■v ' f'< rin?5?]ror:rT7xTT;^vvr IN MEMORIAM FLORIAN CAJORI y- \' TABLES DUAL LOGARITHMS, ANGULAR MAGNITUDES, TEIGONOMETIIICAL LINES. TABLES OF DUAL LOGAEITHMB,;;.,; DUAL NUMBERS, AND CORRESPONDING NATURAL NUMBERS; WITH PROPORTIONAL PARTS OF DIFFERENCES FOR SINGLE DIGITS AND EIGHT PLACES OF DECIMALS TABLES OF ANGULAR MAGNITUDES, TRIGONOMETRICAL LINES, AND DIFFERENCES GRADED TO THE HUNDREDTH PART OF A SECOND FOR SINGLE DIGITS. BY OLIVER BYRNE, formerly professor of mathkmatics, college for civil engineers ; inventor of the art and sciknce of dual arithmetic ; and of the calculus of form, a new mathematical science, author of "dual arithmetic, a new art," "the young dual arithmetician," Stc. etc. LONDON : * BELL AND DALDY, 186, FLEET STREET. 1867. [All riylita rcservnl.] LONDON : 1!. CLAY, SON, AND TAYLOR, PIIINTERS, BREAD STREET HILL. CAJORI JB'J PREFACE When tables of dual logaritlims are employed and operations performed witli dual numbers in their lowest terms, it is not necessary that tables should range beyond the natural numbers from I'oooooooo to 1*4142 1356 ascending; and from i'oooooooo to 70710678 descending. Tables I. and II. of the present work far exceed these limits ; however, dual tables extending from I'OOOOOOOO to 2 "99 161 136 ascending, and from i'oooooooo to '29916 114 descending, possess the greatest power to economize the time and labour of a calculator, who depends solely upon the use of logarithmic tables. An abridgment of these general tables are given in " The Young Dual Arithmetician." The operations usually performed through the use of tables of common logarithms are more readily and accurately effected by consulting these general dual tables, \ since the dual logarithms of natural numbers, great and small, may be obtained <^om merely inspecting them ; a change in the position of the decimal point being all the preparation required, and that not in all cases. Tables of dual logarithms not only supply logarithms of more easy and extensive use than Q1l*>f^ vi PREFACE. common logarithms, but they also furnish, at the same time, complete and extensive tables of hyperbolic logarithms, and the logarithms of the reciprocals of numbers and the reciprocals themselves. Table III., accompanied by differences and proportio.nal parts for single digits, exhibits the natural sines and cosines of given arcs and angles, graded to the looth part of a second. Besides the quantities registered in these three tables, and just specified, many other magnitudes, often required by practical men, may be found by very trifling transformations which are fully explained in the succeeding introduction. With this power of extension, logarithmic sines and cosines, log tangents, and cotangents, and other trigonometrical functions may be found. Having thus briefly described the nature, and succinctly defined the scope of these original tables, it is only necessary to show how easily their practical use may be obtained, how simply such tables may be constructed, and to point out how to extract from them the quantities just enumerated. The art and science of Dual Arithmetic being fully treated of in my other works, no attempt is made in this to lay down principles or deliver demonstrations, but the student must be careful not to imagine that he knows all about Dual Arithmetic when he is able to do all that may be accomplished through consulting these tables. OLIVER BYKNE. EXPLANATION DUAL NUMBEES AND DUAL LOGARITHMS. As Table I. is a register of Common Numbers and their corresponding Dual Numbers and Dual Logarithms, it may be deemed necessary to define what we mean by dual numbers and their logarithms. A dual number of the ascending scale is always a continued product of powers of tlie numbers I'l, [Oi, rooi, roooi, &c. taken in order, the powers of the numbers alone being expressed. To distinguish these numbers from ordinary numbers the sign ^ precedes them. Thus ^6,g,y,6 = (rif x (voif x (rooi)^ x (roooi)^ 4^0,0,0,6 = (i-if x (i-oif X (rooi)*^ x (roooi)^ The numbers which follow the sign ^ are called dual digits, and the position they occupy after the sign ^ shows the number of which they are the power. Thus |6 = (ri)', ^,6 = (i-oi)', 4,0,0,6 = (rooi)'. C"^ When all but the last digit of a dual number are zeros, we call the dual number a dual logarithm. Thus ^I^,o,o,o,o,0,OJ599702, whicli can be shown to be the equivalent of the dual number >I,o,o,6, and the natural number 1*00601502, we call a dual logarithm. i^ Or we say that the whole number 599702 is the dual logarithm of the common number i '00601 502. ' ' ' " ~ ""^ For the construction and properties of dual numbers we must refer to the " Dual Arithmetic," confining ourselves here to the construction and use of the following tables : — TABLE I. Containing all the dual numbers of the ascending branch of Dual Arithmetic from 4,0,0,0,1 to >I,7,3,i,9, and their corresponding dual logarithms and natural numbers. To these are added marginal tables, by means of which all dual numbers of eight digits, and their corresponding dual logarithms and natural numbers, may be easily derived. SH7oi <^%, 'y^ki/J fcyio^j ho^o EXPLANATION Of DUAL NUMBERS AND DUAL LOGARITHMS. TABLE II. • Du^l logalrithms and dual numbers of the descending branch of Dual Arithmetic from 'o'o'o'iVbVb'I^.t.o '3'6'9'9'o'o'o'o f with corresponding natural numbers. To this table are iAts.d added yn'^rginal tables, by means of which all intermediate dual numbers of eight digits 'and'their corresponding dual logarithms and natural numbers may be instantly derived. In " Dual Arithmetic," Parts I. and TI., and also in the " Young Dual Arithmetician,"' it is shown that when operations are performed with dual numbers in their lowest terms, and tables employed, it is not necessary that such tables should range beyond the natural numbers from 1-41421356 to I* and from i- to 70710678; or which is the same thing, a table of the ascending branch ranging from 4, o,o,o,o,o,OAO, to 4,3,6,0,9,4,1,0,7, and another of the descending branch ranging from 'o'o'o'o'o'o'o'o t to '3'3'o'3'4'i'o'i f with natural numbers and dual logarithms to correspond, proper reductions being made involving powers of both 10 and 2. GENERAL TABLES. However, when general tables are employed no reductions require to be made ; in this case powers of 10 only are involved. The natural numbers of the general table of the ascending branch range from roooooooo to 2-991611362 the natural numbers of the general table of the descending branch range from •99999999 to -2991611362. It must be remembered that dual logarithms are whole numbers, those of the descending brancli have a comma to the left above, and those of the ascending to the right below ; thus, the dual logarithm of 2- as well as the dual logarithm of ^ is the whole number 693 147 18 but written 4,, (2-) =69314718, ^, (-5) = '693 147 1 8 sum = 00000000 = ^, (r) If the dual logarithms of the ascending branch be considered positive, those of the descending branch must be taken as negative, and vice versa. In the particular example just given (•99999999)+ ^3x47.8^.^ (I-OOOOOOOI)"^^^'*''^-. 2- z> EXPLANATION OF DUAL NUMBEES AND DUAL LOGARITHMS. 9 To put this matter in a more general form, let B = the base i "00000001 ; B = I '000000001 ; B^ — I'oooooooooi ; &c. And also let h = the descending base •99999999 ; \ = '999999999 ; \ = -9999999999 ; &c. Now B is very nearly = 7- and ^ = 5 ? B '.B^-~-^- and B-^ is also = hK Suppose B^ — n, tlien ^, (n) = /, but B may be put = r b-' = ^ =B^ = n. bi B' n Whence to the base h, ^, |-) = 7; consequently we change the base by simply \nj changing the position of the comma from right to left or from left to right, as the case may be. Generally, when greater accuracy is required, B,n - J- and b,„ = „- Then if {Bm )' = n, ^[,, (w) = I, to the base B^ ; •*• >!'»(/ = — ^ written Y. Pn~Tr = bm = - •*. >l, (- I = I, to the base hmt tut = 7 to the base B^. When the logarithm of n to either of the bases is represented by Z, to the other concordant base it will be represented by 7 and in all cases ?, + '/ = o. The base of the hyperbolic system of logarithms e = 271828182845904523536028747 I, (6) = ^, (271828183) = io\ ; to 5,; ^, (e) = I0^ to B^; ^ (e) = IO^^ to .5^, ^^,(e)= lO«+'». When general tables are employed like those we have described, numbers and their corresponding logarithms are obtained by mere inspection, and with far less inconvenience B 10 EXPLANATION OF DUAL NUMBERS AND DUAL LOGARITHMS. than with a table of common logarithms. The number of places of figures the decimal point has to be removed to the right or left may be noted on a line as at (A) and (B) ; the dual logarithms of any numbers, as 186565 5 or -84821877 may be employed to represent the logarithm of (A.) (B.) 3 •001865655 2 •01865655 I •1865655 1-865655 I 18-65655 2 1865655 3 1865-655 &c. •00084821877 3 •0084821877 2 •084821877 I •84821877 8-4821877 I 84821877 2 848-21877 3 &c. In practice it is not necessary, as we shall presently show, to set down as at (A) and (B) the number of places the decimal point is removed to the right or left to produce the number operated with. It must be observed that 34567844, is a positive dual logaiithm, the same as + 34567844 a positive whole number; and '45678921 is a negative dual logarithm, the same as — 45678921 a negative whole number, without regard to their respective bases. A dual logarithm is changed from positive to negative, and from negative to positive, by simply changing the position of the comma from right to left or from left to right, as the case may be. The arithmetical complements of dual logarithms (ar. co.) do not retain the comma. To jiad the arithmetical complement of a dual logarithm. Rule. — Begin at the left, set down minus i, written i, outside the given number, then take each of the given figures from 9, except the last figure to the right, which must be taken from 10. 45665423, dual log. '76543298 dual log. ^54334577 ar. co. T2 345 6702 ar. co. Ex. I. — The dual logarithms of the numbers (A) may be found at once in the general tables : it is required to find how many places of figures must the decimal point be removed to the right or left in the continued product of the natural numbers (A), to give the continued product of the natural numbers (B). (A.) (B).. •57689327 point removed 3 to the right becomes 576-^89327 1-23457 2 to left •0123457 2047623 I to right „ 2047623 1-983415 4 to right „ 19834-15 •666789 4 ■6667S() 2-345127 ^IAS^^7 1000 4 to left „ 0001 2 diflference to the right. EXPLANATION OF DUAL NUMBERS AND DUAL LOGARITHMS. 11 When the decimal pohit is removed to places to the right, the continued product of (A) is altered to the continued product of (B). Ex. 2. — How many places of figures must the decimal point be removed to the right or left in the continued product of 365-1768; 7454-83; i650"22 ; -000829 divided by the continued product of 18-636; 83-344; -22222? Multiply •3651768 3 • 745483 4 1-65022 3 -829 3 Divide by 1-8636 •83344 2-2222 I 5 The number found for the factors of the divisor is changed from right to left or from left to right before being incorporated with the number obtained for the factors of the dividend. Thus, in the last example, 2 is changed to the left, then 7 on the right and 2 on the left make together 5 to the right. With little experience, a glance at the numbers to be incorporated, and those whose logarithms are found, will be sufficient to decide the position of the decimal point, without entering into any formal method of calculation. EXAMPLES. Ex. 3.-Find the cube root of (1865-655) (-02691098) (848-21877) . ^ (3287077) (•134659655) (6296-168) Ans. -53462388. Representing by (A) and (B) the numerator and denominator of the given fraction 4,, (1-865655) = 62361219, I, (2-691098) = 98994929, \, (-84821877) = '16461667 >!', (-3287077) ='111258635 I, (^-34659555) = 29758037, \, (-6296168) = '46264392 Z) 2 o times, and 2 to the left over, 12 EXPLANATION OF DUAL NUMBERS AND DUAL LOGARITHMS. To move two places to the left is the same as dividing by loo or lo^. 62361219, 137638781 ar. CO. 98994929, 1 0100507 1 ar. CO. '16461667 '16461667 1 1 1258635, 1888741365 ar. CO. 29758037, J29758937 '46264392 153735608 ar. CO. '460517018 '460517018 3; '187857574 4,, (-53462388) = '62619182 Mi^) Before taking the arithmetical complements, the commas of the logarithms of the Uviding factors have to be changed from the right to the left, or from the left to the right, as the case may be. Then, the arithmetical complements of the logarithms with the comma to the left, if that class be least in amount, have to be taken. On the contrary, the arithmetical complements of the other class, if that class be less in amount, are to be taken. It is evident that no allowance has to be made on account of having employed arithmetical complements, which is one of the many advantages of this over any other system. Ex. 4. — Required the reciprocal of i'379 and its logarithm. I, (i*379) = 32135863, Table! .-. '32135863 = 4,, (7251624) Table II. .'. 7251624 is the reciprocal of 1*379 > .'. "007251624 = reciprocal I37'9; &a &c. Ex. 5. — Required the reciprocal of "8419 and 8419- \, ('8419) = '17209406 Table II. But 17209406, = ^, (ri 877895 5) Table I. .-. 1-18778955 is the reciprocal of '8419 ; and .-. -oooi 18778955 is the reciprocal of 8419. EXPLANATION OF DUAL NUMBERS AND DUAL LOGARITHMS, 13 A brief inspection of the limits exhibited in the following concatenated arrangement will immediately show that the logarithms of all natural numbers between O and 00 , may be taken from Tables I. and II. ; the simple preparation of multiplying or dividing by 2 being sometimes necessary. I'OOOOOOOO Natural numbers situated between, may be found in Table I. 2'00000000 Natural numbers situated between, when divided by 2, may be found in Table I. 4-00000000 Natural numbers situated between, when multiplied by 2, will be found in either Taf-le T. or II. •68000000 Natural numbers situated between, may be found in Table II. •99999999 USE or TABLE III. IN COMBINATION WITH TABLES L AND II. Ex. 6. — Given an angle of 28° 39' 56"74, to find the length of its arc to radius i ; its natural sine and cosine ; log sine and log cosine ; log tangent and log cotangent ; log secant and log cosecant ; versine and log versine ; natural tangent and cotangent ; natural secant and cosecant, through inspecting Tables III. II. and I. Table III. In the column headed Arc. For 28 39 •5000370 50"- 2424 > 6 • 291 1 From the gTaded differences 7 34 ( of arc in the margin. •04 2) Arc of 28° 39' s6"-74 = -5003121 14 EXPLANATION OF DUAL NUMBERS AND DUAL LOGARITHMS. To find the sine, Table III. In the column headed Sine. 28° 39' '4794579 Co"' 2 1 ''7^ ■^ ^ " I From the s-raded differences 6 • 255 f -1 --111 i- .1 V m the middle 01 the page \ for 28 degrees. Sine of 28° 39' 56"74 = -4796993 To find the cosine, Table III. From the column marked cosine at bottom ofi jyage for 28 degrees. 28° 39' -8775649 50"- 1 162 •7 16 •04 I 1318 Cosine of 28° 39' 56"-74 = -8774331 From Table II. To fina the log cosine. Next greater from Table II. -87751 28 3 dual log = '13066370 Given cosine '87743 3 1 o '9087 Taken from multiples of difference ^77 given in the margin. 87743310 ••t — 797 3 7897 '9 'ence ) 7 6 J 70 '8 '13075457 = >^. (-8774331) 7 '. Dual log cosine of 28° 39' 56"-74 = '13075457. EXPLANATION OF DUAL NUMBERS AND DUAL LOGARITHMS. Otherwise thus : 15 Given cosine '877433 i o Next less from Table II. -877425108 dual log = 'i 3076371 914, 8j0 2 719 o 9, Taken from multiples of difference ) i 877 given in the margin. 3 I, 4, '13075457 = >^. (-8774330 To find the lo(j sine. Table II. Sine mult, by 2 = '47969930 x 2 = "95939860. Next greater, Table II. '95944 3 5 0; dual logarithm of '4140185 Given •9593986 4l49 3838 '4 6 52 5 75 '6 77 7 7 '8 o\ '0 '4145865 '69314 7 18 = I (h '4680 '4145865 Dual log sine = '73460583 = 4,, (•4796993)- Log sin '73460583 from log cos '13075457 take '60385126 log tangent 60385126, log cotangent 13075457, == log secant and 73460583, = log cosecant. 16 EXPLANATION OF DUAL NUMBERS AND DUAL LOGARITHMS. To find the natural secant. Table I. ' Log sec 13075457, Next less given in Table I. 13065 867, natural number i-i395!787i — f 10256 \ Taken from multi- 9'5'9'Oj I cynL P^^s of difference C for 1 1 39 given in ^^ ^ the margin. Natural secant i * 1 396 8800 To find the natural cosecant. Table I. Given Next less in Table I. Given Found in Table I. 4145 8 6 5 414008 2, 5,7,8,3, Dual log of 1042 2 From the multiples of difference for 1 042 given in the margin. 1-04233002 1*04233002 2 2*08466004 natural cosecant. To find the natural cotangent. Table I. 60385 126, 60381 107, Dual log of r8290i7627 ^1 Taken from margin iS V r o 16 j ^'''^'^• 4,0,1,9, Natural cotangent = 1-82914977 To find the natural tangent. Table I. Log 2. Given log 69314718, ) '60385126 j Add. 8929592, EXPLANATION OF DUAL NUMBERS AND DUAL LOGARITHMS. 17 Given Next less in Table I. Difference 8929 5 9 2, 8919 8 I 4, Dual log of 1-0932 t 2 ) 1*09340416 9725 9840 N 765 /From margin for 77 i 1093. Q/ 1093404 1 6 •54670208 natural tangent. Otherwise thus: Given 8929 592, Table I. next greater log 8929814, Dual log of 1*093401658 Diflference 22 2 219 22 2 243 As before 1-09340415 ^nd the versine and log verstne. Table I. Radius = roooooooo Cosine = '87743310 12256690 versine. Versine multiplied by 10 = r225669. Given The dual log of 12256 t 1-22566900 4795 2 I 05 1226 879 858 2 I I 2 9 9 taken from I. = 20346969, 1717, I, 7, 20348686, 7, 18 EXPLANATION OF DUAL NUMBEES AND DUAL LOGARITHMS. ^' (77;) " '230258509 ^ 20348686, '209909823 dual log versine. Recapitulation of the trigonometrical functions and angular magnitudes just obtained, almost as simply as bj mere inspection, and with the least possible chance of involvinj^- error, from Tables I. II. III. NATURAL. LOGARITHMIC. Sine •47969930 '73460583 Cosine •87743310 '13075457 Tangent •54670208 '60385126 Cotangent 1-82914977 60385126, Secant 1-13968800 13075457, Cosecant 2-08466004 73460583, Versine •12256690 '209909823 Ex. 7.— Given of 67° 48' 25"^93 to find the length of its arc to radius i ; its natural sine and cosine ; log sine and log cosine ; log tan and log cot ; log sec and log cosec ; versine and log versine. Natural tan and cot ; nat sec and cosec ; fiom Tables I. II. III. To find the length of arc that measures the angle of 6f 48' 25"^93 to radius i. Table III. 67° 48' 1-1833333 from column headed arc 20"- 970) 5 • •9 242 43 Arc diff margin. •03 i; Arc of 67^ 48' 25 "-9 = 1-1834689 length. EXPLANATION OF DUAL NUMBERS AND DUAL LOGARITHMS. 19 To find the natural sine. Table 111. >7' 48' •9258706 from column headed sine. 20" • 366 j 5 • 92! From differences in middle of •9 16/ page for 67 degrees, at top. •03 I ; Sine of 6f 48' 25"-93 = -9259181 To find the natural cosine. Table III. For finding the natural cosine, the degrees are to be found at the bottom of the page, Table III., then the proportional parts for seconds, &c. are to be subtracted ; the same result may be found by taking the given angle from 90° ; finding the remainder at the top of the page, and adding the proportional parts for seconds, &c. 90" o' o "• 67 48 25 93 22 II 34 -07 22" II' •zim'^A 1347) Proportional parts of graded 1 80s. differences in the middle of ■07 3 \ page for 22° at top. Sine of 22° 11' 34"-07 = -3777244 cosine of 6f 48' 25"-93 30 4 To find the log sine. Table II. Next greater in Table II. 92593 i i 6 dual log '7695538 Given nat sin Taken from multiples o^ ' difference 925 given in the margin, Table II. •92591 8 I o t I 306 926 3 3 80 70 I 9 '141 1 '7696949 log sine 20 EXPLANATION OF DUAL NUMBERS AND DUAL LOGARITHMS. To find the log cosine. Table II. Cosine multiplied by 2 = -3777244 x 2 = 7554488. Next greater given in Table 11. 75546066 dual log '28042757 given Taken from multiples of difference ) 755 given in the margin. ) 75544880 1570 1 186 75 5 I 'I 43 378 ' 53 53 '28044327 \Ah) '28044327 '693 1 47 1 8 '97359045 dual log cosine. From '7696949 log sin Take '97359045 log cos 89662096, log tangent '89662096 log cotangent. Log secant = 97359045, ; log cosecant = 7696949, To find the natural tangent. Table I. Log tan 89662 096, 693147 I 8, = 1,(2) Next less Table I. 20347 378, 20346 969, natural number i 22564' 795 * 't !490 0,4,0,9, 1 1 122565296 1-22565296 2 2-45130592 nat tan. EXPLANATION OF DUAL NUMBERS AND DUAL LOGARITHMS. 21 To find the natural cotangent. Table II. '8966 2096 log cot 6931 47 I 8, \, (2) '2034 7378 Next less log, Table II. '2034 1707 natural number 81593 '5'6yi t 4< Found in the) margin j 5 7 I 7^ 080 489 4627 •81589 160 2)-8i589i6o •40794580 natural cotangent. To find the natural secant. Table I. Log secant = 97359045. 69314718, = \, (2) From Table I. 28044327, = \, (13237 1644) 1-32371644 2 2 -64743 2 88 natural secant. To find the natural cosecant. Table I. Log cosec = 7696949, the natuial number corresponding found in Table I. = 1080009 13 ^^^ cosec. 22 EXPLANATION OF DUAL NUxMBERS AND DUAL LOGARITHMS. To find the versine and Jog verstne. Kadius = i oooooooo •37772440 nat cos •62227560 natural versine 2 Dual log of I -2445 5 1 20 = 2 1 877498, 21877498, '69314718 = I a) '47437220 = dual log versine. Secapitulatton. Given angle, 6f 48' 25"93 length of arc to radius r equal ri834689. NATURAL. LOGAKITHMIC. Sine •9259181O '7696949 Cosine •37772440 '97359045 Tangent 2-45130592 89662096, Cotangent •40794580 '89662096 Secant 2^64743288 97359045, Cosecant I •0800091 3 7696949, Versine •62227560 '47437220 EXPLANATION OF DUAL NUMBERS AND DUAL LOGARITHMS. 23 Description of Table I. Under the column headed "Dual Numbers " the dual numbers are arranged in order, beginning from vI^OAi, >I'0,o,2, &c., to 4^7,3,1,9,. In the next column are placed the corresponding natural numbers, and in the third their dual logarithms. In the margin is placed a table of the multiples by the first nine digits of the first four digits of the natural numbers found on that page of the table. At the foot of every page is also placed the dual logarithms of 2, 4, and 8, and of all powers of 10, from i to 9. Use of Table I. as a Table of Logarithms. These dual logarithms possess the same properties as any of the systems of logarithms hitherto calculated. They can be used in all cases where ordinary logarithms are useful, and admit of application where common logarithms would fail. They possess this advantage over those' hitherto used, that they can always be verified in five minutes by a very simple arithmetical process. To verify an ordinary logarithm, except it be that of a very small number or a multiple of small numbers, is almost impossible within any degree of arithmetical labour at all practicable. This is a matter of considerable importance, as it is admitted by every one conversant with the subject that no logarithmic tables hitherto calculated are free from errors, no logarithm taken from one of these tables can be free from doubt. It is even doubtful whether the application of machinery to the calculation and printing of tables will be able to produce results entirely free from error. To find the logarithm of any number consisting of eight digits^ employing owZ^^Table I. Ex. 8.— To find the logarithm of 365-25638. We first divide the number by 2, 4, or 8, so as to make the first digit of the result i. 2)365-25638 182*62819 We now divide this result by such a power of 10 as to make the decimal point stand after the first figure. 