO 5o 7i56 7407 7 65 7 7 9 o8 8i58 84o8 9 5o 9 2 9 8 9 5o 7 97 i5 9923 .i3i ,338 9 5i 8658 8908 9 i58 9407 9 65 7 9906 8 5i 9 .oio546 075^ o 9 6i 1169 1376 i583 8 52 8.93oi55 o4Oi! o653 0902 n5o l3 99 7 52 1790 i 99 7 2204 2411 2618 2824 7 53 1647 iSgS 2143 2391 2639 2887 6 53 3o3i 323 7 3444 365o 3856 4062 6 54 3i34 338i 362 9 3876 4i23 4369 5 54 4268 4474 468o 4886 5091 529 7 5 55 46i6 4862 5io 9 5355 56oi 5847 4 55 55o2 5 7 o 7 5 9 i3 6118 6323 65 2 8 4 56 6o 9 3 6339 6584 683o 7075 7320 3 56 6732 6 9 3 7 7 l42 7346 7 55i 77 55 3 57 7565 7810 8o55 8299 8544 8788 2 5 7 79 5 9 8i64 8368 85 7 2 8776 8979 2 58 9 o32 9276 9 52O 9764 ...7 .251 I 58 9 i8c 938 7 9 5 9 o 9794 9997 .200 I 5 9 8. 9 4o4 9 4 0738 o 9 8i I22/i 1467 1709 O 5 9 9 .o2o4o3 0606 o8o 9 1012 I2l5 1418 O 60" 50" 40" 30" 20" 10" 3 60" 50" 40" 30* 20" 10" a Co-tangent of 85 Degrees. 1 Co-tangent of 84 Degrees. i p p t < 1"2" 3" 4" 5" 6" 7" 8" 9" p p , ( 1" 2" 3" 4" 5" 6" 7" 9" 9" irl \ 27 54 81 108 135 162 188 215 242 ' art 22 44 66 88 110 132 154 177 199 LOGARITHMIC SINES. A Sine of 6 Degrees. J Sine of 7 Degrees. s 0" 10" 20" 30" 40" | W 8 0" 10" 20" 30" 40" 50" o 9.019235 9 435 9 635 9 83!> ..35 .235 5 9 9.086894 6066 6237 6409 6680 6 7 5i 5 9 I 9.o2o435 o635 o834 io34 1233 i433 58 I 6922 79 3 7264 7435 7606 7777 58 2 :632 i83i 2o3o 2229 2428 2627 57 2 7947 8118 8288 845 9 862 9 8800 57 3 2826 3024 3223 342i 36i 9 38i8 56 3 89709140 9 3io 9480 9 65i 9820 56 4 4oi6 42i^ 44i2 46io 48o 7 5oo5 55 4 999 .160 .33o .600 .66 9 .83 9 55 5 620: 54oo 55 9 8 5 79 5 6992 6189 54 5 9.091008 1178 1 347 i5i6 1686 i855 54 6 6386 6583 6780 6 977 7174 7370 53 6 2024 2I 9 3 2362 253o 2 6 99 2868 53 7 7667 77 63 7 9 6o8i56 8352 8548 52 7 3o3 7 3206 3374 3542 3 7 n 38 79 52 8 8 7 44 8 9 4o 9 i36| 9 33 2 9 52 7 9723 61 8 4047 4216 4384 455 2 4 7 20 4888 61 9 9918 .114 .3o 9 |.5o4 .6 99 8 9 4 5o 9 5o56 5223 53 9 i 555 9 5 7 26 58 9 4 5o 10 9.031089 1284 1479 i6 7 3 186^2062 49 10 6062 622 9 63 9 6 6564 6 7 3i 6898 4 9 ii 2267 2461 2646 2 83 9 3o3J 3227 48 H 7066 7232 7399 7666 77 33 7900 43 12 342i 36i5 3809 4002 4i 9 6 438 9 47 12 8066 8233 83 99 8566 8 7 32 8899 47 i3 4582 4776 4969 6162 53555548 46 i3 9066 9 23l 9 3 9 8 9 564 97 3o 9896 46 i4 5 7 4i 5 9 33 6126 63i 9 65i 116703 45 i4 9. 100062 0227 o3 9 3 0669 0726 0890 45 16 6896 7088 7280 7472 7 664 7 856 44 16 1066 1221 1387 1662 1717 i883 44 16 8o48 823 9 843i 8623 88i4 9 oo5 43 16 2048 2213 2378 2543 2708 28 7 3 43 i 7 9197 9388 9 5 79977 99 6i .162 42 17 3o37 32O2 336 7 353i 36 9 6 386o 42 i8 9 .o4o342 o533 0724 o 9 i4 1 106 I2 9 5 4i 18 4026 4i8 9 4353 45i 7 4682 4846 4i '9 i486 1676 1866 2066 2246 2435 4o i 9 5oio 6174 533 7 55oi 5665 6829 4o 20 9626 2816 3oo4 3i 9 4 3383 3572 39 20 6992 6166 63i 9 6483 6646 6810 3 9 21 3762 3 9 5i 4i4o 432 9 45i8 4707 38 21 6 97 3 7i36 72 99 7462 7626 77 88 38 22 48 9 5 5o84 52 7 3 546i 565o 5838 3 7 22 7961 8n4 8277 843 9 8602 8 7 65 3? 23 6026 6214 6402 65 9 o 6 77 8 6 9 66 36 23 9 o 9 o 9 252 9 4i4 9 5 77 9739 36 -24 7164 7342 7 5 2 9 '77i7 794 8o 9 i 35 24 9901 ..63 .225 .38 7 .649 .711 35 25 8279 8466 8653884o 9 02 7 9 2l4 34 25 9.110873 io34 n 9 6 i358 1619 1681 34 26 9400 9687, 9774 99 6o . i4 7 .333 33 26 1842 2003 2166 2326 2487 2648 33 2 7 9.060619 0706 0892 io 7 8 1264 i45o 32 27 2809 2 9 70 3i3i 3292 3453 36i3 32 28 i635 1821 2007 2I 9 2 2378 2563 3i 28 3 77 4 3 9 35 4o 9 5 4266 44i6 45 77 3i 2 9 2749 2 9 34 3n 9 33o4 348 9 36 7 4 3o 29 4 7 3 7 48 97 6067 6218 5378 5538 3o 3o 385 9 4o44 4228 44i3 45 97 4782 20 3o 56 9 8 5858 6017 6177 633 7 6497 29 3l 4966 6160 5335 55i 9 6703 6887 28 3i 6656 6816 6976 7 i35 7294 7453 28 32 6071 6264 64386622 6806 6 9 8 9 27 32 7 6i3 7772 79 3i 8090 8249 84o8 27 33 7172 7356 7 53 9 7722 7 9 o5 8088 26 33 8667 8726 8884 9 o43 9202 936o 26 34 8271 8454 86378820 9 OO2 9 i85 25 34 9619 9677 9 836 9994 !l52 .3ii 25 35 9 36 7 9 55o 97 3 2 99 i4 .. 9 6 .278 24 35 0627 0786 o 9 43 HOI 1269 24 36 9.060460 0642 0824 1006 1 1 88 i36 9 23 36 1417 i5 7 4 1732 1890 2047 2205 23 37 1661 1732 i 9 i4 20 9 5 2276 2457 22 37 2362 2620 2677 2835 2992 3i49 22 38 2639 2820 3opi 3i8i 3362 3543 21 38 33o6 3463 3620 3777 3 9 34 4091 21 3 9 3724 3 9 o4 4o85 4265 4445 4626 2O 3 9 4248 44o4 456i 4718 48 7 4 5o3i 2O 4o 48o6 4 9 86 6166 5346 6626 6706 '9 4o 6187 5344 55oo 5656 6812 6969 '9 4i 5885 6066 6244 6424 66o3 6 7 83 18 4i 6126 6281 6437 65 9 3 6748 6904 1 8 42 6962 7i4i 7320 74 99 7 6 7 8 7867 17 42 7060 7216 7371 7627 7682 7 838 7 43 8o36 8216 83 9 3 8672 8761 8 9 2 9 16 43 799 3 8149 83o4 845 9 86i4 8770 16 44 9107 9 286 9 464 9642 9820 999 8 i5 44 8926 9080 9 235 9 3 9 o 9544 9699 16 45 9.070176 o354 o53 2 0709 0887 1066 i4 45 9 854 . . .9 .163" .3i8 .472 .627 i4 46 1242 1420 1697 i 77 4 1961 2128 i3 46 9.130781 o 9 36 io 9 o 1244 i3 9 8 1662 i3 47 23o6 2482 26692836 3oi3 3i 9 o 12 47 1706 1860 20l4 2168 2322 2476 12 48 3366 3543 37193896 4072 4248 II 48 263o 2 7 83 2 9 3 7 3o 9 i 3244 3398 II 49 4424 46oo 4777 4962 6128 53o4 IO 49 355i 3 7 o4 3858 4on 4i64 43i 7 IO 5o 548o 5656 583i 6007 6182 6358 9 5o 4470 4623 4776 4 9 2 9 6082 5 2 35 9 61 6533 6708 6883 7068 7233 74o8 8 Si 5387 554o 56 9 3 5845 6998 6160 8 62 7583 7758 7933 8107 8282 845 7 7 62 63o3 6455 6607 676.) 6 9 i2 7 o64 7 53 863i 8806 8980 9164 9328 9 5o2 6 53 7216 7368 7620 76727824 7976 6 54 9676 9 85o ..24 .108 .3 7 2 .545 5 54 8128 82 79 843i 86828734 8886 5 55 9.080719 o8 9 2 1 0*6 6 1239 i4i3 1686 4 55 9 o3 7 9 i88 9 34o 94919643 979 3 4 56 1769 I 9 32 2106 227812461 2624 3 56 9944 . .96 .247 .3 9 8 .548 .699 3 57 2797 2 9 6 9 3 1 42 33i4 348 7 365 9 2 57 9.140860 looi n5i i3o2 i453 i6o3 2 58 3832 4oo4 4176 4348 4620 46 9 2 I 58 175411904 2066 2206 2355 2606 1 69 4864 5o36 6208 538o 555i 6723 O 5 9 2655 28o6'2 9 56 3io6 3256 34o5 O 60" 50" 40" 30" 20" 10" E 60" 50" 40" | 30" 20" i 10" . Co-sine of 83 Degrees. Co-sine of 82 Degrees. a _ < 1" 2" 3" 4" 5" 6" 7" 8' 9" p p .< 1" 2" 3" 4" 5" 6" 7" S" 9'' irt { 18 37 55 74 92 111 129 148 166 "{ 16 32 48 64 80 96 112 128 144 LOGARITHMIC TANGENTS. .5 Tangent of 6 Degrees. .a Tangent of 7 Degrees. m 0" 10" | 20" j 30" 40" 50" s 0" 10" 20" 30" 40" 50" o 9 .021620 I823J2O25 2227 2430 263a 5 9 o 9 .o8 9 i44 9318 9 4 9 2 9666 9 83 9 ..i3 5 9 i 2 834 3o36 3238 343 9 364i 3843 58 i 9 .o 9 oi8 7 o36i o534 0708 0881 io54 58 2 4o44 424514447 4648 4849 5o5o 57 2 1228 i4oi i5 7 4 I 7 47 I 9 2O 2093 57 3 5 2 5i 5452 5653 5853 6o54 6254 56 3 2266 243 9 2612 2 7 84 2 9 57 3129 56 4 6465 66556855 7 o55 7 255 7455 55 4 33o2 3474 364 7 38ic; 3 99 i 4i63 55 5 7 655 7 8558o55 8254 8454 8653 54 5 4336 45o8 468o 485i 5o23 5i 9 5 54 6 8852 9 o52 9 25i 9 45o 9649 9 848 53 6 536 7 5538 5710 588i 6o53 6224 53 7 9.o3oo46 0245 o444 o64a 0841 io3 9 52 7 63 9 5 656 7 6 7 38 6909 7080 725i 52 8 i23y i435 i633 i83i 2029 222 7 5i 8 7422 7 5 9 3 7764 7934 8io5 8276 5i 9 2425 2623 2820 3017 32i5 3412 5o 9 8446 8616 8787 8 9 5 7 9 I2 7 9298 5o 10 3609 38o6 4oo3 4200 43 97 45 9 4 49 10 9 468 9 638 9 8o8 9978 .i48 .3i 7 49 1 1 4791 4987 5i84 538o 55 7 6 5 77 3 48 ii 9 . 100487 o65 7 0827 0996 1166 i335 48 12 5 9 6 9 6i65 636i 655 7 6753 6 9 48 4 7 12 i5o4 i6 7 4 i843 2012 2181 235o 47 i3 7i44 7339 7 535 77 3o 7926 8121 46 i3 25l 9 2688 2807 3026 3i 9 4 3363 46 i4 83i6 85n 8 7 o6 8901 9095 9 2 9 45 i4 3532 3 7 oo 386 9 4o3 7 42o5 43 7 4 45 i5 9 485 9679 9 8 7 4 ..68 .262 .456 44 i5 4542 47,10 48 7 8 5o46 52i4 5382 44 16 9 . o4o65i o845 1039 1232 1426 1620 43 16 555o 5 7 i8 5885 6o53 6221 6388 43 17 i8i3 2007 22OO 23 9 4 2 58 7 2 7 8o 42 *7 6556 6723 68 9 o 7o58 7225 7 3 9 2 4a 18 2 97 3 3i66 3359 3552 3 7 45 3 9 3 7 4i 18 7 55 9 7726 7893 8060 8227 83 9 4 4i 19 4i3o 4322 45i5 4707 48 99 5o 9 2 4o r 9 856o 8727 88 9 4 9060 9 22 7 9 3 9 3 4o 20 5284 5476 5668 585 9 6o5i 6243 3 9 20 9 55 9 9726 9 8 9 2 ..58 .224 .3 9 o 3 9 21 6434 6626 6817 7009 7200 7 3 9 i 38 21 9 .no556 0722 0888 io54 I2I 9 i385 38 22 7 582 7773 7964 8:55 8346 8536 37 22 i55i I 7 i6 1882 2047 2213 23 7 8 37 23 8727 8917 9108 9298 948 9 9 6 79 36 23 2543 2 7 o8 28 7 3 3o3 9 32O4 3368 36 24 9869 ..5 9 .249 .439 .629 .818 35 24 3533 36 9 8 3863 4028 4l 9 2 435 7 35 25 9 .o5ioo8 1197 i38 7 1576 1766 i 9 55 34 25 452i 4686 485o 5oi5 5l Z9 5343 34 26 ai44 2333 2522 2711 2900 3o88 33 26 55o 7 56 7 i 5835 5 999 6i63 632 7 33 27 3277 3466 3654 3843 4o3i 42I 9 32 2 7 64 9 i 6655 6818 6982 7i45 7 3o 9 j32 28 4407 45 9 6 4784 4972 5i5 9 534 7 3i 28 7472 7 636 7799 7962 8126 828 9 j3i 29 5535 6723 5910 6098 6285 64 7 2 3o 2 9 8452 86i5 8778 8941 9104 9 266 3o 3o 6659 6847 7o34 7221 7 4o8 7 5 9 4 2 9 3o 9429 9 5 9 2 97 54 9917 79 .242 2 9 3i 7781 7968 8i55 834i 85 2 8 8 7 i4 28 3i 9.120404 o56 7 7 2 9 0891 io53 I2l5 28 32 8900 9086 9273 9 45 9 9 645 9 83i 2 7 32 i3 77 i53 9 I 7 OI i863 2O25 2l8 7 2 7 33 9.060016 O2O2 o388 0573 o 7 5 9 o 9 44 26 33 2348 25lO 26 7 I 2833 2 99 4 3i5626 34 n3o i3i5 i5oo i685 1870 2o55 25 34 33i 7 3478 364o 38oi 3 9 62 4123125 35 2240 2425 2610 2 79 5 2 979 3i64 24 35 4284 4445 46o6 4766 4 9 27 5o88 24 36 3348 3533 3 7 i 7 3 9 oi 4o85 4269 23 36 5249 54o 9 55 7 o 5 7 3o 58 9 i 6o5i 23 3? 4453 463 7 4821 5oo5 5i88|53 7 2 22 3? 6211 6371 6532 6692 6852 7 OI2 22 38 5556 5 7 3 9 5922 6106 69896478 21 38 7 I 7 2 7 332 7 4 9 2 7 65i 7811 797i 21 3 9 6655 6838 7021 7204 73877670 20 3 9 8i3o 82 9 O 844 9 8609 8768 8 9 28 2O 4o 77 5 2 79 35 8117 83oo 8482 8664 I 9 4o 9o8 7 9 246 9 4o5 9 564 9723 9 882 T 9 4i 8846 9029 9211 9 3 9 3 9 5 7 5 97 56 18 4i 9. i3oo4i 0200 o35 9 o5i8 0676 o835 18 42 99 38 . I2O .3oi .483 .664 .846 *7 42 0994 Il52 i3n 1469 1628 i 7 86 *7 43 9.071027 1208 i38 9 1570 i 7 5i I 9 32 16 43 1944 2102 2261 2419 25 77 2 7 35 16 44 2Il3 2294 2475 2655 2836 3oi6 i5 44 2893 3o5o 3208 3366 3524 368i i5 45 3i 97 33 77 3558 3738 3 9 i8 4o 9 8 i4 45 383g 3997 4i54 4312 446 9 4626 i4 46 4278 4458 4638 48i 7 4997 5i 77 i3 46 4784 4 9 4i 5o 9 8 5 2 55 5412 556 9 i3 4? 5356 5536 5 7 i5 58 9 5 6o 7 4'6253 12 47 5 7 26 5883 6o4o 6i97 6353 65io 12 48 6432 6611 6 79 o 6 9 6 9 7 i48 7 32 7 II 48 666 7 6823 6 9 8o 7i36 7 2 9 2 744 9 II 49 7 5o5 7 684 7 862 8o4i 82i 9 83 9 8 10 49 7 6o5 7761 79 i8 8o 7 4 8230 8386 10 5o 8576 8 7 54 8 9 32 9 no 9 288 9 466 9 5o 854a 86 9 8 8854 9009 9 i65 9 32I 9 5i 9644 9822 .... .177 .355 .532 8 5i 9476 9 632 9788 9943 .. 9 8 .254 8 52 9.080710 o88 7 1064 1241 i4i 9 i5 9 6 7 52 9.140409 o564 0720 0875 io3o n85 7 53 1773 i 9 5o 2126 23o3 2480 265 7 6 53 i34o i495 i65o i8o5 i 9 5 9 2Il4 6 54 2833 3oio 3i86 3362 353 9 3 7 r5 5 54 2269 2424 25 7 8 2733 2887 3o42 5 55 38 9 i 4067 4243 44i9 45 9 5 4 77 i 4 55 3196 335o 35o4 365 9 38i3 3967 4 56 4947 5l22 52 9 8 5473 564 9 5824 3 56 4l2I 4275 4429 4583 4 7 3 7 4890 3 57 58 6000 7 o5o 6i 7 5 7 225 635o 7 4oo 65 2 5 7 5 7 4 6 7 oo68 7 5 77 4 9 | 79 24 2 I 5 7 58 5o44 5 9 66 5i 9 8 61 1 9 535i 6272 55o5 6425 565 9 65 79 58i2 6732 2 I 5 9 8098 82 7 3 8447 8621 8 79 5 8 97 o O 5 9 6885 7 o38 7191 7344 7497 7 65o O 60" 50" 40" 30" 20" 10" rj 60" 50" 40" 30" j 20" 10" A Co-tangent of 83 Degrees. .y Co-tangent of 82 Degrees. i P Prt5 l " 2 " 3// 4 " 5 " 6// 7 " 8 " 9 " p p .2 2l82 23ll 244i 2571 2700 3i 29 3634 3 77 8 3922 4o6 7 4211 4355 3o 2 9 2 83o 2060 3o8 9 32i8 3348 3477 3o 3o 4499 4643 4 7 8 7 493i 5075 52i8 29 3o 3607 3 7 36 3865 3 99 4 4124 4253 2 9. 3i 5362 55o6 565o 5 79 3 5 9 3 7 6080 28 3i 4382 45n 464o 4 7 6 9 48 9 8 5027 28 32 6224 6367 65n 6654 6797 6941 27 32 5i56 5 2 85 54i4 5543 5671 58oo 27 33 7084 7227 7 3 7 o 7 5i3 7656 7800 26 33 5 9 2 9 6o58 6186 63i5 6443 6572 26 34 7 9 4a 8o85 8228 83 7 i 85i4 865 7 25 34 6700 6829 6 9 5 7 7086 7214 7342 25 35 8799 8942 9 o85 922-7 9 3 7 o 9512 24 35 747 1 7 5 99 77 2 7 7855 7983 8111 24 36 9 655 9797 99 3 9 ..82 .224 .366 23 36 8 2 3 9 8368 84 9 6 8623 8 7 5i 8879 23 37 9.i8o5o8 o65o o 79 2 o 9 34 1076 1218 22 3? 9007 9i35 9263 9 3 9 o 9 5i8 9 646 22 38 i36o 1502 1 644 i 7 86 I 9 2 7 2069 21 38 9773 9901 ..29 .166 .284 .4n 21 3 9 221 I 2352 2494 2 635 2777 2918 20 3 9 9.23o53 9 0666 o 79 3 O 9 2I io4& 1175 2O 4o 3o59 32OI 3342 3483 3625 3766 19 4o 1302 i43o i55 7 1 684 1811 i 9 38 *9 4i 3907 4o48 4i8 9 433o 447i 4612 18 4i 2o65 2192 23l 9 2446 2 5 7 3 2699 18 4a 4?52 48 9 3 5o34 5175 53i5 5456 17 42 2826 2 9 53 3o8o 3206 3333 346o 17 43 55 97 5 7 3 7 58 7 8 6018 6i58 6299 16 43 3586 3713 383 9 3 9 66 40 9 2 4219 16 44 643 9 65 79 6 7 20 6860 7000 7140 i5 44 4345 447i 45 9 8 4724 485o 4 97 6 i5 45 7280 7420 7 56o 7700 7840 7980 i4 45 5io3 5229 5355 548i 5607 5 7 33 i4 46 8120 8259 83 99 853 9 8678 8818 i3 46 585 9 5 9 85 61 ii 6237 6362 6488 i3 47 8 9 58 9097 9 236 9 3 7 6 9 5i5 9 655 12 47 66i4 6 7 4o 6865 6 99 i 7117 7242 12 48 9794 99 33 ..72 .212 .35i .490 II 48 7 368 7 4 9 3 7619 7744 7870 799 5 II 49 9. 190629 0768 0907 io46 1184 i323 IO 49 8120 8246 83 7 i 84 9 6 8621 8 7 4 7 IO 5o 1462 1 60 1 i 7 3 9 1878 2017 2i55 9 5o 8872 8997 9 I22 9 247 9 3 7 2 9497 9 5i 2294 2432 25 7 I 2709 2848 2986 8 5i 9622 974? 9 8 7 2 999 6 . 121 .246 8 52 3l24 3262 34oi 353 9 36 7 7 38i5 7 52 9.24o3 7 i 0495 062O o 7 45 o86 9 o 99 4 7 53 3 9 53 4091 4229 436 7 45o5 4642 6 53 1118 1243 i36 7 l4 9 2 1616 1741 6 54 4780 4918 5o56 5ig3 533i 5468 5 54 i8f5 1989 2114 2238 2362 2486 5 55 56o6 5 7 43 588i 6018 6i56 6293 4 55 26^0 2 7 34 2858 2 9 82 3io6 323o 4 56 643o 656 7 6705 6842 6979 7116 3 56 3354 3478 36o2 3 7 26 385o 3 97 4 3 57 7253 7 3 9 7 5 . 2 7 7 664 7801 7938 2 57 4097 4221 4345 4468 45 9 2 4?i5 a 58 8o 7 4 8211 8348 8484 8621 8 7 58 I 58 483 9 4962 5o86 52O 9 5333 5456 i 5 9 88 9 4 go3i 9167 9 3o4 9 44o 9 5 7 6 O 5 9 55 79 5703 5826 5 9 4 9 6072 6i 9 6 o 60" 50" 40" 30" 20" 10" a 60" 50" 40" 30" 20" 10" d Co-tangent of 81 Degrees. Co-tangent of 80 Degrees. 1 P P f o4i 3i63 3284 34o5 352 7 5o. 9 4684 79^ . 9 o5 5oi6 5l2 7 238 O 10 3648 3 7 6 9 38 9 o ion 4i32 4253 49 10 5349 546o 55 7 i 568i 5 79 2 9 c3 9 n 43 7 4 4495 46i6 4 7 37 4858 4979 48 n 6oi3 6124 5 2 35 6345 6456 6566 8 12 5 1 oo 5221 534i 5462 5583 5 7 o3 47 12 6677 6787 6898 7008 7 ii 9 722 9 7 i3 5824 5 9 45 6o65 6186 63o6 642 7 46 i3 745o 7 56o 7670 778i 7891 6 i4 654? 6668 6 7 88 6908 7 02 9 7149 45 i4 8001 8111 8221 8332 8442 8552 5 i5 7 26 9 7 38 9 7 5io 7 63o 77 5o 7870 44 i5 8662 8772 8882 899 2 9102 9 2I2 4 16 799 8110 823o 835o 84 7 o 85 9 o 43 16 9322 943 1 9 54i 9 65i 97 6i 9 8 7 I 43 i 7 8710 883o 8950 9069 9 i8 9 9 3o 9 42 17 9980 .90 200 .3o 9 4i 9 52 9 2 18 9429 9 548 9668 9787 997 ..27 ii 18 9.3oo638 0748 o85 7 o 9 6 7 io 7 6 186 I I 9 9.260146 0266 o385 o5o4 0624 o 7 43 4o 1 9 1295 i4o5 i5i4 1624 i 7 33 842 O 20 o863 9 82 IIOI I22O i34o i45 9 3 9 20 1951 2061 2I 7 227 9 2388 24 9 7 9 21 i5 7 8 6 97 1816 1935 2o54 2I ? 3 38 21 2607 2716 2825 2 9 34 3o43 3i5 2 8 22 2292 2411 2 53o 2649 2 7 68 2 88 7 37 22 3261 3370 34 7 9 3588 36 97 38o5 7 23 3oo5 124 3243 336! 348o 35 99 36 23 3 9 i4 4i32 424i 434 9 4458 36 24 3 7 i 7 3836 3 9 54 4o 7 3 4191 43io 35 24 456 7 46 7 5 4 7 84 48 9 3 5ooi 5no 35 25 4428 454 7 4665 4783 4902 5O2O 34 25 52i8 532 7 5435 5544 5652 5 7 6i 34 26 5i38 5 2 56 53 7 5 5493 56ii 5 7 2 9 33 26 586 9 5 977 6086 6i 9 4 63o2 64io 33 27 5847 5 9 65 6o83 6201 6319 643 7 32 2 7 65i 9 6627 6 7 35 6843 6 9 5i 7o5 9 32 28 6555 66 7 3 6 79 o 6908 7026 7 i44 3i 28 7168 7276 7 384 74 9 2 7 6oo 7708 i 2 9 7261 7 3 79 74 9 7 7614 77 32 7 84 9 3o 2 9 7816 7923 8o3i 8i3 9 824-7 8355 lo 3o 7967 8o84 8202 8319 843 7 8554 2 9 3o 8463 8570 86 7 8 8786 88 9 3 9001 29 3i 8671 8 7 8 9 8 9 o6 9023 9140 9 258 28 3i 9109 9216 9 324 9 432 9 53 9 9 64? 28 32 9 3 7 5 9492 9 6o 9 9726 9 843 99 6o 2 7 32 9754 9862 99 6 9 ..76 .184 .2 9 I 27 33 9,2 7 oo 77 0194 o3ii 0428 o545 0662 26 33 9.310399 o5o6 o6i3 0720 0828 o 9 35 26 34 779 o8 9 5 1012 II2 9 1246 i362 25 34 1042 1x49 1256 i364 i4 7 i i5 7 8 25 35 i4 79 i5 9 5 I 7 I2 i82 9 1945 2062 24 35 i685 1792 i8 99 2006 2113 2220 24 36 2I 7 8 2294 2411 2527 2644 2 7 6o 23 36 2327 2433 254o 2647 2 7 54 286l 23 37 28 7 6 2992 3io 9 3225 334i 345 7 22 37 2968 3o 7 4 3i8i 3288 33 9 4 35oi 22 38 35 7 3 368 9 38o5 3 9 2I 4o3 7 4i53 21 38 36o8 3 7 i4 382i 3927 4o34 4i4o 21 3 9 4269 4385 45oi 4617 4 7 33 484 9 2O 3 9 4247 4353 446o 4566 46 7 2 4779 2O 4o 4g64 5o8o 5i 9 6 53i2 542 7 5543 I 9 4o 4885 4991 5o 9 8 52o4 53io 54i6 1 9 4i 5658 5 77 4 58 9 o 6oo5 6121 6236 1 8 4i 55 2 3 5629 5 7 35 584i 5 9 47 6o53 18 42 635i 646 7 6582 66 9 8 68i3 6 9 28 17 42 6i5 9 6 2 65 63 7 i 6477 6583 668 9 17 43 7 o43 7 i5 9 7 2 7 4 7 38 9 7 5o4 7 6i 9 16 43 6 79 5 6901 7 oo 7 7 ii3 7 2l8 7324 16 44 7734 7849 7 964 819^ 83o 9 i5 44 7 43o 7536 7 64i 774 7 7 853 79^8 i5 45 8424 853 9 8654 8 7 6c 8884 8 99 8 i4 45 8o64 8170 82 7 5 838i 8486 85 9 2 i4 46 9 n3 9228 9 342 9 45 7 95-72 9 686 i3 46 86 97 88o3 8 9 o8 9 oi3 9 ii 9 9224 i3 47 9801 99 i5 ..3o i44 . 2 5 9 .3 7 3 12 4 7 9 33o 9 435 9 54o 9 645 97 5i 9 856 12 48 9.280488 0602 7 I 7 o83i o 9 45 io5 9 II 48 9961 ..66 .171 .277 .382 .487 II 49 n 7 4 1288 1402 i5i6 i63o i 7 4^ IO 49 9.320592 0697 0802 o 9 O7 IOI2 1117 10 5o i858 i 97 3 2087 2201 23l/ 2428 g 5o 1222 1326 i43i i536 i64i 1746 9 5i 2542 2656 2770 2884 2 99 8 3iu 8 5i i85i i 9 55 2060 2i65 226 9 23 7 4 8 52 3225 333 9 3453 3566 368o 3 79 3 7 52 24-79 2583 2688 2793 28 97 3oo2 7 53 3 9o 7 4021 4i34 4248 436i 44 7 4 6 53 3io6 3211 33i5 3420 3524 3628 6 54 4588 4 7 oi 48i5 4 9 28 5o4i 5i54 5 54 3 7 33 383 7 3 9 4i 4o46 4i5o 4254 5 55 5268 538i 549^ 56o 7 5 7 2O 5833 4 55 4358 4463 456 7 4671 4 77 5 4879 4 56 5 9 47 6060 617^ 6286 63 99 65i2 3 56 4Q83 5o8 7 5i 9 i 52 9 5 53 99 55o3 3 5? 6624 6 7 3 7 685o 6 9 63 7 o 7 6 7 i8 9 2 57 56o 7 5 7 n 58i5 5 9 i 9 6o23 6127 2 58 7 3oi 7 4iJ 7527 7 63 9 77 5 2 7 865 I 58 623i 6334 6438 6542 6646 6 7 49 I 5 9 7977 8o 9 o 8202 83i5 842 7 854o 5 9 6853 6 9 5 7 7060 7 i64 7267 737 O 60" 50" 40" 30" 20" 10" . 60" 50" 40" 30" 20" 10" d Co-tangent of 79 Degrees. % Co-tangent of 78 Degrees. i P Port 5 l " %" 3 " 4 " 5 " 6 " 7 " 8 " 9 " ( 1" 2" 3" 4" 5" 6" 7" S" 9" irl \ 12 23 35 47 59 70 82 94 106 P.PartJ n 22 32 43 54 65 75 86 97 36 LOGARITHMIC SINES. Jj Sine of 12 Degrees. Sine of 13 Degrees. 53 0" 10" 20" 30" 40" 50" * 0" 10" 20" 30" 40" 50" o 9-3i7879 797 8077:81768275 83 7 4 i> 9 09.352088 2179 22 7 2362 2453 2544 5 9 i 8473 85 7 2 86 7 i 8 7 6 9 8868 8 9 6 7 58 I 2635 2-726 28l ? 2908 2 999 3o 9 o 58 2 9 o66 9i65 9 263 9 362 9 46i 57 2 3i8i 3272 3363 3454 3545 3636 57 J 9 658 97 5 7 9 855 99 54 ..52 9 i5? 56 '. 3 7 26 38i 7 3 9 o8 3 999 4o 9 4i8o 56 L 9 .32024 9 o348 o446 o545 o643 7 42 55 L 42 7 I 4362 4452 4543 4634 4724 55 e o84o o 9 38 io3 7 ii35 1233 i332 54 t 48i5 4 9 o6 4 99 6 5o8 7 5i 77 5 2 68 54 6 i43o i5 2 8 1626 1-724 1822 I 9 2I 53 6 5358 544 9 553 9 563o 5 7 20 58io 53 7 20I 9 2II 7 2215 23i3 2411 25o 9 52 7 5 9 oi 5 99 i 6081 6172 6262 635 2 52 8 26o 7 2 7 o5 28O2 2 9 OO 2 99 8 3o 9 6 5i 8 6443 6533 66 2 3 6 7 i3 68o3 68 9 4 Si 9 3i 9 4 3292 338 9 l348 7 3585 3683 5o 9 6 9 84 7074 716^ 7344 7434 5o 10 9 .3 2 3 7 8o 38 7 8 3 97 54o 7 3 4171 4268 49 10 9 .35 7 524 76i4 774 7794 7 884 7974 4 9 ii 4366 4463 456i 4658 4?56 4853 48 ii 8064 8i54 8243 8333 8423 85i3 48 12 4 9 5o 5o48|5i45 5 2 43 534o 543 7 47 12 86o3 86 9 2 8 7 8 2 88 7 2 8962 9 o5i 47 i: 5534 5632 5-729 5826 5 92 3 6020 46 i3 9 i4i 9 23l 9 320 9 4io 9499 9 58 9 46 i4 6ii 7 62i563i2 64o 9 65o6 66o3 45 ii 9678 97 68 9 858 9947 ..36 .126 45 i5 6 7 oo 6 7 9 7 6894 6 99 i 7 o8 7 7184 44 i5 9 .36o2i5 o3o5 o3 9 4 o484 o5 7 3 0662 44 16 7281 7 3 7 8 7 4 7 5 7 5 7 2 -7668 7765 43 16 7 52 o84i o 9 3o ioi 9 1109 ii 9 8 43 i 7 7862 79 58 8o55 8i5 2 8248 8345 42 17 I28 7 i3 7 6 i465 1 554 1 644 I 7 33 42 18 8442 85388635 8 7 3i 8828 8 9 24 4i 18 1822 i 9 n 2OOO 208 9 2I 7 8 226 7 4i i 9 9 02I 9 II 79 2l3 9 3io 9 4o6 9 502 4o 19 2356 2445 2534 2623 2 7 II 28OO 4o 20 9 .32 9 5 99 9695 9 79 i 9 888 9984 ..80 3 9 20 9 .36288 9 a 97 8 3o6 7 3i56 3244 3333 3 9 21 9 .33oi 7 6 02 7 2 o368 o465 o56i o65 7 38 21 3422 35n 35 99 3688 3777 3865 38 22 o 7 53 0849 945 io4i 1187 1233 3 7 22 3 9 54 4042 4i3i 4220 43o8 43 97 37 23 i32 9 l424 l520 1616 I 7 I2 1808 36 23 4485 45 7 4 4662 4 7 5i 483 9 4 9 2 7 36 24 I 9 o3 I 999 |2o 9 5 2I 9 I 2286 2382 35 24 5oi6 5io4 5i 9 3 5281 536 9 545 7 35 25 24 7 8 25 7 3 2669 2-764 2860 2 9 56 34 25 5546 5634 5 7 22 58io 58 99 5 9 8 7 34 26 3o5i 3i47 3242 333 7 3433 35 2 8 33 26 6o 7 5 6i63 6 2 5i 633 9 642-7 65i6 33 27 3624 3 7 i 9 38i4 3 9 io 4oo5 4ioo 32 27 66o4 66 9 2 6 7 8o 6868 6 9 56 7o44 32 28 4i 9 5 4291 4386 448 1 45 7 6 46 7 i 3i 28 7 i3i 7 2I 9 7 3o 7 7 3 9 5 7483 7 5 7 i 3i 2 9 4 7 6 7 4862 4 9 5 7 5o5 2 5i4 7 5242 3o 29 7 65 9 7747 7834 79 22 8010 8098 3o 3o 9 .33533 7 5432 55 27 5622 5 7 i6 58ii 2 9 3o 9 .368i85 82 7 3 836i 8448 8536 8624 2 9 3i 5 9 o6 6001 6o 9 6 6i 9 i 6 2 85 638o 28 3i 8711 8799 8886 8 97 4 9 o6i 9 i4 9 28 32 6475 65 7 o 6664 6 7 5 9 6854 6 9 48 2 7 32 9 236 9 4n 9 4 99 9 586 9 6 7 3 27 33 ?o43 7 l3 7 7 232 7 3 2 6 7421 7 5i5 26 33 9761 9 848 99 36 ..23 . no .i 97 26 34 7 6io 77 o4 7799 7 8 9 3 7988 8082 25 34 9 .3 7 0285 o3 7 2 o45 9 o546 o634 7 2I 25 35 81-76 82-71 8365 845 9 8553 8648 24 35 0808 o8 9 5 0982 io6 9 ii56 1243 24 36 8 7 42 88368 9 3o 9 024 9 ii8 9 2I2 23 36 i33o 1417 i5o4 i5 9 i 16-78 i 7 65 23 3 7 9 3o 7 9401^495 9 58 9 9 683 9777 22 37 i85 2 i 9 3 9 2026 2113 2200 228-7 22 38 9871 9964 -.58 .246 .34o 21 38 23 7 3 2460 254-7 2634 2 7 2I 28o 7 21 3 9 9. 34o434 05280621 o 7 i5 o8o 9 0903 2O -39 2894 2 9 8i 3o6 7 3i54 324i 332 7 2O 4o 9.340996 1090 1184 I2 7? i3 7 i 1 464 '9 4o 9 .3 7 34i4 35oo 358 7 36 7 4 3 7 6o 384 7 '9 4i i558 1 652 i 7 45 i83 9 I 9 32 2026 18 4i 3 9 33 4O20 4io6 4l 9 2 42 79 4365 18 42 2119 2212 23o6 23 99 24 9 3 2586 '7 42 4452 4538 4624 4 7 n 4797 4883 1 7 43 2 6 79 2 77 2 2866 2 9 5 9 3o52 3i45 16 43 4 97 o 5o56 5i42 5228 53i4 54oi 16 44 323 9 3332 3425 35i8 36ii 3704 i5 44 548 7 55 7 3 565 9 5 7 45 583i 5 9 i 7 i5 45 3 797 38 9 o3 9 83 4o 7 6 4i6 9 4262 i4 45 6oo3 6o8 9 6i 7 5 6261 6347 6433 i4 46 4355 4448454i 4634 4 7 2 7 |4820 i3 46 65i 9 66o5 6691 6777 6863 6 9 4 9 i3 47 4912 5oo5 5o 9 8 5i 9 i 5283l53 7 6 12 47 7 o35 -7120 -7206 7 2 9 2 7 3 7 8 7464 12 48 546 9 6024 556i 5654 61 17)62 10 5 7 4 7 63o2 583 9 |5 9 32 63 9 5648 7 II IO 48 4 9 7 54 9 8o63 7 635 8i4 9 8235 7 8o6 8320 7 8 9 2 84o6 7978 84 9 i II 10 5o 9 .3465 79 66-72 6 7 64 685 7 6 9 4 9 7 o4i 9 5o 9 .3 7 85 77 8662 8 7 48 8833 8919 9 oo4 9 5i 7 i34 -7226 7 3i8 7 4io 7 5o3 7 5 9 5 8 5i 9 o8 9 9 i 7 5 9260 9 346 943i 9 5i6 8 52 7 68 7 77797871 79 63 8o568i48 7 52 9 6oi 9 68 7 9772 9 85 7 9942 ..28 7 53 8240 8332 8424 85i6 8608 8 7 oo 6 53 9 .38oii3 oi 9 8 0283 o368 o454 o53 9 6 54 8 79 2 8884189-76 9 o6 7 9 i5 9 9 25i 5 54 0624 o 7 o 9 0-794 0879 o 9 64 io4 9 5 55 9 343 9 435 9 526 9 6i8 97 io 9 8o2 4 55 1 1 34 I2I 9 i3o4 i38 9 1474 i55 9 4 56 9 8 9 3 99 85 77 .168 .260 .35 2 3 56 i643 1-728 i8i3 i8 9 8 i 9 83 2068 3 57 9.35o443 o535 0626 0-718 o8o 9 0901 2 57 2l52 223 7 2322 2406 24 9 I 25 7 6 2 58 0992 1084 n 7 5 1266 i358i44 9 I 58 266l 2 7 45 283o 2 9 i4 2999 3o84 I 5 9 i54o i632 i 7 23 1814 I 9 o6|i 997 O 5 9 3i68 3253 333 7 3422 35o6 35 9 i 60" 50" ! 40" 30" 20" 10" a 60" 50" 40" 30" 20" 10" d Co-sine of 77 Degrees. 1 Co-sine of 76 Degrees. 1 P Part 5 l " 2 " 3 " 4 " 5 " 6// 7 " 8// 9 " p p (1" 2" 3" 4" 5" 6" 7" 8" 9" I 9 19 28 38 47 57 66 76 85 {9 18 26 35 44 53 61 70 79 LOGARITHMIC TANGENTS. ri Tangent of 12 Degrees. I Tangent of 13 Degrees. 0" 10" 20" 30" 40" 50" m 0" 10" 20" 30" 40" 50" o 9 .32 7 4 7 5 7 5 7 8 7 682 77 85 7 888 799 2 5 9 o 9. 363364 346o 3556 3652 3 7 48 3844 5 9 I 8o 9 5 8i 99 8302 84o5 85o 9 8612 58' i 3 9 4o 4o36 4i3 2 4228 4324 4420 58 2 8 7 i5 8819 8922 9 025 9 I28 9 23l 5 7 2 45i5 46u 4707 48o3 48 99 4 99 4 5 7 3 9 334 9 438 9541 9 644 9747 9 85o 56 3 5o 9 o 5i86 5282 53 77 5473 5568 56 4 99 53 ..56 .i5 9 .262 .365 .468 55 4 5664 5 7 6o 5855 5 9 5i 6o46 6142 55 5 9.330570 o6 7 3 0776 o87 9 9 82 1084 54 5 623 7 6333 6428 6524 66 I9 6 7 i5 54 6 1187 1290 i3 9 3 i4 9 5 i5 9 8 1701 53 6 6810 6 9 o5 7001 70 9 6 7i 9 i 7287 53 7 i8o3 1906 2008 2III 22l3 23i6 52 7 7 38a 7477 7572 7668 7763 7 858 52 8 2418 2521 2623 2726 2828 2 9 3o 5i 8 79 53 8o48 8i43 8 2 3 9 8334 842 9 5i 9 3o33 3i35 323 7 334o 3442 3544 5o 9 8524 8619 8714 88o 9 8 9 o4 8 999 5o 10 9.333646 3 7 48 385i 3 9 53 4o55 4i5 7 49 10 9 .36 9 o 9 4 9 i8 9 9 284 9 3 7 8 9 4 7 3 9 568 49 ii 4259 436i 4463 4565 466 7 476 9 48 ii 9 663 9758 9 853 9947 ..42 .i3 7 48 12 48 7 i 4 97 3 5o 7 5 5i 77 5 279 538o 47 12 9 .3 7 0232 o326 O42I o5i6 0610 o 7 o5 4 7 i3 5482 5584 5686 5 7 88 588 9 5 99 i 46 i3 799 o8 9 4 o 9 8 9 io83 n 7 8 I2 7 2 46 i4 6093 6194 6296 63 9 8 64 99 6601 45 i4 i36 7 i46i i556 i65o 1744 i83 9 45 i5 6702 6804 6905 7 oo 7 7 io8 7210 44 T5 i 9 33 2028 2122 2216 23ll 24o5 44 16 7 3n 74i3 ?5i4 7 6i5 77 I 7 7818 43 16 2499 25 9 3 2688 2 7 82 28 7 6 2 97 43 *7 79 * 9 8021 8122 8223 8324 8426 42 17 3o64 3i5 9 3 2 53 334 7 344i 3535 42 18 852 7 8628 8729 883o 8 9 3i 9 o32 4i 18 362 9 3 ?2 3 38i 7 3 9 n 4oo5 4o 99 4i 9 91 33 9 234 933$ 9 436 9 53 7 9 638 4o J 9 4i 9 3 4287 438i 4475 456 9 4662 4o 20 9 .33 97 3 9 9840 9941 ..42 .i43 .243 3 9 20 9 .3 7 4 7 56 485o 4 9 44 5o38 5i3i 5225 3 9 21 9 .34o344 o445 o546 o646 0747 o848 38 21 53i 9 54i3 55o6 56oo 56 9 4 5 7 8 7 38 22 b 9 48 1049 n5o I25o i35i i45i 37 22 588i 5 97 5 6068 6162 6255 634 9 37 23 i552 i65 2 1753 i853 i 9 54 2o54 36 23 6442 6536 662 9 6723 6816 6 9 io 36 24 2i55 2255 2355 2456 2556 2656 35 24 7 oo3 70 9 6 7 I 9 7283 7 3 7 6 7 4 7 o 35 25 2 7 5 7 2 85 7 2957 3o5 7 3i58 3258 34 25 7 563 7656 7 7 5o 7843 7936 8o2 9 34 26 3358 3458 3558 3658 3 7 58 3858 33 26 8122 8216 83o 9 8402 84 9 5 8588 33 27 3 9 58 4o58 4i58 4258 4358 4458 32 27 8681 8774 8867 8 9 6o 9 o53 9 i46 32 28 4558 4658 4758 4858 4 9 5 7 5o57 3i 28 9 23 9 9 332 9 425 9 5i8 9 6n 97 o4 3i 29 5i5 7 525 7 535 7 5456 5556 5656 3o 29 9797 9 8 9 o 99 83 .. 7 5 .168 .261 3o 3o 9 .345 7 55 5855 5 9 54 6o54 6i54 6253 2 9 3o 9 .38o354 o446 o53 9 o632 O 7 25 0817 2 9 3i 6353 645 2 6552 665i 6751 685o 28 3i 0910 ioo3 io 9 5 1188 1280 1373 28 32 6 9 4 9 7049 7i48 7 248 ?34 7 7446 2 7 32 i466 i558 i65i 1743 i836 I 9 28 27 33 7 545 7645 7744 7 843 7 9 42 8042 26 33 2020 2Il3 22O5 22 9 8 23 9 o 2482 26 34 8i4i 8240 833 9 8438 853 7 8636 25 34 2 5 7 5 2667 2 7 5 9 2852 2 9 44 3o36 25 35 8 7 35 8834 8 9 33 9 o3 2 9 i3i 9 23o 24 35 3l29 3221 33i3 34o5 34 9 7 358 9 24 36 9 32 9 9428 9 52 7 9 626 97 24 9 823 23 36 3682 3 77 4 3866 3 9 58 4o5o 4i42 23 37 99 22 . .21 . I2O .218 .817 .4i6 22 37 4234 4326 44i8 45io 4602 46 9 4 22 38 9 .35o5i4 o6i3 0712 0810 o 9 o 9 1007 21 38 4 7 86 48 7 8 4 97 o 5o62 5i53 5245 21 3 9 1106 I2O4 i3o3 i4oi i5oo i5 9 8 2O 3 9 533 7 542 9 552i 56i2 5704 5 79 6 2O 4o 9 .35i6 97 I 7 95 i8 9 4 I 99 2 2O 9 O 2i8 9 J 9 4o 9 385888 5 979 6o 7 i 6i63 6254 6346 J 9 4i 228 7 2385 2483 2582 2680 2778 18 4i 6438 65 29 6621 6712 68o4 68 9 5 18 42 28 7 6 29 7 4 3o 7 3 3i 7 i 326 9 336 7 17 42 6 9 8 7 7 o 7 8 7 i 7 o 7261 7353 7444 i? 43 3465 3563 36Gi 3 7 5 9 385 7 3 9 55 16 43 7536 7 62 7 77i8 7810 7 9 oi 799 2 16 44 4o53 4i5i 424 9 434 7 4445 4542 i5 44 8o84 8i 7 5 8266 8358 844 9 854o i5 45 464o 4 7 38 4836 4 9 34 5o3i 5l2 9 i4 45 863i 8722 88i4 8 9 o5 8 99 6 9 o8 7 i4 46 522 7 5324 5422 5520 56i 7 5 7 i5 i3 46 9178 9 26 9 9 36o 9 45i 9 542 9 633 i3 47 58i3 5910 6008 6io5 6203 63oo 12 47 9724 9 8i5 99 o6 9997 ..88 .179 12 48 63 9 8 6495 65 9 3 66 9 o 6787 6885 II 48 9.390270 o36i o452 o543 o633 7 24 II 49 6 9 82 779 7177 7274 7 3 7 i 746 9 10 49 o8i5 o 9 o6 997 1087 1178 I26 9 IO 5o 9 .35 7 566 7 663 7760 7 85 7 7954 8o5 2 9 5o 9.391360 i45o i54i i63 2 1722 i8i3 9 5i 8i4 9 8246 8343 844o 853 7 8634 8 5i 1903 i 99 4 2080 2175 2266 2356 8 52 8 7 3i 8828 8 9 25 9 O22 9119 9 2l6 7 52 2447 253 7 2628 2718 2808 2 8 99 7 53 9 3i3 9 4o 9 9 5o6 9 6o3 9700 9797 6 53 2989 3o8o 3i 7 o 3260 335i 344i 6 54 9 8 9 3 999 ..87 .184 .280 .3 77 5 54 353! 3622 3 7 I2 38o2 38 9 2 3 9 83 5 55 9 .36o4 7 4 o5 7 o 0667 o 7 63 0860 o 9 5 7 4 55 4o 7 3 4i63 4253 4343 4433 4523 4 56 io53 n5o 1246 1 343 i43 9 i535 3 56 46i4 4704 4794 4884 4 9 74 5o64 3 57 i632 I 7 28 1825 I 9 2I 2017 2Il4 2 5 7 5i54 5 2 44 5334 5424 55i4 56o4 2 58 22IO 23o6 2 4o3 24 99 2 5 9 5 26 9 I I 58 56 9 4 5 7 83 58 7 3 5 9 63 6o53 6i43 I 5 9 2 7 8 7 2884 2 9 8o 3o 7 6 3172 3268 5 9 6233 6322 64i2 65o2 65 9 2 6681 60" 50" 40" 30'' 20" 10" ^ 60" 50" 40" 30" 20" 10" Co-tangent of 77 Degrees. Co-tangent of 76 Degrees. s p p C 1" 2" 3" 4" 5" 6" 7" 8" 9" . C 1" 2" 3" 4" 5" 6" 7" 8" 9" I 10 20 30 40 50 60 70 80 90 r.rari^ 9 ig 2g 3? 46 f>6 65 74 gg LOGARITHMIC SINES. .3 Sine of 14 Degrees. d Sine of 15 Degrees. 1 0" 10" 20" 30" j 40" 50" 9 0" 10" 20" "30" 40" 50" 9 .3836 7 5 3 7 6o 38443 9 28i4oi3 4o 97 5 9 o 9 .4i2 99 6 3o 7 5 3i53 3232 33io 338 9 5 9 I 4182 4266 435o443545i 9 46o3 58 I 346 7 3546 3624 3 7 o3 3 7 8i 386o 58 2 468 7 477 2 48564 9 4o5o 2 4 5io8 57 2 3 9 38 4oi6 4o 9 5 4i 7 3 4252 433o 5 7 3 4 5l 9 2 56 97 5277 5 7 8i 536i 54455520. 5865 5 9 4 9 '6o33 56i3 6n 7 56 55 3 4 44o8 48 7 8 4486 4 9 56 4565 5o34 4643 5lI2 4 7 2I 5i 9 o 48oo 5 2 6 9 56 55 5 6201 6 2 85 636 9 6452 6536 6620 54 5 534 7 5425 55o3 558i 565 9 5 7 3 7 54 6 6704 6788 6872 6 9 55 7 o3 9 7 I23 53 6 58i5 58 9 3 5 97 i 6o4 9 6l2 7 6205 53 7 7207 72 9 o 7374 7458 7 54i 7 625 52 7 6 2 83 636i 643 9 65i 7 65 9 5 66 7 3 52 8 7709 7792 7876 7 9 5 9 8o43 8l2 7 5i 8 6 7 5i 6828 6 9 o6 6 9 84 7 o62 7 i4o 5i 9 8210 820.4 83778461 8544 862 7 5o 9 7217 7 2 9 5 7 3 7 3 7 45i 7 5 2 8 7 6o6 5o 10 9 . 388711 879488788961 9 o44 9 I28 49 10 9 .4i 7 684 7761 7 83 9 79 i 7 7994 8o 7 2 49 ii 9 2II 9 2 9 4 9 3 7 8 9 46i 9 544 9 62 7 48 1 1 8i5o 8227 83o5 8382 846o 853 7 48 12 97" 9794 98779960 ..43 .126 47 12 86i5 86 9 2 8 77 o 884 7 8 9 25 9 002 4 7 i3 9 .3 9 02IO o2 9 3 o3 7 6 o45 9 o542 0625 46 i3 979 9 i5 7 9 234 9 3l2 9 38 9 9 466 46 i4 0708 O7 9 i 0874 o 9 57 io4o 1123 45 i4 9 544 9 62I 9 6 9 8 977 6 9 853 99 3o 45 i5 1206 I28 9 i3 7 i 1454 i53 7 1620 44 i5 9 .42OOO 7 oo85 0162 023 9 o3i6 o3 9 3 44 16 1703 1786 1868 i 9 5i 2o34 2117 43 16 o4 7 o o548 0625 0702 779 o856 43 *7 2i 99 22822365 244 7 253o 26i3 42 17 o 9 33 IOIO io8 7 n64 1241 i3i8 42 18 26 9 5 2778 2860 2 9 43 3 02 5 3io8 4i 18 i3 9 5 1472 i54 9 1626 I 7 o3 1-780 4i J 9 3i 9 i 32 7 3 3356 3438 35 2 o 36o3 4o ! 9 i85 7 I 9 33 2010 2087 ai64 224l 4o 3O 9 .3 9 3685 3 7 68 385o 3 9 3 2 4oi5 4o 97 3 9 20 9 .4223l8 2 3 9 4 24 7 I 2548 2625 2 7 OI 3 9 21 4179 4262 4344 4426 45o8 45 9 i 38 21 2 77 8 2855 2 9 3i 3oo8 3o85 3i6i 38 22 46 7 3 475548374919 5O02 5o84 37 22 3238 33i5 33 9 i 3468 3544 362i 3 7 23 5i66 5 3 48 533o 54i2 54 9 4 55 7 6 36 23 36 97 3 77 4 385o 3927 4oo3 4o8o 36 24 5658 5740 5822 5 9 o4 5 9 86 6068 35 24 4i56 4233 43o 9 4386 4462 4538 35 25 6i5o 623 2 63i4 63 9 5 64 77 655 9 34 25 46i5 46 9 i 4 7 6 7 4844 4 9 20 4 99 6 34 26 664i 67236805 6886 6 9 68. 7o5o 33 26 5o 7 3 5i49 5225 53oi 53 7 8 5454 33 27 7132 7213 72 9 5 7377 7 458 754o 32 27 553o 56o6 5682 5758 5835 5 9 n 32 28 7621 77 o3 77 85 7866 79 48 8o2 9 3i 28 5 9 8 7 6o63 6i3 9 6ai5 62 9 i 636 7 3i 29 8111 8l 9 2 8274 8355 843 7 85i8 3o 2 9 6443 65i 9 65 9 5 6671 6 7 4 7 6823 3o 3o 9 .3 9 86oo 8681 8762 8844 8 9 25 9 oo7 2 9 3o 9 .4268q 9 6 97 5 7 o5i 7127 7 2O2 7 2 7 8 29 3i 9 o88 9 i6 9 9 25o 9 332 9 4i3 9 4 9 4 28 3i 7 354 7 43o 7 5o6 7 582 7 65 7 7733 28 32 9 5 7 5 9 65 7 9738 9 8i 9 99 oo 99 8i 2 7 32 7 8o 9 7 885 79 6o 8o36 8112 8i8 7 2 7 33 9 . 400062 Ol44 0225 o3o6 o38 7 o468 26 33 '8263 833 9 84i4 8490 8566 864i 26 34 o54 9 06300711 o 79 2 o8 7 3 o 9 54 25 34 8 7 i 7 8 79 2 8868 8 9 44 9 OI 9 9 o 9 5 25 35 io35 1116 n 9 7 1277 i358 i43 9 24 35 9 i 7 o 9 246 9 32I 9 3 97 9 4 7 2 9 547 24 36 l520 1601 1682 1762 i843 I 9 24 23 36 9 623 9 6 9 8 9774 9 84 9 99 24 .... 23 - 3 7 2005 2085 2166 2247 2328 2408 22 37 9 .43oo 7 5 oi5o 0226 o3oi o3 7 6 o45i 22 38 248 9 25 7 o 265o 2731 2811 280,2 21 38 o52 7 0602 o6 77 0752 0828 o 9 o3 21 3 9 2 97 e 3o53 3i33 32i4 32 9 4 33 7 5 20 3 9 o 97 8 io53 1128 1203 I2 7 8 i354 20 4o 9 .4o3455 3536 36i6 36 97 3777 385 7 I 9 4o 9 .43i42 9 i5o4 i5 79 1 654 I 7 2 9 1804 '9 4i 3 9 38 4oi8 4o 9 8 4i 7 9 425 9 433 9 18 4i i8 79 i 9 54 2O2 9 2104 2I 79 2254 18 4s 4420 45oo458o 466o 474i 4821 17 42 232 9 24o3 24 7 8 2553 2628 2 7 o3 17 43 4 9 oi 4981 5o6i 5i4i 5221 5302 16 43 2 77 8 2853 2 9 2 7 3002 3o 77 3i5 2 16 44 5382 5462 5542 5622 5 7 02 5 7 82 i5 44 3226 33oi 33 7 6 345 1 3525 36oo i5 45 .5862 5 9 42 6022 6102 6181 6-261 i4 45 36 7 5 3 7 4 9 3824 38 9 8 3 97 3 4o48 i4 46 634i 6421 65oi 658 1 6661 6 7 4o i3 46 4122- 419-7 42 7 I 4346 4420 44 9 5 i3 4? 48 6820 7 2 99 6 9 oo 6 9 8o 7 3 7 8 7 458 7 o6o 7 538 7 i3 9 7 6i 7 7219 7697 12 II 47 48 456 9 5oi6 4644 5o 9 i 4 7 i8 5i65 4793 523 9 486 7 53x4 4 9 42 5388 12 II ' 49 7777 7 856 7 9 368oi5 8o 9 5 8i 7 4 10 49 5462 553 7 56n 5685 5 7 6o 5834 10 5o 9 . 4o8 2 54 8333 84i3 8492 85 72 865i 9 5o 9 .435 9 o8 5 9 82 6o56 6i3i 62o5 62 79 9 5i 8731 8810 888 9 8 9 6 9 9 o48 9 i2 7 8 5i 6353 642 7 65o2 65 7 6 665o 6 7 24 8 52 0,207 0.286 9 365 9 445 9 524 9 6o3 7 52 6 79 8 68 7 2 6 9 46 7020 7 o 9 4 7168 1- 53 0,682 9762.9841 99 20 9999 ..78 6 53 7242 7 3i6 7 3 9 o 7464 7 538 7612 6 54 9 .4ioi57 O23 7 o3i6 o3 9 5 o4 7 4 o553 5 54 7 686 77 6o 7 834 79 o8 79 Sl 8o55 5 55 o63 2 0711 o 79 o o86 9 O 9 48JIO2 7 4 55 8i2 9 8 2 o3 82 77 835i 8424 84 9 8 4 56 1 1 06 n85 1264 i343 1422 i5oo 3 56 85 7 2 8646 8 7 i 9 8 79 3 886 7 8 9 4i 3 5 7 i5 79 i658 i 7 3 7 1816 i8 9 5 i 97 3 2 57 9 oi4 9 o88 9 l62 9 235 9 3o 9 9 382 2 58 2052 2l3l 2210 2288 236 7 2446 I 58 9 456 9 53o 9 6o3 9 6 77 97 5o 9 824 I 5 9 2524 26o3 2682 2 7 6o 283 9 2 9 l8 O 5 9 9 8 97 997 i ..44 .118 .101 .265 GO" 50" 40" 30" 20" 10" e 60" 50" 40" 30" 20" 10" c Co-sine of 75 Degrees. i Co-sine of 74 Degrees. 5 (I// o" Q' P Pni-t) J ' 4" 5" Q" 7" 8" 9" , ( 1" 2" 3" 4" 5" 6" 7" 8" 9" Ul } 8 16 24 33 41 49 57 65 73 irt } 8 15 23 30 38 46 53 61 68 LOGARITHMIC TANGENTS. a Tangent of 14 Degrees. a Tangent of 15 Degrees. . 0" 10" 20" 30" 40" 50" m 0" 10" 20" 30" 40" 50" o 9,396771 6861 6 9 5o 7040 7 i3o 7 2I 9 5 9 o 9 . 428052 8137 8221 83o5 838 9 84 7 3 69 i 7 3o 9 7 3 99 7 488 7 5 7 8 7 66 7 77 5 7 58 i 8558 8642 8 7 26 8810 88 9 4 8978 58 2 7 846 7936 8025 8n5 8204 8294 5 7 2 9062 9i46 9 23o 9 3i4 9 3 9 8 9482 5 7 3 8383 8472 8562 865i 8 7 4o 883o 56 3 9 566 9 65o 97 34 9 8i8 9902 9986 56 4 8919 9008 9 o 9 8 9 l8 7 9 2 7 6 9 365 55 4 9.430070 oi54 023 7 0321 o4o5 o48 9 55 5 9 455 9544 9 633 97 22 9811 9900 54 5 o5 7 3 0657 o 7 4o 0824 0908 0992 54 6 999 79 .168 .25 7 .346 .435 53 6 1075 iiSg 1243 i326 i4io i494 53 7 9 ,4oo524 o6i3 O 7 O2 o 79 i 0880 0969 52 7 i5 77 1661 1745 1828 1912 i 99 5 52 8 io58 ii4? 1236 i325 i4i3 1502 5i 8 20 79 2162 2246 232 9 24l3 2496 5i 9 1591 1680 i 7 6 9 i85 7 1946 2035 5o 9 258o 2663 2747 283o 2914 2997 5o 10 9.402124 2212 2301 2390 24-78 2 56 7 49 IO 9.433o8o 3i64 3247 333i 34i4 34 9 7 4 9 ii 2656 2 7 44 2833 2922 3oio 3o 99 48 ii 358o 3664 3 7 4 7 383o 3914 3997 48 12 3187 3276 3364 3453 354i 363o 47 12 4o8o 4i63 4246 433o 44i3 4496 47 i3 3 7 i8 38o 7 38 9 5 3983 40 7 2 4i6o 46 i3 45 7 9 4662 4745 4828 4912 4995 46 i4 4249 433 7 4425 45i4 4602 4690 45 U 5o 7 8 5i6i 5 2 44 532 7 54io 5493 45 i5 4778 486 7 4 9 55 5o43 5i3i 5219 44 i5 5^ 7 6 565 9 5 7 42 58 2 5 5907 5 99 o 44 16 53o8 5396 5484 55 7 2 566o 5 7 48 43 16 6o 7 3 6i56 623 9 6322 64o5 6488 43 17 5836 5924 6012 6100 6!88 62 7 6 42 17 65 7 o 6653 6 7 36 68i 9 6901 6 9 84 42 18 6364 6452 654o 6628 6 7 i6 68o4 4i 18 7 o6 7 7i5o 7 232 7 3!5 7 3 9 8 7 48o 4i 19 6892 6980 7 o68 7 i55 7243 7 33i 4o J 9 7 563 7 646 77 28 7811 7894 797 6 4o 20 9.407419 7 5 7 7 5 9 4 7 682 777 7 858 3 9 20 9.438059 8i4i 8224 83o6 838 9 84 7 i 3 9 21 79 45 8o33 8121 8208 8296 8384 38 21 8554 8636 8719 8801 8884 8966 38 22 8471 855 9 8646 8 7 34 8821 8909 37 22 9048 9 i3i 9 2l3 9 2 9 6 9 3 7 8 9 46o 37 23 8996 9084 9171 9259 9 346 9434 36 23 9 543 9625 977 979 9872 9954 36 24 9521 9609 9696 9783 9871 99 58 35 24 9.44oo36 0119 0201 0283 o365 o44 7 35 25 9 .4ioo45 oi33 O22O o3o 7 o3 9 5 0482 34 25 o52g 0612 o6 9 4 o 77 6 o858 0940 34 26 0569 o656 7 43 o83i 0918 ioo5 33 26 IO22 no4 1186 1268 i35o i432 33 27 1092 1179 1266 i353 i44i i5 2 8 32 27 i5i4 i5 9 6 i6 7 8 i 7 6o 1842 1924 32 28 i6i5 1702 1789 i8 7 6 i 9 63 2o5o 3i 28 2006 2088 2I 7 2252 2334 2416 3i 29 2 1 37 2224 23lO 2 3 97 2484 25 7 I 3o 2 9 249-7 2 5 79 266l 2 7 43 2825 2 9 7 3o 3o Q, 4i2658 2 7 45 2832 2 9 I 9 3oo5 3092 2 9 3o 9.442988 3070 3i5 2 3234 33i5 33 97 29 3i 3i79 3266 3352 343 9 3526 36i3 28 3i 34-79 356o 3642 3724 38o5 388 7 28 32 36 99 3 7 86 3873 3 9 5 9 4o46 4i3 2 2 7 32 3968 4o5o 4l32 4213 42 9 5 43 7 6 27 33 4219 43o6 43 9 2 4479 4565 4652 26 33 4458 453 9 4621 4702 4784 4865 26 34 4?38 48 2 5 4911 4 99 8 5o84 5i 7 i 25 34 4947 5o28 5no 5i 9 i 5272 5354 25 35 525 7 5343 543o 55!6 56o3 5689 24 35 5435 55i 7 55 9 8 56 7 9 5761 5842 24 36 5 77 5 5862 5 9 48 6o34 6120 620-7 23 36 5923 6oo5 6086 6167 6248 633o 23 37 6293 63 79 6465 655i 6638 6 7 24 22 37 64n 64 9 2 65 7 3 6654 6735 681-7 22 38 6810 6896 6982 7 o68 7i54 7 240 21 38 6898 6 979 -7060 7141 7222 7 3o3 21 3 9 7326 74i3 7499 7 585 7 6 7 i 77 5 7 2O 3 9 7384 7 465 7 546 7627 7708 7789 20 4o 9.417842 79 28 8014 8100 8186 A 82 7 2 J 9 4o 9.44787 79 5i 8o3 2 8n3 8i 9 4 82 7 5 19 4i 8358 8444 853o 8616 8 7 oi 8 7 8 7 18 4i 8356 843 7 85i8 85 99 8680 8-760 18 42 8873 8 9 5 9 9044 9 i3o 9216 9302 l l 42 884i 8 9 22 9 oo3 9 o84 9 i64 9 245 J 7 43 9 38 7 9 4 7 3 9 55 9 9 644 97 3o 9816 16 43 9326 9 4o 7 9 48 7 9 <42 9608 9 6 7 5 26 3/ 5o44 5n5 5i86 59.56 5327 53q8 25 34 Q7/I 0808 0874 no/ 1 74 25 to to < 0> Ui4 546 9 58 9 3 553 9 5 9 63 56io568i 6o346io4 */ 1 14. 9 .5 9 oi88 v / / 025o vv^v o3i3 o3 7 5 o43 7 0499 43 I? 779 7774 7 83 9 7 9 o3 7968 8o33 42 l? o562 0624 0686 o 7 48 0811 o8 7 3 42 18 8o 9 8 8162 8227 82 9 2 8356 8421 4i 18 o 9 35 0997 1060 1122 1184 1246 4i J 9 8486 855o 86i5 8680 8744 88o 9 4o J 9 i3o8 1370 i433 1495 i55 7 1619 4o 20 9 .5688 7 3 8 9 38 9 oo3 9 o6 7 9132 9 i 97 3 9 20 9 .5 9 i68i 1743 i8o5 1868 igSo 1992 3 9 21 9 26l 9 326 9390 9455 9 5i 9 9 584 38 21 2o54 2116 2178 224O 2302 2364 38 22 9 648 97 i3 9777 9842 9906 997 1 37 22 2426 2488 255o 26l2 2 6 7 4 2 7 3 7 37 23 9 . 570035 OIOO oi64 0229 0293 o358 36 23 2 799 2861 2923 2 9 85 3o4 7 3109 36 24 0422 0487 o55i 0616 0680 o 7 44 35 24 3i 7 i 3232 3294 3356 34i8 348o 35 25 o8o 9 0873 o 9 38 IOO2 1066 n3i 34 25 3542 36o4 3666 3 7 28 3790 3852 34 26 n 9 5 I25 9 1324 i388 1452 i5i7 33 26 3 9 i4 3 97 6 4o38 4o 99 4i6i 4223 33 27 i58i 1 645 1710 1774 i838 I 9 o3 32 27 4285 4347 4409 44 7 i 4532 4594 32 28 1067 2031 2095 2160 2224 2288 3! 28 4656 4718 4780 4842 4903 4965 3i 29 2352 2417 2481 2 545 2609 2673 3o 2 9 5027 5o8 9 5i5o 5212 5274 5336 3o 3o 9 .5 7 2 7 38 2802 2866 2930 2994 3o5 9 2 9 3o 9.595398 545 9 552i 5583 5644 5706 29 3i 3i23 3i8 7 3 2 5i 33i5 33 79 3443 28 3i 5 7 68 583o 58 9 i 5 9 53 6oi5 6076 28 32 35o7 3571 3636 3700 3 7 64 38 2 8 27 32 6i38 6200 6261 6323 6385 6446 27 33 38 9 2 3 9 56 4020 4o84 4i48 4212 26 33 65o8 6570 663i 6693 6 7 54 6816 26 34 4276 434o 44o4 4468 4532 45 9 6 25 34 6878 6 9 3 9 7001 7062 7124 7 i85 25 35 466o 4724 4788 4852 4916 4 9 8o 24 35 7247 7 3o 9 7 3 7 o 7432 7493 7 555 24 36 5o44 5io8 5172 5236 5299 5363 23 36 7616 7678 77 3 9 7801 7862 7924 23 3 7 5427 54 9 i 5555 56i 9 5683 5747 22 37 7985 8047 8108 8170 823i 8293 22 38 58io 58 7 4 5 9 38 6002 6066 6i3o 21 38 8354 84i5 8477 8538 8600 8661 21 3 9 6i 9 3 625 7 632i 6385 6449 65i2 2O 3 9 8722 8784 8845 8907 8968 9029 20 4x> 9 .5 7 65 7 6 664o 6704 6767 683i 68 9 5 1 9 4o 9.599091 9152 9213 9 2 7 5 9 336 9 3 9 8 '9 4.i 6 9 5 9 7022 7086 7 i5o 72i3 7277 18 4i 945 9 9520 9 58i 9 643 974 9765 18 4s 734i 74o4 7 468 7 532 7 5 9 5 7 65 9 17 42 9827 9888 9949 . . ii ..72 .i33 *7 43 77 23 7786 7 85o 79 J 4 7977 8o4i 16 43 9.600194 O256 0317 o3 7 8 0439 o5oo 16 44 8io4 8168 8 2 3i 82 9 5 835 9 8422 i5 44 o562 0623 o684 0745 0806 0868 i5 45 8486 854 9 86i3 8676 8 7 4o 88o3 i4 45 0929 0990 io5i III2 1174 1235 i4 46 8867 8 9 3o 8 99 4 9 o5 7 9 I2I 9 i84 i3 46 1296 i35 7 i4i8 1479 i54o 1601 i3 47 9 248 9 3n 53 7 5 9 438 9 502 9 565 12 47 1663 1724 i 7 85 1 846 1907 i 9 68 12 48 9 62 9 9 6 9 2 97 55 9819 9 882 99 46 II 48 2029 2090 2l5l 2212 2273 2334 II 49 9 .58ooo 9 0072 oi36 0199 0262 o3.26 IO 49 2395 2456 2517 25 7 8 2639 2700 IO 5o 9 .58o38 9 o453 o5i6 o5 79 0642 0706 9 5o 9.602761 2822 2883 2944 3oo5 3o66 9 5i o 7 6 9 o832 o8 9 6 0939 1022 1086 8 5i 3127 3i88 3249 33io 33 7 i 3432 8 52 n4o 1212 I2 7 5 i33 9 I4O2 i465 7 52 34 9 3 3554 36i5 36 7 5 3736 3797 7 53 i528 i5 9 i i655 1718 1781 1 844 6 53 3858 3 9 ! 9 3 9 8o 4o4i 4lO2 4162 6 54 I 9 07 1971 2034 2097 2l6o 2223 5 54 4223 4284 4345 44o6 446 7 452 7 5 55 2286 235o 24i3 2476 253 9 2602 4 55 4588 4649 4?io 4771 483i 48 9 2 4 56 2665 2728 2 79 i 2 854 2 9 I 7 2 9 8o 3 56 4953 5oi4 5o 7 4 5i35 5i 9 6 5257 3 *7 3o44 3107 3i 7 o 3233 32 9 6 335 9 2 57 53i 7 5378 543 9 55oo 556o 562i 2 58 3422 3485 3548 36n 36 7 4 3 7 3 7 I 58 568 2 5 7 42 58o3 5864 5 9 24 5 9 85 I 5 9 38oo 3863 3 9 26 3 9 8 9 4o5 2 4n4 5 9 6o46 6106 6167 6228 6288 634 9 O 60" 50" 40" 30" 20" 10" a 60" 50" | 40" 30" 20" 10" . a Co-tangent of 69 Degrees. S Co-tangent of 68 Degrees. i p p. ( 1" 2" 3" 4" 5" 6" 7" 8" 9" p p < 1" 2" 3" 4" 5" 6" 7" 8" 9" $ 6 13 19 26 32 39 45 51 58 irl j 6 12 19 25 31 37 43 49 56 46 LOGARITHMIC SINES. .a Sine of 22 Degrees. d Sine of 23 Degrees. B 0" 10" 20" 30" 40" 50" jjj 0" 10" 20" 30" 40" 50" o 9 .5 7 35 7 5 36 2 8 368o3 7 323 7 84 3836 5 9 9 .5 9 i878 I 9 28 I 977 202 7 20-76 2126 5 9 I 3888 3 9 4o 3 99 2 4o44 4o 9 6 4i4858 I 2176 2225 22 7 5 2324 2 3 7 4 2423 58 2 4200 4262 43o44356,44o8 446o 57 2 24 7 3 2522 25 7 2 2621 26-71 2720 57 3 45ia 4564 46i646684 7 2o 4 77 2 56 3 2770 28l 9 286 9 2 9 i8 2 9 68 3017 56 4 4824 48 7 6 4 9 28 4 9 8o 5o32 5o84 55 4 3067 3n6 3i65 32i5 3 2 64 33i4 55 5 5i36 5187152395291 5343 53 9 5 54 5 3363 34i2 3462 35n 356i 36io 54 6 544 7 5499 555o56o2 5654 5 7 o6 53 6 365 9 3 7 o 9 3 7 58 38o 7 385 7 3 9 o6 53 7 5 7 58 58io|586i 6913 5 9 65 6oi 7 52 7 3 9 55 4oo5 4o54 4io3 4i53 4202 52 8 6o6 9 6120 6172 6224 6276 632 7 5i 8 4261 43oi 435o 43 99 4448 44 9 8 5i 9 643i 6482 6534 6586 6638 5o 9 4547 45 9 6 4645 46 9 5 4 7 44 4 79 3 5o 10 9 .5 7 668 9 6 7 4i 6 79 3 6844 6896 6 9 48 49 IO 9 .5 9 4842 48 9 i 4 9 4i 4 99 o 5o3 9 5o88 4 9 ii 6999 7061 -7102 7 i54 -7206 7 25 7 48 ii 5i3 7 5i86 5236 5 2 85 5334 5383 48 12 7 3o 9 736074127464 7 5i5 756 7 47 12 5432 548 1 553o 558o 562 9 56 7 8 47 i3 7618 7 6 7 o 77 2i 777 3 7 8 2 4 7 8 7 6 46 i3 6727 5 77 6 58 2 5 58 7 4 5 9 23 5 97 2 46 a 79 2 7 7979 8o3o8o82 8i33 8i85 45 i4 6021 6o 7 o 6ii 9 6168 621-7 6266 45 i5 8236 8288 833 9 83 9 i 8442 84 9 4 44 i5 63i5 6364 64i3 6462 65n 656o 44 16 8545 85 9 6 8648 86 99 8 7 5i 8802 43 16 66o 9 6658 6 7 o 7 6 7 56 68o5 6854 43 ! 7 8853 8 9 o5 8 9 56 9 oo8 9 o5 9 9 T io 4? x? 6 9 o3 6 9 5 2 7 OOI 7 o5o 799 7i48 42 18 9 l62 9 2l3 9 264: 9 3i6 9 36 7 9 4i8 4i 18 7 i 9 6 7 245 7 2 9 4 7 343 7392 744 1 4i i 9 9 4 7 o 9 52I 9 5 7 2 9 623 9675 972 6 4o '9 74 9 o 7 53 9 7 58 7 7 636 7 685 7734 4o 20 21 9- 5 79777 9 .58oo85 9 828 9 88o 99 3i oi36oi8 7 'o238 99 8 2 O28 9 ..33 o34i 39 38 20 21 9 .&o 77 83 8o 7 5 7 83i 8124 -7880 8i 7 3 7929 8222 7978 82-70 802-7 83i 9 39 38 22 o3 9 2 o443 o4 9 4 o545 o5 9 6 o64 7 37 22 8368 84i 7 8465 85i4 8563 8612 37 23 o6 99 o 7 5o 0801 0862 o 9 o3 o 9 54 36 23 8660 8 7 o 9 8 7 58 8806 8855 8 9 o4 36 24 ioo5 1066 110-7 ix58 I2O 9 1261 35 24 8 9 52 9 ooi 9 o5o 9 o 9 8 9 i4 7 9 i 9 5 35 25 l3l2 i363 x4x4 i465 1616 1667 34 25 9 244 9 2 9 3 9 34i 9 3 9 o 9 438 9 48 7 34 26 1618 i66 9 1-720 i 77 i 1822 i8 7 3 33 26 9 536 9 584 9 633 9 68i 97 3o 9778 33 27 I 9 24 i 97 5 2026 2O 7 6 2I2 7 2178 32 27 9 8 2? 9 8 7 6 99 a4 9973 . .21 .. 7 o 32 28 222 9 22802331 2382 2433 2484 3i 28 9 . 600118 016-7 02l5 0264 O3l2 o36i 3i 29 2535 2585 2636 2 68 7 2 7 38 2 7 8 9 3o 2 9 o4o 9 o45 7 0606 o554 o6o3 o65i 3o 3o 9,582840 28 9 O 2 9 4l 2 99 2 3o43 3o 9 4 2 9 3o 9 .6oo 7 oo o 7 48 797 o845 o8 9 3 o 9 42 29 3i 3i45 3i 9 5 3246 32 97 3348 33 9 8 28 3i o 99 o io38 io8 7 n35 n84 1232 28 32 3449 35oo355i 36oi 3652 3 7 o3 27 32 1280 l32 9 i3 77 1426 i4 7 4 12 2 7 33 3754 38o4 3855 3 9 o6 3 9 56 4007 26 33 i5 7 o i6i 9 i66 7 i 7 i5 i 7 63 1812 26 34 35 36 4o58 436i 4665 4io8 4i5 9 '42io 44i2446345i3 4 7 i64 7 66!48i 7 426o43n 456446x5 486749x8 25 24 23 34 35 36 1860 2i5o I 9 o8 2I 9 8 248 7 i 9 5 7 2246 2535 2O05 22 9 4 2583 2o53 2342 2632 2101 23 9 I 2680 26 24 23 37 4968 5oi 9 5o 7 o 5l20 5l 7 IJ522I 22 37 2 7 28 2 77 6 2824 28-72 2 9 2O 2 9 6 9 22 38 6272 5322 53 7 3 5423 54 7 4i55 2 4 21 38 3oi 7 3o65 3n3 3i6i 320 9 3 2 5 7 21 3 9 55 7 4 5625 56 7 5 5 7 26 5 77 6 682-7 2O 39 33o5 3353 34oi 344 9 34 97 3546 2O 4o 9. 5858 77 5 9 2 7 5 97 8 6028 6o 79 6i2 9 1 9 4o 9 .6o35 9 4 3642 36 9 o 3 7 38 3 7 86 3834 I 9 4i 6179 623o 6280 633i 638i 643i 18 4i 3882 3 9 3o 3978 4026 4o 7 4 4l22 18 42 6482 6532658 2 6633 6683.6 7 33 17 42 4i 7 o 4218 4266 43i3 436i 44o 9 17 43 6 7 83 6834 6884 6 9 34 6 9 85 7 o35 16 43 445 7 45o5 4553 46oi 464 9 46 97 16 44 45 7086 7386 7 i35 743 7 718617236 7 48 7 7 53 7 7 286 7 336 7 58 77 63 7 i5 x4 44 45 4 7 45 5o32 4 79 3 5o8o 484i 6128 4888 5i 7 6 4 9 36 5223 4 9 84 52 7 I i5 i4 46 7688 7738 77 88 7 838 78887938 i3 46 53i 9 536 7 54i5 5462 55io 5558 i3 47 7989 8o3 9 8o8 9 8i3 9 8i8 9 823 9 12 47 56o6 5654 5 7 oi 5 7 4 9 5 797 5845 12 48 49 8289 8590 833 9 838 9 864o 86 9 o 843 9 8 7 4o 8489:8540 87968840 II IO 48 49 58 9 2 5 9 4o 6226 5 9 88 62 7 4 6o35 6322 6o836i3i 636 9 |64i7 II IO 5o 9.588890 8 9 4o 8 99 o 9 o4o 9 o 9 o 9 i4o 9 5o 9 .6o6465 65i2 656o 6608 6655 6 7 o3 9 5i 9190 9 24o 9 2 9 O 9 34o 9 38 99 43 9 8 5i 6 7 5i 6798 6846 68 9 3 6 9 4i 6989 8 52 9489 9 53 9 9 58 9 9 63 9 96809730 7 52 7 o36 7084 7 i3i 7179 7227 7 2 7 4 7 53 9789 9 83 99 88 9 ! 99 38 99 88;..38 6 53 7 322 7 36 9 7 4i 7 7464 7612 7 55 9 6 54 9.690088 oi38 ; oi88 023 7 028-7 o33 7 5 54 7 6o 7 7654 77 02 7749 7797 7 844 5 55 o38 7 o43 7 o48 7 o536 o586o636 4 55 7 8 9 2 79 3 9 7987 8o34 8082 8129 4 56 0686 o 7 35 o 7 85 o835 o885 o 9 34 3 56 8177 8224 82 7 I 83i 9 8366 84i4 3 57 0984 io34 io84 n33 H83J233 2 57 846 1 85o8 8556 86o3 865i 8698 a 58 1282 i33 2 i38 2 i43i i48i i53i I 58 8 7 45 8793 884o 888 7 8 9 35 8982 i 5g 1680 i63o 1680 1729 i 779 1828 O 5 9 9 02 9 977 9 I24 9171 9 2I 9 9266 60" 50" 40" 30" 20" 10" . 60" 50" 40" 30" 20" 10" c Co-sine of 67 Degrees. a Co-sine of 66 Degrees. a" PPartJ 1 " 2 " 3/ ' 4" 5" 6" 7" 8" 9" p p ( 1" 2" 3" 4" 5" 6" 7" 8" 9" \ 5 10 15 20 25 31 36 41 46 ff I 5 10 15 19 24 29 34 39 44 LOGARITHMIC TANGENTS. 4-7 1 Tangent of 22 Degrees. J Tangent of 23 Degrees. s 0" 10" 20" | 30" 40" 50" 2 0" 10" 20" 30" 1 40" 50" o 9.606410 6470 653l 6691 6652 6713 5 9 o 9.627852 7910 7969 8028 8086 8:45 5 9 i 6 77 3 6834 68 9 4 69 5 5 7 oi5 7076 58 i 8203 8262 8320 83 79 843 7 8496 58 2 3 4 7 i3 7 7600 7863 7197 7 56o 79 23 7258 7 3i8 7621 76811 79 84 8o44i 7 3 79 77 42 8io5 7439 7802 8i65 ^7 56 55 2 3 4 8554 8905 9 255 8612 8963 93i4 8671 9022 9 3 7 2 8 7 2 9 9080 943 1 8 7 88 9 i38 9 48 9 8846 9i 97 9 54 7 57 56 55 5 8 22 5 8286 8346 84o 7 846 7 85 2 8 54 5 9606 9 664 9722 978i ;83 9 9 8 97 54 6 8588 8648 8709 8 7 6 9 883o 8890 53 6 9956 ..i4 .. 7 3 .i3i i8 9 .247 53 1 SgSo 9011 9071 V 3i 9 I 9 2 9252 52 7 9.63o3o6 o364 0422 o48i o53 9 o5 97 52 8 9312 9 3 7 3 9 433 9 4 9 3 9 554 9614 5i 8 o656 o 7 i4 77 2 o83o o88 9 o 9 47 5i 9 9674 97 35 979 5 9 855 99 i5 9976 5o 9 ioo5 io63 1122 1180 1238 1296 5o 10 9 .6ioo36 0096 oi56 02I 7 02 77 o33 7 49 TO 9 .63i355 i4i3 i4 7 i 1529 !58 7 1640 4y I ii o3 97 o458 o5i8 o5 7 8 o638 0698 48 II 1704 I 7 62 1820 i8 7 8 1936 i 99 5 48 12 7 5 9 0819 o8 79 o 9 3 9 999 1059 47 12 2o53 2III 2169 222 7 2285 2343 4? i3 II2O 1180 1240 i3oo i36o l42O 46 i3 2402 246o 25i8 25 7 6 2634 26 9 2 46 i4 i48o i54o 1601 1661 I 7 2I I 7 8! 45 i4 2750 2808 2866 2924 2982 3o4o 45 i5 i84i 1901 i 9 6i 2O2I 2081 2l4l 44 i5 3o 99 3!5 7 32i5 32 7 3 333i 338 9 44 16 2201 2261 2321 238l 244i 2 5oi 43 16 3447 35o5 3563 362i 36 79 3 7 3 7 43 i? 256l 2621 2681 2 7 4l 2801 2861 42 1 7 3 79 5 3853 3911 3969 4o2 7 4o85 42 18 2921 2981 3o4i 3ioi 3i6i 3221 4i| 18 4i43 4201 425 9 43i6 43 7 4 4432 4i *9 328l 334i 34oi 346i 352i 358i 4o J 9 44 9 o 4548 46o6 4664 4 7 22 4 7 8o 4o 20 9.6i364i 3701 3 7 6o 3820 388o 394oj3 9 20 9 . 634838 4896 4 9 54 Son 5069 5l2 7 3 9 21 4ooo 4o6o 4l20 4i8o 423 9 4299 38 21 5i85 5243 53oi 5359 54:6 5474 38 22 435 9 44i9 44 79 453 9 45 9 8 4658 37 22 5532 55go 5648 5 7 o6 5 7 63 582i 37 23 4718 4778 4838 48 97 4 9 5 7 5017 36 23 58 79 5 9 3 7 5 99 5 6o52 6110 6168 36 24 5077 5i36 5i 9 6 5256 53i6 53 7 5 35 24 6226 6283 634i 63 99 645 7 65i4 35 25 5435 54 9 5 5555 56i4 56 7 4 5 7 34 34 25 65 7 2 663o 6688 6 7 45 68o3 6861 34 26 5 79 3 5853 SgiS 5 97 2 6o32 6092 33 26 6 9 i 9 6976 7 o34 7 o 9 2 7149 7207 33 27 6i5i 6211 62 7 I 633o 63 9 o 645o 32 27 72 65 7322 7 38o 7 438 7495 7 553 32 28 6509 656 9 6628 6688 6 7 48 6807 3i 28 7 6n 7668 77 26 7783 7841 7899 3i 29 6867 6926 6986 7 o46 7 io5 7i65 3o 29 79 56 8oi4 8o 7 2 8129 8187 8244 3o 3o 9 617224 7284 7343 74o3 7 462 7522 29 3o 9 . 638302 8359 84i 7 8475 8532 85 9 o 29 3i 7582 ?64 1 77 oi 77 6o 7 820 7879 28 3i 864 7 8705 8 7 62 8820 8877 8935 28 32 79 3 9 799 8 8o5 7 8n 7 8i 7 6 8236 27 32 8 99 2 9o5o 9 io 7 9 i65 9222 9280 2 7 33 8295 8355 84i4 8474 8533 85 9 3 26 33 9 33 7 9 3 9 5 9 45 2 9 5io 9 56 7 9625 26 34 8652 8711 8771 883o 88 9 o 8949 25 34 9 682 9740 9797 9 855 99 I2 99 6 9 25 35 9008 9 o68 9 I2 7 9 i86 9246 9 3o5 24 35 9 .64oo2 7 oo84 Ol42 oi 99 O25 7 o3i4 24 36 9 364 9 424 9 4S3 9 543 9 6o2 966! 23 36 o3 7 i 0429 o486 o544 0601 o658 23 37 9720 0780 9 83 9 9808 99 58 ..17 22 37 o 7 i6 o 77 3 o83o 0888 o 9 45 1002 22 38 9.620076 oi36 oi 9 5 0254 o3i3 o3 7 3 21 38 1060 1117 n 7 4 1232 1289 1 346 21 3 9 0432 0491 o55o 0610 o66 9 0728 2O 3 9 i4o4 i46i i5i8 i5 7 5 i633 1690 20 4o 9.620787 o846 o 9 o6 o 9 65 1024 io83 1 9 4o 9 .64i 7 47 i8o5 1862 19x9 19-76 2o34 I 9 4i n4a 1201 1261 1320 i3 79 i438 18 4i 2091 2148 22O5 2263 2320 2 3 77 18 42 i4 9 7 i556 1616 i6 7 5 i?34 i 79 3 *7 42 2434 2491 2549 2606 2663 2 7 20 17 43 i852 1911 i 97 o 2029 2088 2147 16 43 2777 2834 2892 2 9 4 9 3oo6 3o63 16 44 2207 2266 2325 2384 2443 25O2 i5 44 3l20 3i77 3235 3292 334 9 34o6 i5 45 256i 2620 26-79 2 7 38 2797 2856 i4 45 3463 3520 35 77 3634 3691 3 7 4 9 i4 46 2915 2974 3o33 3092 3i5i 32IO i3 46 38o6 3863 3920 3977 4o34 4o 9 i i3 47 3269 3328 338 7 3446 35o5 3564 12 47 4i48 42o5 4262 43 1 9 43 7 6 4433 12 48 3623 3682 3 7 4i 38oo 3858 3 9 i 7 II 48 4490 4547 46o4 466i 4718 4 77 5 II 49 3 97 6 4o35 4o 9 4 4i53 4212 4271 IO 49 4832 4889 4946 5oo2 5o6o 5n 7 IO 5o 9.62433o 4388 444 7 45o6 4565 4624 Q 5o 9 .645i 7 4 523i 5 2 88 5345 54o2 545 9 9 5i 4683 4742 48oo 485 9 4918 4977 & 5i 55i6 55 7 3 563o 568 7 5 7 44'58oi 8 62 5o36 5og4 5i53 5212 5271 533o 7 52 585 7 5gi4 5 97' 6028 6o856i42 7 53 5388 5447 55o6 5565 5623 5682 6 53 6199 6 2 56 63i3 636 9 64266483 6 54 574i 58oo 5858 5 9I7 5 97 6 6o35 5 54 654o 65 9 7 6654 6710 6 7 6 7 ; 6824 5 55 6o 9 3 6i5 2 6211 6269 6328 638 7 4 55 6881 6 9 38 6995 7o5i 7 io8; 7 i65 4 56 6445 65o4 6563 6621 6680 6739 3 56 7222 7279 7 335 7 3 9 2 7 449 7 5 6 3 57 6797 6856 6 9 i5 6 97 3 7032 7090 2 57 7 56 2 7619 7 6 7 6 7733 7789*7846 2 58 7149 7208 7266 7 325 7383 7442 I 58 79 o3 7960 8016:807!: 8i3o8i86 I 5 9 75oi 7 55 9 7 6i8 7 6 7 6 7735 779 3 5 9 8243 83oo835684i3 8470:8626 60" 50" 40" 30" 20" 10" . 60" | 50" | 40" | 30" 20" 1 10" . Co-tangent of 67 Degrees. S3 Co-tangent of 66 Degrees. a P P A I" 2" 3" 4" 5" 6" 7" 8" 9" .( 1" 2" 3" 4" 5" 6" 7" 8" 9" trc 6 12, 18 24 30 36 42 48 54 in \ 6 12 17 23 29 35 40 46 52 LOGARITHMIC SINES. FT Sine of 24 Degrees. a Sine of 25 Degrees. 0" 10" 20" | 30" 40" 50" 9 0" 10" 20" 30" 40 V 50" I 9 6o 9 3i3 9 5 97 9 36i 9 644 9691 9 455 97 3 9 9502 9786 9 55o 9 833 59 58 o I 9.625948 6219 5 99 3 62^4 6039 6o84 6129 63o 9 6354i64oo 6i 7 4 6445 5 9 58 2 9 88o 99 28 997 5 ..22 ..69 .116 57 2 6490 6535 658o 6625 6670 6 7 i5 5 7 3 9.610164 O2II 0258 o3o5 o352 o3 99 56 3 6760 68o5 685o 6895 6940 6 9 85 56 4 o44? o4 9 4 o54i o588 o635 0682 55 4 7o3o 7 o 7 5 7120 7165 7210 7255 55 5 6 o 7 2 9 IOI2 0776 io5 9 0823 o8 7 i 1106 u53 0918 1 200 0965 1247 54 53 5 6 73oo 7 5 7 o 7345 76i5 7 3 9 o 7660 7435 77 5 7 48o 77 5o 7 5 2 5 779 5 54 53 8 1294 i5 7 6 i34i i6 2 3 i388 i6 7 o i435 1717 1482 1764 1529 1811 52 5i 7 8 7 84o 8109 7 885 8i54 792979748019 8i 99 ]8a448a8 9 8o64 8333 52 5i 9 i858 I 9 o5 1952 1999 2046 2093 5o 9 83 7 8 8423 8468 85 1 3 8558 8602 5o 10 9.612140 2l8 7 2234 2280 2327 2874 49 10 9.628647 86 9 2 8 7 3 7 8782 8826 88 7 i 49 n 2421 2468 2 5i5 2562 2609 2655 48 n 8916 8961 9 oo6 9o5o 9 o 9 5 9 i4o 48 12 2 7 02 2 7 4 9 2 79 6 2843 2890 2936 47 12 9 1 85 9229 9 2 7 4 9 3i 9 9 363 9 4o8 47 i3 i4 2983 3264 3o3o 33u 3o 77 3358 34o4 3171 3217 345 1 34 9 8 46 45 i3 i4 9 453 97 2I 9498 9766 9810 9 58 7 9 855 9632 9900 9 6 7 6 99 44 46 45 i5 3545 35 9 i 3638 3685 3 7 3a3 77 8 44 i5 9989 ..34 ..78 .123 .168 .212 44 16 3825 38 7 2 3 9 i83 9 65 4oia|4o58 43 16 9.63o25 7 o3oi o346 o3 9 i o435 o48o 43 17 4io5 4i52 41984245 4292 4338 42 17 o524 0569 o6i3 o658 o 7 o3 o 7 4y 42 18 4385 4432 44784525 45 7 i 46i8 4i 18 792 o836 0881 O 9 25 o 97 o 1014 4i 19 4665 4711 4758 48o4 485i 48 9 8 4o J 9 1059 iio3 ii48 II 9 2 I23 7 1281 4o 20 9 .6i4 9 44 4991 5o3 7 5o84 5i3o 5i 7 7 39 20 9 .63i326 1370 i4i5 i45 9 i5o4 1 548 3 9 21 5223 52 7 O 53i6 5363 54o 9 5456 38 21 i5 9 3 i63 7 1681 1726 I 77 i8i5 38 22 55o2 5549 55 9 5 5642 5688 5 7 35 37 22 1859 1904 i 9 48 I 99 2 203 7 2081 3 7 23 5 7 8i 5828 58 7 4 5921 5 9 6 7 6oi3 36 23 . 2125 2170 22l4 225 9 23o3 234 7 36 24! 6060 6106 6i53 6i 99 6245 6292 35 24 2392 2436 2480 2525 2569 26i3 35 25 6338 6385 643i 6477 65 2 4 65 7 o 34 25 2658 2702 2 7 46 2 79 2835 2 8 79 34 26 6616 6663 6 7 o 9 6 7 55 6802 6848 33 26 2923 2968 3012 3o56 3ioo 3i45 33 27 68 9 4 6 9 4i 6 9 8 7 7 o33 7080 7 I26 32 27 3189 3233 3277 3322 3366 34io 32 28 7 I 7 2 7 2l8 7 265 7 3ii 735 7 74o3 3i 28 3454 3498 3543 358 7 363i 36 7 5 3i 29 7 45o 7496 7542 7 588 7 635 7681 3o 29 3 7 i 9 3 7 64 38o8 3852 38 9 6 3 9 4o 3o 3o 9.617727 7773 7819 786617912 7958 29 3o 9 .633 9 84 4028 4o 7 3 4ii 7 4i6i 42o5 2 9 3i 8oo4 8o5o 80968143 8189 8235 28 3i 424 9 4293 433 7 438i 4426 447 28 32 8281 832 7 83 7 3 84i 9 846585i2 27 32 45i4 4558 4602 4646 4690 4734 27 33 34 8558 8834 86o4 8880 865o 86968742 89268972 9018 8788 9064 26 25 33 34 4778 4822 5o86 4866 5i3o 4 9 io 5i 7 4 4954 5 2 i8 4 99 8 5262 26 25 35 91 10 9 i56 9202 9248 9294 9340 24 35 53o6 535o 53 9 4 5438 5482 5526 24 36 9 386 9 43 2 9 4 7 8 9 5 2 4 957 9616 23 36 55 7 o 56i4 5658 5 7 O2 5 7 46 5-790 23 37 9662 97 o8 97 54 9 8oo 9 846 9892 22 37 5834 58 7 7 5 9 2I 5 9 65 6009 6o53 22 38 99 38 99 84 ..3o ..76 . 121 .167 21 38 6o 97 6i4i 6i85 6229 62-72 63i6 21 3 9 9. 6. 02 i 3 025 9 o3o5;o35i o3 97 o443 20 39 636o 64o4 6448 64 9 2 6535 65 7 9 2O 4o 9.620488 o534 o58o 0626 0672 0718 19 4o 9. 636623 6667 6711 6 7 54 6798 6842 19 4i o 7 63 0809 o855 0901 o 9 47 0992 18 4l 6886 6930 6 97 3 7017 7061 7 io5 18 42 io38 1084 n3d 1 17511221 1267 '7 42 7i48 7192 7236 7 28o 7323 7 36 7 7 43 i3i3 1 358 i4o4 i45o i4 9 6 i54i 16 43 7 4n 7455 7498 7 542 7 586 7 62 9 16 44 i58 7 i633 i6 7 8 1724 1770 1816 i5 44 7 6 7 3 7717 7760 7 8o4 7 848 7 8 9 i i5 45 46 1861 2i35 I 9 o 7 2181 i 9 53 i 99 8 2044^2089 2226 2272 23i8 2363 i4 i3 45 46 79 35 8197 7979 8240 8022 8284 8066 8328 8110 83 7 i 8i53 84i5 i4 i3 47 2409 2454 25ooj2546 25 9 i 2 63 7 12 47 8458 85o2 8546 858 9 8633 86 7 6 12 48 3682 2 7 28 2 77 3 28i 9 2865 2910 II 48 8 7 20 8 7 63 8807 885i 88 9 4 8 9 38 II 4 9 2 9 56 3ooi 3o4 7 3o 9 2 3i38 3i83 10 49 8981 9025 9068 9 I 12 9 i55 9*99 10 5o 9.623229 32 7 4 3320 3365 34n 3456 9 5o 9.639242 9286 9 32 9 9 3 7 3 9 4i6 9 46o 9 5i 35o2 354 7 35 9 3 3638 3683 3 7 2 9 8 5i 95o3 9 546 9 5 9 o 9 633 9677 97 20 8 52 3 77 4 3820 3865 3 9 n 3 9 56 4ooi 7 52 9764 9807 9 85i oil 4 99 3 7 99 8i 7 53 4o47 40 9 2 4i38 4i83 4228 4274 6 53 9.640024 0068 on i oi 9 8 024l 6 54 43i9 4364 44io 445545oo 4546 5 54 0284 o328 0371 o4i4 o458 o5oi 5 55 56 45 9 i 4863 4636 4 9 o8 4682 4954 47*274772 4999 5o44 48i8 5o8 9 4 3 55 56 o544 o588 o8o4lo848 o63i o8 9 i o6 7 4o 7 i8 0934:0978 o 7 6i 1 02 I j 5? 5i35 5i8o 5225 5270 53i6 536i 2 57 1064 1 107 i i5i 1 194 i23 7 1280 2 58 54o6 545i 54 9 6 5542 558 7 5632 I 58 i324 i36 7 i4io i453 !4 9 6 i54o I 5 9 56 77 5 7 22 5 7 68 58i3;5858 5 9 o3 O 5 9 i583 1626 1669 1712 i 7 56 1799 o 60" 50" 40" J 30" 20" 10" B 60" 50" 40" 30" 20" i 10" 1 ^ Co-sine of 65 Degrees. Co-sine of 64 Degrees. ^ P T> t f 1" 2" 3" 4" 5" 6" 7" 8" 9" p p ( 1" 2" 3" 4" 5" 6" 7" S" 9" 1 P ' Part { 5 9 14 18 23 28 32 37 42 ij ^4 9 13 18 22 26 31 35 40 LOGARITHMIC TANGENTS. 49 A Tangent of 24 Degrees. A Tangent of 25 Degrees. m 0" 10" 20" 30" 40" 50" m 0" 10" 20" 30" 40" 50" o 9.648583 864o 8696 8 7 53 88lO 8866 5 9 o 9. 6686 7 3 8728 8782 883 7 88 9 2 8 9 47 5 9 1 8923 8 9 8o 9o36 9 o 9 3 9i5o 9 2O6 58 I 9 OO2 9 5 7 9112 9167 9 222 9277 58 2 9263 9 3i 9 9 3 7 6 9 433 948 9 9 546 5 7 2 9 332 9 38 7 9442 9497 9 552 9606 5 7 3 9602 9659 97 i5 9772 9829 9885 56 3 9 66i 9716 9771 9826 9 88l 99 36 56 4 9942 9998 ..55 .in .168 .224 55 4 999 1 ..45 IOO .i55 .210 .265 55 5 9.650281 o33 7 o3 9 4 o45o 0507 o563 54 5 9.670320 o3 7 5 0429 o484 o53 9 o5 9 4 54 6 0620 0676 o 7 33 0789 o846 0902 53 6 o64g 0703 o 7 58 o8i3 0868 0923 53 7 0959 ioi5 IO 7 2 1128 n85 1241 52 7 0977 1032 087 1142 1197 I25l 52 8 1297 i354 l4lO i46 7 i523 1579 5i 8 i3o6 i36i 4i6 1470 i5 2 5 i58o 5! 9 i636 1692 i 7 49 i8o5 1861 1918 5o 9 i635 1689 744 i 799 i853 1908 5o 10 9.65i 9 74 2031 2o8 7 2i43 220O 2256 49 10 9.671963 2018 2072 2127 2182 2236 49 ii a3ifl 236 9 2425 2481 2538 2 5 9 4 48 ii 229*1 2346 2400 2455 25lO 2564 48 12 ^65o 2707 2 7 63 2819 2875 2 9 32 4 7 12 2619 2674 2728 2 7 83 2838 2892 47 1 3 J 9 88 3o44 3ioi 3i57 32i3 326 9 46 i3 2947 3ooi 3o56 3m 3i65 3220 46 i4 3326 3382 3438 3494 355i 3607 45 i4 32 7 4 332 9 3384 3438 34 9 3 3547 45 i5 3663 3 7 i 9 3 77 6 3832 3888 3 9 44 44 i5 36o2 365 7 3 7 n 3 7 66 3820 38 7 5 44 16 4ooo 4o5 7 4n3 4169 4225 4281 43 16 3 9 2 9 3 9 84 4o38 4o 9 3 4i48 4202 43 J 7 4337 4394 445o 45o6 4562 46i8 42 J 7 43n 4366 4420 4475 452 9 [2 18 46 7 4 4 7 3i 4 7 8 7 4843 48 99 4 9 55 4i 18 4584 4638 46 9 3 4 7 4 7 4802 4856 [l I 9 Son 5067 5i23 5i 79 5236 52 9 2 4o i 9 . 4911 4 9 65 5oi 9 5o 7 4 5i28 5i83 io 20 ^.655348 54o4 546o 55i6 5572 5628 39 20 9.675237 5292 5346 54oi 5455 SSog 9 21 5684 5740 5796 5852 5908 5964 38 21 5564 56i8 56 7 3 5 7 2 7 5781 5836 38 22 6020 6076 6i32 6188 6244 63oo 3 7 22 5890 5 9 45 5 999 6o53 6108 6162 3 7 23 6356 64l2 6468 6524 658o 6636 36 23 6217 6271 6325 638o 6434 6488 36 24 6692 6 7 48 68o4 6860 6916 6972 35 24 6543 65 97 665i 6706 6760 68i4 35 25 7028 7084 7140 7196 7252 73o8 34 25 6869 6 9 23 6 977 7032 7086 7140 34 26 7364 7419 7 4 7 5 7 53! 7 58 7 7643 33 26 7194 7249 7 3o3 7 35 7 7412 7 466 33 27 7699 77 55 7811 7867 7922 7978 32 27 7 52O 7 5 7 4 7629 7 683 7737 7791 32 28 8o34 8090 8i46 8202 8a58 83i3 3i 28 7 846 79 79 54 8008 8062 8117 3i 29 8369 8425 848 1 853-7 85 9 2 8648 3o 2 9 8171 8225 82 79 8334 8388 8442 3o 3o 9.658704 8 7 6o 8816 8871 8 9 27 8 9 83 29 3o 9.678496 855o 8604 865 9 8 7 i3 8767 2 9 3i 9 o3 9 9095 9 i5o 9206 9 262 9 3i8 28 3i 8821 88 7 5 8929 8 9 84 9 o38 9092 28 32 9 3 7 3 9429 9 485 9 54o 9 5 9 6 9 652 27 32 9146 9 20O 9 3o8 9 363 9417 2 7 33 0.708 9763 9819 9 8 7 5 99 3o 99 86 26 33- 9471 9 525 9 5 79 9 633 9687 97 4i 26 34 9 . 660042 oo 9 8 oi53 O20 9 0265 0320 25 34 979 5 9849 9904 99 58 . . 12 ..66 25 35 o3 7 6 o43i o48 7 o543 o5 9 8 o654 24 35 9.680120 0174 0228 0282 o336 o3 9 o 24 36 0710 o 7 65 0821 o8 77 9 32 o 9 88 23 36 o444 0498 o55 2 0606 0660 Q 7 i4 23 37 io43 1099 ii55 1210 1266 1321 22 37 0768 0822 o8 7 6 o 9 3o o 9 84 io38 22 38 i3 77 1432 i488 1 544 l5 99 i655 21 38 1092 n46 I2OO 1254 i3o8 i36 2 21 3 9 1710 1766 1821 1877 1932 i 9 88 20 3 9 1416 1470 1524 i5 7 8 i632 1686 20 4o 9 . 662o43 20 99 2' 1 54 2210 2265 2321 I 9 4o 9 .68i 7 4o 1794 i84 7 I 9 OI i 9 55 2O0 9 I 9 4i 2 3 7 6 2432 2487 2543 2598 2654 18 4i 2o63 2117 2I 7 I 2225 2279 2333 1 8 42 27O 9 2765 2820 2876 2931 2 9 87 17 42 238 7 2440 2494 2548 2602 2656 17 43 3o42 3o 97 3i53 3208 3264 33i 9 16 43 2710 2764 28l 7 2871 2925 2979 16 44 33 7 5 343o 3485 354l 35 9 6 365i i5 44 3o33 3o8 7 3i4o 3i 9 4 3248 33o2 i5 45 3 7 o 7 3762 38i8 38 7 3 3928 3 9 84 i4 45 3356 34io 3463 35i 7 3571 36 2 5 i4 46 4o3 9 4o 9 4 4i5o 42o5 4260 43i6 i3 46 3679 3 7 32 3 7 86 384o 38 9 4 3 9 4 7 i3 47 4371 4426 4482 453 7 4592 4648 12 47 4ooi 4o55 4109 4162 4216 42 7 12 48 47o3 4758 48i4 486 9 4 9 24 4979 II 48 4324 43 77 443 1 4485 453 9 45 9 2 II 49 5o35 5o 9 o 5i45 5200 5 2 56 53n 10 49 4646 4700 4753 4807 486i 4 9 i4 10 5o 9 . 665366 542i 54 7 7 5532 5587 5642 9 5o 9.684968 5022 5o 7 5 5 1 29 5i83 5236 9 5i 56 9 8 5 7 53 58o8 5863 5 9 i8 5 97 4 8 5i 5290 5344 53 97 545i 55o5 5558 8 52 6o2 9 6o84 6139 619^ 6240, 63o5 7 52 56i2 5666 5 7 i 9 5 77 3 582 7 588o 7 53 636o 64i5 6470 65 2 5 658o 6636 6 53 5934 5987 6o4i 6o 9 5 6i48 6202 6 54 66 9 i 6 7 46 6801 6856 6 9 n 6966 5 54 6255 63o 9 6363 64i6 6470 6523 5 55 7021 7076 7 l32 7187 7242 7297 4 55 65 77 663o 6684 6 7 3 7 6791 6845 4 56 7352 7407 7 462 7 5i 7 7 5 7 2 7627 3 56 6898 6 9 5 2 7oo5 7059 7112 7166 3 57 7682 7737 7792 7 84 7 79 3 79 58 2 57 7 2I 9 7273 7326 7 38o 7433 748 7 2 58 8oi3 8068 8i23 8178 8233 8288 I 58 y54o 759^ 7647 7701 77 54 7 8o8 I 5 9 8343 83 9 8 8453 85o8 8563 8618 O 5 9 7861 79 i5 7968 8021 8075 8128 60" 50" 40" 30" 1 20" 10" . 60" 50" 40" 30" 20" 10" j Co-tangent of 65 Degrees. a Co-tangent of 64 Degrees. s r !// 2 // 3 // 4 // 5 // 6 // 7 // 8 " 9" ( 1" 2" 3" 4" 5" 6" 7" 8" 9" in { 6 11 17 22 28 33 39 45 50 art { 5 11 16 22 27 33 38 43 49 50 LOGAIIIHMIC SINES. .9 Sine of 26 D -grees. d Sine of 27 Degrees. I 0" 10"p 20"p 1 0" ' 40" J NV' 3 0" 10' H 20" 30" | 40" 50" o 9.641842 i885|i92S 1971 2oi5 ao'8 5 9 O 9 . 667047 7068 7129 7 I 7 I 7 2I2 7253 5 9 I 2101 2144 2187:2230 2273 23 7 58 I 7295 7336 7 3 77 74i8 7 46o 7 5oi 58 2 236o 24o3 2446 2489 2532 25 * 5 7 2 7542 7 58.i 7 6 2 5 7666 7707 7749 57 3 2618 2661 2704 2747 2790 28;' i 56 3 779 7 83i 7 8 7 2 79i3J7 9 55 7996 56 4 2877 2920 2963 j3oo63o49 3oc. 55 4 8o3 7 8o 7 8 8119 8161 8202 8243 55 5 3i35 3l78 3221 3 2 6433o 7 i33!,o 54 5 8284 83 2 5 836 7 84o8 8449 8490 54 6 33 9 3 34363479 35223565 36o 7 53 6 853i 85 7 2 86i3 8655 8696 8 7 3 7 53 7 365o 36933736 3779 3822 3865 52 7 8778 8819 8860 8901 8942 8983 52 8 9 3908 4x65 3 9 5i 3 99 4 42084261 4o374o8o4i23 42 9 4!433 7 i438o 5x 5o 8 9 9025 9271 9066 9312 9i<>7 9 353 9i48 9394 9189 9 435 9230 9476 5i 5o 10 9.644423 4465 45o8 455i ^5 9 4 463 7 49 10 9 .65 9 5i7 9558 9 5 99 9640 9681 9722 4 9 ii 468o 4722 4765 48o8485i 48 9 4 48 II 97 63 9 8o4 9 845 9886 99 2 7 9968 48 12 4 9 36 4979 5O22 5o65 5io8 5i5o 4? 12 9.66ooo 9 oo5o 0091 Ol32 oi 7 3 02l4 47 i3 5i 9 3 52365279 532i 5364 54o 7 46 i3 0255 02 9 6 o33 7 o3 7 8 0419 o46o 46 i4 545o 54925535 55 7 8 5620 5663 45 i4 o5oi o54i o582 0623 o664 0706 45 16 5706 5 7 495 79 i 5834 58 77 5 9 i 9 44 i5 o 7 46 0787 0828 0869 0909 0960 44 16 5962 6oo5 6047 6090 6:33 6i 7 5 43 16 o 99 i 1032 io 7 3 1 1 14 u54 1 195 43 7 6218 6260 63o3 6346 6388 643i 42 l l 1236 1277 i3i8 i35 9 l3 99 i44o 42 18 6474 65i6655 9 6601 6644 6686 4i 18 i48i l522 i563 i6o3 1 644 i685 4i '9 6729 67726814 685 7 6899 6 9 42 4o '9 1-726 1766 i8o 7 1 848 1889 1929 4o 20 9.646984 7027 7069 71 12 7i54 7i 97 3 9 20 9.66i 97 o 201 I 2O52 2092 2i33 2174 3 9 21 7240 7282 7325 7 36 7 7409 7452 38 21 2214 2255 2296 233 7 2 3 77 2418 38 22 7494 75377579 7622 7 664 7707 37 22 2 45 9 2499 254o 2 58i 2621 2662 37 23 7749 7792 7 834 7877 7919 7 9 6i 36 23 2 7 o3 2743 2 7 84 2825 2865 2906 36 24 8oo4 8o46 8089 8i3i 8173 8216 35 24 2946 2987 3o 2 8 3o68 3109 3i49 35 25 8258 83oi 8343 8385 8428 8470 34 25 3190 323i 32 7 I 33i2 3352 33 9 3 34 26 85i2 855585 97 863 9 8682 8724 33 26 3433 34 7 4 35i5 3555 35 9 6 3636 33 27 8766 8809 885i 88 9 3 8936 8978 32 27 36 77 3 7 i 7 3 7 58 3 79 8 383 9 38 79 32 28 9020 9063 9105 9147 9189 9232 3i 28 3920 3960 4ooi 4o4i 4082 4l22 3i 29 9274 93169358 94oi 9443 9 485 3o 29 4i63 4203 4244 4284 4325 4365 3o 3o 3i 9.649527 9781 9570 9612 98239865 9 654 9907 9 6 9 6 97 3 9 9949999 2 29 28 3o 3i 9.6644o6 4648 4446 4689 4486 4 7 2 9 452 7 4769 456 7 48io 46o8 485o 2 9 28 32 9.65oo34 0076 01 18 0160 0202 O245. 27 32 4891 493i 4g 7 i 5012 5o5 2 5o 9 3 27 33 0287 0329 0371 o4i3 o455 o4 9 7 26 33 5i33 5i 7 3 5 2 i4 5 2 54 5 29 4 5335 26 34 o53 9 o582 0624 0666 0708 0750 25 34 53 7 5 54i5 5456 5496 5536 55 77 25 35 0792 o834 0876 0918 0960 1 002 24 35 56i 7 565 7 56 97 5 7 38 5 77 8 58x8 24 36 io44 1086 1128 1171 I2l3 1255 23 36 5859 58 99 5 9 3 9 5 979 6020 6060 23 3? 1297 1339 i38i i423 i465 i5o7 22 37 6100 6i4o 6181 6221 6261 63oi 22 38 1 549 i5 9 i i633 i6 7 5 1716 1758 21 38 6342 6382 6422 6462 65o2 6543 21 3 9 1800 1842 1884 1926 1968 20IO 20 3 9 6583 6623 6663 6 7 o3 6 7 43 6 7 84 2O 4o 9.652o52 2094 2 1 36 2178 2220 2262 J 9 4o 9.666824 6864 6904 6 9 44 6 9 84 7 025 '9 4i a3o4 2345 2387 2429 2471 25i3 18 4i 7 o65 7 io5 7i45 7 i85 7225 72 65 18 42 2555 25972638 2680 2722 2764 17 42 7 3o5 7 346 7 386 7426 7 466 7 5o6 17 43 2806 2848 2890 2931 2973 3oi5 16 43 7546 7 586 7 626 7666 7706 77 46 16 44 3o5 7 3099 3 1 4o 3i8 2 32243266 16 44 7786 7826 7 866 7906 7946 79 86 i5 45 33o8 33493391 3433 347535i6 i4 45 8027 8067 5io 7 8r4 7 8i8 7 822 7 i4 46 3558 36oo 3642 3683 37253767 i3 46 8267 83o 7 834 7 8386 8426 8466 i3 47 38o8 385o38 9 2 3 9 34 3976 4017 12 47 85o6 8546 8586 8626 8666 8 7 o6 12 48 4059 4ioo 4*42 4i84 42254267 I I 48 8 7 46 8786 8826 8866 8906 8 9 46 II 49 43o 9 435o;43 9 2 4434 44 7 545i 7 IO 49 8986 9026 9 o65 9io5 9i45 9 i85 IO 5o 9.654558 46oo 4642 4683 4 7 254 7 66 9 5o 9.669225 9 265 9 3o5 9 345 9 384 9 424 9 5i 48o8 48504891 4933 4974 5oi6 8 5i 9464 9 5o4 9 544 9 584 9624 9 663 8 52 5o58 6099 5i4i 5i8 2 52245265 7 52 97 o3 9743 9783 9823 9862 99 02 7 53 53o 7 534853 9 o 543 1 547355i4 6 53 99 42 9982 . .22 ..61 .101 .i4i 6 54 5556 55 97 563 9 568o 5722 5763 5 54 9 . 670181 022O 0260 o3oo o34o o3 79 5 55 58o5 58465888 5 9 2 9 5971 6012 4 55 o4i 9 o45 9 0499 o538 o5 7 8 0618 4 56 6o54 6096 6i36 6178 6219 6261 3 56 o658 0697 o 7 3 7 0777 0816 o856 3 57 63o2 63446385 6426 6468 65o 9 2 57 o8 9 6 o 9 35 o 97 5 ioi5 io54 io 9 4 2 58 655i 65 9 26633 66 7 5 67166757 I 58 n34 n 7 3 I2l3 1253 1292 i332 I 5 9 6799 684o!688i 6923 6964 7005 O 5 9 1372 i4 1 1 i45i 1490 i53o 1670 60" 40" | 30" 20" j 10" a 60" 50" 40" 30" 20" 10" a Co-sine of 63 Degrees. i Co-sine of 62 Degrees. 1 P Part 5 !" 2// 3// 4// 5 " 6 " 7" 8' 9" p p .(!" 2" 3" 4" 5" 6" 7" 8" 9" I 4 8 13 17 21 25 30 34 38 {T I 4 8 12 16 20 24 28 32 36 LJGARITHMIC TANGENTS. .3 Tangent of 26 Degrees. Tangent of 27 Degrees. SI 0" 10" 20" 30" 40" 50" S 0" 10" 20" 30" 40" 50" o 9.688182 8235 828 9 8342 83 9 5 8449 5 9 o 9.707166 -7218 7 2 7 7322 7374 7426 69 i 85o2 8556 86o 9 8663 8 7 i6 8 7 6 9 58 I 7478 7 53o 7 582 7634 7686 77 38 58 2 8823 8876 8 9 3o 8 9 83 9 o36 9 o 9 o 57 2 779 7 842 7 8 9 4 79-46 799 8 8o5o 5 7 3 9i43 9196 9 25o 9 3o3 9 356 9 4io 56 3 8102 8i54 8206 8 2 58 83io 8362 56 4 9 463 9 5 7 9 623 9676 97 3o 55 4 84i4 8466 85i8 85 7 o 8622 86 7 4 55 5 9783 9 836 9890 99 43 999 6 ..5o 54 5 8726 8778 883o 8882 8 9 34 8 9 85 54 6 9.690103 oi56 02IO 0263 o3i6 o36 9 53 6 9 o3 7 9089 9 i4i 9 ! 9 3 9 245 9297 53 7 o423 0476 0529 o582 o636 0689 52 7 9 34 9 9401 9 453 9 5o4 9 556 9608 52 8 7 42 o 79 5 0849 9 02 o 9 55 1008 5i 8 9 66o 9712 97 64 9 8i6 9 868 9919 5i 9 IO62 iu5 1168 1221 1274 i3 2 8 5o 9 997 i ..23 .. 7 5 .127 .179 .231 5o 10 9.6 9 i38i i434 i48 7 i54o i5 9 4 i64 7 49 10 9 . -710282 o334 o386 o438 0490 o542 49 ii I 7 00 1753 1806 i85 9 I 9 i3 1966 48 II o5 9 3 o645 o6 97 o 7 4 9 0801 o852 48 12 2019 2072 2125 2178 2232 2285 47 12 o 9 o4 0956 1008 io5 9 mi n63 47 i3 2338 23 9 I 2444 24 9 7 2 55o 2 6o3 46 i3 I2l5 1267 i3i8 i3 7 o l422 i474 46 i4 2656 2710 2 7 63 2816 2860. 2922 45 i4 i5 2 5 i5 77 i62 9 1681 1732 1784 45 i5 2 97 5 3028 3o8i 3i34 3i8 7 324o 44 i5 i836 1887 i 9 3 9 1991 2043 2094 44 16 32 9 3 3346 34oo 3453 35o6 3559 43 16 2 1 46 2198 224 9 2301 2353 24o5 43 J 7 36i2 3665 3 7 i8 3 77 i 3824 38 77 42 17 2456 2608 2 56o 2611 2663 2 7 l5 42 18 3 9 3o 3 9 83 4o36 4o8 9 4i42 4i95 4i 18 2-766 2818 28 7 2921 2973 3o25 4i i 9 4248 43oi 4354 4407 446o 45i3 4o '9 3o 7 6 3i28 3i 79 323i 3283 3334 4o 20 9.694566 46i 9 46 7 2 4724 4777 483o 3 9 20 9 . 7 i3386 3438 348 9 354i 35 9 2 3644 39 21 4883 4936 4989 5o42 5o 9 5 5i48 38 21 36 9 6 3 7 4 7 3 799 385o 3 9 02 3 9 54 38 22 5201 5 2 54 536o 54i2 5465 37 22 4oo5 4o5 7 4io8 4i6o 4211 4263 37 23 55i8 55 7 i 5624 5677 5 7 3o 5 7 83 36 23 43i4 4366 44i8 446 9 452i 45 7 2 36 24 5836 5888 5g4i 5 99 4 6o4 7 6100 35 24 4624 46 7 5 4 7 2 7 4 77 8 483o 488 1 35 25 6i53 6206 6258 63n 6364 6417 34 25 4 9 33 4984 5o36 5o8 7 5i3 9 5i 9 o 34 26 64 7 o 6522 65 7 5 6628 6681 6 7 34 33 26 5242 5293 5345 53 9 6 5448 54 99 33 27 6787 6839 68 9 2 6 9 45 6 99 8 7o5o 32 27 555i 56o2 5654 5 7 o5 5 7 5 7 58o8 32 28 7 io3 7 i56 7 20 9 7262 7 3i4 7 36 7 3i 28 586o 5911 5 9 62 6oi4 6o65 6117 3i 29 7 420 7 4 7 3 7 5 2 5 7 5 7 8 7 63i 7 684 3o 2 9 6168 6220 62-71 6322 63 7 4 6425 3o 3o 9 .6 977 36 7789 7 842 7 8 9 4 7947 8000 29 3o 9 . 7 i64 77 6528 65 79 663i 6682 6 7 34 2 9 3i 8o53 8io5 8i58 8211 8263 83i6 28 3i 6 7 85 6836 6888 6 9 3 9 6991 7 o42 28 32 836 9 8421 84 7 4 8627 85 79 8632 2 7 32 . 7093 7i45 7 i 9 6 7247 7299 7 35o 2 7 33 8685 8737 8 79 o 8843 8895 8 9 48 26 33 7 4oi 7 453 7 5o4 7 555 7 6o 7 7 658 26 34 9 ooi 9o53 9 io6 9 l5 9 9211 9264 25 34 779 77 6i -7812 7 863 79 i5 79 66 25 35 9 3i6 9 36 9 9 422 9 4 7 4 9 52 7 95-79 24 35 80 1 7 8069 8120 8171 8223 82 7 4 24 36 9 632 9685 97 3 7 979 9 842 9895 23 36 83 2 5 83 7 6 8428 8479 853o 858i 23 3? __ /_ 53 9 f . IOD !i58 .210 22 37 8633 8684 8 7 35 8786 8838 888 9 22 ** / 38 9 . -700263 o3i5 o368 0420 o4 7 3 o5 2 5 21 / 38 8 9 4o 8991 w / 9 o43 / 9094 9i45 r 9196 21 39 o5 7 8 o63o o683 o 7 36 o 7 88 0841 20 3 9 02.4.0 9 2 99 9 35o 9 45 2 9 5o4 20 4o 9 . 7 oo8 9 3 o 9 46 0998 io5i no3 n55 I 9 4o 9.719555 9 6o6 9 65 7 97 o8 9 7 6o 9811 19 4i 1208 1260 i3i3 i365 i4i8 i4 7 o 18 4i 9 862 99 i3 9964 ..16 ..67 .118 18 42 i5 2 3 i5 7 5 1628 1680 i 7 33 i 7 85 7 42 9 . 720160, 022O O2 7 I O322 o3 7 4 o425 17 43 i83 7 i8 9 o 1942 i 99 5 204 7 2IOO 16 43 0476 0527 o5 7 8 0629 0680 7 32 16 44 2l52 22O4 225 7 23o 9 2362 24i4 i5 44 o 7 83 o834 o885 0936 o 9 8 7 io38 i5 45 2466 25l 9 25 7 I 2623 26-76 2-728 i4 45 io8 9 n4o 1191 1243 1294 i345 i4 46 2 7 8l 2833 2885 2 9 38 2 99 3o42 i3 46 i3 9 6 i447 1498 I 549 1600 i65i i3 47 3o 9 5 3i4 7 3i 99 3252 33o4 3356 12 47 i -702 I7 53 i8o4 i855 1906 i 9 5 7 12 48 34o 9 346i 35i3 3566 36i8 36 7 o I I 48 200 9 2060 2III 2162 22l3 2264 II 49 3722 3 77 5 382 7 3879 3 9 32 3 9 84 IO 49 23 1 5 2366 24l7 2468 2519 25 7 10 5o 9 .7o4o36 4o88 4i4i 4i93 4245 4297 9 5o 9. -722621 26-72 2723 2 77 4 2825 28 7 6 9 5i 435o 4402 4454 45o6 455 9 46n 8 5i 292 7 2 97 8 3o2 9 3o8o 3i3o 3i8i 8 52 4663 4 7 i5 4 7 68 4820 48 7 2 4924 7 52 3232 3283 3334 3385 3436 348 7 7 53 4 97 6 5o2 9 5o8i 5i33 5i85 523 7 6 53 3538 358 9 364o 3691 3 7 42 3 79 3 6 54 52 9 o 5342 53 9 4 5446 54 9 8 555i 5 54 3844 38 9 5 3 9 45 3 99 6 4o4 7 4o 9 8 5 55 56o3 5655 5707 5 7 5 9 58n 5863 4 55 4i49 4200 425i 4302 4353 44o3 4 56 5 9 i6 5 9 68 6020 6o 7 2 6124 6176 3 56 4454 45o5 4556 46o 7 4658 4 7 Q9 3 57 6228 6280 6333 6385 643 7 6489 2 5 7 4 7 6o 48io 486i 4 9 I2 4963 5oi4 2 58 654i 65 9 3 6645 66 97 6 7 49 6801 I 58 5o65 5u5 5i66 52i 7 5268 53i 9 I 5 9 6854 6 9 o6 6 9 58 -7010 -7062 7114 O 5 9 53 7 o 5420 547i 5522 5573J5624 O 60" 50" 40" 30" 20" 10" . 60" 50" 40" 30" 20" 10" ^ Co-tangent of 63 Degrees. S Co-tangent of 62 Degrees. s p p A I" 2" 3" 4" 5" 6" 7" 8" 9" ( V 2" 3" 4" 5" 6" 7" 8" 9" I 5 11 16 21 26 32 37 42 47 ar > 5 10 15 21 26 31 36 41 46 52 LOGARITHMIC SINES. d Sine of 28 Degrees. g Sine of 29 Degrees. s 0" 10" 20" 30" 40" 50" 9 0" 10" 20" 30" l 40" 50" 9.671609 1649 1688 I 7 28 i 7 68 i8o 7 5 9 o 9 .6855 7 i 56o 9 5647 5685 5 7 23 5 7 6i 5 9 I i847 1886 1926 i 9 65 2005 2o45 58 I 5 799 5837 5875 5 9 i3 5 9 5i 5 9 8 9 58 2 2084 2124 2i63 2203 2242 2282 5 7 2 6o2 7 6o65 6io36i4i 6i 7 8 6216 57 3 2321 236i 2400 2440 24 7 9 2519 56 3 6254 6292 633o ! 6368 64o6 6444 56 4 2558 2598 2637 26 77 2 7 l6 2 7 56 55 4 6482 6519 655 7 65 9 5 6633 66 7 i 55: 5 2795 2835 2874 2914 2 9 53 2992 54 5 6 7 o 9 6 7 4 7 6 7 85 6822 6860 68 9 8 54 ; 6 3o32 3071 3m 3i5o 3190 322953 6 6 9 36 6 97 4 7 OI2 7 o4 9 7 o8 7 7 I25 53 7 3268 33o8 334? 338 7 3426 3465 52 7 7 i63 7201 7 238 7276 7 3i4 7 352 52 8 35o5 3544 3583 3623 3662 3 7 02 5i 8 7 38 9 7427 7 465 75o3 7 54i 7 5 7 8 5ii 9 3 7 4i 3780 38203859 38 9 83 9 38 5o 9 7616 7654 7 6 9 2 7729 77 6 7 7 8o5 5o 10 9.673977 4oi6 4o56 4095 4i34'4i 7 3 49 10 9 . 687843 7880 79 i8 79 56 7993 8o3i 49 ii 42l3 4252 4291 433i 43 7 o'44o 9 48 ii 8o6 9 8106 8i44 8182 8220 825 7 48 12 4448 4488 45274566 46o64645 47 12 82 9 5 8333 83 7 o 84o8 8446 8483 47 i3 4684 4723 4762:4802 484i 488o 46 i3 852i 855 9 85 9 6 8634 86 7 i 8 7 o 9 46 i4 4919 4959 4998:5037 5o 7 6 5n5 45 i4 8 7 47 8 7 84 8822 8860 88 97 8 9 35 45 i5 5i55 5i94 52335272 53n 535o 44 i5 8 97 2 9010 9 o48 9 o85 9 I23 9 i6o 44 16 5390 5429 5468 55o 7 5546 5585 43 16 9 i 9 8 9235 9 2 73 9 3n 9 348 9 386 43 J 7 5624 5664 5 7 o35 7 42 5 7 8i 5820 42 *7 9 423 9461 9498 9 536 9 5 7 3 9 6n 42 18 585 9 58 9 8 5 9 3 7 5 97 6 6016 6o55 4i 18 9 648 9686 9723 97 6i 979 8 9 836 4i 19 20 60946133 9 .6 7 63 2 8636 7 6172 621 1 64o66445 625o 6289 64846523 4o 3 9 *9 20 9 8 7 3 9.600098 9911 oi36 9948 0173 9986 02 I I ..23 0248 ..61 0286 4o 3 9 21 656266oi 664o 6679 6 7 i86 7 5 7 38 21 'o323 o36i o3 9 8 o435 o4 7 3 o5io 38 22 6 79 66835 68746913 6952 6991 37 22 o548 o585 0622 0660 o6 97 o 7 35 37 23 7o3o 7069 71087147 7 i86 7 225 36 23 0772 0809 0847 o884 9 22 o 9 5 9 36 24 7264 73o3 7342 7381 7420 -7459 35 24 0996 io34 1071 no8 n46 n83 35 25 7498 7 536 7 5 7 5 7 6i4 7 653 7 6 9 2 34 25 1220 1258 I2 9 5 i33 2 i3 7 o i4o 7 34 26 773i 777 78097848 7 886 792 5 33 26 1 444 1482 i5i 9 i556 i5 9 4 i63i 33 27 79 6 4 8oo3 80428081 8i2o8i58 32 2 7 1668 1706 1743 i 7 8o i8i 7 i855 32 28 8197 8236 8 27 5^83i4 8353 83 9 i 3i 28 1892 1929 i 9 66 2004 2041 20 7 8 3i 29 843o 846 9 85o8854 7 85858624 3o 2 9 2Il5 2i53 2I 9 O 222 7 2264 2302 3o 3o 3i 9.678663 88 9 5 8702 8 9 34 87408779 8973 9012 88i8|885 7 goSo 9089 2 9 28 3o 3i 9.692339 i562 23 7 6 2 5 99 24i3 2636 245o 2 6 7 4 2488 2 7 II 2525 2 7 48 2 9 28 32 9128 9167 9205 9244 9 283 9 32I 2 7 32 2 7 85 2822 285 9 2 8 97 2 9 34 2 97 I 2 7 33 9360 9 3 99 94389476 95i5 9 554 26 03 3oo8 3o45 3o82 3119 3i5 7 3i 9 4 26 34 9692 963i 9670 9708 9747 97 86 25 34 323i 3268 33o5 3342 33 79 34i6 25 35 9824 9863 99029940 9979 ..17 24 35 3453 3490 35 2 8 3565 36o2 363 9 24 369.68oo56 0095 oi33 0172 0210 0249 23 36 3676 3 7 i3 3 7 5o 3787 3824 386i 23 3? 0288 o326 o365 o4o3 0442 o48i 22 37 38 9 8- 3 9 35 3972 4009 4o46 4o83 22 38 o5ig o558 o5 9 6orns 06730712 21 38 4l2O 4i5 7 4194 423i 4268 43o5 I Sg 1 o 7 5o 0789 0828 0866 0905 0943 2O 39 4342 43 79 44i6 4453 44 9 o452 7 2O 409.680982 IO2O io5 9 1097 u36 n 7 4 '9 4o 9 .6 9 4564 46oi 4638 46 7 5 4 7 . 2 4 7 4 9 '9 4i I2i3 I25l 1290 i328 i366 i4o5 18 4i 4786 4823 486o 4897 4934497> i a 42 i443 1482 l520 iSSg i59 7 i636 17 42 5007 5o44 5o8i 5n8 5i55'5i 9 2 17 431 1674 I 7 i3 1751 1789 1828 1866 16 43 522 9 5266 53o3 5339 53 7 6 54i3 16 44 1905 1943 1981 2O2O 2o58 20 97 i5 44 545o 548 7 5.524 556i 55 9 8 5634 i5 45 2i35 2173 2212 225o 2288 232 7 i4 45 56 7 i 5 7 o8 5 7 45 5 7 8258i9 5855 i4 46 2365 24o3 2442 2480 2519 255 7 i3 46 58 9 2 5 9 2 9 5 9 66 6oo3 6039 6o 7 6 i3 4 7 2595 2633 2672 2710 2748 2 7 8 7 12 47 6n3 6i5o 6187 6223 6260 62 97 12 48: 2825 2863 2902 2940 2978 3oi6 II 48 6334 6370 6407 6444i648i 65i 7 II 49 3o55 3o 9 3 3i3i 3170 3208 3246 IO 49 6554 65 9 i 6628 6664'6 7 oi 6 7 38 10 509.683284 3323 336i 33 99 343 7 34 7 5 9 5o 9 .6 9 6 77 5 6811 6848 6885 6 9 2I 6 9 58 9 5i 35i4 3552 3590 3628 366 7 3 7 o5 8 5i 6 99 5 7o3i 7068 7 io5 7 i4i 7178 8 52! 3y43 3 7 8i 38i 9 3858 38 9 6 3 9 34 7 52 7 2l5 725i 7288 7 3 2 5 7 36i 7398 7 53i 3972 4oio 4o48 40874125 4i63 6 53 7435 7471 7 5o8 7 545 7 58i 7 6i8 6 54 4201 4239 4277 43i54353 43 9 2 5 54 7 654 7 6 9 i 7728 77 64 7 8oi 7 838 5 55j 443o 4468 45o6 45444582 4620 4 55 7 8 7 4 79 n 7947 7 9 84 8020 8o5 7 4 56 4658 46 9 6 4 7 35 477348ii 4849 3 56 8o 9 4 8i3o 8167 82038240 82 7 6 3 5 7 4887 4925 4963 5ooi|5o39 5o 77 2 57 83i3 834 9 8386 8423 845 9 84 9 6 2 58 5n5 5i53 5191 5229^267 53o5 I 58 8532 856 9 86o5 8642 86 7 8 8 7 i5 I 5 9 5343 538i 54i9 545 7 5495 5533 5 9 8 7 5i 8788 8824 886i|88 97 8 9 34 60" 50" 40" 30" 20" 10" c 60" 50" 40" 30" 20" 10" a Co-sine of 6 1 Degrees. Co-sine of 60 Degrees. i t < \" 2" 3" 4" 5" 6" 7" 8" 9" in \ 4 8 12 16 19 23 27 31 35 p p . < 1" 2" 3" 4" 5" 6" 7" 8" 9" irt } 4 7 11 15 19 22 26 30 33 LOGARITHMIC TANGENTS. 53 1 Tangent of 28 Degrees. c Tangent of 29 Degrees. s 0" 10" 20" 30" 40" 50" 9 0" 10" 20" 30" 40" 50" o 9.725674 5 72 5 5 77 6 5827 58 7 8 5 9 28 5 9 9 . 7 43 7 52 3802 385i 3 9 oi 3 9 5i 4ooo 5 9 I 5 979 6o3o 6081 6i3i 6182 6233 58 I 4o5o 4o 99 4i4 9 4i 99 4248 42 9 8 58 2 6284 6334 6385 6436 648 7 653 7 5 7 2 4348 43 97 444 7 44 9 6 4546 45 9 6 5 7 r C 6588 663 9 66 9 o 6 7 4o 6791 6842 56 /; 4645 46 9 5 4744 4794 4844 48 9 3 56 i. 6892 6 9 43 6 99 4 7 o45 79 5 7i46 55 4 4943 4 99 2 5o42 5o 9 2 5i4i 5i 9 i 55 t 7197 7247 72 9 8 7 34 9 7 3 99 745o 54 c 524o 52 9 o 533 9 538 9 543 9 5488 54 6 75oi 7 55i 7602 7 653 77 3 77 54 53 6 5538 558 7 563 7 5686 5 7 36 5 7 85 53 7 76o5 7 855 7 9 o6 79 5 7 8007 8o58 52 7 5835 5884 5 9 34 5 9 83 6o33 6082 5 2 8 8109 8i5 9 8210 8261 83n 836 2 5i 8 6i32 6182 623i 6281 633o 638o 5i 9 8412 8463 85i4, 8564 86i5 8665 5o 9 6429 64 79 6528 65 77 6627 66 7 6 5o 10 9.728716 8767 8817 8868 8918 8969 49 IO 9.746726 6 77 5 68 2 5 68 7 4 6 9 24 69'/3 4 9 ii 9020 9070 9 I2I 9171 9222 9272 48 ii 7023 7 7 2 7122 7171 7221 7 2 7 48 12 9323 9 3 7 4 9 424 9 4 7 5 9 5 2 5 9 5 7 6 47 12 7 3i 9 7 36 9 7 4i8 7 468 7517 7 56 7 47 i3 9626 9677 9727 9778 9 828 9879 46 i3 7616 7 665 77 i5 7764 7814 7 863 46 i4 9929 99 8o ..3o ..81 .132 .182 45 i4 79 i3 79 62 8011 8061 8110 8160 45 i5 9. 7 3o233 0283 o333 o384 0434 o485 44 i5 820 9 8 2 58 83o8 835 7 84o6 8456 44 16 o535 o586 o636 0687 0737 0788 43 16 85o5 8555 86o4 8653 8 7 o3 8 7 52 43 i? o838 o88 9 o 9 3 9 99 io4o 1091 42 !7 8801 885i 8 9 oo 8 9 4 9 8999 9 o48 42 18 n4i u 9 i 1242 I2 9 2 1 343 i3 9 3 4i 18 997 9 i4 7 9 i 9 6 9 245 9295 9 344 4i J 9 i444 i4 9 4 1 544 i5 9 5 1645 i6 9 6 4o T 9 9 3 9 3 9 443 9 4 9 2 9 54i 95 9 i 9 64o 4o 20 9.73i746 i7 9 6 1847 i8 97 i 9 48 i 99 8 3 9 20 9 -74 9 68 9 9739 97 88 9 83 7 9886 99 36 3 9 21 2048 2o 99 2l4 9 2200 2250 23oo 38 21 99 85 ..34 ..84 .133 .182 .23l 38 22 2 35i 2401 245 1 2502 2552 2602 37 22 9 . 750281 o33o o3 79 0428 0478 o52 7 37 23 2653 2703 2 7 53 28o4 2854 2 9 o4 36 23 o5 7 6 o6 2 5 o6 7 5 0724 o 77 3 0822 36 24 2 9 55 3oo5 3o55 3io6 3i56 3 2 o6 35 24 0872 9 2I o 97 o ioi 9 1069 1118 35 25 3257 33o 7 335 7 34o8 3458 35o8 34 25 1167 1216 1265 i3i5 1 364 i4i3 34 26 3558 36o 9 365 9 3 79 3 7 6o 38io 33 26 1462 i5n i56i 1610 i65 9 1708 33 27 386o 3 9 io 3 9 6i 4on 4o6i 4m 32 2 7 i 7 5 7 1806 i856 I 9 o5 1954 2003 32 28 4162 4212 i262 43i2 4363 44i3 3i 28 2O52 2IOI 2l5l 220O 2249 22 9 8 3i 29 4463 45i3 4564 46i4 4664 47i4 3o 2 9 2347 23 9 6 2446 2 4 9 5 2544 2 5 9 3 3o 3o 9.734764 48i5 4865 4 9 i5 4 9 65 5oi5 2 9 3o 9 . 752642 26 9 I 2 7 40 2789 2 83 9 2888 2 9 3i 5o66 5i 16 5i66 52i6 5 2 66 53i7 28 3i 2 9 3 7 2 9 86 3o35 3o84 3i33 3i82 28 32 5367 5417 546 7 55i7 556 7 56i8 27 32 323i 3280 333o 33 7 9 3428 3477 27 33 5668 5 7 i8 5 7 68 58i8 5868 5 9 i8 26 33 3526 35 7 5 3624 36 7 3 3722 3 77 i 26 34 5 9 6 9 6oi 9 6069 6n 9 6i6 9 62I 9 25 34 3820 386 9 3 9 i8 3967 4oi6 4o66 25 35 6269 63i 9 6370 6420 6470 6520 24 35 4n5 4:64 4213 4262 43n 436o 24 36 6570 6620 6670 6720 6770 6820 23 36 44o 9 4458 45o 7 4556 46o5 4654 23 3? 6870 6921 6971 7021 7071 7121 22 37 4703 4 7 5 2 48oi 485o 4899 4 9 48 22 38 7171 7221 7271 7321 73 7 i 7421 21 38 4997 5o46 5o 9 5 5i44 5i 9 3 5242 21 3 9 7471 7521 7571 7621 7671 7721 2O 39 52 9 I 534o 538 9 5438 5487 5536 2O 4o 9.787771 7821 7871 7 9 2I 797 1 8021 J 9 4o 9 . 755585 5634 5682 5731 5780 5829 I 9 4i 8071 8121 8171 8221 8271 832i 18 4i 58 7 8 5 9 2 7 5 97 6 6o25 6074 6i23 18 42 8371 8421 8471 852i 85 7 i 8621 I 7 42 6l 7 2 6221 62-70 63i9 6368 64i6 I 7 43 8671 8721 8771 8821 88 7 i 8 9 2I 16 43 6465 65i4 6563 6612 6661 6710 16 44 8971 9 O2I 97 I 9 I2I 9, 1 ? 1 9 22I i5 44 6 7 5 9 6808 685 7 6905 6 9 54 7oo3 i5 45 9271 9 32I 9 3 7 i 9 420 9 4 7 o 9 52O i4 45 7 o52 7 IOI 7 i5o 7199 7247 7296 i4 46 9 5 7 9 62O 9 670 9 720 9770 9 820 i3 46 7345 7 3 9 4 7 443 7492 ?54i 7 58 9 i3 4? 9870 99 20 9969 ..I 9 ..60 .II 9 12 47 7638 7 68 7 7736 7785 7834 7882 12 48 9.740169 O2I 9 0269 o3i 9 o368 0418 II 48 79 3! 79 8o 8o2 9 8078 8127 8i 7 5 II 49 o468 o5i8 o568 0618 0668 0717 IO 49 8224 82 7 3 8322 83 7 i 84i 9 8468 IO 5o 9.740767 0817 0867 0917 o 9 6 7 1016 9 5o 9 . 7 585i 7 8566 86i5 8663 8712 8761 9 5i 1066 1116 166 1216 1265 i3i5 8 5i 8810 8858 8 9 o 7 8 9 56 9 oo5 9o53 8 52 i365 i4i5 465 i5i4 i564 1614 7 52 9 I02 9 i5i 9 200 9 248 9 2 97 9 346 7 53 i664 i 7 i4 7 63 i8i3 i863 I 9 i3 6 53 9 3 9 5 9 443 9 4 9 2 9 54i 9 5 9 o 9 638 6 54 1962 2OI2 2062 2112 2161 2211 5 54 9 68 7 9736 9785 9 833 9 882 99 3i 5 55 2261 23ll 36o 24lO 2460 25lO 4 55 9979 ..28 '77 . 126 i 7 4 .223 4 56 2 55 9 26o 9 65 9 2 7 9 27 58 2808 3 56 9 . 7 6o2 7 2 0320 o36 9 0418 o466 o5i5 3 5? 2858 2007 9 5 7 3007 3o56 3io6 2 5 7 o564 0612 0661 0710 o 7 58 0807 2 58 3i56 3206 3 2 55 33o5 3355 34o4 I 58 o856 o 9 o4 o 9 53 1 002 io5o 1099 I , 5 9 .3454 35o4 3553 36o3 3653 3702 O 5 9 n48 n 9 6 1245 I2 9 3 1 342 1391 O 60" 50" 40" 30" 20" 10" d 60" 50" | 40" 30" 20" 10" . Co-tangent of 61 Degrees. 9 g Co-tangent of 60 Degrees. i P Part* l " 2 " 3// 4// 5 " 6 " 7// 8" 9" . ( 1" 2" 3" 4" 5" 6" 7" 8" 9" irl $ 5 10 15 20 25 30 35 40 45 IIL } 5 10 15 20 25 29 34 39 44 54 LOGARITHMIC SINES. 1 Sine of 30 Degrees. * Sine of 3 1 Degrees. s 0" 10" 20" 1 30" | 40" 50" 0" | 10" 20" 30" 40" 50" 9 .6 9 8 9 7o 9 oo6 9043 9079 9116 9 l52 5 9 o 9 . 7 n83 9 i8 7 4 I 9 o 9 1944 I 979 2Ol4 5 9 I 9189 9 225 9 262 9298:9334 9 3 7I 58 i 2o5o 2o85 2120 2i55 2I 9 2225 58 2 9407 9 444 94809517:9553 9 58 9 5 7 2 2260 22 9 5 2330 2365 240O 2434 57 r 9626 9 662 969997359771 9808 56 3 246 9 25o4 253 9 2 5 7 4 26o 9 2644 56 4 9844 9 88o 99 i 799 53 999 o .,26 55 4 2 6 79 2 7 l4 2 7 4 9 2784 28i 9 2854 55 i 9.700062 oo 99 oi35 oi 7 i 0208 0244 54 5 288 9 2 9 24 2 9 5 9 2994 3o2 9 3o63 54 6 0280 0317 o353o38 9 0425 0462 53 6 3o 9 8 3i33 3i68 3 2 o3 3238 3 27 3 53 7 0498 o534 o5 7 i o6o 7 o643 0680 52 7 33o8 3343 33 77 34i2 3447 3482 52 8 0716 7 52 07880825 0861 o8 97 5i 8 35i 7 3552 358 7 362i 3656 36 9 i 5i 9 o 9 33 0970 1006 1042 1078 in5 5o 9 3 7 26 3 7 6i 3 W 6 383o 3865 3900 5o IO 9.701151 1187 1223 I25g 1296 i33 2 49 IO 9 . 7 i3 9 35 3 97 o 4oo5 4039 4074 4109 49 ii i368 i4o4 i44o i4 77 i5i3 i54 9 48 ii 4i44 4i79 4213 4248 4283 43i8 48 12 i585 1621 i658 i6 9 4 1730 1-766 47 12 435 2 438 7 4422 445 7 44 9 i 4526 47 i3 1802 i838 i8 7 4 i 9 n 1947 i 9 83 46 i3 456i 45 9 6 463o 4665 4700 4735 46 i4 2019 2o55 2O 9 I 2I2 7 2164 22OO 45 i4 476 9 48o4 483 9 48 7 3 4 9 o8 4943 45 i5 2236 22 7 2 23o8- 2 344 238o 2416 44 i5 4 9 78 5012 5o4 7 5o82 5n6 5i5i 44 16 2452 2488 25242561 25 97 2633 43 16 5i86 522O 5 2 55 5290 5324 535 9 43 17 2669 2 7 o5 2741^777 28i3 284 9 42 '7 53 9 4 5428 5463 5498 5532 556 7 42 18 2885 2 9 2I 2 9 57 2 99 3 3029 3o65 4i 18 56o2 5636 56 7 i 5 7 o5 5 7 4o 5 77 5 4i i 9 3ioi 3i3 7 3173 3209 3 2 45 3281 4o i 9 58o 9 5844 58 7 f 5 9 i3 5 9 48 5 9 82 4o 20 9 . 7 o33 I7 3353 338 9 ! 3425 346i 34 97 3 9 20 9 . 716017 6o5i 6086 6121 6i55 6190 39 21 3533 356 9 36o5 364i 3677 3 7 i3 38 21 6224 6 2 5 9 62 9 3 63 2 8 6362 63 97 38 22 3 7 4 9 3 7 84 38203856 38 9 2 3 9 28 37 22 6432 6466 65oi 6535 65 7 o 66o4 3 7 23 3 9 64 4ooo 4o36j4o72 4io8 4i44 36 23 663 9 66 7 3 6 7 o8 6 7 42 6777 6811 36 24 4i79 42i5 425i428 7 4323 435 9 35 24 6846 6880 6 9 i5 6949 6 9 84 7018 35 25 43 9 5 443i 4466j45o2 4538 45 7 4 34 25 7o53 7 o8 7 7 I22 7 i56 7i 9 i 7225 34 26 46io 4682'47i7 4753 4 7 8 9 33 26 7 25 9 7 2 9 4 7 328 7 363 7397 7432 33 27 4825 486i'4896|4932 4968 5oo4 32 27 7 466 7 535 7 56 9 7604 7 638 32 28 5o4o 5075 5ni 5i47 5i83 52I 9 3i 28 7 6 7 3 777 77 4i 7776 7810 7844 3i 2 9 5254 5290 5326 5362 53 97 5433 3o 2 9 7879 79 i3 7948 79 82 8016 8o5i 3o 3o 9 .7o546 9 55o5 554o 55 7 6 56i2 5648 2 9 3o 9 . 718085 8n 9 8i54 8188 8223 8 2 5 7 29 3i 5683 5719 5755 5 79 5826 5862 28 3i 82 9 I 8326 836o 83 9 4 842 9 8463 28 32 58 9 8 5 9 33 5 9 6 9 6oo5 6o4o 6o 7 6 2 7 32 84 9 7 853i 8566 8600 8634 8669 27 33 6112 61476183 6219 6254 62 9 o 26 33 8 7 o3 8 7 3 7 8772 8806 884o 88 7 4 26 34 6326 636i 63 97 6433 6468 65o4 25 34 8 9 o 9 8 9 43 8977 9 on 9 o46 9080 25 35 653 9 65 7 5 6611 6646 6682 6 7 i8 24 35 9 n4 9 i48 9 i83 9 3I 7 9 25l 9285 24 36 6 7 53 6789 6824 6860 68 9 5 6 9 3i 23 36 9 320 9 354 9 388 9 422 9 456 9491 23 37 6 9 6 7 7002 7o38 7 o 7 3 7109 7i45 22 37 9 5 2 5 9 55 9 9 5 9 3 9 62 7 9 662 9696 22 38 7180 7216 7 25i 7287 7322 7358 21 38 97 3o 97 64 979 s 9 833 9867 9901 21 3 9 7 3 9 3 7429 7464 7 535 7 5 7 i 20 39 99 35 99 6 9 ...3 ..38 ..72 . 106 2O 4o 9 . 707606 7642 7677 77 i3 7748 7784 I 9 4o 9 . 720140 oi 7 4 0208 0242 0276 o3n '9 4i 7819 7855 7 8 9 o 7926 7961 7997 18 4i o345 o3 79 o4i3 o44 7 o48i o5i5 18 42 8o3 2 8068 8io3 8i3 9 8174 8210 i 7 42 o54 9 o583 0617 o652 0686 7 20 1 7 43 8245 8^80 83i6 835i 838 7 8422 16 43 0754 o 7 88 0822 o856 0890 0924 16 44 8458 8^3 85 2 8 8564 85 99 8635 i5 44 o 9 58 99 2 1026 1060 1094 1128 i5 45 8670 8 7 o5 8 7 4i 8776 8811 8847 i4 45 1162 1 1 9 6 1230 1264 1298 i332 i4 46 8882 8918 8 9 53 8988 9024 9 o5 9 i3 46 1 366 i4oo i434 1 468 1 602 i536 i3 47 9 o 9 4 9i3o 9 i65 9200 9236 9271 12 47 1570 i6o4 i638 l6 7 2 1706 i 7 4o 12 48 9 3o6 9 342 9377 9412 9 448 9 483 II 48 i 77 4 1808 1842 i8 7 6 1910 1944 II 49 9 5i8 9 553 9 58 9 9624 9659 9695 IO 49 i 97 8 2012 2046 2080 2114 2148 10 5o 9 . 7 o 97 3o 9 765 9 8oo 9 836 9871 9906 9 5o 9 . 722181 22l5 2249 2283 2317 235i 9 5i 99 4i 9977 . . 12 ..4 7 ..82 .118 8 5i 2385 24l 9 2453 2 48 7 2520 2554 8 52 9 . 7 ioi53 01880223 0259 02 9 4 032 9 7 52 2588 2622 2656 26 9 o 2724 2 7 5 7 7 53 o364 o3 99 o435 0470 o5o5 o54o 6 53 27 9 I 2825 28592893 2927 2960 6 54 o5 7 5 06 1 1 o646 0681 0716 0751 5 54 2. 99 4 3028^062 3o 9 6 3i3o:3i63 5 55 0786 08220857 0892 9 27 9 62 4 55 3i 97 323il3265:32 99 !3332 3366 4 56 997 I032 ! 1067 no3 n38 n 7 3 3 56 34oo 3434 3468;35oi 3535 356 9 3 5 7 1208 1243 1278 i3i3 i348 i383 2 57 36o3363636 7 o3 7 o43 7 38377i 2 58 i4i 9 i454 1489 i524 i55 9 i5 9 4 I 58 38o5:383 9 3873 3 9 o6 3 9 4o3 97 4 i 5 9 i62 9 1664 1699 1734 1769 1 8o4 O 5 9 4oo 7 4o4i 4075 4io 9 4i42 4176 o 60" 50" 40" | 30" | 20" i 10" a 60" 50" . 40" 30" 20" 10" 1 . Co-sine of 59 Degrees. fl Co-sine of 58 Degrees. ' . ( 1" 2" 3" 4" 5" 6" 7" 8" 9" J 1" 2" 3" 4" 5" 6" 7" 8" 9" "{ 4 7 11 14 18 21 25 29 32 \ 3 7 10 14 17 21 24 27 31 LOGARITHMIC TANGENTS. .5 Tangent of 30 Degrees. Jj Tangent of 3 1 Degrees. 0" 10" 20" 30" 40" 50" 0" 10" 20" 30" 40" 50" 9. -761439 i486 i53 7 i585 i634 1682 5 9 o 9 . 778774 8821 886 9 8 9 i 7 8 9 64 9OI2 5 9 i I 7 3i 1-780 1828 1877 I 9 25 i 97 4 58 i 9060 9 io8 9 i55 9203 9 25l 9 2 9 8 58 2 8O22 20-71 2I2O 2168 2217 2266 57 2 9 346 9 3 9 4 9 44i 9489 9 53 7 9 584 5 7 3 23l4 2363 2411 2460 25o8 255 7 56 3 9 632 9 6 79 97 2 7 977 5 9 822 9 8 7 o 56 4 2606 2654 2 7 o3 2751 2800 2848 55 4 99I 8 99 65 ..61 .108 .i56 55 5 2 8 97 2 9 45 2 99 4 3o43 3o 9 i 3i4o 54 5 9 . 780203 025l 02 99 o346 o3 9 4 o44i 54 6 3i88 323 7 3285 3334 3382 343i 53 6 o48 9 o53 7 o584 o632 o6 79 7 2 7 53 7 34 7 9 3528 35 7 6 3625 36 7 3 3 7 22 52 7 0775 0822 o8 7 o o 9 i 7 o 9 65 ioi3 52 8 3 77 o 38i 9 386 7 3 9 i6 3 9 64 4oi3 5i 8 1060 1108 n55 1203 I25o 1298 5i 9 4o6i 4no 4i58 4207 4255 43o4 5o 9 1 346 i3 9 3 i44i i488 i536 i583 5o 10 9. 7 64352 44oo 4449 4497 4546 45 9 4 49 IO 9 . 781631 i6 7 8 1-726 i 77 4 1821 1869 4 9 II 4643 46 9 i 4 7 4o 4788 4836 4885 48 ii i 9 i6 i 9 64 2OII 2o5 9 2106 2 I 54 48 12 4933 4 9 82 5o3o 5079 5127 5i 7 5 47 12 22OI 224 9 22 9 6 2344 23 9 I 243 9 47 i3 5224 52 7 2 532i 536 9 54i8 5466 46 i3 2486 2 534 258i 262 9 26-76 2 7 24 46 i4 55i4 5563 56n 566o 5 7 o8 5 7 56 45 i4 2771 28l 9 2866 2 9 i4 2961 3OO9 45 i5 58o5 5853 5901 SgSo 5 99 8 6o4 7 44 i5 3o56 3io4 3i5i 3i 99 3246 32 9 4 44 16 6095 6i43 6192 6240 6288 633 7 43 16 334i 3388 3436 3483 353i 35 7 8 43 i 7 6385 6433 6482 653o 65 7 8 662 7 42 '7 3626 36 7 3 3 7 2I 3 7 68 38i6 3863 42 18 66 7 5 6 7 23 6 77 2 6820 6868 691-7 4i 18 3 9 io 3 9 58 4oo5 4o53 4ioo 4i48 4i 19 6 9 65 7 oi3 -7062 7110 7i58 7 20 7 4o 19 4i 9 5 4242 4290 433 7 4385 4432 4o 20 9. 7 6 7 255 7 3o3 7 35 2 74oo 7448 7496 3 9 20 9.784479 452 7 45 7 4 4622 466 9 4 7 i6 3 9 21 7 545 7 5 9 3 7 64i 7690 7738 77 86 38 21 4764 48u 485 9 4 9 o6 4953 5ooi 38 22 7 834 7 883 79 3i 7919 8027 80-76 37 22 5o48 5o 9 5 5i43 5i 9 o 5238 5 2 85 37 23 8124 81-72 8221 826 9 83i7 8365 36 23 5332 538o 542 7 54 7 4 5522 556 9 36 24 84i4 8462 85io 8558 8606 8655 35 24 56i6 5664 5 7 n 5 7 58 58o6 5853 35 25 8 7 o3 8 7 5i 8 799 8848 88 9 6 8944 34 25 5 9 oo 5 9 48 5 99 5 6042 6090 6i3 7 34 26 8992 9 o4o 9 o8 9 9 i3 7 9 i85 9 233 33 26 6i84 6232 62 79 6326 63 7 4 6421 33 27 9281 9 33o 9 3 7 8 9 426 9 4 7 4 9522 32 27 6468 65i6 6563 6610 665 7 6 7 o5 32 28 95 7 i 9 6i 9 9667 9 7i5 97 63 9811 3i 28 6752 6 799 684 7 68 9 4 6941 6 9 88 3i 2 9 9860 99 o8 99 56 ...4 ..52 . 100 3o 29 7o36 7 o83 7 i3o 7178 7 225 7 2 7 2 3o 3o 9. 77 oi48 oi 97 0245 02 9 3 o34i o38 9 2 9 3o 9 . 7 8 7 3 I9 7 36 7 7 4i4 746 1 7 5o8 7 556 29' 3i o43 7 o485 o534 o582 o63o 06-78 28 3i 7 6o3 7 65o 7 6 97 7745 77 9 2 7 83 9 28 32 0-726 o 77 4 0822 0870 o 9 i 9 096-7 2 7 32 -7886 79 34 79 8i 8028 8o 7 5 8122 2 7 33 ioi5 io63 1 1 1 1 n5 9 1207 1255 26 33 81-70 821-7 8264 83n 835 9 84o6 26 34 i3o3 i35i i3 99 i448 i4 9 6 1 544 25 34 8453 85oo 854 7 85 9 5 8642 868 9 25 35 i5 9 2 i64o 1688 1736 1784 i832 24 35 8 7 36 8 7 83 883o 88 7 8 8 9 25 8 97 2 24 36 1880 I 9 28 i 9 76 2024 2072 2I2O 23 36 9 oi 9 9 o66 9 n4 9161 9 2o8 9 255 23 37 2168 2216 2264 23l2 236i 2409 22 37 9 3o2 9 34 9 9 3 97 9 444 9 4 9 i 9 538 22 38 245 7 2 5o5 2553 2601 264 9 26 97 21 38 9 585 9 63 2 9 6 79 97 2 7 9774 9 82I 21 QQ 2 7 45 2703 2841 2 88 9 2O37 2985 2O 3o 9 868 ooi 5 0062 5 7 . i o4 2O 4o 9 . 77 3o33 /v w 3o8i 3i2 9 3i 77 7 / 3225 32 7 3 J 9 / 4o 9 . 79 oi5i vv x ^ oi 9 8 fl 0245 O2 9 2 o33 9 o386 19 4i 332i 336 9 3417 3465 35i2 356o 18 4i o434 o48i o528 o5 7 5 0622 o66 9 18 42 36o8 3656 3704 3 7 5 2 38oo 3848 '7 42 O 7 i6 o 7 63 0810 o85 7 ogoS O 9 52 17 43 38 9 6 3 9 44 3992 4o4o 4o88 4i36 16 43 999 io46 1093 n4o 1187 1234 16 44 4i84 4232 4280 4328 43 7 5 4423 i5 44 1281 i328 !3 7 5 l422 1469 i5i6 i5 45 44 7 i 45i 9 456 7 46i5 4663 4 7 n i4 45 i563 1611 i658 I 7 o5 I 7 52 i 799 i4 46 4 7 5 9 48o 7 4855 4 9 02 4 9 5o 4998 i3 46 1 846 i8 9 3 1940 i 9 8 7 2o34 2081 i3 47 5o46 5o 9 4 5i42 5i 9 o 5238 5 2 86 12 47 2128 2I 7 5 2222 226 9 2 3i6 2363 12 48 5333 538i 5429 5477 5525 55 7 3 II 48 2410 245 7 25o4 2 55i 25 9 8 2645 II 49 562! 5668 5716 5764 58i2 586o IO 4 9 26 9 2 2 7 3 9 2 7 86 2833 2880 2 9 2 7 IO 5o 9. -7-75908 5 9 56 6oo3 6o5i 6o 99 6i4 7 9 5o 9-79 2 974 3O2I 3o68 3n5 3i6 2 320 9 9 5i 6195 6243 6290 6338 6386 6434 8 5i 3 2 56 33o3 335o 33 97 3444 34 9 i 8 52 6482 6529 6577 66 2 5 6673 6 7 2I 7 52 3538 3585 3632 36 79 3 7 26:3 77 3 7 53 6 7 68 6816 6864 6 9 I2 6960 77 6 53 38i 9 3866 3 9 i3 3 9 6o 4oo 7 4o54 6 54 7 o55 7 io3 7 i5i 7i 99 7246 7294 5 54 4ioi 4i48 4i95 4242 42894336 5 55 7 342 7 3 9 o 7437 7485 7 533 7 58i 4 55 4383 443o 4 56 -7628 7 6 7 6 7724 7772 7 8i 9 7867 3 56 4664 4 7 n 4 7 58 48o5 4852 48 99 3 57 79 i5 79 63 8010 8o58 8106 8i54 2 57 4 9 46 4 99 2 5o3 9 5o865i335i8o 2 58 8201 824 9 8297 8344 83 9 2 844o I 58 522 7 52 7 453 2 i 536 7 !54i4546i I 5 9 8488 85358583 863i 86 7 8 8726 O 5 9 55o8 5555 56o 2 564 9 5696 5 7 42 O W 50" 40" 30" 20" 10" ~T~ 60" 50" ) 40" i 30" 20" , 10" G Co-tangent of 59 Degrees. S3 Co-tangent of 58 Degrees. 1 P Part* l " ~" 3 " 4 " 5 " 6 " 7 " 8 " 9 " C l" 2" 3" 4" 5" 6" 7" 8" 9" \ 5 10 14 19 24 29 34 39 43 irt \ 5 9 14 19 24 28 33 38 43 bfl LOGARITHMIC SINES. _g Sine of 32 Degrees. .s Sine of 33 Degrees 9 10" 20" 30" 40" 50" 2 0" 10" 20" | 30". 40" 50" o 9.724210 4243 4277:4311 4344 43 7 8 5 9 9 . 7 36io 9 6i4i 6i 7 4 6206 6 2 38 62 7 I 5 9 i 44i2 4445 447 9 45i3 4546 458o 58 I 63o3 6336 636864oo 6433 6465 58 2 46i4 4647 468i 4 7 i5 4748 4782 5 7 2 6498653066626696 662 7 665 9 57 3 48i6 4849 4883 4 9 i7 4 9 5o 4 9 84 56 3 6692,6-724 6 7 5 7 |6 7 8 9 6821 6854 56 4 5oi 7 5o5i 5o85' 5n8 5i5 2 5i85 55 4 6886'6 9 i8;6 9 5iJ6 9 83 7 oi5 7 o48 55 5 5219 5253 5286 5320 5353 5387 54 5 7080 7112 7145)7177 7 20 9 7241 54 6 5420 5454 5488 552i 5555 5588 53 6 7274 7 3o6 7 338| 7 3 7 i 7 4o3 7435 33 7 5622 5655 568 9 5722 5 7 56 5 7 8 9 52 7 7 46 7 7 5oo 76327664 7 5 97 7 62 9 52 8 9 10 5823 6024 9.726225 5856 6o5 7 6258 58 9 o5 9 23 6091 6124 6292 6325 5 9 5 7 6i58 635 9 5 99 o 6i 9 i 63 9 2 5i 5o 49 8 9 10 7 66i 7 855 9.788048 7693772617768 788779197961 8o8o8ii28i45 779 7983 8i 77 7 822 8016 820 9 Si 5o 49 ii 6426 645 9 6493 6526 656o 65 9 3 48 ii 8241 82 7 3 83o68338 83 7 o 8402 48 12 6626 6660 6693 6727 6760 6704 47 12 8434 846684 9 9|853i 8563 85 9 5 47 i3 6827 6860 6894 6927 6961 6994 46 i3 86278659 86 9 2 8 7 24 8 7 56 8 7 88 46 i4 7027 7061 7094 7128 7161 7 i 9 4 45 i4 88208852 8884 8 9 i 7 8 9 4 9 8 9 8i 45 i5 7228 7261 7294 7328 736i 7 3 9 4 44 i5 9013 9045 977 9 io 99 i4i 9 i 7 3 44 16 7428 746 1 7494 7 5 2 8 7 56i 7 5 9 4 43 16 9206 9238 9 2 7 9 3o2 9 334 9 366 43 17 7628 7661 7694 7728 7761 7794 42 J 7 9 3 9 8 9 43o 9 462 9494 9 526 9 558 42 18 7828 7861 7 8 9 4 7 9 28 7961 7994 4i 18 9 5 9 o 9622 9 654 968? 97 i 9 97 5! 4i I 9 8027 8061 80948127 8161 8i 9 4 4o J 9 9783 9 8i5 9847 9 8 79 99 n 99 43 4o 20 9.728227 8260 82948327 836o 83 9 3 3 9 20 9 . 7 3 997 5 ...7 ..3 9 .. 7 i ,io3 .i35 3 9 21 8427 846o 849385 2 6 856o85 9 3 38 21 9 . 740167 oi 99 023l 0263 O2 9 5 o32 7 38 22 8626 865 9 8692 8726 8 7 5 9 !8 79 2 37 22 o35 9 o3 9 i o423 o455 o48 7 o5i 9 3? 23 8825 8858 8892 8 9 25 89588991 36 23 o55o o582 06 1 4 o646 o6 7 8 7 IO 36 24 25 9024 9223 9 o58 9 25 7 9091 9290 9 I24 9 323 915719190 9356 9 38 9 35 34 24 25 0742 o 9 34 0774 o 9 66 0806 997 o838 I02 9 o8 7 o 1061 O 9 02 io 9 3 35 34 26 9422 9 455 9489 9522 9 555 9 588 33 26 1125 1 15 7 n8 9 1221 1253 1284 33 27 9621 9 654 96879720 97 53 9787 32 27 i3i6 1 348 i38o 1412 1 444 i4 7 6 32 28 9820 9 853 9886 9919 9952 99 85 3i 28 i5o8 i53 9 1671 i6o3 i635 i66 7 3i 29 9.730018 oo5i oo84 0117 oi5o oi83 3o 2 9 i6 99 1730 1762 i 79 4 1826 i858 3o *3o 9.730217 025o 0283 o3i6 0349 o382 2 9 3o 9 . 7 4i88 9 I 9 2I i 9 53 i 9 85 20I 7 204 9 2 9 3i o4i5 o448 0481 o5i4 o547 58o 28 3i 2080 2112 2i44 2I 7 6 22O 7 223 9 28 32 o6i3 0646 06790712 o 7 45 0778 27 32 2271 2 3o3 2335 2366 2 3 9 8 2 43o 27 33 0811 o844 0877 o 9 io o 9 43 o 97 6 26 33 2462 2493 25 2 5 2 55 7 2 58 9 2620 26 34 1009 1042 1075 1 1 08 n4i n 7 3 25 34 2652 2684 2 7 l5 2 7 4 7 2779 28 1 i 25 35 1206 1239 1272 i3o5 i338 i3 7 i 24 35 2842 28-74 2 9 o6 2 9 3 7 2 9 6 9 3ooi 24 36 i4o4 i43 7 1470 i5o3 i536 i56 9 23 36 3o33 3o64 3o 9 6 3128 3i5 9 3i 9 i 23 37 1602 1 634 1667 1700 i 7 33 1766 22 37 3223 3 2 54 3 2 86 33i8334 9 338i 22 38 1799 i832 i865 i8 97 I 9 3o i 9 63 21 38 34i3 3444 34 7 6 35o8 3539 35 7 i 21 3 9 1996 2029 2062 20 9 5 2127 2160 20 39 36o2 3634 3666 36 97 3729 3 7 6i 20 409.732193 2226 2259 2292 2325 235 7 I 9 4o 9 .743 79 2 3824 3855 388 7 3 9 i 9 3 9 5o J 9 4i 2390 2423 2456 2489 2521 2 554 18 4i 3 9 82 4oi3 4o45 4o 77 4io8 4i4o 18 42 2587 2620 2653 2685 2718 2 ? 5l 17 42 4i 7 i 4203 4234 4266 429-7 432 9 17 43 2784 2816 2849 2882 2 9 l5 2 9 48 16 43 436i 43 9 2 4424 4455 448 7 45i8 16 44 2980 3oi3 3o46 3o 79 3in 3i44 i5 44 455o 458i 46i3 4644 46 7 6 4 7 o 7 i5 45 3i 77 3210 8242 32 7 5 33o8 334o i4 45 4 7 3 9 4 77 o 4802 4833 4865 48 9 6 i4 46 33 7 3 34o6 34393471 35o4 353 7 i3 46 4 9 28 4 9 5 9 4 99 i 5022 5o54 5o85 i3 47 48 49 356 9 3 7 65 3 9 6i 36o2 3 79 8 3 99 4 3635 36673700 383i 3863|38 9 6 4027 4o59 4092 3 7 33 3 9 2 9 4i25 12 II IO 47 48 49 5n 7 53o6 5494 5i48 533 7 5526 5i8o 536 9 555 7 5211 5400 558 9 5243 543i 5620 52 7 4 5463 565i 12 II IO 5o 9.734157 4i 9 o 4222 4255 4288 4320 9 5o 9 . 7 45683 5 7 i4|5 7 46 5 777 58o8 584o 9 5i 4353 4386 44i8 445 1 4483 45i6 8 5i 58 7 i 69036934 5 9 65 5 997 6028 8 52 4549 458i 46i4 4646 46 79 4 7 n 7 52 6060 6091 6122 6 1 54 6 1 85 6216 7 53 4744 4?77 4809 4842 48 7 4 4 9 o 7 6 53 6248!62 79 !63io 63426373 64o4 6 54 4939 4 9 7 2 5oo4 5o37 5069 5l02 5 54 6436 646 7 64 9 8 653o656i 65 9 2 5 55 5i35 5i6 7 52OO 5 2 3 2 5 2 65 52 97 4 55 6624 6655 6686 6 7 i86 7 4 9 6 7 8o 4 56 533o 5362 53 9 5 5427 546o 5492 3 56 68i2'6843 68 7 4 6 9 o5 6 9 3 7 6 9 68 3 5 7 5525 555 7 55 9 o 5622 5655 568 7 2 5 7 6 999 ! 7 o3i -7062 7 o 9 3 7124 7 i56 2 58 5 7 i 9 5 7 5 2 5 7 84 58i 7 584 9 5882 I 58 71877218 7 24 9 728lJ73l2 7 343 I 5 9 5gi4 5 9 4 7 5 979 601 1 6o44 6o 7 6 O 5 9 7 3 7 4| 7 4o6 7 43 7 7468)7499 753o O 60" 50" 40' 30" 20" 10" B 60" 50" 40" 30" 20" 10" a Co-sine of 57 Degrees. i Co-sine of 56 Degrees. i .< 1" 2" 3" 4" 5" 6" 7" 8" 9" p p C 1" 2" 3" 4" 5" 6" 7" 8" 9" P.PMtj 3 7 10 13 17 20 23 26 30 1 n \ 3 6 10 13 16 19 22 25 29 LOGARITHMIC TANGENTS. r l Tangent of 32 Degrees. d Tangent of 33 Degrees. * 0" 10" 20" 30" 40" 50" a 0" 10" 20" 30" 40" 00" o 9-79578 9 5836 58835 9 3o 5 977 6023 5 9 o 9 .8i25i7 2563 2610 2656 2 7 O2 2748 5 9 I 6070 6n 7 616416211 6258 63o4 58 i 2794 2840 2886 2932 2 97 8 3o24 58 6 635i 63 9 8 6445 6492 653 9 6585 57 2 3070 3n6 3i63 3209 3255 33oi 57 3 6632 66 79 6 7 26 6773 68i 9 6866 56 3 334 7 33 9 3 343 9 3485 353i 35 77 56 4 6 9 i3 6 9 6o 7 oo 7 7 o53 7100 7 i4 7 55 4 3623 366 9 3 7 i5 3 7 6i 38o 7 3853 55 5 7i 9 4 7 24l 7287 7334 7 38i 7 428 54 5 38 99 3 9 45 3 99 i 4o3 7 4o83 4i2 9 54 6 7 4 7 4 7 52I 7 568 7 6i5 7662 77 o8 53 6 4176 4222 4268 43i4 436o 44o6 53 7 77 55 7 802 7 84 9 7895 7942 7989 5 2 7 4452 44 9 8 4544 4590 4636 4682 5 2 8 8o36 8082 8i2 9 8176 8223 826 9 5i 8 4728 4774 4820 4866 4 9 I2 4 9 58 5i 9 83i6 8363 84o 9 8456 85o3 855o 5o 9 5oo4 5o5o 5o 9 6 5i42 5i88 5 2 34 5o 10 9 . 79 85 9 6 8643 8690 8737 8 7 83 883o 49 10 9 .8i528o 53 2 6 5371 5417 5463 55o 9 4 9 ii 88 77 8 9 23 8 97 o 9017 9 o63 9 no 48 ii 5555 56oi 5647 56 9 3 5 7 3 9 5 7 85 48 12 9 i5 7 9 204 925o 9 2 97 9 344 9 3 9 o 47 12 583i 5877 5 9 23 5969 6oi5 6061 47 i3 9 43 7 9 484 9 53o 9 5 77 9 6 2 4 9 6 7 o 46 i3 6107 6i53 6i 99 6245 62 9 I 6336 46 i4 97 i 7 97 64 9810 9 85 7 99 o4 99 5o 45 i4 6382 6428 6474 6520 6566 6612 45 i5 9997 ..44 ..90 .i3 7 .184 .230 44 i5 6658 6704 6750 6796 6842 6888 44 16 9 .8oo2 77 0324 o3 7 o o463 o5io 43 16 6 9 33 6979 7025 7071 7117 7 i63 43 I 7 o55 7 o6o3 o65o o6 97 o 7 43 79 42 17 7 20 9 7 255 73oi 7 34 7 7 3 9 2 7438 42 18 o836 o883 ogSo o 97 6 1023 I0 7 O 4i 18 7484 7 53o 7 5 7 6 7622 7 668 7714 4i 19 1116 n63 1209 1256 i3o3 1 349 4o i 9 77 5 9 7805 785i 7897 7943 79 8 9 4o 20 9 .8oi3 9 6 1442 1489 i535 i58 2 1629 3 9 20 9 .8i8o35 8081 8126 8172 8218 8264 3 9 21 1675 1722 1768 i8i5 1862 1908 38 21 83io 8356 8402 8447 84 9 3 853 9 38 22 i 9 55 2OOI 2048 so 9 4 2l4l 2l8 7 3 7 22 8585 863i 8677 8722 8 7 68 8814 37 23 2234 228l 2327 23 7 4 2420 246 7 36 23 8860 8 9 o6 8 9 52 8997 9 o43 9 o8 9 36 24 2 5i3 256o 2606 2653 26 99 2 7 46 35 24 9 i35 9 i8i 9 226 9272 9 3i8 9 364 35 25 2 79 2 283 9 2886 2 9 32 2979 3o25 34 25 9 4io 9 455 9 5oi 954 7 9 5 9 3 9 63 9 34 26 3072 3n8 3i65 3211 3 2 58 33o4 33 26 9684 97 3o 9776 9822 9 868 99 i3 33 27 335i 33 97 3444 34 9 o 353 7 3583 32 2 7 99 5 9 ..96 .142 .188 32 28 363o 3676 3 7 23 3 7 6 9 38i6 3862 3i 28 9.820234 0280 o3 2 5 o3 7 i o4i 7 o463 3i 29 3 9 o 9 3 9 55 4ooi 4o48 4o 9 4 4i4i 3o 2 9 o5o8 o554 0600 o646 o6 9 i o 7 3 7 3o 3o 9 .8o4i8 7 4234 4280 432 7 43 7 3 4420 2 9 3o 9:820783 o82 9 o8 7 4 0920 0966 1012 2 9 3i 4466 45i3 4559 46o5 465 2 46 9 8 28 3i 1057 no3 n4 9 iigS 1240 1286 28 32 4745 47 9 i 4838 4884 4 9 3o 4977 27 32 i33 2 i3 77 1423 1469 i5i5 i56o 2 7 33 5o23 5070 5n6 5i63 520 9 5 2 55 26 33 1606 i652 i6 97 1743 1789 i835 26 34 5302 5348 53 9 5 544i 548 7 5534 25 34 1880 I 9 26 I 97 2 2017 ao63 2I0 9 25 35 558o 5627 56 7 3 5 7 i 9 5766 58i2 24 35 2i54 22OO 2246 2292 -33 7 2383 24 36 585 9 5 9 o5 5 9 5i 5 99 8 6o44 6091 23 36 2429 24 7 4 2520 2566 2611 265 7 23 37 6i3 7 6i83 623o 62 7 6 6322 636 9 22 37 2703 2 7 48 2 79 4 2840 2885 2 9 3i 22 38 64i5 6462 65o8 6554 6601 664 7 21 38 2977 3022 3o68 3n4 3i5 9 3 2 o5 21 3 9 66 9 3 6740 6786 6832 68 79 6925 20 3 9 3 2 5i 32 9 6 3342 338 7 3433 34 79 20 4o 9 806971 7018 7064 7 IIO 7 i5 7 7 203 I 9 4o 9 . 823524 35 7 o 36i6 366i 3 7 o 7 3 7 53 1 9 4i 7249 7296 7342 7 388 7435 7 48i 18 4i 3798 3844 388 9 3 9 35 3 9 8i 4026 18 42 7527 7 5 7 4 7620 7 666 77 i3 77 5 9 17 42 4072 4u 7 4i63 4209 4254 43oo 17 43 7 8o5 7 85i 7898 79 44 799 8o3 7 16 43 4345 43 9 i 44?7 4482 4528 45 7 3 16 44 8o83 8129 8176 8222 8268 83i4 i5 44 46i 9 4665 4710 4756 48oi 4847 i5 45 836i 84o 7 8453 84 99 8546 8592 i4 45 48 9 3 4 9 38 4 9 84 5029 5o 7 5 5l2O i4 46 8638 8685 8 7 3i 8777 88a3 88 7 o i3 46 5i66 5212 525 7 53o3 5348 53 9 4 i3 4 7 8 9 i6 8962 9008 9 o55 9 ioi 9147 12 47 54>9 5485 553i 55 7 6 5622 5667 12 48 9 i 9 3 9240 9286 9 332 9 3 7 8 9424 II 48 5 7 i3 5 7 58 58o4 5849 58 9 5 5 9 4o II 49 947i 9 5i 7 9 563 9 6o 9 9 656 9 7 02 IO 49 5 9 86 6o32 6077 6i23 6168 6214 IO 5o 9 .8o 97 48 9794 9840 9887 99 33 9979 9 5o 9 .82625 9 63o5 635o 63 9 6 644i 648 7 9 5i 9 . 810025 0071 0118 0164 0210 0256 8 5i 6532 65 7 8 6623 6669 6 7 i4 6760 8 52 o3o2 o34 9 o3 9 5 o44i o48 7 o533 7 52 68o5 685i 68 9 6 6942 6 9 8 7 7o33 7 53 o58o 0626 0672 0718 o 7 64 0810 6 53 7078 7 I24 7 i6 9 7 2l5 7260 7 3o6 6 54 o85 7 o 9 o3 0949 o 99 5 io4i io8 7 5 54 735i 7397 7 442 7 488 7 533 7 5 79 5 . 55 1 1 34 1180 1226 I2 7 2 i3i8 1 364 4 55 7624 7 6 7 o 77 i5 776i 7806 7 85i 4 56 i4io i45 7 i5o3 I 549 i5 9 5 i64i 3 56 7897 7942 7988 8o33 8o 79 8124 3 5 7 1687 i 7 33 1780 :826 l8 7 2 1918 2 57 8170 82i5 8261 83o6 835i 83 97 2 58 i 9 64 2010 2o56 2IO2 2l4 9 2195 I 58 8442 8488 8533 85 7 9 8624 866 9 1 5 9 224l 228 7 2333 2 3 79 2425 2471 O 5 9 8 7 i5 8760 8806 885i 88 97 8 9 42 O 60" 50" 40" 30" 20" 10" a 60" 50" | 40" ?0" 20" 10" . Co-tangent of 57 Degrees. a Co-tangent of 56 Degrees. a f 1 // a// o// AH c// en 7/7 Q// a/i P T*nrt I **** ^* ** "D ' o I/ . ( 1" 2" 3" 4" 5" 6" 7" 8" 9" ir I 5 9 14 18 23 27 32 37 41 58 LOGARITHMIC SINES .3 Sine of 34 Degrees. rf Sine of 35 Degrees. 1 s 0" 10" 20" 30" 40" 50" s 0" | 10" | 20" 30'' 40" 50" o 9.747562 7 5 9 3 7624 7655 7 686 7718 5 9 o 9 . 7 585 9 i 8621 865i 8681 8712 8 7 42 5 9 I 7749 77 8o 7811 7842 7874 79 5 58 i 87728802 8832 8862i88 9 2 8922 58 2 7936 7967 7998 8o3o 8061 8o 9 2 5 7 2 8 9 52 8 9 82 9 OI2| 9 042 9072 9IO2 57 L 8i23 83io 8i54 834i 8i8582i6 83 7 2 84o3 8248 8434 8466 56 55 L 9 l32 9 l62 9 3l2 9 342 9 1 9 2 9 222 9262 9 3 7 2 9 4o2 9 432 9282 9 462 56 55 5 8497 85 2 8 85598590 8621 8652 54 5 9 4 9 2 9 522 95529582 9612 9 642 54 6 8683 8 7 i4 8745,8777 8808 883 9 53 6 9 672 97 02 9732 97 6 2 979 2 9822 53 7 8870 8901 8 9 328 9 63 8 99 4 9 025 52 7 9 852 9 88i 99" 99 4i 99-71 ... I 5 2 8 9 o56 9 o8 7 9118 9149 9180 9 2I2 5i 8 9 . 76003 1 0061 0091 OI2I oi5i 0181 5i 9 9 243 9 274' 9 3o5 9 336 9 36 7 9 3 9 8 5o 9 O2I I 0240 02 7 o3oo o33o o36o 5o 10 9 . 7 4 9 42 9 9460 9491 9522 9 553 9 584 49 IO 9. 760390 0420 o45o o48o 0509 o53 9 49 n 9 6i5 9646 967-7 9-708 9739 9770 48 n o56 9 o5 99 0629 o65 9 0689 0718 48 12 9 8oi 9832 9863 9894 99 25 99 56 47 12 o 7 48 o 77 8 0808 o838 0868 0898 47 i3 9987 ..18 ..48.. 79 . no 46 \l 9 2 7 o 9 5 7 o 9 8 7 IOI 7 io4 7 1076 46 i4 9 . 750172 0203 0234 0265 O2 9 6 032 7 45 i4 I I 06 ii36 1166 1196 1225 1255 45 i5 o358 0389 0420 o45i 0482 O5l2 44 i5 1285 i3i5 1 345 i3 7 4 i4o4 i434 44 16 o543 o5 7 4 o6o5;o636 066-7 o6 9 8 43 16 1 464 i4 9 4 i5 2 3 i553 i583 i6i3 43 I 7 o 7 2 9 0760 0791 0821 o85 2 o883 42 17 1642 16-72 I 7 02 I 7 32 i 7 6i 1791 42 18 o 9 M 0945 O9 7 6 ioo 7 io3 7 1068 4i 18 1821 i85i 1880 1910 1940 1969 4i 19 io 99 ii3o i i6i|i 192 1222 1253 4o '9 1999 2O2 9 2059 2088 21 18 2148 4o 20 9 . 7 5i284 i3i5 i346 1377 i4o 7 i438 3 9 20 9. 7 62i 77 22O 7 223 7 2267 2296 2326 39 21 i46 9 i5oo i53i i56i l5 9 2 1623 38 21 2356 2385 2 4i5 2445 24 7 4 25o4 38 22 i654 1 685 1715 1746 I 777 1808 37 22 2534 2563 25 9 3 2623 2652 2682 37 23 i83 9 1869 1900 1931 I 9 62 I 99 2 36 23 2 7 I2 2 7 4i 2 77 I 2801 283o 2860 36 24 2O23 2o54 2o85 2ii5 2146 2I 77 35 24 2889 2 9 I 9 2949 2978 3oo8 3o38 35 25 22O8 2238 2269 23oo 233o 236i 34 25 3o6 7 3o 97 3i26 3i56 3i86 3 2 i5 34 26 23 9 2 3423,2453 2484 2 5i5 2545 33 26 3245 32 7 4 33o4 3333 3363 33 9 3 33 27 2576 26o 7 263 7 2668 26 99 2 7 2 9 32 27 3422 3452 348i 35ii 354o 35 7 o 32 28 2760 2 79 I 2822 2852 2883 2 9 i4 3i 28 36oo 362 9 365 9 3688 3 7 i8 3 7 4 7 3i 2 9 2 9 44 2 97 5 3oo5 3o36 3o6 7 3o 97 3o 29 3777 38o6 3836 3865 38 9 5 3 9 25 3o 3o 9 . 7 53i28 3i5 9 3l8g 3220 3 2 5i 3281 2 9 3o 9 . 7 63 9 54 3 9 84 4oi3 4o43 4o 7 2 4102 2 9 3i 33i2 3342 33 7 3 34o4 3434 3465 28 3i 4i3i 4i6i 4i 9 o 4249 42 7 9 28 32 . 34 9 5 3526 355 7 358 7 36i8 3648 2 7 32 43o8 4338 436 7 43 9 6 4426 4455 2 7 33 36 79 3 7 io 3 7 4o 3 77 i 38oi 3832 26 33 4485 45i4 4544 45 7 3 46o3 4632 26 34 3862 38 9 3 3923 3 9 54 3 9 85 4oi5 25 34 4662 46 9 i 4 7 20 475o 4779 48o 9 25 35 36 4o46 422 9 4o 7 6 4io 7 42594290 4i3 7 4320 4i684i 9 8 435i 438i 24 23 35 36 4838 5oi5 4868 5o44 48 97 5o 7 4 5io3 4g56 4 9 85 5i6 2 24 23 37 44 1 2 4442 4473 45o3 4534 4564 22 37 5i 9 i 5221 525o 5279 53o 9 5338 22 38 45 9 5 46254656 4686 4 7 i 7 4 7 4 7 21 38 536 7 53 97 5426 5456 5485 55i4 21 3 9 4778 48o8 4839 486 9 4 9 oo 4 9 3o 20 3 9 5544 55 7 3 56o2 5632 566i 5690 20 4o 9. 754960 4991 5o2t 5o52 5o8 2 :5n3 I 9 4o 9 . 765720 5 7 4 9 5778 58o8 583 7 5866 I 9 4i 5i43 5i 7 3 52o4 5 2 34 5265 52 9 5 18 4i 58 9 6 5 9 25 5 9 54 5 9 84 6oi3 6042 18 42 5326 53565386 54i 7 54475478 17 42 6072 6101 6i3o 6i5 9 6189 6218 i 7 43 55o8 5538 5569 55 99 562 9 566o 16 43 6247 62 77 63o6 6335 6364 63 9 4 16 44 5690 5 7 2I 5 7 5i 5 7 8i 58i2;5842 i5 44 6423 6452 648 1 65n 654 656 9 i5 45 58 7 2 5 9 o3 5 9 33 5 9 63 5 99 4 6024 i4 45 65 9 8 6628 665 7 6686 6 7 i5 6 7 45 i4 46 6o54 6o856n5 6i45 61766206 i3 46 6 77 4 68o3 6832 6862 6891 6 9 20 i3 47 6 2 36 626 7 629 7 632 7 63586388 12 47 6 9 4 9 6 97 8 7 oo8 7 3 7 7 o66 7 o 9 5 12 00 O O xjxjvo 64i8 6600 9.756782 6448 64 7 9 663o 6660 6812 6842 65o 9 653 9 |65 7 o 66 9 ii6 7 2i:6 7 5i 68 7 2 6 9 o3 6 9 33 IO 9 48 49 5o 7124 73oo 9 . 767475 7 i54 7 3 29 7 5o4 7 i83 7 358 7 533 7212 7 38 7 7 562 7241 7 4i6 7 5 9 i 7270 7 445 7 620 I I IO 9 5i 6 9 63 6993 7 O23 7 o54 708417114 8 5i 7679 77 o8 77 3 7 7766 779 5 8 52 7i44 7 i 7 5 7 2o5 7 235 7265 72 9 5 7 52 7824 7 853 7882 -7912 79 4i 797 7 53 7 3 2 6 7 356 7 386 7 4i6 7446 7477 6 53 7999 8028 8o5 7 8086 3ii5 8i44 6 54 7507 7537 7 56 7 7 5 97 7627 7658 5 54 8i 7 3 82o3 8232 8261 ^290 83i 9 5 55 7688 77187748 7778 7808 783 9 4 55 83488377 84o6 8435 8464 84 9 3 4 56 7869 7899 7929 7959 7 9 8 9 8oi 9 3 56 85228551 8580860986388668 3 57 58 8o5o 823o 8080 8110 8i4o 826082908321 8170 8200 835i 838i 2 57 58 86 9 7 8726 8871 8 9 oo 8 7 558 7 84 8 9 2 9 !8 9 58 88 1 3 8842 8987 9016 2 5 9 84ii 844i 8471 85oi 853i 856i O 5 9 9 o45 9 o 7 4 9 io3 9 i32 9 i6i 9 i 9 o O 60" 50" : 40" 30" 20" 10" . 60" 50" 40" | 30" 20" 10" 1 Co-sine of 55 Degrees. s Co-sine of 54 Degrees. P '*H 1 3 2 e' 3 9" 4" 5" 6" 7" 8" 9" 12 15 18 21 25 28 p p .< 1" 2" 3" 4" 5" 6" 7" B" 9" } 3 6 9 12 15 18 21 24 27 LOGARITHMIC TANGENTS. 1 -S Tangent of 34 Degrees. .3 Tangent of 35 Degrees. 9 0" 10" | 20" 30" 40" 50" 9 0" 10" 20" 30" 40" 50" 9.828987 9 o33 9 o 7 8 9124 9 i6g! 9 2i5 5 9 o 9 . 845227 52 7 2 53i6 536i 54o6 545 1 5 9 I 9260 9 3o5 9 35i 9 3 9 6 9 442 9 48 7 58 I 54 9 6 554o 5585 563o 56 7 5 5 7 2O 58 2 9 532 9 5 7 8 9 623 9669 97 i4 97 5 9 57 2 5 7 64 58o 9 5854 58 99 5 9 44 5 9 88 5 7 9805 9 85o 9 8 9 5 gg4i 99 86 ..32 56 3 6o33 6o 7 8 6i23 6168 6212 625 7 56 4 9.830077 0122 0!68 02l3 0258 o3o4 55 4 63o2 6347 63 9 i 6436 648i 65 2 6 55 c o349 o3 9 5 o44o o485 o53i o5 7 6 54 5 6570 66i5 6660 6 7 o5 6 7 5o 6 79 4 54 6 0621 o66 7 7 I2 7 5 7 o8o3 0848 53 6 683 9 6884 6 9 2 9 6 97 3 7 oi8 7 o63 53 7 0893 o 9 3 9 o 9 84 1029 io 7 5 1120 52 7 7108 7i52 7 i 9 7 -7242 7287 7 33i 52 n65 I2II 1256 i3oi i34 7 i3 9 2 5! 8 7 3 7 6 7 42i 7465 7 5io 7 555 7 6oo 5i 9 i43 7 i483 i5 2 8 i5 7 3 i6i 9 1 664 5o 9 7 644 7 68 9 77 34 7779 7 8 2 3 -7868 5o 10 9.831709 i 7 55 1800 i845 i8 9 i i 9 36 49 IO 9 .84 79 i3 79 5 7 8002 8047 8092 8i36 49 ii 1981 2026 2O 7 2 2117 2162 2208 48 ii 8181 8226 8270 83i5 836o 84o5 48 12 2253 22 9 8 2 343 2 38 9 2434 24 79 4? 12 844 9 84 9 4 853 9 8583 8628 86 7 3 47 i3 2525 25 7 O 26i5 2660 2-706 2751 46 i3 8 7 i 7 8762 8807 885i 8896 8 9 4i 46 i4 2796 2842 2 88 7 2 9 32 2977 3o23 45 i4 8 9 86 9 o3o 9 o 7 5 9 I20 9164 9 20 9 45 i5 3o68 3n3 3i58 3204 324 9 32 9 4 44 i5 92 54 9 2 9 8 9 343 9 388 9 43 2 9477 44 16 333 9 3385 343o 3475 3520 3566 43 16 9 522 9 566 9 6n 9 656 97 oo 9745 43 ! 7 36ii 3656 3 7 oi 3 7 4 7 3 79 2 3837 42 17 979 9 834 9879 99 24 9968 . .i3 42 ' 18 3882 3927 3 97 3 4oi8 4o63 4io8 4i 18 9 .85oo5 7 OIO2 0147 oi 9 i 0236 0281 4i 19 4i54 4199 4244 428g 4334 438o 4o i 9 o325 0370 o4i5 o45 9 o5o4 o548 4o 20 9.834425 44 7 o 45:5 456i 46o6 465i 3 9 20 9 .85o5 9 3 o638 0682 7 2 7 77 2 0816 39 21 4696 4 7 4i 4 7 8 7 4832 48 7 7 4 9 22 38 21 0861 o 9 o5 o 9 5o o 99 5 1039 1084 38 22 4967 5012 5o58 5io3 5i48 5i 9 3 37 22 II2 9 u 7 3 1218 1262 i3o 7 i352 37 23 5238 5 2 84 532 9 53 7 4 54i 9 5464 36 23 i3 9 6 i44i i485 i53o i5 7 5 i6i 9 36 24 55o 9 5555 56oo 5645 56 9 o 5 7 35 35 24 1 664 1708 i 7 53 i 797 1842 i88 7 35 25 5780 58 2 6 58 7 i 5 9 i6 5 9 6i 5oo6 34 25 I 9 3i i 9 76 2O2O 2o65 2110 2i54 34 26 6o5i 6o 9 6 6 1 42 6i8 7 6232 62 77 33 26 2199 2243 2288 2332 23 77 2422 33 2 7 6322 636 7 6412 6458 65o3 6548 32 27 2466 25ll 2 555 2600 2644 2689 32 28 65 9 3 6638 6683 6728 6 77 3 68i 9 3i 28 2 7 33 2778 2823 286-7 2912 2 9 56 3i 29 6864 6 9 o 9 6 9 54 6 999 7 o44 7o8 9 3o 29 3ooi 3o45 3ogo 3i34 3i 79 3223 3o 3o 9 .83 7 i34 7 J 79 7 225 7 2 7 7 3i5 7 36o 2 9 3o 9. 353268 33i3 335 7 3402 3446 34 9 i 2 9 3i 74o5 7 45o 7 4 9 5 7 54o 7 585 7 63o 28 3i 3535 358o 3624 366 9 3 7 i3 3 7 58 28 32 7 6 7 5 7721 77 66 7 8n 7 856 7 9 oi 2 7 32 38o2 3847 38gi 3 9 36 3 9 8o 4o25 2 7 33 7946 799 1 8o36 8081 8126 8171 26 33 4o6 9 4n4 4i58 4203 424 7 4292 26 34 8216 8261 83o 7 8352 83 97 8442 25 34 4336 438i 4425 44 7 o 45i4 455 9 25 35 848 7 8532 86778622 8667 8712 24 35 46o3 4648 46 9 2 4 7 3 7 4781 4826 24 36 8 7 5 7 8802 884 7 88 9 2 8937 8 9 8a 23 36 48 7 o 4 9 i5 4 9 5 9 5oo4 5o48 5o 9 3 23 37 9 02 7 9 7 2 9 n 7 9 l62 9 20 7 9 252 22 37 5i3 7 5i82 5226 52 7 I 53i5 536o 22 38 9 2 97 9 343 9 388 9 433 9 478 9 523 21 38 54o4 544 9 54 9 3 5537 5582 5626 21 39 9 568 9 6i3 9 658 97 o3 97 48 9793 2O 39 56 7 i 5 7 i5 5760 58o4 584 9 58 9 3 2O 4o 9 .83 9 838 9 883 99 28 9973 ..18 ..63 I 9 4o 9 .855 9 38 5 9 82 6026 6071 6n5 6160 19 4i 9 .84oio8 oi53 oi 9 8 0243 0288 o333 18 4i 6204 624 9 62 9 3 6338 6382 6426 1 8 42 o3 7 8 0423 o468 o5i3 o558 o6o3 '7 42 647i 65i5 656o 66o4 6649 66g3 17 43 o648 o6 9 3 o 7 3 7 0-782 0827 0872 16 43 6 7 3 7 6782 6826 6871 6915 6 9 5 9 16 44 o 9 i 7 9 62 100-7 1052 io 97 Il42 i5 44 7 oo4 7 o48 7 o 9 3 7 i3 7 -7182 7226 i5 45 n8 7 1232 I2 77 1322 i36 7 l4l2 i4 45 7 2 7 7 3i5 7 35 9 7404 7 448 7 4 9 2 i4 46 i45 7 1502 1 54? l5 9 2 i63 7 1682 i3 46 7 53 7 7 58i 7 626 7670 77 i4 77 5g i3 47 I 7 2 7 1771 1816 1861 1906 i 9 5i 12 47 7 8o3 7 848 7 8 9 2 7936 7981 8c25 12 48 I 99 6 2o4l 2086 2l3l 2176 2221 I I 48 8o6 9 8n4 8i58 8203 8247 82 9 i II 49 2266 23ll 2355 2400 2445 24 9 IO 49 8336 838o 8424 846 9 85i3 8558 10 5o 9 842535 2 5 80 2625 26-70 2715 2760 9 5o 9 . 858602 8646 86 9 i 8735 8779 8824 9 5i 2 8o5 2 84 9 2894 2 9 3 9 2 9 84 3o2 9 8 5i 8868 8 9 I2 8 9 5 7 9 ooi 9045 9090 8 52 3o 7 4 3ii 9 3i64 320 9 3253 32 9 8 7 52 9 i34 9 i 7 8 9 223 9267 9 3n 9 356 7 53 3343 3388 3433 34 7 8 3523 3568 6 53 9 4oo 9 444 9 48 9 9 533 9 5 77 9622 6 54 36i2 365 7 3702 3 7 4 7 3 79 2 383 7 5 54 9 666 97 io 97 55 9799 9843 9888 5 55 3882 3 9 2 7 3 97 i 4oi6 4o6i 4io6 4 55 99 32 997 6 . .21 ..65 .109). i54 4 56 4i5i 4i 9 6 4241 4285 433o 43 7 5 3 56 9 .86oi 9 8 0242 028 7 o33i o3 7 5io42o 3 5 7 4420 4465 45io 4554 45gg 4644 2 5 7 o464 o5o8 o55 2 o5 9 7 o64i o685 2 58 5 9 468 9 4 9 58 4 7 34 5oo3 4779 5o48 48 2 3 5o 9 2 4868 5i3 7 5?8 2 I 58 5 9 o 7 3o o 99 5 0774 io4o 0818 io84 0862 090-7,0951 II28JII72 1217 I O 60" 50" 40" 30" 20" 10" . 60" [ 50" 40" 30" 20" j 10" a Co-tangent of 55 Degrees. & Co-tangent of 54 Degrees. .< \" 2" 3" 4" 5" 6" 7" 8" 9" .( 1" 2" 3" 4" 5" 6" 7" S" 9" in \ 5 9 14 18 23 27 32 36 41 irt l 4 9 13 18 22 27 31 36 40 LOGARITHMIC SINES. d D Sine of 36 Degrees. _ s - Sine of 37 Degrees. H 0" 10" 20" 30' 40" 50" s 0" 10" 20" | 30" 1 40" 50" o 9.769219 92489277 9 3o6 9 335 9 364i5 9 o 9-779463 9 4 9 i 9 5i 9 | 9 547 9 575 9603 5 9 i 9 3 9 3 9421 9 45o 9 47 9 9 5o8 953-7 58 i 9 63i 9 65 9 9 686 9 7i4 9742 977 58 2 9 566 9 5 9 5 9 624 9 653 9682 9711 5? 2 979 8 9 826 9 854 9 882 9910 9938 57 3 97 4o 9769 979 8 9 82 7 9 856 9884 56 3 99 66 999 3 . .21 . .4 9 77 .io5 56 4 99 i3 9942 997 i . . . . ..29 ..58 55 4 9 . 78oi33 0161 oi8 9 0216 0244 0272 55 5 9.770087 0116 oi45 0173 O202 O23l 54 5 o3oo o3 2 8 o356 o384 o4n o43 9 54 6 0260 0289 o3i8o347 0376 o4o4 53 6 0467 o4 9 5 o523 o55i o5 7 8 0606 53 7 o433 0462 o4 9 i O520 o54 9 jo577 52 7 o634 0662 o6 9 o 0718 o 7 45 077$ 52 8 0606 o635 o664 o6 9 3 072210750 5i 8 0801 o82 9 o85 7 0884 0912 0940 5i 9 0779 0808 08370866 0895 0923 5o 9 o 9 68 o 99 6 1023 io5i 1079 1107 5o 10 9.7709520981 IOIO io3 9 1067 1096 49 IO 9.781134 1162 II 9 O 1218 1246 1273 49 ii ii 2 5ii54 n83 121 I 1240)1269 48 ii i3oi i32 9 i35 7 1 384 l4l2 i44o 48 12 1298 i326 i355 1 384 i4i3 i44i 47 12 i468 i4 9 5 i523 i55i 1578 1606 47 i3 1470 1499 i5 2 8 i556 i585 1614 46 i3 i634 1662 i68 9 1717 1745 1772 46 i4 1 643 1671 1700 I 7 2 9 1758 1786 45 i4 1800 1828 i856 i883 1911 1939 45 i5 i8i5 1 844 1872 I 9 OI i 9 3oi 9 5 9 44 i5 i 9 66 i 99 4 2O22 204 9 2077 2105 44 16 1987 2016 2o45 2073 2102 2l3l 43 16 ' 2l32 2160 2188 22l5 2243 2271 43 17 2159 2188 2217 2245 2274 23o3 42 17 22 9 8 2326 2354 2 38i 2409 2437 42 18 233i 236o 238 9 2417 2446 2475 4i 18 2464 24 9 2 252O 2547 25 7 5 2602 4i I 9 25o3 2532 2 56i 258 9 2618 2646 4o i 9 263o 2658 2685 2713 2741 2768 4o 20 9 . 772675 2704 2732 2761 2790 2818 39 20 9 .7827 9 6 2823 2 85i 287 9 2906 2 9 34 39 21 2847 28 7 5 2 9 04 2 9 33 2961 2 99 38 21 2 9 6i 2 9 8 9 3017 3o44 3072 3o 99 38 22 3oi8 3o47 8076 3io4 3i33 3i6i 37 22 3127 3i54 3i8 2 3210 3 2 3 7 3 2 65 3 7 23 3190 3219 3247 32 7 6 33o4 3333 36 23 32 9 2 3320 334 7 33 7 5 34o2 343o 36 24 336i 3390 34i8 3447 34 7 6 35o4 35 24 3458 3485 35i3 354o 3568 35 9 5 35 25 3533 356i 35 9 o 36i8 364 7 36 7 5 34 25 3623 365o 36 7 8 3 7 o5 3 7 33 3 7 6o 34 26 3704 3 7 3 2 3 7 6i 3789 38i8 3846 33 26 3788 38i5 3843 3870 3898 3 9 25 33 27 38 7 5 3903 3 9 6o 3 9 8 9 4017 32 2 7 3 9 53 3 9 o 4oo8 4o35 4o63 4o 9 o 32 28 4o46 4074 4io34i3i 4i6o 4i88 3i 28 4n8 4i45 4i73 4200 4228 4255 3i 29 4217 4245 42 7 4 4302 433i 435 9 3o 2 9 4282 43io 433 7 4365 43 9 2 4420 3o 309.774388 44x6 4445 4473 45oi 453o 2 9 3o 9 . 784447 4475 45o2 452 9 455 7 4584 2 9 3i 4558 458 7 46i5464446 7 2 4700 28 3i 4612 463 9 466 7 45 9 4 4721 4 7 4 9 28 32 4729 4 7 5 7 4786 48i4'4842 48 7 i 27 32 4776 48o4 483i 4858 4886 4 9 i3 2 7 33 34 48 99 5070 4928 5098 4 9 564 9 855oi3|5o4i 5i265i55|5i835 2 i2 26 25 33 34 4 9 4i 5io5 4 9 68 5i32 4 99 5 5 1 60 5o 2 3 5187 5o5o 5 2 i4 5o 7 8 5242 26 25 35 524o 5268 52 9 7 53255353 5382 24 35 5 2 6 9 52 9 6 5324 535i 53 7 8 54o6 24 36 54io 5438 5467 54 9 5 55 2 3 5552 23 36 5433 546i 5488 55i5 5543 55 7 o 23 37 558o 56o8 563 7 5665 56 9 3 5722 22 37 55 97 5624 5652 567 9 5 7 o6 5 7 34 22 38 5 7 5o 5 77 8 58o 7 5835 5863 58 9 2 21 38 5 7 6i 5 7 88 58i6 5843 58 7 o 58 9 8 21 39 5920 5 9 48 5977 6oo5 6o33 6061 2O 39 5 9 25 5 9 52 5 979 6007 6o34 6061 2O 4o'9 776090 61186146 61756203 6 2 3i '9 4o 9.786o8 9 6116 6i43 6170 6198 6225 I 9 4i 6259 6288 63i6 63446372 64oi 18 41 6252 627 9 63o 7 6334 636i 6388 18 42 6429 645 7 6485 65i46542 65 7 o 17 42 64i6 6443 64 7 o 64 9 7 6525 6552 '7 43 44 65 9 8 6 7 68 6627 6796 6655 6824 6683 6852 6711 6880 6739 6 9 o 9 16 i5 43 44 65 7 9 6742 6606 6634 6770 6707 6661 6824 6688 685i 6 7 i5 6878 16 i5 45 6 9 3 7 6 9 65 6 99 3 7021 7o5o 7078 i4 45 6 9 o6 6 9 33 6 9 6o 6 9 8 7 7014 7042 i4 46 7106 7i34 7162 7191 7219 7247 i3 46 7o6 9 70 9 6 7123 7i5o 7177 7 2o5 !3 4 7 7275 73o3 733i 7 35 9 7388 74i6 12 47 7232 7 25 9 7286 73i3 734o 7 36 7 12 48 7444 7472 75oo 7528 7556 7 585 II 48 7 3 9 5 7422 744 9 7476 7 5o3 7 53o II 4 9 7613 764i 7 66 9 7697 77 25 77 53 IO 49 7 55 7 7 585 7612 7 63 9 7666 7693 10 5o 5i 9.777781 795o 7810 7978 7 838 8006 7866 7 8 9 4 80348062 79 22 8o 9 i | 5o 5i o. 787720 7883 7747 79 io 7774 79 3 7 7801 7964 7829 799 l 7 856 8018 1 52 8119 8i4? 8175 8203 823i 825 9 7 52 8o45 8072 8o 99 8127 8i54 8181 7 53 8287 83i5 8343 83 7 i 83 99 8427 6 53 8208 8235 8262 8 2 8 9 83i6 8343 6 54 8455 8483 85n 853 9 856 7 85 9 5 5 54 83 7 o 83 9 7 8424 845 1 8478 85o5 5 55 8624 8652 8680 870818736 8 7 64 4 55 8532 855 9 8586 86i3 864o 8667 4 56 8792 8820 8848 8876180.04 8 9 3 2 3 56 86^8721 8748 8 77 5 8802 88 29 3 57 8960 8988 9 oi6 9 o44 9 7 2 9 ioo 2 57 8856 8883 8 9 io 8 9 3 7 8 9 648 99 i 2 58 9128 9 i56 9 i83 9 2II 9 23 9 9 26 7 I 58 9 oi8 9 o45 9 072 9099 9126 91 53 I 59 9 2 9 5 9 3 2 3 9 35i 93799407 9 435 5 9 9 i8o 9 2O7' 9 234! 9 26i 9 288 9 3i5 o 60" 50" 40" 30" 20" 10" d 60" 50" 40" i 30" 20" 10" Co-sinb of 53 Degrees. Co-sine of 52 Degrees. % P Parti l " 2// 3 " 4 " 5" 6" 7" 8" 9" p p A \" 2" 3" 4" 5" 6" 7" 8" 9" l.rartj 3 6 9 n 14 17 20 23 26 m \ * 5 8 11 14 16 19 22 25 LOGARITHMIC TANGENTS. .s Tangent of 36 Degrees. Tangent of 37 Degrees. m 0" 10" 20" 30" 40" 50" s 0" 10" 20" 30" 40" 50" 9.861261 i3o5 i35o i3 9 4 i438 1482 5 9 O 9-877114 7 i58 7 202 7 246 7290 7 333 5 9 1 1527 1571 1616 :65 9 1704 1748 58 I 7 3 77 7 42I 7 465 7 5o 9 7 552 7 5 9 6 58 2 1792 1837 1881 I 9 25 i 9 6 9 2Ol4 5 7 2 7640 7 684 7?2 8 777 i 7 8i5 7 85 9 5 7 3 2o58 2102 2!46 2 I 01 2235 227 9 56 3 79 3 7947 799 8o34 8078 8122 56 4 2323 2368 2412 s456 25oo 2545 55 4 8i65 8209 8253 8 297 834i 8384 55 5 2689 2633 2677 2721 2766 2810 54 5 8428 8472 85i6 855 9 86o3 864 7 54 6 2854 2898 2 9 43 2 9 8 7 3o3i 3075 53 6 86 9 i 8 7 34 8 77 8 8822 8866 8 9 o 9 53 7 3119 3i64 3208 3 2 52 32 9 6 334i 52 7 8 9 53 8 997 9041 9 o85 9128 9 I 7 2 52 8 3385 3429 3473 35i 7 3562 36o6 5i 8 9216 9260 9 3o3 9 34 7 9 3 9 i 9 435 5i 9 365o 36 9 4 3 7 38 3 7 83 3827 3871 5o 9 9478 9522 9 566 9 6o 9 9 653 9 6 97 5o 10 9.863 9 i5 3 9 5 9 4oo4 4o48 40 9 2 4i36 49 10 9-879741 9784 9828 9 8 7 2 99 i6 99 5 9 4 9 ii 4i8o 4225 4269 43i3 4357 44oi 48 ii 9 .88ooo3 0047 0091 oi34 0178 O222 48 12 4445 44 9 o 4534 45 7 8 4622 4666 47 12 0265 oSog o353 o3 97 o44o o484 47 i3 4710 4755 4799 4843 4887 4 9 3i 46 i3 o528 o5 7 i o6i5 o65 9 0703 o 7 46 46 i4 4 97 5 5O2O 5o64 5io8 5i5 2 5i 9 6 45 i4 07 9 o o834 o8 77 9 2I o 9 65 1008 45 i5 5240 5285 5329 53 7 3 54i7 546i 44 i5 IO52 1096 n4o n83 1227 1271 44 16 55o5 554 9 55 9 4 5638 568 2 5 7 26 43 16 i3i4 i358 1402 i445 i48 9 i533 43 |7 5770 58i4 5858 5' 9 o3 5 9 4 7 5 99 i 42 1 7 i5 77 1620 1 664 I 7 o8 1751 i 79 5 42 18 6o35 6o 79 6i23 6167 6211 6256 4i 18 i83 9 1882 1926 I 97 20l3 2067 4i J 9 63oo 6344 6388 6432 64 7 6 6520 4o J 9 aioi 2i44 2188 2232 2275 23i 9 4o 20 9.866564 66o 9 6653 66 9 7 6741 6 7 85 3 9 20 9 . 882363 2406 245o 2494 253 7 2 58i 3 9 21 6829 68 7 3 6917 6 9 6i 7006 7o5o 38 21 2625 2668 2 7 I2 2 7 56 2 799 2843 38 22 7094 7 i38 7182 7226 7270 73i4 37 22 2887 2930 2 97 4 3oi8 3o6i 3io5 37 23 7358 7402 7446 74 9 i 7 535 7 5 79 36 23 3i48 3192 3 2 36 32-79 3323 336 7 36 24 7623 7667 7711 77 55 7799 7843 35 24 34io 3454 3498 354i 3585 3628 35 25 7887 79 3i 797 5 8oi 9 8o64 8108 34 25 36 7 2 3 7 i6 3 7 5 9 38o3 3847 38 9 o 34 26 8i52 8i 9 6 8240 8284 8328 83 7 2 33 26 3 9 34 3 977 4O2I 4o65 4io8 4i5 2 33 27 84i6 846o 85o4 8548 85 9 2 8636 32 2 7 4i 9 6 423 9 4283 4326 43 7 o 44i4 32 28 8680 8724 8768 88i3 885 7 8 9 oi 3i 28 445 7 45oi 4544 4588 4632 46 7 5 3i 29 8 9 45 8 9 8 9 9 o33 977 9 I2I 9 i65 3o 2 9 4719 4-762 48o6 485o 48 9 3 4 9 3 7 3o 3o 0.860209 9 253 9 2 97 9 34i 9 385 9 42 9 2 9 3o 9 .884 9 8o 5o24 5o68 5m 5i55 5i 9 8 2 9 3i 94 7 3 9 5l 7 9 56i 9 6o5 9 64 9 9 6 9 3 28 3i 5242 5286 532 9 53 7 3 54i6 546o 28 32 9?3? 9781 9 825 9 86 9 99 i3 99 5 7 27 32 55o4 554 7 55 9 i 5634 56 7 8 5721 27 33 9.870001 oo45 oo8 9 oi33 0177 O22I 26 33 5 7 65 58o 9 5852 58 9 6 5 9 3 9 5 9 83 26 34 O265 oSog o353 o3 97 o44i o485 25 34 6026 6o 7 o 6n4 6i5 7 6201 6244 25 35 0529 o573 0617 0661 0705 074 9 24 35 6288 633i 63 7 5 64i 9 6462 65o6 24 36 o 79 3 683 7 0881 6 9 25 o 9 6 9 ioi3 23 36 654 9 65 9 3 6636 6680 6723 6767 23 3? 1057 IIOI n45 u8 9 1233 1277 22 37 6811 6854 68 9 8 6 9 4i 6 9 85 7028 22 38 1321 i365 i4o 9 i453 i4 9 7 i54i 21 38 7072 7116 7 i5 9 7 2O2 7246 72 8 9 21 3 9 i585 1629 i6 7 3 1717 1761 i8o5 2O 3 9 7 333 7377 7 420 7 464 7 5 7 7 55i 2O 4o 9.871849 1893 i 9 3 7 i 9 8o 2024 2068 1 9 4o 9 .8875 9 4 7 638 7 68i 7725 7768 7812 I 9 4i 2112 2i56 230O 2244 2288 2332 18 4i 7 855 7 8 99 79 42 7986 8o2 9 8o 7 3 18 42 2376 2420 2 464 25o8 2552 25 9 6 17 42 8116 8160 8203 8247 82 9 I 8334 1 7 43 264o 2684 2727 2771 2815 285 9 16 43 83 7 8 8421 8465 85o8 8552 85 9 5 16 44 29O3 2947 2 99 I 3o35 3079 3i23 i5 44 863 9 8682 8-726 8769 88i3 8856 16 45 3i6 7 3211 3255 32 99 3342 3386 i4 45 8 9 oo 8 9 43 8 9 8 7 9o3o 9 Q74 9117 i4 46 343o 3474 35i8 3562 36o6 365o i3 46 9161 9 204 9 248 9291 9 334 9378 i3 4? 36 9 4 3 7 38 3781 38 2 5 386 9 3 9 i3 12 47 9421 9 465 9 5o8 9552 9 5 9 5 9 63 9 12 48 3 9 5 7 4ooi 4o45 4o8 9 4i33 4177 II 48 9682 97 26 9769 9813 9 856 9900 II 49 4220 4264 43o8 4352 43 9 6 444o 10 49 9943 99 8 7 ..3o .. 7 4 .117 .160 10 5o 9,874484 4528 45 7 2 46i5 465 9 47o3 9 5o 9.890204 024 7 02 9 I o334 0378 O42I 9 5i 4747 4791 4835 487 9 4 9 23 4 9 66 8 5i o465 o5o8 o552 o5 9 5 o63 9 0682 8 52 5oio 5o54 5o 9 8 5i42 5i86 523o 7 52 O 7 25 o 7 6 9 0812 0856)0899 o 9 43 7 53 52 7 3 53i 7 536i 54o5 544 9 54 9 3 6 53 0986 io3o io 7 3 1116 1160 1203 6 54 553 7 558o 5624 5668 5712 5756 5 54 1247 1290 i334 i3 77 1421 1 464 5 55 58oo 5843 588 7 5 9 3i 5 97 5 6oi 9 4 55 1507 i55i i5 9 4 i638 1681 1725 4 56 6o63 6107 6i5o 6i 9 4 6 2 38 6282 3 56 1768 1811 i855 1898 I 9 42 i 9 85 3 5 7 6326 6370 64i3 645 7 65 OI 6545 2 57 2028 2O 7 2 2Il5 2i5 9 22O2 2246 a 58 6589 6632 6676 6720 6 7 64 6808 I 58 2289 2332 23 7 6 2419 2463 25o6 i 5 9 6852 68 9 5 6 9 3 9 6 9 83 7027 7071 O 5 9 2549 25g3 2636 2680 2723 2766 o 60" 50" 40" 30" 20" 10" , 60" 50" 40" 30" 20" | 10" . Co-tangent of 53 Degrees. 1 Co-tangent of 52 Degrees. S p p .< 1" 2" 3" 4" 5" 6" 7" 8" 9" , I" 2 " 3" 4" 5" 6" 7" 8" 9" lrt { 4 9 13 18 22 26 31 35 40 J.-fartj 4 9 13 17 22 26 31 35 39 LOGARITHMIC SINES. .a Sine of 38 Degrees. _g Sine of 39 Degrees. m 10" 20" 30" 40" 50" % 0" 10" 20" 30" | 40" 50" 9. 789342 9 36 9 9 3 9 6; 9 423 9 45o' 9 4 77 5 9 O 9.798872 8898 8 9 24 8 9 5o8 9 76 9002 5 9 I 9604 9 53i 9 55 7 9 584 9 6i i 9 638 58 I 9028 9064 9 o8o 9 io6 9 i32 9168 58 2 9666 9692 97x0074607739800 67 2 9184 9210 9 236 9 262 9 2&7 9 3i3 57 3 9827 9 854 ! 9 88o 9907 9934 9961 56 3 9 33 9 9365 9 3 9 i 9 4i7 9 443 9469 56 4 9988 ,.x5..4a .,6 9 .. 9 6 . 122 55 4 949519621 9 54 7 9 5 7 3 9 5 99 9626 55 5 9-7 9 oi4 9 0176:0203 O23o 0267 0284 54 5 9661 9677 97 o3 9 728 97 54 9-780 54 6 o3io o337o364o3 9 i o4i8 o445 53 6 9806 9 83 2 9 858 9 884 9910 9936 53 8 0471 o632 o4 9 8 o65 9 0626 0686 0662 0679 071310740 0606 0767 52 5i 8 9962 9.8001 17 9987 oi43 oi6 9 ..3 9 oi 9 5 ..65 O220 ..91 0246 52 5! 9 0793 08200847 0874 0901 0927 5o 9 0272 0298 o324 o35o o3 7 6 o4oi 5o 10 9.790954 0981 1008 io34 1061 1088 49 IO 9.800427 o453 o479 0606 o53i o556 49 ii xxx5 1142 1168 1 196 1222 1249 48 ii 0682 0608 o634 0660 0686 7 I I 48 12 1276 1302 1329 i356 1382 1409 47 12 o 7 3 7 o 7 63 o 7 8 9 0816 o84o 0866 47 i3 i436 i463 1489 1616 i543 1670 46 i3 0892 0918 o 9 44 o 9 6 9 0996 1021 46 i4 i5 9 6 1623 i65o 1676 1703 1730 45 U 1047 1073 io 9 8 1124 1 160 n 7 6 45 i5 1767 i 7 83 1810 i83 7 i863 1890 44 16 1201 1227 1263 I2 79 i3o5 i33o 44 16 I 9 i7 i 9 43 1970 1997 2024 2060 43 16 i356 1 382 i4o8 1433 i45 9 i486 43 17 2077 2104 2i3o 2167 2184 22IO 42 17 i5n 1 536 1662 1 588 i6i3 i63 9 42 18 2237 2264 2290 2317 2344 2370 4i 18 1666 1691 1716 1742 i 7 68 i 79 4 4i 19 2 3 97 2423 2460 2477 25o3 253o 4o 19 1819 1846 1871 i8 9 6 1922 1948 4o 20 21 9 . 