100 ) 182-62819 1-8262819 Hence 365*25638 = 2 x 10^ x 1-8262819 ; .'. log 365-25638 = log 2 + log lo^ + log 1-8262819. Turning to the table we find the next smallest natural number to 1-8262819 registered there to be 1-82615387 ; we subtract this from the number whose logarithm we require, and divide the result by the first four figures common to the two numbers, thus — 2i EXPLANATION OF DUAL NUMBEES AND DUAL LOGARITHMS. 1-82628190 1-82615387 1826 ) 12803 ( 7012 12782 21 . . 18.. I 1826 2 3652 3 5478 4 7304 5 9130 6 10956 7 12782 8 14608 9 16434 This division is readily performed by means of the table in the margin, which gives all the multiples of 1826 from i to 9. We now add this quotient to the logarithms of the number 1-82615387 and of 2 and 100, taken from the table. Thus 60221207, 7012, 693 147 1 8, 4605 1 70 1 9, 590059956, log of 1-82615387 found in the table. It, or found at foot of the page of tables, log of 10^ > ^ ° log log of 365-25638 In the same way we may find the logarithms of the following numbers, omitting unnecessary figures. Ex. 9. — To find the logarithm of 2-71828183. 2)2-71828183 1-35914092 1 1085 30683070, log of 1-35914092 found in table, 2212, 693 1 47 1 8, log of 2. 3007 (2212 r 2718 Multiples of 13 5 9, found in the margin of table, and making -> proper allowances for the omitted figures. 289 272 1 00000000, = log of 2-7 1 828 1 83 17 14 I. In the above example we had only to divide the number by 2 to bring it into the fonn necessary for Table I.; the divisor was 1359, the multiples of which will be found in the margin. EXPLANATION OF DUAL NUMBERS AND DUAL LOGARITHMS. Ex. 10. — To find the logarithm of 86400, the number of seconds in 24 hours. 8 ) 86400 25 loooo ) 10800 1-0800 1-07998679 ) I32I ( 1223 1080 Multiples of ro8o, found in margin of < table. 241 216 25 22 3 3 7694883, log of 1-07998679. 1223, 207944154, log of 8. 921034037, log of lO^ 1 136674297, = log of 86400. 1080 was the divisor; since, allowing for the figure after 1079 Tt)eing greater than 5, 1079 became 1080. In the previous examples, the numbers whose logarithms have been found were all greater than i ; when the numbers are less than i, they are reduced to a form fitted for the table by multiplication instead of division by powers of 10. Ex. II.— To find the logarithm of -017453293. 17453293 •017453293 = 100 Hence log -017453293 = log 1-7453293 - log 100. 17453293 55685354, 17268 8975, 15662(8975 55694329, 13960 1702 . I57I . 131 .. 4605 1 70 1 9, = log 100 122 . . 55694329, 9. .. - 404822690, = log -017453293 9... '404822690 written. 26 EXPLANATION OF DUAL NUMBERS AND DUAL LOGARITHMS. Ex. 12.— To find the logarithm of -00177421952. 177421952 •00177421952 = 1000 177421952 57336058 21940 7 1774) 00012 ( 0007 57336065 12 690775528 = log lO' 57336065 - 633439463 = log -00177421952. Written I, (00177421952) = '633439463. The logarithm of a number being given, to find the number, employing Table I. only. We first subtract from the given logarithm the logarithms of the nearest powers of 10 and 2 it contains, if it be greater than the logarithms of 10 and 2. We then subtract from this result the nearest logarithm to it in the tables ; if there be a remainder, we multiply the first four digits of the number corresponding to the logarithm in the table by the first four digits in the remainder, setting each line one figure back, and neglecting every figure after the eight place, and add these four lines to the common number found in the table. This result is then multiplied by the powers of 10 and 2, which had been subtracted from the given logarithm in the first part of the process, and the result is the common number required. Ex. 13. — Given the logarithm 590059956, to find the common number corresponding to it, employing Table I. only. 590059956, 4605 1 70 1 9, = log of 10", nearest power of 10 129542937, 693 147 1 8, = log of 2, nearest power of 2 60228219, 60221207, = log of 1-82615387 — 2 12782 = 1826 X 7 ' 18 = 1826 X T^ 3 = 1826 X ^'^^ 1-82628190 200 365-2563800 .-. 365-2563800 is the number whose logarithm is 590059956, It may be noted that the multiples of 1826 will be found registered in the margin of the table near the number 1-82615387. EXPLANATION OF DUAL NUMBERS AND DUAL LOGARITHMS. 27 Ex. 14. — To find the common number corresponding to the logarithm 1 00000000. 1 00000000, 693 1 47 1 8, = log of 2 30685282, 30683070, = log of 1-359] 1 1085 2212, 2718 = 1359 X 2 272 = 1359 X tV 14= 1359 X T^ 3 = 1359 X T7^ 1-35914092 2 2-718 28184 .-. 27 1 828 184 is the number whose logarithm is loooooooo. Ex. 15. — To find the number whose logarithm is 1 136674297, 1 1 36674297, 921034037, = log of 10* 215640260, 207944154, = log of 2^ 7696106, 7694883, = log of 1-07998679 1080 ^' 216 22 3 I 08000000 80000 86400-00000000 .*. 86400 is the number whose logarithm is 11 36674297, AVhen the logarithm is negative, we subtract the logarithm from the nearest logarithm of powers of 10, and proceed with the result as when the logarithm is positive, only we divide the final result by the power of 10 we have used to reduce it to a logarithm contained in Table I. 28 EXPLANATION OF DUAL NUMBERS AND DUAL LOGARITHMS. Ex. i6. — To find the number whose logarithm is — 404822690. Conventionally written '404822690 460517019, = log of 100 '404822690 55694329, I 55685354, = log of 1745^7268 8975 ^^ ^'^ 1 57 1 122 9 .-. "017453293 is the number whose logarithm is — 404822690. That is 4^, ('01 745 3293) = '404822690. Ex. 17. — To find the number whose logarithm is — 53527575. 690775527, = = log of 10^ '535275757 155499770, 138629436, = = log of 2^ 16870334, 16866099, = = log of I-: [8371875 4235 4735 237 35 6 I- 18376888 004 •00473507552 .•. 00473507552 is the number whose logarithm is —404822690. That is 4', ("00473507552) = '404822690. To test tables of common and Naperiau logarithms, we give a rule by means of which the dual logarithms can be converted into common and hyperbolic logarithms. EXPLANATION OF DUAL NUMBERS AND DUAL LOGARITmiS. 29 To CONVERT Dual Logarithms into Naperian and Common Logarithms. As there is no known method of testing the accuracy of Naperian and common logarithms, we show how readily dual logarithms can be converted into those of the other systems, and can thus be used for testing their accuracy. To convert a dual logarithm into a Naperian or hyperbolic one, divide the dual logarithm by lO^. To convert a dual logarithm into a common one, divide the dual logarithm by the dual logarithm of lo. This is easily eflfected by the use of Table I. at the foot of every page of which are given all the multiples of the logarithm of lo from i to 9. Ex. 18. — A siderial revolution of the earth expressed in days is 365*25638 ; we have shown, Ex. 8, that its dual logarithm is 590059956, — — ^8 ^ = 5*90059956, Naperian logarithm of 365-25638. 590059956 ( 2-5625978, common logarithm of 36525638 4605 1 70 1 9 129542937 . II5I29255 . I44I3682 . . I38I55II • • 598I7I • . 460517.. 137654 •• II5I29 . . 22525 . . 20723 . . 1802 . . I6I2 . . 190 . . 184. . . . . 30 EXPLANATION OF DUAL NUMBERS AND DUAL LOGARITHMS. Ex. 19. — The base of the hyperbolic or Naperian system of logarithms is 2 7 1828 183 we have shown, Ex. 9, that its dual logarithm is 1 00000000, = 10®. lOOOOOOOO 10^ = I Naperian logarithm of 271828183. lOOOOOOOO . ( . 434294482 common logarithm of 27 1828 183. 921034037 78965963 69077553 9888410 9210340 678070 460517 217553 207233 10320 9210 mo . 921 . 189 184 5 5 Ex. 20. — The number of seconds in 24 hours is 86400; we have shown, Ex. 10, that 1 136674297, is the dual logarithm of this number. — 108 ^ 11-36674297 Naperian logarithm of 86400. 1 1 36674297 ( 4*93651375 common logarithm of 86400 921034037 215640260 . 207232658 . 8407602 . . 6907755 • • 1499847 . . 1381551 •• 1 18296 . . EXPLANATION OF DUAL NUMBEES^AND DUAL LOGARITHMS. 31 118296 . . 1I5I29 . . 3167 .. 2303 • • 864. . 691 . . 173 •• 161 . . 12 . . 12 . . Wlieii the dual logarithm is negative, it must be subtracted from the logarithm of the power of 10 which is next greater than itself, in order to convert it into a common logarithm. Ex. 21. — Thus the arc of 1° is "017453293 ; its dual logarithm, Ex. 11, is —404822690. '404822690 lO^* = — 4-04822690 Naperian logarithm. 4605 1 7019, = dual logarithm of 100. '404822690 55694329 ( -2418774 .*. 2*2418774 common logarithm of the 46051702 . length of the arc of i'. 9642627 9210340 432287 230259 202028 . 184207 . 1 782 1 16118 1703 1612 91 Table I. is not only a tabic of logarithms every one of whose numbers can be easily verified, but it is also a table by means of which the dual digits of any number to 8 places of figures and the converse may be readily obtained. For the properties, uses of dual numbers we must refer the reader to the " Dual Arithmetic a New Art." Parts I. and II. ; and to the " Young Dual Arithmetician." 32 EXPLANATION OF DUAL NUMBERS AND DUAL LOGAEITHMS. To find the dual number of the ascending hranch corresponding to any ^iven common number by the use of Table I. Prepare the number, not as if you had to find its dual logarithm. Instead, however, of writing down the dual logarithm corresponding to the number found in the table, set down its dual number ; add to this number, as additional digits, the quotient found by dividing tlie difference of the prepared number and that in tlie table by the first 4 digits common to them both. Ex. 22. — To find a dual number corresponding to 365*25638. Referring to Ex. 8. 2 ) 365-25638 100 ) 182-62819 1-82628190 i"826i5387 = number whose dual number is ^6,3,0,5. Multiples of 1-826] 12803 ( 7012 found in margin of v 12782 table. j ~ 18 3 3 A dual number corresponding to 365*25638 is 2 x 10^4,6,3,0,5,7,0,1,2, Ex. 23. — To find a dual number of the number 27 1828 183. See Ex. 9. 2)2-71828183 1-35914092 1-35911085 = number whose dual number is >[, 3,2,1,0, 3007 (2212 2718 289 272 17 3 3 .-. 2-71828183 = 2 ^I, 3,2,1,0,2,2,1,2, •:■ EXPLANATION OF DUAL NUMBEES AND DUAL LOGARITHMS. 33 Ex. 24. — To find a dual number equal to 86400. See Ex. 10. 8 ) 8 6400 10* ) I 0800 I -0800 1-07998679 = >J, 0,7,7,3, 1321 ( 1223 1080 241 216 25 22 3 3 .-. 2*20*4,0,7,7,3,1,2,2,3 = 86400. Ex. 25. — To find a dual number corresponding to '017453293. •017453293 = ih^ X 17453293 174532930 174517268 = 4,5,8,0,7, 15662 ( 8975 13960 1702 1571 131 122 ^ •■ ;j^. 4^5,8,0,7,8,9,7,5, = •oi7453293- 34 EXPLANATION OF DUAL NUMBEKS AND DUAL LOGARITHMS. Ex. 26. — To find a dual number corresponding to '00177421952. •OO177421952 = ^3 1 77421952 177421952 177421940 = 16,0,1,5, 12 ( 0007 12 •'• IP |6A^5A0A7> = 00177421952. To find the common or natural number corresponding to any dual number by the use of Table I. Find the number corresponding to that of the first four digits of the dual number ; add to this number the multiples of its first four digits, by the last four of the dual number, putting each line one step back as shown below, making the proper allowances when the omitted figure is greater than 5. Ex. 27. — To find the natural number equal to the dual number 4^3,2,1,0,2,2,1,2, ,J, 3,2,1,0, = 1-35911085 found in Table I. "~ ^59 j These multiples of 1359 will be found jjy ly I -j^ ^jjg margin of the same pages of the — 3i»y T^ 1 ^g^i^ig j^^ which ,1,3,2,1,0 is registered. 3 = 1359 "^ looo \ 1-55914092 = ,1,3,2,1,0,2,2,1,2, Ex. 28. — Find the natural number equal to the dual number 4,6,3,0,5,7,0,1,2, |6,3,o,5,= 1-82615387 12782 = 1826 X 7 18 = 1826 X Yhs \ Multiples of 1826 as given in 3 = 1826 X Tirtnr 1 margin of table. 1-82628190 EXPLANATION OF DUAL NUMBERS AND DUAL LOGARITHMS. 35 Construction of Table I. In constructing this table, no arithmetical oJ>eration beyond that of addition is necessary. To find the natural numbers corresponding to any dual number of one digit. ^ I = ri II 4r2 = 1-21 121 4^3 = I-33I 1331 ,1,4 = 1-4641 1 464 1 4,5 = 1-61051 161051 ^6 = 1-771561 1771561 4.7 = 1-9487171 19487171 4.8 = 2-14358881 214358881 4.9 = 2-357947691 The above table is formed by simple addition, each line being obtained from the preceding one by commencing a figure farther to the right, and adding each digit of the line above to the line on its left. To find the natural numbers corresponding to dual numbers of two digits. 4,0,1 = I'OJI iio I 4,0,2 = 10 20,1 ^0,3 = vo I 301 1 ^0,4= 10 40j6o|40|i 1040I60I4 4,0,5 = 1-051 01 005 &c. = &c. 35 EXPLANATION OF DUAL NUMBERS AND DUAL LOGARITHMS. Here commencing with >l,o,i = I'Oi, we pursue the same process as before only placing the figures to be added to the preceding line two figures farther to the right, instead of one, neglecting all figures after the eighth decimal place. When the first dual digit is greater than one, we start with the value of tliat digit. Thus :— |6= 17 7ij56ii 171715611 ^6,1 = r7|89|27j66!i \6,2 = r8jo7|i6|93 li8!o7ii6 >^6,3 = 1-8 25124 18I25 I0j7 2411 ^6,4 = I -8143 18 49|34;8 43'49'3 ,1,6,5 = r8 6i 92 84 I &c. = &c. In this way the common numbers corresponding to all dual numbers of two digits may be computed and tabulated. Again, \ 0,0, i = i 'OOi i 100 I 4,0,0,2 = TOO 200; 1 100200 ,j, 0,0,3 = TOO 3001300 ! 1001300 4,0,0,4 = roo|40o|6oo I100I400 4,0,0,5 = rooi5oij00o I100I501 4r 0,0,6 = TOO 601 501 &C. = &C. Same as before, only setting the line to be added three figures back. EXPLANATION OF DUAL NUMBERS AND DUAL LOGARITHMS 37 4f 6,5,0 = r86 1921841 i86|i93 >I,6,5,i = r86|379|034 |i86'379 ,1,6,5,2 = r86i565i4i3 ! 1 86! 565 ,1, 6,5,3 = 1-86751978 &c. = &c. In this manner the common numbers of all dual numbers of three digits can be found and tabulated. 4^0,0,0,1 = rooo loooji ^0,0,0,2 = rooo|2000|i I10002 ^ 0,0,0,3 = I 000 3000 3 Or the common numbers corresponding to dual numbers of four digits are found as those of three digits, setting the line to be added four figm-es back. 4.6.5.2.0 = 1865 4.6.5.2.1 = 1865 654113 i86|l7^ 840710 1 865 Is 4,6,5,2,2 = r866 027218 18660 4^6,5,2,3 = I -866 2138 1866 4,6,5,2,4= r866|4005jO 1 1 8664 4,6,5,2,5 = 1-86658714 &c. = &c. In this way, by common addition alone, the common numbers corresponding to the dual numbers can be obtained throughout the whole table. Next to compute the dual logarithms. The dual logarithm of 4^ I =9531018 io,i = 995033 „ „ 4,0,0,1 = 99950 „ „ 4^0,0,0,1 = 1 0000 38 EXPLANATION OF DUAL NUMBERS AND DUAL LOGARITHMS. For the calculation of these three numbers, see "Dual Arithmetic," Part II,, and " The Young Dual Arithmetician." From these three numbers all the dual logarithms in the table can be found by simple addition. log ^ I, = 9531018 written 4r, I, 9531018 log ^ 2, = 19062036 9531018 . Yj 2, ^og^3, = 28593054 9531018 ^, 3, log 4,4, = 38124072 9531018 4') 4i ^og^S, = 47655090 9531018 >> vj 5> log ^6, &c. = 57186108 = &c. 4r, 6, Or the dual logarithms of all dual numbers of one digit are found by the successive addition of the number 9531 01 8. log >I, 0,1= 995033 written ,^, o, I , 995033 log 4rO,2 = 1990066 „ 4'> 0,2, 995033 log Jr 0,3 = 2985099 „ 4^0,3, 995033 log 1 0,4 = 3980132 „ \,OA, &c. = &c. and log>l,6 =57186108 „ ^,6, 995033 log 4^6,1 = 5818I 141 „ >lr, 6,1, 995033 log 4,6,2 = 59176174 „ I, 6,2, 995033 log 4^6,3 = 601 7 1 207 „ ^,6,s, 995033 log 4,6,4 = 61 166240 „ 4r, 6,4, &C. = &C. EXPLANATION OF DUAL NUMBERS AND DUAL LOGARITHMS. 39 Thus the dual logarithms of dual numbers of two digits are derived from those of one digit by the successive addition of the number 995 03 3. log yj, 0,0, 1 , = 99950, written 4^" I, 99950, log 4,0,0,2, = 199900, „ ^\2, 99950, log 4,0,0,3, = 299850, „ 4,', 3, 99950, log 4,0,0,4, = 399800, „ 4,^ 4, &c. = &c. but log 4^ 6,4,0, = 6 1 1 66240, „ 4'5 6>4.o, 99950, log 4^6,4,1, = 61 266 1 90, „ 4^? ^:4>i, 99950, log 4,6,4,2, = 61 366140, „ 4" 6>4,2, 99950, log 4,6,4,3, = 61466090, „ 4,, 6,4,3, &c = &c. Thus the dual logarithms of all dual numbers of three digits are derived from those of two digits by the successive addition of the number 99950. log 4r 0,0,0, 1 , = 1 0000, written 4^*, I, 1 0000, log 4- 0,0,0,2, = 20000, „ 4'*> 2, 1 0000, log 4,0,0,0,3, = 30000, „ 4,^ 3, 1 0000, log 4, 0,0,0,4, = 40000, „ 4,*, 4, &c. = &c. but log 4r 6,4,3,0, = 61466090, „ 4,, 64,3,0, 1000, log 4,6,4,3,1, = 61467090, „ 4,, 6,4,3,1, 1000, log 4,6,4,3,2, = 61468090, „ ^,6,4,^,2, 1000, log4,6.4,3,3, = 61469090, „ 4,, 6,4,3,3, &c. = &c. 40 EXPLANATION OF DUAL NUMBERS AND DUAL LOGARITHMS. Or the dual logarithms of all dual numhers of four digits may be derived from those of three digits by the successive addition of the number looo. For the calculation of the dual logarithms of the common numbers 2 and lo, see the second part of " Dual Arithmetic," and " The Young Dual Arithmetician." "With the exception, therefore, of the calculation of the dual logarithms of ,1, i, >^o,i, 4,0,0,1* and 4,0,0,0,1, and of the dual logarithms of 2, and 10 — all of which can be verified by the methods shown in the dual arithmetic in ten minutes — every result in the table of dual numbers, their coiTCsponding common numbers, and dual logarithms, can be calculated as shown above by simple addition, without the aid of any other arithmetical operation. The construction of Table II. is equally simple and the extension of both, until they become general dual tables, effected with great ease. The consecutive descending natural numbers of Table II., from which the descending branch takes its name, can be found by common subtraction, while the corresponding dual numbers and dual logarithms are obtained by common addition as in Table I. Limits of the Ranges of General Tables of Dual Numbers. Ascendmg. NATURAL NUMBERS. DUAL NUMBERS. DUAL LOGARITHMS. I-OOOOOOOI continued to 2-99161136 4/ 0,0,0,0,0,0,0,1, continued to 4, 11,4,7,6,0,2,3,9, OOOOOOOI, continued to 109581215, Descending. NATURAL NUMBERS. DUAL NUMBERS. DUAL LOGARITHMS. •99999999 continued to -29916114 'o'o'o'o'o'o'o'i f continued to 'ii'4y6'o'2'3'9f '0000000 I continued to '120677239 An abridgment of these General Tables to three dual digits is given in " The Young Dual Arithmetician." TABLE L DUAL LOGARITHMS AND DUAL NUMBERS, CORRESPONDING NATURAL NUMBERS. ASCENDING BRANCH. Nat. No. 1-0000 to 1-0099 D. I Natural Dual Dual Numbers. Logarithms. Numbers. I'OOOOOOOO 00000, ,,0,0,0,0,0,0,0,0, loooo I ,,0,0,0,1,0,0,0,0, 2000I 2 ,,0,0,0,2,0,0,0,0, 30003 3 ,,0,0,0,3,0,0,0,0, 40006 4 , ,0,0,0,4,0,0,0,0, 50010 5 ,,0,0,0,5,0,0,0,0, 60015 6 ,,0,0,0,6,0,0,0,0, 70021 7 ,,0,0,0,7,0,0,0,0, 80028 8 ,,0,0,0,8,0,0,0,0, 90036 9 4,0,0,0,9,0,0,0,0, I -oo 1 00000 99950, ,,0,0,1,0,0,0,0,0, lOOIO 10 ,,0,0,1,1,0,0,0,0, 20021 II ,,0,0,1,2,0,0,0,0, 30033 12 ,,0,0,1,3,0,0,0,0, 40046 13 ,,0,0,1,4,0,0,0,0, 50060 14 ,,0,0,1,5,0,0,0,0, 60075 15 ,K>,o, 1,6,0,0,0,0, 70091 16 ,,0,0,1,7,0,0,0,0, 80108 17 ,,0,0,1,8,0,0,0,0, 90126 18 ,K),0, 1,9,0,0,0,0, 1 '00200 100 199900, ,rO,0,2, 0,0,0,0,0, I0I20 20 ,,0,0,2,1,0,0,0,0, 2OI41 21 ,0,0,2,2,0,0,0,0, 30163 22 ,,0,0,2,3,0,0,0,0, 40186 23 ,,0,0,2,4,0,0,0,0, 50210 24 ,,0,0,2,5,0,0,0,0, 60235 25 , ,0,0,2,6,0,0,0,0, 70261 26 ,,0,0,2,7,0,0,0,0, 80288 27 ,,0,0,2,8,0,0,0,0, 90316 28 ,,0,0,2,9,0,0,0,0, 1*00300300 299850, ,,0,0,3,0,0,0,0,0, 10330 30 ,,0,0,3,1,0,0,0,0, 20361 31 ,,0,0,3,2,0,0,0,0, 30393 32 > '0,0,3,3,0,0,0,0, 40426 33 > '0,0,3,4,0,0,0,0, 50460 34 > '0,0,3,5,0,0,0,0, 60495 35 ,,0,0,3,6,0,0,0,0, 70531 36 ^ '0,0,3,7,0,0,0,0, 80568 37 , ,0,0,3,8,0,0,0,0, 90606 38 > '0,0,3,9,0,0,0,0, I '00400600 399800, ,,0,0,4,0,0,0,0,0, 10640 40 ,,0,0,4,1,0,0,0,0, 20681 41 ,,0,0,4,2,0,0,0,0, 30723 42 ,,0,0,4,3,0,0,0,0, 40766 43 4,0,0,4,4,0,0,0,0, 50810 44 ,1,0,0,4,5,0,0,0,0, 60855 45 ,,0,0,4,6,0,0,0,0, 70901 46 ,,0,0,4,7,0,0,0,0, 80948 47 , ,0,0,4,8,0,0,0,0, 90996 48 4'0,o,4,9,o,o,o,o, D. Log. 00 .... to 98 ... . D. No. 4.0,0,0,0, to |0,0,9,9, [1 Natural Numbers. 1*00501001 11051 2II02 31154 41207 51261 61316 71372' 81429 91487 1*00601502 II562 21623 31685 41748 51812 61877 71943 82010 92078 1*00702104 I2174 22245 32317 42390 52464 62539 72615 82692 92770 1*00802806 12886 22967 33049 43132 53216 63301 73387 83474 93562 1*00903608 13698 23789 33881 43974 54068 64163 74259 84356 94454 Dual Logarithms. 499750, 50 51 52 53 54 55 56 57 58 599700, 60 61 62 63 64 65 66 67 68 699650, 70 71 72 73 74 75 76 77 78 799600, 80 81 82 83 84 85 86 87 88 899550, 90 91 92 93 94 95 96 97 98 Dual Numbers. ,5,0,0,0,0,0 ,5,1,0,0,0,0. ,5,2,0,0,0,0 ,5,3,0,0,0,0 ,5>4,o,o,o,o ,5,5>o,o,o,o ,5,6,0,0,0,0 ,5»7, 0,0,0,0 ,5,8,0,0,0,0 ,5)9,0,0,0,0 ,6,0,0,0,0,0 ,6,1,0,0,0,0 ,6,2,0,0,0,0 ,6,3,0,0,0,0 ,6,4,0,0,0,0 ,6,5,0,0,0,0, ,6,6,0,0,0,0 ,6,7,0,0,0,0 ,6,8,0,0,0,0, ,6,9,0,0,0,0 ,7,0,0,0,0,0 ,7,1,0,0,0,0 ,7,2,0,0,0,0 ,7,3,0,0,0,0 ,7)4,0,0,0,0 ,7,5)0,0,0,0 ,7,6,0,0,0,0 ,7)7)0,0,0,0 ,7,8,0,0,0,0 ,7,9,0,0,0,0 ,8,0,0,0,0,0, ,8,1,0,0,0,0 ,8,2,0,0,0,0 ,8,3,0,0,0,0 ,8,4,0,0,0,0 ,8,5,0,0,0,0 ,8,6,0,0,0,0 ,8,7,0,0,0,0 1,8,8,0,0,0,0 1,8,9,0,0,0,0 1,9,0,0,0,0,0 1,9,1,0,0,0,0 1,9,2,0,0,0,0 ',9)3)0,0,0,0 1,9,4,0,0,0,0 ',9)5,0,0,0,0 1,9,6,0,0,0,0 ',9)7,0,0,0,0, ',9,8,0,0,0,0 ',9)9,0,0,0,0 Multiples of Differences. rooo 2000 3000 4000 5000 6000 7000 8000 9000 1 1 1003 2 1 2006 3 3009 4 4012 5 S015 6 6oi8 7 7021 8 {8024 9 19027 lOOI 2002 3003 4004 5005 6006 7007 8008 9009 1004 2008 3012 4016 5020 6024 7028 8032 9036 1006 1007 2012 2014 3018 4024 3021 4028 5030 6036 5035 6042 7042 8048 9054 7049 8056 9063 1002 2004 3006 4008 5010 6012 7014 8016 9018 1005 2010 3015 4020 5025 6030 7035 8040 9045 1008 2016 3024 4032 5040 6048 7056 8064 9072 I 1009 2 2018 3 3027 4 4036 ■> ,S04S 6 6054 7 7063 8 8072 9 9081 lOIO 2020 3030 4040 5050 6060 7070 8080 9090 Dual Logarithms of powers of 2 and 10. L 2 =: 69314718, I, 10 = 230258509, 4,, 10* = 921034037, J,, 10'' = 1611809565, 4,, 4 = 138629437, 4,, Io2 = 460517019, 4,, Io5 = II51292546, ,„ IO« =r 1842068074, 4,, 8 == 207944154, 4,, io3 = 690775528, I, 106 = 1381551056, 1) io9 = 2072326584, B 2] Nat. No. I'OIOO to . C2C0 D. Log. «9.... to 198.... D. No. iO,l,0,0, to 10,1,9,9, Natural Numbers. I "01000000 lOIOO 2020I 30303 40406 50510 60615 70721 80828 90936 I'OIIOIOOO IIIIO 2I22I 31333 41446 51560 61675 7179I 81908 92026 I'01202IOI I222I 22342 32464 42587 52711 62836 72962 83089 93217 I "01303303 13433 23564 33696 43829 53963 64098 74234 84371 94509 I •01404606 14746 24887 35029 45173 55318 65464 75611 85759 95908 Dual Logarithms. 995033, 100 01 02 03 04 05 06 07 08 1094983, 10 II 12 13 14 15 16 17 18 ii94933» 20 21 22 23 24 25 26 27 28 1294883, 30 31 32 33 34 35 36 37 38 1394833. 40 41 42 43 44 45 46 47 48 Dual Numbers. 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 I,0; 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 2,0 2,1 2,2 2,3 2,4 2,5 2,6 2,7 2,8 2,9 3,0 3,1 3,2 3,3 3,4 3,5 3,6 3,7 3,8 3,9 4,0 4,1 4,2 4,3 4,4 4,5 4,6 4,7 4,8 4,9 Natural Numbers. l'Oi5o6oil 16162 26314 36467 46621 56776 66932 77089 87247 97406 i"oi6o75i7 17678 27840 38003 48167 58332 68498 78665 88833 99002 1*01709125 19296 29468 39641 49815 59990 70166 80343 90521 I "01800700 10834 21015 31197 41380 51564 61749 71935 82122 92310 i'oi902499 12644 22835 33027 43220 53414 63609 73805 84002 94200 1*02004399 Dual Logarithms. 1494783, 50 51 52 53 54 55 56 57 58 1594733, 60 61 62 63 64 65 66 67 68 1694683, 70 71 72 73 74 75 76 77 78 1794633, 80 81 82 83 84 85 86 87 88 1894583, 90 91 92 93 94 95 96 97 Dual Numbers. 