79 255 7 2716 2 583 2 7 43 2610 2636 2770 2796 2663 2823 2690 2849 3 9 38 20 21 9 .8oi 9 73 2128 1999 2i53 2026 2I 79 2061 2206 2O 7 6 223O 2102 2256 3 9 38 22 2876 2 9 o3 2929 2966 2982 3009 3 7 22 2282 2307 2333 235 9 2384 24lO 37 23 3o35 3o62 3o8 9 3n5 3 1 42 3i68 36 23 2436 2461 2487 2612 2538 2564 36 24 3i 9 5 3222 3248 32 7 5 33oi 3328 35 24 2 58 9 2616 2641 2666 2692 2 7 l8 35 25 3354 338i 3407 3434 346o 348 7 34 25 2743 2769 27 9 4 2820 2846 28 7 I 34 26 35i4 3540 3667 35 9 3 3620 3646 33 26 2 8 97 2922 2 9 48 2 9 74 2999 3o 2 5 33 2 7 36 7 3 36 99 3726 3 7 52 3 779 38o5 32 27 3o5o 3076 3lO2 3l2 7 3i53 3i 7 8 32 28 3832 3858 3885 3911 3 9 38 3 9 64 3i 28 32o4 3229 3255 3281 33o6 3332 3i 2 9 3 99 i 4oi 7 4o44 4070 4097 4123 3o 29 335 7 3383 34o8 3434 345 9 3485 3o 3o 3i 9 . 79 4i5o 43o8 4i 7 642o3 4335436i 4229 4388 4255 44i4 4282 444 1 2 9 28 3o 3i 9 .8o35n 3664 3536 3689 3562 3 7 i5 3687 3?4o 36i3 3 7 66 3638 3 79 i 2 9 28 32 446 7 44 9 3 4620 4546 45 7 3 45 99 27 32 38i 7 3842 3868 38 9 3 3 9 i 9 3 9 44 2 7 33 4626 4652 46 7 8 4706 473i 47*8 26 33 3 97 o 3 99 5 4021 4o46 4o 7 2 409-7 26 34 4784 48io483 7 4863 4890 4 9 i6 25 34 4123 4i48 4i?4 4199 4226 4260 26 35 4 9 42 4 9 6 9 4996 5022 5o48 5o 7 4 24 35 4276 43oi 432 7 4352 43 77 44o3 24 36 5ioi 5i2 7 5i54 5i8o 6206 5 2 33 23 36 4428 4454 4479 45o5 453o 4556 23 37 5 2 5 9 6286 53i2 5338 5364 53 9 i 22 3-7 458i 4607 4632 465 7 4683 4 7 o8 22 38 54i7 5443 54 7 o 5496 5522 554 9 21 38 4734 4769 4784 48io 4835 486i 21 3 9 55 7 5 56oi 6628 5654 568o 6707 2O 3 9 4886 4 9 I2 4 9 3 7 4962 4988 5oi3 2O 4o 9.796733 5 7 5 9 5 7 86 6812 5838 5865 I 9 4o 9.806039 5o64 5o8 9 5n5 5i4o 5i65 J 9 4i 6891 5 9 i 7 5 9 43 6970 5 99 6 6022 18 4i 6191 6216 6242 6267 6292 53i8 18 42 6049 6o 7 5 6101 6127 6i54 6180 '7 42 5343 5368 53 9 4 5419 5444 54 7 o 17 43 6206 6233 6269 6286 63n 6338 16 43 54 9 5 6620 5546 55 7 i 55 97 6622 16 44 6364 63 9 o64i66443 6469 64 9 5 i5 44 6647 56 7 3 56 9 8 5 7 23 5 7 48 5 77 4 16 45 6621 654 7 65 7 4 6600 6626 6662 i4 45 6799 6824 585o 58 7 5 6900 6926 i4 46 6679 6 7 o5 6 7 3i 6767 6783 6810 i3 46 5 9 5i 5 97 6 6002 602-7 6062 6o 77 i3 47 6836 6862 6888 6 9 i4 6941 6 9 67 12 47 6io3 6128 6i53 6179 6204 6229 12 48 6 99 3 7 oi 9 7045 7072 7098 7124 II 48 6264 6280 63o5 633o 6355 638i II 49 7 i5o 7 I 7 6 7 202 7229 7255 7281 IO 49 64o6 643 1 6456 6482 65o 7 6532 10 5o 9.797307 7 333 7 3 5 9 7 386 7412 7438 9 5o 9 . 806667 6583 6608 6633 6658 6684 9 5i 7464 7 4 9 o 7 5i6 7642 7669 7 5 9 5 8 5i 6 79 6 7 34 6 7 5 9 6 7 85 6810 6835 8 52 7621 7 64 7 76737699 7725 7761 7 62 6860 6885 6 9 n 6 9 36 6961 6986 7 53 7777 7 8o4 783oJ7856 7882 7908 6 53 7011 7 o3 7 7062 7 o8 7 7 II2 7 i3 7 6 54 79 34 79 6o 79 86 8012 8o38 8o65 5 54 7i63 -7188 7213 7 238 7 263 7288 5 55 56 5 7 8091 8247 84o3 8n 7 8i43 8i6 9 8i 9 5'822i 82 7 382 99 !8325835i 83 77 842 9 8455 848il85o8 8534 4 3 2 55 56 57 7 3i4 7465 7616 7339 7490 7 64i ?364 7616 7666 7 38 9 7 54o 7 6 9 i 74i4 7 565 77 i6 743 9 -7690 774i 4 3 2 58 856o 858686128638 86648690 I 58 7766 779 i 78167842 7 86 7 7 8 9 2 I 5 9 8716 8-742 87688794 8820 8846 O 5 9 7917 7942 79 6 7 7992 8017 8042 o 60" 50" I 40" | 30" 20" 10" S" 60" 50" j 40" 30" 20" i 10" e - Co-sine of 51 Degrees. S, Co'Sine of 50 Degrees. S f i// nil o/ P Part) 4" 5" 6" 7" 8" 9" .$ 1" 2" 3" 4" 5" 6" 7" 8" 9" l \ 3 5 8 11 13 16 19 21 24 iri j 3 5 8 10 13 15 18 20 23 LOGARITHMIC TANGENTS. J Tangent of 38 Degrees. .s Tangent of 39 Degrees. s 0" 10" 20" ] 30" 40" 50" si 0" 10" 20" 30" 40" 50" 9.892810 2853 28 9 7 2 9 40 2983 3O27 r o 9 . 9 o836 9 8412 8455 84 9 8 854i 8584 5 9 I 3070 3u4 3i5 7 32OO 3244 3a8 7 58 I 8628 8671 8714 8 7 5 7 8800 8843 58 2 333i 33 7 4 34i7 346i 35o4 3547 57 2 8886 8929 8972 9 oi5 9 o58 9101 $7 3 35 9 i 3634 3678 3721 3 7 64 38o8 56 3 9i44 9187 9230 9 2 7 3 9 3i6 9 35 9 56 4 385i 38 9 4 3 9 38 3 9 8i 4o25 4o68 55 4 9402 9445 9 488 9 53i 9 5 7 4 9 6l 7 55 5 4i 1 1 4i55 4198 4241 4285 43 2 8 54 5 9660 973 9 746 9789 9 832 9 8 7 5 54 6 43 7 2 44i5 4458 45o2 4545 4588 53 6 9918 9961 ...5 ..48 .. 9 i .i34 53 7 4632 46 7 5 4 7 i8 4762 48o5 4848 52 7 9.910177 O220 0263 o3o6 o34 9 o3 9 2 52 8 4892 4 9 35 4979 5022 5o65 5 1 09 5i 8 o435 0478 O52I o564 0607 o65o 5i 9 5i5 2 5i 9 5 523 9 5282 53 2 5 536 9 5o 9 0693 o 7 36 779 0822 o865 o 9 o8 5o 10 9.895412 5455 54 99 i5542 5585 5629 4 9 10 9.910951 0994 1037 1080 1123 1 166 4y ii 5672 5 7 i5 5 7 5 9 58o2 5845 588 9 48 ii 1209 1252 I2 9 5 i338 i38i i424 48 12 5 9 32 5 97 5 6oi 9 6062 6io5 6149 47 12 1467 i5io i553 i5 9 6 i63 9 1682 47 i3 6192 6235 6278 6322 6365 64o8 46 i3 1725 1768 1810 i853 i8 9 6 i 9 3 9 46 i4 6452 6495 6538 6582 66 2 5 6668 45 i4 1982 2025 2068 21 II 2i54 2I 97 45 15 6712 6 7 55 6 79 8 6842 6885 6928 44 i5 2240 2283 2326 236 9 |24l2 2455 44 16] 6971 7Oi5 7 o58 7101 7i45 7188 43 16 2498 254i 2584 262 7 ]26 7 2713 43 17 7231 7 2 7 5 7 3i8 736i 74o4 7448 42 I? 2756 2799 2842 26862928 2 97 I 42 18 7491 ?534 7 5 7 8 7621 7 664 7707 4i 18 3oi4 3o57 3ioo 3i43 3i85 3228 4i *9 77 5i 7794 7 83 7 7881 7924 7967 4o J 9 3271 33i4 335 7 34oo 3443 3486 4o 20 9.898010 8o54 8o 97 8i4o 8i83 8227 3 9 20 9.913529 3572 36i5 3658 3701 3744 3 9 21 8270 83i3 835 7 84oo 8443 8486 38 21 3 7 8 7 383o 38 7 3 3 9 i6 3 9 5 9 4ooi 38 22 853o 8573 8616 865 9 8 7 o3 8 7 46 37 22 4o44 4o8 7 4i3o 4i 7 3 4216 425 9 37 23 8789 8832 88 7 6 8919 8962 gooS 36 23 4302 4345 4388 443 1 4474 45i 7 36 24 9049 9092 9 i35 9178 9222 9 265 35 24 456o 46o3 4645 4688 473i 4774 35 25 9308 935i 9 3 9 5 9 438 9 48i 9 5 2 4 34 25 48i 7 486o 4 9 o3 4 9 46 4989 5o32 34 26 9 568 9611 9 654 9697 97 4i 97 84 33 26 5o 7 5 5ii8 5i6i 5 2 o3 5246 5289 33 27 0827 0870 QQl4 QC)57 43 32 27 5332 5375 54i8 546 1 55o4 5547 32 * / 28 v / 9.900087 v / oi3o yy.n4 0173 77 / 02l6 025 9 o3o3 3i * 1 28 55 9 o 5633 56 7 5 5 7 i8 5761 vs^x 44. i 58o4 3i 20 o346 o38 9 0432 0476 o5i 9 o562 3o 2 9 5847 5890 5 9 33 5 97 6 6019 6062 3o 3o 9.900605 o648 o6 9 2 o 7 35 0778 0821 2 9 3o 9.916104 6i47 6i 9 o 6233 6276 63 I9 29 3i 0864 o 9 o8 o 9 5i 0994 1037 1081 28 3i 6362 64o5 6448 64 9 i 6533 65 7 6 28 32 1124 1167 I2IO 1253 I2 9 7 i34o 27 32 6619 6662 6705 6 7 48 6791 6834 2 7 33 i383 1426 i46 9 i5i3 i556 i5 99 26 33 6877 6919 6 9 62 7005 7 o48 7091 26 34 1642 i685 T 7 2 9 1772 i8i5 i858 25 34 7i34 7177 7220 7262 7 3o5 7348 25 35 1901 i 9 44 i 9 88 2031 2074 2117 24 35 7 3 9 i 7434 7477 7520 7563 7 6o5 24 36 2160 2204 2247 2290 2333 23 7 6 23 36 7 648 7691 7734 7777 7820 7 863 23 3? 2420 2463 2 5o6 2549 25 9 2 2635 22 37 7906 7948 799 l 8o34 8077 8120 22 38 2679 2722 2765 2808 285i 28 9 4 21 38 8i63 8206 8248 820.1 8334 83 77 21 3 9 2 9 38 2 9 8i 3o24 3o6 7 3no 3i53 2O 3 9 8420 8463 85o6 8548 8591 8634 2O 4o 9.903197 324o 3283 33 2 6 336 9 34i2 I 9 4o 9.918677 8720 8 7 63 88o5 8848 88 9 i T 9 4i 3456 34 99 3542 3585 3628 36 7 i 18 4i 8 9 34 8977 9020 9 o63 9io5 9 i48 18 42 37i4 3 7 58 38oi 3844 388 7 3 9 3o I 7 42 9191 9 234 9277 9 320 9362 9 4o5 1 1 43 3 97 3 4oi6 4o6o 4io3 4i46 4i8 9 16 43 9448 9491 9 534 9 5 77 9619 9662 16 44 4232 42 7 5 43i8 4362 44o5 4448 i5 44 9705 9748 9791 9 8S4 9876 99 i 9 i5 45 449i 4534 45 77 4620 4663 4707 i4 45 9962 ...5 . 48 .. 9 i .i33 . 176 i4 46 475o 4793 4836 48 79 4 9 22 4 9 65 i3 46 9.920219 0262 o3o5 o348 oSgo o433 i3 4? 5oo8 5o5 2 5o 9 5 5i38 5i8i 5224 12 47 0476 oSig 0062 o6o4 0647 0690 12 48 5267 53io 5353 53 97 544o 5483 II 48 o 7 33 0776 0819 0861 0904 0947 II 49 55 2 6 556 9 56i2 5655 6698 574i 10 49 0990 io33 1075 1118 1 161 1204 IO 5o 9.905785 58 2 8 5871 5 9 i4 5 9 5 7 6000 9 5o 9.921247 1289 i33 2 i3 7 5 i4i8 i46i 9 5i 6o43 6086 6129 6172 6216 625 9 8 5i i5o3 1 546 i58 9 i632 i6 7 5 1717 8 52 63o2 6345 6388 643i 6474 65i 7 7 52 1760 i8o3 i846 i88 9 1931 i 9 74 7 53 656o 66o3 6646 6690 6 7 33 6776 6 53 2017 2060 2103 2i45 2188 223l 6 54 6819 6862 6905 6 9 48 6991 7034 5 54 2274 2 3i6 2 35 9 2402 2445 2488 5 55 7077 7120 7i63 7207 7 25o 7 2 9 3 4 55 2 53o 2 5 7 3 2616 2 65 9 2702 2 7 44 4 56 7336 7 3 79 7422 7465 75o8 7 55i 3 56 2787 283o 2873 2 9 l5 2958 3ooi 3 5? 7 5 9 4 7 63 7 7680 7723 7766 7 8o 9 2 57 3o44 3087 3i2 9 3172 32i5 3 2 58 2 58 7853 7896 79 3 9 7982 8025 8068 I 58 33oo 3343 3386 342 9 347i 35i4 I 5 9 Bin 8i54 8i 97 8240 8283 8326 5 9 355 7 36oo 3642 3685 3728 3 77 i O 60" 50" 40" 30" 20" 10" CJ 60" 50" 40" 30" 20" 10" j Co-tangent of 5 1 Degrees. s Co-tangent of 50 Degrees. s p p a %t 5 *" 2 " 3 " 4 " 5 " 6// 7 " 8// 9 " . < I" 2" 3" 4" 5" 6" 7" 8" 9" 1 lrl { 4 9 13 17 22 26 30 35 39 irt \ 4 9 13 17 21 26 30 34 39 64 LOGARITHMIC SINES. g- Sine of 40 Degrees. J Sine of 41 Degrees. 5 0" 10" 20" ! 30" 40" 50" S 0" 10" 20" 30" | 40" 50" 9 . 808067 8o 9 3 8u88i43 8168 8i 9 3 5 9 O 9 .8i6 9 43 6 9 6 7 6991 7 0l6 7 o4o 7 o64 5 9 I 8218 824382688293:83188343 58 I 7088 7 I 12 7 i3 7 -7161 7 i85 -7209 58 2 8368 8393 8419 8444 8469 8494 57 2 7 233 7 258 7 282 7 3o6 7 33o 7 354 57 3 85i 9 8544 8569859^ 8619 8644 56 Q 7379 74o3 7 42 7 7 45i 7 4 7 5 7499 56 4 866 9 8694 8-719 8744.8769 8 79 4 55 l\ 7 524 7 548 7 5 ? 2 7 5 9 6 -7620 7644 55 5 8819 8844886988948919 8944 54 5 -7668 7 6 9 3 7717 77 4i 7765 7789 54 6 8969 8994 9019 9044 9069 9 o 9 4 53 6 7 8i3 7 83 7 7862 7 886 79 10 7934)53 7 9119 9144 9169 9194 9219 9244 52- 7 7958 -7982 8006 8o3o 8o55 8o 79 52 8 9269 9294 9319 9344 9369 9394 5i 8 8io3 812-7 8i5i 8i 7 5 8199 8223 5i 9 9419 9444 9469 9494 9 5i 9 9 544 5o 9 8 2 4 7 82 7 2 8296 8320 8344 8368 5o 10 9.809569 9594 9619 9643:9668 9 6 9 3 4 9 10 9.818392 84i6 844o 8464 8488 85i2 4 9 ii 9718 97 43 97 68 9 79 3 9 8i8 9 843 48 ii 8536 856o 8584 86o 9 8633 865 7 48 12 i3 9868 9.810017 9893 9918 99 43'9 9 6 7 0042 oo6 7 0092;! 1 7 9992 Ol42 47 46 12 i3 8681 8825 8 7 o5 8849 8729 88 7 3 8 7 53 8897 8777 8921 8801 8 9 45 47 46 i4 0167 0191 O2l6 t O24l 0266 0291 45 i4 8969 8 99 3 9017 9041 9065 9089 45 i5 o3i6 634xo366 o3 9 o o4i5 o44o 44 i5 9113 9i3 7 9161 9i85 9209 9233 44 16 o465 0490 o5i5 o54o o564 o58 9 43 16 9 25 7 9281 9 3o5 9 32 9 9353 9377 43 17 0614 06390664 0689 o 7 i3 o 7 38 42 17 9 4oi 9425 9 449 9 4 7 3 9497 9521 42 18 o 7 63 078808*3 o838 0862 o88 7 4i 18 9 545 9 56 9 9 5 9 3 9 6i 7 9641 9665 4i *9 0912 093-7 0962 0986 ion io36 4o '9 9689 97 i3 9737 97 6i 9785 9809 4o 20 9 811061 1086 mo n35 1 1 60 u85 39 20 9.819832 9856 9880 99 o4 9928 99 5 2 39 21 1210 1234 1259 1284 1 309 1 334 38 21 99 7 6 . . . . ..24 ..48 .. 7 2 .. 9 6 38 22 i358 i383 i4o8 i433 i45 7 1482 37 22 9.820120 oi43 oi6 7 oi 9 i 02l5 0239 37 23 1507 i532i556 i58i 1606 i63i 36 23 0263 028-7 o3n o335 0359 o382 36 24 i655 1680 I 7 o5 i 7 3o i 7 54 i 779 35 24 o4o6 o43o o454 o4 7 8 o5o2 o5 2 6 35 25 26 1804 1952 1828 i853'i8 7 8 19-7-7 200112026 1903 2o5i 1927 20-76 34 33 25 26 o55o 0693 o5 7 3 7 I 7 o5 97 o 7 4o 0621 o 7 64 0645 o 7 88 0669 0812 34 33 2 7 28 2IOO 2248 2125 2l5o!2I 7 4 2273 2298;2322 2199 2224 234 7 J23 7 2 32 3i 27 o836 979 0860 ioo3 o883 1026 090-7 io5o 0931 io 7 4 o 9 55 io 9 8 32 3i 9 23 9 6 2421 2446 2470 2495 J252O 3o 29 1122 n46 1 169 n 9 3 I2I 7 1241 3o 3o Q. 812544 2569 2594 2618 26432668 29 3o 9.821265 1288 l3l2 i336 i36o 1 384 29 3i 2692 2 7 I 7 2 7 42 2 7 66 2791 28i5 28 3i i4o 7 i43i i455 1479 i5o2 i526 28 32 2840 2865 2889 2914 2939 2963 27 32 i55o i5 7 4 i5 9 8 1621 i645 1669 2 7 33 2988 3oi2 3o3 7 3o62 3o86 3m 26 33 1693 1-716 i 7 4o i 7 64 i -788 1811 26 34 3i35 3!6o3i85 3209 3234 3258 25 34 i835 1869 i883 1906 1930 1954 25 35 3283 33o 7 3332335 7 338i 34o6 24 35 I9 77 2001 2025 204 9 20-72 20 9 6 24 36 343o 3455 34 7 9 35o4 352 9 ! 3553 23 36 ei2o 2i44 216-7 2191 22l5 2238 23 37 3578 36o2 362 7 365i 36 7 6 3 7 oo 22 37 2262 2286 2309 2333 235 7 2 38 1 22 38 3725 3 7 49 3 77 4 3 799 3823 3848 21 38 2404 2428 2452 2 4 7 5 2499 2523 21 3 9 38 7 2 389-73921 3946 3970 3995 2O 39 2546 25 7 O 2 5 9 4 261-7 2641 2665 2O 4o 9.814019 4o44 4o68 40934117 4142 '9 4o 9.822688 2 7 I2 2 7 36 2 7 5 9 2 7 83 280-7 19 4i 4i66 4191 42i5 424042644289 18 4i 283o &854 28 7 8 2901 2925 2 9 48 18 42 43x3 43384362|438 7 |44n 4436 i 7 42 2 97 2 2996 3oi 9 3o43 3o6 7 3o 9 o 17 43 446o 4484 45o 9 4533 45584582 16 43 3n4 3i3 7 3i6i 3i85 32o8 3232 16 44 46o 7 463i 4656 468o 47044729 i5 44 3255 32 79 33o3 3326 335o 33 7 3 i5 45 4753 4 77 848o2 482-7 485 1 48 7 6 i4 45 33 9 7 342i 3444 3468 3491 35i5 i4 46 4900 4924 4949 4973 499 8 5022 i3 46 353 9 3562 3586 3609 3633 3656 i3 47 5o46 5o 7 i 6095 5l20 5i44 5i68 12 47 368o 3 7 o4 3 7 2 7 3 7 5i 3 77 4 3 79 8 12 48 49 5i 9 3 533 9 52I 7 5242 5266 53645388|54i2 5290 543 7 53i5 546i II IO 48 49 382i 3 9 63 3845 3986 3868 4oio 38 9 2 4o33 3 9 i5 4o5 7 3 9 3 9 4o8o II IO 5o 9 .8i5485 55io5534i5558 5583 5607 9 5o 9.824104 412-7 4i5i 4i 7 4 4198 4221 9 5i 5632 5656 568o 5 7 o5 5729 5753 8 5i 4245 4268 42 9 2 43i5 433 9 4362 8 52 5 77 8 58o2 5826 585i 58 7 5 58 9Q 7 52 4386 4409 4433 4456 448o 45o3 7 53 54 5924 6069 5g48 59-72 599616021 6o45 609461186142 616-76191 6 5 53 54 452 7 4668 455o 46 9 i 45 7 4 45 9 7 4 7 38 4621 4 7 6i 4644 4 7 85 6 5 55 62i5 6240 6264 6288:6312 633 7 4 55 48o8 4832 4855 48 79 4 9 02 4926 4 56 636i 6385 64o 9 '6434 6458 6482 3 56 4949 49 7 2 4 99 6 5o43 5o66 3 57 58 5 9 65o 7 665 2 6 79 8 653i.6555j6579 66o4 6628 66 7 6 6 7 oi 6 7 25i6 7 4 9 6 77 3 6822 6846 687016894 6919 2 I O 57 58 5 9 5090 523o 53 7 i 5n3 5254 53 9 4 5i36 52 77 54i 7 5i6o 53oo 544i 5i83 5324 5464 52O 7 534 7 5488 2 I O 60" 50" ; 40" 30" | 20" , 10" c 60" 50" j 40" 30" 20" 10" fl Co-sine of 49 Degrees. 1 Co-sine of 48 Degrees. P. Part J 2 5 7 10 5" 6" 7" 12 15 17 8" 9" 20 22 p p . $ 1" 2" 3" 4" 5" 6" 7" A" 9" r*\ 25 7 10 12 14 17 19 21 LOGARITHMIC TANGENTS. .5 Tangent of 40 Degrees. .S Tangent of 41 Degrees. i 0" 10" 20" 30" 40" 50" i 0" 10" 20" 30" 40" 50" o 9.923814 3856 38 99 3942 3 9 85 402 7 59 o 9.939163 9206 9 248 9291 9 333 9 3 7 6 5 9 i 4070 4n3 4i56 4198 424i 4284 58 I 94i8 946 1 95o3 9 546 9 588 9 63i 58 2 432 7 436 9 44i2 4455 4498 4540 5 7 2 9 6 7 3 9716 97 58 9801 9 843 9886 57 3 4583 4626 466 9 4711 4 7 54 4797 56 3 9928 9971 ..i3 ..56 ..98 .141 56 4 484o 4882 4925 4968 Son 5o53 55 4 9.940183 0226 0268 o3n o354 o3 9 6 55 5 5o 9 6 5 1 39 5i8i 5224 526-7 53io 54 5 0439 o48i o524 o566 0609 o65i 54 6 5352 53 9 5 5438 5481 5523 5566 53 6 0694 o 7 36 0779 0821 o864 0906 53 7 5609 5652 56g4 5 7 3 7 5 7 8o 5822 52 7 0949 0991 io34 io 7 6 1119 1161 52 8 5865 5908 5 9 5i 5 99 3 6o36 6o 79 5i 8 1204 1246 1289 i33i i3 7 4 i4i6 5i 9 6122 6i64 620 7 6260 6292 6335 5o 9 i45 9 i5oi 1 544 i586 1628 16-71 5o 10 9.926378 6421 6463 65o6 654 9 65 9 i 49 IO 9.941713 1-756 1798 i84i i883 1926 49 ii 6634 6677 6 7 2O 6-762 68o5 6848 48 ii 1968 2011 2o53 2096 2i38 2181 48 12 6890 6933 6 97 e 7 oi 9 -7061 7 io4 47 12 2223 2266 23o8 235i 2393 2436 47 i3 7147 7189 7232 7 2 7 5 7 3i 7 7 36o 46 i3 2478 2521 2563 2606 2648 2691 46 i4 7 4o3 7446 7 488 7 53i 7 5 7 4 7 6i6 45 i4 2 7 33 2776 2818 286! 2903 2 9 45 45 i5 7669 7702 77 44 7787 7 83o 7 8 7 2 44 i5 2988 3o3o 3o 7 3 3n5 3i58 3200 44 16 7915 79 58 8001 8o43 8086 8129 43 16 3243 3285 3328 33 7 o 34i3 3455 43 I 7 8171 8214 825 7 82 99 8342 8385 42 I 7 3498 354o 3583 36 2 5 366 7 3-710 42 18 8427 8470 85i3 8555 85 9 8 864i 4i 18 3 7 52 3 79 5 383 7 388o 3922 3 9 65 4i J 9 8684 8726 8769 8812 8854 8897 4o *9 4oo 7 4o5o 4092 4i35 4i77 4219 4o 20 9.928940 8982 9025 9 o68 9 no 9i53 39 20 9.944262 43o4 434 7 438 9 4432 44 7 4 3 9 21 9196 9 238 9281 9 3 2 4 9 366 9409 38 21 45i 7 455 9 4602 4644 4686 4-729 38 22 9 45 2 94g4 9 53 7 9 58o 9622 9 665 37 22 477i 48i4 4856 48 99 494i 4984 37 23 9708 97 5o 979 3 9 836 9 8 7 8 9921 36 23 5o26 5o6 9 5m 5i53 5196 5238 36 24 9964 ...6 ..49 .. 9 2 .134 .177 35 24 5281 53 2 3 5366 54o8 545i 54 9 3 35 25 9.930220 0262 o3o5 o348 0390 o433 34 25 5535 5578 562O 5663 5 7 o5 5 7 48 34 26 o4 7 5 o5i8 o56i o6o3 0646 0689 33 26 5 7 90 5832 58 7 5 5 9 i 7 5960 6002 33 2? o 7 3i 0774 o8i 7 o85 9 0902 o 9 45 32 2 7 6o45 6087 6i3o 61-72 6214 6 2 5 7 32 28 0987 io3o io 7 3 in5 n58 1 200 3i 28 62 99 6342 6384 642 7 6469 65n 3i 29 1243 1286 i328 i3 7 i i4i4 i456 3o 2 9 6554 65 9 6 663 9 6681 6-724 6 7 66 3o 3o 9.931499 1 542 i584 162-7 1669 1712 29 3o 9 . 9 468o8 685i 68 9 3 6 9 36 6 97 8 -7021 29 3i i 7 55 1797 i84o i883 1925 1968 28 3i 7 o63 7io5 7 i48 7 i 9 o 7 233 7 2 7 5 28 32 2010 2o53 2096 2i38 2181 2224 2 7 32 7 3i8 736o 7 402 7445 7 48 7 7 53o 27 33 2266 2309 2 35i 2 3 9 4 243 7 2479 26 33 7 5 7 2 7614 7 65 7 7 6 99 7742 7784 26 34 2522 2565 2607 265o 2692 2 7 35 25 34 7827 7869 7911 79 54 799 6 8o3 9 25 35 2778 2820 2863 2 9 o6 2948 2991 24 35 8081 8i23 8166 8208 8 2 5i 8293 24 36 3o33 3o 7 6 3n 9 3i6i 3204 3 2 46 23 36 8335 8378 8420 8463 85o5 8548 23 37 3289 3332 33 7 4 34i 7 345 9 35o2 22 37 8590 8632 86 7 5 8 7 i 7 8 7 6o 8802 22 38 3545 358 7 363o 36 7 2 3 7 i5 3 7 58 21 38 8844 8887 8 9 2 9 8 97 2 9 oi4 9 o56 21 3 9 38oo 3843 3885 3 9 28 3 97 i 4ot3 20 3 9 9099 9i4i 9 i84 9 226 9 268 g3ii 2O 4o 9.934o56 4o 9 8 4i4i 4i84 4226 4269 X 9 4o 9 . 9 4 9 353 9 3 9 6 9 438 9 48o 9 5 2 3 9 565 '9 4i 43n 4354 43 97 443 9 4482 4524 18 4i 9608 9 65o 9 6 9 2 97 35 9777 9819 18 42 456 7 46io 4652 46 9 5 4 7 3 7 4 7 8o J 7 42 9862 99 o4 9947 9989 ..3i .. 7 4 7 43 4822 4865 4 9 o8 4 9 5o 499 3 5o35 16 43 9. 9 5oii6 oi5 9 O2OI 0243 0286 o328 16 44 5o 7 8 5l2I 5i63 5206 5248 5291 i5 44 o3 7 i o4i3 o455 0498 o54o o582 i5 45 5333 53 7 6 54i 9 546i 55o4 5546 i4 45 0625 0667 0-710 O 7 52 0794 o83 7 i4 46 558 9 5632 56 7 4 5 7 i 7 5 7 5 9 58o2 i3 46 0879 0921 0964 1006 1049 1091 i3 4 7 5844 588 7 5930 5 97 2 6oi5 6o5 7 12 4? 1x33 1176 1218 1261 i3o3 1 345 12 48 6100 6142 6i85 622-7 62-70 63i3 II 48 i388 i43o 1472 i5i5 i55 7 1600 II 49 6355 63 9 8 644o 6483 6525 6568 IO 49 1 642 1 684 I 7 2 7 i 7 6 9 1811 i854 IO 5o 9.936611 6653 6696 6 7 38 6 7 8i 6823 9 5o 9.951896 1938 1981 2023 2066 2108 9 5i 6866 6908 6951 6994 7 o36 779 8 5i 2i5o 2193 2235 22 77 2320 2362 8 52 7121 7 i64 7 2o6 7 249 7 2 9 I 7334 7 52 2 4o5 2447 2489 2532 25 7 4 2616 7 53 7377 7419 7 462 7 5o4 7 54 7 7 58 9 6 53 265 9 2701 2 7 43 2 7 86 2828 28-70 6 54 7 632 7 6 7 4 77 I 7 77 5 9 7 802 7 845 5 54 2913 2 9 55 2998 3o4o 3o823i25 5 55 7887 79 3o 7972 8oi5 8o5 7 8100 4 55 3i6 7 3209 3252 32 9 4 3336 ! 33 79 4 56 8142 8i85 822-7 82-70 83i2 8355 3 56 342i 3463 35o6 3548 35 9 i|3633 3 5 7 8398 844o 8483 85 2 5 8568 8610 2 5 7 3675 3 7 i8 3 7 6o 3802 3845J3887 2 58 8653 86 9 5 8 7 38 8 7 8o 88 2 3 8865 I 58 3 9 2 9 3 97 2 4oi4 4o56 4099 4i4i I 5q 8908 8 9 5o 8 99 3 9 o35 9 o 7 8 9121 O 5 9 4i83 4226 426843io|4353!4395 O 60" 50" 40" 30" 20" 10" . 60" 50" 40" 30" 20" 10" a Co-tangent of 49 Degrees. a Co-tangent of 48 Degrees. i .< 1" 2" 3" 4" 5" 6" 7" 8" 9" .< 1" 2" 3" 4" 5" 6" 7" 8" 9" in \ 4 9 13 17 21 26 30 34 38 in \ 4 8 13 17 21 25 30 34 38 E 66 LOGARITHMIC SINES. c Sine of 42 Degrees. S Sine of 43 Degrees. i 0" 10" 20" 30" 40" ! 50" S 0" I 10" 20" 30" 40" 50" O 9.8255l I 5534 5558558i 56o45628 9 9 .833 7 83 38o6 828 385i 38 7 4 38 9 6 5 9 I 565i 56? 5 5698 5 7 2i 5 7 45;5 7 68 8 I 3 9 i 9 9 4i 964 3986 4oo 9 4o32 58 2 5 79 i 58i5 5838586i 5885 5 9 o8 7 2 4o54 4077 99 4l22 4x44 4i6 7 57 3 5 9 3! 5 9 55 6978 6001 6o25 6o48 6 3 4i8 9 212 4234 4257 4280 43o2 56 4 6071 6095 6n86i4i 6i656i88 5 4 4325 4347 3 7 o 43 9 2 44i5 443 7 55 5 6211 623562686281 63o56328 4 5 446o 4482 5o5 4527 455o 45 7 2 54 6 635i 63 7 563 9 8642i 6444 : 6468 3 6 45 9 5 46i 7 464o 4662 4685 4707 53 7 64 9 i 65i4 6538656i 6584,66o 7 2 7 4 7 3o . 7 52 4 77 5 4797 4820 4842 52 8 663i 6654 6677 6701 6724*6747 I 8 4865 .887 910 4 9 54 4977 5i 9 6770 679468176840 6863 6887 9 4999 5O22 o44 5o6 7 5o8 9 5lI2 5o 10 9.826910 6933 6966 6980 7oo3 7026 9 10 .835x34 5!5 7 i 79 52OI 5224 5246 49 ii 7o4 9 7 o 7 3 7096 7119 7142 7165 8 ii 5269 52 9 I 3i4 5336 5358 538i 48 12 7 i8 9 7 2I2 7 235 7 258 7282 73o5 , 7 12 54o3 54.16 5448 5471 5493 55i5 47 i3 7328 7 35i 73 7 4 7 3 9 8 7421 7444 46 i3 5538 556o 5583 56o5 562 7 565o 46 i4 746 7 7490 7614 7537 75607583 45 i4 56 7 2 56 9 5 5 7 i 7 5 7 3 9 5 7 6 2 5 7 84 45 i5 7606 7629 7 653 7676 7699 7722 44 i5 58o 7 582 9 585i 58 7 4 58 9 6 5 9 i8 44 16 77 45 77 68 7792 7815 7838,7861 .3 16 5 9 4i 5 9 63 5 9 86 6008 6o3o 6o53 43^ 17 7 884 7907 7 9 3i 7954 79778000 .2, l l 6o 7 5 6o 9 7 6120 6142 6i64 6187 42 1 8 8o23 8o46 $069 BogS I 18 6209 623i 6254 6276 6298 632i 4i J 9 8162 8i85 82088231 82548278 .O ! 9 6343 6365 6388 64 10 6432 6455 4o 20 9 . 8283oi 8324 83478370 83 9 384i6 '9 20 9.836477 64 99 6522 65446566 658 9 3 9 21 843 9 8462 8485 85o 9 85328555 38 21 6611 6633 6656 6678 6700 6722 38 22 8578 8601 86248647 86708^93 3 7 22 6 7 45 6767 6 7 8 9 6812 6834 6856 37 23 8716 8739 87628786 88098832 36 23 6878 6 9 oi 6923 6 9 45 6968 6990 36 24 8855 8878 8 9 oi 8 9 24 8947 8970 35 24 7012 7o34 7o5 7 7079 7 IOI 7123 35 25 6 99 3 9016 9 o3 9 9 o62 9085 9108 34 25 7i46 7168 7190 7212 7 235 72 5 7 34 26 9 i3i 9i54 9 i77 9 20o 9223 9246 33 26 7279 73oi 7324 7 346 7 368 7 3 9 33 27 9 26 9 9292 9 3i59338 9 36i 9 384 32 27 7412 7435 7457 7479 7 5oi ^524 32 28 9 4o7 9 43o 9453 9476 9499 9 522 3i 98 7546 7568 7^9 7612 7 635 7 65 7 3i 29 9 545 9 568 9691 9614 96379660 3o 29 7679 7701 77 2 3 7746 7768 779 3o 3o 9 .82 9 683 9 7o6 97299752 97759798 29 3o 9.837812 7834 7 85 7 7879 7901 79 23 2 9 3i 9 82I 9 844 9867 9890 99 i3 9936 28 3i 79 45 7967 799 8012 8o34 8o56 28 32 99 5 9 99 8 2 ...5 ..28 .. 7 4 27 32 8078 8100 8i23 8i45 8167 8i8 9 27 33 9 .83oo 9 7 0120 0142 oi65 0188 0211 26 33 8211 8233 8256 8278 83oo 8322 26 34 0234 0267 0280 o3o3 o326 0349 25 34 8344 8366 8388 84io 8433 8455 25 35 0372 o3 9 5 0417 o44o o463 o486 24 35 84 7 7 8499 852i 8543 8565 858 7 24 36 o5o 9 o53 2 o555 0678 0601 0624 23 36 8610 8632 8654 86 7 6 8698 8 7 20 23 37 o646 o66 9 0692 0715 o 7 38 0761 22 37 8742 8 7 64 8786 8808 883i 8853 22 38 0784 0807 0829 o85 2 o8 7 5 o8 9 S 21 38 8875 8897 8919 8 9 4i 8963 8 9 85 21 3 9 O 9 2I o 9 44 0967 0989 1012 io?5 20 3 9 9007 9029 9o5i 9 o 7 3 9 o 9 5 9 n8 2O 4o 9 .83io58 1081 no4 1127 n4 9 1 172 19 4o 9.839140 9162 9182 9 2o6 9228 9 25o 19 4i 1195 1218 1241 1263 1286 i3o 9 18 4i 9272 9294 9316 9 338 9 36o 9 38 2 18 42 1332 i355 i3 7 8 i4oo i423 1 446 17 42 9404 9426 9448 9 4 7 o 9492 g5i4 ! 43 i46 9 l4 9 2 i5i4 i53 7 i56o i583 16 43 9 536 9 558 9 58o 9 6o2 9624 9 646 It 44 1606 1628 i65i i6 7 4 i6 97 1720 i5 44 9668 9690 9712 9734 9756 9778 i5 45 1742 1765 1788 1811 i833 i856 i4 45 9800 9822 9844 9 866 9888 9910 i4 46 i8 79 1902 1924 194-7 i 9 7o i 99 3 i3 46 99 3 2 9954 9976 9998 . .20 . .42 i3 47 20l5 2o38 2061 2084 2106 2129 12 4? 9 .84oo6/! 0086 0108 Ol52 O\n 12 48 2l52 2I 7 5 2197 222O 2243 2266 II 48 0196 0218 0240 0262 0284 o3o6 II 49 2288 23ll 23342356 2 3 79 2402 IO 49 o328 o35o 0372 o3 9 3 o4i5 o43 7 10 5o 9 . 832425 244 7 2470 2493 25i5 2538 9 5o 9.840459 o48i o5o3 o525 o54y o56 9 9 5i 2 56i 2584 2606 2629 2652 2674 8 5i oSgi 06 1 ^ o635 o65 7 0678 0700 8 52 26 97 2 7 20 2742 2 7 65 2788 2810 7 52 0722 074^ 0766 0-7880810 o83 2 7 53 2833 2856 2878 2901 2 9 24 2946 6 53 o854 0876 0897 0919 0941 o 9 63 6 54 2 9 6 9 2992 3oi4 3o3 7 3o6o 3082 5 54 0985 1007 1029 io5i 1072 109^ 5 55 3io5 3i28 3i5o 3i 7 3 3 I9 6 32i8 4 55 1116 n38 1 1 60 1182 \izoi 1226 4 56 3s4 i 3263 3286 3309 333i 3354 3 56 1247 1269 1291 i3i3 i335 i35 7 3 , 57 3377 33 99 3422 3444 346 7 34 9 o 2 5 7 i3 7 8 i4oo 1422 i444i466 i486 58 35i2 3535 3557 358o 36o3 3625 I 58 i5og i53 i553 i5 7 5 i5 9 7 1619 5 9 3648 36 7 o 3693 3 7 i6 3 7 38 3 7 6i O 5 9 1640 1662 1 684 I 7 06;I 7 28 i 7 4 9 o 60" 50" 40" 30" 20" 10" d 60" 50" 40" 30" 20" 10" d Co-sine of 47 Degrees. g Co-sine of 46 Degrees. 1 PPartJ 1 " 2 " 3 " 4// 5" 6" 7" 8" 9" . f 1" 2" 3" 4" 5" 6" 7" 9" 9" F>lart { 2579 11 14 16 18 21 in \ 2 4 7 9 11 13 16 18 20 LOGARITHMIC TANGENTS. 1 Tangent of 42 Degrees. a Tangent of 43 Degrees. s 0" 10" 20" 1 30" 40" 50" 0" 10" 20" 30" 40" 50" o 9.954437 448o 4522 4564 4607 464 9 5 9 9 . 9 6 9 656 9698 97 4o 9783 9825 9 86 7 5 9 I 46 9 i 4734 4776 4819 486 1 4 9 o3 58 I 999 99 5i 9994 ..36 .. 7 8 . 120 58 2 4g46 4988 5o3o 5o 7 3 5n5 5r5 7 57 2 9 . 97 oi62 O205 0247 0289 o33i o3 7 3 57 3 5200 5242 5284 532 7 536 9 54n 56 3 o4i6 o458 o5oo o54 2 o584 0627 56 4 5454 5496 5538 558i 5623 5665 55 4 o66 9 0711 o 7 53 0796 o838 0880 55 5 5 7 o8 5 7 5o 5 79 2 5835 58 77 5 9 r 9 54 5 O 9 22 o 9 64 1007 1049 1091 n33 54 6 5 9 6i 6oo4 6o46 6088 6i3i 6i 7 3 53 6 n 7 5 1218 1260 1302 1 344 i386 53 7 62i5 6258 63oo 6342 6385 6427 52 7 1429 1471 i5i3 i555 i5 9 7 i64o 52 8 6469 65i2 6554 65 9 6 663 9 6681 5i 8 1682 1724 1766 1808 i85i i8 9 3 5i 9 6723 6 7 66 6808 685o 68 9 3 6 9 35 5o 9 i 9 35 i 977 20I 9 2062 2104 2l46 *)0 10 9.956977 7 020 7062 7104 7 i46 7 :8 9 4 9 10 9.972188 2230 2273 23i5 2 35 7 2 3 99 4 9 ii 7231 7 2 7 3 7 3i6 7358 7400 7443 48 ii 244i 2484 2526 2568 2610 2652 48 12 7485 7 5 27 7 5 7 o 7612 7 654 7 6 97 47 12 2695 2737 2779 2821 2863 2 9 o5 47 i3 77 3 9 7781 7823 7866 79 o8 7 9 5o 46 i3 2948 2 99 3o32 3o 7 4 3n6 3i5 9 46 i4 799 3 8o35 8077 8120 8x62 8204 45 i4 3201 3243 3 2 85 332 7 33 7 o 34l2 45 i5 8247 8289 833i 83 7 3 84i6 8458 44 i5 3454 3496 3538 358i 3623 3665 44 16 85oo 8543 8585 8627 8670 8712 43 16 3 7 o 7 3 7 4 9 3 79 i 3834 38 7 6 3 9 i8 43 i? 8 7 54 8796 8839 8881 8 9 23 8 9 66 42 I 7 3960 4O02 4o45 4o8 7 4129 4171 42 18 9008 goSo 9093 9 i35 9 i 77 9 2I 9 4i 18 42 I 3 4255 42 9 8 434o 4382 4424 4i J 9 9262 9 3o4 9 346 9 38 9 9 43i 9 4 7 3 4o J 9 4466 45o 9 455i 45 9 3 4635 46 77 4o 20 9.959516 9558 9 6oo 9 642 9 685 97 2 7 3 9 20 9.974720 4762 48o4 4846 4888 4 9 3o 3 9 21 9769 9812 9 854 9 8 9 6 99 38 998! 38 21 4973 5oi5 5o5 7 5099 5i4i 5i83 38 22 9.960023 oo65 0108 oi5o OI 9 2 0234 37 22 5226 5268 53io 5352 53 9 4 543 7 37 23 0277 0319 o36i o4o4 o446 o488 36 23 5479 552i 5563 56o5 564 7 56 9 o 36 24 o53o 0573 o6i5 0667 0700 0742 35 24 5 7 3 2 5 77 4 58i6 5858 5 9 oi 5 9 43 35 25 0784 0826 o86 9 o 9 n o 9 53 o 99 6 34 25 5 9 85 6027 6o6 9 6m 6i54 6i 9 6 34 26 io38 1080 1122 n65 1207 i24 9 33 26 6238 6280 6322 6364 64o 7 644 9 33 2 7 1292 i334 i3 7 6 i4i8 i46i i5o3 32 27 6491 6533 65 7 5 6617 6660 6702 32 28 1 545 i58 7 i63o 1672 1714 i 7 5 7 3i 28 6744 6786 6828 6870 6 9 i3 6 9 55 3i 2 9 1799 i84i i883 I 9 26 I 9 68 2010 3o 29 6997 7 3 9 7081 7123 7 i66 7208 3o 3o 9.962062 2095 2137 2I 79 2222 2264 2 9 3o 9>9 7725o 7292 7334 7377 7 4i9 746 1 2 9 3i 23o6 2348 23 9 I 2433 2475 2517 28 3i 7 5o3 7 545 7 58 7 763o 7672 7714 28 32 256o 2602 2644 2686 2 7 2 9 2771 2 7 32 77 56 7798 7840 7882 792 5 79 6 7 27 33 28i3 2856 28 9 8 2 9 40 2 9 82 3o25 26 33 8oo 9 8o5i 8o 9 3 8i35 8178 8220 26 34 3o6 7 3109 3i5i 3i 9 4 3236 32 7 a 25 34 8262 83o4 8346 8388 843 1 8473 2 5 35 3320 3363 34o5 3447 348 9 3532 24 35 85i5 855 7 85 99 864i 8684 8726 24 36 35 7 4 36i6 365 9 3701 3 7 43 3 7 85 23 36 8 7 68 8810 8852 88 9 4 8 9 3 7 8979 23 37 38 2 8 3870 3 9 I2 3 9 54 3 997 4o3 9 22 37 9 O2I 9063 9 io5 9 i47 9 i 9 o 9 232 22 38 3 9 4o8i 4335 4l23 43 77 4i66 44i 9 4208 446 1 4260 45o4 42 9 2 4546 21 20 38 3 9 0274 9 52 7 9 3i6 9 56 9 9 358 9611 9 4oo 9 653 9 442 9 6 9 5 9 485 9738 21 2O 4o 9.964588 463o 46?3 47i5 4 7 5 7 4799 J 9 4o 9 . 9797 8o 9 822 9 864 99 o6 99 48 999 19 4i 4842 4884 4 9 26 4 9 68 Son 5o53 18 4i 9.980033 oo 7 5 0117 oi5 9 0201 0243 18 4a 5o 9 5 5i3 7 5i8o 5222 5264 53o6 17 42 .0286 o328 o3 7 o o4i2 0454 o4 9 6 l l 43 534 9 53 9 i 5433 5475 55i8 556o 16 43 o538 o58i 0623 o665 0707 074 9 16 44 56o2 5644 568 7 5 7 2 9 5 77 i 58i3 i5 44 0791 o834 0876 o 9 i8 o 9 6o IOO2 i5 45 5855 58 9 8 5 9 4o 5 9 82 6oa4 6067 i4 45 1044 1086 1129 1171 I2l3 1255 i4 46 6109 6i5i 6i 9 3 6236 6278 6320 i3 46 1297 i33 9 I38 2 i424 i466 i5o8 i3 47 6362 64o5 6447 648 9 653i>5 7 4 12 47 i55o l5 9 2 1634 1677 I7i 9 1761 12 48 6616 6658 6700 6742 6785 6827 II 48 i8o3 i845 1887 I 9 2 9 I 97 2 2Ol4 II 49 6869 6911 6 9 54 6 99 6 7o38 7080 10 49 2o56 20 9 8 2l4o 2l82 2224 2267 10 5o 9.967123 7i65 7 20 7 7 24 9 7 2 9 i 7334 9 5o 9.982309 2 35i 23 9 3 2435 2477 25l 9 9 5i 7 3 7 6 74i8 7 46o 7 5o3 7545 7 58 7 8 5i 2562 2604 2646 2688 2730 2772 8 52 7629 7672 77 i4 7756 779 8 7 84o 7 52 2814 2 85 7 2899 2 9 4i 2 9 83 3o25 7 53 7 883 7925 79 6 7 8oo 9 8o52 8o 9 4 6 53 3067 3io 9 3i5 2 3i 9 4 3236 32 7 8 6 54 8i36 8178 8220 8263 83o5 834 7 5 54 3320 3362 34o4 3447 348 9 353i 5 55 838 9 8432 84?4 85i6 8558 8600 4 55 35 7 3 36i5 365 7 36 99 3 7 4z 3 7 84 4 56 8643 8685 8 7 2 7 8769 8812 8854 3 56 3826 3868 3910 3 9 52 3 99 4 4o3 7 3 5 7 8896 8938 8980 9023 9 o65 9 io 7 2 57 4079 4l2I 4x63 42o5 4247 428 9 a 58 9149 9192 9234 9276 9 3i8 9 36o I 58 433 2 43 7 4 44i6 4458 45oo 4542 i 5 9 9 4o3 9445 948 7 9 5 29 9 5 7 i 9 6i4 O 5 9 4584 462 7 466 9 4711 4753 47 9 5 o 60" 50" 40" 30" 20" 10" a 60" 50" 40" 30" 20" 10" . Co-tangent of 47 Degrees. 1 Co-tangent of 46 Degrees. 1 P Part 5 l " 2 " 3// 4 " 5 " 6 " 7 " 8 " 9 " PPoff 1 " 2 " 3 " 4 " 5 " 6 " 7" 8" 9" 4 8 13 17 21 25 30 34 38 m \ 4 8 13 17 21 25 30 34 38 68 LOGARITHMIC SINES. jj Sine of 44 Degrees. .3 Sine of 45 Degrees. i 0" 10" 20" 30" 40" 50" Si 0" 10" 20" 30" 40" 50" 9 . 841771 i 79 3 i8i5ii83 7 i858 1880 5 9 09.849485 9 5o6 9 5 27 9 54* 9 56 9 9 5 9 o 5 9 I I 9 02 I 9 24 i 9 46 i 9 6 7 i 9 8 9 2OII 58 i 9 6n 9 632 9 653 9 6 7 4 9 6 9 5 97 i6 58 2 2o33 2o55 2O 7 6 20 9 8 2I2O 2l42 5? 2 9738 97 5 9 97 8o 9 8oi 9 822 9 843 57 r . 2i63 2i85 220 7 222 9 225o 2272 56 *H 9 864 9 885 99 6 9927 99 48 9969 56 4 22 9 4 23i6 233 7 235 9 238l 24o3|55 4 999 . .11 ..32 ..53 .. 7 4 .. 9 5 55 i 242^ 2446 2468 24 9 25ll 253354 e 9 .85oi 16 oi3 7 oi58 oi 79 O200 O22I 54 6 2555 2577 25 9 8'262o 2642 2663 53 6 0242 0263 0284 o3o5 o326 o347 53 \ 2685 2707 2 7 2 9 2 7 5o 2 77 2 27^ 52 7 o368 o388 o4o 9 o43o o45i 0472 52 28i5 283 7 285 9 J288o 2 9 O2 5i 8 0493 o5i4 o535 o556 o5 77 o5 9 8 5i 9 2 9 46 2 9 67 2 9 8 9 3on 3o32 3o54 5o 9 06 1 9 o64o 0661 0682 0703 0724 5o 10 9 . 843o 7 6 3097 3n 9 {3i4i 3i62 3i84 49 10 9 .85o 7 45 o 7 66 0787 o8o 7 0828 o84 9 49 ii 3206 3227 324 9 3271 32 9 2 33i4 48 ii 0870 o8 9 i O 9 I2 o 9 33 o 9 54 o 97 5 48 12 3336 3357 33 79 34oi 3422 3444 47 12 o 99 6 IOI 7 io38 io58 io 79 IIOO 4 7 i3 3466 348 7 l35o 9 353o 3552 35 7 4 46 i3 II2I 1 14- n63 1184 I2O5 1226 46 i4 35 9 5 36i 7 363 9 366o 3682 3 7 o3 45 i4 1246 126-7 1288 i3o 9 i33o i35i 45 i5 3725 3 7 4 7 3768 3 79 o 38n 3833 44 i5 1372 i3 9 3 i4i3 i434 i455 i4 7 6 44 16 3855 38 7 6 38 9 8 3 9 i 9 3 9 4i 3 9 63 43 16 i4 9 7 i5i8 i53 9 i55 9 i58o 1601 43 17 3 9 84 4oo6 4o2 7 4o4 9 4071 4o 9 2 42 17 1622 1 643 1 664 i685 1705 I 7 26 42 18 4n4 4i354i5 7 4178 4200 4222 4i 18 1747 i 7 68 i 7 8 9 1810 i83o 1861 4i '9 20 4243 9. 8443 7 2 4265428643o8 43 9 4 44i6443 7 432 9 445 9 435i 448o 4o 3 9 J 9 20 1872 9 .85i 99 7 i8 9 3 2018 2o3 9 i 9 35 2o5 9 i 9 55 2080 i 97 6 2IOI 4o 3 9 21 45o2 452345454566 4588 46o 9 38 21 2122 2i43 2i63 2184 22O5 2226 38 22 463i 4652 46 7 4 ! 46 9 6 4717 4 7 3 9 37 22 2247 226 7 2288 23o 9 233o 2 35o 37 23 4760 4 7 8 2 48o3 4825 4846 4868 36 23 2371 23 9 2 c4i3 2434 2454 2 4 7 5 36 24 488 9 4 9 n 4 9 32 4 9 54 497 5 4997 35 24 24 9 6 25l 7 253 7 2558 2 5 79 2600 35 25 5oi8 5o4o 5o6i 5o83 5io4 5i26 34 25 2620 2641 2662 2683 2 7 o3 2724 34 . 26 5i47 5i68 5i 9 o 5211 5233 5254 33 26 2 7 45 2766 2786 28o 7 2828 2 84 9 33 27 52 7 6 52 97 53i 9 534o 5362 5383 32 27 286 9 28 9 2 91 J 2 9 3i 2 9 52 2973 32 28 54o5 5426 544 7 546 9 54 9 o 55i2 3i 28 2 99 4 3oi4 3o35 3o56 3o 7 6 3o 97 3i 2 9 5533 5555 55765598 56i 9 564o 3o 29 3n8 3i3 9 3i5 9 3i8o 3201 3221 3o 3o 9 . 845662 5683 57055726 5 7 4 7 5769 29 So 9 . 853242 3263 3 2 83 33o4 3325 3345 2 9 3i 5 79 58i2 58335855 58 7 6 58 97 28 3i 3366 3387 34o8 3428 344 9 34 7 o 28 32 5 9 i 9 5 9 4o 5 9 62 5 9 83 6oo4 6026 27 32 34 9 o 35n 3532 3552 35 7 3 35 9 4 2 7 33 6047 6o6 9 6o 9 o 6m 6i336i54 26 33 36i4 3635 3655 36 7 6 36 97 37i7 26 34 6i 7 5 6197 6218 6240 6261 6282 25 34 3738 3 7 5 9 3779 38oo 382i 384i 25 35 63o4 6325 6346 6368 638 9 64io 24 35 3862 3883 3 9 o3 3 9 24 3 9 44 3 9 65 24 36 6432 6453 64?4 64 9 6 65i 7 653 9 23 36 3 9 86 4oo6 4027 4o4 7 4o68 4o8 9 23 37 656o 658i 66o3 6624 6645666 7 22 37 4io 9 4i3o 4i5i 4171 4l 9 2 4212 22 38 6688 6 7 o 9 6 7 3i 67^267736794 21 38 4233 4254 42 7 4 42 9 5 43i54336 21 3 9 6816 683 7 6858 6880 6 9 oi 6 9 22 2O 3 9 4356 43 7 7 43 9 8 44i8 44394450 2O 4o 9 .846 9 44 6 9 65 6986 7008 jO2 9 7o5o 19 4o 9 . 85448o 45oo 452i 4542 4562 4583 19 4i 7071 7 o 9 3 7114 7 i35 71577178 18 4i 46o3 4624 4644 4665 4686 4706 18 42 7i 99 7220 7242 7 263 7284^305 17 42 4 7 2 7 4 7 4 7 4 7 68 4 7 88 48r>9 482 9 17 43 7 348 7 36 9 7 3 9 i 7 4i2 7 433 16 43 485o 4870 48 9 i 4 9 n 4 9 3 2 4 9 53 16 44 7454 7476 74 9 7 7 5i8 753 9 7561 i5 44 4 97 3 4 99 4 5oi4 5o35 5o55 5o 7 6 i5 45 7582 7603 7624 7 645 7 66 7 7688 i4 45 5o 9 6 5n 7 5i3 7 5i58 5i 7 8 5i 99 i4 46 779 77307752 777 3 779 4 7 8i5 i3 46 52I 9 524o 5260 5281 53oi 5322 i3 47 7 836 7 858 7 8 79 79 oo 79 2ij 79 43 12 47 .5342 5363 5383 54o4 5424 5445 12 48 7964 7 9 85 ] 8oo6 8027 8o4 9 8070 II 48 5465 5485 55o6 5526 554 7 556 7 II 49 8o 9 i 8112 8i33 8i54 81768^7 10 49 5588 56o8 562 9 564 9 56 7 o 56 9 o IO 5o 9 . 848218 823 9 8260 8282 83o383 2 4 9 5o 9 .855 7 n 5 7 3i 5 7 5i 5772 5 79 2 58i3 9 5i 8345 8366 838 7 84o 9 843o845i 8 5i 5833 5854 58 7 4 58 9 5 5 9 i5 5 9 35 8 52 8472 84 9 3 85i4 8535 85578578 7 52 5 9 56 5976 5 997 6017 6o38 6o58 7 53 85 99 86208641 8662 8683 8 7 o5 6 53 6o 7 8 6o 99 6n 9 6i4o 6160 6180 6 54 8726 8 7 4 7 '8 7 68 8 7 8 9 8810 883i 5 54 6201 6221 6242 6262 6282 63o3 5 55 8852 88 7 4 88 9 5 8 9 i6 8 9 3 7 8 9 58 4 55 6323634463646384 64o5 6425 4 56 8979 9 000 9 O2I 9 o42 9 o63 9 o85 3 56 6446 6466 6486 6507 6527 6547 3 5 7 9 io6 9 I2 7 9 i48 9 i6 9 9 I 9 9 2II 2 57 6568 6588 66o 9 66s 9 664 9 6670 2 58 9 232 9 253 9 2 749 2 95 9 3i6' 9 338 I 58 66 9 o 6 7 io 6 7 3i6 7 5i:6 77 i 6 79 2 i 5 9 9 35 9 9 38o 9 4oi 9 422 9 443 9 464 O 5 9 6812 6832 6853 68 7 3|68 9 36 9 i4 o 60" 50" | 40" 30" 20" 10" j 60" | 50" 40" i 30" i 20" 10" _. Co-sine of 45 Degrees. 1 Co-sine of 44 Degrees. s t tn o" *V' P Part I 4" 5" 6" 7" 8" 9" p P ,51" 2" 3" 4" 5" 6" 7" 8" 9" : "{ 2 4 6 9 11 13 15 17 19 m \ 2 4 6 8 10 12 14 17 19 LOGARITHMIC TANGENTS. 1 Tangent of 44 Degrees. a Tangent of 45 Degrees. jg 0" 10" 20" 30" 40" j 50" * 0" 10" 20" 30" 40" 50" o 9.98483-7 48 79 4 9 2I 4964 5oo6 5o48 5 9 o IO.OOOOOO OO42 oo84 0126 0168 O2II 5 9 i 5090 5i32 5i 7 4 52i6 525 9 53oi 58 I 0253 02 9 5 o33 7 o3 79 O42I o463 58 2 5343 5385 542-7 5469 55n 5553 5 7 2 o5o5 o54 7 o5 9 o o632 o6 7 4 o 7 i6 57 3 55 9 6 5638 568o 5 7 22 5 7 64 58o6 56 3 o 7 58 0800 0842 0884 0926 o 9 6 9 56 4 5848 5891 5 9 33 5 97 5 6oi 7 6o5 9 55 4 IOII io53 io 9 5 n3 7 "79 1221 55 5 6101 6i43 6i85 6228 62 7 63i2 34 5 1263 i3o5 1 348 1390 1432 i4 7 4 54 6 6354 63 9 6 6438 648o 6523 6565 53 6 i5i6 i558 1600 1642 1 684 1727 53 7 66o 7 6649 66 9 i 6 7 33 6 77 5 68i 7 52 7 i 7 69 1811 i853 i8 9 5 i 9 3 7 i 979 52 8 6860 6902 6 9 44 6986 -7028 7 o 7 o 5i 8 2O2I 2o63 2106 2148 2190 2232 5i 9 7 II2 7i54 7 i 97 7 s3 9 -7281 7 323 5o 9 22 7 4 23i6 2358 2400 2442 2485 5o 10 9 . 9 8 7 365 7 4o 7 744 9 749 1 7 534 7 5 7 6 49 10 IO.OO252 7 256 9 2611 2653 2695 2 7 3 7 4 9 ii -7618 7 66o 77 02 77 44 77 86 7 82 9 48 ii 2 779 2821 2864 2906 2948 2 99 48 12 7871 79 i3 79 55 7997 8o3 9 8081 47 12 3o32 3o 7 4 3n6 3i58 3200 3243 47 i3 8i23 8166 8208 825o 82 9 2 8334 46 i3 3285 332 7 336 9 34n 3453 3495 46 i4 83 7 6 84i8 846o 85o3 8545 858 7 45 i4 353 7 35 79 3622 3664 3 7 o6 3 7 48 45 !5 862 9 86 7 i 8 7 i3 8 7 55 8797 884o 44 i5 379 3832 38 7 4 3916 3 9 58 4ooi 44 16 8882 8924 8966 9008 9 o5o 9092 43 16 4o43 4o85 4l2 7 4i6 9 4211 4253 43 l l 9 i34 9i 77 9219 9261 9 3o3 9 345 42 I 7 42 9 5 433 7 438o 4422 4464 45o6 42 18 9 38 7 9429 9471 9 5i3 9 556 9 5 9 8 4i 18 4548 45 9 o 463 2 46 7 4 4 7 i6 4 7 5 9 4i 19 9 64o 9682 9724 97 66 9808 985o 4o 19 48oi 4843 4885 4 9 2 7 4969 Son 4o 20 9 . 9 8 9 8 9 3 99 35 9977 ..61 .io3 3 9 20 io.oo5o53 5o 9 5 5i38 5i8o 5222 5264 39 21 9 . 99 oi45 oi8 7 0230 O2 7 2 o3i4 o356 38 21 53o6 5348 53 9 o 5432 54 7 4 55i 7 38 22 o3 9 8 o44o 0482 0524 o56 7 0609 37 22 555 9 56oi 5643 5685 5 7 2 7 5 7 6 9 37 23 o65i 0693 o 7 35 777 0819 0861 36 23 58! i 5854 5896 5 9 38 5980 6022 36 24 o 9 o3 0946 0988 io3o IO 7 2 ni4 35 24 6o64 6106 6i48 6i 9 o 6233 62 7 5 35 25 n56 1198 1240 1283 i325 i36 7 34 25 63i 7 635 9 64oi 6443 6485 652 7 34 26 i4o 9 i45i 1493 i535 1-577 1620 33 26 656 9 6612 6654 6696 6 7 38 6 7 8o 33 27 1662 i 7 o4 i 7 46 i 7 88 i83o l8 7 2 32 2 7 6822 6864 6906 6949 6991 7 o33 32- 28 i 9 i4 1956 1999 2o4l 2o83 2125 3i 28 7 o 7 5 7117 7 l5 9 7 20I 7243 7 285 3i 29 2l6 7 2209 r 225l 22 9 3 2 336 23 7 8 3o 2 9 7 3 2 8 7 3 7 o 7 4i2 7 454 7496 7 538 3o 3o 9 . 99 2420 2462 2504 2546 2 588 2 63o 2 9 3o io.oo 7 58o -7622 7 664 777 7749 779 1 2 9 3i 26 7 2 2 7 l5 2 7 5 7 2799 2841 2883 28 3i 7 833 7 8 7 5 79 i 7 79 5 9 8001 8o44 28 32 2925 296? 3009 3o5i 3o 9 4 3i36 2 7 32 8086 8128 81-70 8212 8254 82 9 6 27 33 3i 7 8 3220 3262 33o4 3346 3388 26 33 8338 838o 8423 8465 85o 7 854 9 26 34 343i 34 7 3 35i5 355 7 35 99 364i 25 34 85 9 i 8633 86 7 5 8 7 i 7 8 7 6o 8802 25 35 3683 3 7 25 3 7 6 7 38io 3852 38 9 4 24 35 8844 8886 8928 8g 7 o 9012 9 o54 24 36 3 9 36 3978 4020 4062 4io4 4i46 23 36 997 9 i3 9 9181 9223 9 265 9 3o 7 23 37 4189 423i 42 7 3 43i5 435 7 43 99 22 37 9 34 9 9 3 9 i 9 433 9476 9 5i 9 56o 22 38 444i 4483 4526 4568 46io 465 2 21 38 9 6O2 9 644 9686 9?2 8 977 o 9 8!3 21 39 46 9 4 4736 4 7 78 4820 4862 4905 2O 3 9 9 855 9897 99 3 9 998i ..23 ..65 2O 4o 9-994947 4989 5o3i 5o 7 3 5n5 5i5 7 I 9 4o IO.OIOI0 7 oi5o 0192 0234 02 7 6 o3i8 '9 4i 5199 5 2 84 53 2 6 5368 54io 18 4i o36o 0402 o444 o48 7 o52 9 o5 7 i 18 42 5452 5494 5536 55 7 8 5620 5663 ! 7 42 o6i3 o655 o6 97 o 7 3 9 0-781 0823 17 43 5 7 o5 5 7 4 7 5 7 8 9 583i 58 7 3 5 9 i5 16 43 0866 0908 o 9 5o 99 2 io34 io 7 6 16 44 5 9 5 7 5 999 6o42 6o84 6126 6168 i5 44 1118 1 1 60 1203 1245 I28 7 i32 9 i5 45 6210 6252 6294 6336 63 7 8 6421 i4 45 i3 7 i i4i3 i455 i4 9 7 i54o i582 i4 46 6463 65o5 654 7 658 9 663i 66 7 3 i3 46 1624 1666 I 7 o8 i 7 5o I 79 2 i834 18 47 6 7 i5 6 7 5 7 6800 6842 6884 6926 12 47 i8 77 1919 i 9 6i 2O03 2045 208-7 12 48 6968 7010 7 o52 7 o 9 4 7 i36 7 i 7 9 II 48 2I2 9 2I 7 I 22l4 2256 22 9 8J234o II 49 7221 72 63 7 3o5 7347 7 38 9 7 43i 10 49 2382 2424 2466 25o 9 2 55i 25 9 3 IO 5o 9.99 7 4 7 3 7 5!5 7 558 7 6oo 7 642 7 684 9 5o 10.012635 26 77 2719 2 7 6l 2 8o3 2846 9 5i 77 26 77 68 7 8io 7 85 2 789417937 8 5i 2888 2930 2 97 2 3oi4 3o56 3o 9 8 8 52 7979 8021 8o63 8io5 8i4 7 |8i8 9 7 52 3i4o 3i83 3225 326 7 33o 9 335i 7 53 823i 82 7 3 83i6 8358 84oo 8442 6 53 33 9 3 3435 34 77 3520 3562 36o4 6 54 8484 8526 8568 8610 8652 86 9 5 5 54 3646 3688 3 7 3o 3772 38i5 385 7 5 55 8 7 3 7 8779 8821 8863 8 9 o5 8 9 4 7 4 55 38 99 3g4i 3 9 83 4o25 4o6 7 4109 4 56 5 7 8989 9031 9242 928^ 90-74 9 326 9 n6 9 368 9 i58 9 4io 9200 9 453 3 2 56 4i5 2 44o4 4i94 444 7 4236 448 9 42 7 8 453i 4320 45 7 3 4362 46i5 3 2 58 9495 953 79 5 79 9 62I 9 663 97 o5 I 58 465 7 4699 4 7 4i 4?84 4826 4868 I 5 9 9747 97 8 99 832 9 8 7 4 99 i6 99 58 5 9 4 9 io 4 9 5 2 4 99 4 5o36 5o 79 j5i2i 60" 50" 40" 30" 20" 10" . 60" 50" 40" 30" 20" | 10" - Co-tangent of 45 Degrees. s . Co-tangent of 44 Degrees. s A 1" 2" 3" 4" 5" 6" 7" 8" 9" p p ( 1" 2" 3" 4" 5" 6" 7" 8" 9" .rartj 4 8 13 17 21 25 29 34 38 P.Part^ 4 g 13 17 21 25 29 34 38 70 LOGARITHMIC SINES. d Sine of 46 Degrees. d Sine of 47 Degrees. ii 0" | 10" | 20" i -30" 40" 50" 0" | 10" 20" [ 30" 50" 0^9. 866934 6964 6976 ,6995 7016 7036 69 09.86412-7 4i4 7 4167 4186,4206 4226 69 i 7066 7076 7097 7117 71377168 58 i 4245 42664284 43o4!4324 4343 58 2 7178 7 i 9 8 7219 7239 7269 727967 2 4363 4383 4402 4422;444i 446 1 57 3 4 7 3oo 7422 7320 7442 7340 7361 7462 7482 7 38i 7 4oi 56 7603762355 3 4 448 1 45 9 8 45oo 46i8 4620 463 7 453 9 !4559 465 7 46 7 6 45 79 46 9 6 56 55 5 7 543 7 563 7584 7604 7624 7645 54 5 4716 4735 4755 4774 4794 48i3 54 6 7665J 7 685 7706 7726 77 46 7766 53 6 4833 4853 4872 4892 4911 4 9 3i 53 7 8 7786 7908 7807 79 28 7827 7948 7847 7968 7867 7989 7888 8009 62 5i 8 4960 5o68 49704990 5o87j5io7 6009 6126 6029 5i46 5o48 6166 62 5i 9 8029 8o4 9 8070 8o 9 o 8no;8i3o 5o 9 5i85 6204 6224 6244 5263 5283 5o 10 9.868161 8171 8191 8211 823i 82'52 49 10 9-865302 5322 534i 536i 538o 54oo 49 ii 8272 82 9 2 83i2 8332 8353 83 7 3 48 ii 5419 543 9 5458 5478 54 97 55i 7 48 12 83 9 3 84i3 8433 8454 8474 84 9 4 47 12 5536 5556 55 7 5 55 9 5 56i4 5634 47 i3 85i4 8534 8554 8676 86968616 46 i3 5653 56 7 3 6692 6712 5 7 3i 5 7 5i 46 i4 8635 8655 8676 8696 8 7 i6:8 7 36 45 i4 6770 6790 6809 6828 5848 586 7 45 16 8766 8776 87968817 88378867 44 16 6887 6906 6926 5 9 45 6966 5 9 84 44 16 8877 88 97 8917 8 9 3 7 89688978 43 16 6oo4 6023 6042 6062 6081 6101 43 17 8998 9 oi8 9o38 9068 9078:9098 42 17 6120 6.i4o 6169 6179 6198 6217 42 18 9119 9 i3 9 91699179 91999219 4i 18 6237 6266 6276 6296 63i5 6334 4i 19 9 23 9 9269 9279 gSoo 9320^340 4o '9 6353 63 7 3 63 9 2 6412 643i 645o 4o 20 o.o5o3oo 9 38o QdOO 9420 944o 9460 3 9 20 9.866470 648 9 65o 9 6628 654 7 6667 3 9 21 9 48o 9601 9621 9641 9661 9681 38 21 ,6586 6606 6626 6644 6664 6683 38 22 9601 9621 9641 9661 9681 9701 37 22 6703 6 7 22 6 7 4i 6761 6780 6800 37 23 9721 9741 97 6i 9.781 9 8o2 9822 36 23 6819 6838 6858 6877 6896 6916 36 24 9842 9862 9882 9902 9922 9942 35 24 6 9 35 6 9 54 6 97 4 6 99 3 7013 7032 35 26 9962 9982 . . .2 . .22 . .42). .62 34 25 7061 7071 70 9 o 7109 7129 7148 34 26 9.860082 OI02 0122 0142 0162 0182 33 26 7167 7187 7206 7226 7245 7264 33 27! O2O2 0222 O242 O262 0282 o3o2 32 2 7 7 283 7 3o3 7322 7341 7 36i 7 38o 32 28 0322 0342 o362 o382 o4o2 o422 3i 28 7399 7419 7438 745 7 7 4 7 6 7496 3 1 29 O442 0462 0482 0602 O522:o542 3o 29 -7616 7534 7554 7 5 7 3 7692 7612 3o 309.860662 0582 0602 0622 0642 0662 29 3o 9-86 7 63i 7660 7660. 7 68 9 77 o8 7727 29 3i 0682 O7O2 0722 0742 0762 0782 28 3i 7747 7766 7785 780/1 7 8 2 4 7843 28 32 0802 0822 0842 0862 0882 0902 27 32 7862 7882 79 oi 7 9 20 79 3 9 7969 2 7 33 O 9 22 094l 0961 9 8l 1001 1 02 1 26 33 797 s 7997 8016 8o36 8o55 8074(26 34 io4i 1061 1081 IIOI.II2I n4i 26 34 8o 9 3 8ii3 8i32 8161 8i 7 o 8190 26 35 1161 1181 1201 1221 I24O 1260 24 35 8209 8228 8 2 4 7 8267 8286 83o5 24 36 1280 i3oo l320 i34o i36o i38o 23 36 8324 8343 8363 8382 84oi 8420 23 37 i4bo l420 i43 9 1469 1479 1499 22 37 844o 845 9 84 7 8 84 97 8616 8536 22 38 1619 i53 9 i55 9 1679 159911618 21 38 8555 85 7 4 85 9 3 8612 8632 865 1 21 3 9 i638 1668 1678 1698 1718 1738 20 3 9 86 7 o 8689 8708 8728 8747 8 7 66 20 4o 9 . 86:768 1777 170.7 1817 1837 1867 '9 4o 9 .868 7 85 8804 88 2 3 8843 8862 8881 19 4i 1877 1897 1916 1936 1966 1976 18 4i 8900 8919 8 9 3 9 8 9 58 8977 8996 1 8 42 i 99 6 2016 2o35 2066 2076 2096 I 7 42 9016 9 o34 9 o53 9 o 7 3 9092 9111 17 43 21 16 2i35 2164 2174 21 9 4 22l4 16 43 9i3o 9149 9 i68 9 i88 9 2 7 9226 16 44 2234 2264 2273 2293 23i3 2333 i5 44 9246 9264 9 283 9 302 9321 9 34i 16 45 2353 2372 23 9 2 J-ll 2 2432 2462 i4 45 936o 9 3 79 9 3 9 8 9 4i7 9 436 9 455 r4 46 2471 2491 2611 253i 2661 2670 i3 46 9474 9494 9 5i3 9 532 9 55i 9 5 7 o i3 47 260.0 2610 263026602669 2689 12 47 9689 9608 9627 9 646 9 665 9 685 12 48 270 9 2729 2748 2768 2788 2808 II 48 9704 9723 9742 9761 9780 9799 IJ 49 2827 2847 2867 2887 2906 2926 IO 49 9818 9 83 7 9866 9876 9894 99x410 5o 9 . 862946 2966 2986 3oo5 3o 2 5 3o45 9 5o 9.869933 9962 9971 9990 ...9 ..28 9 61 3o64 3o84 3io4 3i24 3i43 3i63 8 61 9.8 7 oo4 7 0066 0086 oio4 8 62 3i83 32o3 3222 3242 3262 3281 7 62 f 0161 0180 0199 0218 0238 0267 7 53 33oi 332i 334i 336o 338o 34oo 6 53 O2 7 6 0296 o3i4 o3'33 o35-3 0371 6 54 34i9 343 9 345 9 3478 3498 35i8 5 54 oSgo 0409 0428 o447 o466 o485 5 55 3538 355 7 35 7 7 35 9 7 36i6 3636 4 55 o5o4 0623 0642 0661 0680 0699 4 56 3656 3676 3696 3 7 i5 3 7 34 3 7 54 3 56 0618 o63 7 0666 o6 7 5 0694 o 7 i3i 3 57 3 77 4 3 79 3 38i3 3833 3852 38 7 2 2 57 o 7 32 0761 0770 0789 0808 082 7 2 58 3892 3911 3 9 3i 3 9 5i 3 97 o 3 99 o I 58 o846;o865o884'o9o3 0922 0941 i 5 9 4oio 4029 4049 4069 4o88 4io8 O 69 096009790998101710361064 60" 50" 40" | 30" 20" 10" a 60" i 50" 40" 30" 20" 10" ^ Co-sine of 43 Degrees. S Co-sine of 42 Degrees. ( \n 2" 3" 4" 5" 6" 7" 8" 9" p. f ( 1" 2" 3" 4" 5" 6" 7" 8" 9" P. Part J 2468 10 12 14 16 18 [ "*\ 2 4 6 8 10 12 14 15 17 LOGARITHMIC TANGENTS. 71 1 Tangent of 46 Degrees. .s Tangent of 47 Degrees. s 0" 10" 20" 30" 40" 50" m 0" 10"| 20" 30" 40" 50" o *o.oi5i63 52o5 524 7 5289 533i 53 7 3 5 9 io.o3o344 o386 042 9 0471 o5i3 o555 5 9 i 54i6 5458 55oo 5542 5584 5626 58 i oS 97 o64o 0682 O 7 2<4 o 7 66 0808 58 2 5668 571 1 5 7 53 5 79 5 583 7 58 79 5 7 2 o85i o8 9 3 0935 977 IO20 1062 5 7 3 5921 5 9 63 6006 6o48 6o 9 o 6i3 2 56 3 no4 n46 1188 I23l I2 7 3 i3i5 56 4 6174 6216 6 2 58 63oi 6343 6385 55 4 i35 7 i4oo 1 442 i484 i526 1 568 55 5 6427 646 9 65n 6553 65 9 6 6638 54 5 1611 i653 i6 9 5 1737 1780 1822 54 6 6680 6722 6764 6806 6848 68 9 i 53 6 1864 I 9 o6 1948 i 99 i 2o33 2075 53 7 6933 6 97 5 7017 7 o5' 9 7101 7i43 52 7 2117 2160 2202 2244 2286 2328 52 8 7186 7228 7270 7 3l2 7354 7 3 9 6 5i 8 2371 24l3 2455 2497 254o 2582 5i 9 . 7438 748 1 7 523 7 565 7607 7 64 9 5o 9 2624 2666 2709 2751 2 79 3 2835 5o 10 10.017691 7733 7776 7 8i8 7860 7 9 02 4 9 10 10.032877 2 9 2O 2962 3oo4 3o46 3o8 9 4 9 ii 7944 7986 8028 8071 8ii3 8i55 48 ii 3i3i 3i 7 3 3 2 i5 3258 33oo 3342 48 12 8197 8 2 3 9 8281 83 2 3 8366 84o8 47 12 3384 3426 346 9 35n 3553 35 9 5 47 i3 845o 8492 8534 85 7 6 8618 8661 46 i3 3638 368o 3722 3764 38o 7 384 9 46 i4 8 7 o3 8 7 45 8787 8829 8871 8 9 i4 45 i4 38 9 i 3 9 33 3 97 6 4oi8 4o6o 4lO2 45 i5 8 9 56 8998 9040 9082 9 I24 9 i66 44 :5 4i45 4i8 7 4229 4271 43i3 4356 44 16 9209 9 a5i 9293 9335 9 3 7:7 9 4i 9 43 16 43 9 8 444o 4482 45 2 5 456 7 46o 9 43 *7 9462 9 5o4 9 546 9 588 9 63o 9672 42 17 465 1 46 9 4 4736 4778 4820 4863 42 18 97 i4 975 7 9799 9841 9 883 9925 4i 18 4 9 o5 4 9 4 7 4989 5o32 5074 5u6 4i J 9 9967 . . 10 . .62 94 .136 .178 4o X 9 5i58 52OI 5243 5 2 85 5327 5370 4o 20 IO.O2O22O 0262 o3o5 o34 7 o38 9 o43 1 3 9 20 io.o354i2 5454 5496 553 9 558i 5623 3 9 21 0473 o5i5 o558 0600 0642 o684 38 21 5665 5 7 o8 5750 5 79 2 5834 58 77 38 22 0726 0768 0810 o853 o8 9 5 o 9 3 7 37 22 5 9 i 9 5 9 6i 6oo3 6o46 6088 6i3o 37 23 0979 1021 io63 1106 1148 1190 36 23 6172 62*6 6257 62 99 634i 6384 36 24 1232 1274 i3i6 i35 9 i4oi 1 443 35 24 6426 6468 65ii 6553 65 9 5 6637 35 25 i485 1527 i56 9 1612 i654 1696 34 25 6680 6722 6 7 64 6806 684 9 68 9 i 34 26 i 7 38 1780 1822 i865 I 9 7 1949 33 26 6 9 33 6 97 5 7018 7060 7102 7i44 33 27 1991 2o33 2075 2118 2160 2202 32 27 1 7187 722 9 7271 73i4 7356 7 3 9 8 32 28 2244 2286 23 2 8 23 7 o 24i3 2455 3i 28 744o 7483 7525 7 56 7 76o 9 7 652 3i 29 2497 2 53 9 2 58i 2623 2666 2 7 o8 3o 29 76 9 4 7736 7778 7821 7863 79 o5 36 3o 10.022750 2792 2 834 2877 2 9 I 9 2961 2 9 3o io.o37 9 48 799 8o32 8074 8117 8i5 9 29 3i 3oo3 3o45 3o8 7 3i3o 3l 7 2 3214 28 3i 8201 8243 8286 8328 83 7 o 84i3 28 32 3256 32 9 8 334o 3383 3425 3467 2 7 32 8455 8497 853 9 858 2 8624 8666 27 33 35o 9 355i 35 9 3 3636 36 7 8 3720 20 33 8708 8 7 5i 8 79 3 8835 8878 8 9 2O 26 34 3762 38o4 3846 3889 3 9 3i 3973 25 34 8 9 62 9 oo4 9 o4? 9 o8 9 9 i3i 9 i 7 4 25 35 4oi5 4o5 7 4o 99 4142 4i84 4226 24 35 9216 9 258 9 3oo 9 343 9 385 9 42 7 24 36 4268 43io 4353 43 9 5 443 7 4479 23 36 9470 9 5l2 9 554 9 5 9 6 9 63 9 9 68i 23 3? 452i 4563 46o6 4648 46 9 o 4732 22 37 9723 9766 9 8o8 9 85o 9 8 9 2 99 35 22 38 4774 48i 7 485 9 4901 4 9 43 4985 21 38 9977 . .19 ..62 . 104 .i46 .188 21 3 9 5027 6070 5lI2 5i54 5i 9 6 5 2 38 20 3 9 io.o4o23i 0273 o3i5 o358 o4oo 0442 2O 4o 10.025280 53 2 3 5365 5407 544 9 5491 I 9 4o io.o4o484 0527 o56 9 06 1 1 o654 o6 9 6 I 9 4i 5534 55 7 6 56i8 566o 5 7 02 5745 18 4i o 7 38 0781 0823 o865 o 9 o 7 o 9 5o 18 42 5 7 8 7 5829 5871 5 9 i3 5 9 55 5 99 8 7 42 0992 io34 I0 77 in 9 1161 1204 r 7 43 6o4o 6082 6124 6166 6209 625i 1 6 43 1246 1288 i33o i3 7 3 i4i5 i45 7 16 44 6293 6335 63 7 7 6419 6462 65o4 i5 44 i5oo 1 542 1 584 162-7 i66 9 1711 i5 45 6546 6588 663o 66 7 3 6 7 i5 6757 i4 45 1753 1796 i833 1880 I 9 23 i 9 65 i4 46 6799 684i 6884 6926 6968 7010 i3 46 2007 2o5o 2092 2134 2177 22I 9 i3 4? 7062 7 o 9 5 7 i3 7 7179 7 22I 7263 12 4 7 2261 2 3o3 2346 2388 243o 2473 12 48 7 3o5 7348 7 3 9 o 7432 7 4 7 4 75i6 I I 48 25i5 2557 2600 2642 2684 2727 II 49 7 55 9 7601 7 643 7685 7727 777 10 49 2769 2811 2854 28 9 6 2 9 38 2 9 8o 10 So 10.027812 7854 7896 7938 7981 8023 5o io.o43o23 3o65 3io 7 3i5o 3i 9 2 3234 9 5 1 8o65 8107 8i49 8192 8' 2 34 8276 8 5i 32 77 33i 9 336i 34o4 3446 3488 8 52 83i8 836o 84o3 8445 848 7 852 9 7 52 353i 35 7 3 36i5 3658 3700 3 7 42 7 S3 8571 86i4 8656 8698 8 7 4o 8782 6 53 3 7 85 3827 386 9 3 9 I2 3 9 54 3 99 6 6 54 8825 8867 8909 8 9 5i 8 99 3 9 o36 5 54 4o3 9 4o8i 4123 4i65 4208 425o 5 55 9078 9120 9162 9204 9247 9 28 9 4 55 4292 4335 43 77 44i 9 4462 45o4 4 56 9 33i 9 3 7 3 94i6 9 458 gSoo 9 542 3 56 4546 458 9 463i 46 7 3 4716 4758 3 5 7 9 584 9627 9669 97" 97 53 979 5 2 5 7 48oo 4843 4885 4 9 2 7 4 9 7o 5oi2 2 58 9 838 9880 9922 9964 ...6 ..49 I 58 5o54 5o 9 7 5i3 9 5i8i 5224 5266 I 5 9 io.o3oo 9 i oi33 0175 02 I 7 0260 0302 5 9 53o 9 535i 53 9 3 5436 5478 552o O 60" 50" 40" 30" 20" 10" jj 60" 50" 40" 30" 20" 10" a Co-tangent of 43 Degrees. s Co-tangent of 42 Degrees. i p p C 1" 2" 3" 4" 5" 6" 7" 8" 9" .( 1" 2" 3" 4" 5" 6" 7" S" 9" (4 8 13 17 21 25 30 34 38 ~ i lrl \ 4 8 13 17 21 25 30 34 38 72 LOGARITHMIC SINES. .9 Sine of 48 Degrees. d Sine of 49 Degrees. s 0" 10" 20" | 30" ; 40" 50" 9 0-' 10" 20" 30" | 40" 50" 9.8 7 io 7 3|io92 IIII Il3o Il4 9 1168 59 o 9 . 877780 77 9 8 -7816 7835 7853 78 7 I 39 n8 7 1206 1225 1244 1263 1282 58 I 7 8 9 o 7 9 ofi 7926 7945 79 63 79 8i 58 2 i3oi 1320 i33 9 i358 i3 77 i3 9 5 5 7 2 7 999 8018 8o36 8o54:8o 7 2 8o 9 i 57 [ i4i4 i433 i452 i4 7 i i4 9 o i5o 9 56 '. 8109 8127 8i46 81648182 8200 56 L i5 2 8 i64i i54 7 1660 i566 i585 1604 i6 79 i6 9 8 1-71-7 162255 i 7 3654 L t 8219 83 2 8 823 7 |8 2 55 8346 8365 82 7 3J82 9 2 838384oi 83io 84i 9 55 54 6 i 7 55 i 77 4 i 79 3 i8n!i83o i84 9 53 6 8438 8456 84 7 4 8492851 1 85 29 53 7 1868 i88 7 I 9 o6 1925 1944 I 9 62 52 7 854 7 8565 8583 860218620 8638 52 8 1981 2000 2019 2o38 2o5 7 20-76 5i 8 8656 86 7 5 86 9 3 8 7 n 8 7 2 9 8 7 4 7 5i 9 2095 2Il3 2 I 32 2l5l 2I 7 2i8 9 5o 9 8 7 66 8 7 84 8802 8820 8838 885 7 5o 10 9.8 7 22o8 2226 2245 22642283 23O2 4 9 10 9.8 7 88 7 5 88 9 3 8911 8929 8 9 48 8966 4 9 ii 2321 2 34o 2358 2377 2396 24i548 ii 8 9 84 9002 9020 9 o3 9 9 o5 7 9 o 7 5 48 12 2434 2452 2471 2490 2509 2528 47 12 9093 9111 9129 9148 9166 9184 47 - <: 2 54 7 2565 2584 26032622 2 64i 46 i2 9202 9220 9238 925-7 92 7 5 9293 46 i4 2 65 9 26-78 2697 2716 2 7 35 2 7 53 45 i4 93n 9 3 29 9 34 7 9365 9 384 9402 45 i5 16 2 77 2 2885 2 7 gi 2810 2829 2904 2923 2941 2 84 7 2 9 6o 2866 2979 44 43 i5 16 9420 9 52 9 9438 9 54 7 9 456 9 565 94 7 4 9 583 9^)2 9601 9 5n 9619 44 43 17 2998 3oi63o353o54 3o 7 3 3o 9 i 42 i 7 9 63 7 9 656 9 6 7 4 96 9 2J 97 io 9 7 28 42 18 3no 3i2 9 3i483i66 3i85 3204 4i 18 9746 9764 97 8 2 9800 9819 9 83 7 4i 19 3223 324l 3260 32-79 32 9 8 33i6 4o '9 9855 9 8 7 3 9 8 9 i 9909 9927 99 45 4o 20 9.8 7 3335 335433 7 333 9 i 34io 342 9 39 20 9.879963 99 8i ..18 ..36 ..54 3 9 21 3448 3466 3485 35o43522 354i 38 21 9.880072 oo 9 o 0108 0126 0144 0162 38 22 356o 35 79 35 97 36i63635 3653 37 22 0180 oi 9 8 0216 0234 02 53 02 7 I 37 23 36 7 2 36 9 i 3 7 io 3 7 28 3747 3 7 66 36 23 0289 o3o 7 o325 o343 o36i o3 79 36 24 3 7 84 38o3 3822 384o 385 9 38 7 8 35 24 o3 97 o4i5 o433 o45i o46 9 o48 7 35 25 3896 3 9 i5 3 9 34 3 9 53 3 97 i 3 99 o 34 25 o5o5 o5 2 3 o54i o55 9 o5 77 o5 9 5 34 26 2 7 4009 4l2I 402-7 4o46 4o65 4i3 9 4i584i 77 4o83 4i 9 5 4lO2 42i4 3S 32 26 2 7 o6i3 0722 o63i o 7 4o o64 9 o 7 58 o66 7 o 77 6 0686 o 79 4 o 7 o4 0812 33 32 28 4232 425i 42-704288 43o 7 4326 3i 28 o83o o848 0866 o884 O 9 O2 O 9 20 3i 29 4344 4363 4382 44oo 44i 9 4438 3o 2 9 0938 o 9 56 o 97 4 0992 IOIO 1028 3o 3o 3i 9 .8 7 4456 4568 44 7 544 9 345i2 4586 46o54624 453i 4642 454 9 466i 2 9 28 3o 3i 9.881046 n53 io63 1171 1081 u8 9 1099 I20 7 III 7 1225 n35 1243 28 32 33 468o 4791 46 9 84 7 i 7 48104828 4 7 35 484 7 47544773 48664884 27 26 32 33 1261 1 369 I2 79 i38 7 I2 97 i4o5 i3i5 1423 i333 i44i i35i i45 9 2 7 26 34 35 4903 5oi4 4 9 2i 4 9 4o 5o33 5o5i 4 9 58 5o 7 o 4977499 6 5o885io 7 25 24 34 35 i477 1 584 i4 9 5 1602 l5l2 1620 i53o i638 1 548 i656 1 566 i6 7 4 25 24 36 5i 2 6 5i445i63 5i8i 520052I&23 36 1692 I 7 IO 1-728 i 7 46 i 7 63 1-781 23 37 523 7 5255 52 7 4 52 9 3 53n 533022 37 1799 181-7 i835 i853 18-71 i88 9 22 38 5348 536 7 5385 54o4 5422544i 21 38 1907 1925 I 9 42 1960 1978 I 99 6 21 39 545 9 54 7 8 54 9 6 55i5 55345552 2O 39 1014 2032 2o5o 2068 2086 2103 2O 4o 9 .8 7 55 7 i 558 9 56o8 56 2 6 5645|5663 I 9 4o 9.882121" 2i3 9 2l5 7 2I 7 5 2I 9 3 2211 J 9 4i 5682 5 7 oo 5 7 i 9 5 7 3 7 5 7 565 77 4 18 4i 2229 2246 2264 2282 2300 23i8 IS 42 5 79 3 58n 583o 5848 586 7 5885 l l 42 2336 2354 23 7 i 2389 240 7 2425 I 7 43 5 9 o4 5 9 22 5 9 4i 5 9 5 9 5 97 8 5 99 6 16 43 2443 2461 24 79 2496 25i4 2532 16 44 6oi4 6o33 6o5i 6o 7 o 6088610-7 i5 44 255o 2568 2586 26o3 2621 263 9 i5 45 6i 2 5 61446162 6181 6199 6218 i4 45 2657 26 7 5 26 9 2 2 7 IO 2-728 2 7 46 i4 46 6236 6 2 55 62 7 3 62 9 I 63io6328 i3 46 2764 2 7 82 2 799 281-7 2835 2853 i3 47 634 7 6365 6384 6402 6421 643 9 12 47 2871 2888 2 9 o6 2924 2 9 42 2 9 6o 12 48 645 7 64 7 6 64 9 4 65i3 653i 655o II 48 2977 2 99 5 3oi3 3o3i 3o4 9 3o66 II 49 6568 6586 66o5 6623 66426660 10 49 3o84 3lO2 3l20 3i3 7 3i55 3i 7 3 10 5o 9 .8 7 66 7 8 66 97 6 7 i5 6 7 34 6 7 52 6 77 o 9 5o 9.883191 3209 3226 3244 3262 3 2 8o 9 5i 6 7 8 9 680-76826 6844 68626881 8 5i 32 97 33i5 3333 335i 3368 3386 8 52 6899 6 9 i8 6 9 36 6 9 54 69-73 6991 7 52 34o4 3422 343 9 345 7 34 7 5 34 9 3 7 53 7 OIO -7028 7 o46 7 o65 7 o83 -7101 6 53 35io 35 2 8 3546 3564 358i 35 99 6 54 7120 7 i38 7 i5 7 7 i 7 5 7 I 9 3 7 2I2 5 54 36i 7 3635 365 2 36 7 o 3688 3 7 o5 5 55 7 23o 7248-726-7 7286 7 3o3 7 322 4 55 3723 3 7 4i 3 7 5 9 I 3 77 6 3794 38i2 4 56 57 7 34o 7 45o 7 358 7 3 77 7 468 7 48 7 7 3 9 5 7 5o5 7 4i3 7 432 3 2 56 5 7 3829 3 9 36 384 7 3865 3883 3 9 oo 3 9 i8 3953 39-71 3989^0064024 3 2 58 7 56o 7 5 7 8 7 5 97 7 6i5 7 633 7 652 I 58 4o42 4o6o 4077 4095 4n3 4i3o I 59 7 6 7 o 7 688 77 o 777 25 77 43 77 62 59 4i48 4i66 4i83 4201*4219 4236 60" 50" j 40" 30" 20" 10" a 60" 50" 40" 30" 20" 10" I Co-sine of 41 Degrees. Jl is Co-sine of 40 Degrees. s PPartJ 1 " 2 " 3// 4" 5" 6" 7" 8" 9" .< 1" 2" 3" 4" 5" 6" 7" 8" 9" "1 a 4 6 7 9 11 13 15 17 irl $ 24 5 7 9 11 13 14 16 LOGARITHMIC TANGENTS. 73 1 Tangent of 48 Degrees. .3 Tangent of 49 Degrees. 2 0" 10" 20" 1 30" 40" 50" al 0" 10' 20" 30" 40" 50" i io.o45563 58i 7 56o5564 7 56 9 o5 7 3 2 585 9 5 9 oi 5 9 44J5 9 86 5 77 4 6028 5 9 58 ( i 10.060837 1092 o8 79 n35 9 22 1177 o 9 65 I22O IO0 7 1262 io5o i3o5 5 9 58 2 6071 6n36i556i 9 8 6240 6282 57 9 1 347 i3 9 o 1432 i4 7 5 i5i 7 i56o 57 3 63 2 5 636 7( 64o 9 6452 64 9 4 653 7 56 Q 1602 1 645 1688 1730 i 77 3 i8i5 56 4 65 79 6621 6664 6 7 o6 6 7 48 6 79 i 55 4 i858 I 9 00 1943 i 9 85 2028 2070 55 5 6833 68 7 5i6 9 i8J6 9 6o] 7 oo2 54 c 2Il3 2i55 2198 224l 2283 2326 54 6 7087 7 i3o 7172 7214 7257 7299 53 6 2368 2411 2453 24 9 6 2538 2 58i 53 7 7 34i 7384^426 7468 7 5n 7 553 52 7 2623 2666 2709 275l 2 79 4 2836 52 8 7 5 9 5 7638 7680 7723 77 65 7 8o 7 5i 8 2879 2 9 2I 2964 3oo6 3o4 9 3o 9 2 5i 9 785oJ78 9 2J7 9 34 7977 8019 8062 5o 9 3 1 34 3i 77 3219 3262 33o4 334 7 5o 10 io.o48io48i468i8 9 82 3 1 82 7 3 83i6 49 10 10.063389 3432 3475 35i 7 356o 3bo2 4y 1 1 8358 84oo 8443 8485 85 2 8 85 7 o 48 ii 3645 368 7 3 7 3o 3 77 3 38i5 3858 48 12 8612 8655 86 97 8 7 3 9 8 7 8 2 8824 4 7 12 3 9 oo 3 9 43 3 9 85 4028 4o 7 o 4n3 47 i3 8867 8 9 o 9 8 9 5i 8 99 4 9 o36 9 7 9 46 i3 4i56 4i 9 8 424i 4283 4326 4368 46 i4 9 I2I 9 i63 9 206 9248 9 2 9 o 9333 45 i4 44n 4454 44 9 6 453 9 458i 4624 45 i5 9 3 7 5 9 4i8 9 46o 9 5o2 9 545 9 58 7 44 i5 466 7 470 9 4?52 4794 483 7 48 79 44 16 9 62 9 0.672 97 i4 97^-7 9799 9841 43 16 4 9 22 4 9 65 5007 5o5o 5o 9 2 5i35 43 17 9 884 99 26 99 6 9 ..ii ..53 ..96 42 17 5i 7 8 522O 5263 53o5 5348 53 9 o 42 18 io.o5oi38 0181 0223 0265 o3o8 o35o 4i 18 5433 5476 55i8 556i 56o3 5646 4i 19 o3 9 2 o435 o477 0520 o562 o6o4 4o 19 568 9 5 7 3i 5 77 4 58i6 585 9 5 9 O2 4o 20 io.o5o64 7 o68 9 0732 0774 0816 o85 9 3 9 20 io.o65 9 44 5 9 8 7 6o2 9 6o 7 2 6n5 6i5 7 3 9 21 o 9 oi o 9 44 o 9 86 1028 IO 7 I in3 38 21 6200 6242 6285 6328 6370 64i3 38 22 n56 1198 1240 1283 i325 i368 37 22 6455 64 9 8 654i 6583 6626 6668 3 7 23 i4io 1452 i4 9 5 i537 i58o 1622 36 23 6711 6754 6 79 6 683 9 6881 6 9 24 36 24 i665 1707 i 7 4 9 1792 i834 i8 77 35 24 6967 7oo 9 7 o52 7 o 9 4 7 i3 7 7180 35 25 I 9 i 9 i 9 6i 2004 2046 2o8 9 2l3l 34 25 7222 7 265 73o8 7 35o 7 3 9 3 7435 34 26 2173 2216 2258 2301 2343 2386 33 26 7 4 7 8 7521 7 563 7 6o6 7649 7691 33 2 7 O./IOQ 2470 25i3 2 555 2 5 9 8 2640 32 27 7734 7776 7819 7 862 7904 7947 32 28 2682 2725 2767 2810 2852 2895 3i 28 799 8o32 8o 7 5 8117 8160 8203 3i 2 9 2 9 3 7 2 979 3O22 3o64 3io 7 3i49 3o 29 8245 8288 833i 83 7 3 84i6 8458 3o 3o io.c53i 9 2 3 2 34 32 7 6 33i 9 336i 34o4 2 9 3o io.o685oi 8544 8586 862 9 86 7 2 8 7 i4 2 9 3i 3446 348 9 353i 35 7 3 36i6 3658 28 3 1 8 7 5 7 8800 8842 8885 8 9 2 7 8 97 o 28 32 3701 3 7 43 3 7 86 38 2 8 38 7 o 3gi3 27 32 9013 9 o55 9 o 9 8 9 i4i 9183 9226 27 33 3 9 55 3 99 8 4o4o 4o83 4i25 4i68 26 33 9269 9 3n 9 354 9 3 97 943 9 948? 26 34 4210 4252 42 9 5 433 7 438o 4422 25 34 9 5 2 5 9 56 7 9 6io 9 65 2 9696 9738 25 35 4465 45o 7 454 9 45 9 2 4634 46 77 24 35 97 8o 9 8 2 3 9 866 99 o8 99 5i 9994 24 36 47i 9 4 7 6 2 48o4 4847 488 9 493i 23 36 io.o 7 oo36 oo 79 OI22 oi64 02O 7 O25o 23 37 4 9 74 5oi6 5o5 9 5ioi 5i44 5i86 22 37 02 9 2 o335 o3 7 8 O420 o463 o5o6 22 38 522 9 52 7 I 53i4 5356 53 9 8 544i 21 38 o548 o5 9 i o634 o6 7 6 o 7 i 9 0762 21 3 9 5483 5526 5568 56n 5653 5696 20 3 9 o8o4 0847 o8 9 o 9 32 97 5 1018 20 4o io.o55738 5 7 8i 58 2 3 5865 5 9 o8 SgSo 1 9 4o io.o 7 io6o no3 n46 1188 I23l I2 7 4 I 9 4i 5 99 3 6o35 6078 6120 6i63 62o5 18 4i i3i6 i35 9 I4O2 i445 i48 7 i53o 18 42 6248 62 9 o 6333 63 7 5 64i 7 646o !7 42 i5 7 3 i6i5 i658 I 7 OI 1743 i 7 86 17 43 65o2 6545 658 7 663o 66-72 6 7 i5 16 43 l82 9 1871 i 9 i4 i 9 5 7 i 999 2O42 16 44 6 7 5 7 6800 6842 6885 6 9 2 7 6 97 i5 44 2o85 2128 2170 22l3 2256 2298 i5 45 7 OI2 7 o55 797 7 i3 9 7182 i4 45 234l 2384 2426 246 9 25l2 2554 i4 46 7 26 7 7 3o 9 7 352 7 3 9 4 7 43 7 7479 i3 46 25 97 2640 2683 2 7 25 2 7 68 2811 i3 47 ' - 7 522 7564 7 6o 7 7 6 9 2 77 34 12 4 7 2853 28 9 6 2 9 3 9 2 9 8l 3o24 3o6 7 12 48 7777 7819 7 86 2 794 79 4 7 | 79 8 9 II 48 3no 3i52 3i 9 5 3238 3280 3323 II 49 8o32 8o 7 4 8n 7 8i5 9 8202(8244 IO 4 9 3366 34o 9 345 1 34 9 4 3537 35 79 IO 5o io.o5828 7 832 9 83 7 2 84x4 84568499 9 5o IO.O 7 3622 3665 3 7 o8 3 7 5o 370.3 3836 9 5i 854i 8584 8626 866 9 8 7 n 8 7 54 8 5i 38 7 8 3 9 2I 3 9 64 4oo 7 4o4 9 4o 9 2 8 52 8 79 6 883 9 8881 8 9 24 8 9 66 9 oo 9 7 52 4i35 4178 4220 4263 43o6 4348 7 53 54 9 o5i 9 3o6 9 o 9 4 9 34 9 9 i36 9 3 9 i 9 i 79 9 434 9 22I 9264 9476 9519 6 5 53 54 43 9 i 4648 4434 46 9 o 4477 4733 45i 9 477 6 4562 46o5 48i 9 486i 6 5 55 9 56i 9 6o4 9 646 9 68 9 9732 9774 4 55 4 9 o4 4 9 4 7 4 9 8 9 5o32 5o 7 5j5nd 4< 56 9 8i 7 9 85 9 99 02 99 44 9987 ..29 3 56 5i6o 52o3 5246 528 9 533ii53 7 4 3 5 7 io.o6oo 7 2 on4 oi5 7 oi 99 0242 0284 2 5 7 54i7 546o 55o2 5545 55885631 2 58 o32 7 o36 9 O4l2 o454 0497 o539 I 58 56 7 3 5716 5 7 5 9 58o2 5844 588 7 I 5 9 o582 0624 o66 7 o 7 o 9 0752 0794 5 9 5 9 3o 5 97 3 6oi5 6o58 6ioi|6i44 O 60" 50" 40" 30" 20" 10" d 60" 50" 40" 30" W | 10" Co-tangent of 41 Degrees. 3 Co-tangent of 40 Degrees. 5 P Prt5 l " 1" 3 " 4 " 5 " 6 " 7 " S " 9 " I 4 8 13 17 21 25 30 34 38 v F .( 1" 2" 3" 4" 5" 6" 7" 8" 9" irt } 4 9 13 17 2 X *'o 30 34 38 LOGARITHMIC SINES. 3 Sine of 50 Degrees. -a Sine of 51 Degrees. 4 * ~~ [ 10" I 20" I 30" i 40" 50" 51 0" 10" 20" 30" 40" 50" O 9.S84254!4272|428 9 43074325 4342 5 9 o 9 .8 9 o5o3 0620 o53 7 o554 0671 0688 5 9 I 436oj4378|43 9 5 44i3443i 4448 58 I 0606 0622 o63 9 0666 o6 7 3 o6 9 o 58 2 4466 44S3|45oi 45i 9 '4536 4554 5? 2 0707 0724 0741 0768 o 77 5 79 2 57 "i 4572 458 9 4007 4626 4642 466o 56 2 o8o 9 0826 o843 0860 o8 77 o8 9 4 56 L 4677 46 9 5 47i3 473o ! 4748 476666 4 o 9 n O 9 28 o 9 45 0962 979 o 99 6 55 6 4783 488 9 48oi43i8 4836 4854 4 9 o6 4 9 244 9 42|4 9 5 9 48 7 i54 4 9 77 53 c 6 ioi3 in5 io3o Il32 1047 n4 9 1064 1166 1081 1 1 83 1096 1 200 54 53 7 4 99 4 5oi2 5o3o 5o4 7 !5o65 6082 62 7 1217 1234 1261 1268 1286 1302 52 8 5ioo 5u85i35 5i53 6170 5i885i 8 i3i 9 i336 i353 i3 7 o i38 7 i4o4 5i 9 5 2 o5 6223 6241 6268 52 7 6[52 9 3 5o 9 1 4s i i438 i455 1472 1489 1606 5o 10 9 .8853n 532853465364 5381 5399 4 9 10 9.8 9 i523 1 54o i556 1673 1690 1607 49 ii 54i6 5434545i 546 9 5486 55o4 48 ii 1624 1 64 1 i658 1676 1692 I 7 o 9 48 12 5522 553 9 555 7 55 7 4 55 9 2 56o 9 47 12 1-726 1743 1760 1777 1794 1810 47 t3 6627 5644 5662 56 79 56 97 6714 46 i3 l82 7 1 844 1861 1878 i8 9 5 I 9 I2 46 i4 6732 5 7 4 9 5 7 6 7 5 7 84 6802 6819 45 i4 I 9 2 9 i 9 46 i 9 63 1980 i 99 6 20l3 45 i5 583 7 5855 68726800 5 9 o 7 6926 44 i5 2o3o 2047 2064 2081 2O 9 8 2Il5 44 16 5 9 42 5 9 6o5 977 5 99 5 6012 6o3o 43 16 2l32 2l4 9 2166 2182 2I 99 2216 43 17 6o4 7 6o65 6082 6o 99 6ii 7 !6i34 42 I 7 2233 2260 2267 2284 2300 2317 42 18 6i5 2 6i6 9 6187 6204 62226239 4i 18 2334 2 35i 2368 2385 24O2 2419 4i i 9 6267 6274 62 9 2 63o 9 632 7 6344 4o '9 2435 2462 2 46 9 2486 2 5o3 2620 4o 20 9 . 886362 637 9 63 9 664i4 643 1 644 9 39 20 9 .8 9 2536 2553 2670 2687 2604 2621 39 21 6466 6484 65oi 65i 9 6536 6554 38 21 2638 2664 2671 2688 2706 2722 38 22 65 7 i 6588 6606 66 2 3 664i 6658 37 22 2739 2766 2772 2789 2806 2823 37 23 6676 66 9 3 6710 6728 6 7 45 6 7 63 36 23 283 9 2866 2873 2890 2007 2 9 24 36 24 25 6780 6885 6 79 868i5'6832 6 9 o2 6 9 i 9 |6 9 37 6860 6 9 54 6867 6 9 72 35 34 24 25 2 9 4o 3o4i 2 9 57 3o58 2 97 4 3o 7 5 2 99 I 3o 9 2 3oo8 3io8 3024 3i25 35 34 26 6 9 8 9 7006 7024 7041 7o5 9 7076 33 26 3i42 3i5 9 3i 7 6 3i 9 2 320 9 3226 33 27 28 79 3 7198 7111 7128 7146 7216 7232)7250 7 i63 7267 7180 7286 32 3i 27 28 3243 3343 3 2 5 9 336o 32 7 6 33 7 7 3 29 3 33 9 4 33io 34io 3327 3427 32 3i 29 7 302 73197337 7354 7 3 7 i 7 38 9 3o 29 3444 346i 3477 34 9 4 35ii 3528 3o 3o 9.88 7 4o6 74^3 7 44i 7458 7 4 9 3 2 9 3o 9 .8 9 3544 356i 35 7 8 35 9 5 36n 3628 2 9 3i 7 5io 7628 7545 7562 7 58o 7 5 97 28 3i 3645 3662 3678 36 9 5 3712 3728 28 32 7614 7632 764^7666 76847701 2 7 32 3 7 45 3762 3 779 3 79 5 38i2 382 9 2 7 33 77 i8 77367753:7770 77877806 26 33 3846 3862 38 9 6 3 9 I2 3 9 2 9 26 34 7822 7 83 9 7 85 7 7*74 7 8 9 I i799 25 34 3 9 46 3 9 63 3 979 3 99 6 4oi3 402 9 26 35 7 9 26 79 43 7961 7978 7 99 5 8012 24 35 4o46 4o63 4o7 9 4o 9 6 4n3 4i3o 24 36 8o3o 8047 8o64 8082 8o 99 8u6 23 36 4i46 4i63 4i8o 4i 9 6 42i3 423o 23 37 8i34 8i5i 8168 8i85 82038220 22 3 7 4246 4263 4280 42 9 6 43i3 433o 22 38 8237 82548272 828 9 83o6 8324 21 38 4346 4363 438o 43 9 6 44i3 443o 21 3o 834i 83588375 83 9 3 84108427 2O 3 9 4446 4463 448o 44 9 6 45i3 453o 2O 4o o. 888444 8462 847 9 84 9 6 85i3853i X 9 4o 9 . 