5,0,0,0,0,0, 5,1,0,0,0,0, 5,2,0,0,0,0, 5,3,0,0,0,0, 5,4,0,0,0,0, 5,5,0,0,0,0, 5,6,0,0,0,0, 5,7,0,0,0,0, 5,8,0,0,0,0, 5,9,0,0,0,0, 6,0,0,0,0,0, 6,1,0,0,0,0, 6,2,0,0,0,0, 6,3,0,0,0,0, 6,4,0,0,0,0, 6,5,0,0,0,0, 6,6,0,0,0,0, 6,7,0,0,0,0, 6,8,0,0,0,0, 6,9,0,0,0,0, 7,0,0,0,0,0, 7,1,0,0,0,0, 7,2,0,0,0,0, 7,3,0,0,0,0, 7,4,0,0,0,0, 7,5,0,0,0,0, 7,6,0,0,0,0, 7,7,0,0,0,0, 7,8,0,0,0,0, 7,9,0,0,0,0, 8,0,0,0,0,0, 8,1,0,0,0,0, 8,2,0,0,0,0, 8,3,0,0,0,0, 8,4,0,0,0,0, 8,5,0,0,0,0, 8,6,0,0,0,0, 8,7,0,0,0,0, 8,8,0,0,0,0, 8,9,0,0,0,0, 9,0,0,0,0,0, 9,1,0,0,0,0, 9,2,0,0,0,0, 9,3,0,0,0,0, 9,4,0,0,0,0, 9,5,0,0,0,0, 9,6,0,0,0,0, 9,7,0,0,0,0, 9,8,0,0,0,0, 9,9,0,0,0,0, Multiples of Dififerences. lOIO lOII 2020 2022 3030 3033 4040 4044 5050 6060 5055 6066 7070 8080 7077 8088 9090 9099 IOI3 1014 2026 2028 3039 3042 4052 4056 sobs S070 6078 6084 7091 7098 8104 8112 9117 9126 1016 1017 2032 3048 4064 5080 6096 2034 3051 4068 5085 6102 7112 8128 7119 8136 9144 9153 I 2 X019 2038 3 4 3057 4076 1 509s 6114 7 8 7133 8152 9 9171J Dual Logarithms of powers of 2 and 10. 1, 2 = 69314718, 4,, 10 = 230258509, 4,, 10* = 921034037, \l', 4 = 138629437, L io2 = 460517019, I, lo' = 1151292546, -, 8 = 207944154, 4,, io3 = 690775528, 4,, io« = 1381551056, , lo^ = 161 1809565, 10^ = 1842068074, 10^ = 2072326584, Nat, No. 1*0201 to 1*0302 D. Log. 199.... to 297.... D. No. 4'0,2,0,0, to >H),2,9,9, [3 Natural Numbers. I*020I0000 2020I 30403 40606 50810 6IOI5 04 7I22I 05 81428 06 91636 07 i*02ioi845 08 I20IO 22221 32433 42646 52860 63075 73291 83508 93726 1-02203945 65238 75465 85693 95922 1-02306152 16336 26568 36801 47035 57270 67506 77743 87981 98220 1-02408460 18652 28894 39137 49381 59626 69872 80119 90367 1-02500616 10866 Dual Loffarithms. 1990066, 200 01 02 03 2090016, 10 II 12 13 14 16 17 18 I4I22 2189966, 24343 34565 44788 19 20 21 55012 22 23 24 25 26 27 2289916, 29 30 31 32 ss 34 35 36 37 2389866, 39 40 41 42 43 44 45 46 47 Dual Numbers. Jr0,2,0,0,0,0,0,0- >^,2,0, 1,0,0,0,0, \^0,2,0,2,0,0,0,0- Xo,2,o,3,o,o,o,o, >pO, 2, 0,4,0,0,0,0 >I'0,2,0,5, 0,0,0,0 >rO, 2, 0,6, 0,0, 0,0 >rO,2, 0,7, 0,0,0,0 >, 0,2, 0,8, 0,0,0,0 >fO,2, 0,9,0,0,0,0 >^,2, 1, 0,0,0,0,0 \j^, 2, 1, 1,0,0,0,0, (JfO, 2, 1, 2, 0,0, 0,0 ,2,1,3,0,0,0,0 ,2,1,4,0,0,0,0 >^0,2, 1, 5,0,0,0,0 i 0,2, 1, 6, 0,0, 0,0 0,2,1,7,0,0,0,0 >JfO,2, 1,8,0,0,0,0 |o,2, 1,9,0,0,0,0 > ,0,2, 2,0,0,0,0,0 \rO,2, 2, 1,0,0,0,0 >rO,2,2,2,0,0,0,0 ,,0,2,2,3,0,0,0,0 >,0,2, 2, 4,0,0,0,0 ^j2, 2, 5,0,0,0,0 vO, 2, 2,6,0,0,0,0 ,,0,2,2,7,0,0,0,0, >, 0,2, 2, 8, 0,0,0,0 4,0,2,2,9,0,0,0,0 >^052,3,0,0,0,0,0 wO,2, 3, 1,0,0,0,0 ,,0,2,3,2,0,0,0,0 >'0,2,3, 3,0,0,0,0 4^>2,3,4,o,o,o,o 4^,2,3,5,0,0,0,0 ,io,2,3,6,o,o,o,o 40,2,3,7,0,0,0,0 >^0,2, 3,8,0,0,0,0 io>a»3>9;0,o,o,o 4,0,2,4,0,0,0,0,0 4.0,2,4,1,0,0,0,0 0,2,4,2,0,0,0,0 0,2,4,3,0,0,0,0 0,2,4,4,0,0,0,0, >k',2,4,5>o,o,o,o 4,0,2,4,6,0,0,0,0 io,2,4,7,o,o,o,o 4^0,2,4,8,0,0,0,0 ,1,0,2,4,9,0,0,0,0 Natural Dual Dual Numbers. Logarithms. Numbers. 1*02521071 2489816, ,,0,2,5,0,0,0,0,0, 31323 49 > '0,2,5, 1,0,0,0,0, 41576 50 ,,0,2,5,2,0,0,0,0, 51830 51 ,,0,2,5,3,0,0,0,0, 62085 52 ^ '0,2,5,4,0,0,0,0, 72341 53 4'0,2,5,5,o,o,o,o, 82598 54 ,,0,2,5,6,0,0,0,0, 92856 55 ,,0,2,5,7,0,0,0,0, 1*02603115 56 4,0,2,5,8,0,0,0,0, 13375 57 ,,0,2,5,9,0,0,0,0, 23592 2589766, 4,0,2,6,0,0,0,0,0, 33854 59 4,0,2,6,1,0,0,0,0, 44117 60 j,0,2,6,2,0,0,0,0, 54381 6i 4^5,2,6,3,0,0,0,0, 64646 62 4,0,2,6,4,0,0,0,0, 74912 63 ,0,2,6,5,0,0,0,0, 85179 64 , ,0,2,6,6,0,0,0,0, 95448 65 ,,0,2,6,7,0,0,0,0, 1*02705718 66 ,,0,2,6,8,0,0,0,0, 15989 67 ,,0,2,6,9,0,0,0,0, 26216 2689716, 4,0,2,7,0,0,0,0,0, 36489 69 ,,0,2,7,1,0,0,0,0, 46763 70 ,,0,2,7,2,0,0,0,0, 57038 71 ,,0,2,7,3,0,0,0,0, 67314 72 4'0,2,7,4,0,0,0,0, 77591 73 ,,0,2,7,5,0,0,0,0, 87869 74 ,,0,2,7,6,0,0,0,0, 98148 75 ,,0,2,7,7,0,0,0,0, 1*02808428 76 ,,0,2,7,8,0,0,0,0, 18709 77 ,,0,2,7,9,0,0,0,0, 28942 2789666, ,,0,2,8,0,0,0,0,0, 39225 79 ,,0,2,8,1,0,0,0,0, 49509 80 ,,0,2,8,2,0,0,0,0, 59794 81 ,,0,2,8,3,0,0,0,0, 70080 82 ,,0,2,8,4,0,0,0,0, 80367 83 ,,0,2,8,5,0,0,0,0, 90655 84 ,0,2,8,6,0,0,0,0, 1-02900944 85 ,,0,2,8,7,0,0,0,0, 11234 86 ,,0,2,8,8,0,0,0,0, 21525 87 ,,0,2,8,9,0,0,0,0, 31771 2889616, ,,0,2,9,0,0,0,0,0, 42064 89 ,,0,2,9,1,0,0,0,0, 52358 90 ,,0,2,9,2,0,0,0,0, 62653 91 ,,0,2,9,3,0,0,0,0, 72949 92 ,,0,2,9,4,0,0,0,0, 83246 93 ,,0,2,9,5,0,0,0,0, 93544 94 ,,0,2,9,6,0,0,0,0, 1*03003843 95 ,,0,2,9,7,0,0,0,0, 14143 96 ,,0,2,9,8,0,0,0,0, 24444 97 ,,0,2,9,9,0,0,0,0, Multiples of Differences.^ 1020 102 1 2040 3060 4080 2042 3063 4084 5100 6120 5105 6126 7140 8160 7147 8168 9180 9189 1023 1024 2046 2048 3069 3072 4092 4096 sii"; 5120 6138 6144 7161 7168 8184 8192 9207 9216 1026 1027 2052 2054 3078 3081 4104 4108 S130 ,Si3S 6i=i6 6162 7182 7189 8208 8216 9234 9243 I022t 2044. 3o66< 4088. 5110 6132 7154 8176. 9198 1025 2050 3075 4100 5125 6150 7175 8200 9225 1028^; 2056 3084 4112 5140 6168 7196 8224 9252 I 1029 2 20S8 3 3087 4 4116 ,S .S145 6 6174 7 7203 8 8232 9 9261 1030 2060 3090 4120 5150 6180 7210 8240 9270 i, 2 = 69314718, , 4 = 138629437, , 8 = 207944154, Dual Logarithms of powers of 2 and 10. 10 = 230258509, ,1, 10* = 921034037, y, lo^ = 460517019, ,„ 10^ = 1151292546, 4,, io3 = 690775528, J, io« = 1381551056, L lo^ = 161 1809565, , ,, lo^ = 1842068074, ,,, io» = 2072326584, 4] Nat. No. r0303 to r0405 D. Log. 298.... to 397.... D. No. 10,3,0,0, to 4^0,3,9,9, Natural Numbers. I •03030100 40403 50707 61012 81625 91933 1*03102242 12552 22863 33130 43443 53757 64072 74388 84705 95023 1-03205343 15664 25986 36263 46587 56912 67238 77565 87893 98222 i'033o8552 18883 29215 39499 49833 60168 70504 80841 91179 1-03401518 X1858 22199 32541 42838 53182 63527 73873 • 84220 94568 1-03504917 15267 25619 35972 Dual Logarithms. Dual Numbers. 3l84999> o>3)0,o,o,o,o,o 0,3)0,1,0,0,0,0 0,3,0,2,0,0,0,0 .0,3,0,3,0,0,0,0 \I'0,3,o,4,o,o,o,o, >l'0,3,o,5,o,o,o,o ,,0,3,0,6,0,0,0,0 < '0,3)0,7,0,0,0,0, >['0,3,o,8,o,o,o,o >^o,3,o,9,o,o,o,o, J,o,3, 1,0,0,0,0,0 >, 0,3, 1,1,0,0,0,0, vO,3, 1,2,0,0,0,0, > '0,3,1,3,0,0,0,0, \1'0,3, 1,4,0,0,0,0, >I'0,3, 1,5)0,0,0,0 0,3)1)6,0,0,0,0 0,3)1)7)0,0,0,0 ■0,3)1,8,0,0,0,0 0,3)1)9)0,0,0,0, >, 0,3,2,0,0,0,0,0, >'0,3, 2, 1,0,0,0,0 >'0,3, 2, 2,0,0,0,0, > '0,3)2,3,0,0,0,0, 10,3,2,4)0,0,0,0, ^0,3, 2,5,0,0,0,0 >'0,3)2,6,o,o,o,o > '0,3,2,7,0,0,0,0 ^'0,3, 2, 8,0,0,0,0 >I'0,3, 2,9,0,0,0,0 >I'0,3)3)0)0,o,o,o \'0,3)3) 1)0,0,0,0, \'0,3,3, 2, 0,0,0,0 > '0,3,3)3)0,0,0,0 |o,3, 3, 4,0,0,0,0 10,3)3)5)0,0,0,0 > '0,3,3)6,0,0,0,0 > '0,3)3)7,0,0,0,0 > '0,3,3,8,0,0,0,0 \I'0,3)3)9)0,o,o,o, > '0,3,4,0,0,0,0,0 > '0,3)4)1)0,0,0,0 > '0,3,4,2,0,0,0,0 \ '0,3,4)3)0,0,0,0 4'0)3)4)4,o,o,o,o 4'0,3, 4,5)0)0,0,0 > '0,3)4)6,0,0,0,0 > '0,3,4)7)0)0,0,0, > '0,3,4,8,0,0,0,0 >1'0,3, 4,9)0,0,0,0 Natural Numbers, 1-03546281 56636 66992 77349 87707 98066 1-03608426 18787 29149 39512 Dual Logarithms. 3484849, 49 50 51 52 53 54 55 56 57 49827 3584799) 60192 59 70558 60 80925 61 91293 62 1-03701662 63 12032 64 22403 65 32775 66 43148 67 53478 3684749. 63853 69 74229 70 84606 71 94984 72 1*03805363 15744 26126 36509 46893 57230 67616 78003 88391 98780 I -03909170 I956I 29953 40346 50740 61088 71484 8I88I 92279 1-04002678 13078 23479 33881 44284 54688 73 74 75 76 77 3784699) 79 80 81 82 83 84 85 86 87 3884649, 89 90 91 92 93 94 95 96 97 Dual Numbers. > '0,3)5)0,0,0,0,0, > '0,3)5)1)0)0,0,0, > '0,3,5)2,0,0,0,0, > '0,3,5)3)0,0,0,0, 4'0,3)5)4)0,o,o,o, 10)3)5)5)0,0,0,0, > '0,3,5)6,0,0,0,0, >'0,3)5)7, 0,0,0,0, > '0,3,5)8,0,0,0,0, >I'0,3)5)9)0,o,o,o, > '0,3,6,0,0,0,0,0, > '0,3,6,1,0,0,0,0, \'0,3, 6,2, 0,0,0,0, > '0,3,6,3,0,0,0,0, ^0,3,6,4,0,0,0,0, 0,3)6,5,0,0,0,0, ■0,3,6,6,0,0,0,0, 0,3)6,7,0,0,0,0, 0,3)6)8,0,0,0,0, 0)3)6,9)0,0,0,0, 10,3,7,0,0,0,0,0, > '0,3)7)1,0,0,0,0, > '0,3)7)2,0,0,0,0, > '0,3)7)3)0,0,0,0, 4'0,3)7)4)0,o,o,o, 10,3)7)5)0,0,0,0, \ '0,3)7)6,0,0,0,0, > '0,3)7)7)0,0,0,0, > '0,3,7,8,0,0,0,0, >I'0,3, 7)9)0,0,0,0, 10,3)8,0,0,0,0,0, > '0,3,8,1,0,0,0,0, > '0,3)8,2,0,0,0,0, > '0,3,8,3)0,0,0,0, >I'0,3,8,4)0,o,o,o, >I'0,3,8,5, 0,0,0,0, > '0,3,8,6,0,0,0,0, > '0,3,8,7)0,0,0,0, > '0,3,8,8,0,0,0,0, >I'0,3)8,9,o,o,o,o, > '0,3,9)0)0,0,0,0, > '0,3,9,1,0,0,0,0, > '0,3)9)2)0,0,0,0, > '0,3)9)3)0,0,0,0, 4'0,3)9)4,o,o,o,o, >|'0,3,9)5)0,o,o,o, > '0,3,9,6,0,0,0,0, \'0,3, 9,7, 0,0,0,0, > '0,3,9)8,0,0,0,0, 10,3,9,9,0,0,0,0, Multiples of Differences, 1030 2060 1031 2062 3090 3093 4120 4124 5150 6180 5155 6186 7210 8240 7217 8248 9270 9279 1033 1034 2066 2068 3099 3102 4132 4136 5I6S siro 6198 6204 7231 723» 8264 8272 9297 9306 1036 1037 1038 2072 2074 2076 3108 3"i 3"4 4144 4148 4152 5180 S18S 5190 6216 6222 6228 72^2 72<;9 7266 8288 8296 8304 9324 9333 9342 I 1039 [ 2 2078 3 3" 7 4 4156 S SI9S 6 6234 7 7273 8 8312 9 9351 1040 2080 3120 4160 5200 6240 7280 8320 9360 A, 2 = 6931471J >') 4 = 138629437, Dual Logarithms of powers of 2 and 10, ,|„ io_ = 230258509, 4,, 10* = 921034037, y. ,„ 10^ = 460517019, V, lo^ = 1151292546, V, 10^ = 1842068074, I, 8 = 207944154, 4,, io3 = 690775528, 4,, io« = 1381551056, I, io9 = 2072326584, 10'^ = 1611809565, Nat. No. 1'0406 to r0509 D. Log. 398.... to 496.... D. No. 4.0,4,0,0, to >P0,4,9,9, [5 Natural Numbers. 1-04060401 70807 81214 91622 1-04102031 12442 22853 33265 43679 54093 64461 74877 85294 95713 104206133 16554 26976 37399 47823 58248 68626 79053 89481 99910 1-04310340 20771 31203 41636 52070 62505 72894 83331 93769 1*04404208 14648 25089 35532 45976 56421 66867 77267 87715 98164 I '04508614 19065 29517 39970 50424 60879 71335 Dual Logarithms. 3980132, 99 400 01 02 03 04 . 05 06 07 4080082, 09 10 II 12 13 14 15 16 17 4180032, 19 20 21 22 23 24 25 26 27 4279982, 28 29 30 31 32 33 34 35 36 4379932, 38 39 40 41 42 43 44 45 46 Dual Numbers. 4,0,0 4,0, r 4,o,2: 4,0,3 4,0,4 4,0,5 4,0,6 4,0,7 4,0,8 4,0,9 4,1,0 4,1,1 4,1,2 4,1,3 4,1,4: 4,1,5 4,1,6 4,1,7 4,1,8 4,1,9 4,2,0; 4,2,1 4,2,2 4,2,3 4,2,4 4,2,5 4,2,6 4,2,7 4,2,8 4,2,9 4,3,0 4,3'i 4,3,2 4,3,3 4,3,4 4,3,5 4,3,6 4,3,7 4,3,8 4,3>9 4,4,0 4,4,1 4,4,2 4,4,3 4,4,4 4,4,5 4,4,6 4,4,7 4,4,8 4,4,9 Natural Dual Dual Numbers. Logarithms. Numbers. 1-04581745 4479882, wO,4,5, 0,0,0,0,0, > '0,4,5,1,0,0,0,0, 92203 48 1-04602662 49 Xo,4,5,2,o,o,o,o, >lo,4,5,3,o,o,o,o. 13122 50 23583 5r > '0,4,5,4,0,0,0,0, 34045 52 jo,4,5, 5,0,0,0,0, 44508 53 > '0,4,5,6,0,0,0,0, 54972 54 wO,4,5,7,o,o,o,o, 65437 55 >, 0,4,5, 8,0,0,0,0, 75904 56 10,4,5,9,0,0,0,0, 86326 4579832, >fO,4, 6,0,0,0,0,0, 96795 58 >, 0,4,6, 1,0,0,0,0, 1-04707265 59 wO,4,6,2, 0,0,0,0, 17736 60 > '0,4,6,3^0,0,0,0, 28208 61 ,,0,4,6,4,0,0,0,0, 38681 62 |o,4,6,5,o,o,o,o. 49155 63 >, 0,4,6,6,0,0,0,0, 59630 64 ,,0,4,6,7,0,0,0,0, 70106 65 ^0,4,6,8,0,0,0,0, >, 0,4, 6,9,0,0,0,0, 80583 66 91013 4679782, ,,0,4,7,0,0,0,0,0, 1-04801492 68 ,,0,4,7,1,0,0,0,0, II972 69 ,,0,4,7,2,0,0,0,0, 22453 70 > '0,4,7,3,0,0,0,0, 32935 71 > '0,4,7,4,0,0,0,0, 43418 72 > '0,4,7,5,0,0,0,0, 53902 73 ,,0,4,7,6,0,0,0,0, 64387 74 >'0,4,7,7,o,o,o,o, 74873 75 ,,0,4,7,8,0,0,0,0, 85360 76 > '0,4,7,9,0,0,0,0, 95804 4779732, ,,0,4,8,0,0,0,0,0, 1-04906294 78 ,,0,4,8,1,0,0,0,0, 16785 79 ,,0,4,8,2,0,0,0,0, 27277 80 > '0,4,8,3,0,0,0,0, 37770 81 ,,0,4,8,4,0,0,0,0, 48264 82 ,,0,4,8,5,0,0,0,0, 58759 83 ,,0,4,8,6,0,0,0,0, 69255 84 > '0,4,8,7,0,0,0,0, 79752 85 ,,0,4,8,8,0,0,0,0, 90250 86 4,0,4,8,9,0,0,0,0, 1-05000700 4879682, ,,0,4,9,0,0,0,0,0, 1 1 200 88 ,,0,4,9,1,0,0,0,0, 21701 89 ,,0,4,9,2,0,0,0,0, 32203 90 > '0,4,9,3,0,0,0,0, 42706 91 > '0,4,9,4,0,0,0,0, 53210 92 >'0,4,9,5>o,o,o,o. 63715 93 ,,0,4,9,6,0,0,0,0, 74221 94 > '0,4,9,7,0,0,0,0, 84728 95 ,,0,4,9,8,0,0,0,0, 95236 96 ,,0,4,9,9,0,0,0,0, Multiples of Differences. 1040 I04I 2080 2082 3120 3123 4160 4164 5200 sacs 6240 6246 7280 7287 8320 8328 9360 93^ 1043 2086 3129 4172 5215 6258 7301 8344 9387 1046 1047 1 2092 3138 4184 2094 3I4I 4188 5230 6276 5235 6282 7322 8368 7329 8376 9414 9423 1042 2084 3126 4168 5210 6252 7294 8336 9378 1044 1 1045 2088 2090 3132 3135 4176 4180 5220 5225 6264 I 6270 7308 1 7315 8352 ! 8360 9396 1 9405 1048 2096 3144 4192 5240 6288 7336 8384 9432 1049 2098 3147 4196 5245 6294 7343 8392 9441 1050 2100 3150 4200 5250 6300 7350 8400 9450 X, 2 = 69314718, ,„ 4 = 138629437, 4,, 8 = 207944154, Dual Logarithms of powers of 2 and 10. 10 = 230258509, , io2 =: 4605 1 701 9, io3 = 690775528, ,„ 10* = 921034037, V, lo5 = II51292546, 4,, io« = 1381551056, A, io7 = 161 1809565, V, 10^ = 1842068074, lo^ = 2072326584, 61 Nat. No. 1-0510 to r0614 D. Log. 497.... to 596.... D. No. 10,5,0,0, to 10,5,9,9, Natural Numbers. I"05I0I00S II515 22026 32538 43051 53565 64080 74596 85113 95632 i'o52o6io6 16627 27149 37672 48196 58721 69247 79774 90302 1-05300831 11312 21843 32375 42908 53442 63977 74513 85050 95589 i'054o6i29 16623 27165 37708 48252 58797 69343 79890 90438 1-05500987 "537 22040 32592 43145 53699 64254 74810 85367 95926 1*05606486 17047 Dual Logarithms. 4975165, 98 99 500 01 02 03 04 05 06 5075115. 08 09 10 II 12 13 14 15 16 5175065, 18 19 20 21 22 23 24 25 26 5275015, 28 29 30 31 32 33 34 35 36 5374965* 38 39 40 41 42 43 44 45 46 Dual Numbers. <5,5,o,o,o,o,o,o, 0,5,0,1,0,0,0,0, 4^,5'0,2, 0,0,0,0, >^o,5,o,3, 0,0,0,0, io,5,o,4,o,o,o,o, >^o,5,o,5,o,o,o,o, 4^0,5,0,6,0,0,0,0, 4^0,5,0,7,0,0,0,0, io, 5 > 0,8, 0,0, 0,0, 4^,5>o,9'0,o,o,o, 4^,5>i>o,o,o,o,o, >'0,5, 1, 1,0,0,0,0, >'0,5, 1, 2,0,0,0,0, wO,5, 1,3,0,0,0,0, >^o,5, 1,4,0,0,0,0, >'0,5,i,5,o,o,o,o, >rO,5, 1,6,0,0,0,0, >'0,5, 1, 7,0,0,0,0, > '0,5, 1,8,0,0,0,0, ^0,5, 1,9,0,0,0,0, \'0,5, 2,0,0,0,0,0, ^^0,5, 2, 1,0,0,0,0, > '0,5,2,2,0,0,0,0, > '0,5,2,3,0,0,0,0, 4'0,5, 2,4,0,0,0,0, J'0,5,2,5,o,o,o,o, >'0,5, 2, 6,0,0,0,0, >'0,5, 2, 7,0,0,0,0, > '0,5,2,8,0,0,0,0, ^OjS, 2,9,0,0,0,0, >I'0,5,3,o,o,o,o,o, \'0,S, 3, 1,0,0,0,0, >'0,5, 3, 2,0,0,0,0, \'0,5,3,3,o,o,o,o, ^o, 5, 3, 4, 0,0, 0,0, ['OjS, 3, 5, 0,0,0,0, ,5,3,6,0,0,0,0, 5,5,3,7,0,0,0,0, 10,5,3,8,0,0,0,0, ['0,5,3>9>o,o,o,o, 4^0,5,4,0,0,0,0,0, \ '0,5,4, 1,0,0,0,0, > '0,5,4,2,0,0,0,0, > '0,5,4,3,0,0,0,0, 4^0, 5,4,4,0,0,0,0, > '0,5,4,5,0,0,0,0, >'0,5, 4,6,0,0,0,0, > '0,5,4,7,0,0,0,0, > '0,5,4,8,0,0,0,0, 4'0,5,4,9,o,o,o,o, Natural Numbers. Dual Logarithms. 1-05627562 38125 49689 60254 70820 81387 91955 1-05702524 13094 23665 33190 43763 54337 64912 75488 86066 96645 1-05807225 17806 28388 38923 49507 60092 70678 81265 91853 1-05902442 13032 23623 34215 44762 55256 65852 76449 87047 97646 1*06008246 18847 29449 40052 50707 61313 71919 82526 93134 1-06103743 14353 24964 35576 46190 5474915. 48 49 50 51 52 53 54 55 56 5574865, 58 59 60 6i 62 63 64 65 66 5674815, 68 69 70 71 72 73 74 75 76 5774765, 78 79 80 81 82 83 84 85 86 5874715. 90 91 92 93 94 95 96 Dual Numbers. > '0,5,5,0,0,0,0,0, > '0,5,5,1,0,0,0,0, > '0,5,5,2,0,0,0,0, > '0,5,5,3,0,0,0,0, 4^,5,5,4,0,0,0,0, > '0,5,5,5,0,0,0,0, > '0,5,5,6,0,0,0,0, > '0,5,5,7,0,0,0,0, > '0,5,5,8,0,0,0,0, 4^,5,5,9,0,0,0,0, > '0,5,6,0,0,0,0,0, \ '0,5,6,1,0,0,0,0, > '0,5,6,2,0,0,0,0, >. -0,5, 6,3, 0,0, 0,0, 4^,5.6,4,0,0,0,0, ■0,5,6,5,0,0,0,0, ,5,6,6,0,0,0,0, 0,5,6,7,0,0,0,0, 10,5,6,8,0,0,0,0, 4,0,5,6,9,0,0,0,0, 4'0,5, 7,0,0,0,0,0, > '0,5,7,1,0,0,0,0, > '0,5,7,2,0,0,0,0, > '0,5,7.3,0,0,0,0, 4'0,5. 7,4,0,0,0,0, 0,5,7,5,0,0,0,0, 0,5,7,6,0,0,0,0, ,5,7,7,0,0,0,0, ■0,5,7,8,0,0,0,0, 4'0,5.7.9>o,o,o,o, > '0,5,8,0,0,0,0,0, ,,0,5,8,1,0,0,0,0, >'0,5, 8,2, 0,0,0,0, > '0,5,8,3,0,0,0,0, 4,0,5,8,4,0,0,0,0, > '0,5,8,5,0,0,0,0, > '0,5,8,6,0,0,0,0, > '0,5,8,7,0,0,0,0, ,,0,5,8,8,0,0,0,0, 4^,5,8,9.0,0,0,0, > '0,5,9,0,0,0,0,0, >'0,5, 9,1, 0,0,0,0, > '0,5,9,2,0,0,0,0, ^ '0,5,9.3,0,0,0,0, 4'0,5.9.4>o,o,o,o, 4'0,5,9,5,o,o,o,o, > '0,5,9,6,0,0,0,0, > '0,5,9,7,0,0,0,0, > '0,5,9,8,0,0,0,0, 4'0, 5. 9. 9. 0,0, 0,0, Multiples of Differences. 1051 1052 2102 2104 31 S3 3iSfe 4204 4208 S2,S5 5260 6306 6312 73,'>7 7:M 8408 8416 9459 9468 1054 1055 2108 2110 3162 3165 4216 4220 5270 S27'; 6324 6330 7378 73«S «432 8440 9486 9495 1057 1058 2114 2116 3171 3174 4228 4232 5285 5290 6342 6348 7399 7406 8456 8464 9513 9522 I 1060 2 2120 3 3180 4 4240 S S300 6 6360 7 7420 8 8480 9 9540 I06I 2122 3183 4244 5305 6366 7427 9549 1053 2106 3159 4212 5275 6318 7371 8424 9477 1056 2112 3168 4224 5280 6336 7392 8448 9504 1059 2118 3177 4236 5295 6354 7413 8472 9531 J,, 2 = 69314718, V, 10 = 230258509, Dual Logarithms of powers of 2 and 10. 10* = 921034037, J,, lo'' = 1611809565, ,„ 4 = 138629437, ,„ io2 = 460517019, ,„ io5 = 1151292546, ,„ 108 = 1842068074, 4,, 8 = 207944154, 4, io3 = 690775528, 4'. 10" = 1381551056, 4'. 10^ = 2072326584, Nat. No. 1'0615 to 1-0720 D. Log. 597.... to 695.... D. No. W,0,0, to 4.0,6,9,9, [7 Natural Dual Dual Numbers. Logarithms. Numbers. i'o6i52oi5 5970198, ^IK^,6,o,o,o,o,o,o, 62630 98 >, 0,6,0, 1,0,0,0,0, 73246 99 ,,0,6,0,2,0,0,0,0, 83863 600 , ,0,6,0,3,0,0,0,0, 94481 OI |o,6,o,4,o,o,o,o. i*o6205ioo 02 4,0,6,0,5,0,0,0,0, 15721 03 >, 0,6, 0,6, 0,0,0,0, 26343 04 ,-0,6,0,7,0,0,0,0, 36966 05 ,,0,6,0,8,0,0,0,0, 47590 06 ,K>,6,o,9,o,o,o,o, 58167 6070148, ( ,0,6,1,0,0,0,0,0, 68793 08 ,.0,6,1,1,0,0,0,0, 79420 09 ,K>,6, 1,2,0,0,0,0, 90048 10 ,,0,6,1,3,0,0,0,0, I '06300677 II ,,0,6,1,4,0,0,0,0, 11307 12 , 0,6,1,5,0,0,0,0, 21938 13 ,,0,6,1,6,0,0,0,0, 32570 14 ,0,6,1,7,0,0,0,0, 43203 15 ,0,6,1,8,0,0,0,0, 53837 16 ,0,6,1,9,0,0,0,0, 64425 6170098, ,0,6,2,0,0,0,0,0, 75061 18 ,,0,6,2,1,0,0,0,0, 85699 19 ,,0,6,2,2,0,0,0,0, 96338 20 ,,0,6,2,3,0,0,0,0, i'o64o6978 21 ,0,6,2,4,0,0,0,0, 17619 22 ,0,6,2,5,0,0,0,0, 28261 23 ,,0,6,2,6,0,0,0,0, 38904 24 ,0,6,2,7,0,0,0,0, 49548 25 ,0,6,2,8,0,0,0,0, 60193 26 ,,0,6,2,9,0,0,0,0, 70789 6270048, ,,0,6,3,0,0,0,0,0, 81436 28 ,,0,6,3,1,0,0,0,0, 92084 29 ,,0,6,3,2,0,0,0,0, 1-06502733 30 wO,6,3,3,o,o,o,o, 13383 31 > ^,6,3,4,0,0,0,0, 24034 32 >k>,6,3,5,o,o,o,o. 34686 33 ,,0,6,3,6,0,0,0,0, 45339 34 ^ '0,6,3,7,0,0,0,0, 55994 35 ,,0,6,3,8,0,0,0,0, 66650 36 > '0,6,3,9,0,0,0,0, 77260 6369998, ,,0,6,4,0,0,0,0,0, 87918 37 ,,0,6,4,1,0,0,0,0, 98577 38 ,0,6,4,2,0,0,0,0, I '06609237 39 > '0,6,4,3,0,0,0,0, 19898 40 ,0,6,4,4,0,0,0,0, 30560 41 "0,6,4,5,0,0,0,0, 41223 42 ,,0,6,4,6,0,0,0,0, 51887 43 ,,0,6,4,7,0,0,0,0, 62552 44 ,,0,6,4,8,0,0,0,0, 73218 45 ,,0,6,4,9,0,0,0,0, Natural Dual Dual Numbers. Logarithms. Numbers. 1-06683838 6469948, 40,6,5,0,0,0,0,0, 94506 47 ,,0,6,5,1,0,0,0,0, 1-06705175 48 ,,0,6,5,2,0,0,0,0, 15846 49 "0,6,5,3,0,0,0,0, 26518 50 ,,0,6,5,4,0,0,0,0, 37191 51 > -0,6,5,5,0,0,0,0, 47865 52 ,,0,6,5,6,0,0,0,0, 58540 53 > -0,6,5,7,0,0,0,0, 69216 54 ,,0,6,5,8,0,0,0,0, 79893 55 ,0,6,5,9,0,0,0,0, 90521 6569898, ,0,6,6,0,0,0,0,0, i'o68oi2oo 57 ,0,6,6,1,0,0,0,0, 11880 58 ,0,6,6,2,0,0,0,0, 22561 59 ,,0,6,6,3,0,0,0,0, 33243 60 ,,0,6,6,4,0,0,0,0, 43926 61 ,0,6,6,5,0,0,0,0, 54610 62 ,0,6,6,6,0,0,0,0, 65295 63 ,0,6,6,7,0,0,0,0, 75982 64 ,,0,6,6,8,0,0,0,0, 86670 65 ,,0,6,6,9,0,0,0,0, 97312 6669848, ,0,6,7,0,0,0,0,0, i'o69o8oo2 67 ,0,6,7,1,0,0,0,0, 18693 68 ,,0,6,7,2,0,0,0,0, 29385 69 > '0,6,7,3,0,0,0,0, 40078 70 ,,0,6,7,4,0,0,0,0, 50772 71 ^ '0,6,7,5,0,0,0,0, 61467 72 ,,0,6,7,6,0,0,0,0, 72163 73 ,0,6,7,7,0,0,0,0, 82860 74 ,,0,6,7,8,0,0,0,0, 93558 75 ,0,6,7,9,0,0,0,0, 1*07004209 6769798, , 0,6,8,0,0,0,0,0, 14909 77 ,0,6,8,1,0,0,0,0, 25610 78 ,,0,6,8,2,0,0,0,0, 36313 79 ,0,6,8,3,0,0,0,0, 47017 80 ,,0,6,8,4,0,0,0,0, 57722 8i ,0,6,8,5,0,0,0,0, 68428 82 ,0,6,8,6,0,0,0,0, 79135 83 ,0,6,8,7,0,0,0,0, 89843 84 ,0,6,8,8,0,0,0,0, i'o7ioo552 85 ,0,6,8,9,0,0,0,0, 11213 6869748, ,0,6,9,0,0,0,0,0, 21924 87 ,0,6,9,1,0,0,0,0, 32636 88 ,,0,6,9,2,0,0,0,0, 43349 89 > '0,6,9,3,0,0,0,0, 54063 90 ,,0,6,9,4,0,0,0,0, 64778 91 ,,0,6,9,5,0,0,0,0, 75494 92 ,0,6,9,6,0,0,0,0, 86212 93 4,0,6,9,7,0,0,0,0, 96931 94 ,,0,6,9,8,0,0,0,0, i'o720765i 95 4,0,6,9,9,0^0,0,0, Multiples of Differences. I06I 1062 1063 2122 2124 2126 3i«3 3186 3189 4244 4248 4252 5305 S.Sio S3 IS 6366 6372 6378 7427 7434 7441 8488 8496 8S04 9S49 955« 9567 1064 1065 2128 2130 3192 319s 4256 4260 5320 532 s 6384 6390 7448 74SS 8512 8520 9576 95«5 1067 1068 2134 2136 3201 3204 4268 4272 S33S S340 6402 6408 7469 7476 «S36 8S44 9603 9612 1066 2132 3198 4264 5330 6396 7462 8528 9594 1069 2138 3207 4276 5345 6414 7483 8552 9621 1070 1071 1072 2140 2142 2144 3210 .3213 32 1 6 4280 4284 4288 5.150 5355 53<>o 6420 6426 6432 7490 7497 7504 8s6o 8.S68 8s7(i 9630 9^39 9648 Dual Logarithms of powers of 2 and 10, J,, 2 = 69314718, 4', 10 = 230258509, 4^, lo* = 921034037, 4', 10^ = 1611809565, V, 4 = 138629437, \, io2 = 460517019, A, lo^ = 1151292546, X, 10" = 1842068074, I, 8 = 207944154, I, io3 = 690775528, I, 106 = 1381551056, 4,, io9 = 2072326584, 8] Nat. No. r0721 to r0827 D. Log. 696.... to 795.... D. No. i0,7,0,0, to i0,7,9,9, Natural Dual Dual Natural Dual Dual Numbers. Logarithms. Numbers. Numbers. Logarithms. Numbers. Multiples ot Differences. 1-07213535 6965231, ,^,7,0,0,0,0,0,0, 1*07750676 7464981, > '0,7,5,0,0,0,0,0, 24256 97 ,,0,7,0,1,0,0,0,0, 61451 47 ,,0,7,5,1,0,0,0,0, J Tf\^r^ 1073 2146 34978 98 ,,0,7,0,2,0,0,0,0, 72227 48 ,0,7,5,2,0,0,0,0, 2 2144 ] 2 45701 99 > '0,7,0,3,0,0,0,0, 83004 49 > -0,7,5,3,0,0,0,0, 3 3216 3219 3 56426 700 ,,0,7,0,4,0,0,0,0, 93782 50 vO,7, 5,4,0,0,0,0, 4 5 4288 5360 4292 5365 4 5 67152 01 ,,0,7,0,5,0,0,0,0, 1*07804561 51 vO,7,5,5,o,o,o,o, 6 6432 6438 6 77879 02 ,,0,7,0,6,0,0,0,0, 15341 52 ,,0,7,5,6,0,0,0,0, 7 7504 8576 Q648 75" 8584 7 Q 88607 03 4^0,7,0,7,0,0,0,0, 26123 53 > -0,7,5,7,0,0,0,0, 9 c Q 99336 04 ,,0,7,0,8,0,0,0,0, 36906 54 > '0,7,5,8,0,0,0,0, 1*07310066 05 4,0,7,0,9,0,0,0,0, 47690 55 > -0,7,5,9,0,0,0,0, 20749 7065181, ,,0,7,1,0,0,0,0,0, 58426 7564931, ,,0,7,6,0,0,0,0,0, 31481 42214 07 08 ,,0,7,1,1,0,0,0,0, ,,0,7,1,2,0,0,0,0, 69212 79999 57 58 ,K),7, 6,1, 0,0,0,0, > '0,7,6,2,0,0,0,0, I 2 3 2150 3225 1U70 2152 3228 I 2 3 52948 09 N '0,7, 1,3,0,0,0,0, 90787 59 > '0,7,6,3,0,0,0,0, 4 4300 4304 4 63683 10 > '0,7,1,4,0,0,0,0, 1*07901576 60 > '0,7,6,4,0,0,0,0, 1 5375 6450 5380 6456 5 6 74419 II ,,0,7,1,5,0,0,0,0, 12366 61 > '0,7,6,5,0,0,0,0, 7 7525 7532 7 85156 12 ,,0,7,1,6,0,0,0,0, 23157 62 ,,0,7,6,6,0,0,0,0, 8 9 8600 9675 8608 9684 8 95894 13 ,,0,7,1,7,0,0,0,0, 33949 63 ,,0,7,6,7,0,0,0,0, y 1*07406634 14 ,,0,7,1,8,0,0,0,0, 44742 64 ,,0,7,6,8,0,0,0,0, 17375 15 >lrO,7, 1,9,0,0,0,0, 55536 65 > -0,7,6,9,0,0,0,0, 28069 7165131, > -0,7,2,0,0,0,0,0, 66285 7664881, ,,0,7,7,0,0,0,0,0, I 1078 2156 3234 1079 2158 3237 I 38812 17 ,,0,7,2,1,0,0,0,0, 77082 67 ,,0,7,7,1,0,0,0,0, 2 3 2 ■I 49556 18 ,,0,7,2,2,0,0,0,0, 87880 68 > -0,7,7,2,0,0,0,0, 4 4312 4316 4 60301 19 > '0,7,2,3,0,0,0,0, 98679 69 > -0,7,7,3,0,0,0,0, 5 5390 5395 5 71047 20 ,,0,7,2,4,0,0,0,0, 1*08009479 70 wO,7,7,4,o,o,o,o, 6 7 6468 7546 6474 7553 6 7 81794 21 > '0,7,2,5,0,0,0,0, 20280 71 > '0,7,7,5,0,0,0,0, 8 8624 8632 8 92542 22 ,,0,7,2,6,0,0,0,0, 31082 72 ,,0,7,7,6,0,0,0,0, 9 9702 9711 9 1*07503291 23 ,,0,7,2,7,0,0,0,0, 41885 73 > '0,7,7,7,0,0,0,0, 14041 24 ,,0,7,2,8,0,0,0,0, 52689 74 ,,0,7,7,8,0,0,0,0, 24792 25 ,,0,7,2,9,0,0,0,0, 63494 75 > '0,7,7,9,0,0,0,0, I 1081 1082 35498 7265081, > -0,7,3,0,0,0,0,0, 74251 7764831, > -0,7,8,0,0,0,0,0, 2 3 4 2162 3243 4324 2164 3246 4328 46252 27 ,,0,7.3,1,0,0,0,0, 85058 77 ,,0,7,8,1,0,0,0,0, 57007 28 ,,0,7,3,2,0,0,0,0, 95867 78 ,,0,7,8,2,0,0,0,0, 5 5405 5410 67763 29 > '0,7,3,3,0,0,0,0, 1*08106677 79 > '0,7,8,3,0,0,0,0, 6 6486 6492 78520 30 > '0,7,3,4,0,0,0,0, 17488 80 ,,0,7,8,4,0,0,0,0, 7 8 7567 8648 7574 8656 89278 31 '0,7,3,5,0,0,0,0, 28300 81 ,,0,7,8,5,0,0,0,0, 9 9729 9738 1*07600037 32 '0,7,3,6,0,0,0,0, 39113 82 ,,0,7,8,6,0,0,0,0, 10797 33 '0,7,3,7,0,0,0,0, 49927 83 ,,0,7,8,7,0,0,0,0, 21558 34 '0,7,3,8,0,0,0,0, 60742 84 ,,0,7,8,8,0,0,0,0, 32320 35 '0,7,3,9,0,0,0,0, 71558 85 ,,0,7,8,9,0,0,0,0, 43032 7365031, '0,7,4,0,0,0,0,0, 82326 7864781, ,,0,7,9,0,0,0,0,0, 53796 37 '0,7,4,1,0,0,0,0, 93144 87 ,,0,7,9,1,0,0,0,0, 64561 38 ,0,7,4,2,0,0,0,0, 1*08203963 88 ,,0,7,9,2,0,0,0,0, 75327 39 '0,7,4,3,0,0,0,0, 14783 89 '0,7,9,3,0,0,0,0, 86095 40 '0,7,4,4,0,0,0,0, 25604 90 '0,7,9,4,0,0,0,0, 96864 41 '0,7,4,5,0,0,0,0, 36427 91 -0,7,9,5,0,0,0,0, 1*07707634 42 '0,7,4,6,0,0,0,0, 47251 92 -0,7,9,6,0,0,0,0, 18405 43 '0,7,4,7,0,0,0,0, 58076 93 -0,7,9,7,0,0,0,0, 29177 44 ,0,7,4,8,0,0,0,0, 68902 94 -0,7,9,8,0,0,0,0, 39950 45 '0,7,4,9,0,0,0,0, 79729 95 '0,7,9,9,0,0,0,0, Dual Logarithms Ofl DOwers of 2 a ind 10. ,, 2 = 6931 4718, J ', 10 = 230258509, J,, 10* = 92 51034037, ,,, 10' = 1611809565, ^ 4 = 13862 9437, > ,, io2 = 460517019, ,,, lo* =11! 11292546, , ,, 10^ = 1842068074, ,, 8 = 2079^ ^4154, > '. I o3 = 69077552^ », ,„ io« = 13J 51551056, ,,, 10^ = 207 23 J >.6s 84, Nat. No. r0828 to 1*0936 D. Log. 796.... to 894.... Natural Dual Dual Numbers. Logarithms. Numbers. 1-08285671 7960264, ,,0,8,0,0,0,0,0,0, 96500 97 ,K3,8,o, 1,0,0,0,0, i'o83o733o 98 4,0,8,0,2,0,0,0,0, 18161 99 |o,8,o,3,o,o,o,o, 28993 800 >^o,8,o,4,o,o,o,o, 39826 01 ,,0,8,0,5,0,0,0,0, 50660 02 ,,0,8,0,6,0,0,0,0, 6149s 03 ,,0,8,0,7,0,0,0,0, 72331 04 ,,0,8,0,8,0,0,0,0, 83168 OS ,,0,8,0,9,0,0,0,0, 93957 8060214, ,,0,8,1,0,0,0,0,0, 1*08404796 07 ,,0,8,1,1,0,0,0,0, 15636 08 , ,0,8,1,2,0,0,0,0, 26478 09 ,,0,8,1,3,0,0,0,0, 37321 10 ,,0,8,1,4,0,0,0,0, 48165 II ,,0,8,1,5,0,0,0,0, 59010 12 ,,0,8,1,6,0,0,0,0, 69856 13 ,,0,8,1,7,0,0,0,0, 80703 14 ,,0,8,1,8,0,0,0,0, 91551 15 > -0,8, 1,9,0,0,0,0, f '08502350 8160164, ,,0,8,2,0,0,0,0,0, 13200 17 ,,0,8,2,1,0,0,0,0, 24051 18 ,,0,8,2,2,0,0,0,0, 34903 19 ,,0,8,2,3,0,0,0,0, 45756 20 ,,0,8,2,4,0,0,0,0, 56611 21 ,,0,8,2,5,0,0,0,0, 67467 22 ,,0,8,2,6,0,0,0,0, 78324 23 ,,0,8,2,7,0,0,0,0, 89182 24 ,,0,8,2,8,0,0,0,0, 1-08600041 25 ,,0,8,2,9,0,0,0,0, 10853 82601 14, , ,0,8,3,0,0,0,0,0, 21714 27 "0,8,3,1,0,0,0,0, 32576 28 ,,0,8,3,2,0,0,0,0, 43439 29 > '0,8,3,3,0,0,0,0, 54303 30 > '0,8,3,4,0,0,0,0, 65168 31 > '0,8,3,5,0,0,0,0, 76035 32 ^ '0,8,3,6,0,0,0,0, 86903 33 > '0,8,3,7,0,0,0,0, 97772 34 ,,0,8,3,8,0,0,0,0, 1-08708642 35 wO,8,3, 9,0,0,0,0, 19464 8360064, ,,0,8,4,0,0,0,0,0, 30336 37 ,,0,8,4,1,0,0,0,0, 41209 38 ,,0,8,4,2,0,0,0,0, 52083 39 ,,0,8,4,3,0,0,0,0, 62958 40 > '0,8,4,4,0,0,0,0, 73834 41 ,,0,8,4,5,0,0,0,0, 847 1 1 42 ,,0,8,4,6,0,0,0,0, 95589 43 ,,0,8,4,7,0,0,0,0, 1*08806469 44 ,,0,8,4,8,0,0,0,0, 17350 4S , 0,8,4,9,0,0,0,0, Natural Numbers. 1-08828183 39066 49950 60835 71721 82608 93496 1*08904385 15275 26167 37011 47905 58800 69696 80593 91491 1*09002390 13290 24191 35093 45949 56854 67760 78667 89575 1*09100484 "394 22305 33217 44130 54994 65909 76826 87744 98663 1*09209583 20504 31426 42349 53273 64149 75075 86003 96932 1*09307862 18793 29725 40658 51592 62527 Dual Logarithms. 8460014, 47 48 49 50 51 52 53 54 55 8559964, 56 57 58 59 60 61 62 63 64 8659914, 66 67 68 69 70 71 72 73 74 8759864, 76 77 78 79 80 81 82 83 84 8859814, 86 87 90 91 92 93 94 P. No. 10,8,0,0, to i0,8,9,9, [0 1 Dual , Numbers. Multiples of Differences. ,8,5,0,0,0,0,0, -0,8,5,1,0,0,0,0, \1'0,8,5, 2, 0,0,0,0, 40,8,5,3,0,0,0,0, \l'0,8,5,4,o,o,o,o, nI'O, 8, 5,5,0,0,0,0, >'0,8,5, 6,0,0,0,0, "0,8,5,7,0,0,0,0, \l,o,8,5, 8, 0,0,0,0, >^o, 8, 5,9,0,0,0,0, ,,0,8,6,0,0,0,0,0, ,,0,8,6,1,0,0,0,0, ,K>,8,6, 2,0,0,0,0, > '0,8,6,3,0,0,0,0, 4,0,8,6,4,0,0,0,0, 3,8,6,5,0,0,0,0, D,8, 6, 6,0,0,0,0, j,o,8,6,7, 0,0,0,0, 3,8,6,8,0,0,0,0, 3,8,6,9,0,0,0,0, ,,0,8,7,0,0,0,0,0, ,,0,8,7,1,0,0,0,0, ,K),8,7, 2,0,0,0,0, > '0,8,7,3,0,0,0,0, >I'0,8,7, 4,0,0,0,0, > '0,8,7,5,0,0,0,0, ,,0,8,7,6,0,0,0,0, \'0,8,7, 7, 0,0,0,0, ,,0,8,7,8,0,0,0,0, 4,0,8,7,9,0,0,0,0, , K3, 8, 8, 0,0,0, 0,0, ,,0,8,8,1,0,0,0,0, ,,0,8,8,2,0,0,0,0, ,,0,8,8,3,0,0,0,0, 4^,8,8,4,0,0,0,0, 4'0,8,8,5,o,o,o,o, 4,0,8,8,6,0,0,0,0, 4,0,8,8,7,0,0,0,0, 4/0,8,8,8,0,0,0,0, 4,0,8,8,9,0,0,0,0, J,o,8,9,o,o,o,o,o, J,o,8,9, 1,0,0,0,0, 4,0,8,9,2,0,0,0,0, 4'0,8,9,3,o,o,o,o, 4,0,8,9,4,0,0,0,0, > '0,8,9,5,0,0,0,0, ,,0,8,9,6,0,0,0,0, ,,0,8,9,7,0,0,0,0, ,,0,8,9,8,0,0,0,0, |o,8j 9,9,0,0,0,0, 1082! 2164 3246 4328 5410 6492 7574 8656 9738 1083 I 1084 2166 2168 3249 1 3252 4332 5415 6498 7581 8664 9747 1085 2170 325s 4340 5425 6510 7595 8680 9 ! 9765 ro86 2172 3258 4344 5430 6516 7602 ' 9774 4336 5420 6504 7588 8672 9756 1087 2174 3261 4348 5435 6522 7609 J 696 9783 1088 2176 3264 4352 5440 6528 7616 8704 9792 1091 2182 3273 4364 5455 6546 7637 8728 9819 10F9 '■ 1090 2178 2180 3267 j 3270 4356 4360 5445 I 5450 6534 I 6540 7623 7630 8712 j 8720 9801 I 9810 1092 ' 1093 2184; 2186 3276 3279 4368 5460 6552 7644 8736 9828 4372 "^465 6558 7651 8744 9837 Dual Logarithms of 4,, 2 = 69314718, 4,, 10 = 230258509, 4,, 4 = 138629437, 4', io2 = 460517019, 4,. 8 = 207944154, 4,, 10^ =c 690775528, powers of 2 and 10. ^, 10* = 921034037, 4,, io5 = 1151292546, 4,, lo*^ = 1381551056, 10'' = 161 1809565, , 10^ =• 1842068074, 10^ = 20723265P4, u 10] Nat. No. 1-0936 to 11045 D. Log. 895.... to 994.... D. No. >I.0,9,0,0, to |0,9,9,9, Natural Dual Dual Numbers. logarithms. Numbers. T-09365527 8955297, 4,0,9,0,0,0,0,0,0, 79464 96 ,,0,9,0,1,0,0,0,0, 90402 97 4,0,9,0,2,0,0,0,0, 1-09401341 98 4,0,9,0,3,0,0,0,0, 12281 99 , ,0,9,0,4,0,0,0,0, 23222 900 ,0,9,0,5,0,0,0,0, ,0,9,0,6,0,0,0,0, 34164 01 45107 02 ,0,9,0,7,0,0,0,0, 56052 03 ,,0,9,0,8,0,0,0,0, 66998 04 , 0,9,0,9,0,0,0,0, 77896 9055247, ,,0,9,1,0,0,0,0,0, 88844 06 > '0,9, 1, 1,0,0,0,0, 99793 07 ,,0,9,1,2,0,0,0,0, ,,0,9,1,3,0,0,0,0, 1-09510743 08 21694 09 ,0,9,1,4,0,0,0,0, 32646 10 ,,0,9,1,5,0,0,0,0, 43599 II ,,0,9,1,6,0,0,0,0, 54553 12 ,,0,9,1,7,0,0,0,0, ,,0,9,1,8,0,0,0,0, 65508 13 76465 14 ,K>,9, 1,9,0,0,0,0, 87374 9155197, ,,0,9,2,0,0,0,0,0, 98333 16 ,0,9,2,1,0,0,0,0, I '09609293 17 ,,0,9,2,2,0,0,0,0, 20254 18 ,,0,9,2,3,0,0,0,0, 31216 19 ,,0,9,2,4,0,0,0,0, 42179 20 |o,9,2,5,o,o,o,o, 53143 21 ,K), 9, 2, 6, 0,0,0,0, 64108 22 4,0,9,2,7,0,0,0,0, 75074 23 4,0,9,2,8,0,0,0,0, 86041 24 4,0,9,2,9,0,0,0,0, 96961 9255147, 4,0,9,3,0,0,0,0,0, 1-09707931 26 '4,0,9,3,1,0,0,0,0,1 18902 27 ,,0,9,3,2,0,0,0,0, 29874 28 ^0,9,3.3,0,0,0,0, 40847 29 > '0,9,3,4,0,0,0,0, 51821 30 >'0,9'3,5,o,o,o,o. 62796 31 4/0,9,3,6,0,0,0,0, 73772 32 >'0,9>3»7,o,o,o,o. 84749 33 ,K), 9,3,8,0,0,0,0, 95727 34 > '0,9,3,9,0,0,0,0, 1-09806658 9355097, ,,0,9,4,0,0,0,0,0, 17639 36 ,,0,9,4,1,0,0,0,0, 28621 37 ,,0,9,4,2,0,0,0,0, 39604 38 > '0,9,4,3,0,0,0,0, 50588 39 ,,0,9,4,4,0,0,0,0, 61573 40 > '0,9,4,5,0,0,0,0, 72559 41 > '0,9,4,6,0,0,0,0, 83546 42 4,0,9,4,7,0,0,0,0, 94534 43 ,,0,9,4,8,0,0,0,0, 1-09905523 44 4^0,9,4,9,0,0,0,0, Natural Numbers. 1-09916465 9455047, Dual Logarithms. 27457 38450 49444 60439 7143s 82432 93430 1-10004429 15429 46 47 48 49 50 51 52 53 54 26381 9554997, 373841 56 48388 59393 70399 81406 92414 1-10103423 14433 25444 57 58 59 60 61 62 63 64 36407 I 9654947, 47421 I 66 67 58436 69452 80469 91487 1-10202506 13526 24547 35569 46543 57568 68594 79621 90649 1-10301678 12708 23739 34771 45804 56790 67826 78863 89901 1-10400940 II 980 23021 34063 45106 56151 68 69 70 71 72 73 74 9754897, 76 77 78 79 80 81 82 83 84 9854847, 86 87 88 89 90 91 92 93 94 Dual Numbers. 4,0,9,5 vO,9,5 4'0,9,5 4'0,9,5 >^o,9>5 4'0,9,5 >k,9,5 4^,9,5 4'0,9,5 io,9,5 4^5,9,6 4,0,9,6 4/0,9,6 4^0,9,6 4^,9,6 4,0,9,6 4/0,9,6 4,0,9,6 4'0,9,6 4,0,9,6 4^,9,7 io,9,7 4^,9,7 4,0,9,7 4^,9,7 4^,9,7 {0,9,7 4,0,9,7 4^,9,7 4^,9,7 jo,9,8 ,,0,9,8 ,,0,9,8 ,,0,9,8 4,0,9,8 {0,9,8 ,,0,9,8 ,,0,9,8 ,K>,9,8 |o,9,8 |o,9,9 ,,0,9,9 >'0,9,9 > '0,9,9 4/0,9,9 {0,9,9 > '0,9,9 > '0,9,9 4/0,9,9 4/0,9,9 0,0,0,0 0,0,0 0,0 0,0 0,0, 0,0 0,0, 0,0; 0,0, 0,0, 0,0, 0,0 0,0. 0,0 0,0 0,0 0,0. 0,0, 0,0, 0,0; 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0, 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0. 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 Multiples of Differences. 1093 2186 3279 4372 5465 6558 7651 8744 9837 1096 2192 3288 4384 5480 6576 7672 8768 9864 I 1099 HOC 2 2198 22CX) 3 3297 3300 4 439<> 4400 S S49S 5500 i 6 6S94 6600 7 7693 7700 « 8792 8800 9 9891 9900 1094 ! 1095 2188 ; 2190 3282 I 3285 4376 I 4380 5470 j 5475 6564 j 6570 7658 I 7665 87521,8760 9845 i 9855 1097 I 1098 2194 I 2196 3291 i 3294 4388 4392 5485 5490 6582 6588 7679 ; 7686 8776 : 87S4 9873 i 9882 IIOI 2;o2 3303 4404 5505 66c6 7707 I 1102 1 103 2 2204 2206 3 3.306 3309 4 4408 4412 1 s 55IO 551=;! 6 6612 6618 7 7714 7721 8 8816 8824 9 9918 99271 9909 1 104 2208 3312 4416 5520 6624 7728 8832 9936 Dual Logarithms of powers of 2 and 10. L 2 — 69314718, 4,, 10 = 230258509, 4,, 10* = 921034037, {, 10' = 1611809565, yf, 4 = 138629437, L io2 = 460517019, 4,, lo^ = 1151292546, ,„ lo^ = 1842068074, 4,, 8 = 207944154, 4', io» = 690775528, 4,, 106 = 1381551056, I, lo^* = 2072326584, Nat. No. riOOO tn 1-U09 D. Log. 953.... to 1052.... D. No. 11,0,0,0, to >H,0,9,9, [II Natural Dual Dual Numbers. Logarithms. Numbers. I'lOOOOOOO 9531018, >rl, 0,0,0,0,0,0,0, IIOOO 54 ,,1,0,0,1,0,0,0,0, 2200I 55 ,,1,0,0,2,0,0,0,0, 33003 56 ,,1,0,0,3,0,0,0,0, 44006 57 >j/ 1,0,0,4,0,0,0,0, 55010 58 ,1,1,0,0,5,0,0,0,0, 66016 59 j^i, 0,0,6, 0,0,0,0, 77023 60 j,i, 0,0,7, 0,0,0,0, 88031 6r ,1,1,0,0,8,0,0,0,0, 99039 62 |i,o,o,9,o,o,o,o, I'lOI lOOOO 9630968, 1,1,0,1,0,0,0,0,0, 2IOII 64 , ,1,0,1,1,0,0,0,0, 32023 65 >, 1, 0,1, 2, 0,0,0,0, 43036 66 wr,o, 1,3,0,0,0,0, 54050 67 >l,i, 0,1,4,0,0,0,0, 65065 68 ,^1, 0,1,5,0,0,0,0, 76082 69 ,,r,o,T, 6,0,0,0,0, 87100 70 ,, 1,0,1,7,0,0,0,0, 98119 71 ,,1,0,1,8,0,0,0,0, rio209i39 72 ,,1,0,1,9,0,0,0,0, 20110 9730918, 4,1,0,2,0,0,0,0,0, 31132 74 j,I,0,2, 1,0,0,0,0, 42155 75 ,1,1,0,2,2,0,0,0,0, 53179 76 ,f,i,o, 2,3,0,0,0,0, 64204 77 il,0,2,4,OiO,0,0, 75231 78 ,,1,0,2,5,0,0,0,0, 86258 79 4,1,0,2,6,0,0,0,0, 97287 80 ,,1,0,2,7,0,0,0,0, 1-10308317 81 ,,1,0,2,8,0,0,0,0, 19348 82 ,,1,0,2,9,0,0,0,0, 30330 9830868, 4,1,0,3,0,0,0,0,0, 41363 84 ,,1,0,3,1,0,0,0,0, 52397 85 ,,1,0,3,2,0,0,0,0, 63432 86 "1,0,3,3,0,0,0,0, ,,1,0,3,4,0,0,0,0, 74468 87 85505 88 wi,o,3,5,o,o,o,o, ,-1,0,3,6,0,0,0,0, 96544 89 1-10407584 90 > '1,0,3,7,0,0,0,0, 18625 91 ,,1,0,3,8,0,0,0,0, 29667 92 "1,0,3,9.0,0,0,0, 40660 9930818, ,,1,0,4,0,0,0,0,0, 51704 94 ,,1,0,4,1,0,0,0,0, 62749 95 ,,1,0,4,2,0,0,0,0, 73795 96 > '1,0,4,3,0,0,0,0, 84843 97 ,,1,0,4,4,0,0,0,0, 95892 98 ,,1,0,4,5,0,0,0,0, 1-10506942 99 ,,1,0,4,6,0,0,0,0, 17993 1000 ,,1,0,4,7,0,0,0,0, 29045 01 ,,1,0,4,8,0,0,0,0, 40098 02 ,,1,0,4,9,0,0,0,0, Natural Dual Numbers. Logarithms. 10030768, 04 OS 06 07 08 09 10 II 12 IOI30718, 14 IS 16 17 18 19 20 21 22 10230668, 24 2S 26- 27 28 29 30 31 32 83086 : 10330618, 94174 34 1-109052631 35 16354 36 27446 37 1*10551100 62x55 73211 84268 95326 I -10606386 17447 28509 39572 50636 61651 72717 83784 94852 i'io7o592i 16992 28064 39137 50211 61286 72313 83390 94468 1^10805547 16628 27710 38793 49877 60962 72048 Dual Numbers. 38539 49633 60728 71824 82921 93969 1-11005068 16169 27271 38374 49478 60583 71689 82796 93904 38 39 40 41 42 10430568, 44 45 46 47 48 49 SO S» 52 ^1,0,5,0,0,0,0,0, '1,0,5,1,0,0,0,0, ,1,0,5,2,0,0,0,0, '1,0,5,3,0,0,0,0, '1,0,5,4,0,0,0,0, '1,0,5,5,0,0,0,0, ,1,0,5,6,0,0,0,0, '1,0,5,7,0,0,0,0, 'I,0^5,8,0,0,0,0, ,1,0,5,9,0,0,0,0, 4,1,0,6,0,0,0,0,0, 4rl,0,6, 1,0,0,0,0, ! 1,0,6, 2,0,0,0,0, 1,0,6,3,0,0,0,0, 1,0,6,4,0,0,0,0, >'i,o,6,5,o,o,o,o, ,,1,0,6,6,0,0,0,0, ,,1,0,6,7,0,0,0,0, ,,1,0,6,8,0,0,0,0, 4,1,0,6,9,0,0,0,0, |i,o,7,o,o,o,o,o, ,,1,0,7,1,0,0,0,0, ,,1,0,7,2,0,0,0,0, >'i,o,7)3)0,o,o,o, i*, 0,7, 4,0,0,0,0, vi,o,7, 5, 0,0,0,0, vl, 0,7, 6,0,0,0,0, "1,0,7,7)0,0,0,0, ,,1,0,7,8,0,0,0,0, 4,1,0,7,9,0,0,0,0, ,,1,0,8,0,0,0,0,0, ,,1,0,8, 1,0,0,0,0, ,,1,0,8,2,0,0,0,0, ,,1,0,8,3,0,0,0,0, 4,1,0,8,4,0,0,0,0, >'i, 0,8,5, 0,0,0,0, ,,1,0,8,6,0,0,0,0, ,,1,0,8,7,0,0,0,0, ,,1,0,8,8,0,0,0,0, ,,1,0,8,9,0,0,0,0, 1,0,9,0,0,0,0,0, 1,0,9,1,0,0,0,0, 1,0,9,2,0,0,0,0, i>o,9,3,o,o,o,o, ii,o,9,4,o,o,o,o, 11,0,9,5,0,0,0,0, 4,1,0,9,6,0,0,0,0, t 1,0,9,7, 0,0,0,0, 1,0,9,8,0,0,0,0, 4,1,0,9,9,0,0,0,0, Multiples of. Differences. 1 100 2200 3300 4400 5500 6600 7700 8800 9900 IIOI 2202 3303 4404 5505 6606 7707 9909 3312 4416 5520 6624 7728 1 1 103 1 104 2 2206 2208 313309 414412 5 5515 6 6618 7 7721 i 8 I 8824 8832 9 : 9927 1 9936 i lno6 1107 2212 2214 |33i« 14424 3321 4428 15530 6636 5535 6642! 7742 8848 9954 7749 8856, 9963! no? 22C4. 3306' 4408' 5510V 661 2. • 7714 8816 99I&- 1 105; 2210'^ 3315 4420 5525 6630 7735 8840 9945- 22l(> 33"4 4452 5543 6648 7756 997a I 1109' 2 2218 3 .3.327 4 4436 5 5545 6 6654 7 77(>3 8 8872 9 9981 IIIO 2220 3330 4440 5550 6660 7770 8880 9990 4,, 2 = 693I4718, 4,, 4 = 138629437, 4,, 8 = 207944154, Dual Logarithms of powers of 2 and 10. 4,, 10 = 230258509, 4,, io2 = 460517019, 4,, io=» = 690775528, 4,, 10* = 921034037 4,, lo^ = 115 1 292546 4, fo« = 1381551056 , ,L 10''^ = 161180 , A, 10'' = 184206 , |i, Io9 = 207232 9565. 68074, 6584, 12] Wat. No. 1-1110 to 11220 D. Log. 1052.... to 1151.... D. No. W,1,0,0, to 11,1,9,9, Natural Numbers. I'lIIOOOOO IIIIO 22221 33333 44446 55560 66676 77793 88911 I'II200030 moo 22221 33343 44466 55590 66716 77843 88971 i'ii3ooioo 11230 22311 33443 44576 55710 66846 77983 89121 i*ii4oo26o 1 1400 22541 33633 44776 55920 67066 78213 89361 i"ii5oo5io 11660 22811 33963 45067 56222 67378 78535 89692 i"ii6oo85i 12011 23172 34334 45497 Dual Logarithms. 10526051, > ,1,1,0,0,0,0,0,0, 53 ,-1,1,0,1,0,0,0,0, 54 > ,1,1,0,2,0,0,0,0, 55 vi, 1,0,3,0,0,0,0, 56 vl, 1,0,4,0,0,0,0, 57 ,,1,1,0,5,0,0,0,0, 58 ,,1,1,0,6,0,0,0,0, 59 ,,1,1,0,7,0,0,0,0, 60 ,,1,1,0,8,0,0,0,0, 61 4,1,1,0,9,0,0,0,0, 10626001, ,,1,1,1,0,0,0,0,0, 63 ,,1,1,1,1,0,0,0,0, 64 ,,1,1,1,2,0,0,0,0, 65 wi, 1, 1,3)0,0,0,0, 66 ,,1,1,1,4,0,0,0,0, 67 68 69 70 71 Dual Numbers. |i)i, 1, 5)0,0,0,0, 1,1,1,6,0,0,0,0, 1)1)1)7)0,0,0,0, 1,1,1,8,0,0,0,0, 1,1,1,9,0,0,0,0, I072595I, ,,1,1,2,0,0,0,0,0, 73 ,,i, 1,2,1,0,0,0,0, 74 ,,1,1,2,2,0,0,0,0, 75 \'1, 1,2,3)0,0,0,0, 76 jl, 1,2,4,0,0,0,0, 77 ,,T, 1, 2,5,0,0,0,0, 78 ,,1,1,2,6,0,0,0,0, 79 ,, 1, 1,2,7,0,0,0,0, 80 ,,1,1,2,8,0,0,0,0, 81 ,,I,I,2,9,0,0,OjO, 10825901, ,,1,1,3,0,0,0,0,0, 83 ,,1,1,3,1,0,0,0,0, 84 >'1, 1,3,2,0,0,0,0, 85 ,,1,1,3,3,0,0,0,0, 86 ll, 1,3,4,0,0,0,0, 87 vi,i,3)5)0,o,o,o, 88 ,,1, 1,3,6,0,0,0,0, 89 >'i)i)3)7,o,o,o,o, 90 ,,1,1,3,8,0,0,0,0, 91 ji, 1,3,9,0,0,0,0, I092585I, 93 94 95 96 97 98 99 1 100 1,1,4,0,0,0,0,0, 1)1)4,1,0,0,0,0, 1,1,4,2,0,0,0,0, T, 1,4,3,0,0,0,0, 4,1,1,4,4,0,0,0,0, '1,1,4,5,0,0,0,0, ,1,1,4,6,0,0,0,0, ,1,1,4,7,0,0,0,0, ,1,1,4,8,0,0,0,0, '1)1)4)9)0,0,0,0, Natural Numbers. i*ii6566i2 67778 78945 90113 1*11701282 12452 23623 34795 45968 57143 68269 79446 90624 i*ii8oi8o3 12983 24164 35346 46530 57715 68901 80037 91225 i*ii9024i4 13604 24795 35987 47181 58376 69572 80769 91917 I'i2003ii6 14316 25517 36720 47924 59129 70335 81542 92750 1T2103909 15119 26331 37543 48757 59972 71188 82405 93623 1*12204842 Dual Logarithms. IIO2580I, 03 04 05 06 07 08 09 10 II Dual Numbers. 13 14 15 16 17 18 19 20 21 II2257OI 23 24 25 26 27 28 29 30 31 II32565I, 33 34 35 36 37 38 39 40 41 11425601, 43 44 45 46 47 48 49 50 51 >, 1, 1, 5,0,0,0,0,0, ,,1,1,5,1,0,0,0,0, ,,1,1,5,2,0,0,0,0, >'!,!, 5,3,0,0,0,0, >|'i, 1)5,4,0,0,0,0, 1,1,5)5)0,0,0,0, 1,1,5,6,0,0,0,0, .1,1,5)7,0,0,0,0, Xi, 1, 5,8,0,0,0,0, ii, 1)5)9)0,0,0,0, 11125751, Xi, 1,6,0,0,0,0,0, ,,1,1,6,1,0,0,0,0, ,,1,1,6,2,0,0,0,0, ,,1,1,6,3,0,0,0,0, 4,1,1,6,4,0,0,0,0, wi, 1,6,5,0,0,0,0, ,,1,1,6,6,0,0,0,0, ,,1,1,6,7,0,0,0,0, ,,1,1,6,8,0,0,0,0, |i, 1,6,9,0,0,0,0, ,,1,1,7,0,0,0,0,0, ,,1,1,7,1,0,0,0,0, ,,1,1,7,2,0,0,0,0, >'i, 1)7,3,0,0,0,0, \ki>i>7,4,o,o,o,o, i,i»7.5,o»o,o,o, 1,1,7,6,0,0,0,0, 1,1,7,7)0,0,0,0, 1,1,7,8,0,0,0,0, |i, 1,7)9,0,0,0,0, ,,1,1,8,0,0,0,0,0, ,,1,1,8,1,0,0,0,0, ,,1,1,8,2,0,0,0,0, ,,1,1,8,3,0,0,0,0, |i, 1,8,4,0,0,0,0, Xi, 1,8,5,0,0,0,0, ,,1,1,8,6,0,0,0,0, ,,1,1,8,7,0,0,0,0, ,,1,1,8,8,0,0,0,0, 4,1,1,8,9,0,0,0,0, ,,1,1,9,0,0,0,0,0, ,,1,1,9,1,0,0,0,0, ,,1,1,9,2,0,0,0,0, >ri, 1, 9,3,0,0,0,0, 4,1,1,9,4,0,0,0,0, >Li, 1,9,5,0,0,0,0, ,,1,1,9,6,0,0,0,0, ,,1,1,9,7,0,0,0,0, ,,1,1,9,8,0,0,0,0, |i)i, 9)9)0,0,0,0, Multiples of Differences. Ilii 2222 3333 4444 5555 6666 7777 9999 1112 2224 3336 4448 5560 6672 7784 10008 III4 "I5 2228 2230 3342 3345 4456 4460 5570 5575 6684 6690 7798 780s 8912 8920 10026 10035 1117 1118 2234 2236 3351 3354 4468 4472 5585 5590 6702 6708 7819 7826 8936 8944 10053 10062 1 1 20 1121 1 2240 2242 1 3360 3363 1 4480 4484 5600 5605 6720 6726 7840 7847 8960 8968 10080 10089 III3 2226 3339 4452 5565 6678 7791 8904 10017 1116 2232 3348 4464 5580 6696 7812 8928 10044 1119 2238 3357 4476 5595 6714 7833 8952 10071 2244 3366 4488 5610 6732 7854 897G 10098 Dual Logarithms of powers of 2 and 10. }, 2 = 693147x8, X, 10^ = 230258509, X, io-« = 921034037, X, lo^ = 1611809565, , 4 = 138629437, ,„ lo^ = 460517019, X, lo^ = 1151292546, X, lo^ = 1842068074, , 8 = 207944154, 4,, io3 = 690775528, J, io« = 1381551056, 4,, lo^ = 2072326584, Nat. No. 11221 to 11332 D. Log. 1152.... to 1251.... D. No. >^1,2,0,0, to ^H,2,9,9, [13 Natural Dual Dual Numbers. Logarithms. Numbers. I'I22IIOOO II521084, ,,1,2,0,0,0,0,0,0, ,,1,2,0,1,0,0,0,0, 22221 53 33443 54 ,,1,2,0,2,0,0,0,0, 44666 55 ,,1,2,0,3,0,0,0,0, 55890 56 ,,1,2,0,4,0,0,0,0, 67II6 57 ,,1,2,0,5,0,0,0,0, 78343 58 ,,1,2,0,6,0,0,0,0, 89571 59 ,,1,2,0,7,0,0,0,0, i"i23oo8oo 60 ,,1,2,0,8,0,0,0,0, 12030 61 ,,1,2,0,9,0,0,0,0, 232II 11621034, ,,1,2,1,0,0,0,0,0, 34443 63 ,,1,2,1,1,0,0,0,0, 45676 64 ,,1,2,1,2,0,0,0,0, > '1,2,1,3,0,0,0,0, 56911 65 68147 66 ,,1,2,1,4,0,0,0,0, 79384 67 >'T, 2,1, 5,0,0,0,0, 90622 68 ,, 1,2,1, 6,0,0,0,0, i'i24oi86i 69 wl, 2,1, 7,0,0,0,0, 13101 70 ,,1,2,1,8,0,0,0,0, 24342 71 ,,1,2,1,9,0,0,0,0, 35534 11720984, ,,1,2,2,0,0,0,0,0, 46778 73 ,,1,2,2,1,0,0,0,0, 58023 74 ,,1,2,2,2,0,0,0,0, 69269 75 ,,1,2,2,3,0,0,0,0, 80516 76 ,,1,2,2,4,0,0,0,0, 91764 77 ,,1,2,2,5,0,0,0,0, 1-12503013 78 ,,1,2,2,6,0,0,0,0, 14263 79 ,,1,2,2,7,0,0,0,0, 25514 80 ,,1,2,2,8,0,0,0,0, 36767 81 ,,1,2,2,9,0,0,0,0, 47970 1 1820934, ,,1,2,3,0,0,0,0,0, 59225 83 ,,1,2,3,1,0,0,0,0, ,,1,2,3,2,0,0,0,0, 70481 84 81738 85 > '1,2,3,3,0,0,0,0, 92996 86 ,,1,2,3,4^0,0,0,0, i'i26o4255 87 ,,1,2,3,5,0,0,0,0, 1551S 88 ,,1,2,3,6,0,0,0,0, 26777 89 >'i,2,3,7,o,o,o,o, 38040 90 ,,1,2,3,8,0,0,0,0, 49304 91 ''1,2,3,9,0,0,0,0, 60518 1 1920884, ,,1,2,4,0,0,0,0,0, 71783 93 ,,1,2,4,1,0,0,0,0, 83050 94 ,,1,2,4,2,0,0,0,0, 94318 95 ,,1,2,4,3,0,0,0,0, 1-12705587 96 ,,1,2,4,4,0,0,0,0, 16858 97 ,,1,2,4,5,0,0,0,0, 28130 98 ,,1,2,4,6,0,0,0,0, 39403 99 ,,1,2,4,7,0,0,0,0, 50677 1200 ,,1,2,4,8,0,0,0,0, 61952 01 4,1,2,4,9,0,0,0,0, Natural Dual Dual Numbers. Logarithms. Numbers. 1-12773178 12020834, ,,1,2,5,0,0,0,0,0, 84455 03 > '1,2,5,1,0,0,0,0, 95733 04 ,,1,2,5,2,0,0,0,0, "1,2,5,3,0,0,0,0, 1-12807013 05 18294 06 ,,1,2,5,4,0,0,0,0, 29576 07 wi,2,5,5,o,o,o,o. 40859 08 4.1,2,5,6,0,0,0,0, 52143 09 V '1,2,5,7,0,0,0,0, ^ '1,2,5,8,0,0,0,0, 63428 10 74714 II ,,1,2,5,9,0,0,0,0, 85951 12120784, 4,1,2,6,0,0,0,0,0, 97240 13 ,,1,2,6,1,0,0,0,0, ,,1,2,6,2,0,0,0,0, 1-12908530 14 19821 15 ,,1,2,6,3,0,0,0,0, 4,1,2,6,4,0,0,0,0, 31113 16 42406 17 4,1,2,6,5,0,0,0,0, 53700 18 , ,1,2,6,6,0,0,0,0, 64995 19 ,,1,2,6,7,0,0,0,0, 76291 20 ,-1,2,6,8,0,0,0,0, 87589 21 ,,1,2,6,9,0,0,0,0, 98837 12220734, ,,1,2,7,0,0,0,0,0, 1-13010137 23 ,,1,2,7,1,0,0,0,0, 21438 24 ,,1,2,7,2,0,0,0,0, 32740 25 ,,1,2,7,3,0,0,0,0, 44043 26 ,,1,2,7,4,0,0,0,0, 55347 27 > '1,2,7,5,0,0,0,0, 66653 28 ,,1,2,7,6,0,0,0,0, 77960 29 , ,1,2,7,7,0,0,0,0, 89268 30 ,,1,2,7,8,0,0,0,0, 1-13100577 31 ,-1,2,7,9,0,0,0,0, 1 1836 12320684, ,,1,2,8,0,0,0,0,0, 23147 33 ,,1,2,8,1,0,0,0,0, 34459 34 ,,1,2,8,2,0,0,0,0, 45772 35 ,,1,2,8,3,0,0,0,0, 57087 36 ,,1,2,8,4,0,0,0,0, 68403 37 ,,1,2,8,5,0,0,0,0, 79720 38 ,,1,2,8,6,0,0,0,0, 91038 39 ,,1,2,8,7,0,0,0,0, 1-13202357 40 , ,1,2,8,8,0,0,0,0, 13677 41 ,,1,2,8,9,0,0,0,0, 24948 12420634, ,,1,2,9,0,0,0,0,0, 36270 43 ,,1,2,9,1,0,0,0,0, 47594 44 ,,1,2,9,2,0,0,0,0, 589^9 45 ,,1,2,9,3,0,0,0,0, ,,1,2,9,4,0,0,0,0, 70245 46 81572 47 wl, 2,9,5,0,0,0,0, 92900 48 ,,1,2,9,6,0,0,0,0, 1-13304229 49 ,,1,2,9,7,0,0,0,0, 15559 50 ,,1,2,9,8,0,0,0,0, 26891 51 ,,1,2,9,9,0,0,0,0, Multiples of Differences. 1 122 1123 2244 2246 33(>6 3369 4488 4492 5610 sfeis 6732 673« 7«S4 7861 8976 8984 10098 10107 I 1 125 1 126 2 2250 2252 3 3375 337« 4 4500 4504 5 5625 5630 6 67SO 6756 7 7875 7882 8 9000 9008 9 10125 10134 1 128 1129 2256 2258 33»4 33«7 4512 4516 5640 5645 6768 6774 7896 7903 9024 9032 10152 10161 1 131 1132 2262 2264 3393 3396 4524 4528 scss 5660 6786 6792 7917 7924 9048 9056 10179 10188 1 124 2248 3372 4496 5620 6744 7868 8992 IOII6 II27 2254 3381 4508 5635 6762 7889 9016 IOI43 II30 2260 3390 4520 5650 6780 7910 9040 IOI70 "33 2266 3399 4532 5665 6798 7931 9064 10197 Dual Logarithms of powers of 2 and 10. 4„ 2 = 69314718, I, 10 = 230258509, I, 10* = 921034037, J,, lo'^ = 1611809565, 4., 4 = 138629437, 4^, lo'^ = 460517019, 4^, 10^ = 1151292546, ,,, 10^ =■ 1842068074, 4,, 8 = 207944154, 4,, io3 = 690775528, I, 10^ = 1381551056, I, io» = 2072326584, M] Nat. No. 1-1333 to 11446 D. Log. 1251.... to 1350.... D. No. >H,3,0,0, to il,3,9,9, Natural Dual Dual Numbers. I-I3333IIO Logarithms. 12516117, Numbers. J,i,3,o,o,o,o,o,o, 44443 52 ,,1,3,0,1,0,0,0,0, 55777 53 ,,1,3,0,2,0,0,0,0, 67113 54 >'i,3>o,3,o,o,o,o, 78450 55 ,,1,3,0,4,0,0,0,0, 89788 56 > '1,3)0,5,0,0,0,0, 1-13401127 57 ,,1,3,0,6,0,0,0,0, 12467 58 ^ '1,3,0,7,0,0,0,0, 23808 59 ,,1,3,0,8,0,0,0,0, 35150 60 ,,1,3,0,9,0,0,0,0, 46443 12616067, ,,1,3,1,0,0,0,0,0, -'1,3,1,1,0,0,0,0, 57788 62 69134 ^Z >'r,3,i, 2,0,0,0,0, 80481 64 >'i,3,i, 3,0,0,0,0, 91829 65 ,,1,3,1,4,0,0,0,0, 1-13503178 66 ,,1,3,1,5,0,0,0,0, 14528 67 ,,1,3,1,6,0,0,0,0, 25879 68 ,,1,3,1,7,0,0,0,0, 37232 69 ,,1,3,1,8,0,0,0,0, 48586 70 > '1,3,1,9,0,0,0,0, 59889 12716017, "1,3,2,0,0,0,0,0, 71245 72 ,,1,3,2,1,0,0,0,0, 82602 73 >,I,3,2,2,0,0,0,0, 93960 74 >'i,3,2,3,o,o,o,o. 1-13605319 75 wi,3,2,4,o,o,o,o. 16680 16 >'T,3,2,5,o,o,o,o, 28042 77 ,,1,3,2,6,0,0,0,0, 39405 78 >'i, 3,2, 7,0,0,0,0, 50769 79 ,,1,3,2,8,0,0,0,0, 62134 80 > '1,3,2,9,0,0,0,0, 73449 12815967, ,,1,3,3,0,0,0,0,0, 84816 82 "1,3,3,1,0,0,0,0, 96184 83 ,,1,3,3,2,0,0,0,0, i"i37o7554 84 "t, 3,3,3,0,0,0,0, 18925 85 > '1,3,3,4,0,0,0,0, 30297 86 >'i,3,3,5,o,o,o,o. 41670 87 > '1,3,3,6,0,0,0,0, 53044 88 >'i,3,3, 7,0,0,0,0, 64419 89 ,,1,3,3,8,0,0,0,0, 75795 90 > '1,3,3,9,0,0,0,0, 87122 12915917, ,,1,3,4,0,0,0,0,0, 98501 92 ,,1,3,4,1,0,0,0,0, 1T3809881 93 >'i,3>4,2,o,o,o,o, 21262 94 > '1,3,4,3,0,0,0,0, 32644 95 > '1,3,4,4,0,0,0,0, 44027 96 "1,3,4,5,0,0,0,0, 55411 97 > '1,3,4,6,0,0,0,0, 66797 98 > '1,3,4,7,0,0,0,0, 78184 99 ,,1,3,4,8,0,0,0,0, 89572 1300 >'i, 3,4,9,0,0,0,0, Natural Dual Dual Numbers. Logarithms. Numbers. 1-13900909 13015867, \'i, 3, 5, 0,0,0,0,0, 12299 02 >'i, 3, 5, 1, 0,0,0,0, 23690 03 ,,1,3,5,2,0,0,0,0, 35082 04 > '1,3,5,3,0,0,0,0, 46476 05 "1,3,5,4,0,0,0,0, 57871 06 >'i,3,5,S>o,o,o,o, 69267 07 "1,3,5,6,0,0,0,0, 80664 08 >'i,3, 5,7,0,0,0,0, 92062 09 > '1,3,5,8,0,0,0,0, i-i4oo346i 10 >'i,3,5,9>o,o,o,o, 14810 13115817, > '1,3,6,0,0,0,0,0, 26211 12 ,,1,3,6,1,0,0,0,0, 37614 13 ,,1,3,6,2,0,0,0,0, 49018 14 >'i, 3, 6,3, 0,0,0,0, 60423 15 "1,3,6,4,0,0,0,0, 71829 16 > '1,3,6,5,0,0,0,0, 83236 17 > '1,3,6,6,0,0,0,0, 94644 18 > '1,3,6,7,0,0,0,0, 1-14106053 19 > '1,3,6,8,0,0,0,0, 17464 20 ,,1,3,6,9,0,0,0,0, 28825 I3215767, ,,1,3,7,0,0,0,0,0, 40238 22 \'i, 3, 7, 1, 0,0,0,0, 51652 23 >'i,3,7,2,o,o,o,o. 63067 24 vi, 3,7, 3, 0,0,0,0, 74483 25 "1,3,7,4,0,0,0,0, 85900 26 > '1,3,7,5,0,0,0,0, 97319 27 vi,3,7,6,o,o,o,o, 1-14208739 28 "1,3,7,7,0,0,0,0, 20160 29 > '1,3,7,8,0,0,0,0, 31582 30 vi, 3,7, 9,0,0,0,0, 42954 I3315717, vT, 3, 8,0,0,0,0,0, 54378 32 ,,1,3,8,1,0,0,0,0, 65803 33 ,,1,3,8,2,0,0,0,0, 77230 34 ,,1,3,8,3,0,0,0,0, 88658 35 "1,3,8,4,0,0,0,0, 1-14300087 36 ,,1,3,8,5,0,0,0,0, 11517 37 > '1,3,8,6,0,0,0,0, 22948 38 > '1,3,8,7,0,0,0,0, 34380 39 ,,1,3,8,8,0,0,0,0, 45813 40 ,,1,3,8,9,0,0,0,0, 57197 13415667, ,,1,3,9,0,0,0,0,0, 68633 42 > '1,3,9,1,0,0,0,0, 80070 43 ,,1,3,9,2,0,0,0,0, 91508 44 >'i,3,9,3,o,o,o,o. 1-14402947 45 > '1,3,9,4,0,0,0,0, 14387 46 "1,3,9,5,0,0,0,0, 25829 47 "1,3,9,6,0,0,0,0, 37272 48 "1,3,9,7,0,0,0,0, 48716 49 >'i, 3,9,8,0,0,0,0, 60161 1 50 "1,3,9,9,0,0,0,0, Multiples of Differences. I 1 133 "34 1 2 2266 2268 1 3 3399 3402 4 4532 4S3(> 5 5665 5670 b 6798 6804 7 7931 793« 8 9064 9072 9 10197 10206 1136 "37 2272 2274 3408 34" 4544 4548 5680 S68s 68x6 6822 7952 7959 9088 9096 ,10224 10233 I "39 1140 2 2278 2280 3 3417 3420 4 4,556 4560 5 5695 5700 6 6834 6840 7 7973 7980 8 9112 9120 9 10251 10260 1142 2284 "43 2286 3426 4568 3429 4572 5710 6852 7994 5715 6858 8001 9136 10278 9144 10287 4,, 2 = 69314718, i, 4 = 138629437, , 8 =. 