8 9 4546 4563 458o 45 9 6 46i3 462 9 39 4i 8548 8565 8582 8600 86178634 18 4i 4646 4663 46 79 46 9 6 47i3 472 9 -8 42 865i 866 9 8686|8 7 o3 87208737 17 42 4 7 46 4763 4779 4796 4812 482 9 17 43 8 7 55 8772 878 9 8806 8824 884i 16 43 4846 4862 48 79 48o6 4 9 I2 4 9 2 9 16 44 8858 887588 9 28 9 io 8 9 27 8 9 44 16 44 4 9 45 4 9 62 4979 4 99 5 5oi2 6028 16 45 8 9 6i 8 9 788 99 6 9 oi3 9 o3o 9 o47 i4 45 5o45 6062 6078 5o 9 5 6111 6128 i4 46 9 o64 9 o82 9 o 99 J 9 ii6 9 i33 9 i5o i3 46 6146 6161 6178 5i 9 4 6211 6227 i3 47 9 i68 9 i85 9 202; 9 2I 9 9 236 9 253 12 47 6244 6261 6277 52 9 4 53io 532 7 12 48 9271 9 288 9 3o5| 9 322 9 33 99 356 II 48 5343 536o 53 77 53 9 3 54io 5426 II 49 9 3 7 4 9 3 9 i 9 4o8 9 425 9 442 9 45 9 10 49 5443 545 9 5476 54 9 3 55o 9 6626 10 5o 9 .88 9 477 9 4 9 4 9 5u 0628 9 545 9662 9 5o 9 .8 9 5542 555 9 55 7 5 55 9 2 56o8 6626 9 5i 9 5 79 9 5 979 6i4 963i 9 648 9 665 8 61 564i 5658 56 7 5 56 9 i 5708 6724 8 52 53 9 682 9785 9 6 9997 i6 9 8o2 9 8i 9 973497619768 983698639871 6 62 53 5 7 4i 584o 6767 5856 5 77 4 6873 6790 6889 6807 5 9 o6 58 2 3 5 9 22 6 54 9 888 99 o5 99 22 9939199669973 5 54 5 9 3 9 5 9 55 6972 5 9 88 6oo5 6O2I 5 55 999 . . .7 . .25 ..42 ..5 9 ..76 4 55 6o.38 6o54 6071 6087 6io4 6l20 4 56 5 7 9 .8 9 oo 9 3 oi 9 5 01100127 0212 O23o oi44|0i6i 0178 0247 0264 0281 3 3 56 5 7 6i3 7 6236 6i53 6170 6262 626 9 6186 6286 62o3 63o2 62I 9 63i8 3 2 58 02 9 8 o3i5o332 o34 9 o366o383 I 58 6335635i 6368 6384 64oo 64i7 I 5 9 o4oo 04170434 o45i o468 o486 O 5 9 6433 645o 6466 6483 64 99 65:6 60" 50" i 40" 30" 20" 10" ES 60" 50" | 40" 30" 20" i 10" G Co-sine of 39 Degrees. JB s Co-sine of 38 Degrees s ( 111 O" J" A" P - Part { 2 3 5 7 5" 6" 7" 8" 9" 9 10 12 14 16 C 1" 2 " 3" 4" 5" 6" 7" 8" 9" 1 I 2 3 5 7 8 10 12 13 15 LOGARITHMIC TANGENTS. 75 d fH Tangent of 50 Degrees. d Tangent of 51 Degrees. 3 0" 10" 20" 30" 40" 50" '^ 0" 10" 20" 1 30" | 40" 50" 10.076186 6229 6272 63i5 6358 64oo 5 9 J o 10.091631 1674 1717 I 7 6o i8o3 1846 5 9 I 6443 6486 6529 65 7 i 66i4 665 7 58 i 1889 I 9 32 I 97 5 2018 2061 2IO4 58 2 6700 6742 6785 7 828 68 7 i 6913 5 7 2 2147 2191 2234 22 77 2320 2363 5 7 3 6 9 56 6999 7042 7 o85 -712-7 71-70 56 3 2406 244 9 2492 2535 2 5 7 8 2621 56 4 7213 7 256 7298 7 34i 7 384 742-7 55 4 2664 2707 2 7 5o 2 79 3 2 83 7 2880 55 5 7470 7512 7 555 7 5 9 8 7 64i 7684 54 5 2923 2 9 66 3009 3o52 3o 9 5 3i38 54 6 77*5 7769 7812 7 855 7897 794o 53 6 3i8i 3224 326 7 33io 3354 3397 53 7 79 83 8026 8069 8m 8i54 8197 52 7 344o 3483 35 2 6 356 9 36i2 3655 52 8 8240 8283 8325 8368 84n 8454 5i 8 36 9 8 3 7 4i 3 7 84 38 2 8 38 7 i 3 9 i4 5i 9 8497 853 9 8582 8625 8668 8711 5o 9 3 9 5 7 4ooo 4o43 4o86 4i2 9 4172 5o 10 10.078753 8796 8839 8882 8 9 25 8967 4 9 10 i 0.0942 i 5 425 9 43o2 4345 4388 443 1 ^9 ii 9010 9 o53 9 o 9 6 9 i3 9 9181 9224 48 ii 44 7 4 45i 7 456o 46o3 464 7 4690 i8 12 9267 93io 9 353 9 3 9 6 9 438 948 1 47 12 4733 4776 4819 4862 4 9 o5 4948 47 i3 9524 9 56 7 9610 9 65 2 9 6 9 5 9738 46 i3 4 99 2 5o35 5o 7 8 5l2I 5i64 5207 46 i4 9781 9824 9 86 7 999 9952 9995 45 i4 525o 52 9 3 533 7 538o 5423 5466 45 i5 io.o8oo38 0081 0124 0166 0209 0252 44 i5 55o 9 555 2 55 9 5 5638 568 2 5725 44 16 0295 o338 o38i o423 o466 oSog 16 5 7 68 58n 5854 58 97 5940 5984 43 17 o55 2 o5 9 5 o638 0680 0723 0766 42 17 6027 6070 6n3 6i56 6199 6242 [2 18 0809 o85 2 o8 9 5 o 9 3 7 0980 1023 4i 18 6286 632 9 63 7 2 64i5 6458 65oi ii J 9 1066 1 109 1162 n 9 5 I23 7 1280 4o 1 9 6544 6588 663i 66 7 4 671-7 6760 io 20 io.o8i323 i366 i4o 9 i452 i4 9 4 i53 7 3 9 20 io.o 9 68o3 6847 68 9 o 6 9 33 6976 7019 3 9 21 i58o 1623 1666 1-709 I 7 52 1794 38 21 7062 7106 7 i4 9 -7192 7 235 7278 38 22 i83 7 1880 I 9 23 1966 20O 9 2052 37 22 7321 7365 7 4o8 7 45i 7494 7 53 7 3 7 23 2094 2l3 7 2180 2223 2266 2309 36 23 7 58o 7624 7 66 7 7710 77 53 7796 36 24 2352 2 3 9 5 243 7 2480 2523 2566 35 24 7 84o 7883 7 926 7969 8012 8o56 35 25 2609 2652 2 6 9 5 2 7 38 2 7 8o 2823 34 25 8099 8142 8i85 8228 8271 83i5 34 26 2866 2909 2 9 52 2996 3o38 3o8i 33 26 8358 84oi 8444 848 7 853i 85 7 4 33 27 3i23 3i66 320 9 3252 32 9 5 3338 32 27 8617 8660 8 7 o3 8 7 4 7 8 79 o 8833 32 28 338i 3424 346 7 3509 3552 35 9 5 3i 28 8876 8919 8 9 63 9006 9049 9092 3i 2 9 3638 368i 3724 3 7 6 7 38io 3853 3o 29 9 i36 9179 9 222 9265 9 3o8 9 352 3o 3o 10.083896 3 9 38 3 9 8i 4024 4o6 7 4no 2 9 So 10.099395 9 438 9 48 1 9524 9 568 9611 2 9 3i 4i53 4196 423 9 4282 43 2 5 436 7 28 3i 9 654 9 6 97 97 4i 9784 9827 9870 28 32 44io 4453 4496 453 9 458 2 4625 27 32 99 i3 99 5 7 ..43 ..86 .i3o 27 33 4668 4 7 n 4754 4797 483 9 4882 26 33 10. 100173 0216 0259 o3o3 o346 o38 9 26 34 4925 4968 Son 5o54 5o 97 5i4o 25 34 0432 o4 7 6 oSig o56 2 o6o5 0649 25 35 5i83 5226 5269 53i2 5355 53 97 24 35 0692 o 7 35 o 77 8 0822 o865 0908 24 36 544o 5483 55 2 6 556 9 56i2 5655 23 36 o 9 5i o 99 5 io38 1081 1124 n 68 23 37 5698 5 7 4i 5784 582 7 58 7 o 5 9 i3 22 3? I2II 1254 I2 97 i34i 1 384 1427 22 38 5956 5 999 6o4i 6o84 612-7 6170 21 38 1470 i5i4 i55 7 1600 1 643 1687 21 3 9 62i3 6256 6299 6342 6385 6428 20 3 9 1730 i 77 3 1817 1860 igo3 i 9 46 2O 4o 10.086471 65i4 655 7 6600 6643 6686 I 9 4o 10. ioi 99 o 2o33 2076 2119 2i63 2206 J 9 4i 6729 6 77 2 68i5 6857 6900 6 9 43 18 4i 224 9 22 9 3 2336 2422 2466 18 42 6986 7 02 9 -7072 7 ii5 7 i58 7201 17 42 25o 9 2552 25 9 6 263 9 2682 2725 17 43 7244 7287 7 33o 7 3 7 3 7 4i6 7 45 9 16 43 276 9 2812 2855 28 99 2942 2 9 85 16 44 7502 7 588 7 63i 7 6 7 4 7717 i5 44 3o2 9 3o 7 2 3n5 3i58 3202 3245 i5 45 7760 78o3 7 846 7 88 9 79 32 797 5 i4 45 3288 3332 33 7 5 34i8 3462 35o5 i4 46 8018 8o6l 8 10^ 8i4 7 8i 9 o 8232 i3 46 3548 35 9 2 3635 36 7 8 3722 3 7 65 i3 47 8275 83i8 836i 84o4 8447 84 9 o 12 47 38o8 385i 38 9 5 3 9 38 3981 4o 2 5 12 48 8533 85 7 6 8619 8662 8 7 o5 8 7 48 II 48 4o68 4n i 4i55 4i 9 8 4241 4285 II 49 8791 8834 88 77 8 9 20 8 9 63 9006 10 4 9 4328 4371 44i5 4458 45oi 4545 10 5o 10.089049 9092 9 i35 9 i 7 8 9 22I 9264 9 5o i o.i o4588 463 1 46 7 5 4718 4761 48o5 9' 5i 9307 9 35o 9 3 9 3 9 436 94?9 9 522 8 5i 4848 48 9 i 4935 4 97 8 5O2I 5o65 '8 52 9 565 9608 9694 9737 97 8o 7 52 6108 5i52 5i 9 5 5238 5282 53 2 5 7 53 9823 9866 9909 99 52 9995 ..3 9 6 53 5368 54i2 5455 5498 5542 5585 6 54 10.090082 0125 0168 0211 025^ 0297 5 54 56a8 56 7 2 5 7 i5 5 7 5 9 58o2 5845 5 55 o34o o383 0426 0469 o5i2 o555 4 55 588 9 5 9 32 5 97 5 6019 6062 6106 4 56 o5 9 8 o64i o684 O 7 27 o 77 o o8i3 3 56 6149 6i 9 a 6236 62-79 6322 6366 3 5 7 o856 0899 0942 o 9 85 1028 1071 a 57 6409 6453 64 9 6 653 9 6580 6626 2 58 ni4 ii5 7 1 200 1243 1286 i32 9 i 58 6669 6 7 i3 6 7 56 6800 6843 6886 I 5 9 I3 7 2 i4i6 1459 1502 1 545 1688 o 5 9 6980 6 97 3 7 oi 7 -7060 7 io3 7 i4 7 O 60" 50" 40" 30" 20" 10" . 60" 50" 40" 30" 20" 10" d Co-tangent of 39 Degrees. i Co-tangent of 38 Degrees. a p p . < 1" 2" 3" 4" 5" 6" 7" 8" 9" irt { 4 9 13 17 21 26 30 34 39 P. Part | 4 9 13 17 22 26 30 35 39 LOGARITHMIC SINES. .g Sine of 52 Degrees. .H Sine of 53 Degrees. a 0" 10" 20" 30" 40" | 50" SI 0" 10" 20" 30" 40" 50" o 9 .8 9 6532 654 9 6565658i 6598 6614)59 o 9 . 9 o234 9 2364 238o 2396 24l2 2428 5 9 I 2 663i 664 7 67296746 6664 6680 67 62 6779 669-7 6 7 i3 6-7956812 58 i 2 2444 253 9 246o 2555 2475 2571 2491 2586 25o 7 2602 2523 2618 58 57 3 68286844 6861 68 77 6894 6910 56 3 2634 265o 2666 2681 26 97 2 7 l3 56 4 6 9 26 6 9 43 6 9 5 9 6976 6992 -7009 55 4 2729 2745 2761 2776 2 79 2 2808 55 5 7 025 704 1 7 o58 7 o 7 4 7 o 9 o 7 io 7 54 5 2824 2840 2856 2871 288 7 2 9 o3 54 6 7 I23 7 i4o 7 i56 7 i 7 2 7 i8 9 ! 7 2o5 53 6 2919 2 9 35 2950 2966 2 9 82 2998 53 7 7 222 7 238 7 254 7 2 7 I 7 28 7 7 3o3 52 7 3oi4 3o2 9 3o45 3o6i 3o 77 3o 9 3 52 8 7 320 7 336 7 353 7 36 9 7 385 7 4o2 5i 8 3io8 3i24 3i4o 3i56 3i 7 i 3i8 7 5i 9 74i8 7434 745 1 7 46 7 7 483 7 5oo 5o 9 32o3 3219 3235 325o 3266 3282 5o 10 9 .8 97 5i6 7 533 7 54 9 7 565 7 582 -7598 49 10 9.903298 33i3 332 9 3345 336i 33 7 7 49 ii 7 6i4 7 63i 7 64 7 7 663 -7680 -7696 48 ii 33 9 2 34o8 3424 344o 3455 48 12 7712 7729 7745 7761 77787794 47 12 348 7 35o3 35i8 3534 355o 3566 47 i3 7810 7 82 7 7843 7 85 9 78767892 46 i3 358i 35 97 36i3 3629 3644 366o 46 i4 79 o8 7924 79 4i 79 5 7 797 3 799 45 i4 36 7 6 36 9 i 3 7 o 7 3 72 3 3 7 3 9 3 7 54 45 i5 8006 8022 8o3 9 8o55 8o 7 i 8088 44 i5 3 77 o 3 7 86 38o2 38i 7 3833 384 9 44 16 8io4 8120 8i368i53 8i69'8i85 43 16 3864 388o 38 9 6 3912 3927 3 9 43 43 17 8202 8218 8 2 34 825o 826 7 |8283 42 i 7 3 9 5 9 3 97 4 3 99 o 4oo6 4021 4o3 7 42 18 82 99 83i5 8332 8348 8364838i 4i 18 4o53 4069 4o84 4ioo 4u6 4i3i 4i i 9 83 97 84i3 842 9 8446 84628478 4o i 9 4i47 4i63 4178 4194 4210 4225 4o 2o| 9 .8 9 84 9 4 85n 852 7 8543 8559 85 7 6 3 9 20 9.904241 425 7 4272 4288 43o4 43i 9 3 9 21 85 9 2 8608 86248641 865 7 :86 7 3 38 21 4335 435i 4366 4382 43 9 8 44i3 38 22 868 9 8 7 o6 8 7 228 7 38 8 7 548 77 o 3 7 22 4429 4445 446o 44?6 44 9 2 45o 7 37 23 8787 88o3 88i 9 8835 8852 8868 36 23 4523 453 9 4554 45 7 o 4586 46oi 36 24 8884 8 9 oo 8 9 i68 9 33 8949 8965 35 24 46i 7 4632 4648 4664 46 79 46 9 5 35 25 8 9 8i 8997 9 oi49o3o 9046 9062 34 25 4711 4 7 26 4742 4 7 5 7 4 77 3 4 7 8 9 34 26 9 o 7 8 9 o 9 5 9111 9 I2 7 91439159 33 26 48o4 4820 4836 485i 486 7 4882 33 27 9 i 7 6 9 I 9 2 9 2O8 9 224 92409256 32 27 48 9 8 49144929 4945 4 9 6o 4 97 6 32 28 9273 9 28 9 9 32I 9 33 79 354 3i 28 4992 5oo/ 5oa3 5o38 5o54 5o 7 o 3i 29 9 3 7 o 9 386 9 4o2 9 4i8 9 434 9 45o 3o 29 5o85 5ioi 5n6 5i32 5i48 5i63 3o 3o 9 .8 99 46 7 9 483 9 4 99 9 5i5 9 53i 9 54 7 2 9 3o 9.905179 5i 9 4 52IO 5225 524i 5 2 5 7 2 9 3i 9 564 9 58o 9 5 9 6 9 6i2 9 6 2 8 9 644 28 3i 5272 5288 53o3 53i 9 5334 535o 28 32 9 66o 9 6 77 9 6 9 3 9-709 97 25 97 4i 2 7 32 5366 538i 53 97 54i2 5428 5443 2 7 33 97 5 7 9773 97 8 9 9 8o6 9 822 9 838 26 33 545 9 5474 5490 55o6 552i 553 7 26 34 9 854 9 8 7 o 9 886 99 02 99 i8 99 35 25 34 5552 5568 5583 55 99 56i4 563o 25 35 99 5i 99 6 7 99 83 9999 24 35 5645 566i 5676 56 9 2 5 7 o8 5 7 23 24 36 9 . 9 ooo4 7 oo63 oo 79 oo 9 6 OII2 0128 23 36 5 7 3 9 5 7 54 5 77 o 5 7 85 58oi 58i6 23 37 oi44 0160 01-76 0192 0208 0224 22 37 5832 584 7 5863 58 7 8 58 9 4 5 9 o 9 22 38 0240 0256 O2 7 2 0289 o3o5 0321 21 38 5 9 25 5 9 4o 5 9 56 5 97 i 5 9 8 7 6002 21 3 9 o33 7 o353 o36 9 o385 o4oi 0417 2O 39 6018 6o33 6049 6o64 6080 6o 9 5 20 4o 9.900433 o44 9 o465o48i o4 9 7 o5i3 I 9 4o 9 . 9 o6m 61266142 6i5 7 6i 7 3 6188 I 9 4i 0529 o545 o562o5 7 8 o5 9 4 0610 18 4i 6204 6219 6235 625o 6265 6281 18 42 0626 0642 o658o6 7 4o6 9 o o 7 o6 17 42 62 9 6 63i2 632 7 6343 6358 63 7 4 1 7 43 O 7 22 o 7 38 o 7 54 o 77 o o 7 86 0802 16 43 638 9 64o5 6420 6436 645 1 6466 16 44 O8l8 o834 o85o 0866 0882 o8 9 8 i5 44 6482 6497 65i3 65 2 8 6544 655 9 i5 45 0914 o 9 3o o 9 46 o 9 62 o 97 8 o 99 4 i4 45 6575 65 9 o 66o5 6621 6636 665 2 i4 46 1010 1026 1042 io58 io 7 4 io 9 o i3 46 6667 6683 6698 6 7 i3 6 7 2 9 6 7 44 i3 4 7 1 1 06 I 122 n38 1 1 54 II 7 1186 12 47 6760 6 77 5 6791 6806 6821 683 7 12 48 1202 1218 1234 I25o 1266 1282 II 48 6852 6868 6883 6898 6 9 i4 6 9 2 9 II 49 1298 i3i4 i33o 1 346 i362 i3 7 8 IO 49 6 9 45 6960 6 97 5 6991 7006 7 022 IO 5o 9.901394 i4io 1426 1442 i458 i4 7 4 9 5o 9 . 9 o 7 o3 7 7 o52 -7068 7 o83 799 7 n4 9 5i 1490 i5o5 i5ai i53 7 r553 i56 9 8 5i 7 I2 9 7 i45 7 i6o 7 i 7 5 7i 9 i 7 206 8 52 i585 1601 1617 i633 i64 9 i665 7 52 7222 ?2 3 7 7 252 7 268 7283 7 2 9 8 7 53 1681 i6 97 I 7 i3 I 7 2 9 i 7 45 i 7 6o 6 53 73i4 7329 7 344 7 36o 7 3 7 5 7 3 9 i 6 54 i 77 6 I 79 2 1808 1824 i84o i856 5 54 7406 7 42i 743 7 7452 7 46 7 7 483 5 55) i8 7 2 1888 i 9 o4 1920 i 9 36 i 9 5i 4 55 74 9 8 7 5i3 7 52 9 7 544 7 55 9 7 5 7 5 4 56 196-7 i 9 83 i 999 2Ol5 2031 204 7 3 56 759 O 7 6o5 -7621 7 636 7 65i 7667 3 57 2o63 20 79 2O 9 5 2IIO 2126 2142 2 57 7682 7697 77 i3 77 28 77 43 77 5 9 2 58 2i58 2I 7 4 2I 9 O 22O6|2222 2238 I 58 7774 7789 7 8o5 7 82o 7 835 7 85i I 5 9 2253 226 9 2285 2301 23l 7 2333 O 5 9 7866 7881 7896 79 I2 79 2 7 79 42 60" 50" 40' 30" | 20" 10" O 60" 50" 40" 30" i 20" 10" a Co-sine of 97 Degrees. Co-sine of 36 Degrees. 1 P PartJ l " 2 " 3// * 5" 6" 7" 8" 9" p p . < 1" 2" 3" 4" 5" 6" 7" 8" 9" l.PartJ 2356 8 10 11 13 15 irt \ 2 3 5 6 8 9 11 12 14 LOGARITHMIC TANGENTS. 77 .5 . Tangent of 52 Degrees. .5 Tangent of 53 DC grees. 8 0" 10" 20" | 30" 40" 50" 2 0" 10" 20" 30' 40" 50" 10. 107190 7 234 7277(7320 7 364 7407 5o 10.122886 2929 2 9 73 3o 7 3o6i 3io5 5 9 i 745 1 7494 7 53 77 58i 7624 7668 58 I 3i48 3192 3236 3280 3324 3368 58 2 7711 77 54 7798 7 84i 7 885 7928 5 7 2 34n 3455 3499 3543 358 7 363o 5 7 3 79-72 8oi5 8o58 8l02 8i458i8 9 56 3 36 7 4 3 7 i8 3-762 38o6 385o 38 9 3 56 4 82 7 5 83i 9 8362 84o6 8449 55 4 3 9 3 7 3 9 8i 4o25 4069 4n3 4i5 7 55 5 84g3 8536 85 79 8623 8666 8710 54 5 4200 4244 4288 433 2 43 7 6 4420 54 6 8 7 53 8797 884o 8884 892-7 8970 53 6 4463 4507 455i 45 9 5 463 9 4683 53 7 9014 9101 9144 9188 9 23l 52 7 4727 i 77 o 48i4 4858 1902 4g46 52 8 9 2 7 5 9 3i8 9 36i 94o5 9448 9 4 9 2 5i 8 4 99 o 5o34 5o 77 5l2I 5i65 5209 5i 9 9535 9 5 79 9622 9666 9709 97 53 5o 9 5253 52 97 534i 5385 5428 54 7 2 5o 10 o. io9 7 96 9 84o 9 883 9926 9970 ,.i3 49 10 io.i255i6 556o 56o4 5648 5692 5 7 36 4 9 ii o. noo5 7 OIOO oi44 0187 023l 0274 48 ii 5780 5823 586 7 5 9 n 5 9 55 5 999 48 12 o3i8 o36i o4o5 o.448 0492 o535 4 7 12 6o43 6087 6i3i 6 I? 5 62I 9 6262 47 i3 o5 79 0622 0666 0709 0752 0796 46 i3 63o6 635o 63 9 4 6438 6482 6526 46 i4 o83 9 o&83 0926 0970 ioi3 io5 7 45 i4 6570 66i4 6658 6701 6 7 45 6789 45 i5 I I 00 1 44 1187 I23l 1274 i3i8 44 i5 6833 6877 6921 6 9 65 7009 7 o53 44 16 i36i 4o5 1 448 1492 i535 l5 79 43 16 7097 7141 7 i85 7229 7273 7816 43 l l 1622 666 1709 i 7 53 1797 i84o 42 1 7 736o r4o4 7 448 7492 7536 7 58o 42 18 1884 927 1971 20l4 2o58 2101 4i 18 7624 7668 77 I2 77 56 7800 7844 4i 19 2i45 2188 2232 2275 2 3i 9 2362 4o 19 7888 7 9 32 797 6 8020 8o63 8107 4o 20 o. 112406 2449 2493 2536 2 58o 2623 39 20 10. I28i5i 8i 9 5 8239 8283 8327 8871 3 9 21 266-7 2711 2 7 54 2798 2841 2885 38 21 84i5 845 9 85o3 854? SSgi 8635 38 22 2928 2972 3oi5 3o5 9 3 I 02 3i46 37 22 8679 8723 8 7 6 7 8811 8855 8899 37 23 3i8 9 3233 3277 3320 3364 34o 7 36 23 8 9 43 8987 9075 9119 9 i63 36 24 345 1 3494 3538 358i 3625 366 9 35 24 9207 9251 9 2 9 5 9 33 9 9 383 9427 35 25 3 7 I2 3 7 56 3 799 3843 3886 3 9 3o 34 25 9471 9 5i5 9 55 9 9 6o3 9647 9691 34 26 3 97 4 4017 4o6i 4io4 4i48 4191 33 26 97 35 9779 9 823 9867 9911 99 55 33 27 4235 4279 4322 4366 44o 9 4453 32 27 9999 ..43 ..87 .i3i .i 7 5 .2I 9 32 28 4496 454o 4584 4627 4671 4714 3i 28 io.i3o263 0307 o35i o3 9 5 0439 o483 3i 2 9 4 7 58 4802 4845 4889 4 9 32 4976 3o 29 0527 o5 7 i o6i5 o65 9 o 7 o3 0747 3o 3o IO. Il5o20 5o63 5107 5i5o 5 1 94 5238 29 3o 10. 130791 o835 o8 79 0923 0967 ion 2 9 3i 5281 5325 5368 54i2 5456 5499 28 3i io55 1099 n43 1187 1232 1276 28 32 5543 5586 563o 56 7 4 5717 5 7 6i 27 32 1320 1 364 i4o8 i452 i4 9 6 i54o 2 7 33 58o4 5848 5892 5g35 5979 6o23 26 33 1 584 1628 1672 1716 1760 1804 26 34 6066 6110 6i53 619-7 6241 6284 25 34 1 848 1892 i 9 36 1981 2O25 2o6 9 25 35 6328 6372 64i5 645 9 65o2 6546 24 35 91*3 2i5 7 22OI 2245 2289 2333 24 36 o5oo 6633 6677 6 7 2I 6 7 64 6808 23 36 2377 2421 2465 2509 2554 2 5 9 8 23 37 6852 6895 6 9 3 9 6982 7026 7070 22 37 2642 2686 2780 2774 2818 2862 22 38 7 n3 7 l5 7 7201 7 244 7288 7332 21 38 2906 2g5o 2994 3o3 9 3o83 3!2 7 21 3 9 7 3 7 5 7419 7463 7 5o6 7 55o 7594 20 3 9 3i 7 i 3 2I 5 3259 33o3 3347 3391 2O 4o io.n 7 63 7 7681 7725 77 68 7812 7 856 I 9 4o 10. 133436 348o 3524 3568 36i2 3656 19 4i 7899 79 43 7987 8o3o 8o 7 4 8118 18 4i 8700 3?44 3 7 8 9 3833 38 7 7 8921 18 42 8161 82o5 8249 8202 8336838o : 7 42 3965 4009 4o53 4097 4i42 4i86 i 7 43 8423 846 7 85n 8555 85 9 8 8642 16 43 4230 4274 43i8 4362 44o6 445 1 16 44 8686 8729 8 77 3 88i 7 8860 8904 i5 44 4495 4539 4583 4627 46 7 i 4 7 i5 i5 45 8 9 48 8992 9 o35 90-79 9123 9166 i4 45 4 7 6o 48o4 4848 4892 4g36 4 9 8o i4 46 9 2IO 9254 9 2 97 9 34i 9 385 9429 i3 46 5o25 5o6 9 5ii3 5i5 7 52OI 5245 i3 47 48 9 472 97 35 9 5.6 9778 9 56o 9 822 9602 9866 9 647 999 9691 9 9 53 12 I I 47 48 5290 5555 5334 55 99 5378 5643 5422 568 7 5466 5 7 3i 55io 5 77 5 12 II 49 9997 ..84 .128 .172 ?2i6 10 4 9 5820 5864 5 9 o8 5 9 5 2 5 99 6 6o4i 10 5o IO. 120259 o3o3 o347 oSgi o434 0478 g 5o io.i36o85 6i2 9 6178 6217 6262 63o6 9 5i O522 o565 o6o 9 o653 o6 9 7 0740 8 5i 635o 63g4 6438 6483 652 7 65 7 i 8 52 o 7 84 0828 0872 ogiS o 9 5 9 100: 7 52 66i5 665 9 6704 6 7 48 6792 6836 7 53 io4 7 1091 n34 11-78 1222 1266 6 53 6881 6925 6969 7 oi3 7 5 7 7 IO2 6 54 1309 i353 i3 97 i44i 1 484 i5 2 8 5 54 7146 7190 723^ 7279 7 3 2 3 7 36 7 1 f 55 l5 7 2 1616 i65 9 i 7 o3 1747 1791 4 55 7 4n 7455 75oo 7544 7 588 7 632 4 56 i835 1878 I 9 22 1966 2OIO 2o5!: 3 56 7677 7721 77 65 7809 7 854 7 8 9 8 3 5 7 2O9 7 2r4i 2i85 2229 2272 23i6 2 5 7 7942 7986 8o3i 8075 8119 8i63 2 58 236o 2404 2448 2491 2535 2^79 I 58 8208 8252 8296 834i 8385 8429 I 5 9 2623 2667 2710 2 7 5/! 2798 2842 5 9 84?3 85i8 8562 8606 865o 86 9 5 O 60" 50" 40" 30" 20" 10" d 60" 50" 40" 30" 20" 10" - Co-tangent of 37 Degrees. 1 Co-tangent of 36 Degrees. 1 A 1" 2" 3" 4" 5" 6" 7" 8" 9" in \ 4 9 13 17 22 26 31 35 39 < 1" 2" 3" 4" 5" 6" 7" 8" 9" l-.-farWj 4 9 13 is 2 2 26 31 35 40 78 LOGARITHMIC SINES. I Sine of 54 Degrees. a Sine of 55 Degrees. i s 0" 10" 20" 30" 40" 50" 0" 10" 20" 30" j 40" 50" 9.907958 7973 798880048019 8o34 5 9 o 9 . 9 i3365 33 79 33 9 4 34o 9 3423 3438 5 9 I 8o4 9 8o65 80808095 8111 8126 58 i 3453 3468 34S2 34 9 7 35i2 352 7 5S 2 8i4i 8156:817281878202 821-7 5 7 2 354i 3556 35 7 i 3585 36oo 36i5 57 q 8 2 33 8248 8263 82-79 8294 8309 56 3 363o 3644 365 9 36 7 4 3688 3 7 o3 56 4 83 2 4 834o!835583 7 o8385 84oi 55 4 3 7 i8 3 7 33 3 7 4 7 3 7 62 3 777 3 79 i 55 c 84i6 843 1 8446 8462:8477)8492 54 5 38o6 382i 3836 385o 3865 388o 54 6 8507 8523 85388553^85688584 53 6 3894 3 9 o 9 3 9 24 3 9 38 3 9 53 3 9 68 53 7 85 99 86i4 86298644:86608675 52 7 3982 3 997 4012 4026 4o4i 4o56 52 8 86 9 o 8 7 o5 8721 87368751)8766 5i 8 4070 4o85 4ioo 4n4 4129 4x44 5i 9 8781 8 797 88128827884218857 5o 9 4i58 4i 7 3 4i88 4202 4217 4232 5o JO 9.908873 8888 89038918,8933 8949 49 10 9.914246 4261 42-76 4290 43o5 4320 49 ii 8 9 64 8979 89949009*9025 9040 48 ii 4334 4349 4364 43 7 8 43 9 3 4407 48 12 9 o55 90-70 9 o85 9101 9116 9i3i 47 12 4422 443 7 445 1 4466 448 1 4495 47 i3 9146 9161 9176 9192:9207 9222 46 i3 45io 4524 453 9 4554 4568 4583 46 i4 9 23 7 9252 9267 9283^9298 9 3i3 45 i4 45 9 8 46l2 462 7 464i 4656 46 7 i 45 i5 9328 93439358:93-7419389 9 4o4 44 i5 4685 4 7 oo 47i4 4 7 29 4744 4758 44 16 9419 9434 9449 9464 9480 9 4 9 5 43 16 4773 4 7 8 7 4802 48i 7 483i 4846 43 17 952595409555 9 5 7 9 586 42 17 486o 48 7 5 48 9 o 4904 4919 4 9 33 42 18 9601 96169631 96469661 9 6 7 6 4i 18 4948 4962 4 9 77 4992 5oo6 5021 4i 20 9691 9.909782 9 7 o 7 9 7 22 97 3 797 52 9 7 9 7 9812^827 9 843 9767 9 858 4o 39 '9 20 5o35 9.915123 5o5o 5i3 7 5o64 5i5 2 5o 79 5i66 5o 9 4 5i8i 5io8 5i 9 6 4o 3 9 21 9 8 7 3 9 888 99 o3 9918 9933 99 48 38 21 52IO 5225 523 9 5254 5268 5283 38 22 99 63 997 s 9994 ...9 ..24 ..3 9 37 22 5297 53i2 5326 534i 5356 53 7 o 37 23 9.910054 0069 0084 0099 01 14 0129 36 23 5385 5399 54i4 5428 5443 545 7 36 24 oi44 oi5 9 oi 7 5 0190 O2o5 O22O 35 24 5472 5486 55oi 55i5 553o 5544 35 25 0235 O25o O265 0280 0295 o3io 34 25 555 9 55 7 3 5588 56o2 56i 7 563i 34 26 o325 o34oo355 0370 o385 o4oo 33 26 5646 566o 56 7 5 568 9 5 7 o4 5 7 i8 33 27 o4i5 o43oo446 o46i 0476 o4 9 i 32 27 5733 5 7 4 7 5 7 62 5 77 6 5791 58o5 32 28 o5o6 O52I o536 o55i o566o58i 3i 28 5820 5834 5849 5863 58 7 8 58 9 2 3i 29 0596 0611 0626 o64i 06560671 3o 29 5 9 o 7 5 9 2I 5 9 36 5 9 5o 5 9 65 5 979 3o 3o 9.910686 O 7 OI 0716 o 7 3i o 7 46 o 7 6i 29 3o 9.915994 6008 6023 6037 6o52 6066 29 3i 0776 o 79 i 0806 0821 o836 o85i 28 3i 6081 6o 9 5 6109 6124 K 6i38 6i53 28 32 0866 0881 0896 0911 0926 0941 27 32 6167 6182 6196 6211 6225 6240 27 33 0956 09-71 0986 IOOI 1016 io3i 26 33 6254 6268 6283 6297 63i2 6326 26 34 io46 1061 1076 1091 1106 I 121 25 34 634i 6355 636 9 6384 6398 64i3 25 35 n36 u5i 1166 1181 1196 I2II 24 35 6427 6442 6456 6470 6485 64 99 24 36 1226 1241 1256 1271 1286 i3oo 2 3 36 65i4 65 2 8 6543 655 7 6571 6586 23 37 i3i5 i33o i345 i36o 1375 139022 37 6600 66i5 6629 6643 fi658 6672 22 38 i4o5 1420 i435 i45o i465 i48o 21 38 6687 6701 6 7 i5 6730 6744 7 5 9 21 39 1495 i5io i525 i54o i555i56 9 2O 39 6 77 3 6787 6802 6816 683o 6845 20 4o 9.911584 l5 99 i6i4 1629 i644 i65 9 19 4o 9.916859 68 7 4 6888 6902 6917 6 9 3i r 9 4i 1674 1689 1704 1719 1734 1748 18 4i 6946 6 9 6o 6 97 4 6989 7003 7017 1 8 42 1763 1778 i 79 3 1808 1823 i838 17 42 7032 7046 7060 7075 7089 7104 17 43 i853 1868 i883 1897 1912 1927 16 43 7118 7 l32 7147 7161 7 i 7 5 7i 9 o 16 44 1942 1957 1972 1987 2OO2 2017 i5 44 7204 7218 7233 7247 7261 7276 i5 45 2031 2046 2061 2076 2091 2IO6 i4 45 7290 7 3o4 7 3i 9 7 333 7 34 7 7362 i4 46 2121 2i36 2i5o 2i65 2l8o 2195 i3 46 7 3 7 6 7 3 9 o 74o5 7419 7433 7448 i3 47 22IO 2225 224O 2255 2269 2284 12 47 7462 7 4 7 6 7491 75o5 7 5i 97 534 12 48 2299 23i4 2329 2344 2358 2 3 7 3 II 48 7 548 7 56 2 7 5 7 6 7 5 9 i 7 6o5 :7 6i 9 II 49 2388 24o3 2418 2433 2448 2462 10 49 7 634 7648 7662 7677 -7691 77 o5 IO 5o 9.912477 2492 2507 2522 2 53 72 55i 9 5o 9.9177197734 77 48 7762 7777 779 1 9 5i 2566 2 58i 2596 26l I 2625 2640 8 5i 7805 7819 7 834 7848 7862 7877 8 52 2655 2670 2685 2700 2-714 2-729 7 52 7891 79 o5 7919 79 34 7 53 2 7 44 27 5 9 2774 2 7 88 28o3 2818 6 53 7976 7991 8oo5 8019 8o338o48 6 54 2833 2848 2862 2877 2892 290-7 5 54 806280768090810581198133 5 55 2922 29362951 29662981 2995 4 55 814781628176819082048219 4 56 3*oio 3o 2 5 3o4o3o55j3o693o84 3 56 82338247:8261827682908304 3 5? 3099 3n4 3i283i43:3i583i 7 3 2 57 83i8'8333834 7 836i 83 7 5838 9 2 58 3i8 7 32O2 32173232 32473261 i 58 84o4 84i8 8432 8446 846i 84 7 5 i 5 9 32 7 6 3291 33o6332o!3335335o o 5 9 8489 85o385i 7 853 2 8546856o o 60" 50" 40" 30" 20" 10" . ^ 60" 50" t 40" 30" 20" 10 7 ^ Co-sine of 35 Degrees. i Co-sine of 34 Degrees. ^ T.PartM' 2/ 3 " 4 " 5// 6// 7 * 8// 9 "- '' P P^n" 2// 3// 4// 5 " 6 " 7 " 8" 9" J 2 3 5 6 8 9 11 12 14 ; "^ 1 3 4 6 7 9 10 12 13 LOGARITHMIC TANGENTS, d 1 Tangent of 54 Degrees. a Tangent of 55 Degrees. * 0" 10" 20" 30" 40" 1 50" * 0" 10" 20" 30" | 40" \5(y io.i3873 9 8 7 83 8828 8872 8 9 i6 8 9 6o 5o o 10.154773 48i8 4863 4 9 o8 4 9 52 4997 v i 9 oo5j 9 o4 9 9 o 9 3 9 i38 9 l82 9 226 58 I 5042 5o8 7 5i32 5i 77 5221 5 2 66 58 2 9 2 7 9 3i5 9 35 9 9 4o3 9 448 9 4 9 2 5 7 2 53n 5356 54oi 5446 5490 5535 57 3 9 536 9 58o 9 625 9669 97 l3 97 58 56 3 558o 56255670 5 7 i5 5 7 5 9 58o4 5b 4 9 8o2 9 846 9 8 9 i 99 35 9979 ..24 55 4 584 9 58 9 4 5 9 3 9 5 9 84 6o2 9 6o 7 3 55 5 10. i4oo68 01 12 oi5 7 0201 0245 0290 54 5 6118 6i636 2 o8 6 2 53 62 9 8 6343 54 6 o334 o3 7 8 0423 o46 7 o5ii o556 53 6 6388 6432 64 77 6522 6567 6612 53 7 0600 o644 o68 9 0733 0777 0822 52 7 665 7 6-702 6 7 4 7 6 79 i 6836 688 1 52 8 0866 o 9 io o 9 55 0999 io43 1088 5i 8 6 9 26 6 97 i 7 oi6 7 o6i 7106 7 i5i 5i 9 Il32 1 176 1221 1265 i3o 9 i354 5o 9 7i 9 5 -7240 7 285 7 33o 7 3 7 5 7 4?o 5o 10 io.i4i3 9 8 1442 i48 7 i53i i5 7 6 1620 49 10 io.i57465 7 5io 7 555 7 6oo 7 645 7 68 9 49 ii 1 664 r 79 i 7 53 1797 1842 1886 48 ii 7734 7779 7824 7 86 9 7 9 i4 79 5 9 48 12 I 9 3i i 97 5 2019 2064 2108 2l52 4 7 19 8oo4 8049 8o 9 4 8i3 9 8i84 8229 47 i3 2I 9 7 2241 2286 2 33o 23 7 4 24l9 46 r3 8273 83i8 8363 84o8 8453 8498 46 i4 2463 2 5o8 2552 25 9 6 2641 2 685 45 i4 8543 8588 8633 8678 8723 8 7 68 45 i5 2780 2774 2818 2863 2 9 7 2952 44 ID 88i3 8858 8 9 o3 8 9 48 8 99 3 9 o38 44 16 2 99 6J3o4i 3o85 3i2 9 3i 7 4 3218 43 16 9 o83 9 I28 9 i 7 3 9 2l8 9 263 9 3o 7 43 17 3263 33o7 335i 33 9 6 344o 3485. 42 i 7 9 35 2 9 3 97 948 7 9 532 9 5 77 42 18 35 29 35 7 4 36i8 3662 3707 3 7 5i 4r 18 9 622 9 66 7 97 I2 97 5 7 9 8o2 9 84 7 4i 19 3 79 6 384o 3885 3 9 2 9 3 97 4 4oi8 4o 19 9 8 9 2 99 3 7 9982 ..27 ..72 .n 7 4o 20 10. 144062 4io 7 4i5i 4i 9 6 4240 4285 3 9 20 10. 160162 0207 0252 02 97 0342 o38 7 3 9 21 432 9 43 7 4 44i8 4463 4507 455i 38 21 0432 o4 77 0522 o56 7 0612 o65 7 38 22 45 9 6 464o 4685 472 9 4774 4818 37 22 0703 o 7 48 o 79 3 o838 o883 9 28 3 7 23 4863 4 9 o 7 4 9 5 2 4 99 6 5o4i 5o85 36 23 0973 1018 io63 1108 n53 n 9 8 36 24 5i3o 52 1 9 5263 53o8 5352 35 24 1243 1288 i333 i3 7 8 1423 i468 35 25 53 97 544i 5486 553o 55 7 5 5619 34 25 i5i3 i558 i6o3 1 648 i6 9 3 I 7 3 9 34 26 5664 5 7 o8 5 7 53 5 797 5842 5886 33 26 1784 l82 9 i8 7 4 1919 i 9 64 2O0 9 33 27 5 9 3i 5 97 5 DO2O 6o64 6io 9 6i53 32 27 2o54 20 99 2i44 2i8 9 2234 22 79 32 28 6i 9 8 6242 628-7 633i 6876 6420 3i 28 2325 23 7 24i5 2460 25o5 2550 3i 29 6465 65o 9 6554 65 9 8 6643 668-7 3o 29 25 9 5 2640 2685 2730 2 77 5 2821 3o 3o 10.146732 6 777 6821 6866 6 9 io 6 9 55 29 3o 10. 162866 2 9 II 2 9 56 3ooi 3o46 3o 9 i 29 3i 6 999 7 o44 7 o88 7 i33 7177 7222 28 3i 3i36 3i8i 322 7 3272 33i 7 3362 28 32 7267 7 3n 7 356 7 4oo 7445 748 9 27 32 34o 7 3452 34 97 3542 3588 3633 27 33 7534 7 5 7 8 7 6 2 3 7 668 7712 7757 26 33 36 7 8 3 7 23 3 7 68 38i3 3858 3 9 o4 26 34 7801 7 846 7 8 9 o 79 35 79 8o 8024 25 34 3 9 4 9 3 99 4 4o3 9 4o84 4l2 9 4i 7 4 25 35 8o6 9 8n3 8i58 82o3 8292 24 35 4220 4265 43io 4355 44oo 4445 24 36 8336 838i 8425 84 7 o 85i5 8559 23 36 44 9 i 4536 458i 4626 46 7 i 4 7 i6 23 '3 7 86o4 8648 86 9 3 8 7 38 8782 8827 22 37 4762 48o 7 4852 48 97 4 9 42 4 9 88 22 38 8871 8 9 i6 8 9 6i 9 oo5 9 o5o 9095 21 38 5b33 5o 7 8 5i23 5i68 52i3 5 2 5 9 21 3 9 9 i3 9 9 i84 9 228 9 2 7 3 9 3i8 9 362 20 3 9 53o4 534 9 53 9 4 543 9 5485 553o 20 4o 9 452 9 4 9 6 9 54i 9 585 963o 19 4o IO. 165575 5620 5666 5711 5 7 56 58oi 1 9 4i 9 6 7 5 97i9 9764 9 8o 9 9 853 9898 18 4i 5846 58 9 2 5 9 3 7 5 9 82 6027 6o 7 3 18 42 99 43 99 8 7 ..32 ..76 .121 .166 17 42 6118 6i63 62b8 6253 62 99 6344 17 43 IO. I5O2IO 0255 o3oo o344 o38 9 o434 16 43 638 9 6434 648o 6525 65 7 o 66i5 16 44 0478 o523 o568 0612 o657 0702 i5 44 6661 6706 6 7 5i 67 9 6 6842 688 7 i5 45 0746 o 79 i o836 0880 092!) 0970 i4 45 6 9 32 6 9 77 7 023 7068 7ii3 7 i58 i4 46 ioi4 io5 9 no4 n4 9 ii 9 3 1238 i3 46 7204 7 24 9 7 2 9 4 7340 7 385 7 43o i3 47 1283 l32 7 1872 i4i 7 i46i i5o6 12 47 7475 7 52I 7 566 7611 7 65 7 77 02 12 48 i55i i5 9 5 i64o i685 1780 1774 II 48 7747 779 2 7 838 7 883 79 28 7974 II 49 i8i 9 i864 i 9 o8 i 9 53 i 99 8 2043 10 49 8oi 9 8o64 8io 9 8i55 8200 8245 10 5o 10. 152087 2l32 2177 2221 2266 23ll 9 5o io.i682 9 i 8336 838i 8427 8472 85i 7 9 5i 2356 2400 2445 2/QO 2535 2579 8 5i 8563 8608 8653 86 99 8 7 44 8789 8 52 2624 266 9 2713 2 7 58 28o3 2848 7 52 8835 8880 8 9 25 8 97 i 9 oi6 9061 7 53 28 9 2 2 9 3 7 2 9 82 3027 3o 7 i 3n6 6 53 9107 9 l52 9 i 97 9 243 9 288 9 333 6 54 3i6i 3206 325o 32 9 5 334o 3385 5 54 9 3 79 9 4a4 9 46 9 9 5i5 9 56o 9605 5 55 343o 34 7 4 35i 9 3564 36o 9 3653 4 55 9 65i 9 6 9 6 97 42 9787 9 832 9878 4 56 36 9 8 3 7 43 3 7 88 3832 38 77 3922 3 56 99 23 99 68 ..5 9 .io5 .i5o 3 57 3 9 6 7 4OI2 4o56 4ioi 4i46 4191 2 57 io.i 7 oi 9 5 0241 0286 o33i o3 77 0422 2 58 4236 4280 4325 4370 44i5 446o I 58 o468 o5i3 o558 o6o4 o64 9 0695 I 5 9 45o4 454 9 45 9 4 463 9 4684 4728 O 5 9 o 7 4o o 7 85 o83i 0876 0922 0967 O 60" 50" 40" 30" 20" 10" d 60" 50" 40" 30" 20" 10" c Co-tangent of 35 Degrees. * Co-tangent of 34 Degrees. 3 p p . < 1" 2" 3" 4" 5" 6" 7" 8" 9" I 4 9 13 18 22 27 31 36 40 P. Part J 5 "g 14 ig 23 27 32 36 41 LOGARITHMIC SINES. A Sine of 56 Degrees. c IS Sine of 57 Degrees. 2 0" 10" 20" 30" 40" 50" s 0" 10" 20" 30" 40" 50" o 9.918574 8588 86o3 8617 863i 8645 5 9 9 . 9 235 9 i 36o5 36i 9 3632 3646 366o 5 9 i 865 9 J86 7 4 8688 8 7 02 8716 8 7 3o 58 I 36 7 3 368 7 3 7 oi 37i4 3 7 28 3 7 42 58 2 8 7 45 8 7 5 9 8 77 3 8 7 8 7 8801 88i5 5 7 2 3 7 55 3 7 6 9 3 7 83 3 79 6 38io 38 2 4J5 7 ! 883o 8844 8858 88 7 2 8886 8900 56 3 383 7 385i 3865 38 7 8 38 9 2 3 9 o6!56 4 8 9 i5 9000 8929 9012 8 9 43 9 O28 8 9 5 7 9 042 8 9 7i 8 9 85 9 o56 9 070 55 54 L r. 3 9 i 9 4ooi 3 9 33 4oi5 3 9 46 4028 3 9 6o 4042 3 97 4 4o55 3 9 8 7 4o6 9 r r j -j i 54 6 9 o85 9099 9 n3 9 I2 ? 9 i4i 9 i55 53 6 4o83 4o 9 6 4no 4124 4i3 7 4i5i 53 7 9169 9184 9 i 9 8 9 2I2 9226^9240 52 1 4i64 4178 4l 9 2 42o5 42I 9 4232 52 8 9254 9268 9 282 9 2 9 7 9 3u 9 325 5i 8 4246 4260 42 7 3 4287 43oo 43i4 5i 9 9 33 9 9 353 9 367 9 38i 9 3 9 5 9 4io 5o 9 4328 434i 4355 4368 4382 43 9 6 5o 10 9.919424 9 438 9 452 9 466 9480 9494 49 10 9 . 9 244o 9 4423 4436 445o 4464 4477 4 9 ii 95o8 9 522 9 53 7 9 55i 9565 9579 48 ii 44 9 i 45o4 45i8 453i 4545 455 9 48 12 ivi 9 5 9 3 9677 9607 9692 9 62I 97 o6 9 635 97 20 9649 9663 97 34 9 748 47 46 12 i3 45 7 2 4654 4586 466 7 45 99 468 1 46i3 46 9 4 4626 4 7 o8 464o 4721 4 7 46 iZ 9762 9776 979 9804 9818 9832 45 i4 4 7 35 4748 4 7 62 4776 4 7 8 9 48o3 45 j t 9 846 9860 9 8 7 5 9 88 9 9903 9917 44 i5 48i6 483o 4843 485 7 48 7 o 4884 44 16 99 3i 99 45 99 5 9 997 3 9987 ... i 43 16 48 97 49" 4924 4 9 38 4 9 5 2 4 9 65 43 17 9.920015 0029 oo43 oo5 7 0071 oo85 42 "7 4 9 79 4 99 2 5oo6 5oi 9 5o33 5o46 42 18 0099 OIlS 0127 oi4i oi56 OI 7 4i 18 5o6o 5073 5o8 7 5 1 oo 5n4 5127 4i 19 0182 0198 O2I2 0226 0240 O25^ 4o I 9 5i4i 5i54 5i68 5i8i 5i 9 5 5208 4o 20 9.920268 0282 O2 9 6 o3io 0324 o338 3 9 20 9 . 9 25222 5235 5249 5262 52 7 6 528 9 3 9 21 o352 o366 o38o o3 9 4 o4o8 0422 38 21 53o3 53i6 533o 5343 535 7 53 7 o 38 22 o436 o45o o464 o4 7 8 0492 o5o6 37 22 5384 53 97 54n 5424 5438 545i 37 23 O520 o534 o548 o562 o5 7 6 oSgo 36 23 5465 5478 5491 55o5 55i8 5532 36 24 o6o/! 0618 o632 o646 0660 o6 7 4 35 24 5545 555 9 55 7 2 5586 55 99 56i3 35 25 0688 0702 07160730 o 7 44 o 7 58 34 25 5626 564o 5653 5667 568o 56 9 3 34 26 0772 0786 o8oo|o8i4 0828 0842 33 26 5 77 5720 5 7 34 5 7 4 7 5 7 6i 5 77 4 33 2 7 o856 0869 o883 0897 0911 0925 32 2 7 5 7 88 58oi 58i4 5828 584i 5855 32 28 o 9 3 9 o 9 53 o 9 6 7 0981 o 99 5 1009 3i 28 5868 5882 58 9 5 5 9 o8 5 9 22 5 9 35 3i 29 IO22 1037 io5i io65 1079 1093 3o 2 9 5 9 4 9 5 9 62 5 97 6 5 9 8 9 6OO2 6016 3o 3o 9.921107 II2I n34 n48 1162 n 7 6 2 9 3o 9 . 9 26O2 9 6o43 6o56 6o6 9 6o83 6096 2 9 3r 1190 1204 1218 1232 I2 46 1260 28 3i 6110 6i23 6i36 6i5o 6x63 6177 28 32 1274 1288 1302 i3i5 I32 9 1 343 2 7 32 6i 9 o 6 2 o3 621-7 623o 6244 625 7 27 33 i35 7 l37I i385 i3 99 i4i3 l42 7 26 33 62 7 6284 62 97 63ii 6324 633 7 26 34 i44i i455 1 468 1482 1496 i5io 25 34 635i 6364 63 77 63 9 i 64o4 64i8 25 35 i524 i538 i55 2 i566 i58o i5 9 3 24 35 643i 6444 6458 64 7 i 6484 64 9 8 24 36 1607 1621 i635 i64 9 i663 1677 23 36 65u 65 2 5 6538 655i 6565 65 7 8 23 3? 1691 1704 1718 1732 1746 1760 22 3 '7 65 9 i 66o5 6618 663i 6645 6658 22 38 1 77 4 1788 1802 i8i5 i82 9 i843 21 38 66 7 i 6685 66 9 8 6 7 n 6 7 25 6 7 38 21 3 9 1857 1871 i885 i8 99 i 9 i2 1926 2O 3 9 6 7 5i 6 7 65 6778 6 79 i 68o5 6818 20 4o 9.921940 1954 i 9 68 198211995 2009 J 9 4o 9 . 926831 6845 6858 68 7 i 6885 68 9 8 X 9 4i 2023 203 7 2o5i 2o65 2079 2092 18 4i 6 9 u 6 9 25 6 9 38 6 9 5i 6 9 65 6978 18 42 2106 2I2O 2i34 2148 2162 2I 7 5 '7 42 6991 7oo5 7018 7 o3i 7 o44 7 o58 1 7 43 2189 2203 2217 223l 2244 2258 16 43 707: 7 o84 7 o 9 8 7 in 7 I24 7 i38 16 44 45 2272 2355 2286 2 36 9 23oo 2383 23i3 2327 23 9 624io 234i 2424 i5 i4 44 45 7 i5i 7231 7164 7244 7177 7 25 7 7 i 9 i 7 2 7 7 204 7 284 7 2I 7 7297 i5 i4 46 2438 2452 2465 247 9 24 9 3 2507 i3 46 73io 7 324 7337 7 35o 7 363 7377 i3 47 2520 2534 2548 2562 2576 2589 12 47 7 3 9 o 7 4o3 74i6 7 43o 7 443 7456 12 48 26o3 2617 263i 2644 2658 2672 II 48 7 4 7 o 7483 74 9 6 7 5o 9 7 5 2 3 7 536 II 49 2686 2700 2 ?I 3 2727 2741 2 7 55 IO 49 7 54 9 7 562 7 5 7 6 7 58 9 7602 7 6i5 10 5o 9.922768 2782 2 79 6 28102823 2 83 7 9 5o 9 . 9 2 7 62 9 7 642 7 655 7 668 7 68i 7 6 9 5 9 5i 285i 2865 2878 28 9 2 2 9 O6 2920 8 5i 77 o8 772i 7734 77 48 776i 7774 8 52 2 9 33 2947 2 9 6i 2975 2988 3002 7 52 7787 7 8oi 7814 7 82 7 7 84o 7 853 7 53 3oi6 3o3o 3o43 3o57 3071 3o84 6 53 7867 7 88o 793 7906 79 20 79 33 6 54 3o 9 8 3lI2 3i26 3i3 9 3i53 3167 5 54 7946 79 5 9 797 2 79 86 7999 8012 5 55 3i8i 3ig4 3208 3222 3235 3 2 4 9 4 55 8o25 8o38 8o5 2 8o65 8o 7 8 8o 9 i 4 56 3263 3277 32 9 O 33o433i8 333i 3 56 8io4 8118 8i3! 8i448i5 7 8i 7 o 3 5 7 3345 335 9 3372 338634oo 34i4 2 5 7 8i838i 9 7 8210 8223J8236 8249 2 58 3427 344 1 3455 348j3482 3496 I 58 8263 8276 828 9 83o283i5 8828 i 5 9 35o 9 35 2 3 353 7 355o 3564 35 7 8 O 5 9 834s 8355 8368 838i 83 9 484o 7 i o 60" 50" 40" 30" 20" 10" d 60" 50" 40" 30" 20" 10" e Co-sine of 33 Degrees. Co-sine of 32 Degrees. 1 .$1" 2" 3" 4" 5" 6" 7" 8" 9" P Pnrt5 1/ ~" 3// 4// 5 " 6 " 7 " 8" 9 " irt } 1 3 4 6 7 8 10 11 13 r.ranj i 3 4 5 7 8 9 n 12 LOGARITHMIC TANGENTS. 8) A Tangent of 56 Degrees. .3 Tangent of 57 Degrees. ji 0" 10" 20" 30" 40" | 50" n 0" 10" 20" 30" | 40" | 50" o 10. 171013 io58 no3 1149 1194 I24o 5 9 10.187483 7 52 9 7 5 7 5 7621 7667 7713 5 9 I 1285 i33i i3 7 6 1421 i46 7 l5l2 58 i 77 5 9 7 8o5 7 85i 7898 7944 799 58 2 i558 i6o3 i64 9 1694 i 7 3 9 i 7 85 57 2 8o36 8082 8128 8174 82208267 5? 3 i83o i8 7 6 I 9 2I J 9 6 7 2OI2 ao58 56 3 83i3 835 9 84o5 845 1 8497 8543 56 4 2103 2149 2I 9 4 2239 2285 233o 55 4 85 9 o 8636 8682 8728 8 77 4 8820 55 5 23 7 6 2421 246 7 25l2 2558 26o3 54 5 8866 8 9 i3 8 9 5 9 9005 9 o5i 9097 54 6 2649 2694 2 7 4o 2 7 85 283i 28-76 53 6 9 i43 9190 9 236 9282 9328 9 3 7 4 53 7 2 9 22 2 9 6 7 3oi3 3o58 3io4 3i49 52 7 9 420 9467 9 5i3 9 55 9 9 6o5 9 65i 52 8 3i 9 5 324o 3 2 86 333i 33 77 3422 5i 8 9 6 9 8 9744 9-790 9 836 9882 9929 5i 9 3468 35i3 355 9 36o4 365o 36 9 5 5o 9 997 5 . .21 ..67 .n3 .160 .206 5o 10 10. 173741 3 7 86 3832 38 77 3 9 23 3968 49 10 10. 190252 0298 o344 0391 o43 7 o483 49 ii 4oi4 4o6o 4io5 4i5i 4196 4242 48 1 1 0529 o5 7 6 0622 0668 o 7 i4 0760 48 12 4287 4333 43 7 8 4424 446 9 45i5 47 12 0807 o853 0899 o 9 45 0992 io38 47 i3 456i 46o6 465 2 46 97 4 7 43 4 7 88 46 i3 io84 n3o 1177 1223 1269 i3i5 46 i4 4834 488o 4 9 25 49 7 i 5oi6 5o6 2 45 i4 i362 i4o8 i454 i5oi 1 547 i5 9 3 45 i5 5107 5i53 5i 99 5244 5290 5335 44 i5 i63 9 1686 I 7 32 1778 1824 i8 7 i 44 16 538i 542 7 54 7 2 55i8 5563 56o 9 43 16 1917 i 9 63 2010 2o56 2102 2l4 9 43 17 5655 5 7 oo 5 7 46 5 79 i 583 7 5883 42 17 2195 224l 2287 2334 238o 2426 42 18 5928 59 7 4 6oi 9 6o65 6m 6i56 4i 18 24?3 2519 2565 2612 2658;2 7 o4 4i 19 6202 624 7 62 9 3 633 9 6384 643o 4o *9 2751 2797 2843 2890 2 9 36 2982 4o 20 10.176476 652i 656 7 66i3 6658 6 7 o4 3 9 20 10. 193029 3075 3l2I 3i68 32l4 3260 3 9 21 6 7 49 6 79 5 684 1 6886 6932 6978 38 21 3307 3353 3399 3446 3492 3538 38 22 23 7023 7297 7 o6 9 7 343 7 n5 7 38 9 -7160 7 434 7 206 7 48o 7252 7526 3? 36 22 23 3585 3863 363i 3909 36 7 8 3 9 56 3724 40O2 3 77 o38i 7 4o4 9 4o 9 5 37 36 24 7 5 7 i 7 6l 7 7 663 77 o8 77 54 7800 35 24 4i4i 4i88 4234 4281 432 7 43 7 3 35 25 7 846 7 8 9 i 79 3 7 79 83 8028 8074 34 25 4420 4466 45i3 4559 46o5 4652 34 26 8120 8i65 8211 8 2 5 7 83o3 8348 33 26 46 9 8 4?45 4791 483 7 4884 4 9 3o 33 27 83 9 4 844o 8485 853i 85 77 8623 32 27 4977 5o23 5070 5n6 5i62 520 9 32 28 8668 8 7 i4 8 7 6o 88o5 885i 8897 3i 28 5255 53o2 5348 53 9 5 544 1 548 7 3i 29 8 9 43 8988 9034 9 o8o 9126 9171 3o 2 9 5534 558o 5627 56 7 3 5 7 20 5766 3o 3o IO. I 79 2I 7 9 263 9 3o 9 9 354 9400 9446 29 3o IO. I958l3 585 9 5906 5952 5 999 6o45 2 9 3i 9 4 9 2 9 53 7 9 583 9 62 9 9 6 7 5 9720 28 3i 6091 6i38 6i84 &23l 62 77 6324 zS 32 97 66 9812 9 858 99 o4 9949 999 5 27 32 6370 6417 6463 65io 655666o3 27 33 10. i8oo4i 008-7 Ol32 01-78 0224 0270 26 33 6649 6696 6742 6789 6835 6882 26 34 o3i6 o36i o4o 7 o453 o4 99 o545 25 34 6928 6975 7021 7068 7 n4 7161 25 35 0590 o636 0682 7 28 o 77 4 0819 24 35 7208 7254 73oi 7347 739417440 24 36 o865 0911 o 9 5 7 ioo3 io48 1094 23 36 7 48 7 7 533 7 58o 7626 76737719 23 37 n4o 1186 1232 I2 7 8 i3 2 3 1 369 22 37 7766 7 8i3 7 85 9 7906 79 52 7 999 22 38 i4i5 i46i i5o 7 i553 i5 9 8 1 644 21 38 8o45 8092 8i38 8i85 8232 8278 21 3 9 1690 i 7 36 I 7 82 1828 i8 7 4 1919 20 3 9 83 2 5 8371 84i8 8465 85n 8558 2O 4o 10. 181965 2OII 2o5 7 2103 2l4 9 2195 I 9 4o 10. 198604 865i 8697 8 7 44 8 79 i 883 7 19 4i 2241 2286 2332 23 7 8 2424 2470 18 4i 8884 8 9 3o 8977 9024 9 o 7 o 9 n 7 18 42 25i6 2562 2608 2653 2699 2 7 45 17 42 9164 9210 9 25 7 9 3o3 9 35o 9397 17 43 2 79 I 283 7 2883 2 9 2 9 2 97 5 3021 16 43 9443 9490 9 53 7 9 583 9 63o 16 44 3o6 7 3lI2 3i58 325o 3296 i5 44 9723 9770 9 8i6 9 863 99 io 99 56 i5 45 3342 3388 3434 348o 3526 35 7 2 i4 45 IO.2OOOO3 oo5o oo 9 6 oi43 0190 0236 i4 46 36i8 3664 3-709 3 7 55 38oi 3847 i3 46 0283 o33o o3 7 6 0423 0470 o5i6 i3 47 38 9 3 3 9 3 9 3 9 85 4o3i 4o 77 4i23 12 47 o563 0610 o656 0703 0780 07 9 6 12 48 4169 42i5 4261 43o 7 4353 43 99 II 48 o843 0890 o 9 3 7 o 9 83 io3o 1077 II 49 4445 4491 453 7 4583 4629 46 7 4 10 49 1123 1170 I2I 7 1263 i3io i35 7 10 5o IO. l84 7 2O 4 7 66 4812 4858 4 9 o4 4 9 5o 9 5o I0.20l4o4 i45o i4 97 1 544 i5 9 i i63 7 9 5i 4996 5o42 5o88 5i34 5i8o 5 22 6 8 5i 1 684 1731 I 77 7 1824 1871 1918 8 52 52 7 2 53i8 5364 54io 5456 55o2 7 52 1964 2OII 2o58 2io5 2i5i 2198 7 53 5548 55 9 4 564o 5686 5 7 3 2 5 77 8 6 53 2245 2292 2338 2385 2432 2479 6 54 5824 58 7 i 591-7 5 9 63 6oo 9 6o55 5 54 2526 2572 26l 9 2666 2713 2759 5 55 6101 6i4 7 6193 623 9 6285633i 4 55 2806 2853 2 9 00 2 9 47 2 9 93|3o4o 4 56 63 77 6423 6469 65i5 656i 66o 7 3 56 3087 3i34 3i8i 3227 32 7 4332i 3 57 6653 66 99 6745 6 7 9i 683 7 6884 2 5? 3368 34i5 346i 35o8 35553602 2 58 6930 6 97 6 7 O22 7 o68 7114 7160 I 58 364 9 36 9 6 3742 3 7 8 9 3836|3883 I 5 9 7206 7 252 7 2 9 8 7 344 7 3 9 o 743 7 5 9 3 9 3o 3 9 77 4023 4070 4ii74i64 O 60" 50" 40" 30" 20" 10" j 60" 50" 40" 30" 20" 10" j Co-tangent of 33 Degrees. Co-tangent of 32 Degrees. P P t$ l " 2 " 3// 4 " 5 " 6// 7 " 8 " 9 " (1" 2" 3" 4" 5" 6" 7" S" 9" I 5 9 14 18 23 27 32 37 41 ' art { 5 9 14 19 23 28 33 37 42 LOGARITHMIC SINES. 1 .a Sine of 58 Degrees. c Sine of 59 Degrees. 9 0" [ 10" 20" 30" 40" f50" 0" 10" 20" 30" 40" 50" 9.928420(8434 8447 8460,8473 8486 59 0,9. 933o66 ; 3o78 3o 9 i 3io4 3n6 3129 5o I 8499 85i3;8526853 9 855 2 856558 I 3i4i 3i54 3i6 7 3i79 3192 3 2 o5 58 2 85 7 8 8591 86o586i8863i 8644 5 7 2 32i 7 323o 3243 3 2 55 3268 3 2 8o 5 7 3 4 865 7 86 7 o;8683 8696 8 7 io 87868749 8762 8775 8788 8 7 23j56 8801 55 3 4 32 9 3|33o6 336 9 338i 33i8 33 9 4 333i 34o 7 3344 3419 3356 3432 56 55 5 88i5i88 2 8884i 8854 886 7 888o;54 5 3445 345 7 34 7 o 3482 3495 35o8 54 6 8893 8906 8919 8933 8946 SgSg 53 6 3520 3533 3545 3558 35 7 i 3583 53 7 8972 8985 8998 9011 9024 9 o3 7 52 7 35 9 6 36o8 362i 3633 3646 365 9 52 8 9 9129 9063 9077 9090 9 103:911 6' 5 1 9142 9i55 9168 9181 9194150 8 9 36 7 i 3 7 4 7 3684 3 7 5 9 36 9 6 3 77 2 3 7 o 9 3 7 84 3722 3 797 3 7 34 38io 5i 5o 10 9.929207 9220 9233 924^9260 9273149 10 9.933822 3835 384 7 386o 3872 3885 49 ii 9286 9299 9312 9325 9338 9 35i48 ii 3898(3910 3 9 23 3 9 35 3 9 48 3960 48 12 9 364 9377 9390 9403 9416 9429^7 12 3 97 3 3 9 85 3 99 8 4on 4o 2 3 4o36 47 i3 9442 9 455 9468 9482 9 4 9 5 9 5o846 i3 4o48 4o6i 4o 7 3 4o86 4o 9 8 4in 46 i4 9521 9534 95479560 9573 9 586 ! 45 i4 4l23 4i36 4i48 4i6i 4i74 4i86 45 i5 9 5 99 9612 962596389651 9664 44 i5 4199 4211 4224 4236 4249 4261 44 16 9677 9690 9703 9716 9729 9742J43 16 42 7 4 4286 4299 43n 4324 4336 43 '7 9755 9768 9781 97949807 9820 42 17 4349 436i 43 7 4 4386 43 99 44" 42 18 9833 9846 9859^9872 9885 o8o84i 18 4424 4436 4449 446 1 4474 4486 4i 19 9911 9924 99379950 9963997640 '9 4499 45u 4524 4536 4549 456i 4o 20 9.929989 . . .2 ..i5 ..28 . .41 ..543 9 20 9- 9 345 7 4 4586 4599 46n 4624 4636 3 9 21 9.930067 0080 0093 0106 oi 19 oi32'38 21 4649 466i 46 7 4 4686 4699 4711 38 22 oi45 oi58 0171 oi84 0197 0210)37 22 4 7 23 4 7 36 4 7 48 4761 4773 4786 37 23 O223 O236 0249 2 62 0274 0287 36 23 4 7 98 48n 4823 4836 4848 486i 36 24 25 o3oo o3 7 8 o3i3 0326 0339 0391 04040417 o352 ! o365 o43oo443 35 34 24 25 48 7 3 4948 4885 4 9 6o 4898 4 97 3 4910 4985 4 9 23 4997 4 9 35 5oio 35 34 26 o456 0469 0482 0495 0507 o52O 33 26 5O22 5o35 5o4 7 5o6o 5072 5o84 33 27 28 29 o533 06 1 1 0688 o546 0559 5 7 2 585 598 0624 o63 7 |o65o!o663jo6 7 5 0701 0714 0727 0740 0753 32 3i 3o 27 28 29 5<>97 5i 7 i 5246 5io 9 5i84 5 2 58 5l22 5i 9 6 52 7 I 5i34 5209 5283 5i47 5221 5296 5i5 9 5234 53o8 32 3i 3o 3o 0.930766 07790792 o8o4o8i 7 'o83o 29 3o 9 . 9 3532o 5333 5345 5358 53 7 o 538 2 2 9 3i o843 o856 0869 0882 o8 9 5 0908 28 3i 53 9 5 54o 7 5420 5432 5444 545 7 28 32 0921 0933 0946 o 9 5 9 o 97 2 0985 27 32 546 9 5482 54 9 4 55o6 55i 9 553i 27 33 0998 101 I 1024 io36 io4 9 1062 26 33 5543 5556 5568 558i 55 9 3 56o5 26 34 1075 1088 IIOI in4 1127 1 1 39 25 34 56i8 563o 5642 5655 566 7 5679 25 35 1x5* n65 1178 1191 I2O4 1217 24 35 5692 5 7 o4 5 7 i 7 5729 5741 5 7 54 24 36 1229 1242 1255 1268 1281 1294 23 36 5 7 66 5778 5 79 i 58o3 58i5 58 2 8 23 37 i3o6 i3i 9 i332 1 345 i358 1371 22 37 584o 5852 5865 58 77 588 9 5902 22 38 1383 i3 9 6 1409 l422 i435 1 448 21 38 5 9 i4 5 9 26 5 9 3 9 5 9 5i 5 9 63 5 97 6 21 3 9 i46o i4 7 3 i486 1499 I5l2 i5 2 5 2O 3 9 5 9 88 6000 6oi3 6o25 6o3 7 6o5o 2O 4o 9 . 9 3i53 7 i55o i563 i5 7 6 i58 9 1601 '9 4o 9 . 9 36o62 6o 7 4 6o8 7 6099 61 1 1 6124 9 4i 1614 1627 i64o i653 1666 1678 18 4i 6i36 6i48 6161 6i 7 3 6i85 6198 1 8 42 i6 9 i 1704 1717 i 7 3o 1742 i 7 55 17 42 6210 6222 6234 6247 6259:6271 17 43 1768 1781 1794 1806 1819 i832 16 43 6284 62 9 6 63o8 6320 63336345 16 44 i845 i85 7 1870 i883 1896 1909 i5 44 635 7 63 7 o 6382 63 9 4 6406.6419 i5 45 I 9 2I i 9 34 1947 1960 1972 I9 85 i4 45 643 1 6443 6456 6468 648o 6492 i4 46 I 99 8 2OII 2024 2o36 2049 2062 i3 46 65o5 65i 7 652 9 6542 6554 6566 i3 47 2075 2087 2100 2Il3 2I262I38 12 47 65 7 8 65 9 i 66o3 66i5 6627 664o 12 48 2l5l 2 1 64 2177 2189 2202 22l5 ii 48 665s 6664 66 7 6 668 9 6701 6 7 i3 I I 49 2228 2240 2253 2266 2279 2291 10 49 6 7 25 6 7 38 6 7 5o 6762 6 77 4 6787 IO 5o 9 . 9 323o4 2317 2329 2342 2355 2368 9 5o 9.986799 6811 6823 6836 6848 6860 9 5i 52 53 238o 245 7 2533 23 9 3 2469 2546 2406 2482 2 558 2419 243i 2444 2495|25o8 2520 25 7 i 2584 259-7 8 6 5i 52 53 68 7 2 6884 6 9 46j6 9 58 7 oi 9 7 o3i 6897 6 9 7o 6909 6982 7 o56 6921 6933 6994^007 706817080 8 6 54 26o 9 2622 2635 264 7 26602673 5 54 7 o 9 2 7 io4 71 17 7129 7141 7i53 5 55 56 2685 2762 2698 2774 271 1 2787 2 7 24 2 7 36 2 7 4 9 2800 2812 2825 4 3 55 56 7 i65 7 i 7 8 7 238 7 25i 7190 720217214 7226 72637275 72877299 4 3 5 7 2838 285o 2863 2 8 7 6 2888 2901 2 57 731273247336734873607372 2 58 2914 2926 2939 2952 2964 2977 I 58 7385 7397 7409 7421 7433 7446 i 5 9 2990 3002 3oi5 3028 3o4o 3o53 o 5 9 7458 7470:7482 7494 7506:75 1 S 60" 50" 40" 30" 20" 10" a 60" 50" 40" i 30" 20" 10" ^ Co-sine of 3 1 Degrees. S Co-sine of 30 Degrees. s ! P Part S !" ~" 3 " 4 " 5 " 6 " 7 " 8" 9" o T> -* U" 2" 3" 4" 5" 6" 7" 8" 3" "^13456 8 9 10 12 ut ) 1 2 4 5 6 7 9 10 11 LOGARITHMIC TANGENTS. 1 Tangent of 58 Degrees. c Tangent of 59 Degrees. a 0" 10" 20" 30" 40" 50" 2 0" 10" 20" 30" 40" 50" O 10.204211 4258 43o4 435i 43 9 8 4445 5o 10.221226 I2 7 4 1322 i36 9 i4i 7 i465 5 9 i 44 9 2 453 9 4586 4633 467 9 4 7 26 58 I l5l2 i56o 1608 i656 I 7 o3 i 7 5i 58 2 4 77 3 4820 486 7 4914 4 9 6i 5oo8 5? 2 I 799 1 846 i8 9 4 I 9 42 i 99 o 2037 57 3 5o54 5ioi 5i48 5i 9 5 5242 528 9 56 3 2o85 2i332i8i 2228 22 7 6 2324 56 4 5336 5383 543o 54 77 55 2 4 55 7 o 55 4 23 7 2 94199467 25i5 2563 26lO 55 5 56i 7 5664 5 7 n 5 7 58 58o5 585 2 54 5 2658 2 7 o6 2 7 54 2801 2 84 9 2807 54 6 58 99 5 9 46 5 99 3 6o4o 6087 6i34 53 6 2 9 45 2 99 3 3o4o 3o88 3i36 3i84 53 7 6181 6227 62 7 4 632i 6368 64i5 52 7 3232 32 79 3327, 33 7 5 3423 34 7 i 5 2 8 6462 65o 9 6556 66o3 665o 66 97 5i 8 35i8 3566 36i? 3662 3 7 io 3 7 5 7 5i 9 6 7 44 6791 6838 6885 6. 9 32 6979 5o 9 38o5 3853 3 9 oi 3 9 4 9 3 997 4o44 5o 10 10.207026 7073 7 I20 7 i6 7 72i4 7261 4 9 10 IO.224o 9 2 4i4o 4i88 4236 4284 4332 4 9 ii 73o8 7 355 7 402 7 44 9 74 9 6 7543 48 II 4379 442 7 4475 4523 45 7 i 46 1 9 48 12 7 5 9 o 7 63 7 7 684 77 3i 7778 7825 4 7 12 466 ? 4 7 i4 4762 48io 4858 4 9 o6 47 i3 7872 7919 7 9 66 8oi3 8060 8107 46 i3 4 9 54 5002 5o5o 5o 9 8 5i45 5i 9 3 46 i4 8i54 8201 8248 82 9 5 8342 838 9 45 i4 5241 528 9 533 7 5385 5433 548 1 45 i5 843 7 8484 853! 85 7 8 8625 86 7 2 44 i5 552 9 55 77 5625 56 7 2 5 7 20 5 7 68 44 16 8 7 I 9 8766 88i3 8860 80.07 8 9 54 43 16 58i6 5864 5 9 I2 5 9 6o 6008 6o56 43 I 7 9001 9048 9 o 9 5 9 i43 9 i 9 o 9 23 7 42 17 6io4 6i52 6200 6248 62 9 6 6344 42 18 9284 9 33i 9 3 7 8 9 425 9 5i 9 4i 18 63 9 2 6440 6488 6535 6583 663i 4i i 9 9 566 9614 9661 97 o8 97 55 9 8o2 4o i 9 66 79 6727 6 77 5 68 2 3 68 7 i 6 9 i 9 4o 20 10.209849 9896 99 43 999 T ..38 ..85 3 9 20 io.226 9 67 7Oi5 7 o63 7111 7 i5 9 7 20 7 3 9 21 IO.2IOI32 0179 0226 02 7 3 0321 o368 38 21 7 255 7 3o3 7 35i 7399 7 44 7 7 4 9 5 38 22 o4i5 0462 0509 o556 o6o3 o65i 3y 22 7543 7 5 9 i 7 63 9 7 688 7736 77 84 37 23 0698 o 7 45 7 92 o83 9 0886 o 9 34 36 23 7832 7880 79 28 7976 8024 8o 7 2 36 24 0981 1028 io 7 5 1122 1170 I2I 7 35 24 8120 8168 8216 8264 83i2 836o 35 25 1264 i3n i358 i4o5 i453 i5oo 34 25 84o8 8456 85o4 8552 8601 864 9 34 26 i54 7 i5 9 4 i64i i68 9 1736 i 7 83 33 26 86 97 8 7 45 8 79 3 884i 888 9 8 9 3 7 33 2 7 i83o 1878 1925 I 97 2 2OI 9 2066 32 2 7 8 9 85 9 o33 9 o8i 9 i3o 9178 9 226 32 28 2114 2161 2208 2255 23o3 2 35o 3i 28 9 2 7 4 9 322 9 3 7 o 9 4i8 9 466 9 5i5 3i 2 9 23 97 2444 2492 253 9 2586 2633 3o 2 9 9 563 9 6n 9 65 9 977 97 55 9 8o3 3o So I0.2I268I 2728 2 77 5 2822 2870 2 9 i 7 29 3o I0.22 9 852 99 oo 99 48 999 6 ..44 . .92 2 9 3i 2964 3OI2 3io6 3i53 3201 28 3i io.23oi4o oi8 9 023 7 0285 o333 o38i 28 32 3248 32 9 5 3343 33 9 o 3437 3484 2 7 32 o42 9 o4 7 8 o52<5 o5 7 4 0622 o6 7 o 2 7 33 3532 35 79 3626 36 7 4 3721 3 7 68 26 33 o 7 i 9 0767 o8i5 o863 o 9 n o 9 6o 26 34 38i6 3863 3910 3 9 58 4oo5 4o52 25 34 1008 io56 no4 Il52 1201 I24 9 25 35 4ioo 4i47 4194 4242 428 9 4336 24 35 I2 97 1 345 i3 9 4 1442 l4 9 i538 24 36 4384 443 1 44 7 8 4526 45 7 3 4620 23 36 i586 i635 i683 i 7 3i 1779 1828 23 3 7 4668 47'5 4 7 62 48io 485 7 4 9 o5 22 37 i8 7 6 I 9 24 i 97 3 2021 2o6 9 2II 7 22 38 4952 4999 5o4 7 5o 9 4 5i4i 5i8 9 21 38 2166 22l4 2262 23lO 235 9 240 7 21 3 9 5236 5284 533i 53 7 8 5426 54 7 3 20 3 9 2455 25o4 2552 26OO 2648 26 97 2O 4o IO.2l552I 5568 56i5 5663 5710 5 7 58 *9 4o IO.232 7 45 2793 2842 28 9 2 9 38 2 9 8 7 1 9\ 4i 58o5 5852 5900 5 9 4 7 5 99 5 6042 18 4i 3o35 3o83 3i32 3i8o 3228 32 77 18 42 6090 6i3 7 6i84 6232 627 9 632 7 17 42 33 2 5 3373 3422 34 7 o 35i8 356 7 17 43 63 7 4 6422 6469 65i 7 6564 6612 16 43 36i5 3663 3 7 I2 3 7 6o 38o8 385 7 16 44 6659 6706 6 7 54 6801 684 9 68 9 6 i5 44 3 9 o5 3 9 53 40O2 4o5o 4o 99 4i4 7 i5 45 6944 6991 7 o3 9 7 o86 7i34 7181 i4 45 4i 9 5 4244 42 9 2 434o 438 9 443 7 i4 46 7229 7276 7 3 2 4 7 3 7 i 7419 7 466 i3 46 4486' 4534 4582 463i 467 9 4728 i3 4 7 7 56i 7609 7 656 77o4 77 5i 12 47 4 77 6 48 2 5 48 7 3 4 9 2I 4 9 7Q 5oi8 12 48 7799 7 846 7 8 9 4 79 4i 79 8 9 8o36 II 48 5o6 7 5n5 5i64 5212 526o 53o 9 II 49 8o84 8i3i 8i79 8226 82 7 4 8322 10 49 535 7 54o6 5454 55o3 555i 56oo IO 5o 10.218369 84i7 8464 85i2 855 9 86o 7 9 5o 10,235648 56 9 6 5 7 45 5 79 3 5842 58 9 o 9 5i 8654 8702 8 7 5o 8797 8845 88 9 2 8 5i 5 9 3 9 5 9 8 7 6o36 6o84 6i33 6181 8 52 8940 8987 9o35 9083 9 i3o 9 i 7 8 7 52 623o 6278 632 7 63 7 5 6424 64 7 2 7 53 9225 9273 9321 9 368 9 4i6 9 463 6 53 652i 656 9 6618 6666 6 7 i5 6 7 63 6 54 95n 9 55 9 9606 9 654 97 oi 9749 5 54 6812 6860 6 9 o 9 6 9 5 7 7006 7 o55 5 55 9797 9844 9892 99 3 9 9987 ..35 4 55 7io3 7i52 7 20O 7 24 9 7297 7 346 4 56 10.220082 oi3o oi 7 8 0225 02 7 3 0321 3 56 7 3 9 4 7443 7 4 9 2 7 54o 7 58 9 7 63 7 3 67 o368 o4i6 o463 o5n o55 9 0606 2 5y 7686 7734 7783 7 832 7880 79 2 9 2 58 o654 0702 o 7 49 797 o845 o8 9 2 I 58 7977 802^ 8o 7 5 8i23 8172 8220 I 5 9 0940 0988 io36 io83- n3i II 79 O 5 9 8*69 83i8 8366 84i5 8463 85i2 O 60" 50" 40" 30" 20" 10" . 60" 50" 40" 30" 20" 10" d Co-tangent of 31 Degrees. 1 Co-tangent of 30 Degrees. 3 PPartJ 1 " 2 " 3 " 4// 5 " 6 " 7 " 8// 9// 1 ppartJ 1 " 2 " 3 " 4// 5 " 6 " 7// 8// 9 " a "^ 5 9 14 19 24 28 33 38 43 | irt { 5 10 14 19 24 29 34 39 43 LOGARITHMIC SINES. d Sine of 60 Degrees. a Sine of 61 Degrees. s 0" 10" 20" 30" 40" 50" Si 0" 10" 20" | 30" 40" 50" 9.937531 7543 7 555 7 56 7 7 5 79 75 9 i 5 9 o 9.941819 i83i 1843 i854 1866 1878 5 9 I 7604 7616 7 628 7 64o 7 652 7664 58 I 1889 1901 I9l3 1924 1936 1948 58 2 7676 7689 77 oi 77 i3 7725 7737 57 2 i 9 5 9 i9 7 i i 9 83 i 99 4 2006 2017 5 7 3 774 9 77 6i 777 3 7786 7798 7810 56 3 2029 2041 2052 2064 20-76 2087 56 4 7822 7834 7 846 7 858 7 8 7 o 7883 55 4 2099 2III 2122 2i34 2146 2157 55 5 7 8 9 5 7907 79 Z 9 79 3i 7943 7955 54 5 2169 2l8o 2192 22O4 22l5 2227 54 6 7967 7979 7 992 8oo4 80168028 53 6 223 9 2250 2262 22 7 3 2285 2297 53 7 8o4o 8o5 2 8o64 8o 7 6 80888100 52 7 2 3o8 2320 233l 2343 2355 2366 52 8 8n3 812$ 81378149 8161 8i 7 3 5i 8 2 3 7 8 2 3 9 o 24OI 24i3 2424 2436 5i 9 8i85 8197 8209^221 82338245 5o 9 2448 245 9 2471 2482 2494 25o6 5o 10 9.938258 82-70 8282^294 83o683i8 49 10 9.9425i 7 2529 254o 2552 2563 25 7 5 4 9 ii 833o 8342 8354 8366 83 7 883 9 o 48 1 1 258 7 25g8 2610 2621 2633 2645 48 12 8402 84i4 84268439 845i 8463 47 12 26562668 26 79 26 9 I 2-702 2 7 i4 47 i3 8475 848 7 8499 85i i 85238535 46 i3 2 7 26 2 7 3 7 2749 2760 2 77 2 2 7 83 46 i4 8547 855 9 85 7 i 8583 85 9 5;86o 7 45 i4 2795 2806 2818 2 83o 284l 2853 45 i5 8619 863i 86438655 866 7 ! 86 7 9 44 i5 2864 28 7 6 288 7 2 8 99 2910 2922 44 16 8691 8 7 o3 8 7 i5 8 7 2 7 8 7 3 9 8 7 5i 43 16 2934 2945 2 9 5 7 2 9 68 2980 2991 43 7 8763 8 77 6 8 7 88 8800 88128824 42 '7 3oo3 3oi4 3026 3o3 7 3o4g 3o6o 42 18 8836 8848 8860 88 7 2 8884 8896 4i 18 3o 7 2 3o83 3o 9 5 3io 7 3n8 3i3o 4i 20 8908 9.938980 8920 8992 8 9 32 9004 8 9 44 9 oi6 8956:8968 902819040 4o 39 20 3i4i 9.943210 3i53 3222 3i64 3233 3i 7 6 3245 3i8 7 3256 3i 99 3268 4o 39 21 22 9123 9064 9 i35 9o 7 69o8 7 9099 9 in 9147 9159 9i7ifoi83 38 37 21 22 3279 3348 32 9 I 336o 3302 33 7 i 33i4 3383 3325 33 9 4 333 7 34o6 38 37 23 9 i 9 5 9 20 7 9219 9231 9243 9 255 36 23 34i7 342 9 344o 3452 3463 34 7 5 36 24 9267 9 2 79 9291 9 3o3 9 3i5 9327 35 24 3486 34 9 8 35o 9 352i 3532 3543 35 25 9 33 9 9 35i 93639375 93879399 34 2 5 3555 3566 35 7 8 358 9 36oi 36i2 34 26 9 4io 9 422 94349446 9458 94-70 33 26 3624 3635 3647 3658 36 7 o 368i 33 27 9482 9 4 9 4 95069518 95309542 32 27 3693 3 7 o4 3 7 i5 3 7 2 7 3 7 38 3 7 5o 32 28 9 554 9 566 95789590 9601 9613 3i 28 3 7 6i 3 77 3 3 7 84 3796 38o 7 38i8 3: 29 9625 9 63 7 9649 9661 9673 9 685 3o 29 383o 384i 3853 3864 38 7 6 388 7 3o 3o 3i 9.939697 9768 9709 9780 9721 97 33 979 2 9804 97449756 98169828 29 28 3o 3i 9.943899 3967 3 9 io 3978 3921 3990 4oov 3 9 44 4oi3 3 9 56 4024 29 28 32 9840 9852 9 863 98-75 9887 9899 27 32 4o36 4047 4o58 4070 4o8i 4o 9 3 27 33 9911 9923 9935 9947 99 5 9 997 26 33 4io4 4u5 4127 4i38 4i5o 4i6i 26 34 9982 9994 ...6 ..18 . ,3o ..42 25 34 4172 4i84 4i 9 5 4207 4218 4229 25 359.940054 oo65 0077 0089 oioi oii3 24 35 4241 4252 4264 42 7 5 4286 4298 24 36 oi25 0/37 oi48 0160 oi 7 2 oi84 23 36 43o 9 432i 4332 4343 4355 4366 23 371 0196 0208 O22O O23l 0243 0255 22 3 7 43 77 438 9 44oo 44i2 4423 4434 22 38 0267 0279 0291 oTo> o3l4 o326 21 38 4446 445 7 4468 448o 44 9 i 45o3 21 3 9 o338 o35o o362 o3 7 4o385 o3 9 7 2O 3 9 45i4 45 2 5 453 7 4548 455 9 45 7 i 2O 4o 9 . 9 4o4o 9 0421 o433 o445 o456 o468 1 9 4o 9.944582 45 9 3 46o5 46i6 46 27 463 9 I 9 4i o48o 0492 o5o4 o5i6o5a 7 o53 9 18 4i 465o 466 1 46 7 3 4684 46 9 6 4707 18 42 o55i o563 o5 7 5 o586 o5 9 8 0610 17 42 4718 4 7 3o 4 7 4i 4 7 5 2 4 7 64 4 77 5 17 43 0622 o634 o645 o65 7 0669 0681 16 43 4786 4798 4809 4820 483i 4843 16 44 45 0693 o 7 63 o 7 o4 o 77 5 o 7 i6 0728 0740 0787^0799 081 1 0752 0822 i5 i4 44 45 4854 4922 4865 4933 48 7 7 4945 4888 4g56 48 99 4967 4911 4979 i5 i4 46 o834 o846 o858o8 7 o 0881 o8 9 3 i3 46 4990 5ooi 5oi3 5o24 5o35 5o46 i3 47 ogoS o 9 i 7 0928 0940 0952 0964 12 47 5o58 5069 5o8o 5092 5io3 5n4 12 48 97 5 o 9 8 7 0999 ' ' * IOII 1023 io34 II 48 5i25 5i3 7 5i48 5i5 9 5171 5i82 II 49 io46 io58 10-70 1081 1093 no5 10 49 5i 9 3 52o4 52i6 522-7 5 2 38 5 2 5o IO 5o 9.941117 1128 n4o Il52 n64 u 7 5 9 5o 9.945261 52 7 2 5 2 83 52 9 5 53o6 53i 7 9 5i 1187 11 99 I2II 1222 1234 1246 8 5i 5328 534o 535i 5362 53 7 4 5385 8 52 1258 1269 I28l i2 9 3 i3o4 i3i6 7 52 53 9 6 54o 7 54i9 543o 544i 5452 7 53 i328 1 34o i35i i363 i3 7 5 1387 6 53 5464 5475 5486 54 9 7 55o 9 5520 6 54 i3 9 8 i4io 1422 i433 i445 1457 5 54 553i 55425554 5565 55 7 6 558 7 5* 55 i46 9 56 i53 9 i48o i55o 1492 i562 i5o4 i5 7 4 i5i5 1 586 1527 i5 97 4 3 55 56 55 9 8 5666 56io562i 56 77 ! 5688 5632 5700 5643 5-7II 5655 5722 4 3 5 7 1609 1621 i632 1 644 1 656 1667 2 5 7 5 7 33 5 7 44|5 7 56 5 7 6 7 5 77 8 5789 2 58 i6 79 1691 I 7 02 I7l4 1726 1738 I 58 58oo 58125823 5834 5845 5857 I 5 9 j *74 9 1761 i 77 3 i 7 84 ! i79 6 1808 O 5 9 5868:5879 58 9 o5 9 oi ! 59i3 5 9 24 O 60" 50" | 40" 30" 20" 10" d 60" 50" 40" | 30" 20" 10" d Co-sine of 29 Degrees. Co-sine of 28 Degrees. 5 P TartJ J " 2 " 3 " 4 " 5" 6" 7" 8" 9" ^ 1" 2" V 4" 5" 6" 7" 8" 9" 6 7 8 10 11 irt fc 1 2 3 5 6 7 8 9 10 LOGARITHMIC TANGENTS. I Tangent of 60 Degrees. d Tangent of 61 Degrees. s 0" 10" 20" 30" 40" \ 50" 2 0" 10" 20" 30" 40" 50" o 10. 23856i 8609 8658 8707 8755 88o4 5 9 10.256248 6298 634 7 63 97 644 7 64 9 6 5 9 i 885 2 8901 8g5o 8998 9047 9096 58 I 6546 65 9 6 6645 66 9 5 6 7 45 6 79 4 58 2 9144 9193 9242 9290 9 33 9 9388 5 7 2 6844 6894 6944 6 99 3 7o43 7 o 9 3 5 7 3 9 436 9 485 9 534 9582 963i 9680 56 3 7142 7192 7242 7291 734i 7 3 9 i 56 4 9728 9777 9826 9874 99 23 9972 55 4 744i 7490 754o 7 5 9 7 64o 7680 55 5 10.240021 0069 0118 0167 02l5 0264 54 5 7739 7789 7 83 9 7888 7938 7988 54 6 o3i3 o362 o4io 0459 o5o8 o55 7 53 6 8o38 8087 8i3 7 8187 82378286 53 7 o6o5 o654 0703 0752 0800 0849 52 7 8336 8386 8436 8486 85358585 52 8 0898 0947 o 99 5 io44 1093 1142 5i 8 8635 8685 8 7 35 8 7 84 8834 8884 5i 9 1190 1239 1288 i33 7 i385 1434 5o 9 8 9 34 8 9 84 9 o33 9 o83 9 i33 9 i83 5o 10 io.24i483 i532 1681 1629 1678 1727 49 10 io.25 9 233 9283 9332 9 38 2 9 43 2 9482 49 ii 1776 i825 i8 7 3 1922 1971 2O2O 48 1 1 9532 9 58 2 9632 9 68i 973i 9781 48 12 2069 2118 2166 22l5 2264 23l3 47 12 9 83i 9 88i 99 3i 998i ..3i ..80 47 i3 2362 24n 245 9 25o8 2 55 7 2606 46 i3 io.26oi3o 0180 023O 0280 o33o o38o 46 i4 2655 2704 2 7 53 2801 285o 2899 45 i4 o43o o48o o53o o58o o62 9 0679 45 i5 2948 2997 3o46 3o 9 5 3i43 3l92 44 i5 0729 0779 0829 o8 79 9 2 9 979 44 16 324l 3290 333 9 3388 343 7 3486 43 16 1029 1079 1129 "79 1229 i2 79 43 17 3535 3584 3632 368i 3 7 3o 3779 42 17 1329 i3 79 1429 i47 9 1529 i5 79 42 18 8828 38 7 7 3926 3 97 5 4024 4o 7 3 4i 18 1629 1679 I 7 2 9 i77 9 1829 1879 4i 19 4l22 4i 7 i 4220 4269 43i8 4366 4o J 9 1929 1979 202 9 20 79 2129 2179 4o 20 i O.2444 i 5 4464 45i3 4562 46n 466o 3 9 20 10.262229 2279 232 9 2 3 79 2429 2479 3 9 21 4709 4 7 58 48o 7 4856 4905 4954 38 21 2529 2 5 79 262 9 2679 2729 2779 38 22 5oo3 5o52 5ioi 5i5o 5i 99 5248 37 22 2829 2 8 79 2 9 2 9 2979 3029 3 79 37 23 52 97 5346 5395 5444 54 9 3 5542 36 23 3i3o 3i8o 3230 3 2 8o 333o 338o 36 24 55 9 i 564o 568 9 5 7 38 5 7 8 7 5836 35 24 343o 348o 353o 358o 363o 368 1 35 25 5885 5 9 34 5 9 84 6o33 6082 6i3i 34 25 373i 3 7 8i 383i 388i 3 9 3i 3 9 8i 34 26 6180 6229 6278 632 7 6376 6425 33 26 4o3i 4082 4l32 4182 4232 4282 33 27 6474 6523 65?2 6621 6670 6 7 2O 32 27 4332 4382 4433 4483 4533 4583 32 28 6769 6818 6867 6 9 i6 6 9 65 7 oi4 3i 28 4633 4683 4734 4784 4834 4884 3i 29 7063 7112 7161 7211 7260 7 3o 9 3o 29 4934 4 9 85 5o35 5o85 5i35 5i85 3o 3o 10.247358 7407 7456 75o5 7554 7604 2 9 3o 10.265236 5 2 86 5336 5386 5436 548 7 2 9 3r 7653 7702 77 5! 7800 784 9 7899 28 3i 553 7 558 7 563 7 5688 5 7 38 5 7 88 28 32 7948 7997 8o46 8o 9 5 8i44 8i 9 4 27 32 5838 588 9 5 9 3 9 5 9 8 9 6039 6o 9 o 27 33 8243 8292 834i 83 9 o 843 9 848 9 26 33 6i4o 6190 6240 6291 634i 63 9 i 26 34 8538 858 7 8636 8685 8735 8 7 84 25 34 6442 6492 6542 6592 6643 66 9 3 25 35 8833 8882 8 9 3i 8 9 8i 9 o3o 979 24 35 6 7 43 6794 6844 68 9 4 6945 6 99 5 24 36 3? 9128 9424 9178 9 4 7 3 9 227 9 522 9 2 7 6 9 5 7 2 9 3 2 5 9 62I 9 3 7 5 9 6 7 o 23 22 36 37 7o45 7347 7096 7398 7i46 7448 7196 7498 72477 2 97 75497^99 23 22 38 9719 9769 9 8i8 9867 99 i6 99 66 21 38 ?64 9 7700 77 5o 7800 785 1 7901 21 3 9 io.25ooi5 oo64 on4 oi63 0212 0261 20 3 9 7952 8002 8o52 8io3 8i5382o4 2O 4o io.25o3n o36o 0409 0459 o5o8 o55 7 J 9 4o 10.268254 83o4 8355 84o5 8456 85o6 '9 4i 0607 o656 0705 o 7 55 o8o4 o853 18 4i 8556 8607 865 7 8708 8 7 58 8809 18 42 0903 O 9 52 IOOI io5i IIOO 1149 *7 42 885 9 8909 8 9 6o 9010 9061 9111 7 43 1199 1248 1297 1 347 i3 9 6 i445 16 43 9162 9212 9 263 93i3 9 364 9 4i4 16 44 i495 1 544 i5 9 4 1 643 1692 1742 i5 44 9 465 9 5i5 9 566 9616 9 66 797 i 7 i5 45 1791 i84o 1890 i 9 3 9 1989 2o38 x4 45 9767 9 8i8 9 868 9919 99 70 . .20 i4 46 2087 2137 2186 2236 2285 2335 i3 46 10.270071 0121 0172 O222 0273 o323 i3 47 2384 2433 2483 2532 2582 263i 12 47 o3 7 4 O424 o475 0525 0576 0626 12 48 2681 2730 2779 2829 2878 2928 II 48 0677 7 28 0778 0829 o87 9 0930 II 49 2977 3027 3o 7 6 3i26 3i 7 5 3225 10 49 0980 io3i 1082 Il32 u83 1233 IO 5o 10.253274 3324 3373 3423 3472 352i 9 5o 10.271284 i335 i385 i436 i486 i537 9 5i 35 7 i 3620 3670 3 7 i 9 3 7 6 9 38i8 8 5i i588 i638 i68 9 i 7 3 9 1790 i84i 8 52 3868 3 9 i8 3 9 6 7 4017 4o66 4n6 7 52 1891 1942 i 99 3 2o43 2094 2i45 7 53 4i65 42i5 4264 43i4 4363 44i3 6 53 2195 2246 22 97 234 7 23982449 6 54 4462 45i2 456i 46n 466i 4710 5 54 2499 2 55o 26OI 265i 2702 2733 5 55 4760 48o 9 485 9 4908 4958 5oo8 4 55 28o3 2854 2 9 o5 2 9 55 3oo63o57 4 56 5o57 5107 5i56 5206 5256 53o5 3 56 3io8 3i58 3209 3260 33io336i 3 5 7 5355 54o4 5454 55o4 5553 56o3 2 57 3412 3463 35i3 3564 36i53666 2 58 5652 5702 5 7 52 58oi 585i 5901 I 58 3 7 i6 3 7 6 7 38i8 386 9 391913970 I 5 9 5 9 5o 6000 6049 6099 6:49 6198 5 9 4O2I 4072 4l22 4i73 4224*4275 O 60" 50" 40" 30" \ 20" 10" d 60" 50" 40" 30" 20" j 10" d Co-tangent of 29 Degrees. H s Co-tangent of 28 Degrees. fl S p p a *5 r/ 2 " 3// 4 " - 5 " 6 " 7// 8 " 9 " .( 1" 2" 3" 4" 5" 6" 7" 8" 9" irl \ 5 10 15 20 25 29 34 39 44 Lrt ) 5 10 15 20 25 30 35 40 45 LOGARITHMIC SINES. N Sine of 62 Degrees. J Sine of 63 Degrees. 1 * 0" 10" ' 20" 30" 40" 50" 2 0" 10" 20" 30" 40" 50" 9.945935 5g46 5967 5969 5980 5 99 i 5 9 O 9 . 9 4 9 88i 9 8 9 2 99 O2 99 i3 99 24 99 35 5 9 I 6002 6oi36o246o366o4 7 6o58 58 I 99 45 99 56 99 6 7 9977 9988 9999 58 2 6069 6080 6o 9 2 6zo36n4 6i 2 5 57 2 9.950010 O02O oo3i 0042 OO52 oo63 57 3 6i36 6i4 7 6i5 9 6i 7 o6i8i 6i 9 2 56 \ 0074 0084 oo 9 5 0106 0117 0127 56 4 6203 62146226623-76248 625 9 55 I oi38 oi4 9 oi5 9 0170 0181 oioi 55 5 6270 6281 62 9 3 63o463i5 632654 f O202 02 I ^ 022^ 0234 0245 0256 54 6 6337 6348 635$ 637ii6382 639353 6 0266 0277 0288 02 9 8 o3o 9 0320 53 7 64o4 64i564 2 6 643 7 '644 9 646o 5 2 7 o33o o34i o352 o362 o3 7 3 o384 52 8 6471 648264 9 365o465i5 65 2 6 5i 8 o3 9 4 o4o5 o4i6 0426 o43 7 o448 5i 9 6538 6549 656o65 7 i : 6582 65 9 3 5o 9 o458 o46 9 o48o o4 9 o o5oi O5l2 5o 10 9.94660^ 66i566 27 6638664 9 6660 49 10 9 . 9 5o522 o533 o544 o554 o565 0576 4 9 ii 6671 6682 66 9 3 6704:6715 6 7 26 48 ii o586 o5 9 7 0607 0618 o62 9 o63 9 48 12 6 7 38 6 7 4 9 6 7 6o 6771 6782 6 79 3 47 12 o65o 0661 0671 0682 o6 9 3 0703 47 i3 68o4 68i56826683 7 684 9 6860 46 i3 071^ 0724 o 7 35 o 7 46 o 7 56 0767 46 i4 6871 6882 689369046915 6 9 26 45 i4 0778 0788 799 o8o 9 0820 o83i 45 i5 6 9 3 7 6 9 48 6 9 5 9 6 97 o | 6 9 82 6 99 3 44 i5 o84i o852 0862 o8 7 3 o884 o8 9 4 44 16 700^ 7 oi5 7026.7037 7048 7 o5 9 43 16 o 9 o5 o 9 i5 9 26 o 9 37 o 9 47 o 9 58 43 l l 7070 7 o8i 7 o 9 2 7 io3 7ii4 7 i25 42 17 o 9 68 979 o 99 o IOOO IOII 1021 42 18 7 i36 7 i4 77 i58 7 i 7 o 7181 7I9 2 4i 18 1032 io43 io53 io64 1074 1 08 5 4i '9 720: 7 2l4 7 225 7 236 7247 7 258 4o i 9 io 9 6 1106 1117 1127 n38 n48 4o 20 9.947269 7 280 7 2 9 I 7 302 7 3i3 7324 39 20 9 . 9 5n5 9 1170 1180 n 9 i I2OI 1212 3 9 21 7 335 7 346 7 35 7 7 368 7 3 79 7 3 9 o 38 21 1222 1233 1244 1254 1265 I2 7 5 38 22 74oi 7 4i2 7 423 ,7434 7 445 7456 37 22 1286 I2 9 6 i3o 7 i3i 7 i328 i33 9 37 23 7 46 7 7 4 7 8 7 48 9 7 5oo 7611 7 522 36 23 i34 9 i36o 1370 i38i i3 9 i 1402 36 24 7 533 7 545 7 556 7 56 7 7 5 7 8 7 58 9 35 24 l4l2 i423 i434 1 444 i455 i465 35 25 7600 7 6n -7622 7 633 7644 7 655 34 25 1476 i486 i4 9 7 i5o 7 i5i8 i5 2 8 34 26 7 665 7 6 7 6 7 68 7 7 6 9 8 77 o 9 7720 33 26 i53 9 i54 9 i56o i5 7 o i58i i5 9 i 33 27 77 3i 7742 77 53 7764I7775 7786 32 27 1602 i6i3 1623 i634 1 644 i655 32 28 7797 7 8o8 7 8i 9 783o 7^41 7852 3i 28 i665 1676 1686 i6 97 1707 1718 3i 2 9 7 863 7 8 7 4 7 885 7896 797 7 9 i8 3o 29 1728 i 7 3 9 i74 9 1760 1770 1781 3o 3o 9-9479 2 9 79 4o 79 5i 7962 7973 7084 29 3o 9 . 9 5i7 9 i 1802 1812 1823 i833 1 844 29 3i 799 5 8006801-78028 8o38 8o4 9 28 3i i854 i865 i8 7 5 1886 i8 9 6 1007 28 32 8060 8o 7 i 8082 8o 9 3 8io48n5 2 7 32 I 9 i7 I 9 28 i 9 38 i 9 4 9 i 9 5 9 i 9 6 9 27 33 8126 8i3 7 8i48,8i5 9 8x708181 26 33 I 9 8o i 99 o 2001 201 I 2022 2032 26 34 8l 9 2 8203 82138224 82358246 25 34 2o43 2o53 2064 2074 2085 2O05 25 35 825 7 8268 82 79 8290 83oi 83i2 24 35 2106 2116 2126 2137 2147 2i58 24 36 8323 8334 8344 8355 8366 83 77 23 36 2168 2179 2l8 9 22OO 2210 2221 23 3? 8388 83 99 84io 8421 843 2 8443 22 37 223l 2252 2262 2273 2283 22 38 8454 8464 84 7 5 8486 84 97 85o8 21 38 22 9 4 23o4 23l4 23 2 5 2335 2346 21 3 9 85i 9 853o854i 855 2 8562 85 7 3 2O 39 2356 2367 2 3 77 2 38 7 23 9 8 2408 20 4o 9 . 9 48584 85 9 5 8606 8617 8628 863o I 9 4o 9 . 9 524i 9 242 9 2440 2460 2471 ! 9 4i 865o 8660 86 7 i 8682 86 9 3 8704 18 4i 2481 24 9 2 25O2 2512 2523 2533 18 42 8 7 i5 8 7 268 7 36 8747 8 7 588 7 69 '7 42 2544 2 554 2 565 2 5 7 5 2585 2 5 9 6 17 43 8 7 8o 8 79 i 8802 8812 8823 8834 16 43 2606 2617 2627 2 63 7 2648 2658 6 44 8845 8856 886 7 8878 8888 8899 i5 44 266 9 267 9 268 9 2700 2710 2720 5 45 8 9 io 8 9 2i 8 9 32 8 9 43 8 9 5 t 4;8 9 64 i4 45 2731 2741 2752 2762 2772 2 7 83 4 46 8 97 5 89868997 9008 9019^029 i3 46 2793 28o3 2814 2824 2835 2845 3 47 9 o4o 9o5i 9062 9 o 7 3 9083 9094 12 47 2855 2866 2876 2886 2807 2 9 07 2 48 9 io5 9116 912-7 9 i38 91489169 II 48 2 9 l8 2 9 28 2 9 38 2 9 4 9 2 9 5 9 2 9 6 9 I 49 9 i 7 o 918119192 9202 9213 9224 IO 49 2 9 8o 2 99 3ooo 3on 3021 3o3i O 5o 5i 9 . 9 4 9 235 9 3oo 92469256 93109321 9267 9 33 2 92-789289 9 343 9 354 I 5o 5i 3io4 3o52 3n4 3o62 3i24 3o 7 3 3i35 3o83 3i45 3o 9 3 3i55 I 52 . 