2< Dual Logarithms of powers of 2 and 10. Y' 10^ = 230258509, 4,, 10* = 921034037, 4, io2 = 460517019, 1 lo^ = 1 15 1292546, I, io« = 1381551056, 207944154, 4,, io3 = 690775528, 10''^ = 16118095 )5, 10* = 184206807 \, io9 = 2072326584, Nat. No. 11446 to 11560 D. Log. 1351.... to 1450.... D. No. |1,4,0,0, to |1,4,9,9, [15 Natural Dual Dual Numbers. Logarithms. Numbers. ri446644i 13511150, \, 1, 4,0,0, 0,0, 0,0, ,-1,4,0,2,0,0,0,0, 7788S 52 ^933^ 53 ,,1,4,0,1,0,0,0,0, 1-14500785 54 >^i,4,o,3,o,o,o,o, 12235 55 >I'i,4,o,4>o,o,o,o, 23686 56 4^1,4,0,5,0,0,0,0, 35138 57 4,1,4,0,6,0,0,0,0, 46592 58 vI,i,4,o,7,o,o,o,o, 58047 59 vj/1, 4,0,8, 0,0,0,0, 69503 60 v^i,4,o, 9,0,0,0,0, 80907 13611100, ,,1,4,1,0,0,0,0,0, 92365 62 vl,i,4, 1, 1,0,0,0,0, I "14603824 ^3 ,,r, 4,1, 2,0,0,0,0, 15284 64 ,,1,4,1,3,0,0,0,0, 26746 65 4^^4,1,4,0,0,0,0, 38209 66 4,T, 4, 1,5,0,0,0,0, 49673 67 ,,1,4,1,6, 0,0,0,0, 61138 68 ,,1,4,1,7,0,0,0,0, 72604 69 ,,1,4,1,8,0,0,0,0, 84071 70 ,,1,4,1,9,0,0,0,0, 95488 13711050, ,,1,4,2,0,0,0,0,0, r -14706958 72 ,,1,4,2,1,0,0,0,0, 18429 73 , ,1,4,2,2,0,0,0,0, "1,4,2,3,0,0,0,0, 29901 74 41374 75 ,,1,4,2,4,0,0,0,0, 52848 76 ,,1,4,2,5,0,0,0,0, 64323 77 ,,1,4,2,6,0,0,0,0, 75799 78 ,,1,4,2,7,0,0,0,0, 87277 79 ,,1,4,2,8,0,0,0,0, 98756 80 ,,1,4,2,9,0,0,0,0, 1 •14810183 13811000, > '1,4,3,0,0,0,0,0, 21664 82 >'i, 4,3, 1,0,0,0,0, >'i,4,3,2,o,o,o,o, 33146 83 44629 84 > '1,4,3,3,0,0,0,0, > '1,4,3,4,0,0,0,0, 56113 85 67599 86 wi,4,3,5,o,o,o,o. 79086 87 X '1,4,3,6,0,0,0,0, 90574 88 > '1,4,3,7,0,0,0,0, I 14902063 89 ,,1,4,3,8,0,0,0,0, I35S3 90 • wi, 4,3, 9,0,0,0,0, 24993 13910950, ,,1,4,4,0,0,0,0,0, 36485 92 ,,1,4,4,1,0,0,0,0, 47979 93 ,,1,4,4,2,0,0,0,0, 59474 94 > '1,4,4,3,0,0,0,0, 70970 95 ,,1,4,4,4,0,0,0,0, 82467 96 wi,4,4,5,o,o,o,o, 93965 97 ,,1,4,4,6,0,0,0,0, 1-15005464 98 > '1,4,4,7,0,0,0,0, 16965 99 ,,1,4,4,8,0,0,0,0, 28467 1400 ,,1,4,4,9,0,0,0,0, Natural Numbers, 1-15039918 51422 62927 74433 85940 97449 1-15108959 20470 31982 43495 54958 66473 77990 89508 1-15201027 12547 24068 35590 47114 58639 70113 81640 93168 1*15304697 16227 27759 39292 50826 62361 73897 85383 96922 1-15408462 20003 31545 43088 54632 66177 77724 89272 1-15500768 12318 23869 35421 46975 58530 70086 81643 93201 1-15604760 Dual Logarithms. 1 40 1 0900, 02 03 04 05 06 07 08 09 10 141 10850, 12 13 14 15 16 17 18 19 20 14210800, 22 23 24 25 26 27 28 29 30 I43IO750, 32 33 34 35 36 37 38 39 40 14410700, 42 43 44 45 46 47 48 49 50 Dual Numbers. 4,5,0 ,4,5,1 ,4,5,2 ,4,5,3 ,4,5,4 ,4,5,5 ,4,5,6 ,4,5,7 ,4,5,8 ,4,5,9 ,4,6,0 ,4,6,1 ,4,6,2 ,4,6,3 ,4,6,4 ,4,6,5 ,4,6,6 ,4,6,7 ,4,6,8 ,4,6,9 ,4,7,0: ,4,7,1 ,4,7,2 ,4,7,3 ,4,7,4; ,4,7,5 ,4,7,6 ,4,7,7 ,4,7,8 ,4,7,9 ,4,8,0, ,4,8,1 ,4,8,2 ,4,8,3 ,4,8,4 ,4,8,5 ,4,8,6 ,4,8,7 ,4,8,8 ,4,8,9 ,4,9,0 ,4,9,1 ,4,9,2 ,4,9,3 ,4,9,4 ,4,9,5 ,4,9,6 ,4,9,7 ,4,9,8 ,4,9,9 Multiples of Differences. 1 144 2288 1 145 2290 3432 4576 3435 4580 5720 6864 8008 6870 8015 9152 10296 9160 10305 1 147 1 148 2294 2296 3441 3444 4588 4592 ■573'; 5740 6882 6888 8029 8036 9176 9184 10323 10332 1150 "SI 2300 2302 3450 4600 3453 4604 5750 6900 8050 9200 6906 8057 9208 10350 10359 . "53 "54 2306 2308 3459 3462 4612 4616 5765 5770 6918 6924 8071 8078 9224 9232 10377 10386 II56 2312 3468 4624 5780 6936 8092 9248 10404 1 146 2292 3438 4584 5730 6876 8022 9168 I03I4 "49 2298 3447 4596 5745 6894 8043 9192 10341 1 1 52 2304 3456 4608 5760 6912 8064 9216 10368 "55 2310 3465 4620 5775 6930 8085 9240 10395 Dual Logarithms of powers of 2 and 10. ,!„ 2 -= 693r47i8, ^, lo = 230258509, ^, 10* = 921034037, L 10 7 _ vl„ 4 = 138629437, I, 10 4,, 8 = 207944154, 4,, lo' = 460517019, X, io5 = 1151292546, = 690775528, 4r, lo'' = 1381551056, 1611809565, 1842068074, 4,, TO** = 2072326584, 16] Nat. No. ri561 to ri676 D. Log. 1450.... to 1549.... D. No. |1,5,0,0, to .I'ljSjGjO, Natural Numbers. n56iiio6 22667 34229 45792 57357 68923 80490 92057 1-15703626 15196 26717 38290 49864 61439 73015 84592 96170 1-15807750 19331 30913 42444 54028 65613 77200 88788 1-15900377 11967 23558 35150 46744 58286 \2 81479 93077 1*16004676 16276 27878 39481 51085 626*90 74244 85851 97460 i"i6i0907o 20681 32293 43906 55520 67136 78753 Dual Logarithms. 14506183, 51 52 53 54 55 56 57 58 59 14606133, 6i 62 63 64 65 66 67 68 69 14706083, 71 72 73 74 75 76 77 78 79 14806033, 81 82 83 84 85 86 87 88 89 14905983, 91 92 93 94 95 96 97 98 99 Dual Numbers. ^1,5 U^S 11,5 >I'i,5 fi,5 |i,5 U.S |i,5 wi,5 4'i,5 >l'i»5 >l'i,5 |i,5 |i,5 |i,5 4'i^5 |i,5 ii,5 >I'i,5 4^1,5 4'i>5 Us Us Us U,s Us U,s U.s Us U,s Us U,s ^!'I,5 U,s U,s U^s |i,5 4^1,5 4^1,5 {1,5 |i,5 Us U^s U^ U^s U^s 0,0,0,0,0,0 0,1,0,0,0,0 0,2,0,0,0,0 0,3,0,0,0,0 0,4,0,0,0,0 0,5,0,0,0,0 0,6,0,0,0,0 0,7,0,0,0,0 0,8,0,0,0,0 0,9,0,0,0,0 1,0,0,0,0,0 1,1,0,0,0,0 1,2,0,0,0,0 1,3,0,0,0,0 1,4,0,0,0,0 1,5,0,0,0,0 T, 6,0,0,0,0 1,7,0,0,0,0 1,8,0,0,0,0 1,9,0,0,0,0 2,0,0,0,0,0 2,1,0,0,0,0 2,2,0,0,0,0 2,3,0,0,0,0 2,4,0,0,0,0 2,5,0,0,0,0 2,6,0,0,0,0 2,7,0,0,0,0 2,8,0,0,0,0 2,9,0,0,0,0 3,0,0,0,0,0 3,1,0,0,0,0. 3,2,0,0,0,0 3,3,0,0,0,0 3,4,0,0,0,0 3,5,0,0,0,0 3,6,0,0,0,0 3,7,0,0,0,0 3,8,0,0,0,0 3,9,0,0,0,0 4,0,0,0,0,0 4,1,0,0,0,0 4,2,0,0,0,0 4,3,0,0,0,0^ 4,4,0,0,0,0 4,5,0,0,0,0 4,6,0,0,0,0 4,7,0,0,0,0 4,8,0,0,0,0 4,9,0,0,0,0 Natural Dual Dual Numbers. Logarithms. Numbers. 1-16190319 15005933, ''1,5,5,0,0,0,0,0, 1-16201938 01 >, 1, 5,5, 1, 0,0,0,0, > '1,5,5,2,0,0,0,0, 13558 02 25179 03 wi,5,5.3,o,o,o,o. 36802 04 vi,5,5>4,o,o,o,o. 48426 05 ^'i,5'5,5,o,o,o,o. 60051 06 > '1,5,5,6,0,0,0,0, 71677 07 >'i,5'5>7,o,o,o,o, 83304 08 >, 1, 5,5, 8,0,0,0,0, 94932 09 > '1,5,5,9,0,0,0,0, I-16306509 15105883, ,,1,5,6,0,0,0,0,0, 18140 II wl, 5, 6,1, 0,0,0,0, 29772 12 ,,1,5,6,2,0,0,0,0, 41405 13 ,,1,5,6,3,0,0,0,0, 53039 14 ,,1,5,6,4,0,0,0,0, 64674 15 ,,1,5,6,5,0,0,0,0, ,,1,5,6,6,0,0,0,0, 76310 16 87948 17 ,,1,5,6,7,0,0,0,0, ,,1,5,6,8,0,0,0,0, 99587 18 1-16411227 19 ,,1,5,6,9,0,0,0,0, 22815 15205833, ,,1,5,7,0,0,0,0,0, 34457 21 > '1,5,7,1,0,0,0,0, 46100 22 ,,1,5,7,2,0,0,0,0, 57745 23 vi, 5, 7,3,0,0,0,0, 69391 24 >'i, 5,7,4,0,0,0,0, 81038 25 ^'i, 5, 7,5,0,0,0,0, 92686 26 ,,1,5,7,6,0,0,0,0, >'i, 5, 7,7,0,0,0,0, 1-16504335 27 15985 28 ,,1,5,7,8,0,0,0,0, 27637 29 vi, 5,7, 9,0,0,0,0, 39238 15305783, ,,1,5,8,0,0,0,0,0, 50892 31 ,,1,5,8,1,0,0,0,0, ,,1,5,8,2,0,0,0,0, 62547 32 74203 33 ,,1,5,8,3,0,0,0,0, ,,1,5,8,4,0,0,0,0, 85860 34 97519 35 vi, 5,8,5,0,0,0,0, 1-16609179 36 ,,1,5,8,6,0,0,0,0, 20840 37 wi,5,8,7,o,o,o,o. 32502 38 4,1,5,8,8,0,0,0,0, 44165 39 .'i,5'8,9,o,o,o,o. 55778 15405733, ^ '1,5,9,0,0,0,0,0, 67444 41 vi, 5,9,1,0,0,0,0, 79111 42 ,,1,5,9,2,0,0,0,0, 90779 43 > '1,5,9,3,0,0,0,0, 1-16702448 44 4'i»5,9,4,o,o,o,o, 14118 45 {1,5,9,5,0,0,0,0, 4,1,5,9,6,0,0,0,0, 25789 46 37462 47 4^1,5,9,7,0,0,0,0, 49136 48 4,1,5,9,8,0,0,0,0, 608 1 1 49 4^1, 5, 9,9,0,0,0,0, Multiples of Differences. II56 "57 2312 2314 3468 3471 4624 4628 57«o ,S7«^ 6936 6942 8092 8099 9248 9256 10404 10413 IIS9 1160 2318 2320 3477 3480 4636 4640 5795 5800 6954 6960 8113 8120 9272 9280 1 043 1 10440 1162 1163 2324 2326 3486 3489 4648 4652 5810 5«i5 6972 6978 «i.34 8141 9396 9304 10458 10467 1165 1166 2330 2.332 3495 3498 4660 4664 5825 5830 6990 6996 8155 8162 9320 9328 10485 10494 Dual Logarithms of powers of 2 and 10. 4,, 2 = 69314718, 4^, 10 = 230258509, 4,, 10* = 921034037, 4'' 10^ = 1611809565, J,, 4 = 138629437, 4', lo^ = 460517019, 4', lo^ = 1151292546, \, 10" = 1842068074, 4,, 8 = 207944154, 4,, io3 = 690775528, i, 106 = 1381551056, 4,, io9 = 2072326584, Nat. No. ri676 to 11792 D. Log. 1550.... to 1649.... D. No. |1,6,0,0, to 4^1,6,9,9, [17 Natural Dual Dual Numbers. Logarithms. Numbers. 1-16767217 15501216, ,,1,6,0,0,0,0,0,0, > ,1,6,0,1,0,0,0,0, 78894 51 90572 52 vl, 6, 0,2, 0,0,0,0, i'i68o225i 53 ^156,0,3,0,0,0,0, wl, 6,0,4,0,0,0,0, 13931 54 25612 55 ,,1,6,0,5,0,0,0,0, 37295 56 ,,1,6,0,6,0,0,0,0, 48979 57 ,,1,6,0,7,0,0,0,0, 60664 58 ,,1,6,0,8,0,0,0,0, 72350 59 ,,1,6,0,9,0,0,0,0, 83984 15601166, ,,1,6,1,0,0,0,0,0, 95672 61 ,,1,6,1,1,0,0,0,0, i"i6907362 62 ,,1,6,1,2,0,0,0,0, 19053 63 ,,1,6,1,3,0,0,0,0, 30745 64 ,,1,6,1,4,0,0,0,0, 42438 65 ,,1,6,1,5,0,0,0,0, 54132 66 ,, 1, 6, 1, 6, 0,0, 0,0, 65827 67 ,,1,6,1,7,0,0,0,0, 77524 68 ,,1,6,1,8,0,0,0,0, 89222 69 ,,1,6,1,9,0,0,0.0, i*i7ooo868 T5701116, \i.T, 6,2, 0,0,0,0,0, 12568 71 ,,1,6,2,1,0,0,0,0, 24269 72 ,,1,6,2,2,0,0,0,0, 35971 73 >'i)6,2, 3, 0,0,0,0, 47675 74 ,,1,6,2,4,0,0,0,0, 59379 75 ,,1,6,2,5,0,0,0,0, 71085 76 ,,1,6,2,6,0,0,0,0, 82792 77 ,,1,6,2,7,0,0,0,0, 94500 78 ,,1,6,2,8,0,0,0,0, i'i7io6209 79 4,1,6,2,9,0,0,0,0, 17869 15801066, J,1, 6,3,0,0,0,0,0, |i, 6,3, 1,0,0,0,0, 29581 81 41294 82 >|,i, 6,3,2,0,0,0,0, 53008 83 4^i,6,3,3>o,o,o,o, 64723 84 |i, 6,3, 4,0,0,0,0, 76439 85 1156,3,5,0,0,0,0, 4,1,6,3,6,0,0,0,0, 88157 86 99876 87 ii,6,3,7,o,o,o,o, 4/156,3,8,0,0,0,0, i'i72ii596 88 23317 89 4'i>6,3,9,o,o,o,o, 34987 15901016, ,,1,6,4,0,0,0,0,0, 46710 91 ,,1,6,4,1,0,0,0,0, 58435 92 ,,1,6,4,2,0,0,0,0, 70161 93 "i>6,4,3, 0,0,0,0, 81888 94 4.1,6,4,4,0,0,0,0, 93616 95 4'i.6,4,5>o,o,o,o, i'i73o5345 96 4,1,6,4,6,0,0,0,0, 17076 97 4,1,6,4,7,0,0,0,0, 28808 98 4,1,6,4,8,0,0,0,0, 40541 1 99 4,1,6,4,9,0,0,0,0, Natural Dual Dual Numbers. Logarithms. Numbers. 1-17352222 16000966, ,,1,6,5,0,0,0,0,0, 63957 01 ,,1,6,5,1,0,0,0,0, 75693 02 ,,1,6,5,2,0,0,0,0, 87431 03 1 '1,6,5,3,0,0,0,0, 99170 04 >'i»6,5,4,o,o,o,o. I-17410910 05 > '1,6,5,5,0,0,0,0, ,,1,6,5,6,0,0,0,0, 22651 06 34393 07 >'i,6,5, 7,0,0,0,0, 46136 08 ,,1,6,5,8,0,0,0,0, 57881 09 ,,1,6,5,9,0,0,0,0, 69574 16100916, ,,1,6,6,0,0,0,0,0, 81321 II 4,1,6,6,1,0,0,0,0, 93069 12 ,,1,6,6,2,0,0,0,0, 1-17504818 13 ,,1,6,6,3,0,0,0,0, 16568 14 ,,1,6,6,4,0,0,0,0, 28320 15 ,,1,6,6,5,0,0,0,0, 40073 16 ,,1,6,6,6,0,0,0,0, 51827 17 ,,1,6,6,7,0,0,0,0, 63582 18 ,,1,6,6,8,0,0,0,0, 75338 19 ,,1,6,6,9,0,0,0,0, 87044 162OC866, ,rl, 6,7,0,0,0,3,0, 98803 21 ,,1,6,7,1,0,0,0,0, 1-17610563 22 ,,1,6,7,2,0,0,0,0, 22324 23 ,,1,6,7,3,0,0,0,0, 34086 24 ,,1,6,7,4,0,0,0,0, 45849 25 wi,6,7,5,o,o,o,o. 57614 26 ,,1,6,7,6,0,0,0,0, 69380 27 wi,6,7,7,o,o,o,o. 81147 28 ,,1,6,7,8,0,0,0,0, 92915 29 ,,1,6,7,9,0,0,0,0, 1-17704631 16300816, ,,1,6,8,0,0,0,0,0, 1 640 1 31 ,,1,6,8,1,0,0,0,0, 28173 32 ,,1,6,8,2,0,0,0,0, 39946 33 > '1,6,8,3,0,0,0,0, 51720 34 ,,1,6,8,4,0,0,0,0, 63495 35 vi,6,8,5,o,o,o,o. 75271 36 ,,1,6,8,6,0,0,0,0, 87049 37 ,,1,6,8,7,0,0,0,0, 98828 38 ,,1,6,8,8,0,0,0,0, 1-17810608 39 ,,1,6,8,9,0,0,0,0, 22336 16400766, ,,1,6,9,0,0,0,0,0, 34118 41 ,,1,6,9,1,0,0,0,0, 45901 42 ,,1,6,9,2,0,0,0,0, 57686 43 wi, 6,9,3,0,0,0,0, 69472 44 ,,1,6,9,4,0,0,0,0, 81259 45 ,,1,6,9,5,0,0,0,0, 93047 46 ,,1,6,9,6,0,0,0,0, 1-17904836 47 wi, 6,9,7,0,0,0,0, 16626 48 ,,1,6,9,8,0,0,0,0, 28418 49 ,,1,6,9,9,0,0,0,0, Multiples of Differences. II67 1x68 2334 2336 3501 3504 4668 4672 .■jHi-; 5840 7002 7008 8169 8176 933(> 9344 10503 105 1 2 \ I 1170 1171 2 2340 2342 3 3SIO 3513 4 4680 4684 5 .S«5o ,S«,S5 6 7020 7026 7 8190 8197 8 9360 9368 9 10530 10539 II69 2338 3507 4676 5845 7014 8183 9352 I052I 1172 2344 3516 IJ73 1174 2346 2348 3519 3522 4692 4696 5865 5870 7038 7044 82II 8218 9384 9392 I05S7 10566 1176 1177 2352 2354 3528 3531 4704 4708 5880 .S88S 7056 7062 8232 8239 9408 9216 10584 10593 5860 7032 8204 9376 10548 "75 2350 3525 4700 587s 7050 8225 9400 10575 1178 2356 3534 4712 5890 7068 8246 9424 1060a 1179 2358 3537 4716 589s 7074 8253 9432 1061 1 !, 2 = 69314718, 4,, , 4 = 138629437, L , 8 = 207944154, 4,, Dual Logarithms of 10 = 230258509, lo^ =: 46o5i7or9, 10^ = 690775528, powers of 2 and 10. 4,, 10* = 921034037, 4" 1°^ = 161 1809565, 4,, lo^ = 1151292546, J,, lo^ = 1842068074, I, lo*"' = 1381551056, I, io» = 2072326584, 1.8] Nat. No. 11793 to 1 1910 D. Log. 1649.... to 1748... D. No. 11,7,0,0, to 11,7,9,9, Natural Numbers, 1-17934889 46682 58477 70273 82070 93868 I •18005667 17468 29270 41073 52^4 64029 76435 88243 i'i8iooo52 11862 23673 35485 47299 59"4 70877 82694 94512 i'i82o633i 18152 29974 41797 53621 65446 77273 89048 I-] 8300877 12707 24538 36370 48204 60039 7187s 83712 95550 1-18407337 19178 31020 42863 54707 66552 78399 90247 1-18502096 13946 Dual Logarithms. 16496249, 50 51 52 53 54 55 56 57 58 16596199, 60 61 62 63 64 65 66 67 68 1 6696149, 70 71 72 73 74 75 76 77 78 16796099, 80 81 82 83 84 85 86 87 88 16896049, 90 91 92 93 94 95 96 97 98 Dual Numbers. J,l, 7, 0,0,0,0,0,0 Xl, 7,0,1,0,0,0,0 |l, 7,0,2,0,0,0,0 >|'i,7>o,3>o,o,o,o ,irl,7,0,4,0,0,0,0 >|'i,7,o,5,o,o,o,o 4,1,7,0,6,0,0,0,0 4'i>7,o,7,o,o,o,o 4,1,7,0,8,0,0,0,0 ii,7>o,9>o,o,o,o 4,1,7,1,0,0,0,0,0, 4,1,7,1,1,0,0,0,0 4,1,7,1,2,0,0,0,0 ii,7,i»3»o,o,o,o 4'I.7,i>4jO,o,o,o, 4,1,7,1,5,0,0,0,0 i 1,7, T, 6,0,0,0,0 1,7,1.7.0,0,0,0 4,1,7,1,8,0,0,0,0 >^J, 7, 1,9,0,0,0,0 4^1,7,2,0,0,0,0,0, 4,1,7,2,1,0,0,0,0 4,1,7,2,2,0,0,0,0 ^'i. 7. 2,3, 0,0,0,0 4,1,7,2,4,0,0,0,0. 4,1,7,2,5,0,0,0,0 4,1,7,2,6,0,0,0,0 4'!. 7, 2, 7,0,0,0,0 4,1,7,2,8,0,0,0,0 11,7,2,9,0,0,0,0 4/1,7,3,0,0,0,0,0 11,7,3,1,0,0,0,0 ij:, 7,3,2,0,0,0,0 ii, 7,3,3,0,0,0,0 4'!, 7, 3.4.0,0,0,0 11.7.3.5.0.0,0,0 4^1,7,3,6,0,0,0,0 41,7.3.7.0,0,0,0 J/i, 7, 3,8,0,0,0,0 ii, 7,3,9,0,0,0,0 4,1,7,4,0,0,0,0,0, 4/1,7,4, 1,0,0,0,0 4,1,7,4,2,0,0,0,0 ii. 7.4.3.0.0,0,0 1^,7, 4,4,0,0,0,0 4/1, 7,4,5,0,0,0,0 4,1,7,4,6,0,0,0,0 4/1,7,4,7,0,0,0,0 4/1,7,4,8,0,0,0,0 4/1,7,4,9,0,0,0,0 Natural Numbers. 1-18525744 37597 49451 61306 73162 85019 96878 1-18608738 20599 32461 44270 56134 68000 79867 91735 1-18703604 15474 27346 39219 51093 62914 74790 86667 98546 1-18810426 22307 34189 46072 57957 69843 81677 93565 i"i89o5454 17345 29237 41130 53024 64919 76815 88713 1-19000559 12459 24360 36262 48166 60071 71977 83884 95792 1-19107702 Dual Logarithms. 16995999, 1700 OI 02* 03 04 05 06 07 08 17095949, 10 II 12 13 14 15 16 17 18 17195899, 20 21 22 23 24 25 26 27 28 Dual Numbers. 4/1.7,5.0.0,0,0,0, 4/1.7.5.1.0,0,0,0, 4/1,7.5.2,0,0,0,0, 4/1,7,5,3,0,0,0,0, 4/1,7,5,4,0,0,0,0, 4/1,7,5,5,0,0,0,0, 4/1,7,5,6,0,0,0,0, 4/1,7,5,7.0,0,0,0, 4/1,7,5,8,0,0,0,0, 4/1,7,5,9,0,0,0,0, 4,1,7,6,0,0,0,0,0, 4,1,7,6,1,0,0,0,0, 4,1,7,6,2,0,0,0,0, 4/1.7,6,3,0,0,0,0, ii, 7, 6,4,0,0,0,0, 4/1,7,6,5,0,0,0,0, 4,1,7,6,6,0,0,0,0, 4/1,7,6,7,0,0,0,0, 4,1,7,6,8,0,0,0,0, 4,1,7,6,9,0,0,0,0, 4/1,7,7,0,0,0,0,0, 1,7,7,1.0,0,0,0, 1,7,7,2,0,0,0,0, 1,7,7.3.0,0,0,0, 1,7,7,4,0,0,0,0, 4/1,7,7,5,0,0,0,0, 4/1,7.7.6,0,0,0,0, 4/1,7,7,7,0,0,0,0, i 1, 7, 7, 8.0,0,0,0, 1,7.7,9,0,0,0,0, 17295849,' 4/1,7,8,0,0,0,0,0, 30 Xi, 7,8,1,0,0,0,0, 31 Xi, 7, 8,2,0,0,0,0, 32 4/1,7,8,3,0,0,0,0, 33 4/1,7,8,4,0,0,0,0, 34 4/1,7,8,5,0,0,0,0, 35 ,,1,7.8,6,0,0,0,0, 36 4/1.7.8,7,0,0,0,0, 37 Xi, 7, 8,8,0,0,0,0, 38 J,i, 7,8,9,0,0,0,0, 17395799,' 4/1,7,9.0,0,0,0,0, 40 4/1,7,9,1,0,0,0,0, 41 4/1.7.9,2,0,0,0,0, 42 4/1,7,9,3,0,0,0,0, 43 4/^,7,9,4,0,0,0,0, 44 .4/1,7,9,5,0,0,0,0, 45 wi, 7, 9.6,0,0,0,0, 46 X^. 7. 9.7. 0,0,0,0, 47 Xi. 7. 9.8,0,0,0,0, 48 X^, 7, 9,9,0,0,0,0, Multiples of Differences. II79 1180 235» 2360 3537 3540 4716 4720 5«95 5900 7074 7080 «2S3 8260 9432 9440 10611 10620 II82 2364 3546 4728 5910 7092 8274 9456 10638 1183 2366 3549 4732 5915 7098 8281 9464 10647 II85 1186 2370 2372 3555 355« 4740 4744 5925 5930 7110 7116 8295 8302 9480 9488 10665 10674 1188 1189I 2376 237« 3564 3567 4752 4756 5940 5945 7128 7134 8316 «323 9504 9512 10692 10701 II8I 2362 3543 4724 5905 7086 8267 9448 10629 1 184 2368 3552 4736 5920 7104 8288 9472 10656 1187 2374 3561 4748 5935 7122 8309 9496 10683 1190 2380 3570 4760 5950 7140 8330 9520 10710 1191 2382 3573 4764 5955 7146 8337 9528 1 0719 Dual Logarithms of powers of 2 and 10. X, 2 = 69314718, X. 10^ = 230258509, X. ^o* = 921034037, X. lo^ = 1611809565, 4,, 4 = 138629437, 4/» ^o''' = 460517019, 4') 10^ = 1151292546, X. 10" = 1842068074, X, 8 = 207944154,. X, io3 = 690775528, X, io« = 1381551056, X. 10^ = 2072326584, Nat. No. ri911 to r202» D. Log. 1749.... to 1848.... D. No. >M,8,0,0, to >H,8,9,9, [1^ Natural Dual Dual Numbers. Logarithms. Numbers. 1-19114238 17491282, Xi, 8,0,0,0,0,0,0, 26149 50 wl, 8,0,2, 0,0,0,0, 38062 51 ,,1,8,0,1,0,0,0,0, 49976 52 wl, 8,0,3, 0,0,0,0, 61891 53 ,{,1,8,0,4,0,0,0,0, 73807 54 4,1,8,0,5,0,0,0,0, 85724 55 ,,1,8,0,6,0,0,0,0, 97643 56 ,,1,8,0,7,0,0,0,0, i"i9209563 57 ,,1,8,0,8,0,0,0,0, 4,1,8,0,9,0,0,0,0, 21484 58 33352 17591232, r, 1, 8,1, 0,0,0,0,0, 45275 60 ,,1,8,1,1,0,0,0,0, 57200 61 ,,1,8,1,2,0,0,0,0, 69126 62 ,,1,8,1,3,0,0,0,0, 81053 63 ,,1,8,1,4,0,0,0,0, 92981 64 ,,1,8,1,5, 0,0,0,0, 1-19304910 65 ,,1,8,1,6,0,0,0,0, 16840 66 ,,1,8,1,7,0,0,0,0, 28772 67 ,,1,8,1,8,0,0,0,0, 40705 68 ,,1,8,1,9,0,0,0,0, 52585 1769x182, ,,1,8,2,0,0,0,0,0, 64520 70 ,,x, 8,2, 1,0,0,0,0, 76456 71 ,,1,8,2,2,0,0,0,0, 88394 72 ,,1,8,2,3,0,0,0,0, 1-19400333 73 ,,1,8,2,4,0,0,0,0, 12273 74 ,,1,8,2,5,0,0,0,0, 24214 75 ,,1,8,2,6,0,0,0,0, 36156 76 ,,1,8,2,7,0,0,0,0, 48100 77 ,,1,8,2,8,0,0,0,0, 60045 78 ,,1,8,2,9,0,0,0,0, 71938 1779x132, 4^1,8,3,0,0,0,0,0, 83885 80 ,,1,8,3,1,0,0,0,0, 95834 81 ,,1,8,3,2,0,0,0,0, 1-19507784 82 > '1,8,3,3,0,0,0,0, ,,1,8,3,4,0,0,0,0, 19735 83 31687 84 ,,1,8,3,5,0,0,0,0, 43640 85 ,,1,8,3,6,0,0,0,0, 55594 86 ,,1,8,3,7,0,0,0,0, 67550 87 ,,1,8,3,8,0,0,0,0, 79507 88 ,,1,8,3,9,0,0,0,0, 91410 X789X082, ,,1,8,4,0,0,0,0,0, 1-19603369 90 ,,1,8,4,1,0,0,0,0, 15329 91 ,,1,8,4,2,0,0,0,0, 27291 92 ,,1,8,4,3,0,0,0,0, 39254 93 ,,1,8,4,4,0,0,0,0, 51218 94 4,1,8,4,5,0,0,0,0, 63183 95 ,,1,8,4,6,0,0,0,0, 75149 96 .,1,8,4,7,0,0,0,0, 87117 97 ,,1,8,4,8,0,0,0,0, 99086 98 4^1,8,4,9,0,0,0,0, Natural Dual Dual Numbers. Logarithms. Numbers. I-19711001 17991032, > '1,8,5,0,0,0,0,0, > '1,8,5, 1,0,0,0,0, 22972 1800 34944 01 ,,1,8,5,2,0,0,0,0, 46917 02 ' '1,8,5,3,0,0,0,0, 58892 03 > '1,8,5,4,0,0,0,0, 70868 04 >'i, 8,5, 5, 0,0,0,0, 82845 05 ,,1,8,5,6,0,0,0,0, 94823 06 ,,1,8,5,7,0,0,0,0, 1*19806802 07 ^ '1,8,5,8,0,0,0,0, 18783 08 ,,1,8,5,9,0,0,0,0, 30712 18090982, ,,1,8,6,0,0,0,0,0, 42695 xo ,,1,8,6,1,0,0,0,0, 54679 IX ,,1,8,6,2,0,0,0,0, 66664 12 ,,1,8,6,5,0,0,0,0, 78651 13 ,,1,8,6,4,0,0,0,0, 90639 14 ,,1,8,6,5,0,0,0,0, 1-19902628 15 ,,1,8,6,6,0,0,0,0, 14618 x6 ,,1,8,6,7,0,0,0,0, 26609 17 ,,1,8,6,8,0,0,0,0, 38602 x8 ,,1,8,6,9,0,0,0,0, 50543 18x90932, ,,1,8,7,0,0,0,0,0, 62538 20 ,,1,8,7,1,0,0,0,0, 74534 21 ,,1,8,7,2,0,0,0,0, 86531 22^ > '1,8,7,3,0,0,0,0, 98530 23 ,-1,8,7,4,0,0,0,0, I'20010530 24 ^'1,8,7,5,0,0,0,0, 22531 25 ,,1,8,7,6,0,0,0,0, 34533 26 > '1,8,7,7,0,0,0,0, 46536 27 ,,1,8,7,8,0,0,0,0, 58541 28 ,,1,8,7,9,0,0,0,0, 70494 18290882, ,,1,8,8,0,0,0,0,0, 82501 3^ ,,1,8,8,1,0,0,0,0, 94509 31 ,,1,8,8,2,0,0,0,0, 1-20106518 32 ,,1,8,8,3,0,0,0,0, 18529 33 |i, 8,8,4,0,0,0,0, 30541 34 ,,1,8,8,5,0,0,0,0, 42554 35 ,,1,8,8,6,0,0,0,0, 54568 36 ,,1,8,8,7,0,0,0,0, 66583 37 ,,1,8,8,8,0,0,0,0, 78600 38 ,,1,8,8,9,0,0,0,0, 90564 X8390832, ,,1,8,9,0,0,0,0,0, 1-20202583 40 ,,1,8,9,1,0,0,0,0, ,,1,8,9,2,0,0,0,0, 14603 41 26624 42 > '1,8,9,3,0,0,0,0, 38647 43 ,,1,8,9,4,0,0,0,0, 50671 44 > '1,8,9,5,0,0,0,0, 62696 45 ,,1,8,9,6,0,0,0,0, 74722 46 >'i, 8,9,7, 0,0,0,0, 86749 47 ,,1,8,9,8,0,0,0,0, 98778 48 ,,1,8,9,9,0,0,0,0, Multiples of Differences. II9I 1 192 2382 2384 ?^^7^ 3576 4764 4768 5955 5960 7146 7152 «337 8344 9528 9536 10719 10728 "94 "95 2388 2390 3';«2 3S8s 4776 4780 5970 5975 7164 7170 «35« «365 9552 9560 10746 10755 1 197 1 198 2394 2396 3591 3594 4788 4792 59«5 5990 7182 7188 8379 8386 9576 95«4 10773 10782 I20O- 1 201 2400 2402 3600 3603 4800 4804 6000 6005 7200 7206 8400 8407 9600 9608 10800 10809 "93 2386 3579 4772 5965 7158 8351 9544 10737 1 196 2392 3588. 4784 5980. 7176 8372 9568 10764 1195 2398; 3597- 4796. 5995- 7194 8393 9592 10791 1202 2404 3606 4808 6010 721Z 8414 9616 10818 Dual Logarithms of powers of 2 and 10, 4,, 2 = 69314718, L 10 = 230258509, X, 10* = 921034037, X, lo^ = 1611809565, 4/, 4 = 138629437, 4', lo^ = 460517019, 4'> ^o^ = 1151292546, ,,, 10^ =• 1842068074, 4,, 8 = 207944154, 4,, io3 = 690775528, 4,, io« = 1381551056, I, lo^ = 2072326584, 20] Nat. No. 1-2030 to r2150 D. Log. 1849.... to 1947.... D. No. |1,9,0,0, to U,9,9,9, Natural Dual Dual Numbers. Logarithms. 18486315, Numbers. 1-20305380 Xi, 9, 0,0,0,0,0,0, 17411 49 vl, 9, 0,1, 0,0,0,0, 29443 50 ,,1,9,0,2,0,0,0,0, 41476 51 ,,1,9,0,3,0,0,0,0, 53510 52 ,,1,9,0,4,0,0,0,0, 65545 53 ,,1,9,0,5,0,0,0,0, 77582 54 ,,1,9,0,6,0,0,0,0, 89620 55 ,,1,9,0,7,0,0,0,0, 1*20401659 56 ,,1,9,0,8,0,0,0,0, 13699 57 ,,1,9,0,9,0,0,0,0, 256S5 18586265, ,,1,9,1,0,0,0,0,0, 37728 59 ,,1,9,1,1,0,0,0,0, 49772 60 ,,1,9,1,2,0,0,0,0, 61817 6i ^'i,9>i»3>o»o,o,o. 73863 62 ,,1,9,1,4,0,0,0,0, 85910 ^Z ,,1,9,1,5,0,0,0,0, 97959 64 ,,1,9,1,6,0,0,0,0, 1*20510009 65 ,,1,9,1,7,0,0,0,0, 22060 66 ,,1,9,1,8,0,0,0,0, 34112 67 ,,1,9,1,9,0,0,0,0, 461 1 1 18686215, ,,1,9,2,0,0,0,0,0, 58166 69 ,,1,9,2,1,0,0,0,0, 70222 70 ,,1,9,2,2,0,0,0,0, 82279 71 ,,1,9,2,3,0,0,0,0, 94337 72 4,1,9,2,4,0,0,0,0, 1*20606396 73 4'T,9;2,5,o,o,o,o, ,,1,9,2,6,0,0,0,0, 18457 74 30519 75 ,,1,9,2,7,0,0,0,0, 42582 76 ,,1,9,2,8,0,0,0,0, 54646 77 ,,1,9,2,9,0,0,0,0, 66657 18786165, ,,1,9,3,0,0,0,0,0, 78723 79 ,,1,9,3,1,0,0,0,0, 90791 80 wi,9,3>2,o,o,o,o. 1*20702860 81 <'t,9>3)3>o,o,o,o, 14930 82 >'i,9.3»4,o,o,o,o. 27001 83 >'i,9>3»5>o,o,o,o, 39074 84 >'i,9>3>6,o,o,o,o, >'I,9)3>7jO,o,o,o, 5 1 148 85 63223 86 >ri,9,3>8,o,o,o,o, ,,1,9,3,9,0,0,0,0, 75299 87 87323 1S886115, ,,1,9,4,0,0,0,0,0, 99402 89 ,,1,9,4,1,0,0,0,0, 1*20811482 90 ,,1,9,4,2,0,0,0,0, 23563 91 >'i,9>4,3)0,o,o,o. 35645 92 4,1,9,4,4,0,0,0,0, 47729 93 >'i,9;4,5>o,o,o,o. 59814 94 ,,1,9,4,6,0,0,0,0, 71900 95 ,,1,9,4,7,0,0,0,0, 83987 96 ,,1,9,4,8,0,0,0,0, 96075 97 ,,1,9,4,9,0,0,0,0, Natural Dual Dual Numbers. Logarithms. Numbers. 1*20908110 18986065, >'I,9;5>0,0,0,0,0, 2020I 99 ,,1,9,5,1,0,0,0,0, 32293 1900 ,,1,9,5,2,0,0,0,0, 44386 01 >'Ij9;5;3jO,0,0,0, 56480 02 >'Ij9>5>4,o,o,o,o, 68576 03 >'Ij9)5j5»o,o,o,o, 80673 04 ,,1,9,5,6,0,0,0,0, 92771 '05 >'i,9>5)7>o,o,o,o. 1*21004870 06 >'i)9)5>8,o,o,o,o, >'Ij9>5>9>o,o,o,o, 16970 07 29018 19086015, ,,1,9,6,0,0,0,0,0, 4II2I 09 ,,1,9,6,1,0,0,0,0, 53225 10 ,,1,9,6,2,0,0,0,0, 65330 II ,,1,9,6,3,0,0,0,0, 77437 12 ,,1,9,6,4,0,0,0,0, 89545 13 vi,9>6,5,o,o,o,o. i'2iioi654 14 ,,1,9,6,6,0,0,0,0, 13764 15 ,,1,9,6,7,0,0,0,0, 25875 16 ,,1,9,6,8,0,0,0,0, ,,1,9,6,9,0,0,0,0, 37988 17 50047 I9185965, ,,1,9,7,0,0,0,0,0, 62162 19 ,,1,9,7,1,0,0,0,0, 74278 20 wI>9>7>2, 0,0,0,0, 86395 21 >'i,9>7>3;0,o,o,o, 98514 22 >'I>9>7j4,o,o,o,o, 1*21210634 23 >'i,9>7>5»o,o,o,o, ,,1,9,7,6,0,0,0,0, 22755 24 34877 25 wi,957,7,o,o,o,o, ,,1,9,7,8,0,0,0,0, 47000 26 59125 27 wi,9»7,9>o,o,o,o, 71197 I9285915, yl, 9, 8,0,0,0,0,0, 83324 29 ,,1,9,8,1,0,0,0,0, 95452 30 ,,1,9,8,2,0,0,0,0, 1*21307582 31 > '1,9)8,3,0,0,0,0, ,,1,9,8,4,0,0,0,0, 19713 32 31845 ?>2, ,,1,9,8,5,0,0,0,0, ,,1,9,8,6,0,0,0,0, 43978 34 56112 35 Xi,9,8,7,o,o,o,o, 68248 36 ,,1,9,8,8,0,0,0,0, 80385 37 ,,1,9,8,9,0,0,0,0, 92468 19385865, ,,1,9,9,0,0,0,0,0, 1*21404607 39 ,,1,9,9,1,0,0,0,0, 16747 40 ,,1,9,9,2,0,0,0,0, 28889 41 >'i,9>9»3,o,o,o,o. 41032 42 ,,1,9,9,4,0,0,0,0, 53176 43 r'i,9,9,5,o,o,o,o, 65321 44 ,,1,9,9,6,0,0,0,0, 77468 45 > '1,9,9,7,0,0,0,0, 89616 46 ,,1,9,9,8,0,0,0,0, 1*21501765 47 ,,1,9,9,9,0,0,0,0, Multiples of Differences, 1203 1204 2406 2408 3609 3612 4812 4816 6015 6020 7218 7224 8421 8428 9624 9632 10827 10836 1206 1207 2412 2414 3618 3621 4824 4828 6030 603"; 7236 7242 8442 8449 9648 9656 10854 10863 1209 I2I0 2418 2420 3627 3630 4836 4840 6045 6050 7254 7260 8463 8470 9672 9680 10881 10890 I2I2 I213 2424 2426 .•',636 3639 4848 48 S2 6060 6065 7272 7278 8484 8491 9696 9704 10908 IO917 I2I5 2430 3645 4860 6075 7290 8505 9720 1093s 4,, 2 = 69314718, 4,, 4 = 138629437, ,4,, 8 =L 207944154, Dual Logarithms of powers of 2 and 10. 10 = 230258509, io2 = 460517019, io3 = 690775528, 10* = 921034037, io5 = 1151292546, io« = 1381551056, 4,, io7 = 1611809565, ,„ 10^ = 1842068074, J, lo'' = 2072326584, Nat. No. 1-2100 to 1-2220 D. Log. 1906.... to 2005.... D. No. ,^2,0,0,0, to |2,0,9,9, [21 Natural Isumbers. I '21000000 I2IOO 24201 36303 48407 6oqi2 72618 84725 96833 I '2 1 108943 21000 33"2 45225 57340 69456 81573 93691 I"2I2058lO 1 793 1 30053 42121 54245 66370 78497 90625 1-21302754 14884 27015 39148 51282 75499 87637 99776 i"2i4ii9i6 24057 36199 48343 60488 72634 84726 96874 i'2i509024 21175 33328 45481 57636 69792 81949 94107 Dual Logarithms. 19062036, 07 • 08 09 II 12 13 14 IS I9161986, 17 18 19 20 21 22 23 24 25 I9261936, 27 28 29 30 31 32 33 34 35 19361886, 37 38 39 40 41 42 43 44 45 19461836, 47 48 49 50 51 52 53 54 55 Dual Numbers. 4,2,0,0,0,0,0,0,0, 4,2,0,0,1,0,0,0,0, 4,2,0,0,2,0,0,0,0, 4'2, 0,0,3, 0,0,0,0, 4.2,0,0,4,0,0,0,0, 4.2,0,0,5,0,0,0,0, 4.2,0,0,6,0,0,0,0, >, 2,0,0,7,0,0,0,0, ,,2,0,0,8,0,0,0,0, 4,2,0,0,9,0,0,0,0, 4,2,0,1,0,0,0,0,0, 4.2,0,1,1,0,0,0,0, 4.2,0,1,2,0,0,0,0, 12,0,1,3,0,0,0,0, 4.2,0,1,4,0,0,0,0, 4'250, 1,5,0,0,0,0, J.2,0, 1,6,0,0,0,0, ,,2,0,1,7,0,0,0,0, J.2,0, 1,8,0,0,0,0, 4-2,0,1,9,0,0,0,0, 4,2,0,2,0,0,0,0,0, 4.2,0,2,1,0,0,0,0, 4.2,0,2,2,0,0,0,0, 4^2,0,2,3,0,0,0,0, 4.2,0,2,4,0,0,0,0, 4'2,0,2,5, 0,0,0,0, 4.2,0,2,6,0,0,0,0, 4.2,0,2,7,0,0,0,0, 4-2,0,2,8,0,0,0,0, 4.2,0,2,9,0,0,0,0, >l'2,0,3,0,0,0,0,0, 4'2, 0,3, 1,0,0,0,0, >'2,0,3,2,0,0,0,0, 4^2,0,3,3,0,0,0,0, |2,o,3,4,o,o,o,o, 4'2, 0,3, 5, 0,0,0,0, 4.2,0,3,6,0,0,0,0, 4.2,0,3,7,0,0,0,0, 4^2, 0,3,8,0,0,0,0, 4.2,0,3,9,0,0,0,0, 4.2,0,4,0,0,0,0,0, 4.2,0,4,1,0,0,0,0, 4.2,0,4,2,0,0,0,0, 4.2,0,4,3,0,0,0,0, 4.2,0,4,4,0,0,0,0, |2,o,4,5,o,o,o,o, ,,2,0,4,6,0,0,0,0, 4.2,0,4,7,0,0,0,0, 4.2,0,4,8,0,0,0,0, 4^2,0,4,9,0,0,0,0, Natural Numbers. I"2l6o62II 18372 30534 42697 54861 67026 79193 9I36I i'2i7o353o 15700 27817 39990 52164 64339 76515 88693 I '2 180087 2 13052 25233 37416 49545 61730 73916 86103 98292 1*21910482 22673 34865 47058 59253 71395 83592 95790 I'22007990 20191 32393 44596 56800 69006 8I2I3 93366 1*22105575 17786 29998 422II 54425 66640 78857 91075 I'22203294 Dual Logarithms. 19561786, 57 58 59 60 61 62 63 64 65 19661736, 67 68 69 70 71 72 73 74 75 19761686, 77 78 79 80 81 82 83 84 85 1 986 1 636, 87 88 89 90 91 92 93 94 95 19961586, 97 98 99 2000 01 02 03 04 05 Dual Numbers. 4.2,0,5,0,0,0,0,0, ,.2,0,5,1,0,0,0,0, > '2,0,5,2,0,0,0,0, > '2,0,5,3,0,0,0,0, 4.2,0,5,4,0,0,0,0, ^2,0,5,5, 0,0,0,0, 4.2,0,5,6,0,0,0,0, 4'2,o,5,7,o,o,o,o, 4.2,0,5,8,0,0,0,0, 4.2,0,5,9,0,0,0,0, 4.2,0,6,0,0,0,0,0, ,.2,0,6,1,0,0,0,0, 4.2,0,6,2,0,0,0,0, J.2,0,6,3,0,0,0,0, 4.2,0,6,4,0,0,0,0, 4.2,0,6,5,0,0,0,0, 4.2,0,6,6,0,0,0,0, J.2,0,6,7,0,0,0,0, ,,2,0,6,8,0,0,0,0, 4.2,0,6,9,0,0,0,0, 4'2>o,7,o,o,o,o,o, 4.2,0,7,1,0,0,0,0, 4.2,0,7,2,0,0,0,0, |2,O,7,3,0,O,O,O, 4'2jO,7,4,o,o,o,o, >'2, 0,7, 5, 0,0,0,0, ,,2,0,7,6,0,0,0,0, >'2,o,7, 7, 0,0,0,0, ,,2,0,7,8,0,0,0,0, 4.2,0,7,9,0,0,0,0, ,,2,0,8,0,0,0,0,0, ,,2,0,8,1,0,0,0,0, ,,2,0,8,2,0,0,0,0, ,,2,0,8,3,0,0,0,0, 4.2,0,8,4,0,0,0,0, J,2,o,8,5, 0,0,0,0, ,,2,0,8,6,0,0,0,0, ,,2,0,8,7,0,0,0,0, ,,2,0,8,8,0,0,0,0, 4.2,0,8,9,0,0,0,0, 4.2,0,9,0,0,0,0,0, 2,0,9,1,0,0,0,0, 2,0,9,2,0,0,0,0, 2,0,9,3,0,0,0,0, 2,0,9,4,0,0,0,0, >I'2,o,9,5, 0,0,0,0, 4.2,0,9,6,0,0,0,0, 2,0,9,7,0,0,0,0, 2,0,9,8,0,0,0,0, 2,0,9,9,0,0,0,0, Multiples of Differences. I2I0 1211 2420 2422 3b^o 3633 4840 4844 6050 605s 7260 7266 8470 »477 9680 9688 10890 10899 I2I2 2424 3636 4848 6060 7272 1213 I2I4 2426 2428 3639 3642 48S2 48S6 6065 6070 7278 7284 8491 8498 9704 9712 I09I7 10926 1216 I2I7 2432 2434 3648 3651 4864 4868 6080 6085 7296 7302 8512 8siq 9728 9736 10944 10953 1219 1220 2438 2440 .3657 3660 4876 4880 6095 6100 7314 7320 «S33 8540 97.S2 9760 10971 10980 9696 10908 I2I5 2430 3645 4860 6075 7290 8505 9720 1093s I2I8 2436 3654 4872 6090 7308 8526 9744 10962 2442 3663 6105 7326 8547 9768 10989 1222 2444 3666 6110 7332 8554 9776 10998 j, 2 = 69314718, 4,, 10 = 230258509, 4,, 4 = 138629437, L io2 = 460517019, 4., 8 = 207944154, 4'. io3 = 690775528, Dual Logarithms of powers of 2 and 10. V, 10'* = 92103403 037, L lo^ = 1611809565, 10" = 1151292546, 4') 10^ = 1842068074, io« = 1381551056, I, io» = 2072326584, 22] Nat. No. 1*2221 to 1-2342 D. Log. 2005.... to 2104.... D. No. |2,1,0,0, to |2,1,9,9, Natural Numbers. I*222IOOOO 22221 34443 46666 58891 7III7 83344 95572 I'223078o2 20033 32210 44443 56677 68913 81150 93388 i'22405627 17868 30110 42353 54542 66787 79034 91282 1*22503531 15781 28033 40286 52540 64795 76996 89254 i'226oi5i3 13773 26034 38297 50561 62826 75092 87360 99573 i*227ii843 24114 36386 48660 60935 73211 85488 97767 i'228ioo47 Dual Logarithms. 20057069 06 07 08 09 10 II 12 13 14 20157019, 16 17 18 19 20 21 22 23 24 20256969, 26 27 28 29 30 31 32 33 34 20356919, 36 37 38 39 40 41 42 43 44 20456869, 46 47 48 49 50 51 52 53 54 Dual Numbers. >J,2, 1,0,0,0,0,0,0, > '2, 1,0, 1,0,0,0,0, ,,2,1,0,2,0,0,0,0, w2,1, 0,3,0,0,0,0, J,2, 1,0,4,0,0,0,0, >I'2>I>0,5,0,0,0,0, |2, 1,0,6,0,0,0,0, \I'2, 1,0,7,0,0,0,0, \I,2, 1,0,8,0,0,0,0, >I,2, 1,0,9,0,0,0,0, |2, 1, 1,0,0,0,0,0, ,1,2,1,1,1,0,0,0,0, 4,2,1,1,2,0,0,0,0, >I'2, 1, 1,3,0,0,0,0, 4,2,1,1,4,0,0,0,0, 12,1,1,5,0,0,0,0, 4,2,1,1,6,0,0,0,0, 12,1,1,7,0,0,0,0, 4^2, 1, 1,8,0,0,0,0, 4,2,1,1,9,0,0,0,0, 4,2,1,2,0,0,0,0,0, 4.2,1,2,1,0,0,0,0, 4,2,1,2,2,0,0,0,0, 4.2,1,2,3,0,0,0,0, 4,2,1,2,4,0,0,0,0, 4,2,1,2,5,0,0,0,0, 4,2,1,2,6,0,0,0,0, 4,2,1,2,7,0,0,0,0, 4,2,1,2,8,0,0,0,0, 4,2,1,2,9,0,0,0,0, 4'2,i,3»o,o,o,o,o, 4.2,1,3,1,0,0,0,0, 4,2,1,3,2,0,0,0,0, 4'2, 1,3,3,0,0,0,0, 4'2, 1,3,4,0,0,0,0, 4'2,i,3)5>o,o,o,o, 4,2,1,3,6,0,0,0,0, 4'2, 1,3,7.0,0,0,0, 4'2, 1,3,8,0,0,0,0, 4'2,i,3,9,o,o,o,o, 4,2,1,4,0,0,0,0,0, 4,2,1,4,1,0,0,0,0, 4,2,1,4,2,0,0,0,0, 4'2, 1,4,3.0,0,0,0, |2, 1,4,4,0,0,0,0, 4'2, 1,4, 5,0,0,0,0, 4,2,1,4,6,0,0,0,0, 4.2,1,4,7,0,0,0,0, 4.2,1,4,8,0,0,0,0, 4.2,1,4,9,0,0,0,0, Natural Numbers. 1*22822273 34555 46838 59123 71409 83696 95984 i"229o8274 20565 32857 45095 57390 69686 81983 94281 1*23006580 18881 31183 43486 55790 68040 80347 92655 i*23io4964 17274 29586 41899 54213 66528 78845 91108 1-23203427 15747 28069 40392 52716 65041 77368 89696 1*23302025 14299 26630 38963 51297 63632 75968 88306 1*23400645 12985 25326 Dual Logarithms. Dual Numbers. 20556819, 56 57 58 59 60 61 62 63 64 20656769, 66 67 68 69 70 71 72 73 74 20756719, 76 77 78 79 80 81 82 83 84 20856669, 86 87 88 89 90 91 92 93 94 20956619, 96 97 98 99 2100 01 02 03 04 2,1,5,0,0,0,0,0, 2,1,5,1,0,0,0,0, 2,1,5,2,0,0,0,0, 12,1,5,3,0,0,0,0, 12, 1,5,4,0,0,0,0, 2,1,5,5,0,0,0,0, 2,1,5,6,0,0,0,0, 2,1,5,7,0,0,0,0, 2,1,5,8,0,0,0,0, 4'2, 1,5,9,0,0,0,0, ^2, 1,6,0,0,0,0,0, ['2,1,6,1,0,0,0,0, [,2,1,6,2,0,0,0,0, ['2,1,6,3,0,0,0,0, ^2,1,6,4,0,0,0,0, 12,1,6,5,0,0,0,0, ,,2,1,6,6,0,0,0,0, ,,2,1,6,7,0,0,0,0, ,,2,1,6,8,0,0,0,0, 4.2,1,6,9,0,0,0,0, |2, 1,7,0,0,0,0,0, ,.2,1,7,1,0,0,0,0, ,.2,1,7,2,0,0,0,0, > '2, 1,7,3,0,0,0,0, 12, 1,7,4,0,0,0,0, > '2, 1,7,5,0,0,0,0, ,.2,1,7,6,0,0,0,0, v2, 1,7,7,0,0,0,0, 4.2,1,7,8,0,0,0,0, 4^2,1,7,9,0,0,0,0, [.2,1,8,0,0,0,0,0, ^2,1, 8,1, 0,0,0,0, ,2,1,8,2,0,0,0,0, [.2,1,8,3,0,0,0,0, ^2,1,8,4,0,0,0,0, ,,2,1,8,5,0,0,0,0, ,,2,1,8,6,0,0,0,0, ,,2,1,8,7,0,0,0,0, ,,2,1,8,8,0,0,0,0, 4.2,1,8,9,0,0,0,0, 2,1,9,0,0,0,0,0, 2,1,9,1,0,0,0,0, 2,1,9,2,0,0,0,0, J.2, 1,9,3,0,0,0,0, 4.2,1,9,4,0,0,0,0, [,2,1,9,5,0,0,0,0, 1.2,1,9,6,0,0,0,0, ',2,1,9,7,0,0,0,0, [.2,1,9,8,0,0,0,0, ',2,1,9,9,0,0,0,0, Multiples of Differences. 1222 1223 2444 2446 3666 3669 4888 4892 6110 6us 7332 7338 «SS4 8561 9776 9784 10998 11007 1224 2448 3672 4896 6120 7344 8568 9792 11016 1225 1226 1227 2450 24S2 2454 3^75 3678 3681 4900 4904 4908 6125 6130 613'; 7350 73S6 7362 «57'; 8S82 8589 9800 9808 9816 1 1025 1 1034 1 1043 1228 1229 1230 24'>6 2458 2460 3684 3687 3690 4912 4916 4920 6140 6i4S 6150 7368 7374 73«o 8S96 8603 8610 9824 9«32 9840 11052 iio6i U070 1231 1232 2462 2464 3693 3696 4924 4928 61SS 6160 7386 7392 8617 8624 9848 9856 11079 11088 "33 2466 3699 4932 6165 739? 8631 9864 1109J 1234 2468 3702 4936 6170 7404 8638 9872 11106 Dual Logarithms of powers of 2 and 10. 4,, 2 = 69314718, 4., 10 = 230258509, 4., 10* = 921034037, L io7 = 161 1809565, i, 4 = 138629437, 4^, io2 = 460517019, 4^, io5 = 1151292546, ,., 108 =• 1842068074, I, 8 = 207944154, 4., 10^ = 690775528, 4., 106 = 1381551056, I, lo^ = 2072326584, Nat. No. 1*2343 to 1-2465 D. Log. 2105.... to 2200.... D. No. 4.2,2,0,0, to >I.2,2,9,9, [23 Natural Dual Dual Numbers, Logarithms. Numbers. 1-23432100 21052102, 4,2,2,0,0,0,0,0,0, 44443 06 ^2 2,0,1,0,0,0,0, 56787 07 4,2 2,0,2,0,0,0,0, 69133 08 I2 4.2 2,0,3,0,0,0,0, 81480 09 2,'b,4,o,o,o,o, 93828 10 4.2 2,0,5,0,0,0,0, 1-23506177 II 4^2 2,0,6,0,0,0,0, 18528 12 4.2 2,0,7,0,0,0,0, 30880 13 4.2 2,0,8,0,0,0,0, 43233 14 4,2 2,0,9,0,0,0,0, 55532 2II52052, 4^2 2,1,0,0,0,0,0, 67888 16 \'2 2,1,1,0,0,0,0, 80245 17 w2 2,1,2,0,0,0,0, 92603 18 yr2 2,1,3,0,0,0,0, 1-23604962 19 y'2 2,1,4,0,0,0,0, 27322 20 >-2 2,1,5,0,0,0,0, 39685 21 >.2 2,1,6,0,0,0,0, 52049 22 w2 2,1,7,0,0,0,0, 64414 23 ,,2 2,1,8,0,0,0,0, 76780 24 >.2 2,1,9,0,0,0,0, 79088 21252002, y'2 2,2,0,0,0,0,0, 91456 26 y,2 2,2,1,0,0,0,0, 1-23703825 27 S,2 2,2,2,0,0,0,0, 16195 28 Sf2 S'2 2,2,3,0,0,0,0, 28567 29 2,2,4,0,0,0,0, 40940 30 y>2 2,2,5,0,0,0,0, 53314 31 >r2 2,2,6,0,0,0,0, 65689 32 y,2 2,2,7,0,0,0,0, 78066 33 w2 2,2,8,0,0,0,0, 90444 34 ,r2 2,2,9,0,0,0,0, 1-23802767 21351952, 4.2 2,3,0,0,0,0,0, 15147 36 w2 2,3,1,0,0,0,0, 27529 37 4/2 2,3,2,0,0,0,0, 39912 38 4,2 2,3.3)0,0,0,0, 52296 39 |2 2,3,4,0,0,0,0, 64681 40 y,2 2,3,5,0,0,0,0, 77067 41 4,2 2,3,6,0,0,0,0, 89455 42 w2 2,3,7,0,0,0,0, 1-23901844 43 .,2 y,2 2,3,8,0,0,0,0, 14234 44 2,3,9)0,0,0,0, 26570 21451902, >r2 2,4,0,0,0,0,0, 38963 46 y,2 2,4,1,0,0,0,0, 51357 47 S'2 2,4,2,0,0,0,0, 63752 48 I2 y,2 2,4,3)0,0,0,0, 76148 49 2,4,4,0,0,0,0, 88546 50 w2 2,4,5.0,0,0,0, 1-24000945 51 y'2 2,4,6,0,0,0,0, 13345 52 ^,2 2,4,7,0,0,0,0, 25746 53 y,2 2,4,8,0,0,0,0, 38149 54 >r2 2,4,9,0,0,0,0, Natural Dual Dual Numbers. Logarithms. Numbers. 1-24050497 21551852, "2,2,5,0,0,0,0,0, 62902 56 ,r2, 2,5,1, 0,0,0,0, 75308 57 ,,2,2,5,2,0,0,0,0, 87716 58 > '2,2,5,3,0,0,0,0, 1-24100125 59 v2,2,5,4,0,0,0,0. 12535 60 4'2, 2,5, 5, 0,0,0,0, 24946 61 4.2,2,5,6,0,0,0,0, 37358 62 "2,2,5,7,0,0,0,0, 49772 63 4.2,2,5,8,0,0,0,0, 62187 64 4.2,2,5,9,0,0,0,0, 74547 21651802, ,,2,2,6,0,0,0,0,0, 86964 66 4.2,2,6,1,0,0,0,0, 99383 67 ,,2,2,6,2,0,0,0,0, I -242 1 1803 68 ,,2,2,6,3,0,0,0,0, 24224 69 4,2,2,6,4,0,0,0,0, 36646 70 v2,2,6,5,0,0,0,0. 49070 71 ,,2,2,6,6,0,0,0,0, 61495 72 ,,2,2,6,7,0,0,0,0, 73921 73 ,,2,2,6,8,0,0,0,0, 86348 74 ,,2,2,6,9,0,0,0,0, 98722 21751752, ,,2,2,7,0,0,0,0,0, 1-24311152 76 ,,2,2,7,1,0,0,0,0, 23583 77 ,,2,2,7,2,0,0,0,0, 36015 78 > '2,2,7,3,0,0,0,0, 48449 79 ,,2,2,7,4,0,0,0,0, 60884 80 v2,2,7,5,0,0,0,0. 73320 81 ,,2,2,7,6,0,0,0,0, 85757 82 4.2,2,7,7,0,0,0,0, 98196 83 ,,2,2,7,8,0,0,0,0, 1-24410636 84 ,,2,2,7,9,0,0,0,0, 23021 21851702, ,,2,2,8,0,0,0,0,0, 35463 86 ,,2,2,8,1,0,0,0,0, 47907 87 ,,2,2,8,2,0,0,0,0, 60352 88 ,,2,2,8,3,0,0,0,0, 72798 89 4,2,2,8,4,0,0,0,0, 85245 90 ,,2,2,8,5,0,0,0,0, 97694 91 ,,2,2,8,6,0,0,0,0, 1-24510144 92 ,,2,2,8,7,0,0,0,0, 22595 93 ,,2,2,8,8,0,0,0,0, 35047 94 , ,2,2,8,9,0,0,0,0, 47444 21951652, ,,2,2,9,0,0,0,0,0, 59899 96 ,,2,2,9,1,0,0,0,0, 72355 97 ,,2,2,9,2,0,0,0,0, 84812 98 >. 2, 2, 9,3,0,0,0,0, 97270 99 4,2,2,9,4,0,0,0,0, 1-24609730 2200 > '2, 2,9,5,0,0,0,0, 22191 01 ,,2,2,9,6,0,0,0,0, 34653 02 ,,2,2,9,7,0,0,0,0, 47116 03 ,,2,2,9,8,0,0,0,0, 59581 04 ,,2,2,9,9,0,0,0,0, Multiples of Differences. 1234 1235 2468 2470 3702 3701 4936 4940 6170 6175 7404 74IO 8638 864.; 9872 9880 III06 IU15 1246 2492 3738 4984 6230 7476 8722 9968 II2I4 1236 2472 3708 4944 6180 7416 8652 1237 1238 2474 2476 37" .3714 4948 4952 6185 6190 7422 7428 86S9 8666 9896 9904 ii'33 11142 1240 1241 2480 2482 3720 3723 4960 4964 6200 6205 7440 7446 8680 8687 9920 9928 11160 11169 1243 2486 1244 2488 3729 4972 6215 3732 4976 6220 7458 8701 7464 8708 9944 11187 9952 11196 III24 1239 2478 3717 4956 6195 7434 8673 9912 11151 1242 2484 3726 4968 6210 7452 8694 9936 11178 124s 2490 3735 4980 6225 7470 871S 9960 11205 Dual Logarithms of powers of 2 and 10. L 2 = 693 147 18, 4,, 10 = 230258509, 4,, lo* = 921034037, 4,, lo"^ = 161 1809565, ,„ 4 = 138629437, J,, io2 = 460517019, 4., io5 = 1151292546, 4,, los = 1842068074, 4,, 8 = 207944154, 4,, io3 = 690775528, 4.) lo" = 1381551056, 4,, io9 = 2072326584, 24] Nat. No. 1-2466 to 1-2590 D. Log. 2204. . . . to 2303 .... D. No. 12,3,0,0, to 12,3,9,9, Natural Numbers. I "2466642 1 91356 1-24703825 16295 28767 41240 53714 66189 78666 91087 1*24803566 16046 28528 41011 53495 65980 78467 90955 1-24903444 15878 28370 40863 53357 65852 78349 90847 I '25003346 15846 28348 40794 53298 65S03 78310 90818 1-25103327 15837 28349 40862 53376 65835 78352 90870 i'25203389 15909 28431 40954 53478 66003 78530 Dual Logarithms. 22047135, 05 06 07 08 09 10 II 12 13 22147085, 15 16 17 19 20 21 22 23 22247035, 25 26 27 28 29 30 31 32 33 22346985, 35 36 37 38 39 40 41 42 43 22446935. 45 46 47 48 49 SO SI 52 53 Dual Numbers. |2, 3,0,0,0,0,0,0, ^2,3,0,1,0,0,0,0, j'2,3,o,2, 0,0,0,0, >|'2,3,o,3, 0,0,0,0, >I'2,3,o,4,o,o,o,o, >1'2, 3,0,5, 0,0,0,0, \I'2,3,o,6,o,o,o,o, ^ '2,3,0,7,0,0,0,0, ,, 2,3,0,8,0,0,0,0, |2,3,o,9,o,o,o,o, 4'2,3, 1,0,0,0,0,0, ^2, 3,1, 1,0,0,0,0, 2,3jI>2, 0,0,0,0, 2,3)i>3>o,o,o,o, 2,3> i>4,o,o,o,o, v2,3, 1, 5,0,0,0,0, ,,2,3,1,6,0,0,0,0, v2,3,1, 7,0,0,0,0, ,,2,3,1,8,0,0,0,0, 12,3,1,9,0,0,0,0, ,,2,3,2,0,0,0,0,0, \'2,3,2, 1,0,0,0,0, w2,3,2,2,0,0,0,0, >'2,3j2,3, 0,0,0,0, 4'2,3>2,4,o,o,o,o, 12,3,2,5,0,0,0,0, ,,2,3,2,6,0,0,0,0, >'2, 3,2, 7,0,0,0,0, ,,2,3,2,8,0,0,0,0, 4^2,3,2,9,0 0,0,0, 2,3)3jO,o,o,o,o, 2,353)1)0,0,0,0, 2,3,3»2, 0,0,0,0, .2,3,3,3,0,0,0,0, j'2,3, 3,4,0,0,0 o, /2,3, 3, 5,0,0,0,0, ^2,3,3>6,o,o,o,o, ^2,3,3>7.o,o,o,o, 1^2,3,3,8,0,0,0,0, ^2,3,3)9,0,0,0,0, 2,3,4,0,0,0,0,0, 2,3)4,1,0,0,0,0, 2,3)4)2,0,0,0,0, .2,3,4)3)0,0,0,0, >1'2,3, 4,4,0,0,0,0, 2,3,4)5)0,0,0,0, 2,3)4,6,0,0,0,0, .2,3,4,7,0,0,0,0, t 2, 3)4)8,0,0,0,0, 2,3.4)9)0,0,0,0, Natural Numbers. I"2529IOOI i'2530353o 16060 28592 41125 53659 66194 78731 91269 1-25403808 16292 28834 41377 53921 66466 79013 91561 1-25504110 16660 29212 41708 54262 66817 79374 91932 1-25604491 17051 29613 42176 S4740 67250 79817 92385 I '25704954 17524 30096 42669 55243 67819 80396 92917 1-25805496 18077 30659 43242 55826 68412 80999 93587 1-25906176 Dual Logarithms. 22546885 55 56 57 58 59 60 61 62 63 22646835, 65 66 67 68 69 70 71 72 73 22746785, 75 76 77 78 79 80 81 82 83 22846735, 85 86 87 88 89 90 91 92 93 22946685, 95 96 97 99 2300 01 02 03 Dual Numbers. ^2, 3, 5)0,0,0,0,0, > '2,3)5) 1)0,0,0,0, >['2,3, 5,2, 0,0,0,0, > '2,3)5)3.0,0,0,0, >I'2,3)S)4,o,o,o,o, 2,3)5)5)0,0,0,0, 2,3»5)6,o,o,o,o, 2,3,5,7,0,0,0,0, >l'2,3,5,8,o,o,o,o, \l'2,3,5)9)0,o,o,o, 4,2,3,6,0,0,0,0,0, i 2,3,6, 1,0,0,0,0, 2,3.6,2,0,0,0,0, >I'2,3,6,3,o,o,o,o, 4,2,3,6,4,0,0,0,0, 2,3,6,5)0,0,0,0, 2,3,6,6,0,0,0,0, 2,3,6,7,0,0,0,0, J,2,3,6,8,o,o,o,o, 4^2,3,6,9,0,0,0,0, 4'2,3.7, 0,0,0,0,0, 12,3.7. 1,0,0,0,0, 12,3,7,2,0,0,0,0, 4'2,3,7)3.o,o,o,o, 4'2,3, 7,4,0,0,0,0, 2,3,7.5.0,0,0,0, 2,3.7.6,0,0,0,0, 2,3.7.7,0,0,0,0, .2,3)7.8,0,0,0,0, 4^2,3.7.9)0,0,0,0, 4'2. 3)8,0,0,0,0,0, 2,3)8,1,0,0,0,0, '2,3)8,2,0,0,0,0, 2,3,8,3,0,0,0,0, 2,3)8,4,0,0,0,0, 12,3,8,5,0,0,0,0, 4'2,358,6,o,o,o,o, 2,3)8,7,0,0,0,0, 2,3.8,8,0,0,0,0, 2,3.8,9,0,0,0,0, 12,3,9,0,0,0,0,0, < '2,3.9. 1.0,0,0,0, > '2,3)9)2,0,0,0,0, > '2,3)9)3)0,0,0,0, 12,3,9,4,0,0,0,0, 2,3)9)5.0,0,0,0, 2,3)9)6,0,0,0,0, 2,3)9)7)0,0,0,0, . 2,3,9,8,0,0,0,0, 4'2,3)9) 9)0)0,0,0, Multiples of DifTereuces. I 1246 1247 2 2492 2494 3 3738 3741 4 4984 49S8 5 6230 6235 6 7476 7482 7 8722 8729 8 9968 9976 9 11214 1 1223 I 1249 1250 2 2498 2500 3 3747 3750 4 4996 50(X) 5 6245 6250 b 7494 7500 7 «743 8750 8 9992 lOOOO 9 11241 II250 1252 1253 2504 2506 37S(' 3759 5008 5012 6260 6265 7512 7518 8764 8771 10016 10024 1 1 268 11277 »255 1256 2510 2512 3765 3768 5020 5024 627s 6280 7530 7536 8785 8792 10040 10048 1 1295 11304 124! 249< 374^ 499' 624( 7485 873( 998^ 1251 2502 3753 5004 625s 7506 8757 10008 11259 1254 2508 3762 5016 6270 7524 8778 10032 1 1286 1257 2514 3771 5028 6285 7542 i 8799i ioo!;6 11313 1258 2516 3774 5032 6290 7548 8806 8 1 10064 9 11322 1259 2518 3777 5036 6295 7554 8813 10072 "331 i, 2 = 69314718, L 10 = 230258509, , 8 = 138629437, ,„ io2 = 460517019, 4,, 4 = 207944154, 4,, Io3 = 690775528, Dual Logarithms of powers of 2 and 10. 10* = 921034037, 4'. 10'^ = 1611809565, = 1842068074, 2072326584, 1151292546, L lo^^ = 1381551056, 4'. 10" = Nat. No. 1-2591 to 1-2716 D. Log. 2304.... to 2403.... D. No. ^[,2,4,0,0, to >I.2,4,9,9, [25 Natural Numbers. 23042168, 05 06 07 08 09 10 II 12 13 23142118, 15 16 17 18 19 20 21 22 23 23242068, 25 26 27 28 29 30 31 32 33 91202 23342018, 1-263038311 35 16461 j 36 29093 [ 37 41726; 38 1-25913085 25676 38269 50863 63458 76054 88652 1-26001251 13851 26452 38998 51602 64207 76813 89421 1-26102030 14640 27251 39864 52478 65037 77654 90272 1-26202891 15511 28133 40756 53380 66005 78632 Dual Logarithms. 54360 66995 79632 92270 1-26404909 17493 3013s 42778 55422 68068 80715 93363 i'265o6oi2 18662 31314 Dual Numbers. 39 40 41 42 43 23441968, 45 46 47 48 49 50 SI 52 53 2,4,0,0,0,0,0,0, 2,4,0,1,0,0,0,0, 2,4,0,2,0,0,0,0, ^2,4,0,3,0,0,0,0, 4^2,4,0,4,0,0,0,0, i 2,4,0,5)0,0,0,0, 2,4,0,6,0,0,0,0, >l'2,4,o,7, 0,0,0,0, 12,4,0,8,0,0,0,0, 4^2,4,0,9,0,0,0,0, >[r2,4, 1,0,0,0,0,0, 12,4,1,1,0,0,0,0, 2,4,1,2,0,0,0,0, 2,4,1,3)0,0,0,0, 2,4,1,4)0,0,0,0, ^2,4,1,5,0,0,0,0, ^2,4, 1,6,0,0,0,0, ^2, 4,1, 7, 0,0,0,0, ^2, 4,1, 8,0,0,0,0, >j,2,4, 1,9,0,0,0,0, J,2,4,2,0,0,0,0,0, x'2,4,2, 1, 0,0,0,0, >'2, 4,2, 2,0,0,0,0, ^ '2,4,2,3,0,0,0,0, |2, 4,2, 4, 0,0,0,0, ^2, 4,2, 5,0,0,0,0, i2, 4,2, 6,0,0,0,0, 4,2,4,2,7,0,0,0,0, 42,4,2,8,0,0,0,0, 4,2,4,2,9,0,0,0,0, J 2, 4)3)0,0,0,0,0, 2,4,3)1)0,0,0,0, 42,4,3,2,0,0,0,0, 4-2,4,3,3,0,0,0,0, 4'2,4,3,4,o,o,o,o, 2,4)3)5)0,0,0,0, ■2,4,3)6,0,0,0,0, ■2,4,3)7)0,0,0,0, 2,4,3)8,0,0,0,0, 42,4,3)9)0,0,0,0, 4,2,4,4,0,0,0,0,0, 2,4,4)1)0,0,0,0, 2,4)4,2,0,0,0,0, 2,4,4,3)0,0,0,0, 2,4,4)4)0,0,0,0, ^2,4,4)5)0)0,0,0, ^2,4,4,6,0,0,0,0, ^2,4,4,7,0,0,0,0, ^2,4,4)8,0,0,0,0, ^2,4,4,9)0,0,0,0, Natural Dual Dual Numbers. Logarithms. Numbers. 1-26543911 23541918, v2,4,5, 0,0,0,0,0, 56565 55 > '2,4)5)1)0,0,0,0, 69221 56 ,,2,4,5,2,0,0,0,0, 81878 57 > '2,4,5)3)0,0,0,0, 94536 58 v2,4,5)4,o,o,o,o. I-26607195 59 ^ '2,4)5)5)0,0,0,0, 19856 60 ''2,4)5)6)0,0,0,0, 32518 61 > '2,4,5)7)0,0,0,0, 45181 62 ^ '2,4,5)8,0,0,0,0, 57846 63 \ '2,4,5)9)0,0,0,0, 70455 23641868, ,,2,4,6,0,0,0,0,0, 83122 65 ,,2,4,6,1,0,0,0,0, 95790 66 ,,2,4,6,2,0,0,0,0, 1*26708460 67 w2, 4,6,3, 0,0,0,0, 2I131 68 w2, 4,6,4,0,0,0,0, 33803 69 ' '2,4,6,5,0,0,0,0, 46476 70 ,,2,4,6,6,0,0,0,0, 59^51 71 > '2,4)6,7,0,0,0,0, 71827 72 ,,2,4,6,8,0,0,0,0, 84504 73 ,,2,4,6,9,0,0,0,0, 97125 23741818, ,,2,4,7,0,0,0,0,0, 1-26809805 75 ,,2,4,7,1,0,0,0,0, 22486 76 ,,2,4,7,2,0,0,0,0, 35168 77 w2,4,7,3)0,o,o,o, 47852 78 w2,4,7.4,o,o,o,o, 60537 79 "2,4,7,5,0,0,0,0, 73223 80 ,,2,4,7,6,0,0,0,0, 85910 81 w2,4,7)7.o,o,o,o. 98599 83 ,,2,4,7,8,0,0,0,0, 1*26911289 83 v2,4,7)9)0,o,o,o. 23922 23841768, ,,2,4,8,0,0,0,0,0, 36614 85 ,,2,4,8,1,0,0,0,0, 49308 86 ,,2,4,8,2,0,0,0,0, 62003 87 > '2,4,8,3,0,0,0,0, 74699 88 ,,2,4,8,4,0,0,0,0, 87396 89 > '2,4,8,5,0,0,0,0, 1-27000095 90 ,,2,4,8,6,0,0,0,0, 1279s 91 ,,2,4,8,7,0,0,0,0, 25496 92 ,,2,4,8,8,0,0,0,0, 38199 93 ,,2,4,8,9,0,0,0,0, 50846 23941718, ,,2,4,9,0,0,0,0,0, 63551 95 ,,2,4,9,1,0,0,0,0, 76257 96 ,,2,4,9,2,0,0,0,0, 88965 97 > '2,4,9)3,0,0,0,0, 1-2710x674 98 ,,2,4,9,4,0,0,0,0, 14384 2399 w2, 4,9,5, 0,0,0,0, 27094 2400 ,,2,4,9,6,0,0,0,0, 39807 01 ,,2,4,9,7,0,0,0,0, 52521 02 ,,2,4,9,8,0,0,0,0, 65236 03 > '2,4)9)9)0)0,0,0, Multiples of Differences. 1259 1260 2518 2520 ; 3777 3780 .So^ft 5040 6295 6300 7S,';4 7560 88n 8820 10072 IC080 ii33i 1 1340 1262 1263 2S24 2526 37«6 37«9 5048 5052 6310 6315 7.572 7S7« 8834 8841 10096 10104 "35« 1 1367. I26I 2522 3783 5044 6305 7566 8827 10088 "349 1264 2528 3792 5056 6320 7584 1265 1266 2530 2532 379S 3798 5060 5064 6325 6330 7S90 7S9(> t^-SS 8862 10120 10128 "38s "394 IOII2 11376 1267 2534 3801 5068 633s 7602 1268 1269 2';36 2538 3804 3807 5072 5076 6340 6345 7608 7614 8876 8883 10144 10152 11412 11421 10136 U403 1270 2540 3810 5080 6350 7620 8890 IOI60 1 1430 I27I 2542 3813 5084 6355 7626 8897 IOI68 "439 Dual Logarithms of , 2 = 69314718, 4,, 10 = 230258509, , 4 = 138629437, 4, io2 = 460517019, , 8 = 207944154, 4,, io3 = 690775528, powers of 2 and 10. I, 10* = 921034037, 4, Io5 = II51292546, 4, lo" = 1381551056, |, lo^ = 1611809565, , ,, 10^ =■ 1842068074, ,„ 10^ = 2072326584, 56] Nat. No. 1-2717 to 1*2843 D. Log. 2403.... to 2502.... D. No. |2,5,0,0, to |2,5,9,9, Natural Dual Dual Numbers Logarithms. Numbers. I"27I722l6 24037201, ^2,5,0,0,0,0,0,0, 84933 04 ,,2,5,0,1,0,0,0,0, 97651 05 4,2,5,0,2,0,0,0,0, 1*27210371 06 w2, 5, 0,3,0,0,0,0, 23092 07 > '2,5,0,4,0,0,0,0, 35814 08 ,,2,5,0,5,0,0,0,0, 48538 09 > '2,5)0,6,0,0,0,0, 61263 10 ,,2,5,0,7,0,0,0,0, 73989 II ,,2,5,0,8,0,0,0,0, 86716 12 >'2,5>o,9,o,o,o,o. 99388 24137151^ J,2,5, 1,0,0,0,0,0, x'273i2ii8 14 |2,5,i, 1,0,0,0,0, 24849 15 4,2,5,1,2,0,0,0,0, 37581 16 12,5,1,3,0,0,0,0, 50315 17 |2,5, 1,4,0,0,0,0, 63050 18 ■4'2,5, 1,5,0,0,0,0, 75786 19 > '2,5, 1,6,0,0,0,0, v2,5,1, 7,0,0,0,0, •88524 20 i'274oi263 21 >'2, 5, 1, 8,0,0,0,0, > '2,5, 1,9,0,0,0,0, 14003 22 26687 242371OI, ,,2,5,2,0,0,0,0,0, ,-2,5,2,1,0,0,0,0, 39430 24 52174 25 ,,2,5,2,2,0,0,0,0, 64919 26 > '2,5,2,3,0,0,0,0, 77666 27 > '2,5,2,4,0,0,0,0, 90414 28 > '2,5,2,5,0,0,0,0, 1-27503163 29 ,,2,5,2,6,0,0,0,0, 15913 30 v2,5,2,7,0,0,0,0. 28665 31 ^ '2,5,2,8,0,0,0,0, 41418 32 ,,2,5,2,9,0,0,0,0, 54114 24337051, w2,5,3,o,o,o,o,o. 66869 34 > '2,5,3, 1,0,0,0,0, 79626 35 > '2,5,3,2,0,0,0,0, > '2,5,3,3,0,0,0,0, 92384 36 1-27605143 37 > '2,5,3,4,0,0,0,0, 17904 38 > '2,5,3,5,0,0,0,0, 30666 39 v2,5,3,6,o,o,o,o. 43429 40 > '2,5,3,7,0,0,0,0, 56193 41 ^ '2,5,3,8,0,0,0,0, 68959 42 "2,5,3,9,0,0,0,0, 81668 24437001, ^ '2,5,4,0,0,0,0,0, 94436 44 ,,2,5,4,1,0,0,0,0, 1*27707205 45 "2,5,4,2,0,0,0,0, 19976 46 > '2,5,4,3,0,0,0,0, 32748 47 > '2,5,4,4,0,0,0,0, 45521 48 "2,5,4,5,0,0,0,0, 58296 49 > '2,5,4,6,0,0,0,0, 71072 SO > '2,5,4,7,0,0,0,0, 83849 51 ,,2,5,4,8,0,0,0,0, 96627 52 "2,5,4,9,0,0,0,0, Natural Numbers. 1*27809350 22131 34913 47696 60482 73268 86055 98844 1*27911634 24425 37159 49953 62748 75544 88342 I '23001141 13941 26742 39545 52349 65096 77903 907 II 1*28103520 16330 29142 41955 54769 67584 80401 93161 1*28205980 18801 31623 44446 57270 70096 82923 95751 1*28308581 21354 34186 47019 59854 72690 85527 98366 1*28411206 24047 36889 Dual Logarithms. 24536951, 54 55 56 57 58 59 60 62 24636901, 64 65 66 67 68 69 70 71 72 24736851, 74 75 76 77 78 79 80 81 82 24836801, 84 85 86 87 88 89 90 91 92 24936751, 94 95 96 97 98 99 2500 01 02 Dual Numbers. "2,5 >'2,5 >'2,5 "2,5 12,5 ^2,5 12,5 {2,5 |2,5 |2,5 {2,5 "2,5 >'2,5 ^'2,5 |2,5 >I'2,5 12,5 >'2,5 y'2,5 12,5 |2,5 ^2,5 4'2,5 i2,5 2,5 2,5 .2,5 4'2,5 |2,5 {2,5 >'2,5 >'2,5 h'5 J2,5 "2,5 "2,5 >'2,5 v2,5 J2,5 "2,5 "2,5 "2,5 12,5 >|'2,5 >'2,5 "2,5 "2,5 >'2,5 5,0,0 5,1,0 5,2,0 5,3,0 5,4,0; 5,5,0 5,6,0 5,7,0; 5,8,0: 5,9,0 6,0,0 6,1,0 6,2,0 6,3,0 6,4,0 6,5,0 6,6,0, 6,7,0 6,8,0, 6,9,0 7,0,0 7,1,0 7,2,0 7,3,0 7,4,0; 7,5,0 7,6,0 7,7,0 7,8,0 7,9,0 8,0,0 8,1,0 8,2,0 8,3,0 8,4,0 8,5,0 8,6,0 8,7,0 8,8,0 8,9,0 9,0,0 9,1,0 9,2,0 9,3,0 9,4,0 9,5,0 9,6,0 9,7,0 9,8,0 9,9,0 Multiples of Di&rences. I27I 1272 2542 2544 .3«i3 3816 5084 5088 ft.l.S'? 6360 7626 7632 8897 8904 10x68 10176 "439 11448 I 1274 127'; 2 254« 2S50 .3 3822 .3«2,S 4 5096 5100 S 6370 6375 6 7644 76SO 7 8918 8925 8 10x92 10200 9 XX 466 "475 1277 2554 3831 5108 6385 7662 8939 8 ;xo2i6 9 "493 X278 2556 3834 5112 6390 7668 8946 10224 1 1 502 X 1280 1281 2 2560 2562 3 3840 3843 4 5120 5124 S 6400 6405 6 7680 7686 7 8960 8967 8 10240 10248 9 11520 1x529 X 1283 2 2566 3 3849 4 S1.32 ■; 6415 6 7698 7 8981 8 10264 9 1 1547 1284 2568 3852 SI36 6420 7704 10272 "556 !, 2 = 69314718, , 4 = 138629437, > 8 = 207944154, Dual Logarithms of powers of 2 and lo. A, 10 = 230258509, J,, 10* = 921034037, Y' ^°! = 460517019, ,„ lo^ = 1151292546, 4,, 10=^ = 690775528, v« lo" = 1381551056, 10" = I6II809565, 10^ = 1842068074, lo'' = 2072326584, Nat. No. 1-2844 to 1-2972 D. Log. 2503.... to 2602.... D. No. 12,6,0,0, to >^2,6,9,9, [27 Natural Numbers. 