9 364 9 3 7 5 [9 386 9 3 97 94089418 1 52 3i66 3176 3i86 3i 97 3207 3217 7 53 9 42 9 9 44o' 9 45i 9 462 94 7 2 9 483 6 53 3228 3238 3248 325 9 326 9 3279 6 54 9 4 9 4 9 5o5 9 5i5 9 5 2 6 9 53 7 9 548 5 54 32 9 o 33oo 331013321 333i 334i 5 55 56 9 558 0623 96699680 96349645 9591 9 655 9602 9612 9666 9 6 77 4 3 55 56 33523362337213382 3413342434343444 33 9 3 34o3 3455 3465 4 3 5 7 9 688 9 6 9 8 9709 9720 97 3i 97 4i 2 57 3475 3485 34 9 6 35o6 ; 35i6 352 7 2 58 97 52J 97 63 977 4 97 84 979 5 9 8o6 I 58 3537 3547'355 7 3568 35 7 8 3588 i 5 9 9816(982719838 9 84 9 9 85 9 9 8 7 o O 5 9 35 99 36o 9 36i 9 362 9 364o365o o 60" 50" i 40" 30" 20" 10" . 60" 50" 40" 30" 30" 10" Co-sine of 27 Degrees. a Co-sine of 26 Degrees. ( 1 // O" Q" AH P Part) ** 4 fft { 1 2 3 4 5 7 8 9 10 P - Part | i ~2 3456789 LOGARITHMIC TANGENTS. 87 1 Tangent of 62 Degrees. .5 Tangent of 63 Degrees. 91 0" 10" 2O' 30" 40" 50" 8 0" 10" 20" 30" 40" 50" o 10.274326 43 7 6 4427 44 7 8 4529 458o 5 9 10.292834 2886 2938 2 99 O 3o42 3o 9 4 5 9 i 463o 468i 4?32 4783 4834 4885 58 i 3i46 3i 99 325i 33o3 3355 34o 7 58 2 4935 4986 5o37 5o88 5i3 9 5i 9 o 57 2 345 9 35n 3563 36i5 366 7 3 7 2O 57 3 524o 5291 5342 53 9 3 5444 54 9 5 56 3 3 77 2 3824 38 7 6 3928 3 9 8o 4o3 2 56 4 5546 55 97 5647 56 9 8 5 7 4 9 58oo 55 4 4o84 4i3 7 4i8 9 4241 42 9 3 4345 55 5 585i 5902 5 9 53 6oo4 6o55 6io5 54 5 43 97 444 9 45o2 4554 46o6 4658 54 6 6i56 6207 6258 63o 9 636o 64n 53 6 4710 4763 48i5 486 7 4 9 i 9 4 97 i 53 7 6462 65i3 6564 66i5 6666 6 7 i 7 52 7 5o24 5076 5i28 5i8o 5232 5285 5 2 8 6768 6819 6870 6 9 20 6 97 i 7 022 5i 8 533 7 538 9 544 1 5494 5546 55 9 8 5i 9 7 o 7 3 7124 7 i 7 5 7226 7 2 77 7 328 5o 9 565o 5703 5 7 55 58o 7 585 9 5 9 I2 5o 10 io.2 77 3 79 7 43o 748 1 7532 7 583 7634 4 9 10 io.2 9 5 9 64 6016 6068 6121 6i 7 3 6225 4 9 ii 7 685 7736 7787 7 838 7 88 9 7940 48 ii 6278 633o 6382 6434 648 7 653 9 48 12 7991 8o43 8o 9 4 8i45 8i 9 6 824-7 47 12 65 9 i 6644 6696 6 7 48 6801 6853 47 i3 8298 8349 84oo 845 1 85o2 855^3 46 i3 6 9 o5 6 9 58 7010 7062 7 n5 7 i6 7 46 i4 86o4 8655 8706 8 7 5 7 88o 9 8860 45 i4 7 2I 9 7272 ?324 7377 742 9 748 1 45 i5 8911 8962 9 oi3 9 o64 9 n5 9 i66 44 i5 7534 7 586 7 638 7691 7743 7796 44 16 9217 9268 9 320 9 3 7 i 9 422 9 4 7 3 43 16 7 848 7 9 oo 79 53 8oo5 8o58 8110 43 i? 9524 9 5 7 5 9 626 9 6 7 8 9729 97 8o 42 J 7 8i63 82i5 826? 8320 83 7 2 8425 42 18 9 83i 9 882 99 33 99 84 ..36 ..87 4i 18 8477 853o 8582 8635 8687 8 7 4o 4i J 9 10. 280138 0189 O24o 02 9 2 o343 o3 9 4 4o : 9 8792 8845 88 97 8 9 49 9002 9 o54 4o 20 io.28o445 0496 o548 o5 99 o65o 0701 3 9 20 IO.2 99 IO7 9 i5 9 9 2I2 9264 9 3i 7 9 3 7 o 3 9 21 0752 0804 o855 o 9 o6 o 9 5 7 ioo 9 38 21 9 422 9 4 7 5 9 52 7 958o 9 632 9 685 38 22 1060 mi 1162 I2l4 1265 i3i6 37 22 9737 979 9 842 9 8 9 5 9947 .... 37 23 i36 7 1419 1470 l52I l5 7 2 1624 36 23 io.3ooo53 oio5 oi58 0210 O263 o3i5 36 24 i6 7 5 I 7 26 1777 l82 9 1880 i 9 3i 35 24 o368 0421 o473 o526 o5 7 8 o63i 35 25 1983 2o34 2o85 2l3 7 2188 223 9 34 25 o684 0736 o 7 8 9 o84i o8 9 4 o 9 47 34 26 2291 2342 23 9 3 2445 24 9 6 254 7 33 26 999 IO52 no5 1167 I2IO 1263 33 27 2 5 99 2 65o 2701 2 7 53 2804 2855 32 27 i3i5 1 368 1421 i473 i526 i5 79 32 28 2907 2 9 58 3oo 9 3o6i 3lI2 3i64 3i 28 i63i 1 684 i 7 3 7 1789 1842 i8 9 5 3i 29 32i5 3266 33i8 336 9 3421 3472 3o 2 9 i 9 4 7 2OOO 2o53 2106 2i58 2211 3o 3o ic. 283523 35 7 5 3626 36 7 8 3729 3 7 8o 2 9 3o IO. 3O2264 2 3i6 236 9 2422 24 7 5 252 7 29 3i 3832 3883 3 9 35 3 9 86 4o38 4o8 9 28 3i 258o 2633 2686 2 7 38 2 79 I 2844 28 32 4i4o 4192 4243 42 9 5 4346 43 9 8 27 32 2 8 97 2 9 5o 3OO2 3o55 3io8 3i6i 27 33 4449 45oi 4552 46o4 4655 4707 26 33 32i3 3266 33i 9 33 7 2 3425 3478 26 34 4?58 48io 486i 4 9 i3 4 9 64 5oi6 25 34 353o 3583 3636 368 9 3 7 42 3 79 4 25 35 5o6 7 5ii 9 5170 5222 52 7 3 53 2 5 24 35 384 7 3 9 oo 3 9 53 4oo6 4o5 9 4112 24 36 53 7 6 5428 5479 553i 5582 5634 23 36 4i64 4217 42 7 4323 43 7 6 442 9 23 37 5686 5 7 3 7 5 7 8 9 584o 5892 5 9 43 22 37 4482 4535 4588 464o 46 9 3 4 7 46 22 38 5 99 5 6046 6o 9 8 6i5o 6201 6 2 53 21 38 4799 4852 4 9 o5 4 9 58 Son 5o64 21 3 9 63o4 6356 64o8 645 9 65n 6562 2O 3 9 5n 7 5170 5223 5276 5328 538i 20 4o 10.286614 6666 6717 6y6 9 6821 6872 I 9 4o io.3o5434 548 7 554o 55 9 3 5646 56 99 J 9 4i 6 9 24 6 97 5 7027 779 7 i3o 7182 18 4i 5 7 52 58o5 5858 Sgii 5 9 64 6oi 7 18 42 7234 ?2 85 7337 7 38 9 7 44o 7 4 9 2 17 42 6o 7 o 6i23 6i 7 6 6229 6282 6335 !7 43 7544 7 5 9 5 7647 7699 77 5i 7802 16 43 6388 644i 64 9 4 654? 6600 6654 16 44 7854 79 o6 79 5 7 8oo 9 8061 8n3 i5 44 6 7 o 7 6760 68i3 6866 6 9 i 9 6 97 2 i5 45 8i64 8216 8268 83i 9 83 7 i 8423 i4 45 7 O25 7078 7 i3i 7i84 7237 7 2 9 o i4 46 8475 8526 85 7 8 863o 8682 8 7 33 i3 46 7 344 7 3 97 745o 7 5o3 7 556 7 6o 9 i3 47 8 7 85 8837 888 9 8 9 4i 8992 9 o44 12 47 7662 77i5 77 68 7822 7 8 7 5 79 28 12 48 9 o 9 6 9 i48 9 i 99 9 25l 93o3 9 355 II 48 79 8i 8o34 8o8 7 8i4i 8i 9 4 824 7 II 49 9407 9 458 9 5io 9 56 2 96-14 9 666 IO 49 83oo 8353 84o6 846o 85i3 8566 IO 5o 10.289718 97 6 9 9 82I 9 8 7 3 99 25 9977 9 5o io.3o86i 9 8672 8 7 26 8779 8832 8885 9 5i 10.290029 0081 Ol32 0184 0236 0288 8 5i 8 9 38 8 99 2 9 o45 9098 9 i5i 9 2o5 8 52 o34o o3 9 2 o444 0496 o54 7 o5 99 7 52 9 258 9 3n 9 364 94i8 9 4 7 i 9524 7 53 o65i 0703 o 7 55 0807 o85 9 0911 6 53 9 5 77 9 63i 9 684 9737 979 9844 6 54 0963 ioi5 1066 1118 II 7 1222 5 54 9 8 97 99 5o ...4 ..5 7 . no .164 5 55 1274 i326 1378 i43o 1482 i534 4 55 10.810217 0270 0324 o3 77 o43o o484 4 56 i586 i638 i6 9 o 1742 i 79 4 1 846 3 56 o53 7 oSgo o644 o6 97 o 7 5o 0804 3 5 7 1898 I 9 5o 2OO2 2054 2106 2i58 2 57 o85 7 0910 o 9 64 ioi 7 IO 7 O 1124 2 58 2210 2262 23i4 2366 2418 2470 I 58 1177 I23l 1284 I33 7 i3 9 i 1 444 I 5 9 2522 25 7 4 2626 2678 2 7 3o 2782 5 9 i4 9 8 i55i i6o5 i658 i 7 ii i 7 65 O 60" 50" 40" 30" 20" 10" f 60" 50" 40" | 30" 20" 10" . Co-tangent of 27 Degrees. S Co-tangent of 26 Degrees. i P Part 5 l " 2 " 3" 4// 5// 6// 7 " 8 " 9 " .< 1" 2" 3" 4" -5" 6" 7" 8" 9" } 5 10 15 21 26 31 36 41 46 lrt { 5 11 16 21 26 32 37 42 47 88 LOGARITHMIC SINES. t Sine of 64 Degrees. , d Sine of 65 Degrees. s 0" 10" 20" 30" 40" 50" 9 0" i 10" | 20" [ 30" 40" 50" 9.953660 3722 36 7 o 3 7 32 368i 3 7 42 36 9 i 3 7 53 3701 3 7 63 3712 3 77 3 5 9 58 I 9.95727617286(7295 7 3o5 7 3i5 7 335 7 344 7 354J 7 364I 7 3 7 4 7384 5 9 58 2 3 7 83 3 79 4 38o438i4 3824 3835 67 2 7 3 9 3 74o3 74i3 7423 7433 7 442 57 3 3845 3855 3865 38 7 6 3886 38 9 6 56 3 7 452 7462 7472 7482 7491 75oi 56 4 3906 3 9 i 7 3 9 2 7 3 9 3 7 3 9 4 7 3 9 5 7 55 4 75n 7521 753i 7 54o 7 55o 7 56o 55 5 3 9 68 3978 3 9 88 3 99 8 4009 4oi 9 54 5 7 5 7 7 5 79 7 58 9 7 5 99 7609 7619 54 6 4029 4o3 9 4o5o 4o6o 4o 7 o 4o8o 53 6 7628 7 638 7 648 7 658 7 66 7 7677 53 7 4090 4ioi 4ni 4l2I 4i3i 4i4i 52 7 7687 7697 7707 77 i6 77 26 7736 52 8 4i52 4162 41724182 4192 4203 5i 8 77 46 77 55 7765 777 5 7785 7794 5i 9 4213 4223 42334243 4254 4264 5o 9 7804 7 8i4 7824 7 833 7 843 7 853 5o 10 9.954274 4284 42 9 4 43o5 43i5 43 2 5 49 10 9.957863 7 8 7 2 7882 7 8 9 2 79 02 79" 49 ii 4335 4345 43564366 43 7 6 4386 48 ii 7921 79 3i 794o 7 9 5o 79 6 7970 48 12 43 9 6 44o6 44i7 4427 443 7 444 7 47 12 7979 7989 7999 8oo 9 8oi8 8028 4 7 , i3 445 7 4468 4478 4488 4498 45o8 46 i3 8o38 8o4 7 8o5 7 8067 8o 77 8086 46 i4 45i8 452 9 453 9 454 9 455 9 456 9 45 i4 8096 8106 8n5 8l2D 8i35 8i45 45 i5 45 7 9 458 9 46oo 46io 4620 463o 44 i5 8i54 8i64 8174 8i83 8i 9 3 8203 44 16 464o 465o 466i 46 7 i 468i 46 9 i 43 16 8213 8222 8232 8242 825i 8261 43 17 4 7 oi 4711 4 7 2I 4732 4 7 42 4 7 52 42 17 8271 8280 82 9 O 83oo 83o 9 83i 9 42 18 4762 4823 4772 4833 4782'47 9 2 4843 4853 4802 4863 48i3 48 7 3 4i 4o 18 8329 838 7 833 9 839 7 8348 84o6 83588368 84168426 83 77 8435 4i 4o 20 9 . 9 54883 48 9 4 4 9 o4 4 9 i4 4924 4 9 34 39 20 9 . 9 58445 8455 8464 8474 8484 8493 39 21 22 4944 5oo5 4 9 54 5oi5 4 9 64 4 9 74 5o 2 5 5o35 4 9 85 5o45 4 99 5 38 37 21 22 85o3 856i 85i3 85 7 i 8522 858o 8532 85 9 o 8542 8600 855i 8609 38 37 23 5o65 5o 7 5 5o86 5o 9 6 5io6 5n6 36 23 8619 8628 8638 8648 865 7 8667 36 24 5i26 5i36 5i46 5i56 5i66 5i 7 6 35 24 8677 8686 86 9 6 8706 8 7 i5 8 7 25 35 25 5i86 5i 9 6 5207 5217 522 7 523 7 34 25 8 7 34 8 7 44 8754 8 7 63 8 77 3 8 7 83 34 26 5247 5 2 5 7 5267 5277 5 2 8 7 5 297 33 26 8792 8802 8812 8821 883i 884o 33 2 7 53o7 r )3i 7 5327 533 7 5348 5358 32 27 885o 8860 886 9 8879 8888 8898 32 28 5368 53 7 8 5388 53 9 8 54o8 54i8 3i 28 8908 8917 8027 8 9 3 7 8 9 46 8 9 56 3i 29 5428 5438 ,5448 5458 5468 54 7 8 3o 2 9 8 9 65 8 97 5 8 9 85 8994 9004 9013 3o 3o 9.955488 54 9 8 55o8 55i8 5528 5538 2 9 3o 9.959023 9033 9 042 9 o52 9061 9071 2 9 3i 5548 555 9 556 9 55 7 9 558 9 55 99 28 3i 9080 9090 9 ioo 9109 9119 9128 28 32 5609 56i 9 562 9 563 9 564 9 565 9 27 32 9 i38 9i48 9 l5 7 9167 9176 9186 27 33 566 9 56 79 568 9 56 99 5 7 o 9 5 7 i 9 26 33 9 i 9 5 9205 9 2l5 9224 9234 9243 26 34 5 7 2 9 5 7 3 9 5?4 9 5 7 5 9 5 7 6 9 5 779 25 34 9 253 9262 9 2 7 2 9282 9291 93oi 25 35 5 7 8 9 5 799 58o 9 58i 9 582 9 583 9 24 35 93io 9320 9 32 9 9 33 9 9 348 9 358 24 36 5849 585 9 586 9 5879 588 9 58 99 23 36 9 368 9 3 77 9 38 7 9 3 9 6 9406 94i5 23 37 5909 5 9 i 9 5 9 2 9 5 9 3 9 5949 5 9 5 9 22 37 9425 9434 9 444 9 453 9 463 9 4 7 3 22 38 5 9 6 9 5 979 5 9 8 9 5 999 6009 6019 21 38 9482 9492 9 5oi 95i i 9520 9 53o 21 3 9 4o 4i 6o2 9 9 . 9 56o8 9 6i48 6o3 9 6099 6i58 6o4 9 6o5 9 6108 6118 6168 6178 6069 6128 6188 6o 79 6i38 6i 9 8 2O 19 18 39 4o 4i 9539 9.959596 9 654 95499558 96069615 96639673 9 568 9625 9682 9 5 77 9 634 9692 9 58 7 9644 97 oi 20 19 18 42 6208 6218 6228 6238 6248 6258 17 42 97" 9720 97 3o 9739 9749 97 58 17 43 44 45 6268 632 7 638 7 6278 633 7 63 97 628862 9 863o863i7 6347635763676377 6407641764276437 16 i5 i4 43 44 45 9768 9825 9882 9777 9 834 9891 9787 9 844 99 979619806 98639863 99109919 9 8i5 9 8 7 2 9929 16 i5 46 6447 645 7 6466,6476 6486 64 9 6 i3 46 99 38 9948 99 5 7 996799769986,13 / 7 65o6 65i6 6526 6536 6546 6556 I 2 A7 nnn 5 5 . "4 33 43 12 *7 48 6566 65 7 5 6585 65 9 5 66o5 66i5 II */ 48 Vyy^ 9.960052 0061 0071 0080 0090 0099 1 1 49 6625 6635 6645 6655 6665 66 7 4 10 49 0109 0118 0128 0137 0147 oi56 10 5o 9 . 9 56684 66 9 4 6704 6714 6724 6 7 34 9 5o 9.960165 0175 oi84 019410203 02 I 3 9 5i 6 7 44 6 7 54 6 7 63 6 77 3 6 7 83 6 79 3 8 5i O222 0232 0241 O25o 0260 0269 8 52 68o3 68i3 6823 6833 6843 6852 7 52 0279 0288 02 9 8 o326 7 53 6862 6872 6882 6892 6902 6 9 I2 6 53 o335 o345 o354 o364!o373 o382 6 54 6 9 2I 6 9 3i 6 9 4i 6951 6961 6 97 i 5 54 0392 o4oi o4n 0420 o43o 0439 5 55 6 9 8i 6 99 o 7000 7 oio 7020 7o3o 4 55 o448 o458 0467 o477!o486 o4 9 5 4 56 7040 7ODO 7 5 9 7069 7079 7o8 9 3 56 o5o5 o5i4 o524 o533o542o552 3 5 7 799 7 I0 9 7118 7128 7 i38 7i48 2 67 o56i 0571 o58o o58 9 o5 99 |o6o-< 9 58 7i58 7168 7177 71877197 7207 I 58 0618 0627 o636io646o655 o665 i 5 9 7217 7227 7 236 7246 7256 7266 O 5 9 0674:0683 069^ 0702 071 1 071: 60" 50" 40" 30" | 20" 10" d 60" | 50" 40" j 30" 20" j 10" i ^ Co-sine of 25 Degrees. Co-sine of 24 Degrees. a T PartJ l " 2 " 3 " 4 " I.lartJ ! 2 3 4 5" 6" 7" 8" 9" 56789 .( 1" 2" 3" 4" 5" 6" 7" fi irt \ 1 2 3 4 5 6 7 * !> LOGARITHMIC TANGENTS. c Tangent of 64 Degrees. Jj Tangent of 65 Degrees. 9 0" 10" 1 20" 30" 40" 50" s 0" 10" 20" 30" 40" 50" io.3n8i8 l8 7 2JI 9 25 i 97 9 2032 2o85 5 9 io.33i327 i382 i43 7 1492 1 54 7 1602 5 9 i 2l3 9 2I 9 2 2246 22 99 2353 2406 58 I i65 7 I 7 I2 i 7 6 7 1822 i8 77 1932 58 2 2460 25i3| 2 56 7 2620 2674 2 7 2 7 5? 2 i 9 8 7 2042 20 97 2i53 2208 2263 57 3 2781 2834 2888 2 9 4l 2 99 5 3o48 56 3 23i8 23 7 3 2428 2483 2538 25 9 3 56 A 3io2 3i55 320 9 3263 33i6 33 7 o 55 4 2648 2703 2 7 58 2 8i3 2868 2924 55 5, 3423 34 77 353o 3584 3637 36 9 i 54 5 2 979 3o34 3089 3i44 3i 99 3254 54 6 3745 3798 3852 3 9 o5 3 9 5 9 4oi3 53 6 33o 9 3364 3420 3475 353o 3585 53 7 4o66 4l2O 4i 7 3 422 7 4281 4334 52 7 364o 36 9 5 3 7 5i 38o6 386i 3 9 i6 52 8 4388 4442 44 9 5 4549 46o3 4656 5i 8 3 97 i 4026 4082 4i3 7 1" |ij. .4 j 5i 9 4710 4 7 64 48i 7 48 7 i 4 9 25 4 9 78 5o 9 43o2 4358 44i3 4468 H 4579 5o 10 io.3i5o32 5o86 5i3 9 5i 9 3 5247 53oo 49 io.334634 468 9 4 7 44 48oo 4855 4910 49 ii 5354 54o8 546 1 55i5 556 9 5623 48 1 1 4 9 65 5O2I 5o 7 6 5i3i 5i86 5242 48 12 5676 5 7 3o 5 7 84 5838 58 9 i 5 9 45 47 12 52 97 535 3 54o8 5463 55i8 55 7 4 47 i3 5 999 6o53 6106 6160 6214 6268 46 1 3 562 9 5684 574o 5 79 5 585o 5go6 46 i4 632i 63 7 5 642 9 6483 653 7 65 9 o 45 i4 5 9 6i 6016 6o 7 2 6127 6182 6238 45 i5 6644 66 9 8 6 7 52 6806 6860 6 9 i3 44 i5 62 9 3 634 9 64o4 645 9 65i5 65 7 o 44 16 6967 7021 7 o 7 5 7129 7 i83 7236 43 16 6625 6681 6 7 36 6792 6847 6903 43 17 7290 7 344 7 3 9 8 7452 75o6 7 56o 42 17 6 9 58 7013 7069 7124 7180 7 235 42 18 7 6i3 7667 772i 777 5 7 82 9 7 883 4i 18 7 2 9 X 7346 7 402 745 7 75i3 7 568 4i 19 79 3 7 799 1 8o45 8099 8i53 8206 4o J 9 7624 7 6 79 77 35 779 7 846 79 oi 4o 20 10.818260 83i4 8368 8422 8476 853o 3 9 20 io.33 79 5 7 8012 8068 8i23 81 79 8234 39 21 8584 8638 86 9 2 8 7 46 8800 8854 38 21 82 9 o 8345 84oi 8456 85i2 8568 38 22 8908 8 9 62 9 oi6 9070 9 I24 9 i 7 8 37 22 8623 86 79 8 7 34 8790 8845 8901 37 23 9232 9 286 9 34o 9 3 9 4 9 448 9 5o2 36 23 8 9 5 7 9 OI2 9068 9123 9 J 79 9 235 36 24 9556 9 6io 9 664 9718 977 2 9 826 35 24 9 2 9 O 9 346 9402 9 45 7 9 5i3 9 56 9 35 25 9880 99 34 9988 ..42 ..96 .i5i 34 25 9 624 9 68o 97 35 9791 9 84 7 99 02 34 26 IO.32O205 O25 9 o3i3 0367 0421 0475 33 26 99 58 . . i4 ..70 .125 .181 .23 7 33 27 0529 o583 o63 7 0692 o 7 46 0800 32 27 IO.3402 9 2 o348 o46o o5i5 o5 7 i 32 28 o854 o 9 o8 0962 1016 1071 1126 3i 28 0627 0682 0738 o 79 4 o85o o 9 o5 3i 29 11 79 1233 I28 7 i34i i3 9 6 i45o 3o 29 o 9 6i 1017 1073 1129 u84 1240 3o 3o -o 32i5o4 i558 1612 1666 1721 1775 2 9 3o io.34i2 9 6 i352 i4o8 :463 i5i 9 i5 7 5 29 3i 1829 i883 1938 1992 2046 2IOO 28 3i i63i 1687 1742 1798 1 854 I 9 IO 28 32 2i54 220 9 2263 2317 23 7 I 2426 27 32 i 9 66 2O22 2078 2i33 2l8 9 2245 27 33 2480 2534 2588 2643 2 6 97 2 7 5l 26 33 23oi 235 7 24i3 2469 2525 258i 26 34 2806 2860 2914 2968 3o23 3077 25 34 2 636 26 9 2 2748 2804 2860 2 9 i6 26 35 3i3i 3i86 3 2 4o 3294 334 9 34o3 24 35 2 9 72 3028 3o84 3i4o 3i 9 6 3252 24 36 345 7 35i2 3566 3620 36 7 5 3 7 2 9 23 36 33o8 3364 3420 3476 3532 3588 23 3? 3 7 83 3838 3892 3947 4ooi 4o55 22 37 3644 3700 3 7 56 38i2 3868 3 9 24 22 38 4no 4i64 4219 4273 4327 4382 21 38 3 9 8o 4o36 4092 4i48 4204 4260 21 3 9 4436 44 9 i 4545 4599 4654 4708 20 3 9 43i6 43 7 2 4428 4484 454o 45 9 6 2O 4o 10.324763 4817 4872 4926 4 9 8i 5o35 19 4o 10.344652 4708 4 7 64 4821 48 7 7 4 9 33 19 4i 5089 5i44 5i 9 8 5253 53o 7 5362 18 4i 4 9 8 9 5o45 5ioi 5i5 7 52i3 526 9 18 42 54i6 54?i 5525 558o 5634 568 9 17 42 5326 5382 5438 5494 555o 56o6 I? 43 5 7 43 5 79 8 5852 5907 5 9 62 6016 16 43 5663 6719 5 77 5 583i 5887 5 9 43 16 44 6o 7 i 6i25 6180 6234 6289 6343 i5 44 6000 6o56 6112 6168 6224 6281 i5 45 6398 6453 65o7 656 2 6616 6671 i4 45 633 7 63 9 3 6449 65o6 656a 6618 i4 46 6-726 6780 6835 6889 6 9 44 6 999 i3 46 66 7 4 6731 6787 6843 6899 6 9 56 i3 47 7 o53 7108 7162 7217 7272 7326 12 47 7012 7068 7125 7181 7 23 7 7293 12 48 7 38i 7 436 7 4 9 o 7545 7600 7 654 I I 48 7 35o 7406 7462 7 5l 9 7 5 7 5 7 63i II 49 779 7764 7818 7 8 7 3 792 8 7982 10 49 7688 7744 7800 7 85 7 79 i3 79 6 9 IO 5o io.328o3 7 8o 9 2 8i4 7 8201 8256 83u 9 5o 10.348026 8082 8139 8i 9 5 825i 83o8 9 5i 8365 8420 84 7 5 853o 8584 863 9 8 5i 8364 8421 84 7 7 8533 8690 8646 8 52 8694 8* 7 4 9 88o3 8858 8 9 i3 8 9 68 7 52 8703 8 7 5 9 88i5 8872 8928 8 9 85 7 53 9023 977 9132 9187 9 242 9297 6 53 9 o4i 9098 9i54 9211 9 26 7 0024- 6 54 9 35i 9 4o6 9 46i 9 5i6 9 5 7 i 9 625 5 54 9 38o 943 7 9493 9 55o 9606 9663 5 55 9680 97 35 979 9 845 99 oo 99 55 4 55 9719 9776 9832 9 88 9 9945 . . .2 4 56 io.33oooo oo64 0119 0174 O22 9 0284 3 56 io.35oo58 on5 0171 0228 0285 o34i 3 57 o33 9 o3oA o448 o5o3 o558 o6i3 2 5 7 o3 9 8 o454 o5n o56 7 0624 0681 2 58 0668 7 23 o 77 8 o833 0888 o 9 43 I 58 o 7 3 7 0794 o85o o 9 o 7 0964 IO2O I 5 9 o 99 8 io53ji 108 n63 1218 1272 5 9 io 77 n34 1190 I24 7 i3o4 i36o O 60" 50" | 40" 30" 20" 10" ej 60" 50" 40" | 30" 20" 10" c Co-tangent of 25 Degrees. Z Co-tangent of 24 Degrees. s ,5 1" 2" 3" 4" 5" 6" 7" 8" 9" C 1" 2" 3" 4" 5" 6" 7" 8" 9" irl l 5 11 1/5 22 27 33 38 43 49 irt } 6 11 17 22 28 33 39 45 50 00 LOGARITHMIC SINES. a Sine of 66 Degrees. ^c Sine of 67 Degrees. 9 0" 10" 20" 30" 40" 50" 0" 1 10" 20" 30" 40" 50" 9 . 9 6o 7 3o o 7 4o 7 4 9 0758 o 7 68 777 5 9 o 9 . 9 64o264o35 4o44 4o53 4062 4071 5 9 I 2 o 7 86 o843 o 79 6 o852 o8o5 0861 0814 0871 0824 0880 o833 0889 58 I 2 4o8o 4i33 4o8 9 4i42 4o 9 8 4i5i 4io64n5 4i6o 4i6 9 4178 58 5? 3 0899 0908 9 I 7 0927 0936 0945 56 3 4i8 7 4196 42o5 4214 4222 423i 56 4 o 9 55 0964 o 97 3 o 9 83 0992 1002 55 4 424o 4249 4258 4267 42 7 6 4285 55 5 ion 1020 io3o 1039 io48 io58 54 5 4a 9 4 43o3 43n 4320 432 9 4338 54 6 io6 7 10-76 1086 1095 no4 in3 53 6 4347 4356 4365 43 7 4 4383 43 9 2 53 7 1123 1 1 32 n4i n5i 1160 1169 52 7 44oo 4409 44i8 4427 4436 4445 52 8 n 79 1188 119-7 1207 1216 1225 5i 8 4454 4463 447i 448o 448 9 4498 5i 9 1235 1244 1253 1263 12-72 I28l 5o 9 45o 7 45i6 45 2 5 4534 4542 455i 5o 10 9.961290 i3oo i3o 9 i3i8 i3 2 8 i33 7 49 10 9.964560 456 9 45 7 8 458 7 45 9 6 46o4 4 9 ii 1 346 i356 i365 i3 7 4 1 383 i3 9 3 48 ii 46i3 4622463i 464o 4649 4658 48 12 1402 i4n i4ax i43o i43 9 1 448 47 12 4666 46 7 5 4684 46 9 3 4 7 02 4711 47 i3 i458 i46 7 i4 7 6 i485 i4g5 i5o4 46 i3 4-720 4728 4 7 3 7 4746 4 7 55 4764 46 i4 i5i3 i5 2 3 i532 i54i i55o i56o 45 i4 4773 4781 4790 4799 48o8 48i 7 45 i5 1 569 i5 7 8 i $871597 1606 i6i5 44 i5 4826 4834 4843 4852 486i 48 7 o 44 16 1624 i634 1 643x659 1661 i6 7 i 43 16 48 79 488 7 48 9 6 4go5 4914 4 9 23 43 17 1680 1689 i6 9 8 1708 I 7 i 7 1-726 42 '7 4 9 3i 4g4o 4 9 4o 4 9 58 4 9 6 7 4 97 5 42 18 i 7 35 i 7 45 1754 1763 I 77 2 I 7 82 4i 18 4 9 84 4 99 3 5OO2 Son 502O 5028 4i 1 9 1-791 1800 i8o 9 1819 1828 i83 7 4o 19 5o3 7 5o46 5o55 5o64 5o 7 2 5o8i 4o 20 9.961846 i856 i865 1874 i883 1892 3 9 20 9.965090 5o 99 5io 7 5n6 5i25 5i34 3 9 21 1902 191 1 1920 1929 i 9 3 9 1948 38 21 5i43 5i5i 5i6o 5i6 9 5i 7 8 5187 38 22 i 9 5 7 1966 1975 1985 1 99 4 2OO3 37 22 5i 9 5 52o4 52i3 5222 523o 5239 37 23 2012 2021 2o3l 2o4o 2049 2o58 36 23 5248 5 2 5 7 5266 52 7 4 5283 5292 36 24 2O6 7 20 77 2O86 2095 2104 2Il3 35 24 53oi 53o 9 53i8 532 7 5336 5344 35 25 2123 2132 2l4l 2l5o 2 I 59 2169 34 25 5353 5362 53 7 i 53 79 5388 53 97 34 26 2I 7 8 2l8 7 2196 2205 22l4 2224 33 26 54o6 54i4 5423 5432 544 1 544 9 33 27 2233 2242 225l 226O 2269 22-79 32 27 5458 546 7 54 7 6 5484 54 9 3 55o2 32 28 2288 229 7 23o623i5 2325 2334 3i 28 55u 55i 9 55 2 8 553 7 5546 5554 3i 29 2343 2352 236i 23 7 o 23-79 2389 3o 29 5563 55 72 558o 558 9 5598 56o 7 3o 3c 9.962398 24o 7 2416 2425 2434 2444 29 3o 9 . 9 656i5 5624 5633 5642 565o 565 9 2 9 3i 2453 2462:2471 2480 2489 2498 28 3i 5668 56 7 6 5685 56 9 4 5-702 5 7 i i 28 32 25o8 2 5i 7 2526 2535 2544 2553 27 32 5 7 2o 5 7 2 9 5 7 3 7 5 7 46 5 7 55 5 7 63 2 7 33 2562 25-72 258i 2590 2599 2608 26 33 5772 5 7 8i 5 79 o 5 79 8 58o 7 58i6 26 34 261-7 2626 2635 2645|2654 2663 25 34 5824 5833 5842 585o 585 9 5868 25 35 26-72 2681 2690 2699:2708,2717 24 35 58 7 6 5885 58 9 4 5 9 O2 5911 5 9 20 24 36 2 7 2 7 2 7 36 2745 2754 2763 2772 23 36 5 9 2 9 5 9 3 7 5 9 46 5 9 55 5 9 63 5 97 2 23 3? 2-781 2 79 2799 2809:2818 282 7 22 37 5981 5 9 8 9 5 99 8 600-7 6oi5 6024 22 38 2836 2845 285428632872 2881 21 38 6o33 6o4i 6o5o 6o5 9 6o6 7 60-76 21 39 2890 2899 2909 2918 2927 2 9 36 2O 3 9 6o85 6o 9 3 6102 6111 6119 6128 20 4o 9.962945 2 9 54 2963 2972 2981 2990 19 4o 9.966136 6i45 6i54 6162 61-71 6180 '9 4i 2999 3oo8 3oi8 3027 3o36 3o45 18 4i 6188 6i 97 6206 6214 6223 6232 18 42 3o54 3o63 3072 3o8i 3090 3099 '7 42 6240 624 9 6 2 5 7 6266 62 7 5 6283 1 7 43 3io8|3n 7 3i263i353i443i53 16 43 6292 63oi 63o 9 63i8 63266335 16 44 3i63|3i 7 2 3i8i 31903199 3208 i5 44 6344 6352 636i 63 7 o 63 7 8638 7 i5 45 32I 7 3226 323532443253 3262 i4 45 63 9 5 64o4 64i3 6421 643o6438;i4 46 32 7 I 3280 3289*3298 33o 7 33i6 i3 46 6447 6456 6464 64 7 3 6482 64 9 o ! i3 47 48 5i 3325 33 79 . 3434 9.963488 3542 3334 3388 3443 34 9 7 355i 3343 33 9 8 3452 35o6 356o 3352 34o 7 346 1 35i5 356 9 336i 34i6 3470 3524 35 7 8 33 7 o 3425 3479 3533 358 7 12 II IO 9 8 t-OO O> O i- xt xt xt vo to 64 99 655o 6602 9 . 9 66653 65o 7 6559 6610 6662 6 7 i3 65i6 656 7 66i 9 66 7 o 6 7 22 652565336542 65 7 6658565 9 3 6628663616645 667966886696 678067896748 12 II 10 9 S* 52 3596 36o5 36i4 36233632 364i 7 52 6 7 56 6 7 65 6 77 3 6-782 6 79 oj6 7 9 9 7 53 365o 365 9 3668 3677 3686 3695 6 53 6808 6816 6825 6833 6842 685o 6 54 3 7 o4 3 7 i3 3722 3 7 3o3 7 3 9 3 7 48 5 54 685 9 686-7 68-76 6884 68 9 3 6 9 02 5 55 3 7 5 7 3766 3 77 5 3 7 84i3 79 3 38o2 4 55 6910 6 9 i 9 6 9 2 7 |6 9 36 6 9 44 6 9 53 4 56 38n 3820 3829 3838 384 7 3856 3 56 6961 6 97 o 6 97 8 6987 6 99 5 7 oo4 :; 57 3865 38 7 4 3883 38 9 2 3 9 oi 3910 2 5; 7013 7021 7 o3o 7o38 7047 7 o55 2 58 5 9 3 9 i 9 3972 3 9 28 3 9 8i 3 9 3 7 3990 3946:3955 3999 4oo8 3 9 63 4017 I O 58 5 9 7064 7072 71 i5j 7 i23 7 o8i 7 l32 7089 7098 7106 7 i4o 7 i49' 7 i57 i 60" 50" 40" 30" 20" 10" .c 60" 50" | 40" 30" 20" | 10" Co-sine of 23 Degrees. Co-sine of 22 Degrees. s .< 1" 2" 3" 4" 5" 6" 7" 8" 9" llt $1234 55 67 8 .( 1" -2" 3" 4" 5 /; 6" 7" 3" 9" irt ) 123345678 LOGARITHMIC TANGENTS. 91 c Tangent of 66 Degrees. s Tangent of 67 Degrees. 2 0" 10" 20" 30" 40" 50" 55 0" 10" 20 / 30" 40' | 50" o o.35i4i7 i474 i53o i58 7 644 700 5 9 10.372148 22O 7 2265 2324 2382 244 1 9 I 1757 i8i4 1870 I 9 2 7 9 84 o4o 58 i 2499 2558 2617 2 6 7 5 2734 2 79 2 8 2 2097 2i54 221 I 2267 2324 z38i 5 7 2 285i 2910 2 9 68 3o2 7 3o85 3i44 7 3 2438 2494 255l 2608 2665 2721 56 3 32o3 261 3320 3379 3437 34 9 6 6 4 2778 2 835 28 9 2 2 9 4 9 Ioo5 3o62 55 4 3555 36i3 i6 7 2 3 7 3i 3789 3848 5 5 3119 3: 7 6 3233 32 9 O 3346 34o3 54 5 3 9 o 7 3965 ^024 4o83 4i42 4200 4 6 346o 35i 7 35 7 4 363i 3687 3 7 44 53 6 425 9 43i8 43 77 4435 44 9 4 4553 3 7 38oi 3858 3 9 i5 3 97 2 iO2 9 4086 52 7 4612 i6 7 o 4?2 9 4 7 88 4847 , 9 o6 2 8 4i43 4199 4256 43i3 43 7 427 5i 8 4 9 64 5o23 5o82 5:4i 52OO 5 2 58 I 9 4484 454i 45 9 8 4655 47^2 4769 5o 9 53i 7 53 7 6 5435 54 9 4 5553 56i2 o 10 354826 4883 4 9 4o 4997 5o54 5m 4 9 10 10.375670 5 7 29 5 7 88 5847 5 9 o6 5 9 65 9 ii 5i68 5225 5282 533 9 53 9 6 5453 48 ii 6024 6o83 6142 6200 625 9 63i8 8 12 55io 556 7 56 2 4 568i 5 7 3 5 79 5 4 7 12 63 7 7 6436 64 9 5 6554 66i3 66 7 2 47 i3 5852 5 9 o 9 5 9 66 6023 6080 6i3 7 46 i3 6 7 3i 6-790 684 9 6 9 o8 6 9 67 7026 46 M 6194 6261 63o 9 6366 6423 648o 45 i4 7 o85 7i44 7 203 7262 7 32I 738o 45 i5 6537 65 9 4 665 i 6708 6 7 65 6823 44 i5 7 43 9 7498 7 55 7 7616 7 6 7 5 7734 44 16 6880 6 9 3 7 6 99 4 7o5i 7108 7 i66 43 16 779 3 7 853 79 I2 797 1 8o3o 8o8 9 43 J 7 7223 7280 7 33 7 7 3 9 4 745 1 7 5o 9 42 17 8i48 8267 8266 83 2 5 8384 8444 .2 18 7566 7 6 2 3 7 68o 77 3 7 779 5 7 852 4i 18 85o3 8562 8621 8680 8 7 3 9 8 799 I : 9 7909 7 9 G6 8024 8081 8i38 8i 9 5 4o J 9 8858 8917 8 97 6 9 o35 9 o 9 4 9 i54 ^0 20 0.358253 83io 8367 8425 8482 853 9 3 9 20 io.3 79 2i3 9272 9 33i 9 3 9 o 9 45o 9 5o 9 3 9 21 85 9 6 8654 8711 8 7 68 8826 8883 38 21 9 568 9627 9 68 7 9 746 9 8o5 9 864 38 22 8940 8 99 8 9 o55 9 II2 9 J 7 9 22 7 37 22 99 24 99 83 .42 . IO2 .161 .220 3 7 23 9284 0342 9 3 99 9 456 9 5i4 9^71 36 23 o. 080280 o33 9 o3 9 8 o45 7 o5i 7 o5 7 6 36 24 9629 9 686 9743 9 8oi 9 858 99 i6 35 24 o636 oo v 5 o 7 54 0814 o8 7 3 9 32 35 25 99?3 ..3i ..88 .i45 .203 .260 34 25 99 2 io5i IIIO 1170 I22 9 1289 34 26 o.36o3i8 o3 7 5 o433 o4 9 o o548 o6o5 33 26 1 348 i4o 7 i46 7 i5 2 6 i586 1 645 33 27 o663 0720 o 77 8 o835 o8 9 3 o 9 5o 32 2 7 I 7 o5 1764 1824 i883 i 9 43 20O2 32 28 1008 io65 1123 1180 1238 I2 9 5 3i 28 2061 2121 2180 2240 22 99 235 9 3i 20 i353 i4i 1 46*8 i5 2 5 i583 i64i 3o 2 9 2418 24 7 8 2538 2 5 97 265 7 2716 3o 3o 10.361698 i 7 56 i8i3 1871 I 9 28 i 9 86 29 3o io.382 77 6 2835 28 9 5 2 9 54 3oi4 3074 2 9 3i 2044 2101 2l5 9 2217 22 ? 4 2332 28 3i 3i33 3i 9 3 3252 33i2 33 7 2 343i 28 32 238 9 2447 2 5o5 2562 2620 2678 27 32 34 9 i 355o 36io 36 7 o 3 7 2 9 3 7 8 9 2 7 33 2 7 35 27 9 3 2 85i 2 9 o8 2 9 66 3024 26 33 384 9 3 9 o8 3 9 68 4028 4o8 7 4i47 26 34 3o8i 3i3 9 3i 97 3255 33i2 3370 25 34 420-7 4266 4326 4386 4445 45o5 25 35 3428 3486 3543 36oi 365 9 3717 24 35 4565 46 2 5 4684 4744 48o4 4864 24 36 3 77 4 3832 38 9 o 3 9 48 4oo5 4o63 23 36 4 9 23 4 9 83 5o43 5io: 5i62 5222 23 37 4l2I 4i79 423 7 42 9 4 4352 44io 22 37 5282 5342 54o2 546i 552i 558i 22 38 4468 45 2 6 4584 464i 46 99 4 7 5 7 21 38 564i 5 7 oi 5 7 6i 5820 588o 5 9 4o 21 3 9 48i5 48 7 3 4 9 3i 4 9 8 9 5o46 5io^ 20 3 9 6000 6060 6120 6180 6240 62 99 2O 4o io.365i62 5220 5278 5336 53 9 4 5452 1 9 4o io.38635 9 64i 9 6479 653 9 65 99 665 9 I 9 4i 55io 5568 5626 5684 5 7 4i 5 799 18 4i 67i 9 6779 683 9 68 99 6 9 5 9 7 OI 9 18 4s 585 7 5 9 i5 5 97 3 6o3i 6o8 9 6i4 7 J 7 42 779 7 l3 9 7199 7 25 9 73i 9 7379 17 43 6205 6262 632i 637 9 643 7 64 9 5 16 43 7 43 9 74 99 7 55 9 76i 9 7 6 79 7739 16 44 6553 6611 666 9 6727 6 7 85 6843 i5 44 7799 785 9 79 i 9 7979 8o3 9 8o 99 i5 45 6901 6 9 6o 7018 7076 7 1 34 7 I 9 2 i4 45 8i5 9 82I 9 82 79 833 9 83 99 846o i4 46 725o 7 3o8 7 366 742^ 7 48 2 7 54o i3 46 8520 858o 864o 8700 8 7 6o 8820 i3 47 7 5 9 8 7 65 7 77 i5 777 3 7 83i 7 88 9 12 47 8880 8 9 4i 9 ooi 9061 9 I2I 9 i8i 12 48 7947 8oo5 8o64 8122 8180 8238 II 48 9 24l 9 302 9 362 9 422 9 48 2 9 542 II 49 8296 8354 84:3 84? i 852 9 858 7 10 49 9 6oc 9 663 97 23 97 83 9 844 99 o4 IO 5o io.368645 8 7 o^ 8762 8820 88 7 8 8 9 3 7 9 5o io.38 99 6^ . .22 ..85 .145 .205 .265 9 5i 8 99 5 9 o53 9 m 9 i 7 o 9 228 9 28 8 5i io.3 9 o326 o386 o446 o5o7 0567 0627 8 52 9344 9 4o3 9 46i 9 5i 9 9 5 7 8 9 636 7 52 0688 o 7 48 0808 o86 9 O 9 2 9 o 9 8 9 7 53 9 6 9^ 97 53 9811 9 86 9 99 2 7 99 86 6 53 io5o IIIO II 7 I23l I2 9 I,l352 6 54 10.37004^ oio3 0161 O2I 9 02 7 8 o336 c 54 1412 I4 7 2 i533 i5 9 3 i654 I7i4 5 55 o3 9 ^ o453 o5n o56 9 0628 0686 L 55 i 77 5 i835 i8 9 5 i 9 56 2016 2077 4 56 o 7 45 o8o3 0862 O 9 2O 0978 1037 c 56 2l3 7 2I 9 8 2258 23i 9 2 3 79 244o 3 ^7 1095 1 1 54 1212 I27l|l32 9 i388 2 5 7 25oo 2 56i 2621 2682 2 7 42 28o3 2 58 1 446 i5o4li563 1621 1680 1738 I 58 2863 2 9 2^ 2 9 85 3o45 3io6 3i66 I 5 9 1797 i855 i 9 i4 I 9 72|2o3l 2O 9 5 9 322 7 328-7 3348 3409 3469 353o O 60" 50" | 40" 30" 20" 10" d 60" | 50" 40" 30" 20" 10" Co-tangent of 23 Degrees. % Co- tangent of 22 Degrees. ,(1" 2" 3" 4" 5" 6" 7" 8" 9" II p p .( I" 2" 3" 4" 5" 6" 7" 8" 9'' lrt { 6 12 17 23 29 35 40 46 52 irt 6 12 18 24 30 36 42 48 54 LOGARITHMIC JSlNES. .a Sine of 68 Degrees. Jj Sine of 69 Degrees. i 0" 10" 20" 30" 40" 50" s 0" 10" 20" 30" 40" 50" o 9.967166 7174 7l83 7191 7200 7208 5 9 o 9 970152 0160 0168 OI 7 6 0184 OI 9 2 5 9 I 7217 7225 72347242 7251 725 9 58 I O2OO 0208 O2l6 0222 023: 0241 58 2 7268 7276 7285 7293 7302 73io 5? 2 O249 0257 0265 027: 0281 028 9 57 c 7319 7327 733673447353 7 36i 56 r 0297 o3o5 o3i3 0321 o32 9 o33 7 56 L 7 3 7 o 7378 73877395 7 4o4 7412 55 4 o345 o353 o36i o3 7 o o3 7 8 o386 55 i 7 42I 7429 7 43 7 7 446 7 454 7463 54 f 0394 O4O2 o4io o4i8 0426 o434 54 6 7 4 7 i 7480 7 488 7 49 7 7 5o5 7 5i4 53 6 0442 o45o o458 o466 o4 7 4 0482 53 7 7 522 7 53i 7 539 7 54 7 7 556 7 564 52 "3 0490 0498 o5o6 o5i4 0522 o53o 5 2 8 7 5 7 3 7 58i 7590 7598 7607 7 6i5 5i o538 o546 o554 o56 2 o5 7 o o5 7 8 5i 9 7624 7 632 7640 7649 7657 7 666 5o 9 o586 0594 o6o2 0611 o6i 9 0627 5o 10 9 . 9 6 7 6 7 /i 7683 7691 7699 7708 77 i6 49 10 9.970635 o643 o65i o65 9 o66 7 o6 7 5 4 9 ii 77 25 7733 774277507758 7767 48 ii o683 0691 o6 99 o 7 o 7 o 7 i5 0723 48 12 7775 7784 7792 7801 7809 7 8i 7 4 7 12 0731 o 7 3 9 o 7 4 7 o 7 55 o 7 63 0771 47 i3 7826 7 834 7843 7 85i 7 85 9 7 868 46- i3 0779 0787 o 79 5 o8o3 0811 o8i 9 46 i4 7 8 7 6 7885 7893 7901 7910 79 i845 i4 0827 o835 0842 o85o o858 0866 45 iS 79 2 7 7935 7 9 43 7 9 52 7960 79 6 9 44 i5 0874 0882 o8 9 o o8 9 8 o 9 o6 o 9 i4 44 16 7977 7985 7994 8002 8011 8019 43 16 0922 ogSo o 9 38 o 9 46 o 9 54 O 9 62 43 17 802 7 8o36 8o44 8x>53 8061 8o6 9 42 17 0970 0978 o 9 86 o 99 4 1 002 1010 42 18 8o 7 8 8086 8094 8io38in 8120 4i 18 1018 1026 io34 1042 io5o io58 4i '9 8128 8i368i458i538i6i 8i 7 o 4o 19 1066 1073 1081 io8 9 io 97 no5 4o 20 9.968i 7 8 8i8 7 8i 9 582o3 8212 8220 39 20 9.971113 II2I II2 9 u3 7 n45 n53 39 21 8228 S245 82538262 8270 38 21 1161 1169 1177 n85 iz 9 3 1 200 38 22 82 7 8 ---/ 82 9 583o3|83i2 8320 37 22 1208 1216 1224 1232 1248 37 23 832 9 833 7 8345,83548362 83-p 36 23 1256 1264 1272 1280 1288 I2 9 6 36 24 83 7 9 838 7 83 9 584o484i2 8420 35 34 i3o3 i3n i3i 9 I32 ? i335 1 343 35 25 26 8429 84 7 9 843 7 8445|b454 8462 84 7 o 8520 34 33 25 26 i35i i3 9 8 i4o6 i36 7 i4i4 i3 7 5 i383 i43o i3 9 o i438 34 33 27 85 2 8 853 7 8545 ! 8553 8562 85 7 o 32 27 1 446 1 4 *>. 1462 i46 9 1477 i485 32 28 85 7 8 858 7 85 9 586o3 8612 8620 3i 28 1493 i5oi i5o 9 i5i 7 i525 i53 2 3i 29 8628 863686458653866i 8670 3o 29 i54o 1 548 i556 1 564 1572 i58o 3o 3o 9.9686 7 8 86868694|8 7 o38 7 n 87i 9 29 3o 9.971588 i5 9 5 i6o3 i6ji i6i 9 1627 2 9 3i 8 7 28 8 7 368 7 44 8 7 52 8761 8 7 6 9 28 3i i635 i643 i65i i658 1666 1674 28 32 8777 8786 8794 88028810 88i 9 27 32 1682 1690 i6 9 8 I 7 o6 I 7 i3 1721 2 7 33 882-7 8835 8844 8852 8860 8868 26 33 1729 I 7 3 7 1745 i 7 53 1761 1768 26 34 88 77 8885 88 9 3 8901 8910 8 9 i8 25 34 1776 i 7 84 170.2 1800 1808 i8i5 25 35 8926 8 9 34 8 9 43 8 9 5i 8 9 5 9 8967 24 35 1823 i83i i83 9 i84 7 i855 1862124 36 8 97 6 8984 8992 9000 9 oo 9 9017 23 36 1870 i8 7 8 1886 i8 9 4 I 9 02 1909 23 37 9025 9033 9042 9o5o 9 o58 9066 22 37 1917 I 9 25 i 9 33 i 9 4i I 9 4 9 I 9 56 22 38 9 o 7 5 9083 9091 9099 9 io8 9 n6 21 38 1964 I 97 2 i 9 8o i 9 88 i 99 5 20O3 21 3 9 9124 9132 9141 9149 9167 9 i65 20 39 201 1 20I 9 2027 2o34 2O42 2o5o 20 4o 9.969173 9182 9190 9198 92069215 '9 4o 9.972O58 2066 2073 2081 208 9 20 9 7 i 9 4i 9223 923i 9239 9247 9 256 9264 18 4i 2IO5 2112 2120 2128 2i36 2144 i a 42 9272 92809288 9297 93o5 93i3 17 42 2l5l 2l5 9 2167 *I 7 5 2i83 2I 9 i 7 43 9321 93299338 9 346 9 3549362 16 43 2198 22O6 22l4 2221 222 9 223 ? 16 44 9 3 7 o 93799387 9 3 9 5 9403,9411 i5 44 2245 2253 226O 2268 2276 2284 i5 45 9420 9428 9436 9 444 9 452| 9 46i i4 45 2291 22 99 2307 23i5 J322 233o i4 46 9469 94779485 9 4 9 3 gSoi gSio i3 46 2338 2346 2354 236i 236 9 2 3 77 i3 47 95i8 95269534 9 542 gSSogSSg 12 47 2385 23 9 2 2400 2408 2416 2423 12 48 9567 95759583 9 5 9 i 9599 9608 II 48 243i 243 9 244 7 2454 2462 24 7 II 49 9616 96249632 9640 9648*9657 10 49 2478 2485 24 9 3 25oi 2 5 08 2 5i6 IO 5o 9.969665 96739681 9 68 9 96979705 9 5o 9.972524 2532 253 9 2547 2555 2563 9 5i 9714 97229730 9738 97469754 8 5i 2570 2 5 7 8 2 586 25 9 3 2601 26o 9 8 52 9762 9771 9779 9787 979 5 9 8o3 7 52 2617 2624 2632 2640 2648 2655 7 53 9811 98199828 9 836 9 844 9 85 2 6 53 2663 26 7 I 2678 2686 260,4 2701 6 54 9860 98689876 9 884 9893 9901 5 54 2709 2717 2725 2 7 32 2740 2 7 48 5 55 9909 99179925 99 33 99 4i 9949 4 55 2 7 55 2 7 63 2771 2 77 8 2786 2 79 4 4 56 57 99 57 99 66 99 74 9 . 9 7ooo6 ooi4 0022 9982 oo3o 999 9998 oo38 0047 3 2 56 5 7 2802 2809 2 848 2855 28172825 2863,2871 2832 2878 2840 2886 3 2 58 oo55 oo63 0071 0079 0087 oo 9 5 I 58 28 9 4 2 9 OI 2 9 9 2 9 I7 2 9 24 2 9 32 I 5 9 oio3oiii 0119012701 36 oi 44 o 59 2 9 4o 2 9 4729552963 2 97 20.78 o 60" 50" 40" i 30" 20" 10" | e . 60" i 50" : 40" 30" 20" 10" . Co-sine of 21 Degrees. S Co-sine of 20 Degrees. f ^// 2" 3" 4" 5" 6" 7" 8" 9" D . < 1" 2" 3" 4". 5" 6" 7" 8" 9" P. Part j ! o 2 345677 ul/ > 1 2 2 3 4 5 fi 6 7 LOGARITHMIC TANGENTS. 1 Tangent of 68 Degrees. A Tangent of 69 Degrees. X 0" 10" 1 20" | 30" 40" 50" s 0" 10" | 20" 30" 40" | 50" o i 10.393590 3 9 54 365i 4oi5 3712^772 4o 7 6i4i36 3833 4i 9 7 38 9 4 4258 5o 58 i io.4i5823 6200 5886 6263 5 9 48 63 2 6 6oi I 6074)6137 638 9 645 2 '65i5 5o 58 2 43i8 43 79 444o 45oo 456i 4622 57 t] 65 7 8 664i 6704 6767 683o 68 9 3 57 4 4683 5o47 4 7 43 5io8 48o4 5i6 9 4865 522 9 4 9 26 52 9 &! 56 55 4 6 9 56 7 335 7 O20 7 3 9 8 7083 746 1 7i46 7524 7209 7 58 7 7272 765o 56 55 c 5412 5473 5533 55 9 4 5655 5 7 i6 54 c 77 i4 7777 7 84o 79 3 7966 8o2 9 54 6 5777 5838 58 9 8 5 9 5 9 6020 6081 53 6 8o 9 3 8i56 82I 9 8282 8345 84o 9 53 7 6142 6 2 o3 6264 63 2 5 6385 6446 52 7 8472 8535 85 9 8 8661 8 7 25 8788 52 9 65o 7 6568 662 9 66 9 o 6 7 5i 6812 5i 885i 8 9 i4 8978 9 o4i 9104 9 i68 5i 9 6873 6 9 34 6 99 5 7 o56 7117 7178 5o 9 9 23l 9 2 9 4 9 358 9 42I 9484 9 5 47 5o 10 10.397239 73oo 736i 7422 7483 7 544 49 10 10.419611 9 6 7 4 9738 9 8oi 9 864 99 28 4 9 ii 7605 7666 7727 7788 784 9 79 io 48 II 9991 ..54 .118 .181 .245 .3o8 12 7971 8o32 8o 9 3 8i54 8 2 i5 82 7 6 47 12 I0.4203 7 I o435 0498 o562 0625 o68 9 47 j3 8337 83 99 846o 852i 858 2 8643 46 i3 O 7 52 0816 0879 o 9 43 1006 1070 46 i4 8704 8 7 65 8826 8888 8 9 4 9 9010 45 i4 n33 n 97 1260 1324 i38 7 i45i 45 i5 9071 9 l32 9 i 9 4 92 55 9 3i6 9 3 77 44 i5 i5i4 i5 7 8 i64i I 7 o5 1769 i832 44 16 9 438 9 5oo 9 56i 9 622 9 683 9744 43 16 1896 i 9 5 9 2023 2086 2i5o 22l4 43 J 7 9806 9867 99 28 99 8 9 ..5! . 112 42 l l 22 77 234l 24o5 2468 2532 25 9 6 42 18 10.400173 0235 O2 9 6 o357 o4i 9 0480 4i 18 2659 2 7 23 2787 2 85o 2914 2 97 8 4i J 9 o54i 0602 o664 0725 o 7 8 7 o848 4o Z 9 3o4i 3io5 3i6 9 3233 3296 336o 4o 20 10.400909 0971 1032 io 9 3 n55 1216 3 9 20 10.423424 3488 355; 36i5 36 79 3 7 43 3 9 21 1278 i33 9 i4oo 1462 i523 i585 38 21 38o 7 38 7 o 3 9 34 3 99 8 4062 4126 38 22 1 646 1707 i 7 6 9 i83o l8 9 2 1953 37 22 4190 4253 43i 7 438i 4445 45o 9 37 23 2Ol5 2076 2i38 2I 99 2261 2322 36 23 45 7 3 463 7 4701 4764 4828 48 9 2 36 24 2384 2445 2507 2568 263o 2691 35 24 4g56 502O 5o84 5i48 5212 52 7 6 35 25 2 7 53 2 8i5 2876 2 9 38 2 999 3o6i 34 25 534o 54o4 5468 5532 55 9 6 566o 34 26 3l22 3i84 3246 33o 7 336 9 343o 33 26 5724 5 7 88 5852 5 9 i6 5980 6o44 33 27 3492 3554 36i5 36 7 7 3 7 3 9 38oo 32 27 6108 6172 6236 63oo 6364 642 9 32 28 3862 3 9 24 3 9 85 4o47 4io 9 4170 3i 28 6493 6557 6621 6685 6749 68i3 3i 29 4232 42 9 4 4356 44i7 44 79 454i 3o 2 9 6877 6 9 4i 7006 7 o 7 o 7i34 7 i 9 8 3o 3o io.4o46o2 4664 4726 4788 485o 4911 29 3o 10.427262 7 32 7 7 3 9 i 7 455 7 5i 9 7 583 2 9 3i 4973 5o35 5o 97 5i58 5220 5282 28 3i 7 648 7712 7776 7 84o 7905 7969 28 3 2 : 5344 54o6 5468 552 9 55 9 i 5653 27 32 8o33 8o 9 7 8162 8226 8290 8355 2 7 3$ 5 7 i5 5777 583 9 5 9 oi 5 9 62 6024 26 33 84i 9 8483 8548 8612 8676 8741 26 34 6086 6i48 6210 6272 6334 63 9 6 25 34 88o5 886 9 8 9 34 8998 9062 9 I2 7 25 35 6458 652O 6582 6644 6 7 o6 6 7 68 24 35 9191 9 256 9 320 9 384 9449 9 5i3 24 36 6829 68 9 i 6 9 53 7oi5 777 7 i3 9 23 36 9 5 7 8 9 642 977 977 1 9836 99 23 3? 7201 7263 7326 7388 7 45o 7 5l2 22 37 9965 . .2 9 .. 9 4 .i58 .223 .287 22 38 7 5 7 4 7636 7 6 9 8 7760 7822 7 884 21 38 io.43o352 o4i6 o48i o545 0610 0674 21 3 9 7946 8008 8070 8i32 8i 9 5 825 7 2O 3 9 7 3 9 o8o3 0868 o 9 33 0997 1062 2O 4o io.4o83i9 838i 8443 85o5 856 7 863o 1 9 4o 10.431127 n 9 i 1256 l32O i385 i45o I 9 4i 8692 8 7 54 8816 8878 8 9 4o 9003 18 4i i5i4 l5 79 1 644 1708 i 77 3 i838 18 42 9065 9127 9 l8 9 9 252 9 3i4 9 3 7 6 l l 42 1902 1967 2032 2097 2161 2226 17 43 9 438 95oi 9 563 9 625 9687 9 7 5o 16 43 2291 2356 242O 2485 2 55o 26i5 16 44 9812 9 8 7 4 99 3 7 9999 ..61 .123 i5 44 2680 2744 28o 9 2874 2 9 3 9 3oo4 i5 45 10.410186 0248 o3io 0373 o435 0498 i4 45 3o68 3i33 3i 9 8 3263 3328 33 9 3 i4 46 o56o 0622 o685 0747 0809 o8 7 2 i3 46 3458 3522 358 7 3652 3 7 i 7 3 7 82 i3 47 0934 0997 io5 9 1122 1184 1246 12 47 3847 3 9 I2 3977 4042 4107 4172 12 48 i3o 9 i3 7 i i434 i4 9 6 i55 9 1621 II 48 423 7 4302 436 7 4432 44 97 4562 II 49 1 684 1746 i8o 9 1871 1934 1996 IO 49 4627 46 9 2 4 7 5 7 4822 488 7 4 9 52 IO 5o 10.412059 2121 2184 2246 2309 23 7 I 9 5o 10.435017 5o82 5i47 5212 5277 5342 9 5i 2434 24 9 7 2 55 9 2622 2684 2 7 4 7 8 5i 5407 5473 5538 56o3 5668 5733 8 52 2810 2872 2 9 35 2 997 3o6o 3i 2 3 7 52 5 79 8 5863 5 9 2 9 5994 6o5 9 6124 7 53 3i85 3248 33u 33 7 3 3436 3499 6 53 6i8 9 6254 6320 6385 645o 65i5 6 54 356i 3624 3687 3 7 4 9 38i2 38 7 5 5 54 658i 6646 6711 6776 6842 6 9 07 5 55 3 9 38 4ooo 4o63 4126 4i8 9 425i 4 55 6 9 72 7 o3 7 7io3 7168 7233 7 2 99 4 56 43i4 4377 444o 45o2 4565 4628 3 56 7 364 742 9 7 4 9 5 7 56o 7625 7691 3 5 7 46 9 i 4754 48i 7 48 79 4942 5oo5 2 5 7 7756 7822 7887 79 5 2 8018 8o83 2 58 5o68 5i3i 5i 9 4 5256 SSig 5382 I 58 8i4 9 8214 827 9 8345 84io 84 7 6 I 5 9 5445 55o8 5571 5634 5697 5 7 6o 5 9 854i 8607 8672 8 7 38 88o3 886 9 O 60" 50" 40" 30" 20" 10" . 60" 50" 40" 30" 20" 10" . Co-tangent of 21 Degrees. a Co-tangent of 20 Degrees. a PPartM" 2 " 3 " 4 " 5// 6 " 7 " 8// 9 " .C 1" 2" 3" 4" 5" 6" 7" 8" 9" iri $ 6 12 19 25 31 37 43 49 56 in \ 6 13 19 26 32 39 45 51 58 LOGARITHMIC SINES. 3 Sine of 70 Degrees. | Sine of 7 1 Degrees. 0" 10" 20" 30" 40" 50" 3 0" 10" 20" 30" 40" 50" o 9.972986 2993 3ooi 3oo 9 3oi6 3o24 5 9 o 9.975670 56 77 5685 56 9 2 56 99 5706 5 9 I 3o3 2 3o39 3o47 3o55 3o62 3070 58 I 5 7 i4 5 7 2I 5 7 28 5 7 35 5 7 43 5750 58 2 3078 3o85 3o 9 3 3ioi 3io8 3n6 57 2 5 7 5 7 5 7 64 5 77 i 5 779 5 7 86 5 79 3 57 3, 3i24 3i3i 3i3 9 3i46 3i54 3i6 2 56 3 58oo 58o8 58i5 5822 582 9 583 7 56 4 8169 3i 77 3i85 3i 9 2 3200 3208 55 4 5844 585i 5858 5865 58 7 3 588o 55 5 32i5 3223 3 2 3o 3238 3246 3253 54 5 588 7 58 9 4 5 9 oi 5 9 o 9 5 9 i6 5 9 23 54 6 3261 3269 3276 3284 3291 3299 53 6 5g3o 5 9 38 5 9 45 5 9 52 5 9 5 9 5 9 66 53 7 3307 33i4 3322 333o 333 7 3345 52 7 5 97 4 5 9 8i 5 9 88 5 99 5 6002 6010 52 8 3352 336o 3368 33 7 5 3383 3390 5i 8 6oi 7 6024 6o3i 6o38 6o46 6o53 5i 9 3398 34o6 34x3 342i 3428 3436 5o 9 6060 6o6 7 6o 7 4 6081 6o8 9 6096 5o 10 9.973444 345 1 345 9 3466 3474 3482 49 10 9 . 9 76io3 6110 6n 7 6i25 6i32 6i3 9 49 ii 348 9 34 9 7 35o4 35i2 35i 9 352 7 48 ii 6i46 6i53 6160 6168 6i 7 5 6182 48 12 3535 3542 355o 355 7 3565 35 7 2 47 12 6i8 9 6i 9 6 6203 6211 6218 6225 47 i3 358o 3588 3595 36o3 36io 36i8 46 i3 6232 623 9 6246 6 2 54 6261 6268 46 U 3625 3633 364 1 3648 3656 3663 45 i4 62 7 5 6282 628 9 6296 63o4 63n 45 i5 3671 36 7 8 3686 36 9 4 3701 3 7 o 9 44 i5 63i8 6325 6332 6339 634 7 6354 44 16 3 7 i6 3 7 24 3 7 3i 3 7 3 9 3 7 46 3 7 54 43 16 636i 6368 63 7 5 6382 638 9 63 9 6 43 17 3 7 6i 3769 3777 3 7 84 3 79 2 3 799 42 l l 64o4 64ii 64i8 6425 6432 643 9 42 18 3807 38i4 3822 3829 383 7 3844 4i 18 6446 6454 646 1 6468 64 7 5 6482 4i J 9 3852 385 9 386 7 38 7 5 3882 38 9 o 4o I 9 648 9 64 9 6 65o3 65io 65i8 65 2 5 4o 20 9.973897 3905 3912 3920 3 9 2 7 3 9 35 39 20 9.976532 653 9 6546 6553 656o 656 7 39 21 3 9 42 SgSo 3957 3 9 65 3 97 2 3980 38 21 65 7 4 6582 658 9 6596 66o3 6610 38 22 3 9 8 7 3 99 5 4002 4oio 4oi 7 4o25 37 22 6617 6624 663i 6638 6646 6653 37 23 4o32 4o4o 4047 4o55 4062 4070 36 23 6660 666 7 66 7 4 6681 6688 6695 36 24 4077 4o85 4092 4ioo 4io 7 4n5 35 24 6702 6 7 o 9 6 7 i6 6723 6 7 3i 6738 35 25 4l22 4i3o 4i3 7 4i45 4i52 4i6o 34 25 6 7 45 6 7 52 6 7 5 9 6766 6 77 3 6780 34 26 4l6 7 4i75 4182 4190 4i 9 7 42o5 33 26 6787 6 79 4 6801 6808 68i5 6823 33 27 4212 4220 42274235 4242 425o 32 27 683o 683 7 6844 685i 6858 6865 32 28 425 7 4264 42724279 428-7 4294 3i 28 6872 68 79 6886 6893 6 9 oo 6907 3r 2 9 3o 43o2 9*974347 43o 9 4354 43i 7 4324 436i4369 4332 43 7 6 433 9 4384 3o 29 o 9 3o 6 9 i4 9.976957 6 9 2I 6964 6928 6 97 i 6935 6978 6942 6 9 85 6950 6992 3o 2 9 3i 43 9 i 43 99 44o644r4 442i 4428 28 3i 6999 7006 7 oi3 7020 7 02 7 7o34 28 32 4436 4443 445i 4458 4466 44?3 2 7 32 7o4i 7 o48 7 o55 7062 7 o6 9 7076 27 33 448 1 4488 4495 45o3 45io 45i8 26 33 7 o83 7090 797 7104 7 ni 7118 26 34 45 2 5 4533 454o4547 4555 4562 25 34 7 i25 7132 7 i3 9 7i46 7 i53 7160 25 35 45 7 o 45 77 45854509 45 99 4607 24 35 7167 7174 7181 7188 7195 7202 24 36 46i4 4622 4629 4636 4644 465i 23 36 7209 7216 7 223 7230 723 7 7244 23 37 465 9 4666 46744681 4688 4696 22 37 7 25l 7 258 7 265 7272 7279 7286 22 38 4?o3 4 7 n 47184725 4733 474o 21 38 7293 73oo 7 3o 7 73x4 7 32I 7328 21 3 9 4748 4 7 55 4762477 4777 4784 2O 39 7335 7342 7349 7 356 7 363 7 3 7 o 20 4o 9.974792 4799 48o 7 48i4 4821 4829 19 4o 9.977377 7384 7 3 9 i 7 3 9 8 74o5 7412 J 9 4i 4836 4844 485i 4858 4866 48 7 3 18 4i 74i9 7426 7433 7 44o 7 44 7 7454 18 4a 488o 4888 48954903 4910 4917 '7 42 746 1 7 468 7 4 7 5 7482 748 9 74 9 6 17 43 4925 4 9 3 2 49394947 4 9 54 4961 16 43 7 5o3 75io 7 5i 7 7 524 7 53o 7 53 7 16 44 4969 4976 49844991 4 99 8 5oo6 i5 44 7544 7 55i 7 558 7 565 7 5 7 2 7 5 79 i5 45 5oi3 5020 5o28;5o35 5o42 5o5o i4 45 7 586 7 5 9 3 7600 7 6o 7 7614 7621 i4 46 5o5 7 5o64 5072^079 5o86 5094 i3 46 7628 7 635 7642 7 648 7 655 7662 i3 47 5ioi 5io8 5u6 5i23 5i3o 5i38 12 47 7669 7676 7 683 7 6 9 o 7697 774 12 48 5i45 5i5 2 5i6o 5167 5i74 5i8 2 II 48 7711 7718 77 25 77 32 7739 77 45 II 49 5i8 9 5196 5204 5211 5 2 i8 5226 10 49 7752 77 5 9 7766 7773 7780 7787 10 509.975233 524o 524852555262 5270 9 5o 9-977794 7801 7808 7 8i5 7821 7828 9 5i 5277 5284 5292 5299(5306 53i3 8 5i 7 835 7842 7849 7 856 7 863 7870 8 52 532i 5328 5335 5343 535o 535 7 7 52 7877 7 884 7890 7897 794 7911 7 53 5365 5372 5379 5386 53 9 4 54oi 6 53 79 i8 79 25 79 3 2 79 3 9 7946 79 52 6 541 54o8 54i6 5423 543o543 7 5445 5 54 79 5 9 7966 797 3 79 8 7987 7994 5 55: 545 2 545 9 5467 54 7 4548i 5488 4 55 8001 8oo 7 8oi4!8o2i 8028 8o35 4 56 5496 55o3 55io 55i8,5525 5532 3 56 8042 8o4 9 8o56 8o62|8o6 9 8o 7 6 3 5 7 553 9 5547 5554 556i'5568 55 7 6 2 5 7 8o83 8o 9 o 8o 97 l8io4 81 10 8117 2 58 5583 55 9 o 55 9 8 56o556i2 56i 9 I 58 8i248r3r8i38 8i45!8i52 8i58 I 59 5627 5634 564i 56485656 5663 O 5 9 8i65 81728179 818681938199 O 60" 50" 40" 30" 20" 10" c 60" j 50" 40" j 30" 20" | 10" a Co-sine of 19 Degrees. ii Co-sine of 1 8 Degrees. 1 pp .C 1" 2" 3" 4" 5" 6" 7" 8" 9" irt $ 1 123 44567 P T ^ l' ; 2" 3" 4" 5" 6" 7" <~ trt { 1 1 2 3 4 4 3 ft 6 LOGARITHMIC TANGENTS 95 d Tangent of 70 Degrees. d Tangent of 7 1 Degrees. s 0" 10" 20" ao" 40" 50" s 0" 10" 20" 30" 40" 5 i N m B . .g Sine of 78 Degrees. a Sine of 79 Degrees. s 0" 10" ! 20" 30" i 40" 50" <= 0" 10" 20" 30" 40" 50" 9 . 99 o4o4|o4o9 o4i3 o4i8 0422 0427,59 09.991947 1951 1955 1959 1963 1967 5 9 I 2 o43 1 o458 o436 o44o o445 0449 O454, 58 0462 0467 0471 0476 o48o 57 2 I 97 i|i 97 5 1996 2OOO 1979 i 9 83 2004 2008 1987 2OI2 1992 2016 58 57 3 o485 0489 0494 0498 o5o3 0507 56 3 2O20 2024 2028 2032 2036 2040 56 4 o5i i o5i6 o52o o525 0529 o534 55 4 2044 2049 2o53 2057 2061 2o65 55 5 o538 o543 o547 o552 o556jo56o 54 5 2069 20 7 3 2077 2081 2o85 2o8 9 54 6 o565 05690574 0578 o583 o58 7 53 6 2093 2O9 7 2101 2105 2109 2ii3 53 7 0591 0596 0600 o6o5 0609 0614 52 7 8Xl8 2122 2-126 2i3o 2i34 2i38 5 2 8 0618 0622 0627 o63i o636 o64o 5i 8 2 1 42 2146 2I 5o 2i54 2i58 2162 5i 9 o645 0649 o653 o658 0662 0667 5o 9 2l66 2170 2I 7 4 2178 2182 2186 5o IO 9.990671 0675 o68o l o684o689 0693 49 10 9.992190 2194 2198 2202 2206 2210 49 ii 0697 0702 0706 o 7 i ro 7 i5 071948 i: 88X4 22l8 2222 2226 2230 2234 48 12 0724 0728073307370741 0746 47 12 2239 2243 2247 225l 2255 225 9 47 i3 0750 0755 0759^7630768 0772 46 i3 2263 2267 2271 2275 2279 2283 46 i4 0777 0781 0785 0790 0794 0798 45 i4 228 7 2291 2295 2299 23o3 2307 45 i5 o8o3 08070812 08160820 0825 44 i5 23ll 23i5 2319 2323 2327 233i 44 16 0829 o833 o838 0842 o84 7 o85i 43 16 2335 233 9 2343 2347 235i 2355 43 17 o855 08600864 0868 08 7 3 o8" 77 42 17 2 35 9 2363 2366 2370 23 7 4 2 3 7 8 42 18 0882 088608900895 0899 0903 4i 18 2382 2386 2390 23 9 4 2398 2402 4i 19 0908 0912 0916 0921 0926 0929 4o 19 2406 2410 24i4 2418 2422 2426 4o 20 9.990934 0938 0942 0947 o 9 5i 0955 39 20 9.992430 ^434 2438 2442 2446 2 45o 3 9 21 0960 0964 0969 0973 977 0982 38 21 2454 2458 2462 2466 2470 2474 38 22 0986 09900995 0999 ioo3 1008 37 22 2478 2482 2485 2489 2493 2497 37 23 1012 1016 1021 IO25 1029 io33 36 23 25oi 25o5 2509 25i3 2517 252i 36 24 io38 1042 io46 io5i io55 io5g 35 24 2525 2529 2533 253 7 254i 2545 35 25 1064 1068 1072 1077 1081 io85 34 25 2549 2553 2556 2 56o 2564 2568 34 26 1090 1094 1098 no3 1 107 III! 33 26 2572 25 7 6 258o 2584 2588 2592 33 2 7 iiiS I 120 I 124 1128 n33 n3 7 32 27 2596 2600 2604 2607 261 1 2 6i5 32 28 ii4i n46 i i5o n54 n58 n63 3i 28 2619 2623 2627 263i 2635 263 9 3i 29 1167 1171 1176 1180 1184 1x88 3o 29 2643 2647 265 1 2654 2658 2662 3o 3o 9.991193 I 197 1201 1206 1210 18X4 29 3o 9.992666 2670)2674 2678 2682 2686 20 3i 1218 1223 1227 I23l 1235 1240 28 3i 2690 2693 2697 2701 2705 2709 28 32 1244 1248 1253 1257 1261 1265 2 7 32 2 ? l3 2717 2721 2725 2728 2732 2 7 33 1270 1274 1278 1282 1287 1291 26 33 2736 274^ 2744 2748 2 7 52 2 7 56 26 34 1295 1299 i3o4 i3o8 i3 I2 i3i6 25 34 2 7 5 9 2 7 63 2767 2 77 I 2 77 5 2779 25 35 1321 i325 1329 i333 i338 1 342 24 35 2 7 83 2787 2790 2 79 4 2 79 8 2802 24 36 1 346 i35oi355 i35 9 i363 i36 7 23 36 2806 2810 2814 28l8 2821 2825 23 3 7 i3 7 2 1376 i38o 1 384 i38 9 i3 9 3 22 37 2829 2833 283 7 2841 2845 2848 22 38 i3 97 i4oi i4o6 i4io i4i4 i4i8 21 38 2852 2*56 2860 2864 2868 2871 21 3 9 1422 1427 i43i i435 i43 9 1 444 2O 39 2875 2879 2883 2 88 7 2891 2895 20 4o 9.991448 1452 i456 i46o i465 1469 19 4o 9.992898 2902 2906 2910 2914 2918 I 9 4i i4?3 1477 1482 i486 1490 1494 18 4i 2921 2925 2929 2 9 33 2 9 3 7 2941 18 42 1498 i5o3 1507 i5n i5i5 iSig '7 42 2944 8948 29* 2 9 56 2960 2963 i 7 43 i5 2 4 i5 2 8 i532 i536 i54o 1 545 16 43 2967 2971 2975 2979 2 9 83 2986 16 44 1 549 i553 i557 i56i i566 i5 7 o i5 44 2990 2994 2998 3002 3oo5 Soog i5 45 i5 7 4 i5 7 8i58 2 i586 1591 i5g5 i4 45 3oi3 3017 3O2I 3o24 3028 3o32 i4 46 i5 99 i6o3 1607 1612 1616 1620 i3 46 3o36 3o4o 3o43 3o4 7 3o5i 3o55 i3 47 1624 1628 i632 i63 7 i64i 1 645 12 47 SoSg 3o62 3o66 3070 3o 7 4 3o 7 8 12 48 i64 9 i653i65 7 1662 1666 i6 7 o II 48 3o8i 3o85 3089 3o 9 3 3o 97 3ioo II 49 1674 1678 1682 1687 1691 i6 9 5 IO 49 3io4 3io8 3lI2 3n5 3119 3i23 IO 5o 9.991699 1703 1707 1712 1716 I 7 20 9 5o 9.993127 3i3i 3i34 3i38 3i42 3i46 9 5i 1724 1728 1732 1736 1741 i 7 45 8 5i 3i4 9 3i53 3i57 3i6i 3i65 3i68 8 52 1749 1753x757 1761 i 7 65 I 77 o 7 52 3172 3i 7 6 3i8o 3i83 3i8 7 3191 7 53 1774 1778 1782 1786 i 79 o i 7 g4 6 53 SigSjSigS 3202 3206 3210 32i3 6 54 1799 1803.1807 1811 1816 1819 5. 54 3217 3221 3225 3228 3232 3236 5 55 i8 2 3 1827 i832 i836 i84o 1 844 4 55 324o3s>43 324 7 325i 3 2 553 2 58 4 56 1 848 i85ax856 1860 i865 1869 3 56 3262:3266 3270 3273 32 7 7'328i 3 5 7 i8 7 3 18771881 i885 1889 i8 9 3 2 57 3284 3288 3292 3296^299 33o3 2 58 1897 1901 1906 i 9 io i 9 i4 1918 I 58 33o 7 33n 33x433x83389 3325 I 5 9 1922 1926 1930 i 9 34 1938 1942 O 5 9 332 9 3333 333 7 334o'3344 3348 o 60" 50" |^40" 30" j 20" 10" A 60" 50" 40" 30" ; SO" 10" . Co-sine of 1 1 Degrees. Co-sine of 10 Degrees. ?* P Part* l " 2 " 3 " 4// 5 " 6 " 7// 8" 9" | .(1" 2" 3" 4" 5" 6" 7" 8" 9" iTl i 1 1 2 2 3 3 34 '"} 11222334 LOGARITHMIC TANGENTS. 103 1 Tangent of 78 Degrees. .5 Tangent of 79 Degrees. g 0" 10" 20" 30" 40" 50" % 0" 10" 20" 30" 40" 50" o 10.672525 262 9 2 7 33 2836 2940 3o43 5 9 o 10.711348 i46o i5 7 3 i685 I 79 8 1910 5 9 I 3i4? 325i 3354 3458 3562 3666 58 i 2023 2i35 2248 236i 2473 2586 58 2 3 7 6 9 3873 3 977 4o8i 4i85 428 9 57 2 26 99 2811 2 9 24 3o37 3i5o 3263 57 3 43 9 3 44 9 7 46oi 47o5 48o 9 4 9 :3 56 3 33 7 6 3488 36oi 37i4 382 7 3940 56 4 5017 5l2I 5225 5329 5433 553 7 55 4 4o53 4i6 7 4280 43 9 3 45o6 46i 9 55 5 5642 5 7 46 585o 5 9 54 6059 6i63 54 5 4732 4846 4 9 5 9 5072 5i85 52 99 54 6 6267 63 7 2 6476 658o 6685 6 7 8 9 53 6 54i2 5526 563 9 5 7 5 2 5866 5 979 53 7 68 9 4 6 99 8 7io3 7207 73i2 7417 52 7 6093 62O 7 6320 6434 654 7 6661 52 8 7521 7626 77 3i 7835 794o 8o45 5i 8 6 77 5 6889 7002 7116 723o 7344 5i 9 8149 8254 835 9 8464 856 9 86 7 4 5o 9 7458 7 5 7 2 7686 7799 79 i3 8027 5o 10 8778 8883 8988 9 o 9 3 9198 9 3o3 49 10 8142 8 2 56 83 7 o 8484 85 9 8 8712 49 ii 9 4o8 9 5i3 9618 97 23 9829 99 34 48 1 1 8826 8 9 4i 9 o55 9 l6 9 9283 9 3 9 8 48 12 10 680039 oi44 0249 o355 o46o o565 47 12 9512 962-7 974i 9 856 997 ..85 47 i3 0670 0776 0881 0987 1092 ii 9 7 46 i3 10.720199 o3i4 0428 o543 o658 0772 46 i4 i3o3 1408 i5i4 1619 1725 i83o 45 i4 0887 1 002 1116 I23l 1 346 i46i 45 i5 1936 2042 2147 2253 2359 2464 44 1 5 1576 1691 1806 1921 2036 2l5l 44 16 2570 2676 2782 2887 2993 3o 99 43 16 2266 2 38i 24 9 6 2611 2 7 26 2841 43 !? 32o5 33n 34i7 3523 362 9 3735 42 *7 2 9 5 7 3o 7 2 3i8 7 3302 34i8 3533 42 18 384i 3 9 4 7 4o53 4i5 9 4265 4371 4i 18 364 9 3 7 64 3879 3 99 5 4uo 4226 4i J 9 4477 4584 4690 4796 4902 5oo 9 4o *9 4342 445 7 4573 4688 48o4 4 9 20 4o 20 5n5 5221 53 2 8 5434 554o 5647 3 9 20 5o36 5i5i 5267 5383 5499 56i5 3 9 21 5 7 53 586o 5966 6073 6179 6286 38 21 5731 5847 5 9 63 6o7 9 6195 63ii 38 22 63 9 2 64 99 6606 6712 6819 6 9 26 3? 22 6427 6543 665 9 6775 6891 7008 37 23 7032 7 i3 9 7246 7353 7460 7 56 7 36 23 7124 7240 7 356 7 4 7 3 7 58 9 7706 36 24 7 6 7 3 7780 7887 7994 8101 8208 35 24 7822 7938 8o55 8i 7 i 8288 84o5 35 25 83i5 8422 852 9 8636 8744 885i 34 25 852i 8638 8 7 54 88 7 i 8988 9 io5 34 26 8 9 58 9 o65 9172 9280 9 38 7 9 4 9 4 33 26 9221 9 338 9 455 9 5 7 2 9689 9 8o6 33 27 9601 979 9816 9924 ..3i .i38 32 27 9923 ..4o .i5 7 .274 .3 9 i .5o8 32 28 10.690246 o353 o46i o568 0676 0784 3i 28 io. 7 3o625 0742 0860 977 1094 I2II 3i 29 0891 999 1107 I2l4 1322 i43o 3o 29 1329 1 446 i563 1681 1-798 I 9 i6 3o 3o i53 7 1 645 i 7 53 1861 i 9 6 9 2077 2 9 3o 2 o33 2l5l 2268 2386 25o3 2621 29 3i 2184 22 9 2 2400 25o8 2616 2724 28 3i 2 7 3 9 2856 2 9 74 3o 9 2 32IO 3327 28 32 2832 2 9 4i 3o49 3i5 7 3265 33 7 3 27 32 3445 3563 368i 3799 3 9 i 7 4o35 27 33 3481 35 9 o 3698 38o6 3 9 i4 4023 26 33 4i53 4271 438 9 45o 7 4625 4?44 26 34 4i3i 423 9 4348 4456 4565 46 7 3 25 34 4862 4980 5o 9 8 52i 7 5335 5453 25 35 4782 48 9 o 4999 5107 52i6 53 2 5 24 35 55 7 2 5690 58o 9 5 9 27 6o46 6:64 24 36 5433 5542 565i 5 7 5 9 5868 5 9 77 23 36 6283 64oi 6520 663 9 6 7 5 7 6876 23 3? 6086 6i 9 5 63o3 6412 652i 663o 22 37 6 99 5 7ii3 7232 7 35! 7470 7 58 9 22 38 6739 6848 6957 7066 7175 7284 21 38 77 o8 7827 7946 8o65 8i84 83o3 21 3 9 7 3 9 3 7 5o3 7612 7721 7 83o 79 3 9 20 3 9 . 8422 854i 8660 8 7 8o 8899 9018 2O 4o 8049 8i58 8267 83?6 8486 85 9 5 I 9 4o 9 i3 7 9257 9 3 7 6 9496 9615 97 34 '9 4i 8705 88i4 8924 9 o33 9 i43 9252 18 4i 9 854 997 3 .. 9 3 .213 .332 .452 18 42 9 362 9 4?i 9 58i 9691 9 8oo 99 io r 7 42 io. 7 4o5 7 i 0691 0811 o 9 3i io5o 1170 17 43 10.700020 OI2 9 O23 9 o34g o45 9 o56 9 16 43 1290 i4io i53o i65o 1770 1890 16 44 0678 0788 o8 9 8 1008 1118 1228 i5 44 2OIO 2i3o 225o 23 7 2490 2611 i5 45 i338 1 448 i558 1668 1779 i88 9 i4 45 2 7 3l 2 85i 2 97 I 3o 9 2 3212 3332 i4 46 1999 2I0 9 22I 9 2 33o 244o 2 55o i3 46 3453 35 7 3 36 9 4 38i4 3 9 35 4o55 i3 4? 2661 2771 288l 2992 3l02 32i3 12 47 4176 4297 4417 4538 465 9 4779 13 48 3323 3434 3544 3655 3 7 65 3876 II 48 4900 5O2I 5i42 5263 5384 55o5 II 49 3 9 8 7 4o 9 7 4208 43i9 4429 454o 10 49 5626 5 7 4 7 5868 5 9 8 9 6110 623i IO 5o 465i 4762 48 7 3 4984 5o 9 5 52o5 9 5o 6352 64?3 65 9 5' 6 7 i6 6837 6 9 5 9 9 5i 53i6 5427 5538 5649 5761 5872 8 5i 7080 7201 7 3 2 3 7444 7 566 7687 8 52 5g83 6o 9 4 62o5 63i6 6428 653 9 7 52 7809 79 3o 8o52 8174 82 9 5 8417 7 53 665o 6761 68 7 3 6 9 84 79 5 7207 6 53 853 9 8661 8782 8 9 o4 9026 9 i48 6 54 7 3i8 ?43o 754i 7653 7764 7876 5 54 9270 9 3 9 2 9 5i4 9 636 9758 9880 5 55 7987 8o 99 8211 8322 8434 8546 4 55 io. 7 5ooo2 0124 0247 o36 9 0491 o6i3 4 56 8658 8 7 6 9 8881 8 99 3 9 io5 9 2I 7 3 56 o 7 36 o858 o 9 8o uo3 1225 1 348 3 5 7 9 3 29 9 44i 9 553 9665 9777 9 88 9 2 $7 1470 i5 9 3 1715 i838 1961 2o83 2 58 10.710001 on3 0225 o337 0449 o562 I 58 2206 232 9 2452 25 7 4 2 697 2820 I l ( l 0674 0786 o8 9 8 IOII 1123 1235 5 9 2943 3o66 3i8 9 33i2 3435 3558 O 60" 50" 40" 30" 20" 10" d 60" 50" 40" 30" 20" | 10" . Co-tangent of 1 1 Degrees. .3 s Co-tangent of 10 Degrees. 3 p p* t$ 1" 2// 3 " 4 " 5 " 6// 7" 8'' 9" . ( 1" 2" 3" 4" 5" 6" 7" 8" 9" irt } 11 22 32 43 54 65 75 86 97 in \ 12 23 35 47 59 70 82 94 106 104 LOGARITHMIC SINES. 1 Sine of 80 Degrees. a Sine of 6 1 Degrees. M 0" 10" 20" 30" 40" 50" * 0" 10" 3) ' 30" 50" o 9.993351 3355 335 9 3363 3366 3370 5 9 9 . 99 462o 4623 462 7 463o 4633 463 7 5 9 i 33 7 4 33 77 338i 3385 338 9 33 9 2 58 I 464o : 4643464 7 465o4653 465 7 58 2 3 33 9 6 34i8 34oo 3422 34o3 3426 34o 7 3429 34n 3433 34i4 343 7 56 2 3 466o!4663 466 7 46 7 o ! 46 7 3 468o|4683 4686 46904693 46 7 6 46 9 6 57 56 4 344o 3444 3448 345 1 3455 345 9 55 4 4 7 oo 4 7 o3 4 7 o6 4 7 io 4 7 i3 4 7 i6 55 5 3462 3466 3470 34 7 3 34 77 348i 54 5 4 7 20 4 7 23 4 7 26 4 7 2 9 4 7 33 4 7 36 54 6 3484 3488 34 9 2 3495 34 99 35o3 53 6 4 7 3 9 4 7 43 4 7 46 4 7 4g 4 7 52 4 7 56 53 7 35o6 35io 35i4 35i 7 352i 35 2 5 52 7 4 7 5 9 ! 4 7 62 4766 476 9 4 77 2 4 77 6 52 8 3528 3532 3536 353 9 3543 354 7 5i 8 4 77 u 4 7 S- 4 7 85 4 79 5 5i 9 355o 3554 3558 356i 3565 356 9 5o 9 4 79 8 4802 48o5 48o8 48i2 48i5 5o 10 9 . 99 35 7 2 35 7 6 358o 3583 358 7 35 9 i 49 10 9 . 99 48i8 4821 4825 4828483i 4834 4y ii 35 9 4 35 9 8 36oi 36o5 36o 9 36i2 48 ii 4838 484 1 4844 4848485i 4854 48 12 36i6 3620 36233627 363i 3634 47 12 485 7 486i 4864 486 7 48 7 o 48 7 4 47 i3 3638 364i 3645 364 9 3652 3656 46 i3 48 77 488o 4883 488-714890 48 9 3 46 i4 366o 3663 3667 36 7 o 36 7 4 36 7 8 45 i4 48 9 6 4 9 oo 4 9 o3 4 9 o(i 4909 4 9 i3 45 i5 368i 3685 368 9 36 9 2l36 9 6 36 99 44 i5 4 9 -6 49 T 9 4922 4920 4 9 2 9 4 9 3s 44 16 3 7 o3 3 7 o 7 37103714 3 7 i 7 3721 43 16 4 9 35 4938 4 9 42 49454948 4 9 5i|43 17 3 7 25 3728 3 7 32 3 7 35 3 7 3 9 3743 42 '7 4 9 55 4958 4 9 6i 4 9 64 4 9 68 497 1 4s 1 8 3746 3 7 5o 3 7 53 3 7 5 7 3 7 6i 3 7 64 4i 18 4 97 4 4977 4 9 8o 4984 4 9 8 7 4990 4i 19 3 7 68 3 77 i 3 77 5 3779 3 7 82 3 7 86 4o i 9 4 99 3 4997 5ooo 5oo3 5oo6 5oo 9 4c 20 9.993 7 8 9 3 79 3 3 79 7 38oo 38o4 38o 7 39 20 9 . 99 5oi3 5oi6 5oi 9 5022 5o25 5o2 9 3 9 21 38n 38i4 38i8 3822 3825 382 9 38 21 5o32 5o35 5o38 5o4i 5o45 5o48 38 22 3832 3836 384o 3843 384 7 385o 37 22 5o5i 5o54 5o5 7 5o6i 5o64 5o6 7 3? 23 3854 385 7 386i 3864 3868 38 7 2 36 23 5o 7 o 5o 7 3 5o 77 5o8o 5o83 5o86 36 24 38 7 5 38 79 3882 3886 388 9 38 9 3 35 24 5o8 9 5o 9 2 5o 9 6 5o 99 5 1 02 5io5 35 25 38 97 3 9 oo 3 9 o4 3 9 o 7 3 9 u 3 9 i4 34 25 5ioS 5l 12 5ir5 5 u 8 5l2I 5i24 34 26 3918 3 9 2i 3 9 25 3 9 28 3 9 32 3 9 36 33 26 5l2 7 5i3i 5i345i3 7 5i43 33 27 3 9 3 9 3 9 43 3 9 46 3c;5o 3 9 53 3 9 5 7 32- 27 5i46 5i5o 5i535i56 5i5 9 5i62 32 28 3960 3 9 64 3 9 6 7 3 97 i 3 97 4 3978 3i 28 5i65 5i6 9 ") i - .j 5i 7 5 5i 7 8 5i8i 3i 29 3982 3 9 85 3989 3992 3 99 6 3 999 3o 2 9 5i84 5i88 5i 9 i 5i 9 4 5i 97 520O 3o 3o 9.994003 4oo6 4oio 4oi3 4oi 7 4020 2 9 3o 9 . 99 52o3 5 2 o6 5ai3 5ai6 52I 9 2 9 3i 4024 4027 4o3i 4o34 4o38 4o4i 28 3i 5222 5225 5228 5232 5235 5238 28 32 4o45 4o48 4o5 2 4o55 4o5 9 4062 2 7 32 524i 5-244 524 7 5 2 5o5 2 53 5 2 5 7 2 7 33 4o66 4o6 9 4o 7 3 4076 4o8o 4o83 26 33 5 2 6o 5 2 63 5266 526 9 |52 7 2 52 7 5 26 34 4o8 7 4o 9 o 4094 4097 4ioi 4io4 25 34 52 7 8 5282 5285 5 2 88|52 9 i 52 9 4 25 35 36 37 4io8 4129 4i5o 4m 4l32 4i53 4i364i39 4i5 7 4i6o 4l22 4i43 4i64 4i25 4i46 4i6 7 24 23 22 35 36 37 52 97 53i6 5334 53oo 53i 9 5338 53o3 5322 534i 53o 7 5325 5344 53ro 5328 534 7 53i3 533i 535o 24 23 22 38 4i 7 i 4174 4i 7 84i8i 4i844i88 2 I 38 5353 5356 535 9 5362 5365 536 9 21 3 9 4i 9 i 4i 9 5 4198 4202 42o5 420 9 20 39 53 7 2 53 7 5|53 7 8 538i 5384 538 7 20 4o 4i 42 9.994212 4233 4254 4216 4236 425 7 4219 4223 42404243 42614264 42264230 42474250 42674271 '9 18 17 4o 4i 42 9 . 99 53 9 o 54o 9 542 7 5393 54i2 543o 53 9 6 54i5 5433 53 99 54<>3 543 9 54o6 5424 5442 1 9 1 8 43 4274 4278 4281 4285 4a88 42 9 2 16 43 5446 544 9 5452 5455 5458 546 1 16 44 45 42 9 5 43i6 42 9 8 43i 9 43o2 43o5 43224326 43o 9 ;43i2 432 9 4333 i5 :4 44 45 5464 546 7 5482 5485 54 7 oi54 7 3<54 7 6i54 7 9 ">4 9 i 54 9 4 54 9 7 i5 i4 46 4336 434o 4343 4346435o 4353 i3 46 55oi 55o455o 7 55io55i3|55i6 i3 4 7 435 7 436o 4363 436 7 !43 7 o 43 7 4 12 47 55i 9 5522 5525 5528553i|5534 12 48 43 77 438i 4384 43S 7 43 9 i 43 9 4 I I 48 553 7 554o 5543 5546 5549 555a I I 49 43 9 8 44oi 44o4 44o844n 44i5 10 49 *555 5558556i 5564556 7 :55 7 oio 5o 9 . 9 g44i8 4421 44254428:44324435 9 5o 9 . 99 55 7 3 55 7 6 55 79 5582 55855588 9 5! 4438 4442 4445 4448:4452 4455 8 5 1 55 9 i 55 9 4 55 97 56oi 56o4 56o 7 8 52 445 9 4462 4465 4469 44 7 2 44 7 6 7 52 56io 56i3 56i6 56i 9 56 22 5625 7 53 447 9 4482 4486'448 9 i44 9 2!4496 6 53 56285631,5634 563 7 ,564o5643 6 54 44 99 45o3 45o6 45o 9 :45i345i6 5 54 5646 564 9 5o52 56555658 566i 5 55 45i 9 45 2 3 45 2 6 453o4533 4536 4 55 5664566 7 56 7 o56 7 2 56 7 5 56 7 8 4 56 454o 4543 4546 455o 4553 4556 3 56 568i 5684568 7 56 9 o56 9 3 56 9 6 3 57 456o 4563 4566 45 7 o 45 7 3 45 7 6 2 57 56 99 5 7 02 5 7 o5 5 7 o8 5 7 n 5 7 i4 2 58 458o 4583 458 7 45 9 o 45 9 3 45 97 I 58 5 7 i 7 5 7 2o 5 7 23|5 7 26 5 7 2 9 5 7 3 2 I 5 9 46oo 46o3 46o 7 4610 46i3 46i 7 5 9 5 7 35 5 7 33 5 7 4i 5 7 44 5 7 4 7 5 7 5o 60" 50" 40" 30" 20" 10" S3 60" .50" 40" 30" 20" 10" . Co-sine of 9 Degrees. Co-sine of 8 Degrees. m 5" 6" 7" 8" 9" p p A 1" 2" 3" 4" 5" 6" 7" 8" y ' P.PartJ Q l l l 22233 in \ 1 1 1 2 2 2 3 3 LOGARITHMIC TANGENTS. 105 .5 Tangent of 80 Degrees. d Tangent of 81 Degrees. 2 0" 10" 20" 30" 40" | 50" * 0" 10" | 20" 30" 1 40" i 50" j o 10- a5368i 38o4 3 9 28 4o5i 4l74l42 9 7 r 10.800287 0424 o56o o6 9 6 08330969)59 i 442i 4544 4667 4791 4 9 i4l5o38 58 i Ilo6 1242 i3 79 i5i6 i652 1789^8 2 5i6i 5285 5408 5532 5655 5 779 57 2 I 9 26 2062 2199 2336 2473 2610 5 7 o 5 9 o3 6026 6i5o 6274 63 9 8 6522 56 3 2747 2884 3021 3i58 32 9 5|3433 56 4 6646 6770 68 9 4 7018 7142 7266 55 4 35 7 o 3 7 o 7 3844 3 9 8 2 4i 19 4257 55 5 7 3 9 o 75i4 7 638 7762 78868011 54 5 43 9 4 45J2 4669 48o 7 4944 5o82 54 6 8i35 825 9 8384 85o8 8633 8 7 5 7 53 6 5220 5358i54 9 5 5633 5771 590953 7 8682 9 oo6 9 i3i 9 255 9 38o 9 5o5 52 7 6047 6i85 6323 646 1 65 99 6738|52 8 9 62 9 97 54 9 8 79 ...4 .128 .253 5i 8 6876 7 oi4 7 l52 7 2 9 i 7429756851 9 io. 7 6o3 7 8 o5o3 0628 o 7 53 0878 ioo3 5o 9 7706 7845 7983 8122 8261,8399 5o 10 ii 1128 1880 1253 2oo5 i3 79 2i3o i5o4 2256 238i 2507 49 48 10 II 8538 9 3 7 i 86 77 95io 8816 9649 8 9 54 9 o 9 3 9 232 9 788 99 28 ..67 49 48 12 i3 2532 3386 2 7 58 35i2 2883 3638 3009 3 7 63 3i35!3 2 6o 388 9 4oi5 47 46 12 1 3 10.810206 1042 o345 1182 o485 l322 0624 i46i 0^04. ooo3 1601 i 7 4i 47 46 i4 4i4i 4267 43 9 3 45i 9 46454771 45 i4 1880 2O20 2l6o 23oo 244o 258o 45 i5 48 97 6024 5i5o 5276 5402 552 9 44 i5 2720 2860 3ooo 3i4o 32803421 44 16 5655 5781 5 9 o8 6o34 6161 6287 43 16 356i 3701 3842 3 9 8 2 4122 4263 43 17 64i4 654o 6667 6 79 4 6 9 2o 7047 42 1 7 44o3 4544 4685 4825 4966 5io 7 42 18 7 i 7 4 73oi 7427 7554 7681 7808 4i 18 5248 5388 5529 5670 58n 5 9 52 4i i 9 79 35 8062 8i8 9 83i6 8443 8570 4o r 9 6o 9 3 6234 63 7 5 65i 7 66586 799 4o 20 86 9 8 88 2 5 8 9 5 2 979 9 20 79 334 39 20 6 9 4i 7082 7223 7365 7 5o6 7 648 3 9 21 - 9 46i 9 58 9 97 i6 9 844 997 1 --99 38 21 7789 79 3! 8o 7 3 8214 8356'8498 38 22 IO. 77 O22 7 o354 0482 0610 07370865 3 7 22 864o 8 7 82 8924 9 o66 9208 gSSo 37 23 o 99 3 II2I I24 9 i3 77 i5o4 :632 36 23 9 4 9 2 9 634 9776 99 i8 . .61 .2o3 36 24 1761 i88 9 2OI 7 2i45 2273 2401 35 24 10.820345 o488 o63o o 77 3 0915 io58 35 25 252 9 2 658 2 7 86 2 9 l4 3o43J3i 7 i 34 25 I2OI 1 343 i486 i62 9 I 77 2 igiS 34 26 33oo 3428 355 7 3685 38i4 3 9 42 33 26 2o58 22OO 2344 2487 263o2 77 3 33 27 4o 7 i 4200 432 9 445 7 458647i5 32 27 2 9 i6 3o5 9 32o3 3346 348^3633 32 28 4844 4 97 3 5lO2 523i 536o 548 9 3i 28 3 77 6 3920 4o63 4207 435o!4494 3i 29 56i8 5747 58 7 6 6006 6i35 6264 3o 29 4638 4782 4925 5o6 9 52i3535 7 3o 3o 63 9 3 6523 6652 6782 6 9 n 7041 29 3o 55oi 5645 5 7 8 9 5 9 33 6o 7 8 6222 29 3i 7 i 7 o 73oo 7 42 9 7 55 9 7 68 9 7818 28 3i 6366 65xi 6655 6 799 69447088 28 32 7948 8078 8208 8338 8468 85 9 8 27 32 7 233 7 3 77 7522 7667 7 8i2l 79 56j2 7 33 8728 8858 8 9 88 9118 9 248 9 3 7 8 26 33 8101 8246 8391 8536 8681 8826 26 34 9 5o8 9 63 9 97 6 9 9 8 99 . .2 9 .160 25 34 8971 9116 9261 9407 9 552 9 6 9 7 25 35 10. 7802(20 0421 o55i 0682 0812 o 9 43 24 35 9 843 9988 .i34 .2 79 .425 .5 7 o 24 36 1074 1204 i335 i466 i5 9 7 1727 23 36 10.830716 0862 1008 n53 i2 99 i445 23 37 i858 i 9 b 9 2 I 2O 225l 2382 25i3 22 37 !5 9 I i 7 3 7 i883 2029 2175 2322 22 38 2644 2775 2 9 7 3o38 3i6 9 33oo 21 38 2468 2614 2760 2 9 7 3o53 3200 21 39 3432 3563 36 9 5 3826 3 9 57 4o8 9 20 3 9 3346 3493 363 9 3 7 86 3 9 33'4o8o 20 4o 4220 4352 4484 46i5 4747'487 9 T 9 4o 4226 43 7 3 4520 466 7 48i4 4 9 6i I 9 4i Son 5i42 5 27 4 54o6 5538 5670 18 4i 5i68 5255 54o2 555o 56 9 7 5844 18 42 58o2 5 9 34 6066 6i 9 8 633o6463 l l 42 5 99 2 6139 6287 6434 6582 672 9 i 7 43 65 9 5 6 7 2 7 685 9 6 99 2 7124 7257 16 43 6877 7 025 7172 7320 7468 7616 16 44 7 38 9 7 522 7654 7787 7 9 i 9 8o52 i5 44 7764 79 I2 8060 8208 8356 85o4 i5 45 8i85 83i 7 845o 8583 8716,8849 i4 45 8653 8801 8 9 4 9 9098 9 246 9 3 9 5 i4 46 8 9 82 9 n5 9 248 9 38i 9 5i4 9 647 i3 46 9 543 9692 9 84o 9989 .i38 .287 i3 47 97 8o 99 i3 ..46 .180 .3i3 .446 12 47 io.84o435 o584 o 7 33 0882 io3i 1180 12 48 io.7 9 o58o 0713 0847 o 9 8o ii i4 1247 I I 48 i32 9 i4 7 9 1628 1777 i 9 26 2076 II 49 1 38-i i5i5 1 648 1782 I 9 i6 2o5o IO 49 2225 2375 2524 2674 2823i2 9 73 10 5o 2i83 2317 245 1 2 585 27i 9 2853 9 5o 3123 3372(3422 35 7 2 3722 38 7 2 9 5i 2 9 8 7 3l22 3 2 56 33 9 o 3524J3658 8 5i 4022 4l 7 2j4322 4472 4623^773 8 52 53 3 79 3 46oo 3927 4734 4062 486 9 4196 5oo4 433i 4465 5i38|52 7 3 7 6 52 53 4 9 23 5826 5o 7 4 5224 53 7 4 5977161276278 5525 56 7 5 642 9 658o 7 6 54 54o8 5543 56 7 8 58i2 5 9 47 6082 5 54 6731 6882| 7 o33 7184 7 335 7 486 5 55 6218 6353 6488 6623 6 7 5868 9 3 4 55 7637 778 9 7 9 4o 8o 9 i 8 2 43;83 9 4 4 56 784? 7977 7299 8112 7 435 8248 7570 7706 8384 85i 9 3 2 56 8546 86 9 7 ; 884 9 9001 9456 96081976019912 9 i52 9 3o4 ..64 .216 3 2 58 5 9 8655 9 4?i 8 79 i 9 6o 7 8927 97 43 9 o63 9879 9199 9335 . . i5 . i5i I O 58 5 9 io.85o368 o52o 0672 0825 I282;i434 1 58 7 i 7 39 9 77 II2 9 l8 9 2 2045 I 60" 50" 40" 30" 20" 10" rf 60" i 50" j 40" 30" | 20" i 10" , Co-tangent of 9 Degrees i Co-tangent of 8 Degrees. 3 P Pa t5 *" 2 " 3// 4 " 5 " 6 " 7 " 8// 9 ' J 13 26 39 52 65 78 91 103 116 . ( 1" 2" 3" 4" 5" 6" 7" 8" 9" in ) 14 29 43 58 72 86 101 115 130 00 LOGARITHMIC SINES. g Sine of 82 Degrees. a Sine of 83 Degrees. I 0" 1 10" 20" 30" 40" 50" | s 0" 10" j 2u i ) 50" o 9 . 99 5 7 53 5 7 56 5 7 5 9 5 7 62 5 7 65|5 7 685 9 O 9.996751 6753 6756,675* 6761 6 7 64 5 9 2 5 77 i 5 7 88 5 77 3 5 79 i 5 77 6 5 79 4 5 779 5 797 5 7 825 7 8558 58oo58o35 7 I 2 6 7 66;6 7 6 9 6 77 i 67746777 67826784678767896792 6 779 6 79 5 58 5? 3 58o6 58o 9 58i2 58i5 58i8 582i 56 3 6797 6800 6802 68o5 6807 6810 56 4 5823 5826 582 9 5832 5835 583855 4 68i268i5 6818 682. 