1-28443938 56782 69628 82475 95323 1-28508173 21024 33876 46729 59584 72382 85239 98098 1-28610958 23819 36681 49545 62410 75276 88144 1*28700954 13824 26695 39568 52442 65317 78194 91072 1-28803951 16831 29655 42538 55422 68308 81195 94083 1-28906972 19863 32755 45648 58485 71381 84278 97176 1*29010076 22977 35879 48783 61688 74594 Dual Logarithms. 25032234, 04 05 06 07 08 09 10 II 12 25132184, 14 15 16 17 18 19 20 21 22 25232134, 24 25 26 27 28 29 30 31 32 25332084, 34 35 36 37 38 39 40 41 42 25432034, 44 45 46 47 48 49 50 51 52 Dual Numbers. ^2 6,0,0,0 6,0,1,0 6,0,2,0 6,0,3,0 6,0,4,0 6,0,5,0 6,0,6,0 6,o,7,0; 6,0,8,0, 6,0,9,0 6,1,0,0 6,1,1,0, 6,1,2,0, 6,1,3,0 6,1,4,0 6,1,5,0 6,1,6,0 6,1,7,0 6,1,8,0 6,1,9,0 6,2,0,0, 6,2,1,0, 6,2,2,0 6,2,3,0, 6,2,4,0, 6,2,5,0 6,2,6,0 6,2,7,0 6,2,8,0 6,2,9,0 6,3,0,0 6,3,1,0 6,3,2,0 6,3,3,0 6,3,4,0 6,3,S,o 6,3,6,0 6,3,7,0 6,3,8,0 6,3,9,0 6,4,OjO 6,4,1,0 6,4,2,0 6,4,3,0: 6,4,4,0 6,4, 5,0; 6,4,6,0, 6,4,7,0 6,4,8,0 6,4,9,0 0,0 0,0 0,0, 0,0 0,0 0,0, 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0, 0,0 0,0 0,0 0,0 0,0 OjO 0,0 0,0 0,0 0,0; 0,0, 0,0 0,0 0,0, 0,0 0,0 0,0 0,0, 0,0, 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0; 0,0 0,0 Natural Numbers. 1-29087443 1-29100352 13262 26173 39086 52'000 64915 77831 90749 i*29203'668 1653a 29452 42375 55299 68225 81152 94080 1 '29307009 19940 32872 45747 58682 71618 84555 97493 1*29410433 23374 36316 49260 62205 75093 88041 1*29500990 13940 26891 39844 5-27,98 65753 78710 91668 1*29604568 17528 30490 43453 56417 69383 82350 95318 1*29708288 21259 Dual Logarithms. 25531984, 54 55 5^ 57 58 59 6o> 61 6z 25631934, 64 65 66 67 68 69 70 71 72 25731884, 74 75 76 77 78 79 80 81 82 25831834, 84 85 86 87 88 89 90 91 92 25931784, 94 95 96 97 98 99 2600 01 02 Dual Numbers. |2, 6,5,0 |2,6,5,l >'2,6,5,2 >I'2,6i5,3 >t2,6,5,4, 4-2,6,5,5 4,2,6,5, 6 42,6,5,7 vl,2,6,5,8 i2,6,5,9 X2,6,6,o > '2,6,6, 1 > '2,6,6,2 >'2,6,6,3 4,2,6,6,4, 2,6,6,5 2,6,6,6 2,6,6,7 2,6,6,8 |2,6,6,9 ^2,6,7,0 w2,6,7,i > '2,6,7,2 v2,6,7,3 >1'2,6,7,4 ^2,6,7,5 >'2,6,7,6 12,6,7,7 "2,6,7,8, 4,2,6,7,9 ,,2,6,8,0 > '2,6,8, r. >r2j 6,8,2 ,,2,6,8,3 4,2,6,8,4 J,2,6,8,5 ,,2,6,8,6 ,,2,6,8,7 ,,2,6,8,8 ,,2,6,8,9 2,6,9,0 2,6,9,1 2,6,9,2 2,6,9,3 4,2,6,9,4, 12,6,9,5 4,2,6,9,6 |2,6,9,7 ,,2,6,9,8 4,2,6^9,9, 0,0 0,0 0,0 0,0, 0,0, 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0, 0,0 0,0 0,0, 0,0, 0,0 0,0 0,0 0,0 0,0 0,0 0,0, 0,0 0,0 0,0 0,0 0,0 0,0 0,0, 0,0 0,0 0,0 0,0 0,0 0,0,0 0,0. 0,0 0,0, Multiples of Difierences. 1284 1285 2S68 2570 3«52 .3«SS .■5136 5140 6420 6425 7704 7710 8988 «99.S 10272 10280 "556 "56s 1287 1288 2574 2S76 3861 3864 Si4« ■ilS2 64.3s 6440 7722 7728 9009 9016 10296 10304 "5«3. 11592 1 1290 1 291 2580 2582 3870 3«73 5160 5164 6450 6455 7740 774^ 9030 9037 10320 10328 X1610 11619 1293 1294 2586 2588 3879 3882 5172 <;i7b 646'; 6470 775« 7764 9051 9058 10344 10352 11637 1 1 646 I 1296 2 2592 3 3888 4 ,Si«4 S 6480 6 7776 7 9072 8 10368 9 1 1 664 1286^ 2572 3858 5144 6430 7716 9002 10288 "574 1289 2578! 3867 5156 6445 7734 9023 103 1 2. ii6oii 129*- 25«4 3876. 5168. 6460 7752 9044 10336 II62& 1295 2590 388s 5180 647s 7770 9065 10360 "655 1297 2594 3891 5188 6485 7782 9079 10376 11673 2 = 4 Dual Logarithms of powers of 2 and 10. = 69314718, L 10 = 230258509, J,, lo* = 921034037, = 138629437, 4', io2 = 460517019, ^, io5 = 1151292546, 1- — u,, 10' = 161 1809565, _ ,,, 10^ = 1842068074, , 8 = 207944154, i» 10^ ■= 690775528, ^, 10*5 = 1381551056, \, io3 = 20723265,84, 28] Nat. No. 1-2972 to 1*3101 D. Log. 2602.... to 2701.... D. No. |2,7,0,0, to |2,7,9,9, Natural Numbers. 1-29728377 41350 54324 67299 80276 93254 1*29806233 19214 32196 45179 58105 71091 84078 97066 1 '29910056 23047 36039 49033 62028 75024 87963 1*30000962 13962 26963 39966 52970 65975 78982 91990 1*30104999 17951 30963 43976 56990 70006 83023 96041 1*30209061 22082 35104 48069 61094 74120 87147 1*30300176 13206 26237 39270 52304 65339 Dual Logarithms, 26027267, 03 04 05 06 07 08 09 10 II 26127217, 13 14 15 16 17 18 19 20 21 26227167, 23 24 25 26 27 28 29 30 31 26327117, 33 34 35 36 37 38 39 40 41 26427067, 43 44 45 46 47 48 49 50 51 Dual Numbers. w2, 7, 0,0,0,0,0,0, ,,2,7,0,1,0,0,0,0, >, 2,7, 0,2, 0,0,0,0, w2, 7,0,3,0,0,0,0, 12,7,0,4,0,0,0,0, >I'2, 7,0,5,0,0,0,0, 2,7,0,6,0,0,0,0, 2, 7»o,7, 0,0,0,0, 2,7,0,8,0,0,0,0, 2,7>o,9,o,o,o,o, J,2,7, 1,0,0,0,0,0, , ,2,7,1, 1,0,0,0,0, ,,2,7,1,2,0,0,0,0, w2,7, 1,3,0,0,0,0, 4'2,7>i>4>o,o,o,o, >'2,7>i>5'0,o,o,o, ,,2,7,1,6,0,0,0,0, >'2,7.i>7)0,o,o,o, ,,2,7,1,8,0,0,0,0, |2, 7, 1,9,0,0,0,0, ,,2,7,2,0,0,0,0,0, ,,2,7,2,1,0,0,0,0, ,,2,7,2,2,0,0,0,0, > '2,7,2,3,0,0,0,0, >I'2, 7, 2,4,0,0,0,0, ^2,7,2,5, 0,0,0,0, ,,2,7,2,6,0,0,0,0, ,,2,7,2,7,0,0,0,0, ,,2,7,2,8,0,0,0,0, 4,2,7,2,9,0 0,0,0, |2,7>3>o,o,o,o,o, ^r2, 7, 3, 1, 0,0,0,0, ^'2, 7,3, 2, 0,0,0,0, w2,7, 3,3, 0,0,0,0, > '2,7,3,4,0,0,0 0, 12,7,3,5,0,0,0,0, w2, 7,3,6,0,0,0,0, >'2,7>3)7>o,o,o,o, w2, 7,3, 8,0,0,0,0, |2,7>3>9.o,o,o,o, 2,7»4>o,o,o,o,o, 2,7>4>i>o,o,o,o, 2,7,4)2,0,0,0,0, . 2,7,4,3)0,0,0,0, >I'2, 7, 4,4,0,0,0,0, >I'2, 7, 4,5)0,0,0,0, ,,2,7,4,6,0,0,0,0, v2, 7,4,7,0,0,0,0, ,,2,7,4,8,0,0,0,0, >|'2, 7,4,9)0,0,0,0, Natural Numbers. I '303783 1 7 91355 1-30404394 17434 30476 435^9 56563 69609 82656 95704 1*30508695 21746 34798 47851 50906 63961 77017 90075 1-30603x34 16194 39204 52268 65333 78400 91468 1*30704537 17607 30679 43752 56856 69843 82920 95998 1-30809078 22159 35241 48325 61410 74496 87583 1*30900613 13703 26794 39887 52981 66076 79173 92271 i'3ioo537o 18471 Dual Logarithms. 26527017, 53 54 55 56 57 58 59 60 61 26626967, (>^ 64 65 66 67 68 69 70 71 26726917, 73 74 75 76 77 78 79 80 8i 26826867, 83 84 85 86 87 88 89 90 91 26926817, 93 94 95 96 97 98 99 2700 01 Dual Numbers. 2,7,5)0,0,0,0,0, 2)7)5)1)0,0,0,0, 2,7,5,2,0,0,0,0, 2,7,5)3)0,0,0,0, 2,7)5)4,0,0,0,0, 2,7)5)5)0,0,0,0, 2,7)5)6,0,0,0,0, 2,7)5)7)0,0,0,0, 2,7)5)8,0,0,0,0, >1'2,7, 5, 9,0,0,0,0, ,,2,7,6,0,0,0,0,0, ,,2,7,6,1,0,0,0,0, ,,2,7,6,2,0,0,0,0, >'2,7, 6,3, 0,0,0,0, 4,2,7,6,4,0,0,0,0, 2,7,6,5,0,0,0,0, 2,7,6,6,0,0,0,0, 2,7,6,7,0,0,0,0, 4,2,7,6,8,0,0,0,0, 4,2,7,6,9,0,0,0,0, > '2,7,7,0,0,0,0,0, v2,7, 7, 1,0,0,0,0, > '2,7)7)2,0,0,0,0, v2,7,7,3,o,o,o,o, 12,7,7)4,0,0,0,0, ]'2,7)7>5)0,o,o,o, /2, 7)7)6,0,0,0,0, /2, 7, 7)7, 0,0,0,0, ^2,7,7,8,0,0,0,0, i'2,7>7)9)0)0,o,o, J,2,7, 8,0,0,0,0,0, J,2,7, 8,1, 0,0,0,0, 4,2,7,8,2,0,0,0,0, i 2,7, 8,3,0,0,0,0, 2,7)8,4,0,0,0,0, J'2,7, 8,5,0,0,0,0, ,,2,7,8,6,0,0,0,0, v2,7)8,7,o,o,o,o, ,,2,7,8,8,0,0,0,0, 4,2,7,8,9,0,0,0,0, /2, 7)9)0)0,0,0,0, ^2,7, 9) 1)0)0,0,0, /2, 7, 9)2)0,0,0,0, /2, 7,9,3,0,0,0,0, |'2, 7)9)4)0,0,0,0, 12,7)9)5)0)0,0,0, ,,2,7,9,6,0,0,0,0, w2,7, 9,7, 0,0,0,0, ,,2,7,9,8,0,0,0,0, 4'2,7, 9) 9)0)0,0,0, Multiples of Differences. 1297 1298 2594 2596 3«9i 3894 5188 5192 648s 6490 7782 7788 9079 9086 10376 10384 1 1673 11682 1300 1 301 2600 2602 3900 3903 5200 5204 6500 6505 7800 7806 9100 9107 10400 10408 1 1 700 1 1709 1303 1304 2606 2608 3909 3912 5212 5216 fesis 6520 7818 7824 9121 9128 10424 10432 1 1 1 727 11736 1 1306 2612 1307 2614 39i« 5224 6530 7836 3921! 5228 6535 7842 9142 10448 "754 9149 10456 11 763 1299 2598 3897 5196 6495 7794 9093 10392 11691 1302 2604 3906 5208 6510 7812 9114 10416 11718 1305 2610 3915 5220 6525 7830 9135 10440 "745 1308 2616 3924 5232 6540 7848 9156 10464 11772 I 1309 2 2618 3 3927 4 5236 ■; 6545 6 7854 7 9163 8 10472 9 1 1 781 I3I0 2620 3930 5240 6550 7860 9170 10480 11790 J L 2 = 6931471 ,„ 4 = 13862943 I, 8 — 207944154 Dual Logarithms of powers of 2 and 10. 4,, 10 = 230258509, 4 = 138629437, L io2 = 460517019, , 4,, io3 = 690775528, 10* = 921034037, io5 = 1151292546, 4,, 10*5 = 1381551056, ), 10^ = 1611809565, L 10^ = 1842068074, L io» = 2072326584, Nat. No. r3102 to 1*3232 D. Log. 2702.... to 2801.... D. No. |2,8,0,0, to 12,8,9,9, [^0 Natural Dual Dual Numbers. Logarithms. Numbers. 1-31025661 27022300, ,,2,8,0,0,0,0,0,0, 38764 03 ,,2,8,0,1,0,0,0,0, 51868 04 ,,2,8,0,2,0,0,0,0, 64973 05 > ,2,8,0,3,0,0,0,0, 78079 06 ,,2,8,0,4,0,0,0,0, 91187 07 ,1,2,8,0,5,0,0,0,0, 1*31 104296 08 4,2,8,0,6,0,0,0,0, 17406 09 4,2,8,0,7,0,0,0,0, 30518 10 4,2,8,0,8,0,0,0,0, 43631 H 4,2,8,0,9,0,0,0,0, 56687 27122250, ,,2,8,1,0,0,0,0,0, 69803 13 ,-2,8,1,1,0,0,0,0, 82920 14 ,,2,8,1,2,0,0,0,0, 96038 15 ,,2,8,1,3,0,0,0,0, 1-31209158 16 ,,2,8,1,4,0,0,0,0, 22279 17 ,,2,8,1,5,0,0,0,0, 35401 18 ,,2,8,1,6,0,0,0,0, 48525 19 ,,2,8,1,7,0,0,0,0, 61650 20 ,,2,8,1,8,0,0,0,0, 74776 21 ,,2,8,1,9,0,0,0,0, 87844 27222200, , ,2,8,2,0,0,0,0,0, 1-31300973 23 ,,2,8,2,1,0,0,0,0, 14103 24 , ,2,8,2,2,0,0,0,0, 27234 25 ,,2,8,2,3,0,0,0,0, 40367 26 ,,2,8,2,4,0,0,0,0, 53501 27 ,,2,8,2,5,0,0,0,0, 66636 28 ,,2,8,2,6,0,0,0,0, 79773 29 ,,2,8,2,7,0,0,0,0, 92911 30 ,,2,8,2,8,0,0,0,0, 1-31406050 31 ,,2,8,2,9,0,0,0,0, 19132 27322150, ,,2,8,3,0,0,0,0,0, 32274 33 ,,2,8,3,1,0,0,0,0, 45417 34 4,2,8,3,2,0,0,0,0, 58562 35 4,2,8,3,3,0,0,0,0, 71708 36 4/2,8,3,4,0,0,0,0, 84855 37 4,2,8,3,5,0,0,0,0, 98003 38 4,2,8,3,6,0,0,0,0, i"3i5i"53 39 4,2,8,3,7,0,0,0,0, 24304 40 ^2,8,3,8,0,0,0,0, 37456 41 4^2,8,3,9,0,0,0,0, 50551 27422100, ,,2,8,4,0,0,0,0,0, 63706 43 J2,8,4, 1,0,0,0,0, 76862 44 ,,2,8,4,2,0,0,0,0, 90020 45 > '2,8,4,3,0,0,0,0, 1-31603179 46 4,2,8,4,4,0,0,0,0, 16339 47 > '2,8,4,5,0,0,0,0, 29501 48 > ,2,8,4,6,0,0,0,0, 42664 49 > ,2,8,4,7,0,0,0,0, 55828 50 , ,2,8,4,8,0,0,0,0, 68994 1 51 , ,2,8,4,9,0,0,0,0, Natural Numbers. I-31682102 95270 1-31708440 21611 34783 47956 61131 74307 87484 I -3 1 800663 13784 26965 40148 53332 66517 79704 92892 I -3 190608 1 19272 32464 45598 58793 71989 85186 98385 1-32011585 24786 37988 51192 64397 77544 90752 1-32103961 17171 30383 43596 56810 70026 83243 96461 1-32209622 22843 36065 49289 62514 75740 88968 1-32302197 15427 28659 Dual Logarithms. 27522050, 53 54 55 56 57 58 59 60 61 27622000, 63 64 65 66 67 68 69 70 71 27721950, 73 74 75 76 77 78 79 80 81 27821900, 83 84 85 86 87 88 89 90 91 27921850, 93 94 95 96 97 98 99 2800 Dual Numbers. ,8,5,0,0,0,0,0 ,8,5,1,0,0,0,0 ,8,5,2,0,0,0,0 ,8,5,3,0,0,0,0 )8,5, 4,0,0,0,0, j8,5, 5,0,0,0,0. ,8,5,6,0,0,0,0, ,8,5,7,0,0,0,0 ,8,5,8,0,0,0,0 ,8,5,9,0,0,0,0 ,8,6,0,0,0,0,0 ,8,6,1,0,0,0,0 ,8,6,2,0,0,0,0 ,8,6,3,0,0,0,0; ,8,6,4,0,0,0,0, ,8,6,5,0,0,0,0, ,8,6,6,0,0,0,0 ,8,6,7,0,0,0,0 ,8,6,8,0,0,0,0 ,8,6,9,0,0,0,0 ,8,7,0,0,0,0,0 ,8,7,1,0,0,0,0 ,8,7,2,0,0,0,0, ,8,7,3,0,0,0,0 ,8,7,4,0,0,0,0, ,8,7,5,0,0,0,0, ,8,7,6,0,0,0,0, ,8,7,7,0,0,0,0 ,8,7,8,0,0,0,0, ,8,7,9,0,0,0,0 ,8,8,0,0,0,0,0 ,8,8,1,0,0,0,0 ,8,8,2,0,0,0,0 ,8,8,3,0,0,0,0 ,8,8,4,0,0,0,0 ,8,8,5,0,0,0,0 ,8,8,6,0,0,0,0 ,8,8,7,0,0,0,0 ,8,8,8,0,0,0,0 ,8,8,9,0,0,0,0 ,8,9,0,0,0,0,0 ,8,9,1,0,0,0,0 ,8,9,2,0,0,0,0 ,8,9,3,0,0,0,0 ,8,9,4,0,0,0,0 ',8,9,5,0,0,0,0 :, 8,9,6,0,0,0,0 :, 8,9,7, 0,0,0,0 1,8,9,8,0,0,0,0 1,8,9,9,0,0,0,0 Multiples of Differences. I3I0 nil 1312 2620 2622 2624 3930 3933 3936 5240 5244 5248 6550 b'ISS 6560 7860 7872 9170 9177 9184 10480 10488 10496 II790 11799 1 1808 1313 1314 2626 2628 3939 3942 S2,S2 5256 6S6S 6570 7878 7884 9191 9198 10504 105 1 2 11817 II 826 1316 1317 2632 2634 3948 39"; I 5264 5268 6580 65«S 7896 7802 9212 9219 10528 10536 1 1844 "«S3 I3I9 2638 3957 5276 659s 7914 9233 10552 11871 1322 2644 3966 5288 6610 7932 9254 10576 u8qS 1320 2640 3960 5280 6600 7920 9240 10560 11880 1323 2646 3969 5292 6615 7938 9261 10584 1 1907 131S 2630 3945 5260 6575 7890 9205 10520 "835 1318 2636 3954 5272 6590 7908 9226 10544 1 1 862 1321 2642 3963 5284 6605 7926 9247 10568 Dual Logarithms of powers of 2 and 10. 4" 2 = 69314718, I, 10 = 230258509, 4,, 10* = 921034037, 4,, lo^ = 1611809565, i, 4 = 138629437, i, 8 = 207944154, I, 10' = 690775528, 10^ = 460517019, ., 10^ = 115 1 292546, X, 10" = 1842068074, , lo'^ = 1381551056, I, io9 = 2072326584, 30] Nat. No. r3233 to 1-3365 D. Log. 2801.... to 2900.... D. No. |2,9,0,0, to >^2,9,9,9, Natural Dual 1 Dual Numbers. Logarithms. I Numbers. 1*32335918 28017333, ,1,2,9,0,0,0,0,0,0, 49152 02 vI,2,9,o, 1,0,0,0,0, 62387 03 \I'2,9,0,2,0,0,0,0, 75623 04 \!'2, 9,0,3, 0,0,0,0, 88861 05 ,1,2,9,0,4,0,0,0,0, 1*32402100 06 4'2,9)0,5, 0,0,0,0, 15340 07 ,1,2,9,0,6,0,0,0,0, 28582 08 >l/2,9,o, 7,0,0,0,0, 41825 09 4,2,9,0,8,0,0,0,0, 55069 10 ^2,9,0,9,0,0,0,0, 68254 28117283, 4'2,9, 1,0,0,0,0,0, 81501 12 4,2,9,1,1,0,0,0,0, 94749 13 4,2,9,1,2,0,0,0,0, 1-32507998 14 ,,2,9,1,3,0,0,0,0, 21249 15 ,,2,9,1,4,0,0,0,0, 34501 16 w2,9,l, 5,0,0,0,0, 47754 17 4,2,9,1,6,0,0,0,0, 61009 18 ,,2,9,1,7,0,0,0,0, 74265 19 ,,2,9,1,8,0,0,0,0, 87522 20 ,,2,9,1,9,0,0,0,0, I'326oo722 28217233, 4,2,9,2,0,0,0,0,0, 13982 22 ,,2,9,2,1,0,0,0,0, 27243 23 ,,2,9,2,2,0,0,0,0, 40506 24 >'2,9>2,3,0,0,0,0, 53770 25 ,,2,9,2,4,0,0,0,0, 67035 26 4'2,9>2,5,o,o,o,o, 80302 27 4,2,9,2,6,0,0,0,0, 93570 28 ,,2,9,2,7,0,0,0,0, 1-32706839 29 4,2,9,2,8,0,0,0,0, 20II0 30 ,,2,9,2,9,0,0,0,0, 33323 28317183, 4,2,9,3,0,0,0,0,0, 46596 32 4/2,9,3,1,0,0,0,0, 59871 33 4,2,9,3,2,0,0,0,0, 73147 34 4/2,9,3>3»o,o,o,o, 86424 35 4'2,9»3»4,o,o,o,o, 99703 36 >'2,9>3>5>o,o,o,o. 1-32812983 37 4/2,9.3)6,0,0,0,0, 26264 38 > '2,9.3.7.0,0,0,0, 39547 39 > '2,9,3,8,0,0,0,0, 52831 40 ,,2,9,3,9,0,0,0,0, 66056 284i7i33> ,,2,9,4,0,0,0,0,0, 79343 42 ,,2,9,4,1,0,0,0,0, 92631 43 ,,2,9,4,2,0,0,0,0, 1*32905920 44 ,,2,9,4,3,0,0,0,0, 19211 45 ,,2,9,4,4,0,0,0,0, 32503 46 > '2,9,4.5.0,0,0,0, 45796 47 ,,2,9,4,6,0,0,0,0, 59091 48 ''2,9.4.7,0,0,0,0, 72387 49 ,,2,9,4,8,0,0,0,0, 85684 SO ' '2,9.4,9,0,0,0,0, Natural Dual Dual Numbers. Logarithms. Numbers. 1-32998922 28517083, > '2,9,5,0,0,0,0,0, 1-33012222 52 ,,2,9,5,1,0,0,0,0, 25523 53 ,,2,9,5,2,0,0,0,0, 38826 54 V '2,9,5.3,0,0,0,0, 52130 55 > '2,9,5,4,0,0,0,0, 65435 56 > '2,9,5,5,0,0,0,0, 78742 57 4/2,9,5,6,0,0,0,0, 92050 58 ''2,9,5.7.0,0,0,0, i'33io5359 59 "2,9.5.8,0,0,0,0, 18670 60 > '2,9.5,9,0,0,0,0, 31921 28617033, 4,2,9,6,0,0,0,0,0, 45234 62 ,,2,9,6,1,0,0,0,0, 58549 (>3 4/2,9,6,2,0,0,0,0, 71865 64 > '2,9,6,3.0,0,0,0, 85182 65 4,2,9,6,4,0,0,0,0, 98501 66 4/2.9,6,5,0,0,0,0, 1-33211821 67 ,,2,9,6,6,0,0,0,0, 25142 68 > '2.9,6.7.0,0,0,0, 38464 69 ,,2,9,6,8,0,0,0,0, 51788 70 ,,2,9,6,9,0,0,0,0, 65053 28716983, ,,2,9,7,0,0,0,0,0, 78380 72 ,,2,9,7,1,0,0,0,0, 91708 73 ,,2,9,7,2,0,0,0,0, 1*33305037 74 > '2,9.7.3.0,0,0,0, 18368 75 > '2,9.7.4.0,0,0,0, 31700 76 > '2,9.7,5.0.0,0,0, 45033 77 4,2,9,7,6,0,0,0,0, 58368 78 > '2,9.7.7,0,0,0,0, 71704 79 ,,2,9,7,8,0,0,0,0, 85041 80 ,,2,9,7,9,0,0,0,0, 98318 28816933, ,,2,9,8,0,0,0,0,0, 1-33411658 82 ,,2,9,8,1,0,0,0,0, 24999 83 ,,2,9,8,2,0,0,0,0, 38341 84 ,,2,9,8,3,0,0,0,0, 51685 85 ,,2,9,8,4,0,0,0,0, 65030 86 ,,2,9,8,5,0,0,0,0, 78377 87 ,,2,9,8,6,0,0,0,0, 91725 88 ,,2,9,8,7,0,0,0,0, 1*33505074 89 ,,2,9,8,8,0,0,0,0, 18425 90 ,,2,9,8,9,0,0,0,0, 31716 28916883, ,,2,9,9,0,0,0,0,0, 45069 92 "2,9.9,1,0,0,0,0, 58424 93 ,,2,9,9,2,0,0,0,0, 71780 94 "2,9,9,3.0.0,0,0, 85137 95 ,,2,9,9,4,0,0,0,0, 98496 96 4/2,9.9.5,0.0,0,0, 1-33611856 97 4,2,9,9,6,0,0,0,0, 25217 98 4/2,9,9,7,0,0,0,0, 38580 99 4/2,9,9,8,0,0,0,0, 51944 2900 4,2,9,9,9,0,0,0,0, Multiples of Differences. 1323 2646 3969 5292 6615 7938 9261 10584 9111907 1324 2648 3972 5296 6620 7944 9268 10592 11916 I 1326 1327 2 2652 2654 3 397« .39«i 4 ■5304 S3o8 S 6630 663s 6 79 S6 7962 7 9282 9289 8 10608 10616 9 "934 "943 1329 1330 2658 2660 39«7 3990 S3I6 5320 6645 6650 7974 7980 9303 9310 10632 10640 11961 II 970 1332 1333 2664 2666 3996 3999 S32» 5332 6660 6665 7992 7998 9324 9331 10656 10664 11988 11997 , »32S 265c 3975 5300 6625 7950 9275 10600 1x925 1328 2656 3984 5312 6640 7968 9296 10624 11952 1331 .2662 '3993 5324 6655 7986 9317 10648 11979 1334 2668 4002 5336 6670 8004 9338 10672 12006 1335 1336 2670 2672 4005 4008 S340 5344 6675 6680 8010 8016 9345 9352 10680 10688 12015 12024 Dual Logarithms of powers of 2 and 10. t, 2 = 69314718, 4,, 10 = 230258509, 4,, 10* = 921034037, , 4 = 138629437, 4/. io2 = 460517019, 4/> io5 = 1151292546, 4,, 8 = 207944154, I, 10^ = 690775528, i> 10" = 1381551056, 4'. lo^ = 2072326584, J,, io7 = 1611809565, , ,, 10^ =r 1842068074, Nat. No. 1*3310 to 1*3442 D. Log. 2859.... to 2958.... D. No. A0|0,0, to >1.3,0,9,9, [31 Dual Logarithms. 28593054, 60 61 62 ^Z 64 65 66 67 68 28693004, 70 72 73 74 75 76 77 78 28792954, 80 81 82 83 84 85 86 87 88 28892904, 90 91 92 93 94 95 96 97 98 28992854, 2900 01 02 03 04 05 06 07 08 Dual Numbers. Natural Numbers. 1-33766832 80209 93587 1-33806967 20347 33729 47112 60497 73883 87270 I •33900599 13989 27380 40773 54167 67562 80959 94357 1-34007756 21157 34499 47902 61307 74713 88120 1-34101528 14938 28349 41762 55176 68533 81950 95368 1-34208788 22209 35631 49055 62480 75906 89334 I '34302702 16132 29564 42997 56431 69867 83304 96742 1-34410182 23623 Dual Logarithms. 29092804, 10 II 12 13 14 15 16 17 18 29192754, 20 21 22 23 24 25 26 27 28 29292704, 30 31 32 Z3 34 35 36 37 38 29392654, 40 41 42 43 44 45 46 47 48 29492604, 50 51 52 53 54 55 56 57 58 Dual Numbers. 5>0: 5,1 5,2 5,3 5,4 5,5 5,6 5,7 5,8 5,9 6,0 6,1 6,2 ^,Z 6,4 6,5 6,6 6,7 6,8 6,9 7,0 7,1 7,2 7,3 7,4 7,5 7,6 7,7 7,8 7,9 8,0 8,1 8,2 8,3 8,4 8,5 8,6 8,7 8,8 8,9 9,0 9,1 9,2 9,3 9,4 9,5 9,6 9,7 9,8 9,9 Multiples of DiflFerences. I.l^I 1.332 2662 2()64 399.3 3996 S324 S328 6655 6660 7986 7992 9317 9324 10648 10656 1 1979 11988 1334 133s 2668 2670 4002 4005 .S3.3t> 5340 6670 667"; 8004 8010 9338 9345 10672 10680 12006 12015 1337 2674 401 1 5348 6685 8022 , 9359 8 10696 9 '12033 1338 2676 4014 5352 6690 8028 9366 10704 12042 1340 1341 2680 2682 4020 4023 53(>o 5364 6700 6705 8040 8046 9380 9387 10720 10728 12060 12069 1333 2666 3999 5332 6665 7998 9331 10664 11997 1336 2672 4008 5344 6680 8016 9352 10688 12024 1339 2678 4017 5356 6695 8034 9373 10712 1 205 1 1342 2684 4026 5368 6710 8052 9394 10736 12078 1343 2686 4029 5372 6715 8058 9401 10744 12087 1344 2688 4032 5376 6720 8064 9408 10752 12096 ., 4 = 138629437, Dual Logarithms of powers of 2 and 10. 2 = 69314718, V, 10 = 230258509, io2 = 460517019, V, io5 = 1151292546, 10* = 921034037, J,. 10'^ = 16x1809565, = 207944154, \, lo-'' = 690775528, \, lo*^ = 1381551056,- I, 10^ = 2072326584, 10^ = 1842068074, 32] Nat. No. 1-3443 to 1-3576 D. Log. 2958.... to 3057.... D. No. 13,1,0,0, to J.3,1,9,9, Natural Numbers. I "34431000 44443 57887 71333 84780 98228 1-34511678 25129 38581 52035 65431 78887 92345 1-34605804 19265 32727 46190 59655 73121 86588 99996 1*34713466 26937 40410 53884 67359 80836 94314 1-34807793 21274 34696 48179 61664 75150 88638 I '34902 1 27 15617 29109 42602 56096 69531 83028 96526 I-350I0026 ! 23527, 37029 50533 64038 77544 91052 Dual Logarithms. 29588087, 59 60 61 62 ^Z 64 65 66 67 29688037, 69 70 71 72 73 74 75 76 77 29787987, 79 80 81 82 83 84 85 86 87 29887937, 89 90 91 92 93 94 95 96 97 29987887, 99 3000 01 02 03 04 05 06 07 Dual Numbers. 3,1,0,0,0,0,0,0, 3,1,0,1,0,0,0,0, 3,1,0,2,0,0,0,0, i3'i>o,3, 0,0,0,0, >l'3,i>o,4>o,o,o,o, >|'3»i»o,5, 0,0,0,0, i35i>o,6,o,o,o,o, >l'3,i»o, 7,0,0,0,0, 4,3,1,0,8,0,0,0,0, 4'3>ijO,9,o,o,o,o, 3,1,1,0,0,0,0,0, 3,1,1,1,0,0,0,0, 3,1,1,2,0,0,0,0, 3,1,1,3,0,0,0,0, l3>iji>4,o,o,o,o, >'3,i,i55'0,o,o,o, J3, 1,1.6,0,0,0,0, >'3»i,i»7»o,o,o,o, ,,3,1,1,8,0,0,0,0, i3,', 1,9,0,0,0,0, 13,1,2,0,0,0,0,0, ■3,1,2,1,0,0,0,0, 3,1,2,2,0,0,0,0, 3,1,2,3,0,0,0,0, 3,1,2,4,0,0,0,0, > '3, 1, 2,5,0,0,0,0, > '3, 1,2,6,0,0,0,0, w3, 1,2,7,0,0,0,0, v3, 1, 2,8,0,0,0,0, 13,1,2,9,0 0,0,0, > '3, 1,3,0,0,0,0,0, ^ '3, 1,3, 1,0,0,0,0, >'3, 1, 3,2, 0,0,0,0, ^'3,1,3,3,0,0,0,0, ^'3,1,3,4,0,0,0,0, 3,1,3,5,0,0,0,0, 3,1,3,6,0,0,0,0, 3,1,3,7,0,0,0,0, .3,1,3,8,0,0,0,0, i3, 1,3,9,0,0,0,0, I3, 1,4,0,0,0,0,0, 3,1,4,1,0,0,0,0, 3,1,4,2,0,0,0,0, .3,1,4,3,0,0,0,0, i3, 1,4,4,0,0,0,0, |3. 1,4,5,0,0,0,0, > '3, ^,4,6,0,0,0,0, w3, 1, 4,7, 0,0,0,0, > '3, ^,4,8,0,0,0,0, 4,3,I,4,9;0,0,0,0, Natural Numbers. i"35io4Soi I80II 31523 45036 58551 72067 85584 99103 1-35212623 26144 39606 53130 6665s 80182 93710 i'353o7239 20770 34302 47835 61370 74846 88383 1*35401922 15462 29004 42547 56091 69637 83184 96732 1-35510221 23772 37324 50878 64433 77989 91547 1 "35605 106 18667 32229 45731 59296 72862 86429 99998 1-35713568 27139 40712 54286 67861 Dual Logarithms Dual Numbers. >'3, 1, 5,0,0,0,0,0 ^'3, 1, 5, 1, 0,0,0,0 >'3, 1, 5, 2, 0,0,0,0 v3,i,5,3,o,o,o,o 4'3, 1, 5,4,0,0,0,0 13,1,5,5,0,0,0,0 3,1,5,6,0,0,0,0 3,1,5,7,0,0,0,0 3,1,5,8,0,0,0,0 3,1,5,9,0,0,0,0, v3, 1,6,0,0,0,0,0, v3, 1,6, 1,0,0,0,0 ,,3,1,6,2,0,0,0,0 v3, 1,6,3,0,0,0,0, 4,3,1,6,4,0,0,0,0 13,1,6,5,0,0,0,0 X3, 1,6,6,0,0,0,0 4'3, 1,6,7,0,0,0,0 i 3, 1, 6,8,0,0,0,0 3,1,6,9,0,0,0,0 ['3,1,7,0,0,0,0,0, b, 1,7, 1,0,0,0,0, b, 1,7,2,0,0,0,0, l3, 1,7,3,0,0,0,0 b, 1,7,4,0,0,0,0, '3,1,7,5,0,0,0,0 .3,1,7,6,0,0,0,0 '3,1,7,7,0,0,0,0 .3,1,7,8,0,0,0,0 4'3, 1,7,9,0,0,0,0 13,1,8,0,0,0,0,0 v3, 1, 8,1,0,0,0,0 > '3, 1,8,2,0,0,0,0, > '3,^,8,3,0,0,0,0 13,1,8,4,0,0,0,0 J'3, 1, 8,5, 0,0,0,0 ,,3,1,8,6,0,0,0,0^ >'3, 1, 8,7, 0,0,0,0, v3, 1,8,8,0,0,0,0, is, 1, 8,9,0,0,0,0 13,1,9,0,0,0,0,0 ^'3, 1, 9,1, 0,0,0,0 >'3, 1, 9,2, 0,0,0,0 > '3,1,9,3,0,0,0,0 13, 1,9,4,0,0,0,0 ^s, 1,9,5,0,0,0,0 ,'3,1,9,6,0,0,0,0 > '3, 1,9,7,0,0,0,0^ > '3, 1, 9,8,0,0,0,0 J'S,!, 9,9,0,0,0,0 Multiples of Diflferences. 1344 1345 2688 2690 4032 4035 5376 S3«o 6720 6725 8064 8070 9408 9415 10752 10760 12096 1 2 105 I 2 1347 2694 1348 2696 3 4 5 6 4041 5388 6735 8082 4044 5392 6740 8088 7 8 9429 10776 9436 10784 9 12123 12132 1350 1351 2700 2702 4050 4053 5400 6750 8100 5404 6755 8106 9450 10800 9457 12150 12159 I 1353 i3';4 2 2706 2708 3 4059 4062 4 5412 5416 S 6765 6770 6 8118 8124 7 9471 9478 8 10824 10832 9] 12177 I2I86, 134' 269: 403! 538. 673' 8o7( 942: 1076! l2Ui I34< 269! 404; 539< 674; 809^ 944: 10792 12141 1353 2704 405^ 540J 676c 8112 9464 io8ie l2l(A 135! 271C 4065 542c 677s 813c 94S5 1084c 12195 1 1 1356 2 I 2712 3 I 4068 41 5424 5 6780 61 8136 7 9492 8 10848 9 !l220d 1357 2714 4071 5428 6785 8142 9499 10856 12213 I 2 = 69314718, 4 = 138629437, 8 — 207944154, Dual Logarithms of powers of 2 and 10. L 10 = 230258509, X, lo* = 921034037, ,„ io2 = 460517019, ,„ 10* = 1151292546, 4,, I03 = 690775528, 4,, 10" = I381551056, 10^ = 1611809565, 10^ = 1842068074, lo** = 2072326584, Nat. No. 1-3577 to 1*3712 D. Log. 3058.... to 3157.... D. No. >I.3,2,0,0, to |3,2,9,9, [33 Natural Numbers. Dual Logarithms. i*357753io 1-35802467 16047 29629 43212 56796 70382 83969 97558 1-35911085 24676 38268 51862 65457 79054 92652 1-3600625 1 19852 33454 46996 60601 74207 87814 1-36101423 15033 28645 42258 55872 69488 83043 96661 1-36210281 23902 37524 SI 148 64773 78399 92027 1*36305656 19226 • 32858 46491 60126 73762 87399 1-36401038 14678 28319 41962 30583120, 59 60 61 62 ^Z 64 65 66 67 30683070, 69 70 71 72 73 74 75 76 11 30783020, 79 80 81 82 83 84 85 86 87 30882970, 89 90 91 92 93 94 95 96 97 30982920, 99 3100 01 02 03 04 05 06 07 Dual Numbers. j3>2 4'3>2 >l'3>2 i3,2 4'3>2 4'3>2 13,2 |3>2 >1'3,2 >I'3,2 |3,2 {3,2 ■3>2 3>2 3,2 ■3>2 3,2 3,2 3,2 3,2 3,2 3,2 l3,2 l3,2 |3,2 i3,2 i3,2 >l'3,2 i3,2 >i3,2 >1'3,2 |3,2 {3,2 {3,2 |3,2 >1'3,2 {3,2 ^3,2 i3,2 4'3,2 |3,2 3,2 3,2 .3,2 |3,2 >^3,2 0,0,0,0,0,0 0,1,0,0,0,0, 0,2,0,0,0,0 0,3,0,0,0,0 0,4,0,0,0,0. 