68 2 5 55 5 584i 5844 584 7 585o 5853 585654 5 6828;683o 6833 6835 6838 684i 54 6 585 9 5862 5864 586 7 58 7 o 58 7 353 6 6843 6846 6848 : 685i 6853 6856 53 7 58 7 6 58 79 5882 5885 5888 58 9 ii52 7 6858,686i .6*63 6866 6869 68 7 i 52 8 58 9 4 58 97 58 99 5 9 O2 5 9 o5 5 9 o8 5i 8 68 7 468 7 r 6884 6886 5i 9 5 9 n 5 9 i4 5 9 i 7 5 9 20 5 9 23 5 9 26 5o 9 6889 68 9 1 689 . 6899 6 9 oi 5o 10 9 . 99 5 9 285 9 3i 5 9 34 5 9 3 7 5 9 4o 5 9 43 49 10 9 . 99 6 9 o4;6 9 o6 6909 6 9 i2 6914 6 9 i 7 49 ii 5 9 46 5 9 4 9 5 9 52 5 9 54 5 9 5 7 5960 48 ii 6 9 i 9 '6 9 22 6924 6 9 27 6929 6 9 32 48 12 i3 5 9 63 5980 5 9 66 5 9 83 5 9 6 9 5 97 2 5 9 86 5 9 8 9 5 97 5 5 97 8 5 99 2j5 99 5 47 46 12 i3 6 9 346 9 3 7 6 9 4 9 6 9 52 6939 6942 6954 6957 6944 6 9 5 9 6 9 4 7 4 7 696246 i4 5 99 8 6001 6oo36oo6 6009 6012 45 i4 6 9 64 6967 6969 6 97 2 6 97 4 697745 i5 6oi5 6018 6021 6023 6026,6029 44 i5 6979 6982 6984 6 9 8 7 6 9 8 9 6 99 2 44 16 6o3 2 6o35 6o38 6o4i 6043^046 43 16 6994 6997 6999 7002 7 oo4 7 oo 7 43 17 6049 6o52 6o55 6o58 6061 6o63 42 1 7 7009 701 1 7014 7 oi6 7 or 9 7 O2I 42 18 6066 6069 6072 6o 7 5 6o 7 8 6081 4i 18 -7024 7026 7029 7 o3i 7 o34 7 o36 4i '9 6o83 6086 6089 6o 9 2 6095 6098 4o 1 9 7 3 9 704 1 7044 7 o46 7 o4 9 7 o5i 4o 20 9.996100 6io3 6106 6io 9 61 i2'6n5 3 9 20 9.997053 7o56 7o58 7 o6i 7 o63 -7066 3 9 21 6117 61206123 6126 6i2 9 6i3i 38 21 7068 7071 7 o 7 3 7 o 7 6 7 o 7 8 7 o8o 38 22 6i34 6i3 7 6i4o 6i43 6i466i48 37 22 7 o83 7 o85 7088 7 o 9 o 7 o 9 3 7 o 9 5 37 23 6i5i 6i546i5 7 6160 6162 6i65 36. 2') 7098 7100 7102 7io5 7 io 7 7 I 10 36 24 6168 6171 6i 7 4 6177 6179 6182 35 24 71 12 7 n5 7117 7120 7 I22 7124 35 25 6i85 6188 6i 9 i 619 "> 6196 6199 34 25 7127 7 I2 9 7i32 7i34 7 i3 7 7 i3 9 34 26 6202 62o5 6207 6210 62i3 6216 33 '26 7144 7i46 7149 7 i5i 7 i54 33 27 6219 6221 6224 6227 62306232 32 -7 7^56 7 i58 7161 7i63 7166 7 i68 32 28 6235 6238 6241 6244 6246 6249 3i 28 7170 7173 7i 7 5 7178 7180 -7182 3i 29 6252 6255 6 2 5 7 6260,6263 6266 3o *9 7i85 7^7 7190 7192 7 i 9 4 7 i 97 3o 3o 9.996269 62-71 62746277:62806282 29 Jo 9.997199 7 2O2 7204 7206 7 2O 9 7 2I I 2 9 3i 62856288 6291 6293.62966299 28 3i 7214 7 2l6 7218 7221 7 223 7226 28 32 63o2 63o5 63o 7 63io63i363i6 2 7 32 7228 7 23o 7233 7 235 7 238 -7240 27 33 63i8 632i 6324 6327 632 9 6332 26 33 7242 7 245 7247 7249 7 252 7 254 26 34 6335 6338 634o,6343 6346 634 9 25 34 72 5 7 72 5 9 7261 7264 7266 -7268 25 35 635! 6354 635 7 635 9 6362 ! 6365 24 35 7271 7273 7276 7278 7280 7 283 24 36 6368 6370 6,3 7 3 637663 79 638i 23 36 72.85 7 2S 7 7290 72 9 2 7 2 9 4 7 2 97 23 37 6384 638 7 63 9 o63 9 2 63 9 5 63 9 8 22 37 7299 73o4 7 3o6 7 3o 9 7 3ii 22 38 64oo 64o3 64o6 6409 64 1 1 64i4 21 38 7 3i3 7 3i6 73i8 7 320 7 3 2 3 7 325 21 .3 9 6417 64i 9 6422 6425 6428 643o 2O 3 9 7327 7 33o 7332 7 334 7 33 7 7 33 9 2O 4o 9.996433 6436 6438 644 1 6444 644 7 '9 4o 9 .997341 7 344 7346 7 348 7 35i 7 353 1 9 4 1 6449 6452 6455 645764606463 18 4i 7 355 7 358 7 36o 7 36 2 7 365 7 36 7 18 42 6465 43 6482 6468 6484 6471 6474 647616470. 6487 64 9 o 64 9 2'64 9 5 17 16 42 43 7 36 9 7 383 7 3 7 2 7 386 7 3 7 4 7 3 7 6 7 3 9 o 7379 7 3 9 3 7 38i 7 3 9 5 17 16 44 6498 65oo 65o3 65o6 65o8 65n i5 44 7397 7399 7 402 7 4o4 7 4o6 7 4o 9 1 5 45 65i4 6517 65i 9 6522 65 2 5 652 7 i4 45 74 1 1 74i3 7 4i6 7 4i8 7 420 7 423 i4 46 653o 6533 6535 6538654i 6543 i3 46 7425 74^7 7 429 7 432 7434 7 436 i3 47 6546 654 9 655i 65546557 655 9 12 47 743 9 /44i 7 443 7445 7448 7 45o 12 48 6562 6565 656 7 65 7 o65 7 3 65 7 5 I I 48 7452 7455 745 7 7 45 9 746 1 7 464 II 49 65 7 8 658o 6583^586,6588 65 9 i IO 49 7 466 7 468 7 4 7 i 7 4 7 3J 7 4 7 5 7477 IO 5o 9.996594 65 9 6 65 99 6602:6604 660-7 9 5o 9.997480 7 48 2 7 484 7 48 7 7 48 9 7 4 9 i 9 5i 6610 6612 66i5 6618 6620 6623 8 5i 7 4 9 3 7496 7498 7 5oo 7 5o2 7 5o5 8 52 6625 6628 663i 66336636 663 9 7 52 7507 7509 75ii 7 5i4 75x6 7 5i8 7 53 664 1 6644 6646 66496652 6654 6 53 7520 7 5 2 3 7 52 7 7 53o 7 53 2 6 54 665 7 6660 6662 6665 666 7 66 7 o 5 54 7534 7536 7 53 9 7 54i 7 543 7 545 5 55 56 57 66 7 3 6688 6704 66 7 5 66 9 i 6707 6678^681 6683 66 9 4 66 9 6 66 99 670(^)6712 6714 6686 6 7 oi 6717 4 3 2 55 56 57 7547755o 7 552| 7 554 7 556 7 56i 7 563 7 565 7 568; 7 5 7 o 7 5 7 4 7 5 777 5 797 58i 7 533 7 55 9 7 5 7 2 7 585 4 3 2 58 6720 6722 6720 6 7 2 7 6730 6 7 33 I 58 7 588 7 5 9 o 7592 7 5 9 4 7597 7599 i 5 9 6 7 35 6 7 38 6740 6 7 43 6 7 46 6 7 48 5 9 7601 760^ -6o5 7608 7610 7612 o 60" 50" 40" 30" ; 20" 10" c 60" 50" 40" ! 30" 20" i 10" Co-sine of 7 Degrees. s Co-sine of 6 Degrees. ( 1" 9" <* 4' 1 T T * 1 * -- ' * " 6" 7" 8" 9" ( l" 2" 3" 4" 5" 6" 7" 8 P.PartJ | ! i | 1 2 2 2 2 irt } 00111122 ' LOGARITHMIC TANGENTS. 107 1 Tangent of 82 Degrees. .= Tangent of 83 Degrees. m 0" | 10" 20" 30" 40" 50" " 0" 10" 20" | 30" | 40" 50" o 10.852197 2 35o 25o3 2656 2809 2962 5o O 10.910856 io3o 1205 i3 79 ii553 1727 5 9 i 3n5 3 2 68 3421 35 7 5 3 7 28 388i 58 I I 9 02 2076 225l 2426 2600 2775 58 2 4o34 4i88 434: 4495 464 9 4802 5? 2 2 9 5o 3i 2 53aoo 3475 365o 3825 5 7 3 4g56 5no 5263 54i 7 55 7 i 5 72 5 56 3 4ooo 4i76435i 45 27 4?02 4878 56 4 58 79 6o33 6i8 7 634i 6496 665o 55 4 5o53 5229 54o5 558i 5 7 5 7 5 9 33 55 5 68o4 6 9 58 7 n3 7 26 7 7422 7 5 7 6 54 5 6io 9 6 2 85 646 1 6638 68 1 4 6 99 o 54 6 77 3i 7886 8o4i 8i 9 5 835o 85o5 53 6 7 i6 7 7 343 7 520 7 6 97 7874 8o5o 53 7 8660 88i5 8 97 o 9125 9280 9 436 52 7 822-7 84o4 858i 8 7 5 9 8 9 36 9 n3 52 8 9591 o?46 QQO2 . .57 .212 .368 5i 8 Q2QO o468 o645 0823 178 5i 9 io.86o524 V f* v 0679 77 o835 0991 n46 I3O2 5o 9 77 io. 9 2o356 yi+i"/w o534 V"^"' 7 I2 v 0890 1068 1246 5o 10 i458 1614 1770 1926 2082 223 9 4 9 10 i424 1602 1781 i 9 5 9 2i38 23i6 49 ii 23 9 5 2 55i 2708 2864 3020 3i 77 48 II 24 9 5 2 6 7 3 2852 3o3i 3210 338 9 48 12 3333 3490 3647 38o3 3960 4117 4? 12 3568|3 7 4 7 3 9 26 4io5 4285 4464 47 i3 4274 443i 4588 4745 4902 5o5 9 46 1 3 4644 48 2 3 5oo3 5i83 5362 5542 46 i4 52i6 53 7 4 553i 5688 5846 6oo3 45 i4 5 7 22 5902 6082 6262 644a 6623 45 i5 6161 63 1 9 6476 6634 6792 6 9 5o 44 i5 68o3 6984 7 i64 7345 7 5 2 5 7706 44 16 7107 7 265 7423 7 58i 77 3 9 7 8 9 8 43 16 7 88 7 8068 824 9 843o 8611 8 79 2 43 '7 8o56 8214 83 7 2 853i 8689 8848 42 "7 8973 9i54 9 336 9 5l 7 9699 9 88o 42 18 9006 9166 9 324 9 48 2 964i 9 8oo 4i 18 10.930062 0244 0425 0607 0789 o 9 7i 4i T 9 99 5 9 .118 .277 .436 .5 9 5 7 54 4o T 9 ix54 i336 i5i8 1700 i883 2o65 4o 20 10.870913 I0 7 2 1232 i3 9 i i55i 1710 3 9 20 2248 243o 26i3 2796 2979 3i62 3 9 21 1870 2029 2i8 9 2 34 9 2 5o8 2668 38 21 3345 35 2 8 3 7 u 38 9 4 4078 4261 38 22 2828 2988 3i48 33o8 3468 362 9 3? 22 4444 4628 4812 4 99 5 5179 5363 37 23 3 7 8 9 3949 4109 4270 443o 45 9 i 36 23 554 7 5 7 3 r 5 9 i5 6o 99 6283 646 7 36 24 4?5i 4912 5073 5234 53 9 4 5555 35 24 6652 6836 7 o2i 7205 7 3 9 o 7 5 7 5 35 25 5 7 i6 58 77 6o38 6i 99 636o 6522 34 25 77 6o 79 45 8i3o 83 1 5 85oo 8685 34 26 6683 6844 7006 7167 7 32 9 7 4 9 o 33 26 88 7 o go56 9 24i 9.427 9 6l2 979 8 33 27 7 652 7 8i3 797 5 8i3 7 82 99 846i 32 27 9984 .169 .355 .54i .727 . 9 i4 32 28 8623 8 7 85 8 9 4 7 9 id 9 9271 9 433 3i 28 10.941100 1286 1472 i65 9 1 845 2O32 3i 2 9 9 5 9 6 9758 9921 ..83 .246 .4o8 3o 29 2219 2406 25 9 2 2779 2 9 66 3i53 3o 3o 10.880571 0734 0896 io5 9 1222 i385 2 9 3o 334i 35 2 8 3 7 i5 3902 4o 9 o 42 77 29 3i 1 548 1711 i8 7 4 2o38 22OI 2 364 28 3 1 4465 4653 484i 5o28 52i6 54o4 28 32 2528 2691 2855 3oi8 3i8 2 3345 27 3a 55 9 3 5 7 8i 5969 6i5 7 6346 6534 2-7 33 35o9 36 7 3 383 7 4ooi 4i65 432 9 26 33 6 7 23 6912 7100 7289 7 4 7 8 7 66 7 26 34 4493 465 7 4821 4 9 85 5i5o 53i4 25 34 7 856 8o45 8234 8424 86i3 88o3 25 35 5479 5643 58o8 5 97 2 6i3 7 63o2 24 35 8992 9182 9 3 7 i 9 56i 97 5i 99 4i 24 36 6467 663 2 6796 6961 7127 -7292 23 36 io. 9 5oi3i O32I o5n 0702 o8 9 2 I0 83 23 3? 745 7 7622 7787 79 53 8118 8284 22 37 I2 7 3 i464 i65 i845 2036 222 7 22 38 8449 86i5 8781 8 9 46 91 12 9278 21 38 2418 2609 2800 2991 3i83 33 7 4 21 3 9 9444 9610 9776 9942 .108 .274 20 3 9 3566 3 7 5 7 3 9 4 9 4i4i 4332 4524 20 4o 10.890441 0607 0773 o 9 4o 1 106 1273 <9 4o 4 7 i6 4908 5ioi 52 9 3 5485 5678 19 4i i44o 1606 I77 3 i 9 4o 2107 2274 18 4i 58 7 o 6o63 6255 6448 664i 6834 18 42 a44 1 260812775 2 9 42 3no 32 77 J 7 42 7 02 7 7 22O 7 4i3 7606 7800 7 99 3 J 7 43 3444 36i2J3 779 3 9 4 7 4n5 4282 1.6 43 8i8 7 838o 85 7 4 8768 8 9 6i 9I 55 16 44 445o 4618)4786 4 9 54 5l22 5290 i5 44 9349 9544 9738 99 32 . 126 !3ai i5 45 5458 5626,5795 5 9 63 6i3i 63oo i4 45 10.960515 o 7 io o 9 o5 1099 I2 9 4 i48 9 i4 46 6468 663 7 !68o6 69-74 7 i43 7312 i3 46 1 684 i8 79 2074 2270 2465 2661 i3 4? 7 48i 7 65o 7819 7988 8i5 7 83 2 6 *2 47 2856 3o52 3247 3443 363 9 3835 12 48 8496 8665 8834 9004 9 i 7 3 9 343 I I 48 4o3i 422 7 4424 4620 48i6 5oi3 II 49 9 5i3 9 683 9852 . .22 . 192 .362 IO 49 5209 5406 56o3 58oo 5 997 6i 9 4 10 5o io.coo532 0702 o8 7 3 io43 I2l3 1 384 9 5o 63 9 i 6588 6 7 85 6 9 83 7180 7377 9 5i i554 1-724 i8 9 5 2066 2236 2407 8 5i 7 5 7 5 7773 797 1 8169 8367 8565 8 52 2 5 7 8 2 7 4 9 2920 3091 3262 3433 7 52 8 7 63 8961 9 i5 9 9 358 9 556 97 55 7 53 36o5 3 77 6|3 9 4 7 4119 4290 4462 6 53 99 5 4 .i5a .35i .55o .749 . 9 48 .6 54 4633 48o5!4 977 5i49 5320 5492 5 54 10.971148 1 347 1 546 i?46 1945 2i45 5 55 5664 583 7 6oo 9 6181 6353 6526 4 55 2345 2545 2745 2945 3i45 3345 4 56 5? 6698 7734 6871 ho43 790718080 7216 8253 7 388 8426 7 56i 85 99 3 2 56 5 7 3545 4 7 49 3 7 46 3 9 46 4 9 5o5i5i 4i47 5352 4347 5553 4548 5 7 55 3 2 58 8772 89469119 9292 9 466 9 63 9 i 58 5 9 56j6i57635 9 656i 6762 6 9 64 I 5 9 9 8i3 99 8 7 .161 .334 -5o8 .682 o 5 9 7 i66! 7 368 7 5 7 o 7773 797 5 8i77 O 60" 50" 40"| 30" 20" 10" c 60" 50" 40" 30" 20" 10" a Co-tangent of 7 Degrees. s Co-tangent of 6 Degrees. .< 1" 2" 3" 4" 5" 6" 7" 8" 9" I 16 33 49 65 81 98 114 130 146 . C 1" 2" 3" 4" 5" 6" 7" 8" 9" in \ 19 37 56 75 94 112 131 150 168 108 LOGARITHMIC SINES. .5 Sine of 84 Degrees. .5 Sine of 85 Degrees. a 0" ! 10" | 20" ' 30" 1 40" 50" a 0" 10" 20" 30" 40" 50" ( 9.997^14 7617 7619 7621/7623 7626 5 9 o 9.998344:8346 8348 835o'8352 835j 5 9 I 762817630 7632 7 634: 7 636 7 639 58 8355 835 7 835 9 836il8363 8364 58 2 3 764 J 764376457647:76507662 7 656 76687661 '76637665 56 2 8366 8368 83 77 83 79 83 7 o 838i 83728374 83838385 83 7 5 8386 56 4 7667 7669 7672 7674:7676 7678 55 i 8388 8390 83 9 2 83 9 4 83 9 5 83 97 55 5 7 68o 7682 7686 7687 7689 7691 54 [ 83 99 84oi 84o3 84o4 84o6 84o8 54 6 7 6 9 3 7696 7698 7700 7702 7704 53 ( 84io 8412 84i3 84i5 84i 7 84i 9 53 7 77 o6 77097711 7713:77167717 62 7 8421 8422 8424 8426 8428 843o 52 8 77 i9 7722 7724 7726,7728(7730 61 8 843i 8433 8435 843 7 843 9 844o 5i 9 7732 77 35 77 3 777 3 9 ' 77 4i| 77 43 5o c 8442 8444 8446 8448 844 9 845 1 5o 10 9.997745 77 4 7 7760 7762 77 54: 77 56 4 9 10 9.998453 8455:845618458 846o 8462 ^ ii 12 77 58 7771 7760 77 62 77 65 77 6 7J77 6 9 777 3 777 5 7777 77 8 7782 48 47 ii 8464 84 7 4 84668467 84 7 6 84 7 8 |846 9 8479 84 7 i 848 1 84 7 2 8483 48 47 iJ 77 84 7786 77 88 7790 7792 779 4 46 i' 8485 848 7 848* 84 9 o 84 9 2 84 9 4 46 i4 i5 7797 7 8o 9 779 9 7 8oi 7 8o3 7 8o5 7807 7811 7814 78167818 7 82o 45 44 n 16 8496 85o6 849-718499 85o8|85o 9 85oi 85u 8602 85i3 85o4 85i5 45 44 16 7 822 7 835 78247826782878307833 7 83 77 83 97 84i l 7 843 7 845 43 42 16 17 85ib 85 27 85i8|852o 8629 853o 8522 8532 85-^3 8534 8626 8535 43 42 18 7 84 7 7 84 9 7 85 2 7864:7866 7868 4x 18 853 7 853 9 854i 8542 8544 8546 4i 19 7 86o 7862 7864 7866 7868 7870 4o 19 8548 854 9 855i 8553 8554 8556 4o 20 9-997872 7876 7877 78 79 ; 7 88iJ7883 3 9 20 9.998668 856o 856i 8563 8565 8566 3 9 21 7 885 7887 7889 78917893 7896 38 21 8568 85 7 o 85 7 2 85 7 3 85 7 5 8677 38 22 7897 7900 7902 7904 7906 7908 37 22 85 7 8 858o 8682 8584 8585 8687 37 23 79 io 7912 79x4791679x87^30 36 23 858 9 8690 85 9 2 85 9 4 85 9 5 85 97 36 24 79 22 7924 7926 7929 79' ! 35 24 85 99 8601 8602 86o4 8606 86o 7 35 25 79 35 793779397941 79437945 34 26 86o 9 86x1 8612 86i4 8616 86i 7 34 26 7947 79 4 9 79 5i 79 53 79 55 79 5 7 33 26 86i 9 8621 8622 8624 8626 8627 33 2 7 79 5 9 7 9 6i 79 63 79 65 796^7970 32 27 8629 863: 8633 8634 8636 8638 32 28 2 9 7972 7 984 7974.79761797879807983 79867988799079027094 3i 3o 28 2 9 863 9 864 9 - 865i 8653 8644 8654 8646 8648 86568657 3i 3o 3o 9 . 99799 6 7998 8000 8002 8oo4 8006 29 3o 9 . 99 865 9 8661 8662 8664 8666 8667 2 9 3: 8008 8010 8012 8oi4 8016 8018 28 3i 866 9 86 7 r 86-72 86 7 4 86 7 6 8677 28 32 8020 8022 8024 8026 8028 8o3o 27 32 86 79 8681 8682 8684 8686 8687 27 33 8o32 8o34 8o36 8o38 ; 8o4o 8042 26 33 868 9 8690 8692 86 9 4 86 9 5 86 97 26 34 8o44 8o46 8o48 8060 8062 8o54 26 34 86 99 8700 8 7 02 8704 8 7 o5 8707 25 35 8o56 8068 8060 8062 8o64 8066 24 35 8-708 8710 8712 8 7 i3 8716 8717 24 36 8068 8o 7 o %) 7 2 8074 8076 8078 23 36 8-718 8720 8721 8723 8 72 5 8726 23 37 8080 8082 8o84 8086 8088 8oy<> 1212 37 8 7 28 8739 8 7 3i 8 7 33 8 7 34 8 7 36 22 38 8092 8o 9 4 8o 9 6 8o 9 8 8100 8102 21 38 8 7 38 8 7 3 9 8741 8742 8 7 46 21 3 9 8io4 8106810881108112 8114 20 3 9 8 7 4 7 8 7 4 9 8760 8762 8 7 54 8 7 55 2O 4o 9.998116 8118 81208122 81248126 19 4o 9 . 99 8 7 5 7 8768 8760 8762 8 7 G-; 8 7 65 ! 9 4i 8128 8i3o8i3i 8i338i358i37 18 4i 8766 8768 8769 877J 8773 8 77 4 18 42 8i3 9 8i4i 8i43 8x45 8147 8i4 9 17 42 8776 8777 S 779 8781 8 7 82 8 7 84 J 7 43 8i5i 8i538i558i5 7 8i5 9 8i6i 16 43 8786 S 79 o 8793 6 44 8i63 816581678x6881708179 16 44 8 79 5 8 79 6 8798 8799 88o3 5 45 8i 7 4 8i 7 6 8178 81808x83 8i84 i4 45 88o4 8806 8807 88o 9 8812 4 46 8186 Ji88 8ioof8i 9 2|8io.4 8i 9 5 i3 46 88i3 8816 8817 8818 8820 8821 3 47 8i 97 8i 99 8201 8203^206 8207 12 47 8823 8826 8827 882 9 883i 2 48 8209 8211 83x3 8sx5 83x7 8318 n 48 8832 8834 8835 8837 8838 884o I 49 8220 8222 8224 8226 8228 823o 10 49 884i 8843 8844 8846 8848 884 9 5o 5i 9.998232 8243 8 2 34 8236 8238 823 9 8241 9 82458247|8249J8 3 5i 8263 8 5o 61 9 . 99 885i 8860 8862 8861 8854 8863 8855 8864 885 7 8866 8858 886 7 52 8255 8267 8258:826o j 8262 8264! 7 62 886 9 8870 8872 88 7 3 88 7 5 88 77 7 53 8266 8268 8270 8272 8273 8276 6 53 88 7 8 8880 8881 8883 8884 8886 6 54 8277 82798281 8283:8286 8287 5 54 888 7 888 9 88908892 88 9 3 88 9 5 5 55 8289 8290 8292 8294 8296 8298 4 55 88 9 6 889818899 8 9 oi 8 9 o2 ! 8 9 o4 4 56 83oo 83o2 83o3 83o5 8307 8309 3 56 8 9 o5 8907 8908 8910 891 1 Syi 3 3 5 7 83n 83i383i583i683i8832o 2 5 7 8914 8916 891-7 8919 8920 8922 2 58 8322 8324 8326 8328 8329 833i i 58 8923 8926 8926 892-7 8929 8930 I 5 9 8333 8335 833 7 833 9 834i 8342 o 5 9 8 9 3 2 8 9 33 8 9 35 8 9 36 8 9 38 8 9 3 9 O 60" ] 50" 40" 30" 20" 10" ; . 60" 50" 40" 30" 20" 10" Co-sine of 5 Decrees. a Co-sine of 4 Degrees. a P Part 5 l " ~" 3 " 4 " 5 " 6 " 7 " 8 " 9// P" 2 " 3// 4 " 5// 6 " 7 " 8" *" irt j 001111122;; irt j 1 1 1 1 1 1 LOGARITHMIC TANGENTS. 109 1 Tangent of 84 Degrees. j Tangent of 85 Degrees. | X 0" 10" 20" 30" 40" 50" a 0" 10" 20" 30" 40" 50") 10.978380 8582 8 7 85 8 9 88 9191 9394 5o n.o58o48 8291 8533 8776 9019 9262 5 9 i 9 5 97 9800 ...3 .206 .4io .6i3 58 I 9 5o6 9749 999 3 .236 .480 .724 58 2 10.980817 1021 1224 1428 i632 i836 57 2 ii .060968 1212 i456 1701 1945 2190 57 o 2O4I 2245 2449 2654 2858 3o63 56 3 2435 2680 2925 3170 34i6 366i 56 4 3268 4498 34 7 S 4703 36 77 4909 3882 5n4 4o8 7 5320 4293 5526 55 54 4 5 3 9 o 7 5384 4i53 563i 43 99 58 77 4645 6124 4891 5i38 6371 6619 55 54 6 5 7 32 5 9 38 6i44 635o 6556 6 7 63 53 6 6866 7 n3 7 36i 7609 7 85 7 8io5 53 7 6969 7176 7 382 7 58 9 7796 8oo3 52 7 8353 8601 885o 9098 9 34 7 9 5 9 6 5a 8 8210 84i7 8624 883i 9039 9246 5i 8 9 845 .-94 .343 .5 9 3 .842 I0 9 2j5l 9 9454 9 662 9869 77 .285 .493 5o 9 II.0 7 l342 1592 1842 2O 9 2 2343 25 9 3 5o 10 10.990702 o 9 io 1118 l32 7 i535 1744 4 9 10 2 844 3093 3346 35 97 3848 4ioo 49 ii I 9 53 2162 23 7 I 258o 2789 2998 48 1 1 435i 46o3 4855 5io 7 535 9 '56n 48 12 i3 3208 4466 34i7 46 7 6 362 7 4886 3836 5o 9 6 4o46 53o 7 4256 55i 7 47 46 12 i3 5864 7 38i 6116 7 635 636 9 7 888 6622 8142 68 7 5 7128147 83 9 6865o46 i4 5 7 28 5 9 3 9 6149 636o 65 7 i 6-782 45 i4 8 9 o4 9 l5 9 94i3 9 668 9922 .177 45 i5 6993 7 2o5 7 4i6 7 62 7 7 83 9 8o5i 44 i5 1 1. o8o432 0688 o 9 43 1199 i454 1710 44 16 17 8262 9 535 84 7 4 97 48 8686 9960 8898 .i 7 3 9111 .386 9323 5 99 43 42 16 i 9 66 35o5 2222 3 7 62 24 7 8 4oi 9 2 7 35 42 7 6 2 99 i 3248 453414791 43 42 18 ii .000812 1025 1238 i45i 1 66 5 i8 7 8 4i 18 5o4 9 53o 7 5565 5823 6082,6340 4i 19 2092 2 3o6 2519 2 7 33 2947 3i6i 4o ig 65 99 6858 7117 7 3 7 6 76357894 4o 20 33 7 6 35 9 o 38o4 4019 4234 4448 3 9 20 8i54 84i4 86 7 4 8 9 34 91949454 3 9 21 4663 48 7 8 5093 53o8 5524 5 7 3 9 38 21 9 7i5 997 5 .236 4 97 758 1020 38 22 5 9 55 6i 7 o 6386 6602 6818 7o34 37 22 II .O 9 I28l 1 543 i8o4 2066 2328 2590 3 7 23 7 25o 7 466 7 682 7 8 99 8n5 8332 36 23 2853 3n5 33 7 8 364 1 3904 4167 36 24 8549 8 7 65 8982 9199 9417 9 634 35 24 443o 46 9 4 4 9 5 7 5221 5485 5 7 4 9 35 25 > 9 85i ..69 .286 .5o4 .722 . 9 4o 34 25 6oi3 62-78 6542 68o 7 7072 7 33 7 34 26 ii.oni58 i3 7 6 i5 9 4 i8i3 2031 225o 33 26 7602 7 868 8i33 83 99 8665 8 9 3i 33 27 2468 2 68 7 2906 3i25 3344 3563 32 27 9197 9 463 97 3o 999 6 .263 .53o 32 28 3 7 83 4OO2 4222 444 1 466i 488i 3i 28 11.100797 io65 i332 1600 1868 2i36 3i 29 5ioi 532i 554i 5 7 62 5982 6202 3o 29 2404 26 7 2 2 9 4o 32O 9 34 7 8 3 7 4 7 3o 3o 6423 6644 6865 7 o86 7307 7628 29 3o 4oi6 4285 4555 4824 5094 5364 2 9 3i 7749 197 1 8192 84i4 8636 885 7 28 3i 5634 5 9 o4 6i 7 5 6445 6 7 i6 6 9 8 7 28 32 9079 9524 9746 9968 .191 2 7 32 7 258 7 J2 9 7 8oi 8o 7 2 8344 8616 27 33 o636 o85 9 1082 i3o5 i5 2 8 26 33 8888 9 i6o 9 433 97 o5 9978 .a5i 26 34 1752 i 97 5 2199 2422 2646 28-70 25 34 ii . no524 o 79 8 IO 7 I 1 345 1618 l8 9 2 25 35 3094 33i8 3542 3 7 6 7 3991 4216 24 35 2l6 7 244 1 2 7 l5 2990 3265 354o 24 36 444o 4665 4890 5n5 534o 5565 23 36 38i5 4o 9 o 4366 4642 4917 5i 9 3 23 37 5791 6016 6242 6468 66 9 3 6 9 i 9 22 37 54 7 o 5 7 46 6023 6299 65 7 6 6853 22 38 7i45 7 3 7 2 7 5 9 8 7 8 2 4 8o5i 82 77 21 38 7 i3i 7 4o8 7 686 79 63 8241 8520 21 39 85o4 8 7 3i 8 9 58 9 i85 9412 9 64o 20 3 9 8798 90 7 6 9 355 9 634 99 i3 .192 2O 4o 9867 .. 9 5 .322 .55o .778 1006 : 9 4o ii . 120471 o 7 5i io3i i3n 1691 1871 J 9 4i n.o3i234 1462 i6 9 i 1919 2148 2 3 77 18 4i 2l5l 2432 2 7 l3 2 99 4 32 7 5 3556 18 42 2606 2 835 3o64 3293 3522 3 7 5 2 17 42 3838 4n 9 44oi 4683 4 9 66 5248 i 7 43 3981 4211 444i 46 7 i 4901 5i3i 16 43 553i 58i3 6o 9 6 638o 6663 6 9 46 16 44 536i 55 9 2 5822 6o53 6284 65i4 i5 44 7230 7 5i4 779 s 8082 836 7 865i i5 45 6745 6 977 7208 743 9 7671 7 902 i4 45 8 9 36 9 22I 979 2 77 .363 i4 46 8i34 8366 85 9 8 883o 9062 9 2 9 5 i3 46 n.i3o649 o 9 35 1221 i5o8 1 79 4 2081 i3 47 9527 97 6o 999 2 .225 .458 .691 12 47 2368 2656 2 9 43 323i 35i838o6 12 48 11.040925 ii58 i3 9 i 1625 i85 9 2092 II 48 4og4 4383 46 7 i 4 9 6o 524 9 5538 II 49 2326 2 56i 2 79 5 3029 3 2 64 3498 10 49 582 7 6n 7 6407 66 97 6 9 8 7 7277 10 5o 3 7 33 3 9 68 4203 4438 46 7 3 4908 9 5o 756 7 7 858 8149 844o 873i! 9 o23 9 5i 5i44 53 7 9 56i5 585i 6o8 7 6323 8 5i 93i4 9606 9898 . 190 .483 . 77 5 8 52 6559 6 79 5 7 o32 72 68 7 5o5 77 42 7 52 11.141068 i36i i654 i 9 4? 2241 2535 7 53 7979 8216 8453 8691 8928 9166 6 53 2829 3i23 34i7 3712 4007 43oi 6 54 94o3 9641 9 8 79 .117 .356 .594 5 54 45 97 4892 5187 5483 5 779 6o 7 5 5 55 n.o5o832 IO 7 I i3io 1 549 1-788 202 7 4 55 63 7 2 6668 6 9 65 7262 7 559| 7 856 4 56 2266 2 5o6 2 7 45 2 9 85 3225 3465 3 56 8i54 8452 8 7 5o 9 o48 9346 9645 3 5 7 3 7 o5 3 9 45 4i85 4426 4666 49o 7 2 57 99 43 .242 .542 .84i ix4i i44o 2 58 5i48 5389 563o 5871 6112 6354 I 58 n.i5i 7 4o 2041 234i 2642 2942 3243 I 5 9 65 9 6 683 7 779 7321 7 563 7 8o6 O 5 9 3545 3846 4i48 4449 4 7 52 5o54 O 60" 50" 40" 30" 20" 10" . 60" 50" 40" 30" | 20" 10" j Co-tangent of 5 Degrees. a Co-tangent of 4 Degrees. s P PartJ 1//2 " 3 " 4 " 5 " G// 7 " 8// 9 " ( 1" 2" 3" 4" 5" 6" 7" 8" 9" P. Part ^ 27 54 81 log 135 162 188 215 242 I 10 LOGARITHMIC SINES. 1 Sine of 86 Degrees. Sine of 87 Degrees. H 0" 10" 1 20" ! 30" | 40" 50" s 0" 10" 20" 30" | 40" 50" I 2 3 4 9.998941 8968 8967 8976 8 9 42|8 9 448 9 458 9 47 8961 895389648955 89608961 8 9 638 9 64 8969 8970 8971 8 9 73 8977 8979 89808982 8 9 48 8967 8966 8 97 4 8 9 83 69 58 ll 55 O I L 9.999404 9 4n 9418 9424 943 1 9 4o6 9 4l2 9 4i 9 9 425 9 43 2 9 4o 7 9 4i3 9 4s6 9 433 94o8 9 4i4 9 42I 9 42 7 9 434 ' 9 4o 9 9 4i5 9 428 9 435 9 4io 9 4i6 9 423 9 43o 9 436 5 9 58 56 55 5 8984 8986 8987 898 9 8 99 o 8992 54 5 9 43 7 9 438 9 43 9 9 44o 9 44i 9 442 54 6 89938 99 58 99 6 8 997 8 999 9000 53 6 9443 9 445 9 446 9 447 9 448 9449 53 7 8 9 OO2 9 oio 9 oo3 9 oo5 9 OI2 9 OI^ 9006 9007 9 oo 9 9 oi5 9 oi6J 9 oi7 62 5i 8 9 45o 9 456 9 45i 9 452 9 45 79 458 9 453 9 45 9 9 454 9 46o 9455 946i 62 5i 9 9 OI 9 9 O2O 9 O22 9 023 9 024 9 026 5o 9 9 463 9 464 9 465 9 466 9 467 9 468 5o IO 9- 999 2 7 9 o2 9 9 o3o 9 o32 9 o33 9 o34 49 IO 9 999469 9 47o 9 47i 9472 9 4 7 3 9 474 4 9 ii 9 o36 9 o37 9 o3 9 9 o4o 9 o4i 9 o43 48 ii 9476 9477 9478 9 479 9 48o 48 12 9044 9 o46 9 o47 9 o48 9 o5o 9 o5i 47 12 9 48i 9482 9 483 9484 9 485 9 486 47 i3 9o53 9 o54 9 o55 9067 9 o58 9 o5 9 46 i3 9487 9488 9 48 9 9490 9 4 9 i 9 4 9 2 46 i4 i5 16 9061 9069 9077 9 o62 9 o64 9066 9 o66 9 o68 9 o 7 i 9 o72 9 073j 9 o 7 5 9 o76 9079 9 o8o 9 o82 9 o83 9 o84 45 44 43 i4 16 16 9493)9496 9600 9601 95o6j 9 5o7 9 4 9 6 9497 9602 9603 9608 9609 9 4 9 8 9 5o4 9 5io 9499 9606 9611 45 44 43 17 9086 9087 9 o88 9 o 9 o 9 o 9 i 9 9 2 42 17 9 5i2 9 5i3 9 5i4 9616 9 5i6 9617 42 18 9094 9096 9097 9098 9099 9 IOI 4i 18 9 5i8 9 5i 9 9620 9621 9 522 9 523 4i 19 20 9102 9 . 999 no 9 io3 9106 9 io6 9107 9111 9 ii3 |9 ii4 9 n5 9109 9117 4o 39 '9 20 9 5 2 4 9 . 999 52 9 9 525 9 53o 9626 9 53i 9627 9 53 2 9 5 2? 9 533 9 528 9 534 4o 3 9 21 9118 9 I20 9 I2I 9 I22 9124 9126 38 21 9 535 9 536 9 53 7 9 538 9 53 9 9 54o 38 22 9126 9 I28 9 I2 9 ! 9 i3o 9 l32 9133 37 22 9 54i 9 542 9 543 9544 9 545 9 546 37 23 9i34 9 i36 9 i37 9 i38 9 i4o 9141 36 23 9 547 9 548 9 549 9660 9 55i 9 552 36 24 9 i42 9 i43 9 i45 9 i46 9 i47 9 i4 9 35 24 9 553 9 554 9 555 9 556 9 55 7 9 55 7 35 25 9160 9 i5i 9 i53 9164 9 i55 9 l5 7 34 25 9 558 9 55 9 9660 9661 9662 9 563 34 26 9168 9 i5 9 9 i6i 9 l62 9 i63 9 i65 33 26 9 564 9 565 9666 9667 9668 9 56 9 33 27 9166 9 i67 9168 9170 9 i 7 i 9 I 7 2 32 27 9 5 7 o 9 57i 9 5 7 2 9 5 7 3 9 5 7 3 9 5 7 4 3a 28 9 i 7 4 9176 9176 9178 9179 9180 3i 28 9 5 7 5 9676 9677 9678 9 5 79 9 58o 3i 29 9181 9 i83 9 i84 9 i85 91879188 3c 2 9 9 58i 9682 9683 Q 584 9 585 9 586 3o 3o 7.999189 91909192 9193 91949196 29 3o 9.999686 9687 9688 9 58 9 9 5 9 o 9 5 9 i 2 9 3i 9197 9 i 9 8 9 i 99 9201 9202 9203 28 3i 9692 9 5 9 3 9 5 9 4 9696 9 5 9 6 9 5 97 28 32 9206 9206 9207 9208 92109211 27 32 9697 9698 9 5 99 9600 9601 9 6o2 2 7 33 9212 9213 9215 9216 9 2I 7 9219 26 33 9603 9604 9 6o5 9606 9606 9607 26 34 9220 9221 9222 9224 9 225 9 226 25 34 9608 9 6o 9 9 6io 9611 9612 9 6:3 25 35 9227 9229 9230 9231 9 232 9 234 24 35 9614 9614 9 6i5 9616 9 6i 7 9 6i8 24 36 9 s35 92369237 9 23 9 9 24l 23 36 9619 9620 9 62I 9622 9622 9 623 23 3? 9242 9244924^9246 047 9 24 9 22 37 9624 9 625 9 626 0627 9 6 2 8 9 62 9 22 38 9260 9261 9262 9 254 9266 9 256 21 38 9629 9 63o 9 63i 9 632 9 633 9 634 21 3 9 9267 9 258 9260 9261 9262 9 263 2O 39 9635 9 635 9 636 9 6 3 2 9 638 9 63 9 20 4o 9.999265 9266 926719268 9270 9271 I 9 4o 9.9996409641 9 64i 9 643 9 644 IQ 4i 42 9272 9279 9273 92749276 92809282 9283 9277,9278 9284,9286 18 17 4i 42 9645 9646 96609661 9 647 9 652 9647 9 653 9 648 9 653 9 64 9 9 654 18 43 9287 9288 928919290 9291 9 2 9 3 16 43 9666 9 656 9667 9668 9 658 9 65 9 16 44 9294 9295 9296 9297 9 2 99 9 3oo i5 44 9660 9 66il 9 662 9 663 9 663 9664 16 45 93oi 9302 93o3 9 3o5 9 3o6 9 3o7 i4 45 9666 9 666 9667 9 668 9 668]Q66 9 i4 46 93o8 9309 93109312 9 3i3 |9 3i4 i3 46 9670 9 6 7 i 9672 9 6 7 2 9673 9674 i3 47 48 9 3i5 9322 93i6 9318 9319 932393269326 9 320 9 32I 12 47 48 967696769677 9680968119681 9 6 77 9 6 7 8 9 6 79 9 682 9 683 9 684 12 II 49 9329 933i 93329333 9334!9335 IO 49 968696869686 968796889689 10 5o 9 999 336 9338 9 33 9 9340 934i 9 342 9 5o 9.99968996909691 9692 9 6 9 3 9 6 9 3 9 5i 9 343 9344 9346 9347 9 348 9 34 9 8 5i 9 6 9 4 9 6 9 5 9 6 9 6 9697 9 6 97 9698 8 52 9 35o 935i 9353 9 354 9 355 9 356 7 62 9 6 99 9700 9 7oo 9701 97 02 97 o3 7 53 9 35 7 93589359 936i 9 362 9 363 6 53 9704 9704 97 o5 9706 977 9707 6 54 9 364 9 365 9 366 936 7 93699370 5 54 97o8j 9 7o 9 j 9 7io 9 7i i 97 11 97 12 5 55 9 3 7 i 9 3 72 ' 9 3 7 3 9 3 7 4 9376.9377 4 55 9 7i3 9 7i4 97*4 9716 9716 91*7 4 56 9 3 7 8 9 37 9 ' 9 38o 9 38i 9 382 9 383 3 56 9717 97 l8 97 I 9 97 20 97 20 972i 3 57 9 384 9 385; 9 38 79 388 9 38 9 9 3 9 o 2 57 9 722 9 723 9723 9724 9 725 9726 2 58 9 3 9 i 939293939394 9 3 9 6 9 3 97 I 58 9 726 97 2 7 Q 7 28 97 2 9 97 2 9 97 3o I 5 9 9 3 9 8 9 3 99 ! 9 4oo 9 4oi 9 4o2 9 4o3 O 5 9 97 3i[ 97 32 97 32 97 33 97 34 97 35 O 60" 50" j 40" 30" 20" 10" . CO" 50" 40" 30" 20" | 10" . Co-sine of 3 Degrees. Co-sine of 2 Degrees. i r -Ho' 1 3 o' v 5" 6" 7" 1 1 1 8" 9" 1 1 p p . C 1" 2" 3" 4" 5" 6" 7" V 9" in \ 000001111 LOGARITHMIC TANGENTS. 1 1 1 .5 Tangent of 86 Degrees. d Tangent of 87 Degrees. *% 0" 10" 20" 30" 40" 50" 2 0" 10" 20" 30" 40" 50" 1 1. 155356 565 9 5962 6265 6568 68 7 2 5 9 11.280604 IOO 7 i4n 1814 22I 9 2623 5 9 I 7 i 7 5 7479 7784 8088 83 9 3 86 97 58 I 3oa8 3433 383 9 4245 4652 5o58 58 2 9002 9 3o8 9613 9919 .224 .53o 5 7 2 5466 58 7 3 6281 668 9 7 o 9 8 7 5o 7 57 3 11.160837 n43 i45o 1757 2064 23 7 I 56 3 7 9 i 7 8326 8 7 3 7 9 i47 9 558 9970 56 4 2679 2 9 8 7 32 9 5 36o3 3 9 n 4220 55 4 zz. 990882 o 79 4 1206 1619 2o33 2446 55 5 4529 4838 5i4 7 545 7 5 7 66 6o 7 6 54 5 2860 3 27 5 3690 4io5 452i 4 9 3 7 54 6 638 7 66 97 7008 73i8 7 62 9 794 1 53 6 5354 5 77 o 6188 66o5 7024 7442 53 7 8252 8564 88 7 6 9188 9 5oo 9 8i3 52 7 7861 8280 8700 9120 9 54i 9962 52 8 ii . 170126 o43 9 O 7 f>2 1066 i3 79 i6 9 3 5i 8 ii.3oo383 o8o5 1227 1649 20 7 2 2496 5i 9 2008 2322 2 63 7 2 9 5i 8267 3582 5o 9 2 9 i 9 3344 3 7 68 4i93 46i 9 5o44 5o 10 38 97 42i3 452 9 4845 5i62 54 7 8 4 9 10 547i 58 97 6325 6 7 52 7 i8o 7608 4 9 1 1 5 79 5 6112 643o 6747 7 o65 7383 48 ii 8o3 7 8466 8896 9326 9756 .187 48 12 7702 8020 833 9 8658 8 977 9 T 97 47 12 11.3/0619 io5o i483 1915 2348 2782 4 7 i3 9616 99 36 .256 .5 77 .897 1218 46 !3 32i6 365o 4o85 4520 4g56 5392 46 i4 ii. 181539 1860 2182 25o4 2826 3i48 45 i4 5828 6265 6702 7 i4o 7 5 7 8 8017 45 i5 34?i 3 79 3 4n6 444o 4763 5o8 7 44 i5 8456 88 9 6 9 336 977 6 .217 .65 9 44 16 54n 5 7 35 5o5 9 6384 6709 7 o34 43 16 ii .3 tnoo 1 543 i 9 85 2428 28 7 2 33i6 43 1? 7 35 9 7 685 801 1 833 7 8663 8 99 o 42 7 3761 4206 465i 597 5543 5990 42 18 9 3i 7 9 644 997 1 .299 .626 9 54 4i 18 643 7 6885 7 333 77 82 8 2 3i 8680 4i J 9 11.191283 1611 i 9 4o 2269 2 5 9 8 2 9 28 4o J 9 Qi3o 9 58i ..32 .483 ^35 i38 7 4o 20 3 2 58 3588 3 9 i8 4249 45 79 4 9 io 3 9 20 n.J.Vi84o 22 9 3 2 7 4 7 32OI 3B56 4izi 39 21 6242 55 7 3 6905 6237 6569 6 9 02 38 21 4867 5o23 5480 5 9 3 7 63 9 4 6852 38 22 7235 7 568 79 oi 8235 8568 8 9 02 37 22 7811 777 822 9 8689 9 i5o 961 1 3 7 23 9 23 7 9 5 7 i 9906 .241 .5 77 . 9 I2 36 23 1 1 . ?-4ooy2 o534 o 99 6 i45 9 I 9 23 2 38 7 36 24 II .201248 i584 1921 2257 2 5 9 4 2 9 3i 35 24 285i 33i6 3 7 8i 424 7 47i4 5i8o 35 25 3269 36o6 3944 4282 4621 4 9 6o 34 25 5648 6116 6584 7 o53 7 522 7992 34 26 5299 5638 5 977 63i7 6657 6 997 33 26 8463 8 9 33 9 4o5 9877 34 9 .822 33 27 7 338 7 6 79 8020 836i 8 7 o3 9 o45 32 27 I I. $61296 I 77 2244 2 7 I 9 3i 9 5 3671 32 28 9 38 7 97 2 9 ..72 .4i5 . 7 58 1102 3i 28 4i47 4624 5l02 558o 6o5 9 6538 3i 29 n.2ix446 i 79 o 2134 2479 2823 3i6 9 3o 29 7018 7 4 9 8 7979 846o 8 9 42 9424 3o 3o 35i4 386o 4206 4552 48 9 8 5245 2 9 3o 997 .3 9 o 8 7 4 i35g 1 844 2329 2 9 3i 55 9 2 5 9 3 9 628 7 6635 6 9 83 7 33i 28 3i ii .862816 33o2 3789 42 77 4 7 65 5254 28 32 7 68o 8o2 9 83 7 8 8728 9 o 7 8 9 428 2 7 32 5744 6234 6724 7 2l5 777 8199 2 7 33 9779 .I2 9 .48o .83i n83 i534 26 33 86 9 2 9 i85 9 6 79 .i 7 3 .668 1164 26 34 11.321886 223 9 25gi 2944 32 9 8 365i 25 34 11,371660 2i56 2654 3i5i 365o 4i4g 25 35 4oo5 435 9 4 7 i3 5o68 5423 5 77 8 24 35 4648 5i48 564 9 6i5o 6652 7i54 24 36 6i34 648 9 6845 7202 7 558 79 i5 23 36 7 65 7 8161 8665 91-70 9 6 7 5 .181 23 3? 82 7 3 863o 8988 9 346 97 o5 ..63 22 37 n.38o68 7 n 9 4 1702 2210 2719 3228 22 38 ii .a3o422 7 82 n4i i5oi 1861 2222 21 38 3 7 38 424 9 4760 52 7 2 5 7 85 6298 21 3 9 2583 2 9 44 33o5 3667 4o2 9 43 9 i 20 3 9 6811 7 3a5 7840 8356 88 7 2 9388 2O 4o 4 7 54 5zz6 548o 5843 62O 7 65 7 i *9 4o 99 o6 .424 . 9 42 i46i 1981 25oi I 9 4i 6 9 35 7 3oo 7 665 8o3o 83 9 6 8 7 6 2 18 4i II ,3 9 3O22 3544 4o66 458 9 5n3 563 7 18 4s 9 I28 9 4 9 5 9861 .22 9 .5 9 6 9 64 l l 42 6161 668 7 7213 77 4o 826? 8795 17 43 n.a4i33a I 7 00 2069 2438 28o 7 3i 77 16 43 9 3 2 3 9 853 .382 . 9 i3 1 444 1976 16 44 354 7 3 9 i 7 4288 465 9 5o3o 54oi i5 44 Ii.4o25o8 3o4i 35 7 5 4no 4645 5i8o i5 45 5 77 3 6i45 65i8 68 9 i 7264 7 63 7 i4 45 5 7 i7 6254 6 79 2 7 33o 7 86 9 84o 9 i4 46 Son 8385 8 7 5 9 9 i34 9 5o 9 9 884 i3 46 8 9 4Q 9 4 9 o ..32 5 7 4 1117 1661 i3 4? ii .250260 o636 IOI2 i38 9 i 7 66 2143 12 47 II.4l22o5 2 7 5l 32 9 6 3843 43 9 o 4938 12 48 2521 28 99 32 77 3656 4o34 44i4 II 48 5486 6o3fi 6586 7 i36 7688 8240 II 49 4 79 3 5i 7 3 5553 5 9 34 63i5 66 9 6 IO 49 6 79 2 q346 9 90o Xf^ IOIO i566 10 5o 7 o 7 8 7 46o 7 84a 822^ 86o 7 8 99 i 9 5o II .422123 2681 3a4o|3 799 4358 4919 9 5i 9 3 7 4 9758 .142 .52 7 .912 I2 97 8 5i 548o!6o42 66o5| 7 i68 77 33 8298 8 52 ii. 26i683 2o6 9 2455 2842 322 9 36i6 7 52 8863 9 43o 9997 .565 n33 1702 7 53 4oo4 43 9 2 4 7 8o 5i6 9 5558 5 9 4 7 6 53 11.432273 2843 3 4 i5 3 9 8 7 |456o 5i34 6 54 633 7 6 7 2 7 7117 7 5o8 7899 82 9 I 5 54 5 7 o 9 6284 6860 743 7 8016 85 9 3 5 55 8683 9 o 7 5 9467 9 86o .254 .64 7 4 55 9 I 7 2 97 52 .333 . 9 i5 1497 2080 4 56 11.971041 1435 i83o 2225 2620 3oi6 3 56 11.442664 3248 3834 4420 5oo 7 5595 3 57 58 3412 5 79 6 3809 6195 4206 65 9 4 46o3 6 99 3 5ooo 7 3 9 3 53 9 8 779 3 2 I 57 58 6i83 97 32 6 77 3 .326 7 363 79 548546 . 9 2Ijl5l 7 21 l2 9i38 2711. 2 I 5 9 8i 9 4 85958996 9 3 97 9799 .202 5 9 II.453309 3 9 o845o8|5io 9 !5 7 ii 63i3 o 60" 50" 40" 30" | 20" | 10" A 60" 50" | 40" 30" 20" 10" JL Co-tangent of 3 Degrees. i Co-tangent of 2 Degrees. s p p < 1" 2" 3" 4" 5" 6" 7" 8" 9" 1 ( 1" 2" 3" 4" 5" 6" 7" 8" 9" } 35 69 104 138 173 207 242 276 311 | ir \ 48 97 145 193 242 290 338 387 435 112 LOGARITHMIC SINES. 1 Sine of 88 Degrees. .a Sine of 89 Degrees. 0" 10" 20" 30" 40" 50" m 0" 10" 20" 30" 40" 50" o 9-999735 9736 97 3 7 9738 9738 97 3 9 5 9 9.999934 99 34 99 35 99 35 99 35 9936 5 9 I 974o 9 74o 97 4i 9 742 9743 9743 58 i 9 9 36 99 36 99 3 7 99 3 7 99 3 7 99 38 58 2 9744 97 45 97 46 9 746 9747 9748 57 2 99 38 99 3 9 99 3 9 99 3 9 99 4o 99 4o 5 7 3 9 748 9749 97 5o 9 75i 97 5i 97 52 56 3 99 4o 99 4i 99 4i 99 4i 9942 99 42 56 4 9753 9753 9754 9755 9756 9756 55 4 9943 99 43 994 3 9944 9944 55 5 97 5 7 9758 9758 97 5 9 9760 9760 54 5 99 44 99 45 9945 9945 9946 9946 54 6 976i 9762 9763 9763 9764 97 65 53 6 99 46 9947 9947 9947 9948 9948 53 7 9765 9766 9.767 9767 9768 9769 52 7 99 48 9949 9949 9949 99 5o 995o 52 8 9769 9770 9771 977 2 9772 9773 5i 8 99 5o 99 5i 99 5i 99 5i 99 5 2 99 5 2 5i 9 9774 9774 977 5 9776 9776 9777 5o 9 99 5 2 99 53 99 53 99 53 99 53 9954 5o IO 9-999778 9778 9779 0.780 9780 9781 49 IO 99 54 99 55 99 55 99 55 99 56 49 ii 0782 9782 9783 97 84 9784 9785 48 ii 99 56 99 56 99 56 99 5 7 99 5 7 99 5 7 48 12 9786 9786 9787 97 88 9788 9789 47 12 99 58 99 58 99 58 99 5 9 99 5 9 99 5 9 47 i3 979 979 9791 979 s 9792 979 3 46 i3 99 5 9 9960 99 6o 99 6o 99 6i 99 6i 46 i4 9794 9794 979 5 979 5 9796 9797 45 i4 99 6i 9961 99 62 99 62 99 6 2 99 63 45 i5 9797 9798 9799 9799 9800 9 8oi 44 i5 99 63 99 63 99 63 9964 99 64 9 o64 44 16 9801 9802 9 8o3 9 8o3 9804 9 8o4 43 16 99 64 99 65 99 65 99 65 99 65 9,9,66 43 17 9805 9806 9 8o6 9 8o7 9808 9808 42 17 99 66 9966 99 6 7 99 6 7 99 6 7 99 6 7 42 18 9809 9809 9 8io 9 8n 9811 9 8l2 4i 99 68 9968 99 68 99 68 99 6 9 99 6 9 4i i 9 9813 9813 9 8i4 9 8i4 9 8i5 9 8i6 4o i 9 99 6 9 9969 9970 997 997 997 4o 20 9.999816 9817 9 8i7 9 8i8 9819 9819 3 9 20 9-999971 9971 9971 9971 9972 997 2 3 9 21 9820 9820 9821 9822 9 822 9 823 38 21 9972 9972 997 3 997 3 9973 9973 38 22 9824 9824 9825(9825 9 826 0827 37 22 9973 9974 9974 9974 9974 9 97 5 3 7 23 9827 9828 98289829 9 82 9 9 83o 36 23 997 5 9975 997 5 9976 9976 9976 36 24 9 83i 983i 9 832| 9 832 9 833 9 834 35 24 9976 9976 9977 9977 9977 9977 35 25 9 834 9 835 9 835| 9 836 9 836 9 83 7 34 25 9977 9978 9978 9978 9978 9979 34 26 9 838 9 838 9 83 9 ' 9 83 9 9 84o 9 84o 33 26 9979 9979 9979 9979 99 8o 9980 33 27 9 84i 9 842 9 842' 9 843 9 843 9 844 32 27 99 8o 9980 9980 9981 99 8i 9981 32 28 9 844 9 845 9 846 i9 846 9 84 7 9 847 3i 28 998i 9982 9982 99 82 9982 3i 29 9 848 9 848 9 84 9 ! 9 84 9 9 85o 9 85i 3o 2 9 99 8 2 9983 99 83 99 83 99 83 99 83 3o 3o 9 . 999 85i 9 852 9 852 : 9 853 9 853 9 854 2 9 3o 9 . 9999 83 99 84 9984 99 84 99 84 9984 29 3i 9 854 9 855 9 856 9 856 9 85 7 9 85 7 28 3i 99 85 99 85 99 85 99 85 99 85 99 85 28 32 9 858 9 858 9859*9859 9 86o 9 86o 2 7 32 99 86 9986 99 86 99 86 99 86 99 86 27 33 9 86i 9861 9862 9863 9 863 9 864 26 33 99 8 7 9987 9987 9987 9987 9987 26 34 9 864 9 865 9 865 9866 9 866 9867 25 34 99 88 9988 9988 9988 99 88 99 88 25 35 9 86 7 9868 98689869 9 86 9 9870 24 35 9989 9989 9989 9989 99 8 9 9989 24 36 9 8 7 o 9871 9871 9872 9 872 9873 23 36 99 8 9 999 9990 999 999 999 23 37 9 8 7 3 9874 98749875 9875 9876 22 3 7 999 999 999 * 9991 9991 9991 22 38 9876 9877 9877,9878 9 8 7 8 9879 21 38 999 i 9991 9991 9992 9992 9992 21 3 9 9879 9880 9880 9881 9 88i 0882 2O 3 9 999 2 9992 9992 9992 9992 999 3 2O 4o 9 . 999 882 9883 98839884 9 884 9 885 '9 4o 9-99999 3 999 3 999 3 999 3 999 3 999 3 *9 4i 9 885 9886 98869887 9 887 9 888 18 4i 999 3 999 3 9994 9994 9994 9994 18 42 9888 9889 9889 9890 9 8 9 o 9891 17 42 9994 9994 9994 9994 9994 999 5 17 43 44 45 9891 9894 9897 9892 9894 9897 9892 9892 9893 9 8 9 5 9 8 9 5 9 8 9 6 9 8 9 8 9 8 9 8 9 8 9 8 9 8 9 3 9 8 9 6 9899 16 i5 i4 43 44 45 999 5 999 5 999 6 999 5 999 5 999 6 999 5 999 5 9996 999 5 999 6 999 6 999 5 9996 9996 999 5 9996 9996 16 i5 i4 46 9 8 99 9900 99 oo 99 oi 99 oi 99 02 i3 46 999 6 999 6 9997 9997 9997 9997 i3 47 99 O2 99 3 99 o3 9903 9904 99 o4 12 4 7 9997 9997 9997 9997 9997 9997 12 48 99 o5 99 o5 9906 9906 9906 997 II 48 9997 9997 9997 999 8 999 s 9998 II 49 997 9908 9908 9909 999 99 io IO 49 999 8 999 8 9998 9998 9998 9998 10 5o 9-9999 10 9910 9911 9911 9912 99 I2 9 5o 9-999998 999 8 9998 9998 999 s 999 8 9 5i 52 99 i3 99 i5 99I 3 99 i5 99139914 9916 9916 99 i4 9917 99 i5 99 i 7 7 5i 52 9999 9999 9999 9999 9999 9999 9999 9999 9999 9999 9999 9999 8 7 53 99 i8 99 i8 9918 9919 9919 9920 6 53 9999 9999 9999 9999 9999 9999 6 54 99 2O 9920 9921 9921 9922 99 22 5 54 9999 9999 9999 9999 9999 5 55 99 22 99 23 9923 9924 9924 99 24 4 55 o.oooooo oooo oooo oooo oooo oooo 4 56 99 25 99 25 9926 9926 9926 9927 3 56 oooo oooo oooo oooo oooo oooo 3 57 9927 9927 9928 99289929 9929 2 57 oooo oooo oooo oooo oooo oooo 2 58 99 2 9 9930 99 3o 99 3i 9 93i 99 3i I 58 oooo oooo oooo oooo oooo oooo I 5 9 99 32 99 3 2 99 32 9 9 33| 99 33 99 33 O 59 oooo oooo oooo oooo oooo oooo 60" 50" 40" 30" 20" 10" . 60" 50" 40" 30" 20" 10" d Co-sine of 1 Degree. S Co-sine of Degree. .3 s .( 1" 2" 3" 4" 5" 6" 7'' 8" 9" 1 $0000 00 001 p p .< 1" 2" 3" 4" 5" 6" 7" 8" 9" irl Jo ooo oo ooo LOGARITHMIC TANGENTS. 1 Tangent of 88 Degrees. P. Part 7Z 0" 10" 20" 30" 40" 50" tol". o 11.456916 ii .457520 ii. 458i25 II.45873I n.45|338 11.459945 5 9 60.6 I 46o553 46n63 46i 77 3 462383 46^905 4636o8 58 61.1 2 464221 464836 46545i 466067 466684 46 7 3o2 5 7 61.6 3 467920 46854o 469160 469782 4 7 o4o4 4 7 I02 7 56 62.2 4 47i65i 472276 472902 473528 474i56 4 7 4 7 85 55 62. 7 5 4754i4 476044 476676 4773o8 4779^1 4 7 85 7 5 54 63.3 6 479210' 479846 480482 481120 481759 482398 53 63.8 7 483o39 48368o 484323 484966 4856n 486256 52 64.4 8 486902 487549 488198 488847 489497 490148 5i 65.o 9 490800 49i453 492107 492762 493418 494o 7 5 5o 65.5 10 H.494733 11.495392 ii .496052 11.496713 11.497375 11.498038 4 9 66.1 ii 498702 499367 5ooo33 500700 5oi368 5o2o3 7 48 66.8 12 502707 5o33 7 8 5o4o5i 5o4 7 24 5o53 9 8 5o6o 7 3 47 67^4 i3 506750 507427 5o8io6 5o8 7 85 5o 9 466 5ioi48 46 68.0 i4 5io83o 5u5i4 512199 5i2885 5i3572 514260 45 68.6 i5 5i4g5o 5i564o 5i633i 5i 7 o24 517717 5i84i2 44 6 9 .3 16 519108 519805 52o5o3 52I2O2 521903 522604 43 7 o.o J 7 523307 524oio 5247i5 525421 526128 5 2 683 7 42 7 -7 18 52 7 546 528257 528969 529682 53o3 9 6 53iin 4i 7i.i '9 53i828 532545 533264 533984 5347o5 535428 4o 7 2.1 20 n.536i5i 11.536876 11.537602 ii.53833o ii. 539058 11.539-788 3 9 7 2.8 21 54o5i9 54i25i 541984 542 7 i9 543455 544192 38 7 3.5 22 54493o 5456 7 o 5464n 54 7 i53 547896 54864i 37 74.3 23 54 9 38 7 55oi34 55o883 55i63 2 552384 553i36 36 75.0 24 553890 554645 5554oi 556i5 9 556918 55 7 6 7 8 35 7 5.8 25 55844o 559203 559967 56o 7 33 56i5oo 562268 34 76.6 26 563o38 563809 56458i 565355 566 i 3o 5669O 7 33 77 .5 2 7 567685 568464 569245 5 7 OO2 7 5 7 o8n 5 7 i596 32 7 8.3 28 5 7 2382 5 7 3i 7 o 5 7 3 9 5 9 5 7 4 7 5o 5 7 5542 5 7 6336 3i 7 9 .i 2 9 5 77I 3i 5779*8 578726 579525 58o326 58ii28 3o 80.0 3o 11.581932 n.582 7 3 7 n.583544 n.584353 n.585i63 n.5859 7 4 2 9 80.9 3i 586787 5876-01 5884i7 589235 590054 5908-74 28 81.8 32 591696 592520 593345 594172 595000 5 9 583o 2 7 82.8 33 596662 597495 SgSSSo 599166 6oooo4 6oo844 26 83. 7 34 6oi685 602528 603372 604218 6o5o66 605915 25 84. 7 35 606766 6o 7 6i9 608474 609330 6ioi8 7 6iio4 7 24 85. 7 36 611908 6i2 77 i 6i3636 6i45o2 6i53 7 o 616240 23 86.7 3? 617111 61-7985 618860 6i9 7 3 7 620615 621496 22 87.8 38 622378 623262 624147 625o35 625924 626815 21 88.8 3 9 627708 628603 629500 630399 631299 6322OI 2O 89.9 4o n.633io5 ii .634oi2 ii .634919 11.635829 n.636 7 4i n.63 7 655 I 9 91.1 4i 638570 639488 640407 64i329 642252 643i 77 18 92.2 42 644io5 645o34 645 9 65 646899 64 7 834 648 77 i J 7 93.4 43 649711 65o652 65i595 65254i 653488 654438 16 94.6 44 655390 656343 657299 65825 7 6592i 7 6601-79 i5 9 5. 9 45 66u44 662110 663079 664o5o 665o23 665 99 8 i4 97- 2 46 666 97 5 667<}55 668 9 36 669920 6 7 O9O 7 6-71895 i3 9 8.5 4? 672886 673579 6 7 48 7 4 675871 676871 677873 12 oo. 8 48 678878 6 7 9885 680894 681905 682919 683935 II loi.S 49 684954 6859 7 5 686998 688024 689052 690083 IO 102.7 5o ii .691 116 11.692151 ii .693189 ii .694230 11.695273 11.696318 9 104.2 5i 6 97 366 698417 699470 700526 7oi584 -702645 8 105.7 52 703708 704774 705843 706914 707988 709065 7 107.2 53 710144 711226 712311 713398 714488 7 i558i 6 108.9 54 716677 7 i 777 5 718876 719980 721087 -722196 5 no. 5 55 723309 724424 725542 726663 727787 -728914 4 112 2 56 73oo44 731176 7323i2 7 3345i 734592 735737 3 ii4-o 5? 7 36885 7 38o35 7 3 9 i8 9 7 4o346 7 4i5o6 -742669 2 ii5.8 58 743835 745oo4 746177 7 4 7 352 7 4853i 74971 3 I 117.7 5 9 750898 752087 753279 7 544 7 4 7 556 7 2 7 568 7 4 119.7 60" 50" 40" 30" 20" 10" . Co-tangent of 1 Degree. 1 114 AUXILIARY TABLE FOR SINES, & c. 1 1 Degree. 1 1 1 Degree. I 1 log. sin. A log. A". log. tan. A log. A". log. cot A+ log. A". 1 i log. sin. A log. A". log. tan. A log. A". log. cot A+ log. A". o 4.6855 7 5 4.685575 i5.3i4425 60 36oo 4.685553 4.685619 i5.3i438i 60 60 I 5 7 5 5 7 5 425 5 9 366o I 55 2 620 38o 5 9 120 2 5 7 5 5 7 5 425 58 3720 2 55i 622 3 7 8 58 1 80 3 5 7 5 5 7 5 425 57 3 7 8o 3 55i 623 377 57 240 4 5 7 5 5 7 5 425 56 384o 4 55o 625 3 7 5 56 3oo 5 5 7 5 5 7 5 425 55 3900 5 54 9 627 3 7 3 55 36o 6 5 7 5 5 7 5 425 54 3960 6 548 628 3 7 2 54 420 7 5 7 5 5 7 5 4*5 53 4020 7 54 7 63o 3 7 o 53 48o 8 5 7 4 576 424 52 4o8o 8 54 7 63 2 ] 368 52 54o 9 5 7 4 5 7 6 424 5i 4i4o 9 546 6331 36? 5i 600 10 4.6855 7 4 4.6855 7 6 i5.3i4424 5o 4200 10 4.685545 4.685635 i5.3i4365 5o 660 ii 5 7 4 576 424 49 4260 ii 544 63 7 363 49 720 12 5 7 4 5 77 423 48 4320 12 543 638 362 48 780 i3 5 7 4 5 77 423 47 438o 1 3 542 64o 36o 47 84o i4 5 7 4 5 77 423 46 444o i4 54i 642 358 46 900 i5 5 7 3 5 7 8 422 45 45oo i5 54o 644 356 45 960 16 5 7 3 5 7 8 422 44 456o 16 53 9 646 354 44 IO2O r 7 5 7 3 5 7 8 422 43 4620 17 53 9 647 353 43 I080 18 5 7 3 5 79 421 42 468o 18 538 649 35i 42 n4o i 9 5 7 3 5 79 421 4i 474o '9 53 7 65i 349 4i 1 200 20 4.6855 7 2 4.68558o i5.3i442o 4o 48oo 20 4.685536 4.685653 i5.3i4347 4o 1260 21 5 7 2 58o 420 3 9 486o 21 535 655 345 3 9 1320 22 5 7 2 58i 4i 9 38 4920 22 534 65 7 343 38 i38o 23 5 7 2 58i 4i 9 37 4980 23 533 65 9 34i 37 i44o 24 5 7 i 582 4i8 36 5o4o 24 532 661 33 9 36 i5oo 25 5 7 i 583 417 35 5ioo 25 53i 663 33 7 35 i56o 26 5 7 i 583 4i 7 34 5i6o 26 53o 665 335 34 1620 2 7 5 7 o 584 4i6 33 5220 27 52 9 668 332 33 1680 28 5 7 o 584 4x6 32 5280 28 52 7 670 33o 32 1740 29 5 7 o 585 4x5 3i 534o 29 5 2 6 672 3 2 8 3i 1800 3o 4.68556 9 4.685586 i5.3i44i4 3o 54oo 3o 4.685525 4.6856 7 4 i5.3i43 2 6 3o 1860 3i 56 9 58 7 4x3 29 546o 3i 524 676 324 2 9 1920 32 56 9 587 4x3 28 5520 32 5 2 3 679 321 28 1980 33 568 588 4X9 27 558o 33 522 681 3i 9 27 2O4O 34 568 58 9 4n 26 564o 34 521 683 3i 7 26 2IOO 35 56 7 5 9 o 4io 25 5700 35 520 685 3i5 25 2l6o 36 56 7 5 9 i 4o 9 24 5 7 6o 36 5i8 688 312 24 2220 37 566 592 4o8 23 5820 3? 5i 7 690 3io 23 2280 38 566 5 9 3 407 22 588o 38 5i6 6 9 3 3o 7 22 234o 3 9 566 5 9 3 407 21 5940 3 9 5i5 695 3o5 21 s4oo 4o 4.685565 4.6855 9 4 i5.3i44o6 2O 6000 4o 4.6855i4 4.685697 i5.3i43o3 2O 2460 4i 565 5 9 5 4o5 '9 6060 4i 5 I2 700 3oo '9 2520 42 564 5 9 6 4o4 18 6120 42 5n 702 298 18 258o 43 564 5 9 8 4O2 17 6180 43 5io 7 o5 295 17 2640 44 563 5 99 4oi 16 6240 44 5o 9 707 2 9 3 16 2700 45 562 600 4oo i5 63oo 45 5o 7 710 290 i5 2760 46 562 601 3 99 i4 636o 46 5o6 7 i3 287 i4 2820 47 56i 602 3 9 8 i3 6420 47 5o5 7 i5 285 i3 2880 48 56i 6o3 3 97 12 648o 48 5o3 718 282 12 2940 49 56o 6o4 3 9 6 II 654o 49 502 720 280 I I 3ooo 5o 4.68556o 4.6856o5 i5.3i43 9 5 10 6600 5o 4.6855oi 4.685 7 23 i5. 314277 10 3o6o 5i 55 9 607 3 9 3 9 6660 Si 499 726 274 9 3l20 52 558 608 3 9 2 8 6720 52| 4 9 8 729 271 8 3i8o 53 558 6o 9 3 9 i 7 6780 53 497 7 3 i 269 7 8240 54 55 7 6x1 38 9 6 684o 54 495 7 34 266 6 33oo 55 556 612 388 5 6900 55 494 737 263 5 336o 56 556 6i3 387 4 6960 56 492 740 260 4 3420 5 7 555 6i5 385 3 7020 5 7 491 743 257 3 348o 58 554 616 384 2 7080 58 490 7 45 2 55 2 354o 5 9 554 618 38 2 I 7140 5 9 488 748 252 I 'log. cos. A log. eot A log. tan, A-f * log. co. A log. cot A log. tan. A+ log. c. A". log. c. A". log. c. A." 1 log. c. A". log. c. A". log. c. A". s 89 Degrees. .9 53 88 Degrees. .3 LOGARITHMIC TANGENTS, i Tangent of 89 Degrees. P. Part H 0" 10" 20" 30" 40" 50" tol". 11.758079 11.759287 II .760498 ii .761714 II .762932 n. 7 64i54 5 9 121.7 i 7 653 79 766608 767840 769076 77o3i5 77 i558 58 123.8 2 772805 774o55 7753o8 776566 777826 7799 I 5 7 125.9 3 780359 7 8i63i 782907 784186 785470 7 86 7 5 7 56 128.1 4 788047 789342 790641 791943 79325o 79 456o 55 i3o.4 5 79^874 797192 7985i5 799841 801171 8o25o6 54 132.8 6 8o3844 805187 8o6534 807885 809240 810600 53 x55.3 7 811964 8i3332 814704 816081 817462 8i884 7 52 137-9 8 820237 821632 823o3i 824434 825842 8 27 255 5i i4o.6 9 828672 830094 83i52o 832951 834387 835828 5o i43.4 10 11.837273 11.838724 11.840179 ii.84i639 n.843io4 n.844574 4 9 146.2 II 846o48 84?528 849013 85o5o3 85i 999 853499 48 i49.3 12 855oo4 8565i5 858o3i 85 9 553 861079 862611 47 i5 2 .4 i3 864149 865692 867240 868794 870354 871919 46 i55.7 i4 873490 875067 876649 878237 879831 88i43i 45 i5 9 .i i5 883o37 884648 886266 887890 889519 891155 44 162.7 16 892797 894446 896100 897761 899429 901103 43 166.4 17 902783 904470 906163 907863 909569 911283 42 170.3 18 '9 9i3oo3 923469 914730 925239 916464 927015 918205 928799 9 i 99 53 930590 921707 932388 4i 4o 174.4 178.7 20 11.934194 11.936008 ii .937829 11.939658 11.941494 H.943338 3 9 i83.3 21 945191 94?o5 i 948919 950795 952679 954572 38 188.0 22 9 56473 958382 960299 962225 964160 966103 37 193.0 23 9 68o55 970016 97 i 9 86 97 3 9 65 975952 977949 36 198.3 24 97 99 56 981971 983996 9 86o3o 988074 990128 35 203.9 25 992191 994264 996347 99 844o I2.ooo543 12.002657 34 209.8 26 12.004781 12.006915 12.009060 I2.OII2l5 oi3382 oi555 9 33 216.2 27 017747 019946 O22l56 024378 026611 028855 32 222.7 28 o3mi 033379 o3565 9 o3 79 5i o4o255 042672 3i 229.8 2 9 044900 047242 049596 o5i 9 63 o54342 o56 7 35 3o 237.3 3o 12.059142 I2.o6i56i 12.063994 12.066441 12.068902 I2.0 7 l3 77 2 9 245.4 3i o 7 3866 076369 078887 o8i4i 9 083966 o8652 9 28 254.O 32 089106 091699 094308 o 9 6 9 32 099572 102228 27 263.2 33 104901 107590 110296 n3oi9 115760 n85i 7 26 273.2 34 121292 I24o85 126896 129726 132574 i 3544o 25 283.9 35 138326 I4l23l i44i56 147100 i5oo65 i53o5o 24 2 9 5.4 36 i56o56 159082 i62i3o i65i 99 168290 I 7 i4o4 23 3o8.o 37 i7454o 177698 180880 i84o85 i8 7 3i4 I 9 o56 7 22 321.7 38 193845 197148 200476 2o383o 207210 210616 21 336. 7 3 9 2i4o4 9 217510 220998 2245i5 228060 23i635 2O 353.1 4o 12.235239 I2.2388 7 3 12.242538 12.246235 12.249963 I2.253 7 23 '9 371.2 4i 257516 261342 2652o3 269098 2 7 3028 2 7 6 99 5 18 391.3 42 280997 285o37 289115 293232 29 7 388 3oi584 17 4i3.6 43 3o582i Sioioo 3i4422 318787 323196 32 7 65o 16 438. 7 44 332i5i 336698 341294 345939 35o634 . 35538i i5 467.0 45 36oi8o 365o32 369940 374903 379924 385oo4 i4 499.2 46 390143 3 9 5345 400609 4o5 9 38 4n333 4i6 79 6 i3 536.2 4? 422328 427932 4336io 439362 445192 45noo 12 5 7 9i 48 457091 463i65 46 9 3 2 5 475574 481915 48834 9 II 629.4 49 494880 5oi5io 5o8244 5i5o83 522032 529094 10 68 9 .4 5o 12.536273 12.543572 12.550996 12.558549 12.566236 I2.5 7 4o6i 9 5i 582o3o 590148 5 9 842i 6o6854 6i5454 624228 8 52 633i83 642327 651667 661212 6 7 O9 7 2 68o 9 56 7 53 691175 701641 712365 72336o 7 3464i 7 46223 6 54 758122 770357 782946 795911 8o 9 2 7 5 8 2 3o63 5 55 8373o4 852O2 7 867267 , 883o6i 899452 9 i 6485 4 56 934214 952697 972002 992208 i3.oi3395 i3.o356 7 i 3 5 7 i3.o5 9 i53 13.083976 i3.no3o5 i3. 138334 i6829 7 200482 2 58 235244 273032 3i4425 36oi83 4n335 46 9 32 7 I 5 9 5362 7 4 6i5455 712365 83 7 3o4 i4.oi3395 i4.3i4425 60" 50" 40" 30" 90" 10" c Co-tangent of Degree. i 1 16 NATURAL SINES. .5 X 1 2 3 4 5 6 7 8 9 o oooooo 017452 034899 o52336 069756 o8 7 i56 104528 121869 i3 9I7 3 i56434 60 I 0291 7743 5190 2626 070047 7446 48i8 2i58 946i 6722 5 9 2 o582 8o34 548 1 2917 o33 7 77 35 5107 2447 9749 7009 58 3 0873 83 2 5 5 77 2 3207 0627 8025 53 9 6 2 7 35 140037 7296 57 4 1164 8i6 6062 3498 0917 83i5 5686 3024 o325 7584 56 5 1454 8907 6353 3 7 88 1207 86o5 5 97 5 33i3 o6i3 7871 55 6 1745 9197 6644 4079 1497 88 9 4 6264 36oi 0901 8i58 54 7 ao36 9 488 6 9 34 436 9 1788 9184 6553 3890 1189 8445 53 8 2327 9779 7225 466o 2078 9474 6843 4i79 1477 8 7 32 52 9 2618 020070 ?5i6 495o 2368 9763 7132 446 7 1765 9020 5i 10 002909 O2o36i 037806 o5524i 072658 ogooSS 107421 124756 i42o53 159307 5o ii 32OO o652 8097 553i 2948 o343 7710 5o45 234l 9594 49 12 3491 0942 8388 5822 3 2 38 o633 7999 5333 2629 9881 48 i3 3782 1233 8678 6112 35 2 8 0922 8289 5622 2917 160168 47 i4 4072 i5a4 8969 6402 38i8 1212 85 7 8 5 9 io 3 2 o5 o455 46 i5 4363 i8i5 9260 66 9 3 4io8 i5o2 8867 6199 34 9 3 o 7 43 45 16 4654 2106 955o 6983 43 99 1791 9i56 6488 3 7 8o io3o 44 17 4945 2 3 97 984i 7274 468 9 2081 9445 6776 4o68 i3i 7 43 18 5236 2687 o4oi32 7564 4979 2371 9734 7o65 4356 1604 42 '9 552 7 2978 0422 7 854 5269 2660 IIOO23 7353 4644 1891 4i 20 oo58i8 023269 040713 o58i45 o 7 555 9 092950 Iio3i3 127642 144932 162178 4o 21 6109 356o 1004 8435 584n 3 2 3 9 0602 79 3o 5220 a465 3 9 22 63 99 385i 1294 8726 6i3<, 3529 0891 8219 55o 7 2 7 52 38 23 6690 4i4i i585 9016 6429 38i 9 1180 85o 7 5 79 5 3o3 9 37 24 6981 4432 1876 93o6 6719 4io8 1469 8796 6o83 3326 36 25 7272 4723 2166 9 5 97 7009 43 9 8 i 7 58 9 o84 63 7 i 36i3 35 26 7563 5oi4 245 7 9887 7299 468 7 2047 9 3 7 3 6659 3900 34 27 7854 53o5 2 7 48 060177 7 58 9 4977 2336 9661 6946 4i8 7 33 28 8i45 55 9 5 3o38 o468 7879 5267 2625 9949 7334 44?4 32 29 8436 5886 332 9 0758 8169 5556 2914 i3o238 7522 4761 3i 3o 008727 026177 043619 o6io4 9 078459 095846 u32o3 i3o526 147809 i65o48 3o 3i 9017 6468 3910 i33 9 8749 6i35 3492 o8i5 8097 5334 29 32 93o8 6 7 5 9 4201 1629, 9 o3 9 6425 3781 no3 8385 562i 28 33 9 5 99 7049 449i 1920 9 32 9 6 7 i4 4070 i3 9 i 8672 5908 27 34 9890 734o 4782 22IO 9 6l 9 7004 435 9 1680 8960 6i 9 5 26 35 010181 763i 5073 25oo 999 7293 4648 1968 9248 648a 25 36 0472 7922 5363 2791 o8oi 99 7 583 4 9 3 7 2256 9 535 6769 24 3? o 7 63 8212 5654 3o8i o48 9 7872 5226 2545 9 8 2 3 7o56 23 38 io54 85o3 5944 33 7 i 07 7 9 8162 55i5 2833 i5om 7342 22 3 9 1 344 8 79 4 6235 366i io6 9 845 1 58o4 3l2I o3 9 8 762-; 21 4o oii635 029085 o46525 063952 081359 098741 n6o 9 3 i334io i5o686 167916 2O 4i 1926 9 3 7 5 6816 4242 1649 9o3o 6382 3698 o 97 3 8 2 o3 *9 42 2217 9666 7106 453s 1939 9 320 6671 3986 1261 848 9 18 43 25o8 99 5 7 7397 4823 2228 9 6o 9 6960 4274 1 548 8776 7 44 2799 o3o248 7688 5n3 2 5i8 9 8 99 724 9 4563 i836 9 o63 16 45 3090 0539 7978 54c3 2808 100188 7 53 7 485i 2123 9 35o i5 46 338o 0829 8269 5693 3098 o477 7826 5i3 9 2411 9636 i4 4? 36 7 i 1120 855 9 5 9 84 3388 0767 8n5 5427 26 9 8 99 23 i3 48 3962 i4n 885o 6274 36 7 8 io56 84o4 5 7 i6 2 9 86 170209 12 49 4253 1702 9140 6564 3968 1 346 86 9 3 6oo4 32 7 3 o4 9 6 II 5o oi4544 031992 o4943i o66854 o84258 ioi635 118982 136292 i5356i 170783 10 5i 4835 2283 9721 7i45 4547 1924 9270 658o 3848 1069 9 52 5i26 25 7 4 o5ooi2 7435 483 7 22l4 9 55 9 6868 4i36 i356 8 53 54i6 2864 0302 7725 5127 25o3 9 848 7 i56 4423 i643 7 54 5 7 o 7 3i55 oSgS 8oi5 54i7 2793 120137 7445 4710 1929 6 55 5998 3446 o883 83o6 5707 3082 0426 77 33 4998 2216 5 56 6289 3 7 3 7 H74 8596 5997 33 7I 0714 8021 5285 a5o2 4. 5 7 658o 4027 1 464 8886 6286 366i ioo3 83o 9 55 7 2 3789 3 58 6871 43i8 i 7 55 91761 6576 3 9 5o 1292 8597 586o 8075 a 5 9 7162 4609 2o45 9466J 6866 423 9 i58i 8885 6147 3362 i 89 88 87 86 85 84 83 82 81 80 fl Natural Co-sines. ifl S P. P. , ., tol> 85 4.85 4.84 4.84 4.83 4.83 4.82 4.8i 4.8o 4.78 NATURAL TANGENTS. 117 1 1 2 3 4 5 6 7 8 9 o oooooo 017455 034921 o524o8 o6 99 27 087480. io5io4 122785 i4o54i i58384 60 I 0291 7746 5212 26 99 O7O2I 9 7782 53 9 8 3o8o o83 7 8683 5 9 2 o582 8037 55o3 2 99 I o5u 8o 7 5 56 9 2 33 7 5 n34 8 9 8i 58 3 o8y3 8328 5 79 5 3283 0804 8368 5987 36 7 o i43i 9 2 79 5 7 4 n64 8619 6086 35 7 5 io 9 6 8661 6281 3 9 66 1728 9 5 77 56 5 i454 8910 63 77 3866 i38 9 8 9 54 65 7 5 4261 2024 9 8 7 6 55 6 1745 9201 6668 4i58 1681 9 248 686 9 455 7 2321 160174 54 7 2o36 9492 6960 445o I 97 3 9 54i 7i63 485 2 2618 0472 53 8 2327 9783 7 25l 4742 2266 9 834 7458 5:47 2 9 l5 0771 52 9 2618 020074 7542 5o33 2558 O 9 OI27 77 5 2 5443 3212 iofi 9 5i 10 002909 020365 o3 7 834 o")5325 072851 O 9 o42I io8o46 i25 7 38 i435o8 i6i368 5o ii 32OO o656 8i 2 5 56i 7 3i43 07l4 834o 6o34 38o5 1666 49 12 3491 0947 84i6 5 9 o 9 3435 IOO7 8635 632 9 4lO2 i 9 65 48 i3 3782 1238 8707 6200 3 7 28 i3oo 8 9 2 9 6625 43 99 2263 47 i4 4072 l52 9 8999 64 9 2 4O2O i5 9 4 9 223 6 9 2O 46 9 6 2562 46 i5 4363 1820 9290 6 7 84 43i3 1887 9 5i8 7216 4 99 3 2860 45 16 4654 2III 958i 7076 46o5 2180 9 8l2 75i2 52 9 o 3i5 9 44 I? 4945 24O2 9 8 7 3 7368 48 9 8 2474 110107! 7807 558 7 3458 43 18 5236 2693 o4oi64 7660 5i 9 o 2767 o4oil 8io3 5884 3 7 56 42 J 9 55 2? 2 9 84 o456 7 9 5i , 5483 3o6i o6 9 5 83 99 6181 4o55 4i 20 oo58i8 O23275 040747 o58243 075775 o 9 3354 no 99 o i286 9 4 146478 164354 4o 21 6109 3566 io38 8535 6068 3647 1284 8 99 o 6776 4652 3 9 22 64oo 385 7 i33o 8827 636i 3 9 4i i5 79 9 286 7 o 7 3 4 9 5i 38 23 6691 4i48 1621 9 u 9 6653 4234 i8 7 3 9 582 7 3 7 o 5 2 5o 37 24 6981 443 9 1912 9 4n 6 9 46 4528 2168 9877 7667 554 9 36 25 7272 473i 2204 97 3 7238 4821 2463 130173 7 9 64 5848 35 26 7563 5022 2495 999 5 7 53i 5n5 2 7 5 7 o46 9 8262 6147 34 2 7 754 53i3 2787 060287 7824 54o8 3o52 0765 855 9 6446 33 28 8i45 56o4 3078 o5 79 8116 5702 3346 1061 8856 6 7 45 32 2 9 8436 58 9 5 3370 0871 84o 9 5 99 5 364i i357 9 i54 7044 3i 3o 008727 026186 o4366i 061 i63 078702 o 9 628 9 n3 9 36 i3i65 2 i4 9 45i 167343 3o 3i 9018 6477 3952 i455 8 99 4 6583 4230 i 9 48 9748 7642 29 32 9309 6768 4244 1747 9 28 7 6876 45 2 5 2244 i5oo46 79 4i 28 33 9600 7 o5 9 4535 2 o3 9 9 58o 7170 4820 254o o343 8240 27 34 9891 735o 4827, 233i 9 8 73 7464 5n4 2836 o64i 853 9 26 35 010181 764i 5n8 : 2623 o8oi65 77 5 7 54o 9 3i32 o 9 38 8838 25 36 0472 7 9 33| 54io 2 9 l5 o458 8o5i 5704 3428 1236 9 i3 7 24 3? o 7 63 8224' 5701 3207 0751 8345 5 999 3 7 25 i533 943 7 23 38 io54 85i5 5993 34 99 io44 8638 62 9 4 4021 i83i 9736 22 3 9 1 345 8806 6284 3 79 i i336 8 9 32 6588 43i 7 2I2 9 170035 21 4o on636 029097 o465 7 6 o64o83 o8i62 9 99 226 n6883 i346i3 152426 I 7 o334 20 4i 1927 9388 6867 43 7 5 I 9 22 9 5i 9 7178 4 9 o 9 2724 o634 *9 42 2218 9679 7 i5 9 466 7 22l5 9 8i3 7 4 7 3 5 2 o5 3022 o 9 33 18 43 2509 997 7 45o 4 9 5 9 25o8 100107 7768 55o2 33i 9 1233 *7 44 2800 O3O262 77^2 5 2 5i 2801 o4oi 8o63 5 79 8 36i 7 i532 16 45 3091 o553 8o33 5543 3o 9 4 o6 9 5 8358 6o 9 4 3 9 i5 i83i i5 46 3382 o844 8325 5836 3386 o 9 8 9 8653 63 9 o 42l3 2l3l i4 4? 3673 n35 8617 6128 36 79 1282 8 9 48 6687 45io 2 43o i3 48 3 9 64 1426 8 9 o8 6420 3 97 2 1576 9 243 6 9 83 48o8 2730 12 49 4254 1717 9 200 6712 4265 1870 9 538 7 2 79 5io6 3o3o II 5o oi4545 032009 o4 9 4 9 i 067004 o84558 102164 n 9 833 i3 7 5 7 6 i554o4 I? 332 9 IO 5i 4836 23oo 97 83 7 2 9 6 485 1 2458 120128 7872 5702 362 9 9 52 5127 2 5 9 i o5oo75 ?58 9 5i44 2752 o423 8i6 9 6000 3 9 2 9 8 53 54i8 2882 o366 7881 543 7 3o46 0718 8465 62 9 8 4228 7 54 5 7 o 9 3 I7 3 o658 8173 5730 334o ioi3 8761 65 9 6 45 2 8 6 55 6000 3465 o 9 4 9 8465 6o23 3634 i3o8 9 o58 68 9 4 4828 5 56 6291 3 7 56 1241 8758 63i6 3 9 28 1604 9 354 7 I 9 2 5127 4 5 7 6582 4o47 i533 9 o5o 66o 9 4222 i8 99 9 65i 7 4 9 o 542 7 3 58 68 7 3 4338 1824 9 342 6 9 O2 45i6 2I 9 4 9948 7788 5727 2 5 9 7164 463o 2116 9 635 7 i 9 6 48io 248 9 i 40244 8086 6027 I 89 88 87 86 85 84 83 82 81 ' 80 Natural Co-tangents. * to r'> 85 4.85 4.86 4.8 7 4.88 4-8 9 4. 9 i 4- 9 3 4- 9 6 4. 9 8 lib NATURAL SINES. i 10 11 12 13 14 15 16 17 18 19 o i 7 3648 190809 207 9 I2 224 9 5l 24l 9 22 2588i 9 275637 292872 3o 9 oi7 325568 60 i 3 9 35 1095 8196 5234 2204 9 ioo 5 9 i 7 265o 9 2 9 4 5843 5 9 2 4221 i38o 848 1 55i8 2486 9 38i 6i 97 2928 9 5 7 6118 58 3 45o8 1666 8 7 65 58oi 2 7 6 9 9 662 6476 3206 9 847 63 9 3 5 7 4 4794 I 9 5i 9 o5o 6o85 3o5i 99 43 6 7 56 3484 3ioi23 6668 56 '5, 5o8o 2237 9 334 6368 3333 260224 7 o35 3 7 62 o4oo 6 9 43 55 6 5367 2522 9 6l 9 665 1 36i5 o5o5 7 3i5i 4o4o 0676 7218 54 7 5653 2807 99 3 6 9 35 38 97 o 7 85 7 5 9 4 43i8 o 9 53 7 4 9 3 53 8 5^39 3o 9 3 210187 7218 4i 79 1066 7874 45 9 6 I22 9 77 68 52 9 6226 33 7 8 0472 7 5oi 446i 1 347 8i53 48 7 4 i5o6 8042 5i 10 176512 i 9 3664 210756 227784 s44 7 43 261628 278432 2 9 5l52 311782 3 2 83i 7 5o ii 6798 3949 io4o 8068 0025 I 9 o8 8712 543o 2o5 9 85 9 2 49 12 7o85 4234 13-25 835i 53o 7 2i8 9 8 99 i 5 7 o8 2335 886 7 48 i3 7 3 7 i 452o i6o 9 8634 558 9 2470 9 2 7 5 9 86 2611 9 i4i 4? i4 7 65 7 48o5 i8 9 3 8917 58 7 i 2751 9 55o 6264 2888 9 4i6 46 i5 7044 5090 2178 9200 6i53 3o3i 9 82 9 6542 3i64 9 6 9 i 45 16 823o 53 7 6 2462 9484 6435 33i2 280108 68i 9 344o 99 65 44 '7 85i6 566i 2746 9767 6717 35 9 2 o388 7097 3 7 i6 33o24o 43 18 8802 5 9 46 3o3o 23oo5o 6 999 38 7 3 0667 7 3 7 5 3 99 2 o5i4 42 *9 9088 623i 33i5 o333 7281 4i54 o 9 46 7 653 426 9 0-789 4i 20 179375 I 9 65i7 2i35 99 23o6i6 247563 264434 281225 2 9 7 9 3o 3i4545 33io63 4o 21 9661 6802 3883 0899 7 845 47i5 i5o4 8208 4821 i338 3 9 22 9947 7087 4i6 7 1182 8126 4 99 5 i 7 83 8486 5o 97 1612 38 23 i8o233 7 3 7 2 445 1 i465 84o8 5276 2062 8763 53 7 3 i88 7 37 24 0519 7 65 7 4735 1748 86 9 o 5556 234l _ 9 o4i 564 9 2161 36 25 o8o5 7942 5oi 9 2031 8 97 2 5~83 7 2620 9 3i8 5 9 25 2435 35 26 1091 8228 53o3 23i4 9 253 61 17 2900 9 5 9 6 6201 2 7 IO 34 27 i3 77 85i3 5588 2 5 97 9 535 63 97 3i 79 9 8 7 3 64 77 2984 33 28 i663 8 79 8 58 7 2 2880 9 8i 7 6678 345 7 3ooi5i 6 7 53 3258 32 29 1950 9 o83 6i56 3i63 25oo 9 8 6 9 58 3 7 36 0428 7 O2 9 3533 3i 3o 182236 I 99 368 216440 233445 25o38o 267238 28401 5 800706 3n 7 3o5 3338o 7 3o 3i 2522 9 653 6724 3 7 28 0662 7 5i 9 4294 0983 7 58o 4o8i 2 9 32 2808 99 38 7008 4oi i o 9 43 7799 45 7 3 1261 7 856 4355 28 33 3094 20O223 7 2 9 2 42 9 4 1225 8o 79 4852 i538 8i3 2 4629 2 7 34 33 7 9 o5o8 7 5 7 5 45 77 i5o6 835 9 5i3i i8i5 84o8 4903 26 35 3665 o 79 3 7 85 9 485 9 1788 864o 54io 2093 8684 5i 7 8 25 36 3 9 5i 1078 8i43 5i42 2o6 9 8 9 20 5688 2870 8 9 5 9 5452 24 3? 423 7 1 363 8427 5425 235i 9 2OO 5 9 6 7 2647 9 235 5 7 26 23 38 4523 1 648 8711 5708 2632 9 48o 6246 2924 9 5u 6000 22 3 9 4809 i 9 33 8 99 5 5990 2 9 l4 9760 6525 3202 97 86 6274 21 4o 185095 202218 2I 9 27 9 236273 253i 9 5 270040 286803 3o3479 320062 336547 2O 4i 538i 2502 9 562 6556 3477 0320 7082 3756 o337 6821 J 9 42 5667 2787 9 846 6838 3 7 58 0600 7 36i 4o33 o6i3 7 o 9 5 18 43 5 9 5 2 3072 22Ol3o 7121 4o3 9 0880 7 63 9 43io 0889 7 36 9 '7 44 6238 335 7 o4i4 ?4o3 4321 1160 79 i8 45'S7 1 1 64 7 643 16 45 6524 3642 o6 9 7 7686 4602 i44o 8i 9 6 4864 i43 9 79 i7 i5 46 6810 392 7 o 9 8i 7968 4883 1720 84 7 5 5i4i 1715 8i 9 o i4 4 7 7096 4211 1265 25l 5i65 2000 8 7 53 54i8 1990 8464 i3 48 7 38i 4496 1 548 8533 5446 2280 9 o32 56 9 5 2266 8 7 38 12 49 7667 4 7 8i i832 8816 5727 256o 9 3io 5972 254i 9 OI2 II 5o 187953 2o5o65 222116 239098 256oo8 272840 28 9 58 9 3o624 9 322816 33 9 285 IO 5i 8238 535o 23 99 9 38i 6 2 8 9 3l20 9 86 7 65 2 6 3092 9 55 9 9 52 8524 5635 2683 9 663 65 7 i 3400 2 9 oi45 6So3 336 7 9 83 2 8 53 8810 5 9 2O 2 9 6 7 9946 6852 36 7 9 0424 7 )8o 3642 34oio6 7 54 9095 6204 325o 240228 7 i33 3 9 5 9 O 7 O2 ?35 7 3 9 i 7 o38o 6 55 9 38i 648 9 3534 o5io 74i4 423 9 o 9 8i 7 633 4i 9 3 o653 5 56 9667 6 77 3 3817 o 79 3 7 6 9 5 45i 9 I25 9 7 9 io 4468 9 2 7 4 57 99 52 7 o58 4ioi 1075 797 6 4798 i53 7 8187 4743 1200 3 58 190238 ?343 4384 i357 825 7 5o 7 8 i8i5 8464 5oi8 i4 7 3 2 5 9 o523 762-7 4668 i64o 8538 5358 20 9 4 8740 52 9 3 1747 i 79 78 77 76 75 74 73 ; 72 71 70 . 1 Natural Co-sines. #4.77 | 4. 7 5 4.73 4. 7 i 4.6 9 4.67 4.65 4.62 4.6o 4.5 7 NATURAL TANGENTS. 1 19 J I 10 11 12 13 14 15 16 17 18 19 i 7 632 7 i 9 438o 212667 23o868 249328 2 67 9 4 9 286 7 45 3o5 7 3i 324920 344328 60 I 662 7 4682 2861 1176 9637 8261 7 o6o 6o4g 6241 4653 69 2 6 9 2 7 4984 3i65 i48i 9946 85 7 3 7 3 7 5 636 7 5563 4978 58 ^ 7 22 7 6286 346 9 1788 8885 7 6 9 o , 6685 5885 53o4 57 ^ 7627 5588 3 77 3 209^ 066^ 9197 8oo5 7 oo3 620-7 563o 56 f 7 82 7 6890 4077 2401 0873 8320 7 322 6628 5 9 55 55 6 8l2 7 6192 438i 2707 ii83 9821 8635 7 64o 685o 6281 54 7 8427 6494 4686 3oi4 1492 270133 8 9 5o 7969 -71-72 6607 53 8 8727 6796 4990 332i 1801 o445 9 266 82 77 6 9 33 62 9 9028 7099 629^ 362 7 2III 0767 9 58i 8696 7817 7269 5i 10 179328 197401 216699 233934 262420 271069 28 9 8 9 6 308914 328139 34 7 585 5o ii 9628 773 5 9 o3 4241 2729 i382 2 9 02I I 9233 846 1 7911 4 9 12 9928 8oo5 6208 4548 i6" 9 4 o52 7 9662 8 7 83 8 2 3 7 48 i3 180229 83o8 6612 4855 3348 2006 0842 9871 9106 8563 47 i4 0629 8610 6817 6162 3658 2319 1168 310189 9428 8889 46 1 5 0829 8912 7121 546 9 3 9 68 2 63i i4 7 3 0608 9-761 9216 45 16 n3o 9216 7426 6776 4277 2944 1789 082-7 33oo 7 3 9642 44 1-7 i43o 9617 77 3i 6o83 458 7 3 2 56 2106 u46 0396 9868 43 18 I 7 3i 9820 8o35 6390 48 97 356 9 2420 i465 0-718 360196 42 '19 2031 200122 834o 6697 6207 3882 2 7 36 i 7 84 io4i 0622 4i 20 182332 2OO425 2x8645 237004 266616 274194 2 9 3o52 3i2io4 33i364 35o848 4o 21 2632 0727 8960 7312 6826 4607 3368 2423 1687 1176 3 9 22 2 9 33 io3o 9264 7619 6i36 4820 3684 2 7 42 2OIO 1602 38 23 3234 i333 9669 7926 6446 5i33 4ooo 3o62 2333 1829 37 24 3534 i635 9864 8234 6 7 56 5446 43i6 338i 2666 2166 36 25 3835 1938 220169 854i 7 o66 6769 4632 3 7 oo 2979 2483 35 26 4i36 224l 0474 8848 7377 6072 4 9 48 4020 3302 2810 34 27 443 7 2 544 0779 9166 7 68 7 6385 6266 4340 36 2 5 3i3 7 33 28 4 7 3 7 2847 1084 9464 7997 6698 6681 4669 3 9 4 9 3464 32 29 5o38 3149 i38 9 9771 83o 7 7011 58 97 4979 3 79 i 3i 3o i85339 203462 221696 268618 277326 296213. 316299 334696 354119 3o 3i 564o 3766 2OOO o386 8928 7 638 653o 6619 4 9 i 9 4446 2 9 32 694 1 4o58 23o5 o6g4 9238 7961 6846 5 9 3 9 6242 4 77 3 28 33 6242 436i 2610 1 002 9 54 9 8266 7 i63 6268 5566 5ioi 2 7 34 6543 4664 2916 i3io 9869 8678 7480 65 7 8 58 9 o 6429 26 35 6844 4967 3221 1618 2601-70 8891 7796 6899 62i3 6766 25 36 7i45 6271 3526 1926 o48o 9206 8n3 -7219' 653 7 6084 24 37 7446 55 7 4 383 2 2233 o 79 i 9619 843o 7 53g 6861 6412 23 38 7747 58 77 4i3 7 2641 1 1 02 9 83 2 8 7 4 7 7869 -7186 6740 22 3 9 8o48 6180 4443 2849 i4i3 280146 9063 81-79 7^09 7068 21 4o 188349 206483 224748 243167 261-723 280460 299380 3i85oo 33 7 833 35 7 3 9 6 2O 4i 865i 6787 5o54 3466 2o34 o 77 3 9697 8820 8167 77 2 4 '9 42 8962 7090 536o 3 77 4 2345 1087 3oooi4 9i4i 848 1 8062 18 43 9263 7 3 9 3 5665 4082 2666 i4oi o33i 946i 8806 838o '7 44 9 555 7697 6971 4390 2 9 6 7 1716 0649 97 8 2 9 i3o 8708 16 45 9866 8000 6277 4698 32 7 8 2029 0966 32oio3 9 454 9 3 7 i5 46 190167 83o4 6583 6007 358 9 2343 1283 0423 9779 9365 i4 47 0469 8607 6889 53i5 3 9 oo 2667 1600 o 7 44 34oio3 9694 i3 48 0760 8911 7194 6624 421 1 2971 1918 1066 0428 360O22 12 49 1062 9214 5 9 3 2 4523 3 2 86 2235 i386 0762 o35i II 5o I 9 i363 209618 227806 246241 264834 2836oo 302553 32I 7 O 7 341077 360679 IO 5i 1666 9822 8112 654 9 5i45 3 9 i4 28-70 2028 I4O2 1008 9 52 1966 210126 84i8 6858 545 7 422 9 3i88 2349 1727 i33 7 8 53 2268 0429 8724 7166 5 7 68 4543 35o6 26-70 2062 1666 7 54 2670 o 7 33 9o3i 7476 6o 79 485 7 3823 2991 2377 1996 6 55 2871 1037 9 33 7 7784 63 9 i 5l 7 2 4i4i 33i2 2702 2324 5 56 3i 7 3 i34i 9 643 8o 9 2 6 7 O2 548 7 4469 3634 3027 2 653 4 5 7 3475 1 645 9949 84oi 7 oi4 6801 4777 3 9 55 3352 2982 3 58 3 777 1949 230266 8710 7 326 6116 6096 42 77 36 7 7 33i2 2 5 9 4078 2253 0562 9019 7 63 7 643i 54i3 4698 4002 364i I 79 78 ! 77 76 75 74 73 72 ! 71 70 a Natural Co-tangents. i * 5.o5 6.09 5.i3 5.i 7 5.22 5.2 7 5.33 5.3 9 5.46 120 NATURAL SINES. J X 20 21 22 23 24 25 26 27 28 29 | o 342020 358368 3 7 46o 7 3 9 073i 4o6 7 3 7 422618 4383 7 i 453 99 o 46 9 4 7 2 484 10 60 I 2293 864o 48 7 6 999 7002 2882 8633 425o 97 28 5o64 So 2 256 7 8911 5i46 1267 7268 3i45 88 9 4 45o 9 99 85 53i8 58 3 2840 9 i83 54i6 i534 ?534 34o 9 9 i55 4 7 68 4 7 0242 55 7 3 57 4 3n3 9454 5685 1802 7799 36 7 3 9 4i7 502 7 o4 99 58 27 56 5 338 7 97 25 5 9 55 2070 8o65 3 9 36 9 6 7 8 5286 o 7 55 6081 55 6 366o 9997 6224 233 7 833o 4i 99 99 3 9 5545 1012 6335 54 7 3 9 33 360268 64g4 26o5 85 9 6 4463 44O200 58o4 1268 65 9 o 53 8 4206 o54o 6 7 63 2872 8861 4 7 26 0462 6o63 i5 2 5 6844 52 9 4479 0811 7 o33 3i4o 9 !2 7 4 99 o 7 23 6322 1-782 7 o 9 8 5i 10 344752 361082 3 77 3o2 3 9 34o 7 4o 9 3 9 2 425253 44o 9 84 45658o 4 7 2o38 48 7 35 2 5o ii 5o25 i353 75 7 i 3675 9 658 55i6 1245 6839 22 9 4 7606 49 12 5298 i6 2 5 784i 3 9 42 99 23 5 779 i5o6 7098 2 55i 7 86o 48 i3 55 7 i 1896 8110 420 9 4ioi88 6042 i 7 6 7 7 35 7 28o 7 8n4 47 i4 5844 2l6 7 83 7 9 4477 o454 63o6 2028 76i5 3o63 836 7 46 i5 6117 2438 8649 4744 07i 9 656 9 228 9 7874 3320 8621 45 16 6390 2 7 9 8918 5on o 9 84 6832 2 55o 8i33 35 7 6 88 7 5 44 I? 6663 2980 9187 52 7 8 I24 9 7 o 9 5 2810 83 9 i 3832 9 i2 9 43 18 6 9 36 325i 9 456 5546 i5i4 7358 3o 7 i 865o 4o88 9 382 42 J 9 7208 3522 97 25 58i3 i77 9 7621 3332 8908 4344 9 636 4i 20 34748i 363 7 93 379994 3 9 6o8o 4i2o45 427884 4435 9 3 45 9 i66 4 7 46oo 48 9 8 9 o 4o 21 77 54 4o64 380263 634 7 23lO 8i47 3853 9425 4856 4 9 oi43 3 9 22 8027 4335 o532 66i4 2 5 7 5 84io 4n4 9 683 5lI2 o3 97 38 23 8299 46o6 0801 6881 2840 8672 43 7 5 9942 5368 o65o 37 24 85 7 2 4877 1070 7i48 3io4 8 9 35 4635 460200 5624 o 9 o4 36 25 8845 5i48 i33 9 74i5 336 9 9 i 9 8 48 9 6 o458 588o n5 7 35 26 9117 54i8 1608 7682 3634 9 46i 5i56 0716) 6i36 i4n 34 27 9 3 9 o 568 9 1877 7949 38 99 9723 54i 7 0974 6392 1 664 33 28 9662 5 9 6o 2146 82i5 4i64 99 86 56 77 1232 6647 I 9 i 7 32 29 99 35 623i! 24i5 8482 442 9 43o24 9 5 9 3 7 1491 6903 2I 7 3i 3o 350207 3665oi 382683 3 9 8 7 4 9 4i46 9 3 43o5n 446i 9 8 461749] 4771^9 4 9 s424 3o 3i o48o 6772 2 9 52 9 oi6 4 9 58 0774 6458 2007, 7 4i4 2 6 77 2 9 32 0752 7042 3221 9 283 5223 io36 6 7 i8 2265| 7670 2 9 3o 28 33 IO25 7 3i3 34 9 o 9 54 9 548 7 i2 99 6 979 2523- 7925 3i83 27 34 1297 7 584 3758 9 8i6 5752 i56i 7 23 9 2780' 8181; 3436 26 35 i56 9 7854 4027 400082 6016 1823 74 99 3o38 r 8436 368 9 25 36 1842 8i25 42 9 5 o34 9 6281 2086 775 9 32 9 6 86 9 2; 3 9 42 24 37 2Il4 83 9 5 4564 0616 6545 2348 8oi 9 ! 3554! 8 9 47 4i 9 5 23 38 2386 8665 4832 0882 6810 2610 827 9 ' 38i2 9 2o3 4448 22 3 9 2658 8 9 36 5ioi n4 9 7074 2873 853 9 i 4o6 9 9 458 4 7 oo 21 4o 352 9 3i 36 9 2o6 38536 9 4oi4i5 4i 7 338 433i35 4487 99 464327 47 9 7i3 4 9 4 9 53 20 4i 3 2 o3 9 476 5638 1681 7603 33 97 9 o5 9 ' 4584 99 68 5206 '9 42 3475 9747 5 9 o6 i 9 48 7867 365 9 9 3i 9 4842 480223' 545 9 18 43 3 7 4 7 370017 6i 7 4 2214 8i3i 3 9 2I 9 5 79 5ioo o4 79 i 5 7 n '7 44 4019 0287 6443 2480 83 9 6 4i83 9 83 9 535 7 o 7 34 5 9 64 16 45 4291 o55 7 6711 2 7 4 7 8660 4445 45oo 9 8 56i5 o 9 8 9 621-7 i5 46 4563 0828 6 979 3oi3 8 9 24 4707 o358 58 7 2 1244 646 9 i4 47 4835 io 9 8 7247 32 79 9 i88 4 9 6 9 0618 6129 1499 67,2 i3 48 5io 7 i368 75i6 3545 9 45 2 5 2 3i 0878 6387 i 7 54 6 97 4 12 49 53 79 i638 7784 38n 97 i6 54 9 3 ii3 7 6644 2OO 9 -7226 II 5o 35565i 37i 9 o8 388o52 4o4o 7 8 4i 99 8o 435 7 55 45i3 97 466901 482263 497479 10 5i 5 9 23 2178 8320 4344 420244 6017 i656 7i58 25i8 773i 9 52 6194 2448 8588 46io o5o8 6278 I 9 i6 7416 2773 79 83 8 53 6466 2718 8856 48 7 6 77 2 654o 2175 7 6 7 3 3o28 8236 7 54 6 7 38 2 9 88 9 I24 5:42 io36 6802 2435 79 3o 3282 8488 6 55 7010 3258 9 3 9 2 54o8 i3oo 7 o63 26 9 4 8187 353 7 8 7 4o 5 56 7281 3528 9 66o 56 7 3 i563 7 3 2 5 2 9 53 8444 3 79 2 8 99 2 4 57 7 553 3797 99 28 5 9 3 9 l82 7 7 58 7 32i3 8701 4o46 9 244 3 58 7825 4o6 7 3 9 oi 9 6 62o5 20 9 I 7 848 3472 8 9 58 43oi 9 4 9 6 2 5 9 8096 433 7 o463 64 7 i 2355 8110 3 7 3r 9 2l5 /i 5 5 5 97 48 I 69 68 67 66 65 64 63 62 61 60 d Natural Co-sines. 4.54 4.5i 4-48 4 45 4.4i 4.38 4.34 4.3o 4.26 4.23 ) NATLRAL TANGENTS. 121 E 20 21 22 23 24 25 26 27 28 29 363970 383864 404026 4244 7 5 445229 4663o8 48 77 33 5o 9 525 531709 554309 60 I 43oo 4198 4365 48i8 55 77 6662 8o 9 3 9892 2o83 468 9 5 9 2 4629 4532 4703 5i62 5926 7016 8453 5io258 2456 5070 58 3 4 9 5 9 4866 5o4a 55o5 62 7 5 7 3 7 i 88i3 0625 2829 545o 57 4 5 2 88 5200 538o 584 9 6624 7725 9174 0992 32o3 583i 56 5 56i8 5534 5 7 i 9 6i 9 2 6 97 3 8080 9 534 i35 9 35 77 6212 55 6 5 9 48 5868 6o58 6536 7 322 8434 9 8 9 5 I 7 26 3950 65 9 3 54 7 6278 6202 63 97 6880 7 6 7 i 8789 490256 2093 4324 6974 53 8 6608 6536 6736] 7224 8020 9 i44 0617 2460 4698 7355 52 9 6 9 38 68 7 i 7075 7 568 836 9 9499 0978 2828 5072 7736 5i 10 367268 38 7 2o5 407414 42 79 I2 448-719 46 9 854 491339 5i3ig5 535446 558n8 5o ii 7 5 9 8 7540 77 53 8 2 56 9d68 47O20 9 1700 . 3563 582i 8499 49 12 79 28 7 8 7 4 8092 8601 9 4i8 o564 2061 3g3o 6i 9 5 8881 48 i3 8259 8209 8432 8 9 45 97 68 0920 2422 4298 65 7 o 9263 47 i4 858 9 8544 8 7?I 9289 45on 7 1275 2784 4666 6 9 45 9 645 46 i5 8919 8879 911 1 9 634 o46 7 i63i 3i45 5o34 7 3i 9 560027 45 16 9250 9214 9 45o 9979 081-7 1986 35o7 54o2 76 9 4 0409 44 l l 9 58i 9549 9-790 43o323 n6 7 2342 386 9 5 77 o 8o6 9 0791 43 18 9911 9884 4ioi3o 0668 i5i 7 2698 423l 6i38 8445 1174 42 !Q 370242 390219 o4 7 o ioi3 1868 3o54 45 9 3 65o 7 8820 i556 4i 20 3 7 o5 7 3 390554 4 i 0810 43i358 4522i8 473410 4 9 4 9 55 5i68 7 5 53 9 i 9 5 561939 4o 21 0904 0889 n5o I 7 o3 2568 0766 53i 7 7244 9^7! 2322 3 9 22 1235 1225 i4go 2048 2919 4l22 56 79 7 6i3 9946 2 7 o5 38 23 i566 i56o i83o 23g3 3269 4478 6042 -7982 54o22 3o88 37 24 1897 1896 2I 7 2 7 3 9 3620 4835 64o4 835i o6 9 8 347i 36 25 2228 223l 25ll 3o84 3 97 i Sigi 6767 8 7 20 1074 3854 35 26 2559 256 7 285i 343o 4322 5548 7i3o 9089 i45o 4238 34 27 2890 2903 3192 3 77 5 46 7 3 5 9 o5 7 4 9 2 9 458 1826 4621 33 28 3222 3 2 3 9 3532 4l2I 5o24 6262 7 855 9 828 2203 5oo5 32 29 3553 35 7 4 38 7 3 446 7 53 7 5 6619 8218 52019-7 2570. 538 9 3i 3o 3 7 3885 414214 434812 455 7 26 476976 4 9 8582 52o56 7 542956 565 77 3 3o 3i 4216 4247 4554 5i58 6o 7 8 7 333 8 9 45 o 9 3 7 3332 6i5 7 2 9 32 4548 4583 48 9 5 55o4 642 9 7690 9 3o8 i3o 7 3 7 o 9 654i 28 33 488o 4919 5236J 585o 6 7 8i 8047 0672 i6 77 4o86 6 9 25 27 34 6211 5255 55 77 619-7 7 l32 84o5 5ooo35 2O4 7 4463 73io 26 35 5543 55 9 a 5919 6543 7 484 8762 0399 2417 484o 769.4 25 36 58 7 5 5928 6260 6889 7 836 9120 0763 2787 5218 8079 24 37 6207 6265 6601 7 236 8188 9477 1 127 3i58 55 9 5 8464 23 38 653 9 6601 6 9 43 7 582 854o 9 835 1491 3528 5 97 3 8849 23 3 9 . 6872 6 9 38 7284 7929! 8892 480193 i855 3899 635o 9234 21 4o 377204 3 97 2 7 5 4i 7 626 438276 459244! 48o55i 502219 524270 546 7 28 569619 2O 4i 7 536 7611 7967 8622 9596 0909 2583 464i 7106 570004 19 42 7869 7948 83o 9 8969! 9949 1267 2948 5012 7484 0390 18 43 8201 8 2 85 865i 9316 46o3oi 1626 33i2 5383 7862 0776 T 7 44 8534 8622 8 99 3 9 663 o654 io8/ 3677 5 7 54 8240 1161 16 45 8866 8960 9 335 44oon 1006 234J 4o4i 6i25 8619 i547 i5 46 9199 9297 9677 o358 i35 9 2 7 oi 44o6 6497 8997 1933 i4 47 9 532 9 63/ 4200I 9 0705 I 7 I2 3o6o 4771 6868 9876 23ig i3 48 9864 9971 o36i io53| 2o65 3419 5i36 7240 97 55 2705 12 49 380197 o 7 oZ i4oo 2418 3 77 8 55o2 7612 55oi34 3092 II 5o 38o53o 4oo646 421046 441748 462771 5o586 7 527984 55o5i3 5734-78 IO 5i o863 0984 i38 9 2095! 3i24 44 9 6 6232 8356 o8 9 2 3865 9 5a 1196 1322 I 7 3i 24^3 3478 4855 65 9 8 8728 1271 4252 8 53 i53o 1660 20 7 4 2791 383i 5 2 i4 6963 9100 i65o 4638 7 54 i863 1997 24l7 3i3 9 4i85 55 7 4 7329 9473 2o3o 5026 6 55 2196 2335 2 7 59 3487 4538 5 9 33 7 6 9 5 9 845 2409 54i3 5 56 2 53o 2673 3l02 3835| 4892 629; 806 53o2i8 2789 58oo 4 57 2863 Son 3445 4i83| 5246 6653 8427 o5g 3169 6187 3 58 3i 97 335c 3 7 88 4532J 56oo 7013 8 79 3 0963 3549 6576 2 5 9 353o 3688 4i3s 488o 5g54 7373 9 i5 9 1 336 3 9 29 6962 I 69 68 67 66 65 64 63 62 61 60 s Natural Co-tangenls. P. P. 5 53 5.6o 5.68 5. 7 6 5.85 5. 9 5 6.o5 6 16 6.28 I 6.4o 122 NATURAL SINES. 1 i 30 31 32 33 34 35 36 37 38 39 5ooooo| 5i5o38 529919 544639 55 9 i 9 3 5 7 35 7 6 58 77 85 6oi8i5 6i566i 62 9 320 60 I 0262 5287 53oi66 4883 9 434 38i5 8021 2o4 7 58 9 i 9 546:5q 2 o5o^ 553 7 o4i3 5l2 7 9 6 7 5 4o53 8 2 56 2280 6120 977 2 58 i 0756 5 7 86 o65 9 53 7 i 99 i6 42 9 I 84 9 i 25l2 634 9 999 8 5 7 ^ 1007 6o35 0906 56i5 56oi5 7 452 9 8726 2 7 44 65 7 8 630224 56 | 1259 6284 Il52 5858 o3 9 8 4 7 6 7 8 9 6i 2 97 6 68o 7 o45o 55 6 i5n 6533 i3 99 6102 o63 9 5oo5 9 i 9 6 3208 7 o36 06-76 54 7 1762 6782 1 645 6346 0880 5243 9 43i 3440 7 265 O 9 O2 53 8 201^ 7o3i 1891 658 9 II2I 548 1 9 666 36 7 2 7 4 9 4 1127 52 9 2266 7280 2i38 6833 i36i 5 7 i 9 99 oi 3 9 o4 77 22 i353 5i 10 5o25i7 517529 532384 547076 56i6o2 5 7 5 9 5 7 5 9 oi36 6o4i36 6i 7 95i 63i5 7 8 5o ii 2769 7778 263o 7320 .S43 6i 9 5 0371 436 7 8180 1804 49 12 3020 8027 2876 7 563 2o83 6432 0606 45 99 84o8 2O2 9 48 r3 3271 8276 3l22 7807 2324 66 7 o 0840 483i 863 7 2255 47 i4 3523 85 2 5 3368 8o5o 2564 6 9 o8 1075 5o62 8865 2480 46 i5 3774 8 77 3 36i5 82 9 3 28o5 7 i45 i3io 52 9 4 9094 2705 45 16 4oa5 9022 386i 8536 3o45 7 383 1 544 55 2 6 9322 2 9 3l 44 i? 4276 9271 4io6 8780 3286 7620 i7 79 ' ' 5 7 5 7 9 55i 3i56 43 18 45 2 8 9 5i 9 435 2 9 O23 35 2 6 7 85S 20l3 5 9 88 9779 338i 42 J 9 4779 9768 45 9 8 9 266 3 7 66 8095 2248 6220 62000-7 36o6 4i 20 5o5o3o 520016 534844 54 9 5o 9 564007 5 7 8332 5 9 2482 6o645 i 620235 63383i 4o 21 5 2 8i 0265 5ogo 97 5a 4247 85 7 o 2716 6682 o464 4o56 3 9 22 5532 o5i3 5335 999 5 448 7 88o 7 2 9 5i 6 9 i4 0692 4281 38 23 5 7 83 0761 558i 55o238 4727 9 o44 3i85 7i45 0920 45o6 37 24 6o34 1010 582 7 o48i 4 9 6 7 9 28l 34i 9 7 3 7 6 n48 4 7 3i 36 25 6285 1258 6072 0724 5207 9 5i8 3653 7607 i3 7 6 4 9 55 35 26 6535 i5o6 63i8 o 9 66 5447 97 55 3887 7 838 1604 5i8o 34 2 7 6786 i?54 6563 1209 568 7 999 2 4l2I 8o6 9 i83i 54o5 33 28 7037 2OO2 6809 i45 2 5 9 27 58o22 9 4355 83oo 2059 562 9 32 29 7288 225l 7o54 i6 9 4 6166 o466 458 9 853i 228-7 5854 3i 3o . F o 7 538 522499i 537300 55i 9 3 7 5664o6 58o 7 o3 5 9 4823 608-761 6 22 5i5 636o 7 8 3o 3i 7789 2747 ! 7545 2180 6646 o 9 4o 5o5 7 8 99 2 2 7 42 63o3 29 32 8o4o 2 99 5 ! 779 2422 6886 n 7 6 52 9 o 9 223 2 97 65 27 28 33 8290 3242 8o35 2664 7125 i4i3 55 2 4 9 454 3i 97 6 7 5i 2 7 34 854i 3490 8281 2 9 7 7 365 i65o 5 7 58 9 684 3425 6 9 76 26 35 8791 3 7 38 8526 3i4 9 7 6o4 1886 5 99 i 99 i5 365 2 7200 25 36 9041 3 9 86 8771 33 92 7844 2123 6225 6ioi45 388o 7 424 24 37 9292 4234 9016 3634 8o83 2 35 9 6458 o3 7 6 4io 7 7 648 23 38 9542 448 1 9261 38 7 6 83 2 3 25 9 6 66 9 2 0606 4334 7 8 7 2 22 3 9 9792 4729 9 5o6 4n8 8562 2832 6 9 25 o836 456i 8096 21 4o 5 ioo43 524977 53 97 5i 55436o 5688oi 583o6 9 5 97 i5 9 6uo6 7 624-789 638320 20 4i 0293 5224 999 6 4602 9 o4o 33o5 7 3 9 2 I2 97 5oi6 8544 *9 42 o543 5472 540240 4844 9280 354i 7 625 l52 7 5243 8 7 68 18 43 o 79 3 5 7 i 9 o485 5o86 9 5i 9 3777 7 858 I7 5 7 5470 8 99 2 *7 44 io43 5 9 6 7 0730 5328 9758 4oi4 8092 i 9 8 7 56 97 9 2l5 16 45 1293 6214 o 9 74 55 7 o 9997 425o 8325 22I 7 5 9 23 9 43 9 i5 46 i543 646 1 1219 58i 2 5 7 o 2 36 4486 8558 244 7 6i5o 9 663 i4 4? i 79 3 6709 1 464 6o54 0475 4722 8 79 i 2 6 77 63 77 9886 i3 48 2o43 6 9 56 1708 62 9 6 0714 4 9 58 9024 2 9 7 66o4 64ono 12 49 2293 7203 i 9 53 653 7 O 9 52 5i 9 4 9 256 3i3 7 683o o333 II 5o 5fs543 52745o 542197 556 779 57ii 9 i 58542 9 5 99 48 9 6i336 7 62 7 o5 7 64o55 7 10 5i 2792 7697 2442 7 O2I i43o 5665 97 22 35 9 6 7284 0-780 9 52 3o42 7944 2686 7 262 i66 9 5901 99 55 3826 7 5io ioo3 8 53 3292 8191 2930 7 5o4 I 9 o 7 6i3 7 600188 4o56 7737 1226 7 54 354! 8438 3i74 7745 2146 63 7 2 O420 4285 7963 i45o 6 55 3 79 i 8685 34i9 79 8 7 2384 6608 o653 45i5 8189 i6 7 3 5 56 4o4o 8932 3663 8228 2623 6844 o885 4 7 44 84i6 1896 4 5 7 4290 9179 3 9 o 7 846 9 2861 779 1118 4 9 74 8642 2119 3 58 453 9 9426 4i5r 8710 3 1 oo 7 3i4 i35o 5 2 o3 8868 2342 2 5 9 4789 9 6 7 3 ! 43 9 5 8 9 52 3338 7 55o 1 58 3 5432 9 o 9 4 2565 I 59 58 ! 57 56 55 54 53 52 51 50 Natural Co-sines. 9 s P.P. , to I". 4 ' 18 4.i3 4.09 4-o4 4.oo 3. 9 5 3. 9 o 3.85 1 3.8o 3. 7 4 NATURAL TANGENTS. 123 d is 30 31 32 33 34 35 36 37 38 39 o SyySSo 600861 624869 64g4o8 6745o 9 700208 726543 753554 781286 809784 60 I 7738 1257 5 27 4 9821 4 9 32 o64i 6 9 8 7 4oio 1754 810266 5 9 2 8126 i653 56 79 650235 5355 1075 7 43 2 446 7 2223 o 7 48 58 3 85i4 2049 6o83 0649 5 779 i5o 9 7877 4 9 23 2692 1230 5 7 4 8 9 o3 2445 6488 io63 6203 i 9 43 8322 538o 3i6i 1712 56 5 9291 2842 68 9 4 i4 77 6627 2 3 77 8 7 6 7 583 7 363i 2195 55 6 9680 323 9 7299 1892 7o5i 2812 9 2l3 62 9 4 4 1 00 2678 54 7 58oo68 3635 774 23o6 7 4 7 5 3246 9 658 6 7 5i 4570 3i6i 53 8 o45 7 4o3 2 8110 2 7 2I 7 9 oo 368i 7 3oio4 720 9 5o4o 3644 52 9 o846 4429 85i6 3i36 8324 4n6 o55o 7667 55io 4i~8 5i 10 58i235 604827 628921' 65355i 6 7 8 7 4 9 7 o455i 7 3o 99 6 7 58i 2 5 785981 8 i 46 i 2 5o ii 1625 5224 9 32 7 3 9 66 9i 7 4 4 9 8 7 i443 8583 645 1 5o 9 6 49 12 2Ol4 5622 97 34 4382 9 5 99 5422 i88 9 9 o4i 6922 558o 48 i3 24o3 6019 63oi4o 4797 680025 5858 2336 9 5oo 7 3 9 4 6o65 47 i4 2793 64i7 o546 52i3 o45o 62 9 4 2 7 83 99 5 9 7 865 6549 46 i5 3i83 68i5 0953 562 9 o8 7 6 6 7 3o 3 2 3o 760418 8336 7034 45 16 3573 7213 i36o 6o45 1302 7 i66 36 7 8 0877 8808 7 5i 9 44 J 7 3 9 63 7611 I7 6 7 646 1 I 7 28 7 6o3 4i25 i336 9280 8oo5 43 18 4353 8010 2174 6877 2i54 8o3 9 45 7 3 i 79 6 97 52 84 9 i 42 X 9 4743 84o8 258i 7294 2680 84 7 6 5021 2256 790225 8 97 6 4i 20 585i34 608807 632 9 88 657710 683oo 7 7o8 9 i3 7 3546 9 762716 79 6 97 8i 9 463 4o 21 5524 9205 33 9 6 8127 3433 9 35o 5 9 i 7 3i 7 6 II 7 9949 3 9 22 5 9 i5 9604 38o4 8544 386o 97 88 6366 3636 1 643 820435 38 23 63o6 6iooo3 421 1 8 9 6i 428 7 710225 68i5 4o 97 2II 7 O 9 22 37 24 6697 o4o3 4619 9 3 79 4 7 i4 o663 7264 4558 2590 i4o 9 36 25 7088 0802 5027 979 6 5i42 I IOI 77 i3 5oi 9 3o64 i8 97 35 26 74?9 1201 5436 660214 556 9 i53 9 8162 548o 3538 2384 34 27 7870 1601 5844 o63i 5 997 i 9 77 8611 5 9 4i 4012 2872 33 28 8262 2001 6253 io4 9 6425 2416 9 o6i 64o3 4486 336o 32 29 8653 2401 6661 1467 6853 2854 9 5n 6865 4961 3848 3i 3o 589045 6l28oi 637070 661886 68 7 28i 713293 789961 767827 79 5436 824336 3o 3i 9 43 7 3201 7479 23o4 779 3 7 32 7 4o4i i 7789 5911 4825 2 9 32 9829 36oi 7888 2723 8i38 4171 0862 8252 6386 53x4 28 33 590221 . 4002 8298 3i4i 856 7 46n l3l2 8 7 i4 6862 58o3 2 7 34 o6i3 4402 8707 356o 8 99 5 5o5o i 7 63 9.177 7 33 7 62 9 2 26 35 1006 48o3 9117 3 979 9/125 5490 22l4 9 64o 7 8i3 6782 25 36 i3 9 8 5204 9 52 7 43 9 8 9 854 5 9 3o 2666 770104 8290 7 2 7 2 24 3? 1791 56o5 99 3 7 48i8 6 9 0283 63 7 o 3ii 7 0567 8 7 66 77 62 23 38 2184 6006 640347 523 7 o 7 i3 6810 356 9 io3i 9242 8252 22 3 9 2 5 77 64o8 o 7 5 7 565 7 n43 725o 4020 i495 9719 8 7 43 21 4o 592970 616809 641167 666o 77 6 9 i5 7 2 717691 7 444 7 2 771959 800196 82 9 234 2O 4i 3363 7211 i5 7 8 64 97 2003 8i3 2 4 9 25 2423 0674 972 5 I 9 42 3 7 5 7 7 6i3 1989 6 9 i 7 2433 8573 53 77 2888 n5i 83o2i6 18 43 4i5o 8oi5 2 3 99 7337 2863 9014 583o 3353 1629 o 7 o 7 17 44 4544 84i7 2810 77 58 32 9 4 9 455 6282 38i8 2107 n 99 16 45 4 9 3 7 8819 3222 8i 79 3 7 25 9897 6 7 35 4283 a585 i6 9 i i5 46 533i 9221 3633 85 99 4i56 720339 7 i8 9 4748 3o63 2i83 i4 4? 5 7 25 9624 4o44 9 O2O 458 7 0781 7642 52i4 3542 2 6 7 6 i3 48 6iao 620026 4456 9 442 5oi8 1223 8o 9 6 568o 4O2I 3i6 9 12 49 65i4 0429 4868 9 863 545o i665 854 9 6i46 45oo 3662 II 5o 596908 620832 64528o 6 7 o284 6 9 588 r 722108 7 4 9 oo3 776612 804979 834i55 10 Si 73o3 1235 5692 o 7 o6 63i3 2 55o 9 458 7078 5458 4648 9 62 7698 i638 6io4 1128 6 7 45 2 99 3 99 I2 7545 5 9 38 5i42 8 53 8093 2042 65i6 i55o 7177 3436 7 5o366 8012 64i8 5636 7 54 8488 2445 6929 I 97 2 7610 38 7 9 0821 8479 6898 6i3o 6 55 8883 2849 7342 23 9 4 8042 4323 I2 7 6 8 9 46 7 3 79 6624 5 56 9278 3253 77 55 2817 8475 4766 i 7 3i 9 4i4 7 85 9 7119 4 57 9674 365 7 8168 324o 8 9 o8 52IO 2187 9881 834o 7 6i4 3 58 6ooo6c 4o6i 858i 3662 9 34i 5654 2642 780349 8821 8io 9 2 5 9 o465 4465 8 99 4 4o85 9774 6o 9 8 3o 9 8 0817 93o3 86o4 I 59 58 ' 57 56 55 54 53 52 51 50 . Natural Co-tangents. S tor'. 6 - 53 6.67 6.82 6. 97 7-i4 7 .3i 7.5o 7.70 7.92 8.:4 124 NATURAL SINES. .B X 40 41 42 43 44 45 3 46 47 48 49 642788 656o5 9 66 9 i3i 68i 99 8 694658 707107 7 i 9 34o 7 3i354 7 43i45 7 54 7 io 60 I 3oio 6279 9 34 7 2211 4868 7312 9 542 i55 2 333 9 4 9 oo 5 9 r 3233 6498 9 563 2424 5o 77 7 5i8 97 44 i 7 5o 3534 5o 9 i 58 2 3456 6717 9779 2636 5 2 86 7724 99 46 i 9 4 9 3 7 28 5a8 2 57 4 36 7 9 6 9 3 7 999 5 a84 9 5495 79 2 9 7 2oi48 2l4 7 3 9 23 5472 56 i 3901 7i56 670211 3o6i 5 7 o4 8i34 o34 9 2345 4n 7 5663 55 6 4124 7 3 7 5 0427 32 7 4 5913 834o o55i 2 543 43i2 5853 54 ^ 4346 7 5 9 4 0642 3486 6122 8545 o 7 53 2741 45o6 6o44 53 8 456 9 7814 o858 36 9 8 633o 8 7 5o o 9 54 2 9 3 9 4 7 oo 6234 52 9 4791 8o33 1074 3 9 n 653 9 8 9 56 n56 3i37 48 9 4 6425 5i 10 645oi3 658 2 5 2 67i28 9 684i23 6 9 6 7 48 7 o 9 i6i 7 2i35 7 733334 7 45o88 7566i5 5o ii 5236 8471 i5o5 4335 6 9 5 7 9 366 i55 9 3532 5282 68o5 4 9 12 5458 8689 1721 454 7 7 i65 9 5 7 i I 7 6o 3 7 3o 54 7 6 6 99 5 48 i3 568o 8908 i 9 36 4 7 5 9 7 3 7 4 9776 I 9 62 3927 5670 7i85 47 i4 5902 9127 2l5l 4971 7 582 99 8i 2i63 4i25 5864 7 3 7 5 46 i5 6124 9 346 2 36 7 5i83 779 7ioi85 2364 4323 6057 7 565 45 16 6346 9565 2582 53 9 5 7999 o3 9 o 2565 4520 625i 77 55 44 17 6568 9783 2 797 5607 8207 o5 9 5 2 7 66 4717 6445 79 45 43 18 6790 660002 3oi3 58i8 84i5 0799 ,2 9 6 7 49i5 6638 8i34 42 '9 7012 O22O 3228 6o3o 86 2 3 ioo4 3i68 5lI2 6832 8324 4i 20 64?233 660439 6 7 3443 686242 6 9 8832 7II20 9 7 23369 7353o 9 747025 7 585i4 4o 21 7455 o65 7 3658 6453 9 o4o i4i3 35 7 o 55o6 7218 8 7 o3 3 9 22 7677 o8 7 5 38 7 3 6665 9 248 1617 3 77 i 5 7 o3 7412 88 9 3 38 23 7898 1094 4o88 6876 9 455 1822 3 97 i 5 9 oo 76o5 9 o82 37 24 8120 I3l2 43o2 7088 9 663 2026 4l 7 2 6097 779 8 9 2 7 i 36 25 834i i53o 45i 7 7 2 99 9871 2280 43 7 2 62 9 4 799 i 9 46i 35 26 8563 1748 4 7 3 2 7 5io 700079 2434 45 7 3 64 9 i 8i84 9 65o 34 27 8784 1966 494 7 7721 0287 263 9 4773 6687 83 77 9 83 9 33 28 9006 2184 5i6i 79 3 2 0494 2843 4 9 74 6884 85 7 o 7 6oo28 32 29 9227 2402 53 7 6 8i44 0702 3o47 5i 7 4 7081 8 7 63 02 I 7 3i 3o 649448 662620 6755 9 o 688355 700909 7i325o 72 53 7 4 737277 7 48 9 56 7 6o4o6 3o 3i 9669 2838 58o5 8566 1117 3454 55 7 5 7474 9 i48 o5 9 5 2 9 32 9890 3o56 60 1 9 8776 1 324 3658 5 77 5 7670 9 34i o 7 84 28 33 65oiii 32 7 3 6233 8087 i53i 3862 5 97 5 7867 9 534 97 2 2 7 34 o33 2 349i 6448 9198 i 7 3 9 4o66 6i 7 5 8o63 97 26 1161 26 35 o553 3 7 o 9 6662 9409 i 9 46 426 9 63 7 5 8 2 5 9 99 i 9 i35o 25 36 0774 3926 6876 9620 2i53 4473 65 7 5 8455 7 5oin i538 24 3? o 99 5 4i44 700.0 9 83o 236o 46 7 6 6 77 5 865i o3o3 I 7 2 7 23 38 1216 436i 73o4 690041 256 7 488o 6 97 4 8848 o4 9 6 I 9 i5 22 3 9 i43 7 45 79 7 5i8 O25l 2 77 4 5o83 7 i 7 4 9 o43 0688 2104 21 4o 4i *Ai65 7 1878 664796 5oi3 6 777 32 7946 690462 702981 0672 3i88 7 i5 2 86 54 9 o 7 2 7 3 7 4 7 5 7 3 7 3 9 a3 9 9 435 7 5o88o I0 7 2 7 622 9 2 2480 20 1 9 42 2098 5 2 3o 8160 0882 33 9 5 56 9 3 7773 9 63i 1264 2668 18 43 2319 5448 83 7 3 1093 36oi 58 9 6 7972 9 82 7 i456 2856 i? 44 z53 9 5665 858 7 i3o3 38o8 6o 99 8172 7 4oo23 1 648 3o44 16 45 2760 588 2 8801 i5i3 4oi5 6302 83 7 i 0218 1840 3232 i5 46 2980 6099 9 oi4 1723 4221 65o5 85 7 o o4i4 2032 3420 i4 4? 3200 63i6 9228 i 9 33 4428 6708 8 7 6 9 o6o 9 2223 36o8 i3 48 3421 6532 9 44i 2i43 4634 6 9 n 8 9 6 9 o8o5 24i5 3 79 6 12 49 364i 6749 9 65$ 2353 484 1 7113 9 i68 IOOO 2606 3 9 84 II 5o t5386i 666966 6 79 868 6 9 2565 7 o5o47 7 ' 7 3i6 7 2 9 36 7 7 4n 9 5 7 52 79 8 7 64i 7 i IO 5i 4o8i 7i83 680081 2 77 3 5253 7 5i 9 9 566 i3 9 i 2 9 8 9 435 9 9 52 43oi 7 3 99 O2 9 5 2 9 83 545 9 772i 97 65 i586 3i8i 454 7 8 53 452i 7616 o5o8 3192 5665 7924 : 9963 1781 33 7 2 4 7 34 7 54 4?4i 7833 0721 3402 58 7 2 8i26 ) 7 3oi62 1976 3563 4 9 2I 6 55 4961 8o4 9 o 9 34 36n 6078 8329' o36i 2171 3 7 55 5io 9 5 56 5i8o 8 2 65 n4 7 382i 6284 853i o56o 2 366 3 9 46 52 9 6 4 57 54oo 8482 i36o 4o3o 648 9 8 7 33 o 7 58 2 56i 4i3 7 5483 3 58 5620 86 9 8 i5 7 3 424o 66 9 5 8936 o 9 5 7 2 7 55 4328 56 7 o a J9 583 9 8 9 i4 1786 444 9 6901 9 i38 n55 2 9 5o 45i 9 585 7 1 > 49 48 47 46 45 44 43 42 41 40 c Natural Co-sines. y P. P. , f tol". 3 ' 6 9 3.63 3.5 7 3.5 2 3.46 3.4o 3.34 3.27 3.21 3.i5 NATURAL TANGENTS. 125 i _J 40 41 42 43 44 45 46 47 48 49 o 839100 869287 9 oo4o4, 9 325i5 965689 I.OOOOO i.o3553 1.07237 i. 11061 i.i5o37 60 I 9 5 9 5 9798 oq3i l 3o5 9 625i oo58 36i3 7299 1126 5io4 5 9 2 840092 870309 i458 36o3 68:4 0116 36 7 4 7362 i i 9 i 5172 58 3 o588 0820 i 9 85 4i48 7 3 77 oi 7 5 3 7 34 7425 1256 fo4o 57 4 1084 i33 2 25i3 46 9 3 7 9/.o oa33 3 79 4 7 48 7 l32I 53o8 56 5 i58i i843 3o4i 5a38 85o4 0291 3855 7 55o 1387 53 7 5 55 6 2078 2356 356 9 5 7 83 9o6 7 o35o 3 9 i5 7 6i3 i452 5443 54 7 2 5 7 5 2868 4o 9 8 632 9 9632 0408 3 97 6 7676 i5i7 55 ii 53 8 3o 7 3 338i 4627 68 7 5 9 7 oi96 o46 7 4o36 7738 i582 55 79 52 9 35 7 i 38 9 4 5x56 7422 o 7 6i o5 2 5 4o 9 7 7801 1 648 5647 5i 10 844069 874407 9 o5685 9 37 9 68 9 7 i326 i.oo583 I.o4i58 1.07864 1.11713 i. 15716 5o ii 456 7 4920 62i5 85i5 1892 0642 4218 7927 1778 5783 49 12 5o66 5434 6 7 45 9 o63 2458 O 7 OI 42 79 799 1 844 585i 48 i3 5564 5 9 48 7 2 7 5 9 6io 3o24 7 5 9 434o 8o53 1909 5919 47 i4 6o63 6462 78o5 9 4oi58 3590 0818 44oi 8116 i 97 5 5 9 8 7 46 i5 656a 69.76 8336 0706 4i5 7 o8 7 6 446 1 8179 2041 6o56 45 16 7062 74 9 i 8867 1255 4 7 24 0935 4522 8243 2106 6124 44 17 7562 8006 9 3 9 8 i8o3 5291 0994 4583 83o6 2172 6192 43 18 8062 852i 99 3o 2352 5859 io53 4644 836 9 2238 6261 42 *9 8562 9 o3 7 9 io462 2 9 O2 642 7 III2 4 7 o5 8432 23o3 6329 4i 20 849062 87 9 553 9 io 99 4 9 4345i 97 6 99 6 I.OII7O i.o4 7 66 1.08496 1.12369 i.i63 9 8 4o 21 9 563 88oo6 9 i526 4ooi 7564 1229 482-7 855g 2435 6466 3 9 22 85oo64 o585 2o5 9 455 2 8i33 1288 4888 8622 25oi 6535 38 23 o565 1102 25 9 2 5l02 8 7 o3 1 347 4 9 4 9 8686 2567 66o3 37 24 1067 l6l 9 3i25 5653 9 2 72 i4o6 5oio 8 7 49 2633 6672 36 25 i568 2i36 365 9 6204 9842 i465 5o 7 2 88i3 2699 6741 35 26 2070 2653 4i 9 3 6756 980413 i524 5i33 8876 2765 6809 34 2 7 25 7 3 3l ?I 4727 7 3o 7 0983 i583 5i 9 4 8940 2 83i 6878 33 28 3o 7 5 368 9 526i 7 85 9 i554 1 642 5 2 55 9003 2897 6 9 47 32 29 3578 4207 5 79 6 8412 2126 1702 53i 7 9067 2 9 63 7016 3i 3o 854o8i 884725 9 i633i 9 48g65 98269*7 1.01761 1.06378 1.09131 1.13029 1.17085 3o 3i 4584 5244 .6866 9 5!8 3269 1820 543 9 9 i 9 5 3096 7i54 9 9 32 5o8 7 5763 '7402 950071 3842 1879 55oi 9 258 3i62 7223 28 33 55 9 i 6282 79 38 0624 44i4 1939 5562 9322 3228 7292 27 34 6095 6802 8474 1178 4 9 8 7 1998 5624 9 386 32 9 5 736i 26 35 65 9 9 7321 9 oio I 7 33 556o 2057 5685 945o 336i 7 43o 25 36 7104 7842 9 54? 2287 6i34 2117 5 7 4 7 95i4 3428 75oo 24 37 7608 8362 920084 2842 6 7 o8 2176 58o 9 9 5 7 8 3494 7 56 9 23 38 8n3 8882 0621 33 97 7282 2236 58 7 o 9 642 356i 7638 22 3 9 8619 94o3 iiSg 3 9 53 7 85 7 2295 5 9 32 97 o6 3627 7708 21 4o 859124 889924 921697 9 545o8 988432 1.02355 i.o5 99 4 i.o 9 77o 1.13694 1.17777 2O 4i 9630 890446 2235 5o64 9oo 7 24i4 6o56 9 834 3 7 6i 7 846 J 9 42 86oi36 0967 2 77 3 562i 9 58 2 2474 6117 9 8 99 38 2 8 7916 18 43 o64a i48 9 33i2 6177 99oi58 2533 6179. o 9 63 38 9 4 7986 l l 44 n48 2OI2 385i 6734 o 7 35 2 5 9 3 6241 1.10027 3 9 6i 8o55 16 ,43 i655 2534 4390 720.2 i3n 2653 63o3 oo 9 i 4028 8i25 i5 46 2162 3o5 7 493o 7849 1888 2713 6365 oi56 4095 8194 i4 4? 2669 358o 5470 84o 7 2465 2772 6427 O22O 4162 8264 i3 48 3i 77 4io3 6010 8 9 66 3o43 2832 6489 0285 4229 8334 12 49 3685 4627 655i 9 524 362i 280.2 655i . o34 9 4296 84o4 II 5o 864i93 8 9 5i5i 927091 9 6oo83 994199 I.O2 9 52 i.o66i3 i.io4i4 r. 14363 i.i8474 10 5i 4701 56 7 5 7632 0642 4 77 8 3012 6676 0478 443o 8544 9 52 5209 6199 8174 I2O2 535 7 3072 6 7 38 o543 4498 86i4 8 53 5 7 i8 6724 8 7 i5 1761 5 9 36 3i32 6800 0607 4565 8684 7 54 6227 7249 9257 2322 65i5 3l 9 2 6862 0672 4632 8 7 54 6 55 6 7 36 7774 9800 2882 79 5 3252 6 9 25 o 7 3 7 4699 8824 5 56 7246 8299 93o342 3443 7 6 7 6 33i2 6 9 8 7 0802 4 7 6 7 88 9 4 4 5? 7756 8825 o885 4oo4 8256 3372 7049 0867 4834 8964 3 58 8266 9 35i i4a8 4565 883 7 3433 7112 o 9 3i 4902 9o35 2 5 9 8776 9877 1971 5127 94i8 34 9 3 7174 o 99 6 4969 9io5 I 49 48 47 46 45 44 43 42 41 40 . Natural Co-tangents. *g P. P Q OQ tol". 8 " 38 8.64 8.92 9 21 9 .53 0.99 1.02 I. 06 i. 10 i.i5 126 NATURAL SINES. A X 50 C 51 52 53 54 55 56 57 58 59 766044 777146 788011 7 9 8636 809017 819152 829038 8386 7 i 848o48 85 7 i6 7 60 I 623i ?329 8190 8811 9188 9 3i 9 9200 882 9 8202 73i7 5 9 2 64x8 7512 8369 8 9 85 9 35 9 9486 9 363 8 9 8 7 8356 746 7 58 3 66o5 7 6 9 5 8548 9160 953o 9662 9 5 2 5 9 i46 85io 7616 57 4 6792 7878 8727 9 335 9700 9819 9688 9 3o4 8664 7766 56 5 6979 8060 8905 95io 9871 99 85 9 85o 9 462 8818 79 i5 55 6 7 i65 8243 9084 9 685 810042 820152 83ooi2 9 62O 8.972 8o65 54 7 7352 8426 9263 9 85 9 O2I2 o3i8 0174 9778 9125 8214 53 8 7 538 8608; 9441 8ooo34 o383 o485 o33 7 99 36 9279 8364 52 9 7725 8791 9620 0208 o553 o65i o4 99 84oo 9 4 9 433 85i3 5i 10 767911 778973 789798 8oo383 810723 820817 83o66i 84o25i 849586 858662 5o ii 8097 9 i56 9977 o55 7 0894 o 9 83 0823 o4o 9 97 3 9 8811 49 12 8284 9338 79Oi55 0731 1064 n4 9 o 9 84 o56 7 9 8 9 3 8 9 6o 48 i3 8470 9520 o333 o 9 o6 1234 i3i5 n46 0724 85oo46 9 io 9 47 i4 8656 9702 o5ii 1080 i4o4 i48i i3o8 0882 oi 99 9 258 46 i5 8842 9884 0690 1254 i5 7 4 i647 i4 7 o io3 9 o35 2 9 4o6 45 16 9028 780067 0868 1428 1744 i8i3 i63i 1 196 o5o5 9555 44 7 9214 0249 io46 1602 1914 1978 i7 9 3 1 3 54 o658 9 7o4 43 18 9400 o43o 1224 1776 2084 2i44 i 9 54 i5n 0811 9 852 42 J 9 9585 0612 i4oi i 9 4 9 2253 23lO 2Il5 1668 o 9 64 860001 4i 20 769771 780794 791579 802123 812423 822475 832277 84i825 85iu 7 86oi4 9 4o 21 99 5 7 0976 1757 2297 2592 2641 2438 I 9 82 I26 9 02 9 7 3 9 22 770142 n5 7 1935 2470 2762 2806 2 5 99 2l3 9 1422 o446 38 23 o3 2 8 i33 9 21 12 2644 2g3i 2 97 I 2760 2296 i5 7 5 o5 9 4 37 24 o5i3 l520 2290 2817 3ioi 3i36 2 9 2I 2452 1727 0742 36 25 0699 1702 2467 2991 3270 33o2 3082 26o 9 1879 o8 9 o 35 26 o884 i883 2644 3i64 343 9 346 7 3243 2766 2032 io38 34 27 1069 2o65 2822 333 7 36o8 3632 34o4 2922 2184 1186 33 28 1254 2246 2999 35n 3 77 8 3797 3565 3o 79 2336 i334 32 29 i44o 2427 3176 3684 3^7 3 9 6i 3 7 25 3235 2488 i48i 3i 3o 771625 782608 793353 8o385 7 8i4n6 824126 833886 8433 9 i 85264o 861620. 3o 3i 1810 2789 353o 4o3o 4284 42 9 I 4o46 3548 2 79 2 1777 29 32 i 99 5 2970 3 7 o 7 4203 4453 4456 4207 3 7 o4 2 9 44 I 9 24 28 33 2179 3i5i 3884 43 7 6 4622 4620 436 7 386o 3o 9 6 2072 27 34 2364 3332 4o6i 4548 4791 4?85 452 7 4oi6 3248 2219 26 35 2549 35i3 4238 4721 4959 4 9 4 9 4688 4172 33 99 2366 25 36 2 7 34 36 9 3 44i5 48 9 4 5i28 5u3 4848 4328 355i 2 5i4 24 3? 2918 38 7 4 45 9 i 5o66 5296 5278 5oo8 4484 3702 2661 23 38 3io3 4o55 4768 5239 5465 5442 5i68 464o 3854 28"- 3 9 3287 . 4235 4944 ' 54n 5633 56o6 53 2 8 4795 4oo5 2 9 55 21 4o 773472 784416 795121 8o5584 8i58oi 825770 835488 84495i 854i56 863io2 2O 4i 3656 45 9 6 5297 6756 5 9 6 9 5 9 34 5648 5io6 43o8 3249 19 42 384o 4776 5473 5928 6i38 6o 9 8 58o 7 5262 445 9 33 9 6 1 8 43 4024 4 9 5 7 565o 6100 63o6 6262 5967 54i7 46io 3542 17 44 4209 5i3 7 5826 6273 64?4 6426 6127 55 7 3 4761 36-Sy 1 6 45 43 9 3 53i7 6002 6445 6642 65 9 o 6286 5728 4 9 I2 3836 1 5 46 45 77 54 97 6178 6617 6809! 6 7 53 6446 5883 5o63 3982 14 4? 4761 56 7 7 6354 6788 6977! 6917 66o5 6o38 52i4 4128 i3 48 4944 585 7 653o 6960 7i45 7081 6 7 64 6i 9 3 5364 42 7 5 12 49 5i28 6o3 7 6706 7i32 7 3i3 7244 6 9 24 6348 55i5 44ai ii 5o 775312 786217 796882 807304 817480 827407 837083 8465o3 855665 86456 7] 10 5i 5496 63 9 6 7 5 7 7 4 7 5 7 648 7571 .7242 6658 58:6 4 7 i3| 9 52 56 7 9 6576 7 233 7 64 7 7 8i5 77 34 74oi 68i3 5 9 66 486o] 8 53 5863 6 7 56 7408 7818 7982 7897 7 56o 6 9 67 61 17 5oo6 7 54 6o46 6935 7584 799 8i5o 8060 77i 9 7122 6267 5i5i 6 55 623o 7114 77 5 9 8161 83i 7 8223 7878 7277 6417 52 97 5 56 64i3 7 2 94 79 35 8333 8484 8386 8o36 743 1 656 7 5443 4 5? 6596 7 4 7 3 8no 85o4 865i 8549 8i 9 5 7585 6 7 i8 558 9 3 58 6780 7652 8285 86 7 5 8818 8712 8354 77 4o 6868 5 7 34 2 5 9 6 9 63 7 832 846o 8846 8985 88 7 5 85i2 78 9 4 7017 588o I 39 38 37 36 35 34 33 32 31 30 J s Natural Co-sines. i P P. t tol// 3.o8 3.02 2. 9 5 2.88 s.8i t. 7 5 2.68 2.60 2.53 2.46 NATURAL TANGENTS. 12 4 x 50 51 52 53 54 55 56 57 58 59 o 1.19175 1.23490 1.27994 1.32704 1.37638 1.42815 1.48256 1.53986 i.6oo33 i 66428 60 I 9246 3563 8071 a 7 85 7722 2 9 o3 834 9 4o85 0137 6538 5 9 2 93:6 363 7 8i48 2865 7807 2$ 9 2 8442 4i83 024l 6647 58 3 9 38 7 3710 8225 2946 7891 3o8o 8536 4281 o345 6 7 5 7 5 7 4 9457 3784 83o2 3026 7976 3i6 9 862 9 43 79 o44g 6867 56 5 9 528 3858 83 79 3107 8060 3 2 58 8722 447 o553 6 97 8 55 6 9^99 3 9 3i 8456 3i8 7 8i45 334 7 8816 45 7 6 0657 7088 54 7 9669 4oo5 8533 3268 8229 3436 8 9 o 9 46 7 5 0761 7 i 9 8 53 8 9740 4079 8610 3349 83i4 35 2 5 9 oo3 4774 o865 7 3o 9 52 9 9811 4i53 8687 343o 83 99 36i4 997 48 7 3 o 97 o 7 4i 9 5i 10 1.19882 1.24227 1.28764 i.335ii 1.38484 1.43703 i.4 9 i 9 o 1.54972 1.61074 1.67530 5o ii 99 53 43oi 8842 35 9 2 8568 3 79 2 9 284 5071 "79 7 64i 49 12 1.20024 43 7 5 8 9 i 9 36 7 3 8653 388i 9 3 7 8 5170 1283 7752 48 i3 oogS 4449 8 997 3 7 54 8 7 38 3 97 o 9 472 5269 1 388 7863 4? i4 0166 45 2 3 9 o 7 4 3835 8824 4o6o 9 566 5368 i4 9 3 7974 46 i5 0237 45 97 9 l52 3916 8909 4i4 9 9 66i 546 7 i5 9 8 8o85 45 16 o3o8 4672 9229 3998 8994 423 9 97 55 556 7 1703 8i 9 6 44 i? 3 79 4?46 9 3 7 4079 9079 432 9 9 84 9 5666 1808 83o8 43 18 o45i 4820 9 385 4i6o 9 i65 44i8 99 44 5 7 66 i 9 i4 8419 42 J 9 O522 48 9 5 9 463 4242 925o 45o8 i.5oo38 5866 20I 9 853i 4i 20 1.20593 1.24969 i.2 9 54i 1.34323 1.39336 1.44598 i.5oi33 1.55966 I.62I25 1.68643 4o 21 o665 5o44 9 6i8 44o5 9421 4688 0228 6o65 2230 8 7 54 3 9 22 o 7 36 5n8 9 6 9 6 448 7 9 5 7 4778 0322 6i65 2336 8866 38 23 0808 5i 9 3 977 5 4568 . 9 5 9 3 4868 0417 6265 2442 8979 37 24 0879 5268 9 853 465o 9 6 79 4 9 58 o5i2 6366 2548 99 ; 36 25 095 1 5343 99 3i 4732 9764 5o4g 0607 6466 2654 9 2o3 35 26 1023 54i7 i.3ooo 9 48i4 9 85o 5i3 9 0702 6566 2760 9 3i6 34 27 1094 5492 0087 4896 99 36 522 9 0797 666 7 2866 9 428 33 28 1166 556 7 0166 4978 1.40022 5320 o8 9 3 6 7 6 7 2 9 72 9 54i 32 29 1238 5642 0244 5o6o oio 9 54io 0988 6868 3o 79 9 653 3i 3o I.2l3lO 1.25717 i.3o323 i.35i4a i.4oi 9 5 i.455oi i.5io84 1.56969 i.63i85 1.69766 3o 3i i382 5792 o4oi 5224 0281 55 9 2 1179 7069 32 9 2 9 8 79 2 9 32 i454 5867 o48o 53o7 o36 7 5682 1275 7170 33 9 8 999 2 28 33 i526 5 9 43 o558 538 9 o454 5 77 3 1370 7271 35o5 1.70106 27 34 i5 9 8 6018 0637 5472 o54o 5864 i486 7 3 7 2 36i2 0219 26 35 1670 6093 0716 5554 0627 5 9 55 i562 7474 3 7 i 9 o332 25 36 1742 6169 79 5 5637 0714 6o46 i658 7 5 7 5 3826 o446 24 3? 1814 6244 0873 57i 9 0800 6i3 7 1754 7676 3 9 34 o56o 23 38 1886 63i 9 O 9 52 58o2 0887 622 9 i85o 7778 4o4i 0673 22 3 9 1959 63 9 5 io3i 5885 o 9 74 6320 1946 7879 4i48 0787 21 4o I.22o3l 1.26471 i.3uio 1.35968 1.41061 i.464ii i.52o43 1.57981 1.64256 1.70901 20 4i 2104 6546 II 9 6o5i n48 65o3 2139 8o83 4363 ioi5 J 9 42 2176 6622 I26 9 6i34 1235 65 9 5 2235 8i84 447i 1129 18 43 2249 6698 1 348 6217 l322 6686 2332 8286 45 79 1244 i? 44 2321 6 77 4 1427 63oo i4o 9 6778 2429 8388 468 7 i358 16 45 2394 684 9 i5o7 6383 i4 9 7 8870 2525 8490 479 5 i473 i5 46 2467 6925 i586 6466 1 584 6 9 62 2622 85 9 3 4903 1 588 i4 4? 2539 7001 1666 6549 1672 7o53 2719 86 9 5 5ou 1702 i3 48 26l2 7077 1745 6633 i 7 5 9 7i46 2816 8797 5l2O 1817 12 49 2685 7i53 i8 2 5 6716 1847 7238 2913 8900 5228 1932 II 5o 1.22768 1.27230 i.3i 9 o4 i.368oo 1.41934 i.4733o i. 53oio 1.59002 1.65337 1.72047 IO 5i 2 83i 73o6 1984 6883 2O22 7 422 3107 9106 5445 ai63 9 52 2904 7382 2064 6967 2IIO 75i4 32o5 9208 5554 2278 8 53 2977 7458 2144 7o5o 2I 9 8 7607 33o2 9 3u 5663 2 3 9 3 7 54 3o5o 7535 2224 7i34 2286 7699 34oo 94i4 5 77 2 2609 6 55 3i23 7611 23o4 7218 23 7 4 779 2 34 97 9 5i 7 588i 2625 5 56 8196 7688 2384 7302 2462 7 885 35 9 5 9620 5 99 o 2741 4 5? 3270 77 64 2464 7 386 255o 7977 3693 97 23 6o 99 2867 3 58 3343 7841 2544 7470 2638 8070 3 79 i 0826 62O 9 2 97 3 2 5 9 34i6 7917 262^ 7554 2726 8i63 3888 99 3o 63i8 3o8 9 I 39 38 37 36 35 34 33 32 31 30 a Natural Co-tangents. P. P. to I". 1 ' 80 1.25 i.3i r.3 7 i.44 i.5i i.5 9 1.68 1.78 1.88 NATURAL SINES. 1 60 61 62 63 64 65 66 67 1 68 69 o 866025 8-74620 882948 8 9 ioo7 8 9 8 79 4 9 o63o8 9 i3545 9 2o5o5' 92718^ 9 3358o 60 i 6171 4?6i 3o84 n3 9 8 9 22 643 1 3664 0618 7 2 9 3 3685 5 9 2 63i6 4902 3221 1270 9 o4 9 6554 3782 0732 7 402 378 9 58 3 646i 5o42 335 7 1402 9 i 7 6 6676 3 9 oo o846 7 5io 38 9 '-) 5 7 L 6607 5i83 3493 i534 9 3o4 6 7 99 4oi8 o 9 5 9 76i 9 3 997 56 t 6762 5324 3629 1666 9 43i 6 9 22 4i36 1072 77 28 4ioi 55 6 6897 5465 3 7 66 1798 9 558 7044 4254 n85 7 836 4204 54 7 7042 56o5 3902 1929 9 685 7166 43 7 2 i2 99 79 45 43o8 53 8 7187 5 7 46 4o38 2061 9812 728 9 44 9 o 1412 8o53 44i2 52 9 7 33i 5886 4i 7 4 2192 99 3 9 ?4n 46o 7 i5 2 5 8161 45i5 5i 10 867476 8-76026 884309 892323 9 ooo65 9 07533 9 i4 7 25 9 2i638 9 282 7 O 9 346i 9 5o ii 7621 6i6 7 4445 2455 OI 9 2 7 655 4842 1750 83 7 8 4722 4 9 12 77 65 63o 7 458i 2586 o3i 9 7777 4 9 6o i863 8486 4826 48 l2 7910 644 7 4717 2717 o44-5 7 8 99 5o 77 i 97 6 85 9 4 4 9 2 9 47 i4 8o54 658 7 4852 2848 05 7 2 8021 5i 9 4 2088 8 7 02 5o32 46 i5 8199 6 7 2 7 4988 2979 o6 9 8 8i43 53n 2201 8810 5i35 45 16 8343 6867 5i23 3no 0825 8265 542 9 23l3 8 9 i 7 5238 44 17 848 7 7006 5 2 58 324l o 9 5i 838 7 5546 2426 9025 534i 43 18 863a 7 i46 53 9 4 33 7 i io 77 85o8 5663 2538 9 i33 5444 42 *9 8776 7286 552 9 35o2 1203 863o 5 779 265o 9240 5547 4i 20 868920 8 77 425 885664 8 9 3633 9 oi32 9 9 o875i 9 i58 9 6 922762 929348 9 3565o 4o 21 9064 7 565 5-799 3 7 63 1455 8872 6oi3 28 7 5 9 455 6762 3 9 22 9207 77 o4 5 9 34 3894 i58i 8 99 4 6i3o 2986 9-662 5855 38 23 9 35i 7 844 6069 4024 I 77 9 n5 6246 3o 9 8 9669 5 9 5 7 37 24 9 4 9 5 7983 6204 4i54 i833 9 236 6363 3210 977 6 6060 36 26 9 63 9 8122 6338 4284 i 9 58 9 35 7 64 79 3322 9 884 6162 35 26 9782 8261 64 7 3 44i5 2084 9 478 65 9 5 3434 999 6264 34 27 9926 84oo 6608 4545 2209 9 5 99 6 7 I2 3545 9 3oo 97 6366 33 28 870069 8539 6 7 42 46 7 5 2335 97 20 6828 3657 02 4 6468 32 29 O2I2 86 7 8 68 7 6 48o5 2460 9 84i 6 9 44 3 7 68| o3n 65 7 o 3i 3o 8 7 o356 8 7 88i 7 88-7011 894934 9 o 2 585 9 o 99 6i 9 i 7 o6o 923880 930418 9 366 7 2 3o 3i o499 8 9 56 7 i45 5o64 2710 9 ioo82 7 i 7 6 3 99 i 0624 6 77 4 29 32 0642 9095 7 2 79 5i94 2836 O2O2 7 2 9 2 4lO2 o63i 68 7 6 28 33 o 7 85 9233 7 4i3 5323 2 9 6l o323 7 4o8 42i3 o 7 3 7 6 97 7 2-7 34 0928 9 3 7 2 7 548 5453 3o86 0443 7 523 4324 o843 77 9 26 35 1071 95io 7 68i 5582 3210 o563 7 63 9 4435 o 9 5o 7 i8i 23 36 I2l4 9649 7 8i5 5712 3335 o684 77 55 4546 io56 -7282 24 3? i35 7 9787 79 4 9 584i 346o 0804 7 8 7 o 465 7 1162 7 383 23 38 1499 9925 8o83 5970 3585 o 9 24 79 86 4 7 68 1268 7 485 22 3 9 1642 88oo63 82I 7 6099 3 7 9 io44 8101 48 7 8 i3 7 4 7 586 21 4o 871784 880201 88835o 896229 9 o3834 9 i i i 64 9 i82i6 924989 9 3i48o 9 3 7 68 7 2O 4i 1927 o33 9 8484 6358 3 9 58 1284 833i 5099 1 586 7788 1 9 42 2069 o4 77 86i 7 6486 4o83 i4o3 8446 52IO i6 9 i 7 88 9 18 43 2212 o6i5 8751 66i5 4207 i523 856i 53 2 o| 1797 799 o 17 44 2354 o 7 53 8884 6 7 44 433i i643 86 7 6 543o 1902 8o 9 i 16 45 2496 0891 9017 68 7 3 4455 1762 8 79 i 554i 2008 8i 9 i i5 46 2638 1028 9 i5o 7001 45 79 1881 8 9 o6 565i 2ii3 82 9 2 i4 .4? 2780 1166 9 283 7i3o 4 7 o3 2OOI 9 02I 5761 2219 83 9 3 i3 48 2922 i3o3 9 4i6 7258 4827 2120 9 i35 5871 2324 84 9 3 12 49 3o64 i44i 9 54 9 7 38 7 4 9 5i 223 9 9 25o 5980 2429 85 9 3 II 5o 873206 88i5 7 8 889682 8 97 5i5 505075 9 i2358 9 i 9 364 926090 932534 9 386 9 4 ro 5i 334y 1716 9815 7 643 5i 9 8 2477 9 47 9 6200 263 9 8-794 9 52 348 9 i853 99 48 7771 5322 25 9 6 9 5 9 3 63io 2744 88 9 4 8 53 363i 1990 8 9 oo8o 7 9 oo 5445 2715 97 o 7 64i 9 284 9 8 99 4 7 54 3 77 2 2127 02l3 8028 556 9 2834 9 82I 652 9 2 9 54 9094 6 55 3 9 i4 2264 o345 8i56 56 9 2 2 9 53 99 36 6638; 3o58 9 i 9 4 5 56 4o55 24OI o4 7 8 8283 58i5 3072 9 2oo5o 6 7 4 7 i 3i63 9294 4 5? 4196 2538 0610 84n 5 9 3 9 3i 9 o oi64 685 7 3 2 6 7 93 9 4 3 58 4338 2674 0742 853 9 6062 33o 9 0277 6 9 66 33 7 2 9 4 9 3 2 5 9 44 7 9 2811 o8 7 4 8666 6i85 342 7 o3 9 i 7 o 7 5 34 7 6 9 5 9 3 I 29 28 27 26 25 24 23 22 21 20 Natural Co-sines. ' >3 9 2.3l 2.24 2.16 2.O 9 2.OI i. 9 3 1.86 1.78 1.70 NATURAL TANGENTS. J n 60 61 62 63 64 65 66 67 68 69 1.73205 i.8o4o5 1.88073 1.96261 2.o5o3o 2.i445i 2. 246o4 2.35585 2.47509 2.60509 60 i 332i 0529 82o5 6402 5i8 2 46i4 4 7 80 5 77 6 7716 o 7 36 5 9 2 3438 o653 833 7 6544 5333 4777 4956 5 9 6 7 7924 0963 58 3 3555 0777 846 9 6685 5485 494o 5i3 2 6i58 8x32 1190 57 4 36 7 i 0901 8602 6827 563 7 5io4 53o 9 634 9 834o i4i8 56 5 3 7 88 1025 8 7 34 6969 5 79 o 5 2 68 5486 654i 854 9 1 646 55 6 3905 n5o 8867 7111 5942 5432 5663 6 7 33 8 7 58 1874 54 7 4O22 1274 9000 72 53 6094 55 9 6 584o 6925 8 9 6 7 2103 53 8 4i4o i3 99 9 i33 7 3 9 5 6 2 4 7 5760 6018 7118 9i 77 2332 52 9 425 7 i5 2 4 9266 7538 64oo 5925 6196 7 3u 9386 256i 5i 10 i. 7 43 7 5 1.81649 1.89400 1.97681 2.o6553 2.16090 2.26374 2.37504 2.4959-7 2.62791 5o ii 4492 1774 9 533 7823 6 7 o6 6 2 55 6552 7697 9 8o 7 3021 49 12 46io 1899 9667 7966 6860 6420 6 7 3o 7891 2.5ooi8 3252 48 i3 4728 2O25 9801 8110 7 oi4 6585 6909 8o84 0229 3483 47 i4 4846 2i5o 99 35 8253 7 i6 7 6 7 5i 7 o88 8279 o44o 3 7 i4 46 i5 4964 2276 1.90069 83 9 6 7 32I 6917 7267 8473 o652 3 9 45 45 16 5o82 24O2 0203 854o 7 4 7 6 7083 7 44 7 8668 0864 4177 44 7 5200 2528 o33 7 8684 7 63o 7249 7626 8863 io 7 6 44io 43 18 53i9 2654 0472 8828 7785 74i6 7806 9o58 1289 4642 4a *9 543 7 2780 0607 8972 79 3 9 7582 7987 9 253 I5O2 48 7 5 4i 20 i. 7 5556 1.82906 1.90741 1.99116 2.08094 2.17749 2.28167 2.3 9 44 9 2.5i 7 i5 2.65iO9 4o 21 56 7 5 3o33 0876 9261 825o 7916 8348 9 645 1929 5342 3 9 22 5794 3i59 ' IOI2 9406 84o5 8o84 8528 9 84i 2l42 55 7 6 38 23 5 9 i3 3286 1147 9 55o 856o 8 2 5i 8710 2.4oo38 235 7 58ii 37 24 6o32 34i3 1282 9 6 9 5 8 7 i6 8419 8891 0235 25 7 I 6o46 36 25 6i5i 354o i4i8 9 84i 88 7 2 8587 9 o 7 3 o432 2 7 86 6281 35 26 6271 3667 1 5 54 9986 9028 8 7 55 9 254 0629 3ooi 65i6 34 27 6390 3 79 4 1690 2.00l3l 9184 8 9 23 943 7 0827 32i 7 6 7 52 33 28 65io 3922 1826 0277 934i 9092 9619 IO25 3432 6989 32 29 663o 4049 1962 0423 9498 9261 9801 1223 3648 7225 3i 3o 1.76749 1.84177 1.92098 2.00669 2.09654 2.19430 2.29984 2.4i4ai 2.53865 2.67462 3o 3i 6869 43o5 2235 0715 9811 9 5 99 2.30167 1620 4082 7700 2 9 32 6990 4433 2371 0862 9969 9769 o35i 1819 4299 79 3 7 28 33 7110 456i 25o8 1008 2.10126 9938 o534 2019 45i6 8i 7 5 2 7 34 723o 468 9 2645 n55 0284 2.20108 0718 2218 4734 84i4 26 35 7 35i 48i8 2782 1302 o442 0278 0902 2418 4952 8653 25 36 7471 4946 2920 i449 0600 o44 9 1086 2618 5170 8892 24 3? 7 5 9 2 5o 7 5 3o5 7 i5 9 6 o 7 58 0619 1271 2819 538 9 9i3i 23 38 77 i3 52o4 3i 9 5 1743 0916 0790 i456 3019 56o8 9 3 7 i 22 39 ?834 5333 3332 1891 io 7 5 0961 i64i 3220 582 7 9612 21 4o 1.77955 1.85462 1.93470 2.02039 2.II233 2.2II32 2.31826 2.43422 2.56o46 2.6 9 853 2O 4i 8077 55 9 i 36o8 2187 1392 i3o4 2OI2 3623 6266 2.70094 *9 42 8198 5720 3 7 46 2335 i552 1475 2I 97 38 2 5 648 7 o335 18 43 8319 585o 3885 2483 i 7 n 1647 2383 4027 6707 o5 77 *7 44 844i 5979 4oa3 2 63i i8 7 i 1819 2570 423o 6928 0819 16 45 8563 6109 4162 2780 2o3o 1992 2756 4433 7i5o 1062 i5 46 8685 6239 43oi 2929 2190 2164 2 9 43 4636 73 7 i i3o5 i4 4? 8807 6369 444o 3078 2 35o 2 33 7 3i3o 483 9 7 5 9 3 1 548 i3 48 8929 6499 45 79 3227 25ll 25lO 33i 7 5o43 78i5 I 7 92 f 12 49 9o5i 663o 4718 3376 2671 2683 35o5 5246 8o38 2o36 II 5o i-79 I ?4 1.86760 1.94858 2.o3526 2.12832 2.22857 2.33693 2.4545i 2.58261 2. 7 228l IO 5i 9296 6891 4997 3675 2 99 3 3o3o 388i 5655 8484 2526 9 52 9419 7021 5i3 7 38 2 5 3i54 3204 4o6 9 586o 8708 2 77 I 8 53 9542 7 i52 5277 3 97 5 33i6 3378 4258 6o65 8932 3oi 7 7 54 9665 7283 54i7 4i25 34 77 3553 4447 6270 9 i56 3263 6 55 9788 74i5 555 7 4276 363 9 3 7 2 7 4636 6476 9381 35o 9 5 56 9911 7546 5698 4426 38oi 3902 4825 6682 9606 3 7 56 4 5? i.8oo34 7677 5838 45 77 3 9 63 4077 5oi5 6888 9 83i 4oo4 3 58 oi58 7809 5979 4728 4i25 4252 5 2 o5 7095 2.60057 425i 2 5 9 0281 79 4i 6120 4879 4288 4428 , 53 9 5 7302 0283 4499 I 29 28 27 26 25 24 23 22 21 20 Natural Co-tangents. 33 P P. tol". a ' 2.13 2.27 2.44 2.62 2.82 3.o5 3.3i 3.6i 3. 9 5 130 NATURAL SINES. 70 71 72 73 74 75 76 3 77 78 79 o I 939693 9792 9 455i 9 56i3 95io5 7 n46 966306 961262 6390 i 342 966926 6001 970296 o366 97 43 7 o 4435 97 8i48 8208 9 8i62 7 |6o 1683 5q 2 9891 5 7 o8 1236 64 7 5[ 1422 6076 o436 45oi 8268 i 7 38 58 (. 999 * 58o2 i326 656o 1502 6i5i o5o6 4566 832 9 I 79 3 57 L 940090 58 97 i4i5 6644 i582 6226 o5 77 463i 838 9 1849 56 I 0189 5 99 i i5o5 6-729 1662 63oi o64 7 46 9 6 844 9 1904 55 6 0288 6o85 1 5g4 68i4 i 7 4i 63 7 6 o 7 i6 4 7 6i 85o 9 1969 54 7 o38 7 6180 1 684 6898 1821 645 1 o 7 86 4826 856 9 20l4 53 8 o486 62 7 4 i 77 3 6 9 83 I 9 OI 6626 o856 48 9 i 862 9 2O6 9 52 9 o585 6368 1862! 7067 i 9 8o 6600 9 26 4 9 56 868 9 2123 5i 10 940684 946462 961961 95 7 i5i 962059 9 566 7 5 9799 5 97 5o2o 97 8 7 48 9 82i 7 8 5o ii 0782 6555 2o4o 7 235 2139 6749 io65 5o85 8808 2233 49 12 0881 6649 2129 73i 9 2218 6823 ii34 5i4 9 8867 228-7 48 i3 0979 6 7 43 2218 7 4o4 22 97 6898 1204 52i4 891- 3342 47 i4 1078 683 7 2307 7 48 7 23 7 6 6972 I2 7 3 52 7 8 8986 23 9 6 46 i5 1176 6930 2396 7 5 7 i 2455 7 o46 1 342 5342 9 o45 245o 45 16 1274 7 024 2484 7 655 2534 7120 i4n 54o6 9 io5 25o5 M i? I3 ? 2 7117 25 7 3 77 3 9 * 26i3 7 ig4 i48o 54 7 i 9 i64 2 55 9 43 18 1471 7210 2661 7 822 26 9 2 7 268 i54 9 5535 9 223 26i3 42 '9 i56 9 73o4 275 7906 2 77 7342 1618 55 9 8 9 282 2667 4i 20 941666 947397 9 5 2 838 9 5 799 962849 96 7 4i5 97 i68 7 976662 979 34i 0.82-721 4o 21 1764 7490 2926 8o 7 3 2 9 28 7 48 9 i 7 55 5-726 9 3 99 2 77 4 3 9 22 1862 7 583 3oi5 8i56 3oo6 7 562 1824 5 79 o 9 458 2828 38 23 1960 7676 3io3| 8 2 3 9 3o84 7 636 i8 9 3 5853 9 5l 7 2882 37 24 2057 7768 3i 9 n 8323 3i63 779 i 9 6i 5 9 i 7 9 5 7 5 2 9 35 36 25 2i55 7861 3279 84o6 324i 77 82 2O2 9 5 9 8o 9 634 2 9 8 9 35 26 2252 79 54 3366 848 9 33i 9 7 856 20 9 8 6o44 9 6 9 2 3o42 34 2 7 235o , 8o46 3454 85 7 2 33 97 79 2 9 2l66 610-7 97 5o 3o 9 6 33 28 2447 8i3 9 3542 8654 34 7 5 8002 2234 6i 7 o 9 8o 9 3i4 9 32 2 9 2544 823i 362 9 8 7 3 7 3553 8o 7 5 2302 6233 9 86 7 3*02 3i 3o 942641 948324 9 53 77 9 5882o 9 6363o 9 68i48 972370 97 62 9 6 9799 25 9 83255 3o 3i 2 7 3 9 84i6 38o4 8 9 O2 3 7 o8 8220 2438 635 9 99 83 33o8 29 32 a836 85o8 38 9 2 8985 3 7 86 82 9 3 25o6 6422 9 8oo4i 336i 28 33 2932 8600 3 979 9 o6 7 3863 8366 25 7 3 6485 0098 34x4 2 7 34 3029 8692 4o66 9 i5o 3 9 4i 8438 2641 654 7 oi56 3466 26 35 3i26 8 7 84 4:53 9 232 4oi8 85n 2708 6610 0214 35i 9 25 36 3223 88 7 6 4240 9 3i4 4o 9 5 8583 2776 66-72 O2 7 I ' 35 7 i 24 3? 33i 9 8 9 68 432 7 9 3 9 6 4i 7 3 8656 2843 6 7 35 o32g 3624 23 38 34i6 9 o5 9 44i4 9 4 7 8 425o 8 7 28 291 1 6797 o386 36 7 6 22 3 9 35i 2 9i5i 45oi 9 56o 432 7 8800 2978 685 9 o443 3729 21 4o 943609 949243 9 54588 959642 9 644o4 9 688 7 2 973o45 97 6 9 2i 980600 9 83 7 8i 20 4i 3 7 o5 9 334 46 7 4 97 24 448 i 8 9 44 3lI2 6 9 84 o558 3833 '9 42 38oi 9 425 4 7 6i 9 8o5 455 7 9 oi6 3i79 7 o46 o6i5 3885 18 43 38 97 9 5l 7 484 7 9 88 7 4634 9 o88 3246 -7108 06-72 3 9 3 7 '7 44 3 99 3 9 6o8 4934 99 68 4 7 n 9 i5 9 33i3 7 i6 9 7 28 3 9 8 9 16 45 4089 9699 5020 9 6oo5o 4 7 8 7 9 23i 3379 7 23l o 7 85 4o4i i5 46 4i85 9-790 5io6 oi3i 4864 9 3o2 3446 7 2 9 3 0842 4092 i4 47 4281 9881 5192 0212 4 9 4o 9 3 7 4 35i2 7 354 0899 4i44 i3 "48 43 7 6 997 2 52 7 8 02 9 4 5oi6 9446 35 79 7 4i6 o 9 55 4196 12 49 44 7 2 95oo63 5364 o3 7 5 5o 9 3 9 5i 7 3645 7477 1012 424 7 II 5o 944568 95oi54 95545o 9 6o456 966169 9 6 9 588 97 3 7 i2 977539 981068 984298 IO 5i 4663 0244 5536 o53 7 5245 9 65 9 3 77 8 7 6oo 1124 435o 9 5a 4 7 58 o335 5622 0618 532i 9 7 3o 3844 7661 1181 44oi 8 53 4854 042 5 5 77 o6 9 8 53 97 9 8oi 3910 77 22 I23 7 4452 7 54 4949 o5i6 5 79 3 779 54 7 3! 9 8 7 2 3 97 6 7783 I2 9 3 45o3 6 55 5o44 0606 58 79 0860 5548; 99 43 4042 7 844 1 349 4554 5 56 5i3 9 0696 5 9 64 o 9 4o 5624 97 ooi4 4io8 79 o5 i4o5 46o5 4 57 5234 o 7 86 6o4g 1021 5 7 oo oo84 4i 7 3 79 66 i46o 4656 3 58 532 9 o8 77 6i34 IIOI 5 77 5: oi55 423 9 8026 i5i6 477 2 5 9 5424 096-7 6220 1181 585o 0225 43o5 8o8 7 | i5 7 2 4 7 5 7 I 19 18 17 16 15 14 13 12 11 10 d Natural Co-sines. i ' i.54 i.46 i.38 :.3o I .21 i.i3 1. 06 o-97 0.88 NATURAL GENTS. 131 j 70 71 72 73 74 75 76 77 78 79 o 2.74748 2.90421 3.07768 3.2 7 o85 3.48 7 4i 3. 7 32o5 4.010-78 4.33i48 4- 7 o463 5.14455 60 I 4997 0696 8073 7 426 9 I25 364o i5 7 6 3 72 3 u3 7 6266 5 9 2 6246 0971 83 79 7767 9 5o 9 4o 7 5 20 7 4 43oo i8i3 6068 58 q 6496 1246 8685 8io 9 9 8 9 4 4612 25 7 4 48 79 24 9 6863 57 4 5 7 46 1623 8 99 i 8462 3.5o2 79 4g5o 3o 7 6 545 9 3i 7 o 7671 56 c 6996 1799 9 2 9 8 8795 o666| 5388 35 7 8 6o4o 385i 848o 55 6 624-7 2O 7 6 9 6o6 9 l3 9 io53 6828 4o8i 6623 4534 9 2 9 3 54 7 64 9 8 2354 99 i4 9 483 i44i 6268 4586 7207 52I 9 5.20I0 7 53 8 6 7 5o 2632 3.10223 9 82 9 i82 9 6-709 6092 77 9 3 5 9 o6 O 9 25 52 9 7002 2910 o532 3.3oi 7 4 22I 9 7162 55 99 838i 65 9 5 i 7 44 5i 10 2.77264 2.93189 3.io842 3.3o52i 3 526o 9 3. 77 5 9 5 4.0610-7 4.38 9 6 9 4. 77 286 5.22566 5o ii 7607 3468 ii53 0868 3ooi 8o4o 6616 9 56o 7978 33 9 i 4 9 12 7761 3 7 48 i464 1216 33 9 3 8485 7 I2 7 4.40162 86 7 3 4218 48 i3 8oi4 4028 1776 i565 3 7 85 8931 7 63 9 0746 9 3 7 o 5o48 47 i4 826 9 43o 9 2087 i 9 i4 4i 79 9378 8162 i34o 4.80068 588o 46 16 8523 45 9I 24oo 2264 45 7 3 9 82 7 8666 I 9 36 o 7 6 9 6 7 i5 45 16 8778 48 7 2 2713 2614 4 9 68 3.802-76 9182 2534 i4 7 i 7 553 44 17 9 o33 5i55 3027 2 9 65 5364 0-726 9699 3i34 2I 7 5 83 9 3 43 18 9 28 9 543 7 334i 33i 7 5 7 6i n 77 4.10216 3 7 35 2882 9 235 42 '9 9 545 6-721 3656 36 7 o 6i5 9 i63o o 7 36 4338 35 9 o 5.3oo8o 4i 20 2.7 9 8O2 2.96004 3.i3 9 72 3.34023 3.5655 7 3.82083 4.ii256'4.44 9 42 4.843oo 5.3o 9 28 4o 21 2.8oo5 9 6288 4288 43 77 6 9 5 7 253 7 1778 5548 5oi3 1-7-78 3 9 22 o3i6 65 7 3 46o5 4 7 32 735 7 2992 2301 6i55 5 7 2 7 263i 38 23 0674 6858 4 9 22 5o8 7 7758 3449 2826 6 7 64 6444 348 7 37 24 o833| 7144 6240 5443 8160 3906 335o 7 3 7 4 -7162 4345 36 25 :o 9 i 7 43o 5558 58oo 8662 4364 38 77 79 86 7882 6206 35 26 i35o 77 i 7 58 77 6168 8 9 66 4824 44o5 8600 86o5 6o 7 o 34 27 1610 8oo4 6i 97 65i6 9 3 7 o 6284 4934 9 2l5 9 33o 6 9 36 33 28 1870 8292 65i 7 68 7 5 9775 5 7 45 5465 9 832 4. 9 oo56 7 8o5 32 2 9 2130 858o 6838 7234 3.6oi8i 6208 699-7 4.5o45i o 7 85 86 77 3i 3o 2.823 9 I 2.98868 3.i 7 i5 9 3.3 7 5 9 4 3.6o588 3.866 7 i 4.i653o 4.61071 4.91616 5.3 9 55 2 3o 3i 2653 9168 7 48t 7 9 55; o 99 6 7 1 36 7 o64 i6 9 3 224 9 5.4o42 9 2 9 32 2 9 i4 944 7 7 8o4 8317 i4o5 7601 7600 23i6 2 9 84 i3o 9 28 33 3i 7 6 9738 812-7 86 79 1814 8068 8i3 7 2 9 4i 3 7 2I 2I 9 2 2 7 34 343 9 3.00028 845 1 2224 8536 86 7 5 3568 446o 3o 77 26 35 3702 0319 8775 9 4o6 2636 9004 9216 4i 9 6 6201 3 9 66 25 36 3 9 65 06 1 1 9 ioo 977 1 3o48 9474 9756 4826 5 9 45 485 7 24 37 422 9 o 9 o3 9 426 3.4oi36 346i 9945 4.20298 5458 66 9 o 6761 23 38 44 9 4 n 9 6 97 52 0602 38 7 4 3.90417 0842 6o 9 i 7438 6648 22 39 4768 i48 9 3.20O 79 o86 9 4289 0890 i38 7 6726 8188 7548 21 4o 2.85oa3 3.oi 7 83 3.2o4o6 3.4i236 3.64 7 o5 3. 9 i364 4.21933 4.5 7 363 4- 9 8 9 4o 5.4845i 20 4i 6289 20 77 o 7 34 1604 5l2I 1839 2481 8001 9 6 9 5 9 356 ig 42 5555 23 7 2 io63 I 97 3 5538 23i6 3o3o 864i 5.oo45i 6.60264 18 43 6822 266-7 i3 9 2 2343 5 9 5 7 2 79 3 358o 9 283 1210 1176 I 7 44 6o8 9 2 9 63 I 7 22 2 7 l3 63 7 6 32 7 I 4l32 99 2 7 i 97 i 2000 16 45 6356 3260 2053 3o84 6 79 6 3 7 5i 4685 4.60672 2 7 34 3007 i5 46 6624 3556 2384 3456 7 2I 7 4232 6239 I2I 9 34 99 39 2 7 i4 47 68 9 2 3854 2 7 l5 382 9 7 638 4 7 i3 5795 1868 4267 485i i3 48 7161 4162 3o48 4202 8061 6196 6352 25l8 5o3 7 5777 12 49 743o 445o 338i 45 7 6 8485 568o 6911 3l7I 58o 9 6706 II 5o 2.87700 3*oA'74Q 3.23 7 i4 3.44 9 5i 3.68909 3. 9 6i65 4.2 7 4 7 i 4.63825 5.o6584 5.5 7 638 10 5i 7970 5o4 9 4o4 9 532 7 9335 6661 8o32 448o 7 36o 85 7 3 9 62 8240 534 9 4383 5 7 o3 976i 7 i3 9 8696 5i38 8i3 9 9 5n 8 53 85 1 1 564 9 4 7 r 9 6080 3. 7 oi88 7 62 7 9169 5 797 8 9 2I 6.60462 7 54 8 7 83 5 9 5o 5o55 6458 0616 811-7 9 7 24 6458 97 o4 i3 97 6 55 9 o55 6262 53 9 2 683 7 io46 86o 7 4.30291 7121 5.io4 9 o a344 5 56 9327 6554 5 7 2 9 7216 i4 7 6 999 0860 7786 1270 3a 9 5 4 57 9 6oo 685 7 6o6 7 7 5 9 6 190-7 9 5 9 2 i43o 8462 2069 4248 3 58 9873 7160 64o6 7977 23384.00086 2001 9I2I 1 2862 5205 2 69 2. 9 oi47 7464 6 7 45 835 9 2 77 l| 0682 2 5 7 3 979 i 3658 6166 i 19 18 17 16 15 ! 14 13 12 11 10 . ' Natural Co-tangents. to* I"'. 4 ' 35 4.8a 5.36 6.01 6. -79 7 . 7 3 8.90 10.35 12. 2O i4.6o ! 132 NATURAL SINES. 1 H 80 81 82 83 84 85 86 87 88 89 O 848o8 9 8 7 688 990268 99 2546 994522 99619-5 99 7 564 99 863o 999 3 9 i 999848 [JO I 4858 77 34 o3o 9 2582 455 2 6220 7 584 8645 9 4oi 9 853 5 9 2 4909 7779 o34g 2617 4583 6245 7 6o4 8660 9 4n 9358 58 3 4959 7824 0389 2652 46i3 6270 7 625 86 7 5 9 42I 9 863 5 7 4 5009 7870 0429 2687 4643 6295 7 645 86 9 o 9 43i 9 86 7 56 5 SoSg 79i5 0469 2722 46 7 3 6320 7 664 8 7 o5 944i 9 8 7 2 55 6 5109 7960 oSog 2 7 5 ? 4 7 o3 6345 7 684 : 8719 9 45o 9 8 77 54 7 5i5 9 8oo5 o549 27 9 2 4733 63 7 o 77 o4 8 7 34 9 46o 9881 53 8 5209 8o5o oSSg 2827 4 7 6 2 63 9 5 77 24 8 7 4 9 9 46 9 9886 52 9 5a5 9 8o 9 4 0629 2862 4 7 92 64i 9 7743 8 7 63 9479 9890 5i 10 985309 9 88i3 9 990669 99 28 9 6 994822 996444 9 977 63 998778 999488 9V9 8 94 5o ii 5358 8i84 0708 2 9 3i 485i 6468 7782 8792 9497 9 8 9 8 49 12 54o8 8228 o 7 48 2 9 66 488 1 64 9 3 7801 8806 9 5 7 99 o3 43 i3 545 7 8273 0787 3ooo 4910 65i 7 7821 8820 9 5i6 997 47 i4 55o 7 83i 7 0827 3o34 4 9 3 9 654i 7840 8834 9 5a5 99 io 46 i5 5556 8362 0866 3o68 4 9 6 9 6566 7869 8848 9 534 99 i4 45 16 56o5 84o6 0905 3io3 4 99 8 6590 7878 8862 9 542 99 i8 44 *7 5654 845o 0944 3i3 7 5o2 7 66i4 7897 8876 9 55i 9-932 43 18 5 7 o3 84 9 4 0983 3i 7 i 5o56 663 7 7916 8890 9 56o 99 25 42 J 9 5 7 5a 8538 IO22 32o5 5o84 6661 7934 8 9 o4 9 568 99 2 9 4i 20 985801 9 8858a 991061 99 3238 99 5n3 996685 997953 998917 999577 9999 32 4o 21 585o 8626 IIOO 32 7 2 5i42 6 7 09 7972 8 9 3i 9 585 99 36 39 23 58 99 866 9| n38, 33o6 5i 7 o 6 7 32 799 8944 9594 99 3 9 38 23 5 9 47 8713 1177! 333 9 5i 99 6 7 56 8008 8 9 5 7 9 6o2 99 42 3 7 24 5996 8 7 56 1216' 3373 522 7 6779 8027 8971 9 6io 9945 36 25 6o45 8800 1254 34o6 5 2 56 6802 8o45 8984 9 6i8 9948 35 26 6093 8843 I2 9 2 343 9 5284 6825 8o63 8997 9 626 99 5i 34 27 6i4i 8886 i33i 34 7 3 53i2 6848 8081 9010 9 634 99 54 33 28 6189 8 9 3o i36 9 35o6 534o 6872 8099 9023 9 642 99 5 7 32 29 6238 8 97 3 1407 353 9 5368 6894 8117 9 o35 9 65o 99 5 9 3i 3o 986286 9 8 9 oi6 99 i445 99 35 7 2 99 53 9 6 996917 998135 999048 9 99 65 7 999962 3o 3i 6334 9 o5 9 i483 36o5 5424 6940 8i53 9061 9 665 99 64 2 9 32 638i 9102 l52I 3638 5452 6 9 63 8170 97 3 96-72 99 6 7 28 33 6429 9 i45 i558 36 7 o 5479 6 9 85 8188 9 o86 9680 9969 2 7 34 6477 9187 1596 3 7 o3 55o 7 7008 82o5 9 o 9 8 9 68 7 997 1 26 35 65 2 5 9230 i634 3 7 35 5535 7o3o 8223 9 i ii 9694 9974 25 36 65 7 2 9272 1671 3 7 68 5562 7 o53 8240 9 I2: 97 oi 9976 24 37 6620 93i5' I7o 9 38oo 558 9 7075 8 2 5 7 9 i35 979 9978123 38 6667 9 35 7 1746 3833 56i 7 7097 8274 9147 9 7 i6 9980 22 3 9 6714 9 3 99 I 7 83 3865 5644 7119 8291 9 i5 9 9-722 99 8i 21 4o 986762 9 8 9 442 99 l82O 99 3 897 99 56 7 i 997i4i 99 83o8 999171 999729 9V99 83 2O 4i 6809 9 484 i85 7 3 9 29 5698 7 i63 8325 918: 9736 99 85 '9 42 6856 9 526 i8 9 4 3 9 6i 5 7 25 7 i85 8342 9194 9743 99 86 18 43 690? 9 568 I 9 3i 3 99 3 5 7 52 7207 835 9 9 2o6 9749 99 88 17 44 6 9 5o 9 6io i 9 68 4oa5 5 77 8 7229 83 7 5 9 2l8 9 7 56 9989 16 45 6996 9 65i 2OO5 4o56 58o5 725o 83 9 2 9229 97 62 999 i5 46 7o43 9 6 9 3 2042 4o88 5832 7272 84o8 9240 97 68 9993 i4 47 7090 97 35 2078 4l20 5858 7293 8425 9252 977 5 999 3 i3 48 7I 36 9776 2Il5 4i5i 5884 73i4 844 1 926^ 978i 9994 12 49 7 i83 9818 2l5l 4182 Sgii 7 336 845 7 9274 9787 999 5 II 5o 987229 989859 99 2i8 7 9942i4 99 5 937 997357 99 84 7 3 999285 99979 s 97999 6 10 5i 7 2 7 5 9900 222<^ 4a45 5 9 63 7 3 7 8 848 9 9 2 9 6 9799 9997 9 52 7 322 9942 226o 42 7 6 5 9 8 9 7399 85o5 9307 9804 9997 53 7368 99 83 22 9 6 43o 7 6oi5 7420 852i 9 3i8 9810 999 8 7 54 7 4i4 99002^ 2332 4338 6o4i 744i 853 7 9 328 9816 9998 6 55 7 46o oo65 2368 436 9 6067 7462 855a 9 33 9 9821 9999 5 56 7 5o6 oio5 24O2 44oo 6093 7482 8568 9 35o 9 82 7 9999 4 5 7 55 oi46 243$ 443c 6118 75ov 8583 9 36o 9832 1. 00000 3 58 7 5 9 0187 247^ 446 6i44 7 5 2 3 85 99 9 3 7 9 83 7 oooo 5 764 0228 25ll 44g 6169 7 544 86i4 9 38 9 843 0000 i 9 8 7 6 5 4 3 2 1 c Natural Co-sines. i Jo'*;. - 80 0.72 o.63 o.55 0.46 o.38 o.3o O.2I o.i3 o.o4 NATURAL TANGENTS. 133 j 80 1 81 82 83 84 85 86 87 88 89 5.67128 6.3i375 7.n53 7 8.i4435 9 .5i436 n.43oi i43oo 7 19.0811 28.6363 5 7 .2 9 oo 60 I 8o 9 4; 2566 3o42 6398 4io6 4685 36o 7 1879 8 77 i 58.2612 5 9 2 9064 3761 455-3 83 7 o 6791 5o 7 2 4212 2 9 5 9 29.1220 5 9 .265 9 58 3 5.70037! 4o .oooi454 3 .4014267 48 .8377680 1 60 2.7926268 4o .01x6355 40 .0001939 24 .4188790 49 .85521x3 170 2.9670697 5o .0145444 5o .0002424 25 .4363323 5o -.8726646 1 80 3.1416927 60 .0174533 60 .0002909 ISC) TRAVERSE TABLE. Course. Dist. I. Dist. 2. Dist. 3. Dist. 4. * Dist. 6. Lat Dep. Lat Dep. Lat Dep. Lat Dep. Lat Dep. o / / o i5 I.OOOO c. oo4/4 ? OOOO o.oo8 7 3. oooo o.oiSi 4-OOOO O.OI 7 5 5. OOOO O.O2I$ 89 45 3o OOOO oo8 7 1.9999 oi 7 5 2.9999 0262 3.9998 o34 9 4- 999 8 o436 3o 45 0.9999 oi3i 9998 0262 9997 o3 9 3 9997 o52^! 9996 o654 i5 I O 9998 oi 7 5 9997 o34 9 999 5 o524 9994 o6 9 8 9992 087; 89 o 16 9998 0218 1 999 5 o436 999 3 o654 999 o8 7 3 0988 io 9 i 45 3o 9997 0262 9993 o524 999 o 7 85 99 86 io4 7 5 9 83 i3o 9 3o 45 r 999 5 o3o5 9991 0611 99 86 o 9 i6 99 8i 1222 9977 i5 27 16 2 9994 o34 9 9988 o6 9 8 9982 io4 7 9976 i3 9 6 9970 i 7 45 88 o i5 9992 o3 9 3 99 85 o 7 85 9977 1178 9969 i5 7 o 996i i 9 63 45 3o 9990 o436 99 8i o8 7 2 997i i3o 9 9962 i 7 45 99 5 2 2181 3o 45 0.9988 o.o48o i. 9977 o.o 9 6o 2.9966 o.i43 9 3. 99 54 o.i 9 i 9 4*9942 o. 2 3 99 i5 3 o 9986 o523 9973 io4 7 99 5 9 i5 7 o 99 45 20 9 3 99 3i 26l 7 87 o i5 9984 o56 7 99 68 n34 99 5 2 I 7 OI 99 36 2268 9920 2835 45 3o 9981 0610 99 63 1221 9944 i83i 99 25 2442 9907 3o5 2 3o 45 9979 o654 99 5 7 i3o8 99 36 I 9 62 99 i4 2616 9 8 9 3 32 7 i5 4 o 9976 o6 9 8 99 5i i3 9 5 9927 20 9 3 99 o3 2 79 O 9878 3488 86 o i5 997 3 o 7 4i 99 45 1482 9918 2223 9 8 9 o 2 9 64 9 863 3 7 o* 45 3o 9969 o 7 85 99 38 i56 9 99 o8 2354 9877 3i38 9 846 3 9 23 3o 45 9966 0828 99 3i i656 9 8 97 2484 9 863 33i2 9 828 4i4o i5 5 o 9962 o8 7 2 9924 i 7 43 9 886 2 6i5 9848 3486 9 8io 4358 85 o i5 o. 99 58 o.o 9 i5 1.9916 o.i83o 2 . 9 8 7 4 o.2 7 45 3. 9 832 o.366o 4. 979 o o.45 7 5 45 3o 99 5 4 o 9 58 99 o8 I 9 i 7 9 862 2 8 7 5 9 8i6 3834 977 4 79 2 3o 45 99 5 1002 9 8 99 2004 9849 3oo6 9799 4oo8 97 48 5oo 9 i5 6 o 9945 io45 9 8 9 o 2O 9 I 9836 3i36 978i 4i8i 97 26 5226 84 o i5 9941 1089 9 88i 2I 77 9822 3266 97 62 4355 97 o3 5443 45 3o 9936 iiSa 9 8 7 i 2264 98o 7 33 9 6 9743 4528 9679 566o 3o 45 99 3i n 7 5 9 86i 235l 979 2 3526 9723 4 7 oi 9 653 58 77 i5 7 99 25 1219 9 85i a43 7 9776 3656 97 02 48 7 5 9627 6o 9 3 83 o i5 9920 1262 9 84o 2524 97 6o 3 7 86 9 68o 5o48 9600 63io 45 3o Q9i4 i3o5 9 82 9 2611 9743 3 9 i6 9 658 5221 9 5 7 2 6526 3o 45 0.9909 0.1349 i. 9 8i 7 o.26 97 2.9726 o.4o46 3. 9 635 o.53 9 4 4. 9 543 o.6 7 43 i5 8. o 9903 1392 9 8o5 2 7 83 97 o8 4i 7 5 9 6n 556 7 9 5i3 6 9 5 9 82 o i5 9897 i435 9793 28 7 9 6 9 o 43o5 9 586 5 7 4o 9 483 7175 45 3o 9 8 9 o i4 7 8 97 8o 2 9 56 9 6 7 o 4434 9 56i 5 9 I2 9 45i 7 3 9 o 3o 45 9 884 l52I 97 6 7 3o42 9 65i 4564 9 534 6o85 9 4i8 7606 i5 9 o 9877 1 564 97 54 3i2 9 9 63i 46 9 3 9 5o8 625 7 9 384 7822 81 o i5 9 8 7 o i6o 7 97 4o 32 1 5 9 6io 4822 9 48o 643o 9 35o 8037 45 3o 9 863 i65o 97 26 33oi 9 58 9 4 9 5i 9 45i 6602 9 3i4 8252 3o 45 9 856 i6 9 3 97 n 338 7 9 56 7 5o8o 9 422 6 77 4 9 2 7 8 846 7 i5 10 9 848 I 7 36 9696 34 7 3 9 544 52O 9 9 3 9 2 6 9 46 9 240 8682 80 o i5 o. 9 84o o-i779 i. 9 68i o.355 9 2. 9 52I 0.5338 3. 9 362 o. 7 n8 [.9202 o.88 97 45 . 3o 9 833 1822 9 665 3645 9 4 9 8 546 7 9 33o 7 28 9 9 i63 9 II2 3o 45 9 825 i865 9 64 9 3 7 3o 9 4 7 4 55 9 6 9 2 9 8 746 1 9 I23 9 326 i5 II 9 8i6 1908 9 633 38i6 9 44 9 5 7 24 9 265 7 63 2 9 o8i 9 54o 70 o i5 9 8o8 igSi 9 6i6 3 9 02 9424 5853 9 23l 7804 9 o3 9 9755 45 3o 9799 1994 9 5 9 8 3 9 8 7 9 3 9 8 5 9 8i 9197 797 5 8 99 6 99 68 3o 45 979 2o36 9 58i 4o 7 3 9 3 7 i 6io 9 9 l62 8i46 8 9 52 1.0182 i5 12 o 97 8i ao 79 9 563 4i58 9 344 623 7 9 I26 83i6 8 9 o 7 o3 9 6 78 o i5 977 2 2122 9 545 4244 9 3i 7 6365 9 o8 9 848 7 8862 o6o 9 45 3o 9763 2 1 64 9 526 432 9 9 28 9 64 9 3 9 o52 8658 88i5 0822 3o 45 o. 97 53 O.22O 7 i. 9 5o 7 o.44 1 4 2. 9 26o 0.6621 3. 9 oi4 0.8828 4.8 7 6 7 i.io35 i5 i3 o 97 44 2250 9 48 7 44 99 9 23l 6 7 4 9 8 97 5 8 99 8 8 7 i 9 1248 77 i5 9734 2292 9 468 4584 9 20I 68 7 6 8 9 35 9 i68 866 9 i46o 45 3o 97 24 2334 9 44 7 466 9 9 I 7 I 7 oo3 88 9 5 9 338 8618 l6 7 2 3o 45 97 i3 2 3 77 9 42 7 4 7 54 9 i4o 7 i3i 8854 9 5o 7 856 7 1884 -5 i4 o 97 o3 2419 9 4o6 4838 9 I0 9 7 258 8812 9677 85i5 2O 9 6 7 6 o i5 9 6 9 2 2462 9 385 4 9 23 977 7 385 8 7 6 9 9 846 8462 a3o8 45 3o 9 68i 25o4 9 363 5oo8 9 o44 7 5n 8 7 26 I.OOlS; 8407 25i 9 3o 45 9 6 7 o 2546 9 34i 5o 9 2 9 OII 7 638 8682 0184 8352 2 7 3o i5 i5 o 9 65 9 2588 9 3i 9 5i 7 6 8 97 8 7765 863 7 o353 82 9 6 2 9 4l 7 5 o Dep. Lat Dep. Lat Dep. Lat Dep. Lat. i Dep. Lat Dist. 1. Dist. 2. Dist. 3. Dist. 4. Dist. 5. Couna. TRAVERSE TABLE. 137 Course. Dist. 6. Dist, 7. Dist. 8. Dist. 9. Dist. 10. Lat. Dep. Lat. Dep. Lat. j Dep. Lat i Dep. Lat Dep. o / / o i5 6.9999 .0262 9999 o.o3o5 9999 o.o34 9 9999 O.oSgS 9-9999 o.o436 8 9 45 3o 9998 o524 9997 06 1 1 9997 o6 9 8 9997 o 7 85 999 6 o8 7 3 3o 45 999 5 o 7 85 9994 0916 999 3 io4 7 9992 1178 999 T i3oo i5 : o 9991 1047 9989 1222 9988 i3 9 6 9986 i5 7 i 99 85 I745 1 8 9 o i5 9986 1 309 99 83 l52 7 9981 i 7 45 9979 1963 9976 2181 45 3o 9979 1571 997 6 i832 997 3 2094 9969 2356 99 66 2618 3o 45 9972 i832 9967 2i38 99 63 2443 99 58 2 7 48 99 53 3o54 i5 2 9963 2094 99 5 7 2443 99 5i 2 79 2 9945 3i4i 99 3 9 34 9 o 8 o i5 9954 2 356 9946 2748 99 38 3i4i 99 3i 3533 99 23 3 9 26 45 3o 9943 2617 99 33 3o53 99 24 34 9 o 9914 3926 99 o5 4362 3o 45 5. 99 3i .2879 .9919 0.3358 99 8 0.3838 .9896 o.43i8 . 9 885 0.4798 i5 3 o 9918 3i4o 99 o4 3664 9 8 9 o 4i8 7 9877 4 7 io 9 863 5 2 34 7 o i5 9904 3402 9887 3 9 68 9 8 7 i 4535 9 855 5l02 9 83 9 566 9 45 3o 9888 3663 9869 42 7 3 9 85i 4884 9832 5494 9 8i3 6io5 3o 45 9872 3 9 24 985o 45 7 8 9 82 9 5232 9807 5886 97 86 654o i5 4 o 9 854 4 1 85 9829 4883 9 8o5 558i 9781 62 7 8 9756 6 9 76 6 o 16 9835 444? 9808 5i88 9 78o 5 9 2 9 9753 6670 9725 74n 45 3o 9815 4708 9784 54 9 2 9753 62 77 9723 7061 9 6 9 2 7 846 3o 45 9794 4 9 68 9760 5 797 9725 6625 9691 7453 9 65 7 8281 i5 5 o 9772 522 9 97 34 6101 9 6 9 6 6 97 2 9 658 7844 9 6i 9 8716 5 o i5 5. 97 48 .54 9 o .9706 o.64o5 . 9 664 0.7320 . 9 622 0.8235 . 9 58o o. 9 i5o 45 3o 9724 5 7 5i 9678 67O 9 9 632 7668 9 586 8626 9 54o 9 585 3o 45 9698 6on 9 648 7013 9 5 97 8oi5 9 547 9017 9 4 97 .0019 i5 6 o 9671 6272 9617 7 3i 7 9 562 8362 9 5 7 9408 9 452 o453 84 o i-5 9 643 6532 9 584 7621 9 5 2 5 &70 9 9 465 9798 9 4o6 0887 45 3o 9614 6 79 2 9 55o 7 9 24 9 486 9 o56 9 42I .0188 9 35 7 1320 3o 45 9 584 7052 9 5i5 8228 9 445 9 4o3 9 3 7 6 0578 9 3o 7 1754 i5 7 9553 7312 0478 853i 9 4o4 97 5o 9 32 9 0968 9 255 2187 83 o i5 9520 7 5 7 2 9 44o 8834 9 36o 1.0096 9 28o i358 9 2OO 2620 45 3o 948 7 7832 9 4oi 9 i3 7 9 3i6 o442 9 23o 1747 9 i44 3o53 3o 45 . 9 45 2 o.8o 9 i . 9 36i o. 9 44o 7. 9 26 9 1.0788 8. 9 i 7 8 1.2137 9 . 9 o8 7 1.3485 i5 8 o 94i6 835o 9 3r 9 97 42 9221 n34 91*4 2526 9 027 3 9 i 7 82 o :5 9 3 79 8610 9 276 .0044 9 I 7 2 1479 9 o6 9 2914 8 9 65 434 9 45 3o 934i 886 9 9 23l o347 9 I2I 1825 9 OI I 33o3 8 9 02 4 7 8i 3o 45 9302 9 :2 7 9 i85 o64 9 9 o6 9 2170 8 9 53 3691 8836 5212 i5 9 9261 9 386 9 i38 o 9 5o 9 oi5 2 5i5 88 9 2 4079 8769 5643 81 o i5 9220 9 645 9 o 9 o 1262 8 9 6o 2 85 9 883o 4467 8700 6o 7 4 45 3o 9177 99 o3 9 o4o i553 8 9 o3 3204 8766 4854 8629 65o5 3o 45 9 i33 1.0161 8989 i854 8844 3548 8700 524i 8556 6 9 35 i5 IO O 9088 o4i 9 8 9 3 7 2i55 8 7 85 3892 8633 56 2 8 848 1 7 365 80 o i5 5.9042 1.0677 6.8883 1.2456 7.8723 1.4235 8.8564 i.6oi5 9 .84o4 1.7794 45 3o 8 99 5 o 9 3^ 8828 2756 8660 4579 84 9 3 64oi 8325 8224 3o 45 8 9 4 7 n 9 i 8772 3o5 7 85 9 6 4922 8421 6787 8245 8652 i5 II O 88 9 8 i44 9 8714 335 7 853o 5 2 65 8346 7173 8i63 9 o8i 79 i5 884? I 7 o5 8655 3656 8463 5607 8271 7 558 8079 9 5o 9 45 3o 8 79 5 I 9 62 85 9 5 3 9 56 83 9 4 5 9 4 9 8i 9 3 7943 7992 99 3 7 3o 45 8 7 43 22I 9 8533 4255 8324 62 9 I 8n4 83 2 8 79 5 2.o364 i5 12 O 868 9 24 7 5 8470 4554 8252 6633 8o33 8712 7 8i5 O7 9 i 78 o i5 8634 2 7 3l 84o6 485 2 8178 6 9 74 79 5i 9 o 9 6 7723 1218 45 3o 85 7 8 2986 834i 5i5i 8io4 7 3i5 7867 9 48o 7 63o 1 644 3o 45 5.852 1.3242 6.8274 1.5449 7.8027 1.7656 8.7781 i. 9 863 9 .7534 2.2070 i5 i3 o 8462 34 9 7 8206 5 7 4 7 7 9 5o 799 6 7 6 9 3 2.0246 7437 24 9 5 77 i5 84o3 3 7 5 2 8i3 7 6o44 7870 8336 760^ 0628 7 338 2 9 20 45 3o 8342 4oo 8o6e 634 779 8676 7 5i3 1010 72 3 7 3345 3o 45 828 426 799^ 6638 777 9 oi5 7 42I I3 9 2 7 i34 3 7 6 9 i5 i4 o 8218 45i 7921 6935 7 624 9 354 7 32 7 1773 7o3o 4l 9 2 76 o i5 8i54 4 7 6 9 784C 723 7 538 9 6 9 2 7 23l 2i54 6923 46i5 45 3o 8089 502 777 c 7527 7 452 2.oo3o 7 i33 2534 68i5 5o38 3o 45 802^ 627 7 6 9 : 7822 ?364 o368 7 o34 2 9 l4 6705 546o i5 i5 o 79 5 552 7 6if Six 7 2 7^ 0706 6 9 33 32 9 4 65 9 3 5882 7 5 o Dep. Lat. Dg. Lat. Dep. Lat. Dep. Lat. Dep. Lat Dist. 6. Dist. 7. Dist. 8. Dist. 9. Dist. 10. Course. 138 TRAVERSE TABLE. Course Dist. 1. Dist. 2. Dist. 3. Dist. 4. Dist. 5. Lat. Dep. Lat. Dep. Lat Dep. Lat. Dep. Lat Dep. o / o / i5 i o. 9 64 0.263 I. 9 2 9 6 0.526 2.8 9 4 o. 7 8 9 3.85 9 i 1.052 4823 i.3i5 74 45 3 963e 267 9 2 7 3 534 8 9 o 801 854f o6 9 Si8 336 3o 4 06-26 271^ 9 24 9 542 8874 8i4 84 9 o85 812 35 7 i5 16 o 9613 276 9 225 55i 8838 826 845c 102 806 3 7 8 74 o i 9600 279 9 2OI 55 9 880 83 9 8402 II 9 800 3 99 45 3o 9 588 284 9 : 7 6 568 8 7 65 85 2 8353 i36 794 420 3o 4 9 5 ? 6 288 9 i5i 5764 8727 864 83o3 l52 787 44 1 i5 17 o 9 563 2922 9 I26 584 868 9 877 8 2 5a i6 9 781 46i 7 3 o i5 955o 2 9 65 9 ioo 5 9 3 865i 88 9 8201 186 77 5 482 45 3o 9 53 7 3oo 7 9074 6oi/ 8612 9 O2 8i4 9 202 7686 5o3 3o 45 0.9524 o.3o4 9 i. 9 o48 o.6o 9 2.8572 o. 9 i4 3.8o 9 6 1.219 4.7620 1.5243 i5 18 o 95n 3090 9 O2I 6180 8532 9 2 7 8042 236 7 553 545 7 2 i5 9497 3i32 8 99 4 6263 84 9 i 9 3 9 5 79 88 252 7485 5658 45 3o 9 483 3i 7 3 8 9 66 6346 845o 9 5i 9 7933 2692 7 4i6 5865 3o 45 9469 32i4 8 9 3 9 642 9 84o8 9 643 7877 2858 7 34 7 6072 i5 19 o 9 455 3256 8 9 io 65u 8366 9767 7821 3o23 7276 6278 7 I i5 944i 32 97 8882 65 9 4 8323 9 8 9 i 77 64 3i88 7204 6485 45 3o 9426 3338 8853 6676 8270. 1.0012 7706 3352 7 l32 66 9 o 3o 45 9412 33 79 8824 6 7 58 8235 oi38 7647 35i 7 7 o5 9 68 9 6 i5 20 9 3 97 3420 8 79 4 684o 8i 9 i 0261 7588 368i 6 9 85 7101 7 o o i5 o. 9 38 2 i.346i i.8 7 64 O.6 9 22 2.8146 i.o384 3.7528 1.3845 i.6 9 io i. 7 3o6 45 3o 9 36 7 35o2 8 7 33 7OO; 8100 o5o6 746 7 4oo8 6834 7 5io 3o 45 9 35i 3543 8 7 o3 7086 8o54 o62 9 74o5 4i 7 s 6 7 5 7 77 i5 i5 21 9 336 3584 86 7 2 7167 8007 o 7 5i 7 343 4335 66 79 79 i8 69 o i5 9320 3624 864o 7249 7 9 6o 0873 7280 4498 6600 8122 45 3o 93o4 3665 8608 7 33o 79 i3 o 99 5 7217 466o 652i 8325 3o 45 9288 3706 85 7 6 74n 7864 1117 7 l52 4822 644o 85 2 8 i5 22 9272 3746 8544 7492 7816 1238 7087 4984 635 9 8 7 3o 68 o 15 9 255 3 7 86 85n 7 5 7 3 7766 i35 9 7022 5i46 62-7-7 8 9 32 45 3o 9239 3827 84 7 8 7 654 7716 i48i 6 9 55 53o 7 6r 9 4 9 i34 3o 45 0.9222 o.386 7 1.8444 o. 77 34 3.7666 1.1601 3.6888 1.5468 4-6i 10 . 9 336 i5 23 9205 3907 84io 7816 7 6i5 1722 6820 562 9 6o 2 5 9 53 7 6 7 o i5 9188 3 9 4 7 83 7 6 7 8 9 5 7564 1842 6762 5 79 o 5 9 4o 97 3 7 45 3o 9171 3 9 8 7 834i 7975 7 5l2 I 9 62 6682 5 9 5o 5853 99 3 7 3o 4^ 9 i53 4027 83o6 8o55 7 45 9 2082 6612 6110 5 7 66 2.0l3 7 i5 ,24 o 9 i35 4o6 7 82 7 I 8i35 7 4o6 22O2 6542 6269 56 77 o33 7 66 o i5 9118 4107 8235 8214 7 353 2322 6470 6429 5588 o536 45 3o 9100 4i4? 8i 99 8294 7299 244 1 63 9 8 6588 54 9 8 o 7 35 3o 45 9081 4i8 7 8i63 83 7 3 7244 256o 6326 6 7 46 54o 7 o 9 33 i5 25 9063 4226 8126 8452 7 i8 9 267 9 6252 6905 53i5 u3i 65 o i5 0.9045 0.4266 .8o8 9 o.853i 7 i34 2797 .6178 i. 7 o63 .5223 .1328 45 3o 9026 43o5 8o5 2 8610 7 o 7 8 2 9 l5 6io3 7 22O 5l2 9 i5 2 6 3o 45 9007 4344 8oi4 8689 7021 3o33 6028 7 3 7 8 5o35 I 7 22 i5 26 o 8988 4384 797 6 8767 6 9 64 3i5i 5 9 5 2 7 535 4 9 4o I 9 I 9 64 o i5 8969 4423 79 3 7 8846 6 9 o6 3 2 6 9 58 7 5 -7692 4844 2Il4 45 3o 8949 4462 7 8 99 8924 6848 3386 5 797 7 848 4 7 4 7 23lO 3o 45 8930 45oi 7 86o 9002 6 7 8 9 35o3 5 7 i 9 8oo4 464 9 2 5o5 i5 27 o 8910 454o 7 820 9080 6 7 3o 3620 564o 8160 455o 3 7 OO 3 o i5 8890 45 7 9 77 8o 9i5 7 6671 3 7 36 556i 83i5 445i a8 9 4 45 3o 8870 46i 7 77 4o 9235 6610 3852 548o 84 7 o 435i 3o8 7 3o 45 .885o 0.4656 .7700 .9312 .655o .3 9 68 .54oo 1.8625 4a4 9 .3 2 8i i5 28 o 8829 46 9 5 7 65 9 9 38 9 6488 4o84 53i8 8 779 4i4 7 34 7 4 )2 O i5 8809 4733 7618 9 466 6427 4200 5236 8 9 33 4o45 3666 45 3o 8788 477 2 7 5 7 6 9 543 6365 43i5 5i53 9 o86 3 9 4i 3858 3o 45 8767 48io 7 535 9 620 63o2 443o 5 069 9 24o 3836 4o4 9 i5 39 o 8 7 46 4848 74 9 a 9 6 9 6 623 9 4544 4 9 85 9 3 9 2 3 7 3i 4a4o I O i5 8 7 a5 4886 7 45o 977 2 6i 7 5 465 9 4 9 oo 9 545 36a5 443i 45 3o 8704 4 9 24 74o 7 9 848 6111 4773 48i4 9 6 97 35i8 4621 3o 45 868a 4 9 6a 7364 99 24 6o46 4886 4728 9 84 9 i 34io 48ii i5 3o o 8660 5ooo 7 32I c.oooo 5 9 8i 5ooo 464 1 .0000 33oi 5ooo O Dop. Lat Dep. Lat. Dep. j Lat Dep. Lat Dep. Lat 1 Dist. 1. Dist. 2. Dist. 3. Dist. 4. Dist. 5. ourae. TRAVERSE TABLE. Course. Dist. 6. Dist. 7. Dist. 8. Dist. 9. Dist. 10. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat Dep. o / o / i5 16 5. 7 88 7 1.5782 6. 7 535 i.84i2 7 . 7 i83 2.IO42 8.683i 2.36 7 3 9 .64 79 2.6303 7 4 45 3o 7818 6o34 7 454 8 7 o 7 7 o 9 o i3 79 6 7 2 7 4o5i 6363 6 7 24 3o 45 7?4? 6286 7 3 7 2 9 ooi 6 99 6 I 7 i5 6621 443o 6246 7 i44 r5 16 o 7676 6538 7288 9 2 9 5 6 9 oi 2o5i 65i4 48o 7 6126 7 564 7 4 o i5 7603 6790 7 2o3 9 588 68o4 2386 64o4 5i85 6oo5 79 83 45 3o 7529 7 o4i 7117 9 88i 6 7 o6 2 7 2I 6294 556i 588 2 8402 3o 45 7454 7292 7 o3o 2.0I 7 4 6606 3o56 6181 5 9 38 5 7 5 7 8820 i5 17 o 7 3 7 8 7 542 6 9 4i o466 65o4 33 9 o 6o6 7 63i3 563o 9 23 7 7 3 o T *5 73oi 7792 ' 685i o 7 58 6402 3 7 23 5 9 52 668 9 55o2 9 654 45 3o 7223 8042 6 7 6o io4 9 62 97 4o56 5835 7 o64 53 7 2 3.oo 7 i 3o 45 5. 7 i44 1.8292 6.6668 2.i34i 7.6192 2.438 9 8.5 7 i6 2 . 7 438 9 .524o 3.o486 i5 18 o 7063 854i 65 7 4 i63i 6o85 4 7 2I SSgS 7 8l2 5io6 O 9 O2 7 2 i5 6982 8790 64 79 1921 5 97 6 5o53 54 7 3 8i85 4 97 o i3i6 45 3o 6899 9o38 6383 2211 5866 5384 5349 855 7 4832 i 7 3o 3o 45 6816 9286 6285 2501 5 7 54 5 7 i5 5224 8 9 3o 46 9 3 2i44 i5 19 o 6 7 3i 9 534 6186 2 7 90 564i 6o45 5o 97 9 3oi 4552 255 7 7 I i5 6645 9781 6086 3o 7 8 5527 63 7 5 4968 9 6 7 2 44o 9 2 9 6 9 45 3o 6558 2.0028 5 9 85 3366 54n 6 7 o5 4838 3.oo43 4264 338i 3o 45 6471 0275 5882 3654 52 9 4 7 o33 4 7 o6 o4i3 4n8 3 79 2 i5 20 o 6382 O52I 5 77 8 3941 5i 7 5 7 362 45 7 2 0-782 3 9 6 9 4202 7 o o i5 5.6291 2.0767 6.56 7 3 2.4228 7 .5o55 2. 7 68 9 8.443 7 3.ii5i 9 .38i 9 3.46i2 45 3o 6200 1012 556 7 45i5 4 9 34 8oi 7 43oo i5i 9 366 7 5021 3o 45 6108 1257 545 9 48oo 48n 8343 4162 1886 35i4 542 9 i5 il 6oi5 i5o2 535i 5o86 4686 866 9 4022 2253 3358 583 7 60 o i5 5920 1746 5 24 1 53 7 i 456i 8 99 5 388i 2619 3201 6244 45 3o 5825 1990 5l2 9 5655 4433 9 320 3 7 38 2 9 85 3o42 665o 3o 45 5729 2233 5oi 7 5 9 3 9 43o5 9 645 SSgS 335o 2881 7 o56 16 22 O 563i 2476 4 9 o3 6222 4i 7 5 99 6 9 344 7 3 7 i5 2 7 l8 7 46i 68 o 15 5532 2719 4 7 88 65o5 4o43 3.O2 9 2 3299 4o 7 8 2 554 7 865 45 3o 5433 2961 46 7 2 6 7 88 3 9 io o6i5 3i4 9 4442 2388 8268 3o 45 5.5332 2.3203 6.4554 2. 7 7 7.3776 3.o 9 3 7 8.2 99 8 3.48o4 9 .222O 3.86 7 i i5 23 5 2 3o 3444 4435 7 35i 364o 1258 2845 5i66 2o5o 97 3 5 7 o i5 5127 3685 43i5 7 632 35o3 i58o 26 9 I 552 7 i8 79 9 4 7 4 45 3o 5o24 3 9 25 4i 9 4 79 I2 3365 I 9 00 2535 588 7 1-706 9 8 7 5 3o 45 4919 4i65 4o 7 2 8l 9 2 3225 222O 23 7 8 624 7 i53i 4.o2 7 5 i5 24 o 48i3 44o4 3 9 48 84-72 3o84 253 9 22I 9 6606 i355 o6 7 4 66 o i5 4706 4643 3823 8 7 5o 2 9 4i 2858 2o5 9 6 9 65 11-76 I0 7 2 45 3o 45 9 8 4882 36 97 9 02 9 2 797 3i 7 5 i8 97 7 322 o 99 6 i46 9 3o 45 448 9 5l20 35 7 o 9 3o6 2 65i 3493 : 7 33 7 6 79 o8i4 1866 i5 25 43 7 8 5357 3442 9 583 25o5 38o 9 i568 8o36 o63i 2262 65 o i5 5.4267 2.5594 6.3312 2. 9 86o 7 .2356 3.4i25 8.i4oi 3.83 9 i 9 .o446 4.265 7 45 3o 4i55 583i 3i8i 3.oi36 220 7 444 1 1233 8 7 46 O25 9 3o5i 3o 45 4042 6067 3o4 9 o4u 2o56 4 7 56 io63 9100 OO 7 O 3445 i5 26 o 3928 63o2 2 9 l6 0686 i 9 o4 5o 7 o o8 9 i 9 453 8. 9 8 79 383 7 64 o i5 38i2 6537 2 7 8l o 9 6o i 7 5o 5383 o 7 i 9 9806 9 68 7 422 9 45 3o 36 9 6 6772 2645 1234 i5 9 5 56 9 6 o544 4-oi58 9 4 9 3 462O 3o 45 35 79 7006 25o 9 i5o 7 i438 6008 o368 0509 9 2 9 8 5oio i5 27 o 346o 72 3 9 23 7 1779 1281 63i 9 OI 9 I 0859 9 IOI 53 99 63 o i5 334i 7472 223l 2o5i II2I 663o OOI2 1209 8 9 O2 5 7 8 7 45 3o 3221 7705 20 9 I 2322 o 9 6i 6 9 4o 7 . 9 83i i55 7 8 7 oi 6i 7 5 3o 45 5.3o 99 a. 79 3 7 6.i 9 4 9 3.25 9 3 7-799 3. 7 249 7 . 9 64 9 4.1905 8.84 99 4.656i i5 28 o 2977 8168 1806 2863 o636 7 558 9 465 2252 82 9 5 6 9 4 7 62 o i5 2853 83 99 1662 3i32 o4 7 i 7 866 9 28o 25 99 8o8 9 7 332 45 3o 2729 863o i5i 7 34oi o3o5 8i 7 3 9 o 9 4 2 9 44 7 88a 77 i6 3o 45 2604 885 9 i3 7 i 366 9 oi38 84 7 9 8 9 o5 328 9 7 6 7 3 8o 99 i5 20 O 24?7 9089 1223 3 9 3 7 6. 997 o 8 7 85 8 7 i6 3633 7462 848 1 61 o 15 2 35o 9 3i 7 io 7 5 4203 9 8oo 9090 8525 3 97 6 7 a5o 8862 45 3o 2221 9 545 O 9 25 44 7 o 9 628 9394 8332 43i8 7 o36 9 242 3o 45 2092 977 3 o 77 4 4 7 35 9 456 9 6 97 8i38 465 9 6820 9622 i5 3o o 1962 3.0000 0622 5ooo 9 282 4.0000 79 42 5ooo 66o3 5.0000 60 o Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat Dist. 6. Dist. 7. Dist. 8. Dist. 9. Dist. 10. Course. ?40 TRAVERSE TABLE. Course. Dist. I. Dist. 2. Dist. 3. Dist. 4. Dist. 5. Lat. Dep. Lat Dep. Lat Dep. Lat Dep. Lat Dep. o / 3o i5 0.8638 o.5o38 1.7277 i.oo 7 5 2.5 9 l5 I.5ll3 3.4553 2.Ol5l 4.3192 2.5l8 9 o / 5 9 45 3o 8616 5o 7 5 7 233 oi5i 584 9 5226 4465 0302 3o8i 53 77 3o 45 85 9 4 5n3 7 l88 0226 5 7 8 2 533 9 43 7 6 0452 2 97 5565 i5 3i o 85 7 2 5i5o ai43 o3oi 5 7 i5 545i 428 7 0602 2858 5 7 5 2 5 9 o i5 8549 5i88 7098 o3 7 5 564 7 5563 4i 9 6 o 7 5i 2 7 46 5 9 3 9 45 3o 8526 6226 7o53 o45o 55 79 56 7 5 4io6 o 9 oo 2632 6i 2 5 3o 45 85o4 6262 7007 o524 55u 5 7 86 4oi4 io4 9 2 5i8 63u i5 32 848o 5299 6961 0598 544 1 58 9 8 3 9 22 H97 2402 64 9 6 58 o i5 845y 5336 6916 o6 7 2 53 7 2 6008 382 9 1 345 2286 6681 45 3o 8434 5373 6868 o 7 46 53o2 6u 9 3 7 36 1492 2I 7 O 6865 3o 45 o.84io o.54io 1.6821 1.0819 2.5231 1.622 9 3.3642 2.1639 4.2O52 2 . 7 o4 9 i5 33 o 838 7 5446 6 77 3 0893 5i6o 633 9 354 7 i 7 86 1934 7 232 5 7 o i5 8363 5483 6 7 26 0966 5o8 9 644 9 345i 1932 1814 7 4i5 45 3o 8339 55i 9 66 7 8 1039 5oi 7 6558 3355 20 77 1694 7 5 97 3o 45 83i5 5556 6629 i ii i 4 9 44 6667 3 2 5 9 2223 i5 7 3 7779 ID 34 o 8290 6692 658i 1184 48 7 i 6776 3i6 2 2368 1452 79 6o 56 o i5 8266 56 2 8 6532 1256 4 79 8 6884 3o64 25l2 i32 9 8i4o 45 3o 8241 5664 6483 i328 4 7 24 6 99 2 2 9 65 2656 1206 8320 3o 45 8216 5700 6433 i4oo 464 9 7100 2866 2800 1082 85oo i5 35 o 8192 5 7 36 6383 1472 45 7 5 7207 2 7 66 2 9 43 o 9 58 86 79 55 o i5 0.8x66 0.5771 1.6333 i.i543 2.44 99 i. 7 3i4 3.2666 2.3o86 4.o832 2.885 7 45 3o 8i4i 5807 6282 1614 4423 7421 2565 3 22 8 o 7 o6 9 o35 3o 45 8116 5842 623i i685 434 7 7527 2463 33 7 o o5 79 9212 i5 36 o 8090 58 7 8 6180 i 7 56 42 7 I 7634 236i 35n o45i 9 38 9 54 o i5 8o64 5 9 i3 6l2 9 1826 4i 9 3 77 3 9 2258 3652 0322 9 565 45 3o SoSg 5 9 48 6o 77 1896 4n6 7845 2l54 3 79 3 0193 9 7 4i 3o 45 8oi3 5 9 83 6026 1966 4o38 79 5o 2o5o 3 9 33 oo63 99 i6 i5 3y o 7986 6018 5 97 3 2o36 3 9 5 9 8o54 1945 4o 7 3 3.9932 3.oo 9 i 53 o i5 7960 6o53 5920 2106 388o 8i5 9 i84o 4212 9800 0265 45 3o 79 34 6088 586 7 2I 7 5 38oi 8263 1734 435o 9668 o438 3o 45 0.7907 0.6122 i.58i4 1.2244 2.3 7 2I i.836 7 3.1628 2.448 9 3. 9 534 3.o6i i i5 38 o 7880 6i5 7 6760 23i3 364o 8470 l520 4626 9 4oi o 7 83 52 i5 7 853 6191 5 7 o6 2382 356o 85 7 3 i4i3 4 7 64 9 266 o 9 55 45 3o 7826 6226 6662 245o 34 7 8 86 7 5 i3o4 4 9 oi 9 i3o 1 126 3o 45 7799 625 9 5598 2 5i8 33 97 8778 irgS 5o3 7 8 99 4 I2 9 6 i5 3o o 7771 6293 5543 2586 33i4 8880 1086 5i 7 3 885 7 f466 5i o i5 . 7744 632 7 5488 2654 3232 8 9 8i 0976 53o8 8 7 20 i635 45 3o 7716 636i 5432 2 7 22 3i4 9 9 o82 o865 5443 858i 1804 3o 45 7688 63 9 4 53 77 2 7 8 9 3o65 9 i83 o 7 54 55 7 8 8442 19-72 i5 4o o 7660 6428 532i 2856 2 9 8l 9 284 0642 5 7 I2 83o2 2139 5o o i5 0.7632 o.646i i.5 2 65 1.2922 2.28 97 i. 9 384 3.o52 9 a 5845 3.8162 3.23o6 45 3o 7604 6494 52o8 2989 2812 9483 o4i6 S 97 8 8020 24 7 2 3o 45 7 5 7 6 6528 5i5i 3o55 2727 9 583 o3o3 Oi 10 7 8 7 8 2638 i5 4i o 7547 656i 5094 3l2I 2641 9682 0188 6242 7735 28o3 4 9 o i5 75x8 65 9 3 5o3 7 3i8 7 2 555 9780 0074 63 7 4 7 5 9 2 296-7 45 3o 7490 6626 4979 3252 246 9 9879 2. 99 58 65o5 7 448 3i3i 3o 45 746 1 665g 4921 33i8 2382 9976 9842 6635 7 3o3 32 9 4 i5 4a o 743i 6691 4863 3383 22 9 4 2.0074 9726 6 7 65 7 i5 7 345 7 48 o i5 7402 6724 48o4 344 7 22O7 0171 9609 68 9 5 7 OI I 36i8 45 3o 7 3 7 3 6 7 56 4 7 46 35i 2 2118 0268 9491 7024 6864 3 7 8o 3o 45 0.7343 0.6788 1.4686 i.35 7 6 2.2030 2.o364 2 . 9 3 7 3 2. 7 l52 3.6 7 i6 3.3 9 4o i5 43 o 73i4 6820 462-7 364o I 9 4l o46o 9254 7280 6568 4ioo 4 7 o i5 7284 6852 456 7 3 7 o4 i85i o555 9 i35 7 4o 7 64i 9 425 9 45 3o 7 254 6884 45o 7 3 7 6 7 1761 o65i 9 oi5 7 534 6a6 9 44i8 3o 45 7224 6916 444 7 383o 1671 o 7 45 88 9 5 7661 6n8 45 7 6 i5 44 o 7 i 9 3 6 9 47 438 7 38 9 3 i58o o84o 8 77 4 77 86 5 9 6 7 4 7 33 46 o i5 7i63 6978 4326 3 9 56 i48 9 o 9 34 8652 79 12 58i5 48 9 o 45 3o 7 i33 7009 4265 4oi8 i3 9 8 IO2 7 853o 8o36 5663 5o45 3o 45 7102 7040 4204 4o8o i3o6 II2O 84o 7 8161 55o 9 52OI :5 45 o 7071 7071 4i42 4i42 I2l3 I2l3 8284 8284 5355 5355 45 o Dep. Lat Dep. Lat. Dep. Lat Dep. Lat. | Dep. Lat Dist. 1. Dist. 2. Dist. 3. Dist 4. Dist. 5. Course. TRAVERSE IABLE. 14 Course. Dist. 6. Dist. 7. Dist. 8. Dist. 9. Dist. 10. Lat. Lat. Dep. Lat. Dep. Lat. Dep. Lot. Dep. o / o / 3o i5 5.i83o 3.0226 6.o468 3.5 2 64 6.9107 4.0302 7 .7745 4.5340 8.6384 5.0377 5 9 45 3o 1698 o452 o3i4 5528 8 9 3o o6o3 7547 56 7 8 6i63 o 7 54 3o 45 1 564 0678 oi58 5791 8 7 53 0903 7 34 7 6016 5 9 4i 1129 i5 3i o i43o 9 O2 OOO2 6o53 85 7 3 1203 7145 6353 5 7 i7 i5o^ 5 9 o i5 I2 9 5 1126 5. 9 844 63i4 83 9 ? i5o2 6942 6690 5491 i8 77 45 3o n58 i35o 9 685 6575 8211 1800 6 7 38 7 O25 5264 2250 3o 45 1 02 1 i5 7 3 9 5 2 5 6835 8028 20 97 653a 7359 5o35 2621 i5 32 o883 I7 9 5 9363 7094 7844 2394 6324 7693 48o5 2 99 2 58 o i5 oy44 2017 9201 7 353 7658 2689 6116 8o25 45 7 3 336i 45 3o o6o3 2238 9 o3 7 7611 7471 2984 5 9 o5 835 7 433 9 3 7 3o 3o 45 5.o462 3.2458 5.88 7 3 3.7868 6.7283 4.3278 7 .56 9 4 4.8688 8.4io4 5.409-7 i5 33 o 0320 2678 8 7 o 7 8i25 7094 3571 548o 9018 386 7 4464 5 7 o i5 01-77 2898 854o 838i 6903 3863 5266 9 346 362 9 4829 45 3o oo33 3n6 83 7 2 8636 6711 4i55 5o5o 9674 3389 5i 9 4 3o 45 4.9888 3334 8203 8890 65i8 4446 4832 S.oooi 3i4 7 555 7 i5 34 o 9742 3552 8o33 9144 6323 4?35 46i3 0327 2904 5 9 i 9 56 o i5 9 5 9 5 3 7 68 7861 9 3 9 6 6127 5o24 43 9 3 o652 2659 6280 45 3o 9448 3 9 84 7689 9 648 5 9 3o 53i2 4i 7 i 977 a4i3 664i 3o 45 9299 4200 7 5i5 99 oo 5732 56oo 3 9 48 i3oo 2i65 7000 i5 35 o 9149 44i5 734i 4.oi5o 5532 5886 3724 1622 igiS 7 358 55 o i5 4.8998 3.4629 5.7i65 4.o4oo 6.533i 4.6172 7 .34 9 8 5.1943 8.i664 5. 77 i5 45 3o 884? 4842 6988 o64 9 5129 6456 3270 2263 1412 8070 3o 45 8694 5o55 6810 o8 97 4926 6740 3o42 2582 n5 7 8425 i5 36 o 854i 5267 663: ii45 4721 7023 2812 2901 0902 8779 54 o i5 838 7 5479 645 1 l3 9 2 45i6 73o5 258o 32i8 o644 9i3i 45 3o 823i 568 9 6270 i638 43o 9 7 586 2347 3534 p386 9482 3o 45 8o 7 5 58 99 6088 i883 4ioo 7866 2Il3 3849 OI25 9 83 2 i5 3 7 o 7918 6io 9 5904 2I2 7 38 9 i 8i45 1877 4i63 -7.9864 6.0182 53 o i5 7760 63i8 5720 23 7 I 368o 8424 i64o 44 7 6 9600 0529 45 3o 7601 65 2 6 5535 26i3 3468 8 7 oi 1402 4789 9 335 0876 3o 45 4-?44i 3.6733 5.5348 4.2855 6.3 2 55 4.8 977 7.1162 5.5ioo 7^.9069 6.1222 i5 38 o 7281 6 9 4o 5i6i 3o 9 6 3o4i 9 253 9 2I 54io 8801 1 566 52 i5 7119 7i46 4972 333 7 2825 9528 o6 79 5718 8532 1909 45 3o 6g56 7 35i 4?83 35 7 6 26o 9 9801 0435 6026 8261 225l 3o 45 6 79 3 7555 4592 38i5 23 9 I 5.oo 7 4 oi 9 o 6333 79 88 2592 i5 3o o 6629 77 5 9 44oo 4o52 2172 o346 6. 99 43 663 9 77 i5 2932 5i o i5 6464 7 9 62 4207 4289 i 9 5i 0616 9 6 9 5 6 9 43 7 43 9 327 45 3o 6297 8i65 4oi4 4525 1730 0886 9446 7247 7162 36o8 3o 45 6i3i 8366 3819 4 7 6i i5o7 n55 9196 7 55o 6884 3 9 44 i5 4o o 5 9 63 8567 3623 4995 1284 1423 8 9 44 785i 66o4 4279 5o o i5 4.5794 3.8767 5.3426 4.5229 6.1059 5.1690 6.8691 5.8i5i 7 .6323 6.4612 45 3o 5624 8 9 6 7 3228 546 1 o832 1956 8437 845o 6o4i 4945 3o 45 5454 9 i66 3o3o 56 9 3 o6o5 2221 8181 8 7 48 5 7 56 5276 i5 4i o 5283 9 364 283o 5 9 24 o3 77 2485 7924 9045 54 7 i 56o6 49 o i5 5uo 9 56i 2629 6i54 0147 2 7 48 7666 934i 5i84 5 9 35 45 3o 4 9 3 7 97 5 7 2427 6383 5.9916 3oio 7406 9636 48 9 6 6262 3o 45 4763 99 53 2224 6612 9686 3271 7i45 9929 46o6 6588 i5 42 458 9 4.oi48 2O2O 683 9 , 9 45 2 353o 6883 6.O222 43i4 6913 48 o i5 44i3 o342 i8i5 7066 9217 3 7 8 9 6620 o5i3 4022 7237 45 3o 423 7 o535 1609 7291 8982 4o4 7 6355 o8o3 3 7 28 7 55 9 3o 45 44o5 9 4.0728 5.i4o3 4.75.16 5.8746 5.43o4 6.6089 6.1092 7.3432 6. 7 88o i5 43 o 388i O 9 2O 1195 77 4o 85o8 456o 5822 i38o 3i35 8200 4 7 o i5 3702 IIII 0986 79)53 8270 48i5 5553 1666 2837 85i8 45 3o 3522 i3oi o 77 6 8i85 8o3o 5o68 5284 1952 2 53 7 8835 3o 45 3342 i4 9 i o565 84o6 7789 532i 5oi3 2236 2236 9 i5i i5 44 o 3i6o 1680 o354 8626 7547 55 7 3 474i 2519 i 9 34 9 466 46 o i5 2 97 8 1867 oi4i 8845 ?3o4 5823 446 7 2801 i63o 9779 45 3o 2 79 5 2o55 4.9928 9064 7 o6o 6o 7 3 4i93 3o82 i3 2 5 7.0091 3o 45 2611 2241 97 i3 9281 68i5 632i 3 9 i 7 336i ioi 9 o4oi i5 45 o 2426 2426 9497 9497 656 9 656 9 364o 364o 0711 0711 45 o Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dist. 6. Dist. 7. Dist. 8. Dist. 9. Dist. 10. Course. 142 MERIDIONAL PARTS. LATITUDE. Min. 1 2 3 4 5 6 7 8 9 10 11 12 Min. O o.o 60.0 120.0 1 80. 240.2 3oo.2j 36o. 7 421. 1 48i.6 542.2 6o3. 664. ?2 5.3 O I I.O 61.0 21. 81.1 41.2 01.; 61.7 22.1 82.6 43.3 04. 65. 26.3 I 2 2.O 62.0 22.0 82.1 42.2 02.^ 62.7 23.1 83.6 44.3 o5. 66.1 2 7 .4 2 3 3.o 63.o 23.0 83.i 43.2 o3.4 63. 7 24-1 84-6 45.3 06. i 67.1 28.4 3 4 4.0 64-0 24-0 84.i 44.2 04.4 64-7 25.1 85.6 46.3 O 7 .l 68.2 29.4 4 5 5.o 65.o 25.0 85.i 45.2 o5.4 65. 7 26.1 86.6 4 7 .3 08.2 69.2 3o.5 5 6 6.0 66.0 26.0 86.1 46.2 06.; 66.7 27.1 87.6 48.3 9 .2 7 0.2 3i.5 6 7 7.0 67.0 27.0 87.1 47.2 07.4 67.7 28.1 88.6 4 9 -3 10.2 71.1 32.5 7 8 8.0 68.0 28.0 88.1 48.2 08.; 68.7 2 9 .I 8 9 .6 5o.3 II. 2 7 2.2 33.5 8 9 9.0 69.0 29.0 89.1 4 9 .2 09.4 69.7 3o.i 9-7 5i.4 12.2 7 3.3 34.5 9 10 10.0 70.0 i3o.o 190.1 25O.2 3 io.: 370.7 43i.i 491.7 552.4 6l3.2 6 7 4.3 7 35.6 10 ii I I.O 71.0 3i.o 91.1 5l.2 1 1.2 71.7 32.1 92.7 53.4 14.2 7 5.3 36.6 ii 12 12.0 72.0 32.0 92.1 52.2 12.2 72.7 33.i 9 3. 7 544 15.3 7 6.3 3 7 .6 12 i3 i3.o 7 3.o 33.o 9 3.i 53.2 1 3.4 73.7 34.2 94-7 55.4 i6.3 77.3 38.6 i3 14 14.0 74-0 34.o 9 4.i 54.2 i44 74.7 35.2 9 5. 7 56.4 17.3 78.4 3 9 .6 i4 i5 i5.o 7 5.o 35.o 9 5.i 55.2 i5.4 7 5. 7 36.2 96.7 5 7 .4 i8.3 79-4 4o. 7 i5 16 16.0 76.0 36.o 9 6.i 56.2 16.4 76.8 3 ? .2 97-7 58.4 i 9 .3 80.4 4i. 7 16 J 7 17.0 77.0 3 7 .o 97-i 57.2 i 7 .5 77.8 38.2 98.7 5 9 .4 20.3 81.4 42. 7 l l 18 18.0 78.0 38.o $8.1 58.2 i8.5 78.8 3 9 .2 99.8 6o.5 21.3 82.4 43.7 18 *9 19.0 79.0 3 9 .o 99 .i 5 9 .2 i 9 .5 79 .8 4o.2 5oo.8 6i.5 22.4 83.5 44.8 '9 20 2O.O 80.0 i4o.o 200. i 260.2 320.5 38o.8 44i.2 5oi.8 562.5 623.4 684.5 745.8 20 21 21.0 81.0 4i.o OI.I 61.3 21.5 81.8 42.2 02.8 63.5 24.4 85.5 46.8 21 22 22.0 82.0 42.0 02.1 62.3 22.5 82.8 43.2 o3.8 64.5 25.4 86.5 47-8 22 23 23.0 83.o 43.o o3.i 63.3 23.5 83.8 44.2 o4.8 65.5 26.4 8 7 .5 48. 9 23 24 24.0 84.o 44-0 04. 1 64-3 24-5 84-8 45.2 o5.8 66.6 27.4 88.6 49-9 24 25 25.0 85.o 45.o o5.i 65.3 25.5 85.8 46.3 06.8 6 7 .6 28.5 89.6 5o. 9 25 26 26.0 86.0 46.o 06. i 66.3 26.5 86.8 47-3 07.8 68.6 2 9 .5 90.6 5r. 9 26 27 27.0 87.0 4 7 .o 07.1 6 7 .3 2 7 .5 87.8 48.3 08.9 6 9 .6 3o.5 91.6 53.o 27 28 28.0 88.0 48.o 08. i 68.3 28.5 88.8 4 9 .3 09.9 7 o.6 3i.5 92.6 54.0 28 29 29.0 89.0 49.0 o 9 .i 6 9 .3 2 9 .5 8 9 .8 5o.3 10.9 71.6 32.5 93.6 55.o 2 9 3o 3o.o 90.0 i5o.o 2IO.I 270.3 33o.5 3 9 o.8 45i.3 511.9 572.6 633.5 694.7 7 56.o 3o 3i 3i.o 91.0 5i.o II. I 7 i.3 3i.5 91.8 52.3 12.9 73.7 34-6 95.7 5 7 .i 3i 32 32.0 92.0 52.0 12. 1 7 2.3 3 2 .5 9 2. 9 53.3 i3. 9 74.7 35.6 96.7 58.i 32 33 33.o 93.0 53.i I3.I 7 3.3 33.5 9 3. 9 54.3 i4. 9 7 5. 7 36.6 97-7 5 9 .i 33 34 34.o 94.0 54-1 14.1 7 4.3 34-5 9 4- 9 55.3 <5. 9 76.7 3 7 .6 98.7 60. i 34 35 35.o 95.0 55.i i5.i 7 5.3 35.5 9 5. 9 56.3 i6. 9 77-7 38.6 99.8 61.1 35 36 36.o 96.0 56.i 16.1 7 6.3 36.5 9 6. 9 5 7 .3 18.0 7 8. 7 3 9 .6 700.8 62.2 36 3? 3 7 .o 97.0 5 7 .i 17.1 77 .3 3 7 .5 97-9 58.4 I 9 .o 79-7 4o. 7 01.8 63.2 37 38 38.o 98.0 58.i 18.1 7 8.3 38.5 9 8. 9 5 9 .4 20. o 80.8 4i-7 02.8 64.2 38 3 9 39.0 99.0 59.1 i 9 .i 79- 3 3 9 .6 99-9 60.4 21.0 81.8 42. 7 o3.8 65.2 39 4o 4o.o IOO.O 1 60. i 220.2 280.3 34o.6 oo. 9 46i.4 522.0 82.8 643. 7 04.9 66.3 4o 4i 4i.o 01. 61.1 21.2 8i.3 4i.6 01. 9 62.4 23.0 83.8 44. 7 5.9 6 7 .3 4i 4s 42.0 O2. 62.1 22.2 82.3 42.6 02. 9 63.4 24.O 84-8 45.8 06.9 68.3 42 43 43.o o3.o 63.i 23.2 83.3 43.6 o3. 9 64-4 25. 85.8 46.8 07.9 6 9 .3 43 44 44-0 o4.o 64-1 24.2 84.3 44-6 o4- 9 65.4 26.0 86.8 4 7 .8 09.0 70.4 44 45 45.o o5.o 65.i 25.2 85.3 45.6 o5. 9 66.4 27.1 8 7 . 9 48.8 IO.O 7i.4 45 46 46.o 06.0 66.1 26.2 86.3 46.6 07.0 6 7 .4 28.1 88. 9 4 9 .8 I I.O 72-4 46 4? 47-0 07.0 6 7 .i 27.2 8 7 .3 47.6 08.0 68.4 2 9 .I 8 9 . 9 5o.8 12.0 7 3.4 47 48 48.o 08.0 68.1 28.2 88.3 48.6 o 9 .o 6 9 .5 3o.i 9-9 5i. 9 i3.i 7 4.5 48 49 49.0 09.0 69.1 2 9 .2 8 9 .3 49.6 IO.O 7 o.5 3i.i 91.9 52. 9 i4.x 7 5.5 49 5o 5o.o IIO.O I 7 O.I 230.2 2 9 o.3 35o.6 II. O 4 7 i.5 532.1 9 2. 9 653. 9 i5.i 7 6.5 5o 5i 5i.o II. 71.1 31.2 91.3 5i.6 12.0 7 2.5 33.i 9 3. 9 54- 9 16.1 77 .5 5i 52 52.0 12. 7 2.1 32.2 9 2-4 52.6 i3.o 7 3.5 34.i * r 9 5.o 55. 9 17.1 7 8.6 52 53 53.o i3.o 7 3.i 33.2 9 3.4 53.6 14.0 7 4.5 35.i 9 6.o 5 7 .o 18.2 79-6 53 54 54.o 14.0 74.1 34-2 9 4.4 54.6 i5.o 7 5.5 36.2 97- 58.o 19.2 80.6 54 55 55.o i5.o 7 5.i 35.2 9 5.4 55.6 16.0 7 6.5 3 7 .2 9 8.o 5 9 .o 2O.2 81.7 55 56 56.o 16.0 7 6.i 36.2 9 6.4 56.6 17.0 77.5 38.2 99 .o 60.0 21.2 82. 7 56 5? 5 7 .o 17.0 77 .i 3 7 . 2 97-4 5 7 .6 18.0 7 8.5 3 9 .2 600.0 61.0 22.3 83. 7 5? 58 58.o 18.0 78.1 38.2 98.4 58.6 I 9 .0 79 .5 4O.2 OI.O 62.1 23.3 84. 7 58 5 9 59.0 19.0 79.1 3 9 . 2 99.4 5 9 . 7 20.0 8o.5 41.2. 02. 1 63.i 24.3 85.8 5 9 MERIDIONAL PARTS. 148 LATITUDE. T 13 14 15 16 17 18 19 20 21 22 23 24 .s 786.8 848.5 910.5 972.7 io35.3 1098.2 n6i.5 1225. 1 1289.2 i353. 7 i4i8.6 i484.i o i 87.8 49-5 11. 5 7 3.8 36.3 99.3 62.5 26.2 90.3 54-8 19.7 85. 2 I 2 88.8 5o.5 12.6 74-8 3 7 .4 i loo.S 63.6 2 7 .3 91.3 55.8 20.8 86.3 2 3 89.9 5i.6 i3.6 7 5. 9 38.4 01.4 64- 7 28.3 92.4 56.9 21.9 8 7 .3 3 4 90.9 52.6 i4-6 76.9 3 9 .5 02.4 65. 7 294 93.5 58.o 23.0 88-4 4 5 91.9 53.6 i5. 7 78.0 4o.5 o3.5 66.8 3o.4 94.5 59.0 24*1 89.5 5 6 92.9 54.7 16.7 79.0 4i.6, o4.5 6 7 .8 3i.5 95.6 60.1 25-1 qo.6 6 7 94.0 55. 7 17.7 80.0 42.6 o5.6 68. 9 32.6 96.7 61.2 26-2 91.7 7 8 95.0 56. 7 18.8 81.1 43-7 06.6 7 o.o 33.6 97.8 62.3 27.3 92.8 8 9 96.0 5 7 .8 19.8 82.1 44-7 07.7 7 i.o 34-7 98.8 63.4 28.4 9 3. 9 9 10 797.0 858.8 920.8 9 83.2 io45.8 1108.7 II 7 2.I 1235.8 1299.9 i364.5 1429.5 i4 9 5.o 10 ii 98.1 59.8 21.9 84.2 46.8 09.8 7 3.i 36.8 iSoi.o 65.6 3o.6 96.1 ii 12 99.1 60.9 22.9 85.2 47-9 10.8 7 4-2 37-9 O2.O 66.6 3i.9 97- 2 12 i3 800.1 61.9 23.9 86.3 48. 9 11.9 7 5.2 39.0 o3.i 67.7 32.8 9 8.3 i3 i4 01.2 62.9 25. 87.3 49.9 12.9 7 6.3 4o.o 04.2 68.8 33. 9 99.4 i4 i5 O2. 2 64.o 26.0 88.4 5i.o i4-o 77-4 4i.i o5.3 69.9 34-9 i5oo.5 i5 16 03.2 65.o 27.0 89.4 52.0 1 5.o 78.4 42.2 o6.3 70.9 36.o 01.6 16 l l O4.2 66.0 28.1 90.4 53.1 16.1 79.5 43.2 07.4 7 2.O 3 7 .i 02.7 *7 18 o5.3 67.1 29.1 9 i.5 54.i 17.1 8o.5 44-3 o8.5 7 3.i 38.2 o3.8 18 '9 o6.3 68.1 3o.i 92.5 55.2 18.2 81.6 45.4 09.6 7 4.2 3 9 .3 04.9 '9 20 807.3 869.1 931.2 993.6 io56.2 1119.2 1182.7 1246.4 i3io.6 i3 7 5.3 i44o.4 i5o6.o 20 21 08.4 70.1 32.2 94-6 57.3 20.3 83. 7 47.5 11.7 76.4 4i.5 07.1 21 22 09.4 71.2 33.3 95.6 58.3 21.3 84-8 48.6 12.8 77-4 4a.6 08.2 22 23 10.4 72.2 34.3 96.7 59.4 22.4 85.8 49-6 i3.8 78.5 43.7 OQ.3 23 24 ti.4 7 3.2 35.3 97-7 60.4 23.4 86. 9 50.7 i49 79.6 44-81 10.4 24 25 12.5 74-3 36.3 ^8.8 6i.4 24.5 88.0 5i.8 16.0 80.7 45.8 1 1.5 25 26 i3.5 7 5.3 3 7 4 99 .8 62.5 2 5.5 8 9 .o 5 2 .8 17.1 81.8 46. 9 12.6 26 27 i4-5 76.3 38.4 1000.8 63.5 26.6 90.1 53. 9 18.1 82.8 48.o i3. 7 27 28 i5.5 77-4 3 9 .5 01.9 64.6 27.6 91.1 55.6 19.2 83.9 49.1 i4.8 28 2 9 16.6 78.4 4o.5 02.9 65.6 28.7 92.2 56.o 20.3 85.o 5o.2 i5. 9 29 3o 817.6 879-4 9 4i.6 ioo4.o 1066.7 1129.7 II 9 3.2 1257.1 i32i.4 i386.i i45i.3 1517.0 3o 3i 18.6 8o.5 42.6 o5.o .67-7 3o.8 9 4.3 58.2 22.5 87.2 62.4 18.1 3i 32 19.6 8i.5 43.6 06. i 68.8 3i.8 95.4 59.2 23.5 88.3 53.5 19.2 32 33 20.7 82.5 44-7 07.1 69.8 32.9 96.4 6o.3 24.6 89.4 54.6 20.3 33 34 21.7 83.6 45.7 08.1 70.9 34.o 97 .5 61.4 25.7 90.4 55.6 21.4 34 35 22.7 84.6 46. 7 09.2 72.0 35.1 98.5 62.4 26.7 9 i.5 56. 7 22.5 35 36 23.8 85.6 4 7 .8 10.2 7 3.o 36.1 99.6 63.5 27.8 92.6 5 7 .8 23.6 36 3? 24.8 86.7 48.8 n.3 7 4.i 3 7 .2 1200.7 64-6 28.9 93.7 58. 9 24.7 37 38 2 5.8 87.7 49-9 12.3 7 5.i 38.2 01.7 65.6 3o.o 94-8 60.0 25.8 38 3 9 26.9 88.7 5o. 9 i3.4 76.2 3 9 .3 02.8 66.7 3i.i 9 5.8 61.1 26.9 39 4o 827.9 889.8 951.9 ioi44 1077.2 n4o.3 1203.9 1267.8 i332.i 1396.9 1462.2 i528.o 4o 4i 28.9 90.8 53.o 1 5.4 78.3 4i-4 04.9 68.8 33.2 98.0 63.3 29.1 4i 42 29.9 91.8 54.o i6.5 79 .3 42.4 06.0 69.9 34.3 99.1 644 30.2 42 43 3i.o 92.9 55.i i 7 .5 80.4 43.5 07.1 71.0 35.3 I4OO.2 65.5 3i.3 43 44 32.0 9 3. 9 56.i 18.6 81.4 44-6 08.1 72.1 36.4 QI. 3 66.6 32.4 44 45 33.o 94.9 5 7 .i 19.6 82.5 45.6 09.2 7 3.i 3 7 .5 02.4 6 7 . 7 33.5 45 46 34-1 96.0 58.2 20.6 83.5 46. 7 IO.2 74-2 38.6 o3.4 68.8 34.6 46 4? 35.i 97.0 59.2 21.7 84.6 47-7 n.3 7 5.3 3 9 . 7 o4-5 69.8 35. 7 47 48 36.i 98.0 60.2 22.7 85.6 48.8 12.4 7 6.3 40.7 o5.6 70.9 36.8 48 49 3 7 .2 99.1 6i.3 2 3.8 86.7 49-9 1 3.4 77-4 4i.8 06.7 72.0 3 7 . 9 49 5o 838.2 900.1 962.3 1024.8 1087.7 n5o. 9 i2i4-5 1278.5 i34a. 9 1407.8 i473.i iSSg.o 5o 5i 39.2 01. 1 63.4 25.9 88.8 52.O i5.5 79.5 44.o 08.8 74.2 4o.i 5i 62 4O.2 O2. 2 644 26.9 89.8 53.o 16.6 80.6 45.i 09.9 7 5.3 41.2 52 53 4i.3 03.2 65.5 28.0 9 9 54.i 17.7 81.7 46.i II. O 76.4 42.3 53 54 42.3 o4.3 66.5 29.0 91.9 55.i 18.7 82.8 47.2 12. 1 77 .5 43-4 54 55 43.3 o5.3 67.5 3o.i 9 3.o 56.2 19.8 83.8 48.3 13.2 7 8.6 44-5 55 56 444 o6.3 68.6 3i.i 94.0 5 7 .2 20.9 84-9 49.4 i4.3 79-7 45.6 56 5? 45.4 07.4 69.6 , 32.2 9 5.i 58.3 21.9 86.0 5o.4 1 54 80.8 46.7 57 58 46.4 08.4 70.7 33.2 96.1 5 9 .4 23.0 87.0 5i,5 i6.5 81.9 4 7 .8 58 5 9 47-5 09.4 71.7 34.3 97.2 60.4 24.1 88.1 5 2 .6 i 7 .5 83.o 48.9 5 9 MERIDIONAL PARTS. LATITUDE. Min. 25 26 27 28 29 30 31 32 33 34 35 Mia. O i55o.o iBi6.5 i683.5 1751.2 1819.4 1888.4 i 9 58.o 2028.4 2099.5 2171.5 2244.3 O I 5i.i 17.6 84.6 52.3 2O.6 89.5 5 9 .2 29.6 2IOO. 7 72.7 45.5 I 2 52.2 18.7 85.8 53.4 21.7 90.7 60.4 30.7 01.9 73.9 46.8 2 3 53.3 19.8 86. 9 54.6 22.9 91.9 61.6 3i. 9 o3.i 7 5.i 48.o 3 4 54-4 20.9 88.0 55. 7 24.0 93.0 62.7 33.i o4.3 76.3 4 9 .2 4 5 55.5 22.O 89.1 56.8 25.2 94.1 63. 9 34-3 o5.5 77.5 5o.4 5 6 56.6 23.2 9 o.3 58.o 26.3 9 5.3 65-.0 35.5 06.7 78.7 5i.6 6 7 5 7-7 24.3 91.4 5 9 .i 2 7 .5 9 6.5 66.2 36. 7 07.9 80.0 52. 9 7 8 58.8 25.4 92.5 60.2 28.6 97-6 67-4 37.8 09.1 81.2 54.1 8 9 5 9 . 9 26.5 9 3.6 61.4 29.7 9 8.8 68.5 3 9 .o io.3 82.4 55.3 9 10 i56i.o 1627.6 1694.8 1762.5 1830.9 i8 99 . 9 i 9 6 9 . 7 2040.2 21 II. 5 2i83.6 2256.5 10 ii 62.1 28.7 9 5 -9 63.6 32.0 I 9 OI.I 7-9 4i.4 12.7 84-8 5 7 .8 ii 12 63.2 29.8 97- 64.8 33.2 02.3 72.0 42.6 i3. 9 86.0 5 9 .o 12 i3 644 3i.o 9 8.i 65. 9 34.3 o3.4 7 3.2 43.8 87.2 60.2 i3 i4 65.5 32.1 99 .3 67.0 35.5 04.6 744 44. 9 i6.3 88.4 61.4 i4 i5 66.6 33.2 1700.4 68.2 36.6 05.7 7 5.6 46.i ! 7 .5 8 9 .6 62.7 i5 16 67.7 34.3 oi.5 69.3 3 7 .8 06. 9 76.8 4 7 .3 18.7 9 o.8 63. 9 16 i 7 68.8 35.4 02. 6 70.5 38.9 08.1 77-9 48.5 19.8 9 2.0 65.i 17 18 6 9 . 9 36.5 o3.8 71.6 4o.i 09.2 79.1 4 9 -7 21.0 9 3.3 66.3 18 19 71.0 3 7 .6 o4- 9 72.7 41.2 10.4 80.2 5o.8 22.2 9 4-4 6 7 .5 '9 20 1572.1 i638.8 1706.0 1773.9 1842.4 i 9 n.5 1981.4 2O52.O 2123.4 2i 9 5. 7 2268.8 20 21 7 3.2 39.9 07.1 7 5.o 43.5 12.7 82.6 53.2 24.6 9 6. 9 70.0 21 22 7 4.3 4i.o o8.3 76.1 44.6 i3.8 83. 7 54.4 25.8 98.1 71.2 22 23 42.1 o 9 .4 77.2 45.8 i5.o 84-9 55.6 27.0 99 .3 72.5 23 24 76.5 43.2 io.5 78.4 46. 9 16.2 86.1 56.8 28.2 2200.5 7 3. 7 24 25 77.6 44-3 n.6 79.5 48.i I7 .3 8 7 .3 58.o ^9.4 01.7 74.9 25 26 78.7 45.5 12.8 80.6 49.2 i8.5 88.4 5 9 .i 3o.6 o3.o 76.1 26 27 79 .8 46.6 i3. 9 81.8 5o.4 i 9 .6 89.6 6o.3 3i.8 04.2 ' 77-4 27 23 8o. 9 47-7 i5.o 83.o 5i.5 20.8 90.8 6i.5 33.o o5.4 78.6 28 29 Bft.i 48.8 16.1 84-1 52.7 21.9 92.0 62.7 34.2 06.6 79-8 2 9 3o i583.2 i64 9 . 9 1717.3 1785.2 1853.8 1923.1 I99 3.i 2o63. 9 2i35.4 2207.8 2281.0 3o 3i 84.3 5i.o 18.4 86.4 55.o 24-3 94.3 65.1 36.6 09.0 82.3 3i 32 85.4 52.2 i 9 .5 8 7 .5 56.i 25.4 9 5.5 06.2 37.8 10.2 83.5 32 33 86.5 53.3 20.7 88.6 5 7 .2 26.6 96.6 67-4 3 9 .o 11.4 84-7 33 34 87.6 54.4 21.8 89.8 58.4 27.8 97-8 68.6 40.2 12.7 86.0 34 35 88.7 55.5 22.9 90.9 5 9 .6 28.9 99.0 6 9 .8 4i-4 13.9 87.2 35 36 8 9 .8 56.6 24.0 92.1 60.7 3o.i 2OOO.2 71.0 42.6 i5.i 88.4 36 37 9-9 5 7 .8 25.2 9 3.2 61.9 3i.3 01.3 72.2 43.8 i6.3 89-7 37 38 9 2.O 58. 9 26.3 94.3 63.o 32.4 02.5 7 3.4 45.o i 7 .5 9-9 38 3 9 9 3.i 60.0 27.4 9 5.5 64.2 33.6 03.7 74-5 46.2 18.7 9 2.1 3 9 4o i5 9 4.3 1661.1 1728.6 i7 9 6.6 i865.3 1934.7 2004.9 2075.7 2i4 7 -4 2219.9 22 9 3.3 4o 4i 9 5.4 62.2 29.7 97-8 66.5 35. 9 06.0 76.9 48.6 21.2 9 4.6 4i 42 9 6.5 63.4 3o.8 98.9 67.6 3 7 .i 07.2 78.1 4 9 .8 22.4 9 5.8 42 43 97-6 64.5 31.9 1800.0 68.8 38.2 08.4 79-3 5i.o 23.6 97- 43 44 98.7 65.6 33.1 OI.2 69.9 3 9 .4 09.6 8o.5 52.2 24.8 9 8.3 44 45 99.8 66. 7 34.2 02.3 71.1 4o.5 10.7 81.7 53.4 26.0 99 .5 45 46 1600.9 6 7 .8 35.3 o3.5 72.2 4i. 7 11.9 82. 9 54.6 27.2 2300.7 46 47 02.0 6 9 .o 36.5 o4.6 73.4 42.9 84.o 55.8 28.5 02. o 47 48 o3.i 70.1 3 7 .6 o5. 7 74.5 44.o 14:3 85.2 57.0 29.7 03.2 48 49 04.2 71.2 38. 7 o6. 9 75.7 45.2 i5.4 86.4 58.2 3o. 9 o4-4 49 5o i6o5.4 i6 7 2.3 I739-9 1808.0 1876.8 1946.4 2016.6 2o8 7 .6 2i5 9 .4 2232.1 23o5.7 5o 5i o6.5 7 3.4 4i.o O 9 .2 78.0 4 7 .5 17.8 88.8 60.7 33.3 06. 9 5i 52 07.6 7 4.5 42.1 io.3 79.2 48. 7 19.0 9 o.o 61.9 34.6 08.1 52 53 08.7 7 5. 7 43.2 n.4 8o.3 49.9 2O.2 9 1.2 63.i 35.8 o 9 -4 53 54 09.8 76.8 444 12.6 8i.5 5i.o 21.3 9 2.4 64-3 3 7 .o 10.6 54 55 10.9 77-9 45.5 i3. 7 82.6 52.2 22.5 9 3.6 65.5 38.2 u.8 55 56 12.0 79- 46.6 i4. 9 83.8 53.4 23. 7 9 4-8 66.7 39.4 i3.i 56 5? i3.i 80.2 47.8 1 6.0 84-9 54.5 24.9 96.0 67. 9 40.7 i4.3 57 58 14.2 8i.3 48. 9 17.2 86.1 55. 7 26.0 97- 1 6 9 i 41.9 i5.5 58 5 9 1 5.4 82.4 5o.o i8.3 87.2 56. 9 27.2 98.3 70.3 43.i 16.8 5 9 MERIDIONAL PARTS. LATITUDE. Min. 36 37 38 39 40 41 42 43 44 45 46 Mill. 23i8.o 2392.6 2468.3 2545.o 2622.7 2701.6 2781.7 2863.1 2945.8 3o3o.o 3n5.6 I 19.2 9 3 -9 69.5 46.2 24.0 02.9 83.i 64.5 47.2 3i4 I 7 .0 I 2 20. 5 9 5.i 70.8 4 7 .5 25.3 o4-3 844 65.8 48.6 32.8 i8.5 2 3 21.7 96.4 72.1 48.8 26.6 o5.6 85.8 6 7 .2 5o.o 34.2 19.9 3 4 23.0 97-7 734 5o.i 27.9 06.9 87.1 68.5 5i4 35.6 21.4 4 5 24.2 98.9 74-6 5i.4 29.2 o8.3 88.5 7 o.o 52.8 37.0 22.8 5 6 25.4 2400.2 75.9 52. 7 3o.5 09.6 8 9 .8 71.3 54-2 384 24.2 6 7 26.7 01.4 77.1 54.o 31.9 10.9 9 1.2 72-7 55.6 3 9 .8 25. 7 7 8 27.9 02.7 78.5 55.3 33.2 12.2 9 2.5 7 4.i 57.0 4i.3 27.1 8 9 29.1 03.9 79-7 56.6 34-5 i3.5 9 3.8 754 58.3 42.7 28.5 9 10 233o.4 24o5.2 2481.0 2557.8 2635.8 2714.9 2 79 5.i 2876.8 2959.8 3o44-i 3i3o.o 10 ii 3i.6 06.4 82.2 5 9 .i 3 7 .i 16.2 9 6.5 78.2 61.1 45.5 3i.5 ii 12 32.9 07.7 83.5 60.4 38.4 17.5 97-9 79 .5 62.5 47.0 32.9 12 i3 34.i 09.0 84.8 61.7 39-7 18.9 99- 3 8o. 9 63. 9 484 34.3 i3 i4 35.3 1O.2 86.1 63.o 4i.o 20. 2 2800.6 82.3 65.3 49.8 35.8 i4 i5 36.6 ii. 5 87.4 64.3 42.3 21.5 02.0 83. 7 66.7 5l.2 37.2 i5 16 3 7 .8 12.7 88.6 65.6 43.6 22.9 o3.3 85.o 68.1 52.6 38. 7 16 I 7 39.0 14.0 89.9 66.9 44.9 24.2 o4-7 864 6 9 .5 54-1 4o.i 17 18 4o.3 15.2 91.2 68.2 46.3 25.5 06.0 8 7 .8 7-9 55.5 4i.6 18 J 9 4i.5 i6.5 92.4 69.5 4 7 .6 26.8 o 7 .3 89.1 7 2.3 56. 9 43.o 1 9 20 2342.8 2417-8 24 9 3. 7 2570.7 2648.9 2728.2 2808.8 2890.5 2973.7 3o58.3 3i44-5 20 21 44.o 19.0 95.0 72.0 5o.a 29.5 IO.I 91.9 76.1 59.7 45.9 21 22 45.3 20.3 96.3 7 3.3 5i.5 3o.8 n4 9 3.3 76.5 61.2 474 22 23 46.5 21.5 97.6 74-6 5 2 .8 32.2 12.8 94.7 77-9 62.6 48.8 23 24 47-7 22.8 98.8 7 5. 9 54-1 33.5 14.1 96.0 79-3 64-o 5o.3 24 25 49.0 24.O 2500.1 77.2 55.5 34-8 i5.5 974 80.7 654 5i. 7 25 26 5o.2 25.3 01.4 7 8.5. 56.8 36.2 16.8 98.8 82.1 66.9 53.2 26 2 7 5i.5 26.5 02.7 79.8 58.i 3 7 .5 18.2 2900.2 83.5 68.3 54.6 27 28 52.7 27.8 03.9 81.1 59.4 38.8 i 9 .5 0!.5 84-9 69.7 56.i 28 2 9 54.o 29.1 05.2 82.4 60. 7 4O.2 20. 9 02.9 86.3 71.1 5 7 .5 29 3o 2355.2 243o.3 25o6.5 2583.7 2662.0 274l.5 2822.3 2904.3 2 9 8 7 . 7 3072.6 SiSg.o 3o 3i 56.5 3i.6 07.8 86.0 63.3 42.9 23.6 o5. 7 89.1 74-0 60.4 3i 32 5 7 . 7 3 2 . 9 09.0 86.3 64-6 44-2 25.0 o 7 .i 90.5 754 61.9 32 33 58.9 34.i io.3 87.6 66.0 45.5 26.3 08.4 91.9 76.9 63.3 33 34 60.2 35.4 ii. 6 88.9 6 7 .3 46. 9 27.7 9-7 9 3.3 7 8.3 G4.8 34 35 61.4 36. 7 12.9 90.2 68.6 48.2 2 9 .0 II. 2 94.7 79-7 66.2 35 36 62.7 3 7 . 9 14.2 9 i.5 69.9 49-5 3o4 12.6 96.1 81.1 67.7 36 3? 63. 9 39.2 1 5.4 92.8 71.2 50.9 3i. 7 i4o 97.5 82.6 69.1 37 38 65.2 4o.4 16.7 94.1 7 2.5 52.2 33.i i5.3 98.9 84.o 70.6 38 3 9 66.4 4i-7 18.0 95.4 73.9 53.5 34.5 16.7 3ooo.3 854 72.0 39 4o 2367.6 2443.0 2519.3 2596.7 26 7 5.2 2754.9 2835.8 2918.1 3ooi.8 3o86. 9 3i73.5 4o 4i 68.9 44.2 20. 5 98.0 7 6.5 56.2 3 7 .2 i 9 .5 03.2 88.3 7 5.o 4i 42 70.2 45.5 21.8 99 .3 77 .8 5 7 .6 38.6 20.9 04.6 8 9 . 7 76.4 42 43 71.4 46.8 23.1 2600.5 79.1 58. 9 3 9 . 9 22.3 06.0 9 1.2 77-9 43 44 72.6 48.o 244 01.9 8o.5 60.2 4i-3 23.6 o 7 4 92.6 79 .3 44 45 7 3. 9 49.3 25.7 03.2 81.8 6i.5 42.6 25.0 08.8 9 4-o 80.8 45 46 7 5.i 5o.6 27.0 o4.5 83.i 62.9 44.o 26.4 IO.2 9 5.5 82.3 46 4? 76.4 5i.8 28.3 o5.8 844 64-3 454 2 7 .8 ii. 6 9 6. 9 83. 7 47 48 77.6 53.i 29.5 07.1 85. 7 65.6 46. 7 29.2 i3.o 9 8.3 85.2 48 49 78.9 54-3 3o.8 08.4 87.1 66.9 48.i 3o.6 i44 99-7 86.6 49 5o 238o.i 2455.6 2532.1 2609.7 2688.4 2768.3 284 9 .5 2932.0 3oi5.8 SlOI.2 3i88.i 5o 5i 81.4 56. 9 33.4 II. O 89.7 69.6 5o.8 33.3 I 7 .2 02. 6 89.6 5i 52 82.6 58.i 34.7 12.3 91.0 71.0 52.2 34- 7 18.7 o4.i 91.0 52 53 83.9 59.4 36.o i3.6 92.3 7 2.3 53.5 36.i 20.1 o5.6 9 2.5 53 54 85.i 60.7 3 7 .2 i4. 9 9 3. 7 7 3. 7 54-9 3 7 .5 21.5 O 7 .O 94.0 54 55 86.4 61.9 38.5 16.2 9 5.o 75.0 56.3 38.9 22-9 08.4 9 5.4 55 56 87.6 63.2 3 9 .8 17.5 9 6.3 7 6.3 5 7 . 7 4o.3 24-3 o 9 .8 9 6. 9 56 57 88.9 64.5 4i.i 18.8 97.6 77-7 5 9 .o 4i,7 25. 7 ii. 2 98.4 5 7 58 90.2 65.8 42-4 2O.I 99.0 79- 6o.5 43.i 27.1 12.7 998 58 5 9 91.4 67.0 43.6 21-4 2700.3 80.4 61.1 444 28.5 14.1^3201.3: 5 9 146 MERIDIONAL PARTS. LATITUDE. Min. 47 48 49 50 51 52 53 54 55 56 57 Min. o 3202.7 3291.5 3382.1 3474.5 3568.8 3665.2 3 7 63.8 3864.6 3 9 68.o 4o 7 3-9 4182.6 o I O42 93.0 83.6 76.0 70.4 66.8 65.4 66.3 6 9 . 7 7 5. 7 84.5 I 2 05.7 9 4.5 85.i 77.6 7 2.O 08.4 67.1 68.0 7 i.5 77.5 86.3 2 3 07.1 96.0 86.7 79 .i 7 3.6 7 O.I 68.8 69-7 7 3.2 79.3 88.1 3 4 08.6 97.5 88.2 80.7 7 5.2 71.7 7 o.4 7 i.5 75.0 81.1 90.0 4 5 I O.I 99.0 8 9 . 7 82.3 7 6.8 7 3.3 72.1 7 3.2 76.7 82.9 91.8 5 6 n.5 33oo.5 9 i.3 83.8 7 8.4 7 5.o 7 3. 7 74.9 78.4 84.7 93.7 6 7 i3.o O2.O 9 2.8 85.4 79-9 7 6.6 7 5.4 76.6 80.2 86.4 9 5.5 7 8 i4-5 o3.5 9 4.3 87.0 8i.5 78.2 77.1 78.3 82.0 88.2 97 .3 8 9 i5. 9 o5.o 9 5.8 88.5 83.i 79 .8 78.7 80.0 83. 7 9 o.o 99.2 9 10 3217.4 33o6.5 33 97 .4 34 9 o.i 3584. 7 368i.5 3780.4 388i. 7 3 9 85.4 4091.8 4201.0 10 ii 18.9 08.0 9 8. 9 91.6 86.3 83.i 82.1 83.4 87.2 9 3.6 02.9 ii 12 20.3 09.5 34oo.4 93.2 8 7 . 9 84. 7 83. 7 85.i 88. 9 95.4 o4 7 12 i3 21.8 II. O 02. o 94.7 8 9 .5 86.4 85.4 86.8 9-7 97.2 06.6 i3 i4 23.3 12.5 o3.5 96.3 91.1 88.0 87.1 88.5 9 2.5 99.0 08.4 i4 l5 24.8 i4-o o5.o 97-9 9 2. 7 89.6 88.8 9 0.2 9 4.2 4ioo.8 io.3 i5 16 26.2 i5.5 06.6 99 .4 9 4.3 9 i.3 90.4 9 2.O 9 6.o 02.6 12. 1 16 !? 27.7 17.0 08.1 35oi.o 9 5. 9 92.9 92.1 93.7 97-7 04.4 14.0 1 7 18 29.2 i8.5 o 9 .6 02.6 97 .5 94-5 93.8 95.4 99 .5 06.2 i5.8 18 *9 30.7 2O.O n. i 04.1 99 .i 96.2 9 5.5 97 .I 4OOI.2 08.0 17.7 19 2O 3232.1 3321.5 3412.7 35o5. 7 36oo. 7 36 97 .8 3797-1 38 9 8.8 4oo3.o 4109.8 4219.5 20 21 33.6 23.0 14.2 07.3 02.3 99.4 98.8 3 9 oo.5 o4-7 n.6 21.4 21 22 35.i 24-5 i5. 7 08.8 o3. 9 3 7 oi.i 38oo.5 O2. 2 o6.5 i3.4 23.2 22 23 36.6 26.0 i 7 .3 10.4 o5.5 02. 7 O2. 2 04.0 o8.3 15.2 25.1 23 24 38.o 27.5 18.8 12. O 7 .I o4-4 o3.8 5.7 IO.O 17.1 27.0 24 25 3 9 .5 29.0 20.4 i3.5 o8. 7 06.0 o5.5 07.4 n.8 18.9 28.8 25 26 4i.o 3o.6 21.9 i5.i io.3 o 7 .6 07.2 o 9 .i i3.5 20.7 3o.6 26 27 42.5 32.1 23.5 16.7 n. 9 09.3 08.9 10.8 i5.3 22.5 32.5 27 28 44-0 33.6 25. i8.3 i3.6 10.9 io.5 12.5 17.1 24.3 34.4 28 29 45.4 35.i 26.5 19.8 i5.i 12.6 12.2 i4.3 18.8 26.1 36.2 2 9 3o 3246.9 3336.6 3428.0 3521.4 36i6. 7 3 7 i4.2 38i3. 9 3 9 i6.o 4020.6 4127.9 4238.1 3o 3i 48.4 38.1 2 9 .6 23.0 18.4 i5.8 i5.6 17.7 22.4 2 9-7 4o.o 3i 32 49.9 3 9 .6 3i.i 24.6 20.0 i 7 .5 i 7 .3 i 9 -4 24.1 3i.5 4i.8 32 33 5i.4 4i.i 3 2 . 7 26.1 21.6 19.1 18.9 21.2 2 5. 9 33.3 43.7 33 34 52.8 42.6 34-2 27.7 23.2 20.8 20.6 22. 9 27.7 35.2 45.5 34 35 54.3 44-1 35.8 29.3 24.8 22.4 22.3 24-6 29.4 3 7 .o 47-4 35 36 55.8 45.7 3 7 .3 3o.8 26.4 24.1 24.O 26.3 3l.2 38.8 4 9 .3 36 37 5 7 .3 47.2 , 38.8 32.4 28.0 25.7 25-7 28.1 33.o 4o.6 5i.i 3? 38 58.8 48. 7 4o.4 34.o 2 9 .6 27.4 2 7 4 2 9 .8 34-8 42.4 53.o 38 3 9 6o.3 50.2 4i. 9 35.6 3i.3 29.0 29.1 3i.5 36.5 44-2 54-9 39 4o 3261.7 335i. 7 3443.5 3537.1 3632.8 3 7 3o. 7 383o.8 3 9 33.2 4o38.3 4i46.i 4256.7 4o 4i 63.2 53.2 45.o 38. 7 344 32.3 32.4 35.0 4o.i 479 58.6 4i 42 64-7 54.7 46.6 4o.3 36.i 34.0 34.i 36. 7 4i.8 49.7 6o.5 42 43 66.2 56.2 48.i 4 1. Q 3 7 . 7 35.6 35.8 38.4 43.6 5i.5 62.3 43 44 67.7 5 7 .8 49.7 43.5 3 9 .3 3 7 .3 *3 7 .5 4o.2 45.4 53.4 64.2 44 45 69.2 5 9 .3 5l.2 45.o 4o. 9 38.9 3 9 .2 41.9 47-2 55.2 66.1 45 46 70.7 60.8 5 2 .8 46.6 42.5 4o.6 40.9 43.6 4g.o 5 7 .o 68.0 46 47 72.1 62.3 54.3 48.2 44.i 42.2 42.6 45.4 5o. 7 58.8 69.8 47 48 73.6 63.8 55.8 4 9 -8 45.8 43. 9 44.3 47.1 52.5 60.7 71.7 48 49 7 5.i 65.4 57.4 5i.4 4 7 4 45.5 46.o 48.8 54.3 62.5 7 3.6 49 5o 3276.6 3366. 9 3458. 9 3553.0 364 9 .o 374 7 .2 3847-7 3 9 5o.6 4o56.i 4i64.3 42 7 5.5 5o 5i 78.! 68.4 6o.5 54.6 5o.6 48.8 49.4 52.3 5 7 .8 66.1 77-4 5i 52 79.6 69-9 62.0 56.i 52.2 5o.5 5i.i 54-0 5 9 .6 68.0 79.2 52 53 81.1 71.4 63.6 5 7 . 7 53.8 52.1 52.8 55.8 61.4 69.8 81.1 53 54 82.6 7 3.o 65.2 5 9 .3 55,5 53.8 54-4 5 7 .5 63.2 71.6 83.o 54 55 84.i 74-5 66.7 6o. 9 5 7 .i 55.5 56.i 5 9 .3 65.o 7 3.5 84.9 55 56 85.6 76.0 68.3 62.5 58. 7 57.1 5 7 .8 61.0 66.8 7 5.3 86.8 56 57 87.! 77 .5 6 9 .8 64-0 6o.3 58.8 5 9 .5 62.7 68.5 77.1 88.6 57 58 88.5 79- 71-4 65.6 61.9 60.4 6L2 64-5 7 o.3 70. o 90.5 58 5 9 90.0 80.6 7 3.o 6 7 .2 63.6 62.1 62. 9 66.2 7 2.1 80.8 92.4 5 9 MERILIONAL PARTS. LATITUDE. Min. 58 59 60 61 62 63 64 65 66 67 68 Min. o 4294.3 4409.1 4527.4 4649-2 4775.0 4 9 o4- 9 5039.4 5178.8 5323.5 5474.0 563o.8 I 96.2 n. i 29.4 5i.3 77.1 07.1 4i. 7 81.2 26.0 76.6 33.5 I 2 98.1 i3.o 3i.4 53.4 79 .3 o 9 .4 44.o 83.5 28.4 79.1 36.2 2 3 [3oo.o i5.o 33.4 55.4 81.4 n.6 46.3 85. 9 30.9 8i. 7 38.8 3 4 01.9 16.9 35.4 5 7 .5 83.5 i3.8 48.6 88.3 33.4 84.3 4i.5 4 5 03.7 18.9 3 7 -4 5 9 .6 85.6 16.0 5o. 9 9-7 35.8 86.9 44-2 5 6 o5.6 20.8 3 9 .4 61.6 87.8 18.2 53.i 9 3.i 38.3 89.4 46. 9 6 7 oy.S 22.8 4i-4 63. 7 89.9 20.4 55.4 9 5.4 4o.8 92.0 49.6 7 8 09.4 24.7 43.4 65.8 92.1 22.6 5 7 . 7 97 .8 43.2 94-5 52.3 8 9 n. 3 26.7 45.4 67.8 94.2 24.8 60.0 52OO.2 45-7 97.1 54.9 9 10 43i3.2 4428.6 4547-4 4669.9 4796.3 4927.0 5o62.3 52O2.6 5348.2 5499.7 5657.6 10 ii i5.i 3o.6 49.4 72.0 9 8.5 29.2 64-6 o4- 9 5o. 7 55o2.3 6o.3 ii 12 17.0 32.5 5i.4 74.1 48oo.6 3i.5 66. 9 o 7 .3 53.i 04.9 63.o 12 i3 18.9 34.5 53.5 76.1 02.8 33. 7 6 9 .2 09-7 55.6 07.4 65. 7 i3 i4 20,8 36.4 55.5 78.2 o4-9 35.9 7 i.5 12. 1 58.i IO.O 68.4 i4 i5 22.7 38.4 5 7 .5 8o.3 07.1 38.i 73.8 i4.5 60.6 12.6 71.1 i5 16 24.6 4o.3 5 9 .5 82.4 09,2 4o.3 76.1 i6. 9 63.i 15.2 7 3.8 16 J 7 26.5 42.3 6i.5 84-5 11.4 42.6 784 i 9 .3 65.6 17.8 76.5 J 7 18 28.4 44-2 63.5 86.5 i3.5 44.8 80.7 21.6 68.0 20.4 79.2 18 : 9 3o.3 46.2 65.6 88.6 i5. 7 47.0 83.o 24.0 70.5 23.0 81.9 J 9 20 4332.2 4448.2 456 7 .6 4690.7 4817.8 4949.2 5o85.3 5226.4 5373.0 5525.6 5684.6 20 21 34.1 5o.i 6 9 .6 92.8 2O.O $i.5 87.6 28.8 7 5.5 28.1 8 7 .3 21 22 36.o 52.1 71.6 94.9 22.1 53. 7 9 o.o 3l.2 78.0 30.7 90.0 22 23 3 7 . 9 54.i 73.6 97.0 24-3 55. 9 9 2.3 33.6 8o.5 33.3 92.7 23 24 39.8 56.o 7 5. 7 99.1 26.4 58.2 9 4.6 36.o 83.o 35-9 9 5.5 24 25 4i.8 58.o 77-7 4701.1 28.6 6o.4 96-9 38.4 85.5 38.6 98.2 25 26 43. 7 60.0 79-7 03.2 3o.8 62.6 99- 2 4o.8 88.0 41.2 5700.9 26 27 45.6 61.9 81.7 o5.3 32. 9 64. 9 5ioi.5 43.2 90.5 43.8 o3.6 27 28 47-5 63. 9 83.8 07.4 35.i 67.1 o3.8 45.7 93.0 46-4 o6.3 28 29 49.4 65. 9 85.8 o 9 .5 37.3 69.4 06.2 48.i 9 5.5 49.0 09.1 29 3o 435i.3 4467.8 458 7 .8 4711.6 483 9 .4 4971-6 5io8.5 525o.5 5398.0 555i.6 5 7 n.8 3o 3i 53.2 69.8 8 9 . 9 i3. 7 4i.6 7 3.8 10.8 52. 9 54oo.5 54.2 i4-5 3i 32 55.i 71.8 91.9 i5.8 43.8 76.1 i3.i 55.3 o3.o 56.8 i 7 .3 32 33 5 7 .i 7 3. 7 9 3. 9 17.9 45. 9 78.3 i5.5 5 7 . 7 o5.5 594 20.0 33 34 Sg.o 7 5. 7 96.0 2O.O 48.i 80.6 17.8 60. i 08. i 62.1 22.7 34 35 60.9 77-7 98.0 22.1 5o.3 82.8 20.1 62.6 10.6 64-7 25.5 35 36 62.8 79-7 46oo.o 24-2 52.4 85.i 22.4 65.o i3.i 6 7 .3 28.2 36 37 64,7 81.6 02. i 26.3 54.6 8 7 .3 24.8 6 7 .4 i5.6 69.9 30.9 37 38 66.7 83.6 o4i 28,4 56.8 89.6 27.1 6 9 .8 18.1 72.6 33. 7 38 3 9 68.6 85.6 06.1 3o.5 5 9 .o 91.8 2 9 4 72.2 2O.6 76.2 364 3 9 4o 43 7 o.5 4487-6 4608.2 4 7 3 2 .6 486i.i 4994.1 5i3i.8 6274.7 5423.2 55 77 .8 5 7 3 9 .2 4o 4i 72.4 89.6 10.2 34-7 63.3 9 6.3 34.i 77.1 2 5. 7 80.4 41.9 4i 42 74-3 9 i.5 12.3 36.8 65.5 98.6 36.5 79 .5 28.2 83.i 44-7 42 43 7 6.3 9 3.5 i4.3 3 9 .o 67.7 5ooo.8 38.8 82.0 3o.8 85. 7 4 7 .5 43 44 78.2 9 5.5 16.4 4i.i 69.9 o3.i 4i.i 844 33.3 88.4 5o.2 44 45 80. i 97 .5 18.4 43.2 72.0 o5.4 43.5 86.8 35.8 91.0 52.9 45 46 82.1 99.5 20.5 45.3 74.2 07.6 45.8 89.3 38.4 9 3.6 55.7 46 47 84.o 45oi.5 22.5 4 7 4 76.4 09.9 48.2 91.7 40.9 96.3 58.5 47 48 85. 9 o3.4 24.6 4 9 .5 78.6 12.2 5o.5 94.1 434 98.9 61.2 48 49 87.8 o5.4 26.6 5i.6 80.8 l44 5 2 . 9 96.6 46.o 56oi.6 64.0 49 5o 438 9 .8 4507.; 4628.7 4753.7 4883.0 5oi6. 7 5i55.2 5200.0 5448.5 56o4-2 5 7 66.8 5o 5i 91.7 09.4 30.7 55. 9 85.2 18.9 5 7 .6 53oi.5 5i.o 06.9 69.5 5i 52 9 3.6 II. L 32.8 58.o 8 7 .4 21.2 5 9 . 9 03.9 53.6 o 9 .5 72.3 52 53 9 5.6 i3.4 34.8 60. i 8 9 .5 23.5 62.3 o6.3 56.i 12.2 7 5.i 53 54 97 .5 i5.; 36.9 62.2 91.7 25.8 64.6 08.8 58. 7 i4.8 77-9 54 55 99.4 17.2 3 9 .o 64.4 9 3. 9 28.0 67.0 II. 2 61.2 i 7 .5 80.6 55 56 44oi.2 19.4 4i.o 66.5 96.1 3o.3 69.4 i3. 7 63.8 20.2 834 56 57 o3.3 2.1.1. 43.o 68.6 9 8.3 32.6 71.7 16.1 66.3 22.9 86.2 57 58 o5.3 23.4 45.i 70.7 4 9 oo.5 34-9 7 4.i 18.6 68.9 25.5 89.0 58 5 9 07.2 25.4 47.2 72.9 02.7 3 7 .i 76.4 21. 1 7i.4 28.2 9 i.8 5 9 148 MERIDIONAL PARTS. LATITUDE. Min. 69 70 71 72 73 74 75 76 77 78 79 Min. O 5 79 4-6 5 9 65. 9 6145.7 6334.8 65344 6 7 4i). 7 6 97 o.3 7210.1 7467.2 77 44-6 8o45. 7 O I 97-4 68.8 48.8 38.i 3 7 .8 49.4 74.2 14.2 71.7 49.4 5i.o I 2 58oo.i 71.8 5i. 9 4i.3 4i.3 53.o 78.1 i8.3 76.1 54-2 56.2 2 3 02.9 74-7 54-9 44-6 44-7 56.6 81.9 22.5 80.6 5 9 .o 6i.5 3 4 o5.y 77.6 58.o 4 7 -8 48.i 6o.3 85.8 26.6 85.o 63. 9 66.7 4 5 o8.5 80.6 61.1 5i.i 5i.6 63. 9 89.7 3o.8 8 9 .5 68.7 72.0 5 6 li,3 83.5 64-2 54.3 55.o 67.6 9 3.6 35.o 94.0 7 3.5 . 77-3 6 7 l42 86.4 6 7 .3 57.6 58.5 71.2 97.5 3 9 .i 9 8.5 78.4 82.6 7 8 17.0 89.4 70.4 60.8 61.9 74-9 7001.4 43.3 7 5o3.o 83.3 87.9 8 9 19.8 92.3 7 3.5 64.i 65.3 7 8.5 o5.3 4 7 -5 07.4 88.1 9 3.2 9 10 5822.6 SggS.S 6176.6 636 7 .4 6568.8 6782.2 7009.2 7 25l. 7 7 5n. 9 779 3.o 8098.5 10 n 25.4 98.2 79-7 70.6 72.3 85.9 i3.i 55.8 i6.5 97-9 8io3.8 ii 12 28.2 6001.2 82.8 7 3. 9 7 5. 7 89.6 17.0 60.0 21.0 7802.8 09.2 12 i3 3i.o o4-i 85. 9 77.2 79.2 9 3.2 20.9 64.2 25.5 07-7 14.5 i3 i4 33.8 07.1 89.0 80.4 82.6 96.9 24.8 68.4 3o.o 12.6 19.9 i4 i5 36.7 IO.O 92.1 83. 7 86.1 6800.6 28.8 72.6 34-5 I 7 .5 25.2 i5 16 3 9 .5 1 3.o 95.2 87.0 89.6 o4.3 32. 7 76.8 Sg.i 22.4 3o.6 16 I 7 42.3 1 6.0 9 8.3 90.3 93.0 08.0 36.6 81.1 43.6 2 7 .3 36.o J 7 18 45.i 18.9 6201.4 93.6 96.5 n.6 4o.6 85.3 48.i 32.2 4i.3 18 J 9 48.o 21.9 o4.5 96.9 6600.0 1 5.4 44-5 8 9 .5 52.7 3 7 .2 46. 7 '9 20 585o.8 6024.9 6207.7 64oo.s 66o3.5 6819.1 7048.5 7293.7 7 55 7 .3 7842.1 8i5 2 .i 20 21 53.6 27.8 10.8 o3.4 07.0 22.8 52.4 98.0 61.8 4 7 .i 5 7 .5 21 22 56.5 3o.8 i3. 9 06.7 !0.5 26.5 56.4 7 302.2 66.4 52. 62.9 22 23 5 9 .3 33.8 17.0 IO.I i4-o 30.2 6o.3 06.4 71.0 5 7 .o 68.4 23 24 62.2 36.8 20.2 i3.4 17.5 33.9 64.3 10.7 7 5.5 61.9 7 3.8 24 25 65.o 39.8 23.3 16.7 21.0 37.6 68.3 i5.o 80. i 66.9 79.2 25 26 67.8 42.7 26.5 20. o 24.5 4i.3 72.2 19.2 84-7 7 i. 9 84. 7 26 87 70.7 45.7 29.6 23.3 28.0 45.i 76.2 23.5 89.3 76.9 90.1 27 28 7 3.5 48. 7 3 2 . 7 26.6 3i.5 48.8 80.2 27.7 9 3. 9 81.9 9 5.6 28 2 9 76.4 5i. 7 35. 9 29.9 35.o 52.5 84.2 32.0 98.5 86.9 8201.1 29 3o 58 79 .2 6o54-7 6239.0 6433.3 6638.5 6856.3 7088.2 7336.3 7603.2 7 8 9 I -9 8206.6 3o 3i 82.1 5 7 . 7 42.2 36.6 42.1 60.0 9 2.2 4o.6 07.8 96.9 12. 1 3i 32 85.o 60.7 45.3 3 9 . 9 45.6 63.8 9 6.2 44-9 12.4 7902.0 I 7 .6 32 33 87.8 63. 7 48.5 43.2 49' i 67.5 7100.2 49-2 17.0 O 7 .O 23.1 33 34 90.7 66.7 5i. 7 46.6 52.6 7 i.3 O4.2 53.5 21.7 12.0 28.6 34 35 9 3.6 69.7 54.8 4y-9 56.2 75.0 08.2 5 7 .8 26.3 I7.I 34.i 35 36 9 6.4 72.7 58.o 53.3 59.7 78.8 12.2 62.1 3i.o 22.1 3 9 . 7 36 37 99.3 7 5. 7 61.2 56.6 63.3 82.6 i6.3 66.4 35.6 2 7 .2 45.2 37 38 5902.2 78.8 64.3 60.0 66.8 86.3 20.3 70.7 4o.3 32.3 5o.8 38 3 9 o5.o 81.8 6 7 .5 63.3 70.4 90.1 24.3 7 5.i 45.o 3 7 .3 55.3 3 9 4o 5907.9 6084.8 6270.7 6466.7 6673.9 68 9 3. 9 7128.4 7 3 79-4 7649. 7 7 942.4 8261.9 4o 4i 10.8 87.8 7 3. 9 70.0 77-4 97-7 32.4 83. 7 54.3 4 7 .5 6 7 .5 4i 42 i3. 7 90.8 77.1 73.4 81.0 6901.5 36.4 88.1 Sg.o 5 2 .6 7 3.1 42 43 16.6 9 3. 9 80.2 76.7 84-6 o5.3 4o.5 92.4 63. 7 5 7 . 7 78.6 43 44 19.4 96.9 83.4 80.1 88.2 09.1 44.5 96.8 68.4 62.8 84-3 44 45 22.3 99.9 86.6 83.5 91.7 I2. 9 48.6 74oi.i 7 3.2 68.0 89.9 45 46 25.2 6io3.o 89.8 86.9 9 5.3 I6. 7 52.7 o5.5 77-9 7 3.i 9 5.5 46 47 28.1 06.0 93.0 90.2 98.9 20. 5 56. 7 09.9 82.6 7 8.2 83oi.i 47 48 3i.o 09.0 96.2 93.6 6702.5 24.3 60.8 i4-3 8 7 .3 83.4 06.7 48 49 33. 9 12. 1 99 .4 97.0 06. i 28.1 64. 9 18.6 92.! 88.5 12.4 49 5o 5 9 36.8 6n5.i 6302.6 65oo.4 6709.7 6 9 3i. 9 7i6 9 .o 7423.0 7696.8 799 3 -7 83i8.i 5o 5i 3 9 . 7 18.2 o5.8 o3.8 13.2 35. 7 7 3.i 27.4 77 oi.5 98.9 23.8 5i 52 42.6 21.2 09.1 07.2 16.8 3 9 .6 77.2 3i.8 o6.3 8004.0 29.4 52 53 45.5 24.3 12.3 10.6 20.4 43.4 81.2 36.2 n. i 09.2 35.i 53 54 48.4 2 7 .3 i5.5 i4-o 24.0 47-2 85.3 4o.6 i5.8 i4-4 4o.8 54 55 5i.3 3o.4 18.7 i 7 4 27.7 5x.i 8 9 .5 45.i 20.6 19.6 46.5 55 56 54.2 33.4 21.9 20.8 3i.3 54. 9 9 3.6 49-5 25.4 24.8 52.2 56 5 7 57.2 36.5 25.1 24.2 34.9 58.8 97-7 53. 9 30.2 3o.o 58.o 57 58 60.1 3 9 .6 28.4 27.6 , 38.5 62.6 7201.8 58.3 35.o 35.2 63. 7 58 5 9 63.o 42.6 3i.6 3i.o 42.1 66.5 o5. 9 62.8 3 9 .8 4o.5 69.4 5 9 CORRECTIONS TO MIDDLE LATITUDE. 1 Mid. Lat. DIFFERENCE OF LATITUDE. 1 2 D 3 4 5 6 7 8 9 10 11 12 13 14 15 16* 17 18 19 20 o i5 2 3 5 7 9 12 i5 18 22 26 3i 36 4i 47 52 5 9 65 72 16 o 2 3 4 6 II i4 18 21 25 3o 34 3 9 44 5o 56 62 6 9 17 o 2 3 4 6 8 II i4 !7 20 24 28 33 38 43 48 54 60 66 18 o 3 4 6 8 IO i3 16 2O 23 27 32 36 4i 46 52 58 64 I 9 3 4 6 8 10 i3 16 1 9 22 26 3o 35 4o 45 5o 56 61 20 o 2 4 5 7 IO 12 i5 18 22 25 29 34 38 43 48 54 60 21 o 2 4 5 7 9 12 i5 18 21 25 29 33 37 42 47 52 58 22 ! o 2 4 5 7 9 12 i4 17 21 2/1 28 32 36 4i 46 5i 56 23 2 3 5 7 9 II i4 I 7 2O 23 27 3i 35 4o 45 5o 55 24 o 2 3 5 7 9 II i4 16 20 23 27 3i 35 3 9 44 49 54 25 2 3 5 7 9 II i3 16 I9 23 26 3o 34 3 9 43 48 53 26 2 3 5 6 8 II i3 16 J 9 22 26 3o 34 38 42 47 52 2 7 o 2 3 5 6 8 II i3 16 19 22 25 2 9 33 37 42 47 52 28 o 2 3 5 6 8 10 i3 16 18 22 25 2 9 33 37 4i 46 5i 29 2 3 5 6 8 10 i3 i5 18 21 25 28 32 37 4i 46 5i 3o o 2 3 5 6 8 IO i3 i5 18 21 25 28 32 36 4i 45 5o 3i o 2 3 5 6 8 IO 12 i5 18 21 24 28 32 36 4o 45 5o 32 o o 2 3 4 6 8 IO 12 i5 18 21 24 28 32 36 4o 45 5o 33 o 2 3 4 6 8 10 12 i5 18 21 24 28 32 36 4o 45 49 34 o o 2 3 4 6 8 IO 12 i5 18 21 24 28 32 36 4o 45 49! 35 o 2 3 4 6 8 IO 12 i5 18 21 24 28 32 36 4o 45 49 36 o 2 3 4 6 8 IO 12 i5 18 21 24 28 32 36 4o 45 49 37 o 2 3 4 6 8 10 12 i5 18 21 24 28 32 36 4o 45 49 38 2 3 4 6 8 IO 12 i5 18 21 24 28 32 36 4o 45 5o 3 9 o 2 3 4 6 8 IO 12 i5 18 21 24 28 32 36 4o 45 5o 4o o 2 3 5 6 8 IO i3 i5 18 21 25 28 32 36 4i 45 5o 4i 2 3 5 6 8 IO i3 i5 18 21 25 28 32 37 4i 46 5i j 42 o 2 3 5 6 8 IO i3 i5 18 22 25 20 33 37 4i 46 5i i 43 o 2 3 5 6 8 IO i3 16 18 22 25 2 9 33 37 42 46 52 44 2 3 5 6 8 IO i3 16 J 9 22 25 20 33 38 42 47 52 45 o 2 3 5 6 8 II i3 16 I9 22 26 3o 34 38 43 48 53 46 o 2 3 5 6 8 II i3 16 I 9 22 26 3o 34 38 43 48 53 47 2 3 5 7 9 II i3 16 23 26 3o 35 3 9 44 49 54 48 o 2 3 5 7 9 II i4 17 20 23 27 3i 35 4o 44 5o 55 *9 o 2 3 5 7 9 II i4 17 20 23 27 3i 36 4o 45 5o 56 5o o 9 4 5 7 9 II i4 20 24 28 32 36 4i 46 5i 57 5i 2 4 5 7 9 12 i4 17 21 24 28 32 37 42 47 52 58 52 b 2 4 5 7 9 12 i5 18 21 25 29 33 38 43 48 53 5 9 53 o 2 4 5 7 IO 12 i5 18 21 25 29 34 38 43 49 54 60 54 o 2 4 5 7 10 12 i5 18 22 26 3o 34 3 9 44 5o 56 62 55 o 2 4 6 8 IO i3 16 19 22 26 3i 35 4o 45 5i 57 63 56 o 3 4 6 8 IO i3 16 !9 23 27 3i 36 4i 46 52 58 65 57 o 3 4 6 8 10 i3 16 20 24 28 32 37 42 48 54 60 66 58 2 3 4 6 8 II i4 17 20 24 28 33 38 43 49 55 61 68 5 9 2 3 4 6 8 II i4 21 25 29 34 3 9 45 5o 57 63 70 60 o 2 3 4 6 9 II i4 18 22 26 3o 35 4o 46 52 58 65 72 61 o 2 3 5 7 9 12 i5 18 22 26 3i 36 42 47 53 60 67 75 62 o 2 3 5 7 9 12 i5 19 23 27 32 37 43 49 55 62 7 77 63 2 3 5 7 10 12 16 20 24 28 33 3 9 44 5i 57 64 72 80 64 o 2 3 5 7 10 13 16 20 24 29 34 4o 46 52 5 9 67 75 83 65 o 2 3 5 7 IO i3 I? 21 25 3o 36 4i 48 54 62 6 9 78 86 66 2 3 5 8 II i4 18 22 26 32 37 43 5o 5 7 64 72 81 9 67 o 2 4 6 8 II i4 18 23 28 33 3 9 45 52 5 9 67 76 85 94 68 2 4 6 8 12 i5 19 24 2 9 34 4o 47 54 62 70 79 89 99 6 9 o 2 4 6 9 12 16 20 25 3o 36 42 49 57 65 74 83 9 3 io4 70 . 2 4 6 9 13 16 21 26 32 38 44 52 60 68 78 88 9 8 no o 2 4 7 10 i3 17 22 27 33 4o 47 55 63 72 82 9 3 io4 116 72 o 3 5 7 IO i4 18 23 29 35 42 49 58 67 76 87 9 8 in 124 150 LOGARITHMS FOR COMPUTING COMPOUND INTEREST. In computing compound inter* st for long periods of time, the following logarithms to more than six places. it is necessary to have Number. Logarithm. Number. Logarithm. .0026 .0060 .0076 .0100 .0126 .0160 .0176 .0200 .0226 .0260 .0276 ,o3oo ,o3 2 5 .o35o . P 3 7 5 ,o4oo .00108 438i3 .00216 60618 .oo324 5o548 .00432 13738 .00639 60319 .00646 60422 .00763 44i79 .00860 01718 .00966 33167 .01072 38654 .01178 i83o5 .01283 72247 .01389 oo6o3 .01494 03498 .01698 81064 .01703 33393 .0426 .o45o .0475 .0600 .0626 .0660 .0676 .0600 .0626 .0660 .0676 .0700 .0726 .0760 .0776 .0800 ,01807 6o636 .01911 62904 .020i5'4o3i6 .02118 92991 .02222 21046 .02326 24696 .02428 03760 .O253o 58653 .02632 89387 .02734 96078 .0283678837 .0293837777 .o3o39 73009 .o3i4o 84643 .o324i 72788 .o3342 3 7 555 NUMBERS OFTEN USED IN CALCULATIONS. Circumference < Surface of a spl Area of a circle Area of a circle Capacity of a s[ Capacity of a sp 1 3.1416926 . )f a circle to diameter i } lere to diameter i > 3.1416926 .7863982 .6236988 4.1887902 0.3183099 . 2967796 206264". 8 .0174533 .0002909 .00000486 .00000970 .ooooi454 .00001939 .00002424 .00002909 .00003394 .00003879 .oooo4363 2.7182818 .4342945 1296000 864oo 6280 Logarithms. 0.497l5o 9.896090 9.718999 0.622089 9.602860 i. 7 58i 2 3 5.3i4425 8.241877 6.463 72 6 4.686676 4.986606 6.162696 5.28 7 635 5.384545 5.463 7 26 5.53o6 7 3 5.588665 6.639817 0.434294 9-63 77 84 6. 112606 4.9365i4 3.722634 to radius i .... --) to diameter i >here to diameter i _ >here to radius i Arc equal to rac Arc equal to raci Length of i deg Length of i mit Sine of i secon Sine of 2 secon< Sine of 3 secon Sine of 4 secon Sine of 5 secon Sine of 6 secon Sine of 7 secon Sine of 8 secon Sine of 9 secon Base of Napier Modulus of the 36o degrees ex 24 hours expre Number of feet ius expressed in degrees ius expressed in seconds ree in parts of radius 5i mte in parts of radius ^ i Is 3s is 3s 3s 3s " 3s 3s s system of logarithms. . . common logarithms . . pressed in seconds. . 5sed in seconds in one mile THE END. HABPEB & BBOTHBES will send either of the following Works by Mail, postage paid (for any distance in the United States undei- 3000 miles), on receipt of the Money. L O O M I S'S SERIES OF SCHOOL AND COLLEGE TEXT-BOOKS. THE Course of Mathematics by Professor Loomis has now been for several years before th Public, and has received the general approbation of Teachers throughout the country. The fol- lowing are some of the Institutions in which this Course has been introduced, either wholly or in part: Dartmouth College, N. H. ; "Williams College,' Mass. ; Amherst College, Mass. ; Trin- ity College, Conn. ; Wesleyan University, Conn. ; Hamilton College, N. Y. ; Hobart Free Col- lege, N. Y. ; New York University, N. Y. ; Dickinson College, Penn. ; Jefferson College, Penn. ; Alleghany College, Penn. ; Lafayette College, Penn. ; St. James's College, Md. ; Emory and Henry College, Va. ; Lynchburg College, Va. ; Bethany College, Va. ; South Carolina College, S. C. ; Wofford College, S. C. ; Alabama University, Ala. ; La Grange College, Ala. ; Louisi- ana College, La. ; Transylvania University, Ky. ; Cumberland College, Ky. ; Western Keserve, College, Ohio ; Marietta College, Ohio ; Oberlin College, Ohio ; Antioch College, Ohio ; As- bury University, Ind. ; Wabash College, Ind. ; Illinois College, 111. ; Shurtleif College, 111. ; M'Kendree College, HI. ; Knox College, 111. ; Missouri University, Mo. ; University of Michigan, Mich. ; Beloit College, Wisconsin ; Iowa University, Iowa. Professor Loomis's text-books are distinguished by simplicity, neatness, and accuracy; and are remarkably well adapted for recitation in schools and colleges. I am satisfied no books in use, either in America or England, are so well adapted to the circumstances and wants of American teachers and pupils. W. C. LAEEABEE, late Professor of Mathematics, Indiana Asbury University. A Treatise on Algebra. Eighteenth Edition. 8vo, 359 pages, Sheep extra, $1 00. This treatise is designed to contain as much of algebra as can be profitably read in the time allotted to this study in most of our colleges, and those subjects have been se- lected which are most important in a course of mathe- matical study. Particular pains have been taken to cul- tivate in the mind of the student a habit of generaliza- tion, and to lead him to reduce every principle to its most general form. It is believed that, in respect of dif- ficulty, this treatise need not discourage any youth of fif- teen years of age who possesses average abilities, while it is designed to form close habits of reasoning, and cul- tivate a truly philosophical spirit in more mature minds. In accordance with the expressed wish of many teachers, a classified collection of two hundred and fifty problems is appended to the last edition of this work. Professor Loomis's Algebra is peculiarly well adapted to the wants of students in academies and colleges. The materials are well selected and well arranged ; the rules and principles are stated with clearness and precision, and accompanied with satisfactory proofs, illustrations, and examples. A. D. STANLEY, late Professor of Mathe- matics in Yale College. A Treatise on Arithmetic, Theoretical and Practical. 12mo, 352 pages, Sheep extra, 75 cents. This volume explains, in a simple and philosophical manner, the theory of all the ordinary operations of Arithmetic, and illustrates them by examples sufficient- ly numerous to impress them indelibly upon the mind of the pupil. It is designed for the use of advanced stu- dents in our public schools, and furnishes a complete preparation for the study of Algebra, as well as for the practical duties of the counting-house. The answers to about one third of the questions are given in the body of the work ; but, in order to lead the student to rely upon his own judgment, the answers to the remaining questions are purposely omitted. For the convenience, however, of such teachers as may desire it, there is published a small edition containing all the an- swers to the questions. Elements of Algebra. Designed for the Use of Beginners. Twelfth Edition. 12mo, 281 pages, Sheep extra, 62- cents. This volume is intended for the use of students who have just completed the study of. Arithmetic. It is be- lieved that it will be found sufficiently clear and simple to be adapted to the wants of a large class of students in our common schools. It explains the method of solving equations of the first degree, with one, two, or more un- known quantities ; the principles of involution and of evolution ; the solution of equations of the second de- gree ; the principles of ratio and proportion, with arith- metical and geometrical progression. Every principle is illustrated by a copious collection of examples ; and two hundred miscellaneous problems will be found at the close of the book. I have used Loomis's Elements of Algebra in my school for several years, and have found it fitted in a high de- gree to give the pupil a clear and comprehensive knowl- edge of the elements of the science. I believe teachers of Academies and High Schools will find it all that they can desire as a text-book on this branch of Mathematics. Professor ALONZO GRAY, Brooklyn Heights Seminary. Elements of Geometry and Conic Sec- tions. Fifteenth Edition. 8vo, 234 pages, Sheep extra, 75 cents. The arrangement of the propositions in this treatise is generally the same as in Legendre's Geometry, but the form of the demonstrations is reduced more nearly to the model of Euclid. The propositions are all enunciated in general terms, with the utmost brevity which is con- sistent with clearness. The short treatise on Conic Sec- tions appended to this volume is designed particularly for those who have not time or inclination for the study of analytical geometry. The last edition of this work contains a collection of theorems without demonstrations, and problems without solutions, for the exercise of the pupiL HARPBB & BROTHERS will send either of the following Works by Mail, postage paid (for any distance in the United States under 3000 miles), on receipt of the Money. ELEMENTS OF NATURAL PHILOSOPHY, DESIGNED FOE ACADEMIES AND HIGH SCHOOLS. By Elias Loomis, LL.D. 12mo, 350 pages, Sheep extra, $1 00. This volume is the result of many years of laborious study, and presents in an elementary form the fruits of much research. It is designed particularly for the use of the higher classes in Academies and High Schools, and its primary object is to cultivate the habit of philosophical reflection and observation. The following are a few of the Notices of LOOMIS'S NATCRAL PHILOSOPHY which have been re- ceived by the Publishers : Prof. Loomis's Elements of Natural Philosophy is one of the best and most complete works of the kind that has been published, and possesses a clearness and conciseness seldom equaled. I have seldom seen so much useful in- formation in one volume. EDWARD T. FBISTOB, Profes- sor of Mathematics, Columbian College, D. C. This volume has the merit of being a digest and not a compilation. For a large class of students it is the only suitable work on this subject that I have seen, bringing into use, as it does, all the mathematics usually studied in our academies, and no more. E. W. EVANS, Profes- sor of Natural Philosophy in Marietta College, Ohio. Prof. Loomis's Natural Philosophy is clear, accurate, and methodical. DANIEL KIBKWOOD, Prof essor of Nat- ural Philosophy in Indiana State University. The characteristics of Loomis's Mathematical Work*, which we so highly prize, are fully sustained in his Nat- ural Philosophy. I am glad to find at last a text-book on this subject so logically expressed, so complete and so accurate. N. B. WEBSTER, A.M., President of Virginia Collegiate Institute, Portsmouth, Va. This work of Prof. Loomis claims to be a philosoph- ical treatise. For clearness of style and fullness of illus- tration we have not met its equal. Adapted to the high- er classes in academies and high schools where mathe- matics have been pursued only through plane trigonome- try, it is ready at all times to give a reason for a phenom- enon, while the numerous references to the every-day oc- currences of life make it exceedingly interesting to those who do not care for demonstrations. We hope it will crowd out of our schools the heterogeneous productions that school boys have to stuff themselves with ; and thus give thorough instruction that will tend to develop some faculties besides memory. S, J. C. SWEZEY, Marion, Alabama. Prof. Loomis's Natural Philosophy combines concise- ness with very great clearness of illustration, and is the best text-book of the kind that I have examined. Prof. W. FEEBEL, Nashville, Tenn. Prof. Loomis's treatise has my decided preference as a text-book on Natural Philosopy. It is simple and com- prehensive in its style, and its principles are discussed with clearness and brevity. J. W. FERREE, A.M., Pro- fessor of Mathematics, Dickinson Seminary, Pa. Prof. Loomis's Natural Philosophy is the best elemen- tary work on this subject which I have hitherto seen. It treats is pregnant with useful knowledge. A. W. MASON, Jeansville, Penn. Prof. Loomis's Natural Philosophy is the best text- book on that subject yet published. With all its value as a text-book, it combines a pleasing style, instructive examples and illustrations, and is quite a readable book for others besides school-boys. B. W. MoDorraoLD, Professor in Bethel College, Tenn. While this volume requires of the pupil nothing be- yond a knowledge of the elementary mathematics, it de- velops the philosophy of all the leading principles of me- chanics and physics. Its definitions are clear and con- cise, its statement of principles methodical and accurate. It embraces in a duodecimo volume of 350 pages, a com- plete digest of what is usually spread over three or four times this space. Nor by this condensation is the study* rendered repulsive, but exactly the reverse. We com- mend this work without qualification, as one admirably adapted to interest the pupil, while it cultivates the habit of philosophical reflection and observation. New York Observer. This volume is not only an admirable treatise for the use of the higher classes in schools, but is a most conve- nient compendium of the latest discoveries in Natural Philosophy for the instruction of adult readers. New York Commercial Advertiser. This volume is an admirable compendium of the prin- ciples of Natural Philosophy; yet, strange to say, it is not dull, heavy, or incomprehensible, bir terms that all can comprehend, and that few will be una- ble to remember. Baltimore Dailii 7V Among the numerous books of its class which have originated in this country, this volume has no superior in clearness, accuracy, and comprehensiveness. Boston Courier. Prof. Loomis's works on Arithmetic, Geometry, &c., ' are models of clear and precise style, comprehensive definitions, and accurate language. This work on Nat- ural Philosophy is marked by the same excellences. To- ronto Globe. Ten pages of this book, which may easily be read by every mechanic in his winter evenings, will FO fill his head, as to leave no room for idle thoughts. Newark Daily Advertiser. The study of Prof. Loomis's work will make solid thinkers, not smatterers. While popularizing science, is not only fitted for high schools, but is a perfect treas- he has not frittered away the solidity and accuracy which ure to the private student. Every subject on which it | alone give it a title to that name. a, Y. Daily Ni Also, published by A TREATISE ON ARITHMETIC, Theoretical and Practical. Fifth Edition. I2mo, 352 pages, Sheep extra, 75 cents. ELEMENTS OF ALGEBRA. Designed for the Use of Beginners. Fourteenth Edition. 12mo, 281 pages, Sheep extra, 62^ cents. A TREATISE ON ALGEBRA. Twentieth Edition. 8vo, 359 pages, Sheep extra, $1 00. ELEMENTS OF GEOMETRY AND CONIC SEC- TIONS. Eighteenth Edition. 8vo, 234 pages, Sheep extra, 75 cents. TRIGONOMETRY AND TABLES. Sixteenth Edi- tion. 8vo, 360 pages, Sheep extra, $1 50. The Trigo- nometry and Tables bound separately. The Trigo- nometry, $1 00 ; Tables, $1 00. the same Author. ELEMENTS OF ANALYTICAL GEOMETRY and of the Differential and Integral Calculus. Thirteenth Edition. 8vo, 286 pages, Sheep extra, $1 50. INTRODUCTION TO PRACTICAL ASTRONO- MY. With a Collection of Astronomical Tables. Second Edition. Svo, 497 pages, Sheep extra, $1 50. RECENT PROGRESS OF ASTRONOMY, rs^e- cially in the United States. Revised Edition. 12mo 396 pages, Muslin, $1 00. Also in Press by the sam. Author, ELEMENTS OF ASTRONOMY AND METEOROLOGY, on th same plan as the "Elements of Natural Philosophy-* Published by HARPER & BROTHERS, Franklin Square, N, Y, GENERAL LIBRARY UNIVERSITY OF CALIFORNIA BERKELEY RETURN TO DESK FROM WHICH BORROWED This book is due on the last date stamped below, or on the date to which renewed. Renewed books are subject to immediate recall. ..... NO 19Mnr REC'D LD MAR 21-100m-l,'54(1887sl6)476 YB 17342 UNIVERSITY OF CALIFORNIA LIBRARY