0,5,0,0,0,0 0,6,0,0,0,0 0,7,0,0,0,0 0,8,0,0,0,0 0,9,0,0,0,0 1,0,0,0,0,0 1,1,0,0,0,0 1,2,0,0,0,0 1,3,0,0,0,0 1,4,0,0,0,0 1,5,0,0,0,0 1,6,0,0,0,0 1,7,0,0,0,0 1,8,0,0,0,0- 1,9,0,0,0,0, 2,0,0,0,0,0, 2,1,0,0,0,0, 2,2,0,0,0,0, 2,3,0,0,0,0 2,4,0,0,0,0 2,5,0,0,0,0, 2,6,0,0,0,0 2,7,0,0,0,0 2,8,0,0,0,0 2,9,0,0,0,0 3,0,0,0,0,0 3,1,0,0,0,0 3,2,0,0,0,0 3,3,0,0,0,0 3,4,0,0,0,0 3,5,0,0,0,0 3,6,0,0,0,0 3,7,0,0,0,0 3,8,0,0,0,0 3,9,0,0,0,0 4,0,0,0,0,0 4,1,0,0,0,0 4,2,0,0,0,0, 4,3,0,0,0,0 4,4,0,0,0,0 4,5,0,0,0,0 4,6,0,0,0,0 4,7,0,0,0,0 4,8,0,0,0,0 4,9,0,0,0,0 Natural Numbers, Dual Logarithms. i"36455545 69191 82838 96486 1-36510136 23787 13 37439 14 51093 15 64748 16 78404 17 92001 31182820 1-36605660 19 19321 20 32983 21 46646 22 603 1 1 73977 87644 1-36701313 14983 28593 42266 55940 69616 83293 96971 1-36810651 24332 38014 51698 65322 79009 92697 1-36906386 20077 33769 47462 61157 74853 88550 1-37002187 15887 29589 43292 56996 70702 84409 98117 1-37111827 25538 31082870, 09 10 II 12 23 24 25 26 27 31282770, 29 30 31 32 33 34 35 36 37 31382720, 39 40 41 42 43 44 45 46 47 31482670, 49 • 50 51 52 53 54 55 56 57 Dual Numbers. >'3, 2, 5,0,0,0,0,0 "3,2,5,1,0,0,0,0, > '3,2,5,2,0,0,0,0, >'3, 2, 5, 3,0,0,0,0, >^3,2, 5, 4,0,0,0,0 vl'3,2, 5, 5,0,0,0,0 \!'3, 2, 5, 6,0,0,0,0 >l/3,2,5, 7,0,0,0,0 ^3, 2, 5, 8,0,0,0,0 4'3, 2, 5, 9,0,0,0,0 i 3,2,6,0,0,0,0,0 3,2,6,1,0,0,0,0 >1'3, 2,6,2,0,0,0,0 i3, 2, 6,3,0,0,0,0 3,2,6,4,0,0,0,0 13,2,6,5,0,0,0,0 13,2,6,6,0,0,0,0 3,2,6,7,0,0,0,0 3,2,6,8,0,0,0,0 3,2,6,9,0,0,0,0 I3, 2, 7, 0,0,0,0,0 i3, 2, 7, 1, 0,0,0,0 13,2,7,2,0,0,0,0, >i'3,2,7, 3,0,0,0,0 >i'3,2,7,4,o,o,o,o l'3,2,7,5,o,o,o,o b,2,7, 6,0,0,0,0 ['3,2,7,7,0,0,0,0 ['3,2,7,8,0,0,0,0, l'3,2,7,9,o,o,o,o, ['3,2,8,0,0,0,0,0 13,2,8,1,0,0,0,0 U,2,8,2,0,0,0,0 b, 2, 8,3, 0,0,0,0 ['3,2,8,4,0,0,0,0 >I'3,2, 8,5,0,0,0,0, ,,3,2,8,6,0,0,0,0, \'3, 2, 8,7,0,0,0,0 >'3, 2, 8,8,0,0,0,0 '|'3, 2,8,9,0, 0,0,0 13,2,9,0,0,0,0,0 > '3, 2,9, 1,0,0,0,0 > '3, 2,9,2,0,0,0,0, >'3,2, 9,3,0,0,0,0 '1'3, 2, 9,4,0, 0,0,0 ^3,2, 9,5, 0,0,0,0 > '3,2, 9,6,0,0,0,0 > '3, 2, 9,7,0,0,0,0 >'3, 2, 9,8,0,0,0,0 13,2,9,9,0,0,0,0 Multiples of Differences, 1357 1358 2714 2716 4071 4074 «;428 5432 67«'; 6790 8142 8148 9499 9506 10856 10864 12213 12222 1360 1361 2720 4080 2722 4083 5440 6800 8160 5444 6805 8166 9520 10880 9527 10888 12240 12249 1363 1364 2726 2728 4089 4092 S4,S2 5456 6815 6820 8178 8184 9541 9548 10904 10912 12267 12276 1359 2718 4077 5436 6795 8154 9513 10872 12231 1362 2724 4086 5448 6810 8172 9534 10896 12258 1365 2730 4095 5460 6825 8190 9555 10920 12285 1366 1367 1368 2732 2734 2736 4098 4IOI 4104 5464 5468 5472 68,^0 6835 6840 8196 8202 8206 9562 9569 9576 10928 10936 10944 12294 12303 I23I2 1369 1370 2738 2740 4107 4II0 5476 5480 6845 6850 8214 8220 9583 9590 10952 10960 1 232 1 12330 I37I 2742 4II3 5484 6855 8226 9597 10968 12339 I, 2 = 693 147 18, j, 4 = 138629437, 4,, 8 = 207944154, Dual Logarithms of powers of 2 and 10. L 10 = 230258509, X, 10* = 921034037, >„ lo^ = 460517019, V, 10^ = 1151292546, I, lo^ = 690775528, J, 10" = 1381551056, lo^ = 161 1809565, lo^ = 1842068074, , 10^ = 2072326584, p 34] Hat. No. r3713 to 1-3849 D. Log. 3157.... to 3256.... D. No. >I,3,3,0,0, to >I.3,3,9,9, Natural Numbers. i*37i33o63 46776 60491 74207 87924 1-37201643 15363 29085 42808 56532 70196 83923 97651 i'373ii38i 25112 38845 52579 66314 80051 93789 1-37407466 21207 34949 48692 62437 76183 89931 i"37S0368o 17430 31182 44873 58627 72383 86140 99899 1-37613659 27420 41183 54947 68712 82418 96186 1*37709956 23727 37499 51273 65048 78825 92603 1*37806382 Dual Logarithms. Dual Numbers. 31578153 58 59 60 61 62 64 65 66 31678103, 68 69 70 71 72 73 74 75 76 31778053, 78 79 80 82 83 84 85 86 31878003, 90 91 92 93 94 95 96 31977953; 98 99 3200 01 02 03 04 05 06 >^3>3>o,o,o,o,o,o, > '353)0,1,0,0,0,0, \I'3'3)0,2, 0,0,0,0, >'3>3>o,3,o,o,o,o, \1'3)3jO,4,o,o,o,o, ^I'3)3>o,5, 0,0,0,0, >I'3)3jO,6,o,o,o,o, 3)3)0,7,0,0,0,0, 3)3)0,8,0,0,0,0, ■3)3)0,9,0,0,0,0, 13)3)1,0,0,0,0,0, "3)3,1,1)0,0,0,0, w3)3, 1,2,0,0,0,0, > '3)3) 1)3)0,0,0,0, ^3)3)1,4)0,0,0,0, J'3)3) 1)5)0,0,0,0, 3)3)1)6,0,0,0,0, 3)3)1)7)0,0,0,0, 3,3,1,8,0,0,0,0, 3)3)1)9)0,0,0,0, >'3, 3, 2,0,0,0,0,0, >'3, 3)2, 1, 0,0,0,0, > '3)3)2,2,0,0,0,0, \'3)3)2)3)0,o,o,o, >I'3)3, 2,4,0,0,0,0, |3)3)2, 5)0,0,0,0, > '3,3)2)6,0,0,0,0, > '3)3,2,7)0,0,0,0, > '3)3)2,8,0,0,0,0, >1'3, 3)2,9,0,0,0,0, 13)3)3)0,0,0,0,0, >'3)3)3)i)0,o,o,o, >'3)3)3)2, 0,0,0,0, "3,3,3)3)0)0,0,0, 13)3,3)4)0,0,0,0, 3)3)3)5,0)0,0,0, 3>3)3)6,o,o,o,o, .3)3)3,7)0,0,0,0, >I'3)3, 3)8,0,0,0,0, >i'3)3)3)9)0,o,o,o, 3,3,4,0,0,0,0,0, 3,3)4)1)0,0,0,0, 3,3)4)2,0,0,0,0, .3)3)4,3)0,0,0,0, 4'3)3)4) 4)0,0,0,0, >I'3,3)4)5)0,o,o,o, 13)3)4)6,0,0,0,0, 43)3)4)7)0,0,0,0, 13)3)4)8,0,0,0,0, i3)3)4,9)0,o,o,o, Natural Numbers. i'37820ioo 61450 75236 89024 1-37902813 16603 30395 44188 57920 71716 85513 99312 1-38013112 26913 40716 54520 68325 82132 95878 1-38109688 23499 37311 51125 64940 78756 92574 1*38206393 20214 33974 47797 61622 75448 89276 1-38303105 16935 30767 44600 58434 72208 86045 Dual Logarithms i'384i3724 27565 41408 55252 69098 82945 96793 32077903, 08 09 10 II 12 13 14 15 16 32177853) 18 19 20 21 22 23 24 25 26 32277803, 28 29 30 31 32 34 35 36 32377753 38 /39 40 41 42 43 44 45 46 32477703, 48 49 50 51 52 53 54 55 56 Dual Numbers. >['3)3)5)0)0,o,o,o, >1'3)3)5) 1)0,0,0,0, l3)3)5)2,o,o,o,o, |3)3)5)3)0,o,o,o, \I'3)3)5,4,o,o,o,o, 13,3)5,5)0)0,0,0, > '3)3)5)6,0,0,0,0, 13)3)5)7)0,0,0,0, 13,3)5,8,0,0,0,0, >I'3,3)5)9,o,o,o,o, ['3)3)6,0,0,0,0,0, b)3)6, 1,0,0,0,0, U,3, 6,2, 0,0,0,0, k3)3)6,3,o,o,o,o, l'3)3)6,4,o,o,o,o, 3,3)6,5,0,0,0,0, 3)3)6,6,0,0,0,0, .3,3,6,7,0,0,0,0, 13)3)6)8,0,0,0,0, 13)3)6,9)0,0,0,0, ['3)3,7,0,0,0,0,0, ^3)3)7)I)0,o,o,o, k3,3)7)2,o,o,o,o, k3)3)7,3)0,o,o,o, ['3)3)7,4,0,0,0,0, >'3)3)7)5)0,o,o,o, > '3,3)7)6,0,0,0,0, >'3)3)7,7,o,o,o,o, "3)3)7)8,0,0,0,0, \|'3)3)7)9,o,o,o,o, >I'3)3)8,o,o,o,o,o, >1'3)3, 8, 1,0,0,0,0, j'3, 3)8,2, 0,0,0,0, i 3, 3, 8,3)0,0,0,0, 3)3)8,4)0,0,0,0, J'3)3)8,5, 0,0,0,0, "3)3,8,6,0,0,0,0, >'3)3)8)7)0,o,o,o, >'3, 3)8,8,0,0,0,0, |3,3, 8,9)0,0,0,0, |3)3)9)0)0,o,o,o, > '3)3)9, 1)0,0,0,0, >'3, 3, 9,2, 0,0,0,0, > '3)3)9)3)0)0,0,0, 4'3, 3)9)4)0,0,0,0, J'3, 3, 9,5, 0,0,0,0, "3)3,9)6,0,0,0,0, >'3, 3, 9,7)0,0,0,0, > '3)3,9)8)0,0,0,0, 13)3)9)9)0,0,0,0, Multiples of Differences, 1371 2742 4"3 5484 6855 8226 9597 10968 12339 1372 2744 4116 5488 6860 8232 9604 10976 12348 1374 137^ 2748 2750 4122 4125 5496 5500 6870 t^T\ 8244 8250 9618 9625 10992 1 1000 12366 12375 1377 2754 1378 2756 4131 5508 6885 8262 4134 5512 6890 8268 9639 9646 11016 II 024 12393 12402 1380 1381 2760 2762 4140 4143 5520 5524 6900 6905 8280 8286 9660 9667 11040 1 1048 12420 12429 \ 1373 2746 41 19 5492 6865 8238 961 1 10984 12357 1376 2752 4128 5504 6880 8256 9632 II008 12384 1379 2758 4137 5516 6895 8274 9653 11032 I24II 1382 2764 4146 5528 6910 8292 9674 II056 ! 1 2438 1383 2766 4149 5532 6915 8298 9681 8 j 1 1064 9 '12447 1384 2768 4152 5536 6920 8234 11072 12456 2 = 69314718, 4 = 138629437, ., 8 — 207944154, Dual Logarithms of powers of 2 and 10. 10 = 230258509, X, 10* = 921034037, \, lo" = 1611809565, lo^ = 460517019, \, lo^ = 1151292546, X, 10^ = 1842068074, 10^ = 690775528, I, io« = 1381551056, \y 10^ = 2072326584, Nat. No. r3850 to r3988 D. Log. 3257.... to 3356.... D. No. >I'3,4,0,0, to ^3,^,9,9, [36 Natural Numbers. Dual Logarithms, I '38504393 18243 32095 45948 59803 73659 87516 1-38601375 15235 29097 42897 56761 70627 84494 98362 1-38712232 26103 39976 53850 67725 81540 95418 1-38809298 23179 37061 50945 64830 78716 92604 1-38906493 20322 34214 48107 62002 75898 89796 1-39003695 17595 31497 45400 59242 73148 87055 1-39100964 14874 28785 42698 56612 70528 84445 32573186 58 59 60 61 62 63 64 65 66 32673136 68 69 70 71 72 73 74 75 76 32773086, 78 79 80 82 83 84 85 86 32873036, 88 89 90 91 92 93 94 95 96 32972986, 99 3300 01 02 03 04 05 06 Dual Numbers. \I'35450,o,o,o,o,o, >I'3) 4, 0,1,0,0,0,0, l3>4,o,2, 0,0,0,0, >i'3>4»o,3, 0,0,0,0, 4'3;4>o,4,o,o,o,o, >'3;4) 0,5, 0,0,0,0, > '354,0,6,0,0,0,0, v'3;4,o,7, 0,0,0,0, w3, 4, 0,8, 0,0, 0,0, >I'3'4,o,9,o,o,o,o, l3,4,ijO,o,o,o,o, >l'3;4) 1, 1,0,0,0,0, >'3j4,i, 2,0,0,0,0, >'3>4,i, 3, 0,0,0,0, ^1'3J4, 1,4,0,0,0,0, >I'3, 4, 1,5,0,0,0,0, > '3,4, 1,6,0,0,0,0, >'3, 4,1, 7, 0,0,0,0, > '3,4, 1,8,0,0,0,0, 13,4,1,9,0,0,0,0, |3,4,2,o,o,o,o,o, |3, 4,2,1, 0,0,0,0, >I'3,4,2,2,0,0,0,0, >1'3, 4, 2,3,0,0,0,0, i3,4, 2,4,0,0,0,0, 13,4,2,5,0,0,0,0, >'3, 4,2, 6,0,0,0,0, ^'3,4,2, 7, 0,0,0,0, > '3,4,2,8,0,0,0,0, >1'3>4, 2,9,0,0,0,0, ['3,4,3,0,0,0,0,0, j/3,4,3, 1,0,0,0,0, k3,4,3, 2,0,0,0,0, ^3,4,3, 3, 0,0,0,0, b54,3,4,o,o,o,o, vl'3, 4,3, 5,0,0,0,0, i 3, 4,3,6,0,0,0,0, 3,4,3,7,0,0,0,0, \|/3,4,3, 8,0,0,0,0, ^3,4,3,9,0,0,0,0, 13,4,4,0,0,0,0,0, 4-3,4,4,1,0,0,0,0, ^'S, 4,4,2, 0,0,0,0, >i'3>4,4,3, 0,0,0,0, >1'3, 4,4,4,0,0,0,0, \1'3,4,4,5, 0,0,0,0, t 3, 4,4,6,0,0,0,0, 3,4,4,7,0,0,0,0, 13,4,4,8,0,0,0,0, 4'3, 4,4, 9,0,0,0,0, Natural Numbers. 1-39198301 1-39212221 26142 40065 53989 67914 81841 95769 1-39309699 23630 37500 51434 65369 79306 93244 I -39407 183 21124 35066 49010 62955 76837 90785 1*39504734 18684 32636 46589 60544 74500 88457 1-39602416 16314 30276 ■44239 58203 72169 86136 1-39700105 14075 28046 42019 55930 69906 83883 97861 1-39811841 25822 39805 53789 67774 81761 Dual Logarithms. Dual Numbers. 33072936, 08 09 10 II 12 13 14 15 16 33172886^ 18 19 20 21 22 23 24 25 26 33272836, 28 29 30 31 32 33 34 35 36 33372786, 38 39 40 41 42 43 44 45 46 33472736, 48 49 50 51 52 53 54 55 56 w3,4,5,o,o,o,o,o, > '3,4,5, 1,0,0,0,0, 4-3,4,5,2,0,0,0,0, 4-3,4,5,3,0,0,0,0, 4'3,4,5, 4,0,0,0,0, 4'3, 4,5, 5, 0,0,0,0, 4'3,4,5,6,o,o,o,o, 4'3, 4,5, 7, 0,0,0,0, 43,4,5,8,0,0,0,0, 4'3,4,5,9,o,o,o,o, 4'3, 4,6,0,0,0,0,0, 4.3,4,6,1,0,0,0,0, 4'3, 4,6,2, 0,0,0,0, 4'3,4,6,3,o,o,o,o, 4'3,4,6,4,o,o,o,o, 4'3,4,6,5,o,o,o,o, 4.3,4,6,6,0,0,0,0, 3,4,6,7,0,0,0,0, 3,4,6,8,0,0,0,0, ■3,4,6,9,0,0,0,0, 4'3, 4,7, 0,0,0,0,0, 3,4,7,1,0,0,0,0, ■3,4,7,2,0,0,0,0, 3,4,7,3,0,0,0,0, 3,4,7,4,0,0,0,0, '3,4,7,5,0,0,0,0, ■3,4,7,6,0,0,0,0, ■3,4,7,7,0,0,0,0, .3,4,7,8,0,0,0,0, 4'3,4,7,9,o,o,o,o, > '3,4,8,0,0,0,0,0, > '3,4,8, 1,0,0,0,0, > '3,4,8,2,0,0,0,0, > '3,4,8,3,0,0,0,0, 4'3,4,8,4,o,o,o,o, 13,4,8,5,0,0,0,0, > '3,4,8,6,0,0,0,0, > '3,4,8,7,0,0,0,0, >'3, 4,8,8,0,0,0,0, 4'3, 4, 8, 9, 0,0, 0,0, 3,4,9,0,0,0,0,0, 3,4,9,1,0,0,0,0, 3,4,9,2,0,0,0,0, 4^3,4,9,3,0,0,0,0, 4-3,4,9,4,0,0,0,0, 4'3,4,9,5,o,o,o,o, > '3,4,9,6,0,0,0,0, >'3, 4,9,7, 0,0,0,0, > '3,4,9,8,0,0,0,0, 4'3,4,9,9,o,o,o,o, Multiples of Differences; I 1385 1386 2 2770 2772 3 415s 4i5« 4 5540 ';S44 5 6925 6930 1 6 8310 8316 7 969 S 9702 8 11080 II088 9 12465 12474 1388 1389 2776 2778 4164 4167 5SS2 SSS^) 6940 694s 8328 «334 971b 9723 1 1 104 11112 12492 12501 1391 1392 2782 2784 4173 4176 ,SS64 SS68 fegss 6960 8346 8352 9737 9744 II 128 II 136 12519 12528 1394 2788 4182 5576 6970 8364 9758 III52 12546 1397 2794 4I9I 5588 6985 8382 9779 1 1 176 12573 1395 2790 4185 5580 6975 8370 9765 11160 12555 1398 2796 4194 5592 6990 1387 2774 4161 5548 6935 8322 9709 1 1096 12483 1390 2780 4170 5560 6950. 8340 9730 11120 12510, 1393 2786 4179 5572 6965 8358 9751^ 1 1 144 12537- 1396^ 2792 41 88 5584. 6980. 8376. 9772: 11168 12584 9786 1 1 184 12582. Dual Logarithms of powers of 2 and 10. I, lo* = 921034037, X, io7 = 1611809565, w, lO^ = 1151292546, w, 10^ =• 1842068074, 4., 8 = 207944154, 4-) io3 = 690775528, I, 10'' = 1381 55 1056, J, lo'' = 2072326584, i, 2 = 693 147 18, L 10 = 230258509, 4', 4 = 138629437, i, io2 = 460517019, 36] Nat. No. 1*3988 to 1-4128 D. Log. 3356.... to 3455.... D. No. 13,5,0,0, to 13,5,9,9, Natural Numbers. 1-39889438 I •39903427 17417 31409 45402 59397 73393 87390 1*40001389 15389 29327 43330 57334 71340 85347 99355 1-40113366 27377 41390 55404 69356 83373 97391 i'402ii4ii 25432 39455 53479 67504 81531 95559 1-40309525 23556 37589 51623 65658 79695 93733 1-40407772 21813 35855 49835 63880 77926 91974 1-40506023 20074 34126 48179 62234 76290 Dual Logarithms. 33568219, 57 58 59 60 61 62 63 64 65 33668169, 67 68 69 70 71 72 73 74 75 33768119, 77 78 79 80 81 82 83 84 85 33868069, 87 88 89 90 91 92 93 94 95 33968019, 97 98 99 3400 01 02 03 04 05 Dual Numbers. Natural Numbers. 1-40590285 1-40604344 18404 32466 46529 60594 74660 88727 1-40702796 16866 30875 44948 59022 73098 87175 1-40801253 15333 29415 43498 57582 71606 85693 99782 I-40913872 27963 42056 56150 70246 84343 98441 i'4ioi2478 26579 40682 54786 68891 82998 97106 1-41111216 25327 39440 53490 67605 81722 95840 I -41 209960 24081 38203 52327 66452 80579 Dual Logarithms. 34067969, 07 08 09 10 II 12 13 14 IS 34167919, 17 18 19 20 ' 21 22 23 24 25 34267869, 27 28 29 30 31 32 33 34 35 34367819, 37 38 39 40 41 42 43 44 45 34467769, 47 48 49 50 51 52 53 54 55 Dual Numbers. 5,0 5.1 5,2 5>3 5,4 5,5 5,6 5,7 5,8 5,9 6,0 6,1 6,2 6,4 6,5 6,6 6,7 6,8 6,9 7,0 7,1 7,2 7,3 7,4: 7,5 7,6 7,7 7,8: 7,9 8,0 8,1 8,2 8,3 8,4 8,5 8,6 8,7 8,8 8,9 9,0 9,1 9,2 9,3 9,4 9,5 9,6 9,7 9,8 9,9 Multiples of Differences. 1.398 1399 2796 2798 4194 4197 5592 5596 6990 6995 8388 8394 9786 9793 1 1 184 II 192 12582 12591 1 1401 1402 2802 2804 4203 4206 5604 5608 7005 7010 8406 8412 9807 9814 II 208 11216 12609 12618 1404 1405 2808 2810 4212 4215 5616 5620 7020 7025 8424 8430 9828 9835 1 1232 1 1 240 12636 1264s 1407 1408 2814 2816 4221 4224 5628 5632 7035 7240 8442 8448 9849 9856 11256 II 264 12663 12672 I4IO 2820 4230 5640 7050 8460 . , 9870 8111280 9 1 1 2690 1411 2822 4233 5644 705s 8466 9877 1 1 288 12699 1400 2800 4200 5600 7000 8400 9800 1 1200 12600 1403 2806 4209 5612 7015 841 S 9821 11224 12627 1406 2812 4218 5624 7030 8436 9842 1 1 248 12654 1409 2818 4227 5636 704s 8454 9863 1 1272 12681 1412 2824 4236 5648 7060 8472 9884 1 1296 12708 Dual Logarithms of powers of 2 and 10. j, 2 = 69314718, L 10 = 230258509, \, lo^ = 921034037, \, 10'^ = 161 1809565, 4-, 4 = 138629437, ,1,, io2 = 460517019, L lo^ = 1151292546, 4" 10^ = 1842068074, 4r, 8 = 207944154, 4,, lo3 = 690775528, 4,, 106 = 1381551056, \, Io9 = 2072326584, Nat. No. 1-4128 to 1-4269 D. Log. 3456.... to 3555.... D. No. 13,6,0,0, to 13,6,9,9, [37 Natural Dual Dual Numbers Logarithms. Numbers. 1-41288332 34563252, > '3,6,0,0,0,0,0,0, 1-41302461 57 ,,3,6,0,1,0,0,0,0, 16591 58 >'3, 6,0,2, 0,0,0,0, 30723 59 > '3,6,0,3,0,0,0,0, 44856 60 ,,3,6,0,4,0,0,0,0, 58990 61 >I,3, 6,0,5,0,0,0,0, 73126 62 ,,3,6,0,6,0,0,0,0, 87263 ^3 N'3>6,o,7, 0,0,0,0, 1*41401402 64 ,,3,6,0,8,0,0,0,0, 15542 65 >l'3>6,o,9,o,o,o,o, 29620 34663202, ,,3,6,1,0,0,0,0,0, 43763 67 ^l,3,6, 1, 1,0,0,0,0, 57907 68 ,,3,6,1,2,0,0,0,0, 72053 69 > '3^6, 1,3,0,0,0,0, 86200 70 >'3j6, 1,4,0,0,0,0, 1-41500349 71 \1'3)6, 1,5,0,0,0,0, T4499 72 ,,3,6,1,6,0,0,0,0, 28650 73 >'356,i, 7, 0,0,0,0, 42803 74 4,3,6,1,8,0,0,0,0, 56957 75 i3>6, 1,9,0,0,0,0, 71050 34763152, ,1,3,6,2,0,0,0,0,0, 85207 77 ,,3,6,2,1,0,0,0,0, 99366 78 ,,3,6,2,2,0,0,0,0, 1-41613526 79 > '3,6,2,3,0,0,0,0, 27687 80 l3>6,2,4,o,o,o,o. 41850 81 ,,3,6,2,5,0,0,0,0, 56014 82 ,,3,6,2,6,0,0,0,0, 70180 83 |3>6,2, 7,0,0,0,0, 84347 84 ,,3,6,2,8,0,0,0,0, 98515 85 ,,3,6,2,9,0,0,0,0, 1-41712621 34863102, w3, 6,3,0,0,0,0,0, 26792 87 ,,3,6,3,1,0,0,0,0, 40965 88 ,,3,6,3,2,0,0,0,0, 55139 89 v!/3»6,3,3>o,o,o,o, 69315 90 l3>6,3,4,o,o,o,o. 83492 91 >1'3, 6,3, 5, 0,0,0,0, 97670 92 > '3)6,3,6,0,0,0,0, i'4i8ii85o $3 >1'3)6,3,7, 0,0,0,0, 26031 94 V '3,6,3,8,0,0,0,0, 40214 95 > '3)6,3,9)0,0,0,0, 54333 34963052, >!'3, 6,4,0,0,0,0,0, 68518 97 ,,3,6,4,1,0,0,0,0, 82705 98 vI/3,6,4,2,o,o,o,o, 96893 99 >]/3,6,4,3)0,o,o,o. 1-41911083 3500 >l'3,6,4,4,o,o,o,o, 25274 01 >I'3>6,4,5, 0,0,0,0, 39467 02 'l'3>6,4,6,o,o,o,o. 53661 03 > '3,6,4,7,0,0,0,0, 67856 04 >1'3, 6,4,8,0,0,0,0, 82053 OS l3>6,4,9)0,o,o,o. Natural Dual Dual Numbers. Logarithms. Numbers, I-41996187 35063002, >I'3,6,5,o,o,o,o,o, 1-42010387 07 vl'3,6,5, 1,0,0,0,0, 24588 08 \!'3, 6,5,2,0,0,0,0, 38790 09 \l'3)6,5, 3, 0,0,0,0, 52994 10 \l'3)6,5,4,o,o,o,o, 67199 II vl'3,6,5, 5.0,0,0,0, 81406 12 13,6,5,6,0,0,0,0, 95614 13 > '3)6,5,7,0,0,0,0, 1*42109824 14 v3,6,5, 8,0,0,0,0, 24035 15 w3,6,S)9)0,o,o,o, 38183 35162952, 4,3,6,6,0,0,0,0,0, 52397 17 ,,3,6,6,1,0,0,0,0, 66612 18 ,,3,6,6,2,0,0,0,0, 80829 19 > '3)6,6,3,0,0,0,0, 95047 20 ,,3,6,6,4,0,0,0,0, 1*42209267 21 \^3.6,6,5, 0,0,0,0, 23488 22 ,,3,6,6,6,0,0,0,0, 37710 23 >|'3)6,6,7, 0,0,0,0, 51934 24 vj,3,6,6,8,o,o,o,o. 66159 25 ^3)6,6,9,0,0,0,0, 80321 35262902, >I'3)6,7,o,o,o,o,o, 94549 27 ,,3,6,7,1,0,0,0,0, 1*42308778 28 > '3,6,7,2,0,0,0,0, 23009 29 >^3)6)7)3)0,o,o,o. 37241 30 > '3)6,7,4,0,0,0,0, S1475 31 X '3.6,7,5)0,0,0,0, 65710 32 > '3,6,7)6,0,0,0,0, 79946 2,3 > '3.6,7,7,0,0,0,0, 94184 34 I3, 6,7, 8,0,0,0,0, 1*42408423 35 13)6,7)9)0,0,0,0, 22601 35362852, X3,6,8,o,o,o,o,o, 36843 37 ,,3,6,8,1,0,0,0,0, 51086 38 ,,3,6,8,2,0,0,0,0, 65331 39 > '3)6,8,3,0,0,0,0, 79578 40 > '3)6,8,4,0,0,0,0, 93826 41 V '3)6,8,5,0,0,0,0, 1*42508075 42 ,,3,6,8,6,0,0,0,0, 22326 43 ,,3,6,8,7,0,0,0,0, 36578 44 ,,3,6,8,8,0,0,0,0, 50832 45 ,,3,6,8,9,0,0,0,0, 65023 35462802, > '3)6,9,0,0,0,0,0, 79280 47 > '3,6,9.1)0,0,0,0, 93538 48 > '3.6,9.2,0,0,0,0, 1-42607797 49 > '3)6.9.3)0,0,0,0, 22058 50 vl'3.6)9)4,o,o,o,o, 36320 51 \^3, 6,9)5. 0,0,0,0, 50584 52 ^I'3)6,9)6)0,o,o,o, 64849 S3 >'3.6,9)7. 0,0,0,0, 79115 54 ^ '3)6,9)8,0,0,0,0, 93383 55 \^3)6,9)9)0)0,o,o, Multiples o* DifiFerences 1412 2824 4236 5648 7060 8472 1 1296 12708 1413 2826 4239 5652 7065 8478 9891 1 1 304 12717 1414 2828 4242 5656 7070 8484 I4IS I4I6 2830 2832 4245 4248 5660 5664 7075 7080 8490 8496 9905 9912 1 1320 11328 1273s 12744 1415 1419 2836 2838 4254 4257 5672 5676 7090 709s 8508 ^SH 9926 9933 "344 11352 12762 12771 142 1 1422 2842 2844 4263 4266 5684 5688 7105 71 10 8526 «532 9947 9954 1 1 368 11376 12789 12798 1424 1425 2848 2850 4272 427s 569b 5700 7120 7125 8544 «550 9968 9975 1 1392 1 1400 12816 12825 II3I2 12726 1417 2834 4251 5668 7085 8502 9919 II336 12753 1420 2840 4260 5680 7100 8520 9940 II360 12780 1423 2846 4269 5692 7"S 8538 9961 1 1384 1.2807 1426 2852 4278 5704 7130 8556 9982 1 1408 12834 Dual Logarithms of powers of 2 and 10. 2 = 69314718, 4,, 10 = 230258509, vj,, 10* = 921034037, L To^ = 1611809565, , 4 = 138629437, 1, io2 = 460517019, J,, lo^ = 1151292546, X, lo^ = 1842068074, , 8 = 207944154, I, io3 = 690775528, J, IO<5 = 1381551056, \, Io9 = 2072326584, 38] Nat. No. 1-4270 to 1-4412 D. Log. 3555.... to 3654.... D. No. 13,7,0,0, to 13,7,9,9, Natural Numbers. i'427oi2i5 15485 29757 44030 58304 72580 86857 i"428oii36 15416 29698 43916 58200 72486 86773 i'429oio62 15352 29644 43937 58231 72527 86760 1-43001059 15359 29661 43964 58268 72574 86881 i'43ioii90 .15500 29747 44060 58374 72690 87007 i'432oi326 15646 29968 44291 58615 72877 87204 i"433oi533 15863 30195 44528 58862 73198 87535 I •43401874 Dual Logarithms. 35558285, 56 57 58 59 60 61 62 ^Z 64 35658235, 66 67 68 69 70 71 72 73 74 35758185, 76 77 78 79 80 81 82 83 84 35858135, 86 87 88 89 90 91 92 93 94 35958085, g6 97 98 99 3600 01 02 03 04 Dual Numbers. >I'3>7,o,o,o,o,o,o, \/3,7jO,i, 0,0,0,0, \'3, 7)0,2,0,0,0,0, >'3»7, 0,3, 0,0,0,0, >1'3j7jO,4jO,o,o,o, l3>7»o,5, 0,0,0,0, \I'3)7»o, 6,0, 0,0,0, i3J)0,7, 0,0,0,0, 13)7,0,8,0,0,0,0, j'3, 7,0,9,0,0,0,0, 13,7,1,0,0,0,0,0, 3,7,1,1,0,0,0,0, 3,7,1,2,0,0,0,0, 3,7,1,3,0,0,0,0, >^3, 7, 1,4,0,0,0,0, >1'3, 7, 1,5,0,0,0,0, 3,7,1,6,0,0,0,0, •3,7,1,7,0,0,0,0, 3,7,1,8,0,0,0,0, 3,7,1,9,0,0,0,0, ■3,7,2,0,0,0,0,0, ■3,7,2,1,0,0,0,0, 3,7,2,2,0,0,0,0, .3,7,2,3,0,0,0,0, i3;7,2,4,o,o,o,o, >I'3,7,2,5,o,o,o,o, 13,7,2,6,0,0,0,0, i 3, 7, 2, 7, 0,0,0,0, 3,7,2,8,0,0,0,0, 4-3,7,2,9,0,0,0,0, >I'3, 7,3,0,0,0,0,0, ^3,7,3,1,0,0,0,0, 13,7,3,2,0,0,0,0, 13,7,3,3,0,0,0,0, 4'3, 7,3,4,0,0,0,0, 3,7,3,5,0,0,0,0, 3,7,3,6,0,0,0,0, 3,7,3,7,0,0,0,0, i3, 7,3, 8,0,0,0,0, >^3,7,3,9,o,o,o,o, 3,7,4,0,0,0,0,0, ■3,7,4,1,0,0,0,0, ■3,7,4,2,0,0,0,0, 3,7,4,3,0,0,0,0, >i'3,7,4,4,o,o,o,o, 4'3, 7, 4,5,0,0,0,0, >I'3,7,4,6,o,o,o,o, >I'3, 7, 4,7, 0,0,0,0, \!'3,7,4,8,o,o,o,o, >i'3, 7, 4,9,0,0,0,0, Natural Numbers. 1-43416150 30492 44835 59179 73525 87872 1-43502221 16571 30923 45276 59566 73922 88279 1-43602638 16998 31360 45723 60088 74454 88821 1-43703126 17496 31868 46241 60616 74992 89369 1*43803748 18128 32510 46829 61214 75600 89988 1*43904377 18767 33159 47552 61947 76343 90676 1-44005075 19476 33878 48281 62686 77092 91500 I -44105909 20320 Dual Logarithms, 36058035 06 07 08 09 10 II 12 13 14 36157985, 16 17 18 19 20 21 22 23 24 36257935, 26 27 28 29 30 31 32 3Z 34 56-57885, 36 37 38 39 40 41 42 43 44 36457835, 46 47 48 49 50 51 52 53 54 Dual Numbers. 3,7,5,0,0,0,0,0, 3,7,5,1,0,0,0,0, .3,7,5,2,0,0,0,0, J3,7,5,3,o,o,o,o, >I'3,7,5,4,o,o,o,o, >I'3,7,5,5,o,o,o,o, |3, 7, 5, 6,0,0,0,0, >1'3, 7,5, 7,0,0,0,0, 13,7,5,8,0,0,0,0, \I'3,7,5, 9,0,0,0,0, ['3,7,6,0,0,0,0,0, b,7,6,i,o,o,o,o, U,7,6,2,o,o,o,o, b,7,6,3,o,o,o,o, ['3,7,6,4,0,0,0,0, |3, 7, 6,5, 0,0,0,0, \'3,7, 6,6,0,0,0,0, >I'3, 7, 6,7,0,0,0,0, X3, 7, 6,8,0,0,0,0, \I'3,7,6,9,o,o,o,o, \ '3,7,7,0,0,0,0,0, >'3, 7, 7, 1,0,0,0,0, >'3,7, 7, 2,0,0,0,0, >l'3,7,7,3,o,o,o,o, \I'3,7,7,4,o,o,o,o, ['3,7,7,5,0,0,0,0, k3,7,7, 6,0,0,0,0, ^3,7,7,7,o,o,o,o, b,7,7,8,o,o,o,o, ['3,7,7,9,0,0,0,0, ['3,7,8,0,0,0,0,0, ^3, 7, 8, 1,0,0,0,0, l3,7, 8,2,0,0,0,0, p7, 8,3,0,0,0,0, ['3,7,8,4,0,0,0,0, 13,7,8,5,0,0,0,0, >'3, 7, 8,6,0,0,0,0, >'3, 7, 8,7, 0,0,0,0, > '3,7,8,8,0,0,0,0, >I'3,7, 8,9,0,0,0,0, >I'3, 7, 9,0,0,0,0,0, 3,7,9,1,0,0,0,0, 3,7,9,2,0,0,0,0, ■3,7,9,3,0,0,0,0, ■3,7,9,4,0,0,0,0, i 3,7,9,5,0,0,0,0, 3,7,9,6,0,0,0,0, .3,7,9,7,0,0,0,0, 13,7,9,8,0,0,0,0, !'3,7, 9,9,0,0,0,0, Multiples of Differences. 1427 1428 2854 2856 4281 4284 5708 5712 7135 7140 8562 8568 99S9 9996 II4I6 1 1424 12843 12852 1430 143 1 2860 2862 4290 4293 5720 5724 7150 7155 8580 8586 lOOIO IOOI7 1 1440 1 1448 12870 12879 \ 1429 2858 4287 5716 7145 8574 10003 II432 1 286 1 1432 2864 4296 5728 7160 8592 10024 1 1456 12888 1433 1434 143') 2866 2868 2870 4299 4302 4305 5732 .S73t> 5740 7165 7170 717s 8998 8.604 8610 1003 1 10038 1004=; II 464 11472 1 1480 1I2897 12906 1291S 1436 1437 2872 2874 4308 43" 5744 .S74« 7180 7185 8616 8622 10052 10059 1 1488 11496 12924 12933 1439 1440 2878 2880 4317 4320 5756 5760 719'; 7200 8634 8640 10073 10080 11512 1 1520 12951 12960 1438 2876 4314 5752 7190 8628 IC066 1 1504 12942 I44I 2882 4323 5764 7205 8646 10087 11528 12969 \^, 2 — \'i 4 4'j 8 Dual Logarithms of powers of 2 and 10. = 69314718, 1 10 =230258509, 1,10*= 921034037, ,!,, 10'^ = 1611 = 138629437, I, io2 = 460517019, 4,, lo^ = 1151292546, L lo^ = 1842 - 207944154, ]i, I03 = 690775528, 4,, IO<5 = I381551056, \, \0^ = 2072 809565, 068074, 2326584, Nat. No. r4412 to 1-4556 D. Log. 3655.... to 3754.... D. No. 13,8,0,0, to >I.3,8,9,9, [39 Natural Dual Dual Numbers. Logarithms. Numbers. i"44i28227 36553318, ^|,3,8,0,o,o,o,o,o, 42640 56 ,,3,8,0,1,0,0,0,0, 57054 57 ,,3,8,0,2,0,0,0,0, 71470 58 >'3»8,o,3,o, 0,0,0, 85887 59 ,,3,8,0,4,0,0,0,0, I •44200306 60 ^'3>8,o,5,o,o,o,o, 14726 61 ,,3,8,0,6,0,0,0,0, 29147 62 w3,8,o,7,o,o,o,o, 43570 63 • ,,3,8,0,8,0,0,0,0, 57994 64 ,,3,8,0,9,0,0,0,0, 72355 36653268, ,,3,8,1,0,0,0,0,0, 86782 66 v'3, 8,1, 1,0,0,0,0, 1-44301211 67 ,,3,8,1,2,0,0,0,0, 15641 68 ,,3,8,1,3,0,0,0,0, 30073 69 ,,3,8,1,4,0,0,0,0, 44506 70 ,,3,8,1,5,0,0,0,0, 58940 71 ,,3,8,1,6,0,0,0,0, 73376 72 ,,3,8,1,7,0,0,0,0, 87813 73 ,,3,8,1,8,0,0,0,0, 1-44402252 74 V '3)8, 1,9,0,0,0,0, 16627 36753218, 4,3,8,2,0,0,0,0,0, 31069 76 ,,3,8,2,1,0,0,0,0, 45512 77 ,,3,8,2,2,0,0,0,0, 59957 78 ,,3,8,2,3,0,0,0,0, 74403 79 ,,3,8,2,4,0,0,0,0, 88850 80 > '3,8,2,5,0,0,0,0, i'44503299 81 v,3, 8,2,6,0,0^0,0, 17749 82 >'3,8,2, 7,0,0,0,0, 32201 83 ,1,3,8,2,8,0,0,0,0, 46654 84 ,,3,8,2,9,0,0,0,0, 61044 36853168, ^I'3>8,3,o,o,o,o,o, 75500 86 ^3, 8,3, 1,0,0,0,0, 89957 87 4,3,8,3,2,0,0,0,0, i*446o44i6 88 4'3,8,3,3,o,o,o,o, 18876 89 13,8,3,4,0,0,0,0, 33338 90 > '3,8,3,5,0,0,0,0, 47801 91 ^l'3, 8, 3, 6,0,0,0,0, 62266 92 >'3, 8,3,7,0,0,0,0, 76732 93 >'3, 8,3, 8,0,0,0,0, 91200 94 13,8,3,9,0,0,0,0, 1-44705605 36953118, >1'3, 8,4,0,0,0,0,0, 20076 96 ,,3,8,4,1,0,0,0,0, 34548 97 ,,3,8,4,2,0,0,0,0, 49021 98 v!/3,8,4,3,o,o,o,o. 63496 99 i3,8,4,4,o,o,o,o. 77972 3700 > '3,8,4,5,0,0,0,0, 92450 01 > '3,8,4,6,0,0,0,0, 1-44806929 02 ,,3,8,4,7,0,0,0,0, 21410 03 > '3,8,4,8,0,0,0,0, 35892 04 > '3,8,4,9,0,0,0,0, Natural Dual Dual | Numbers. Logarithms. Numbers. I '448503 1 1 37053068, 13,8,5,0,0,0,0,0, 64796 06 > '3,8,5, 1,0,0,0,0, 79282 07 ,,3,8,5,2,0,0,0,0, 93770 08 13,8,5,3,0,0,0,0, 1-44908259 09 ^3,8,5, 4,0,0,0,0, 22750 10 J3, 8,5, 5, 0,0,0,0, 37242 II 13,8,5,6,0,0,0,0, 51736 12 N '3,8,5,7,0,0,0,0, 66231 13 v3, 8,5, 8,0,0,0,0, 80728 14 ^3, 8, 5, 9, 0,0, 0,0, 95161 37153018, ,,3,8,6,0,0,0,0,0, I -45009661 16 > '3,8,6, 1,0,0,0,0, 24162 17 ,,3,8,6,2,0,0,0,0, 38664 18 ,,3,8,6,3,0,0,0,0, 53^68 19 ,,3,8,6,4,0,0,0,0, 67673 20 > '3,8,6,5,0,0,0,0, 82180 21 ,,3,8,6,6,0,0,0,0, 96688 22 ,,3,8,6,7,0,0,0,0, 1-45111198 23 ,,3,8,6,8,0,0,0,0, 25709 24 ^3, 8,6,9,0,0,0,0, 40156 37252968, > '3,8,7,0,0,0,0,0, 54670 26 ,,3,8,7,1,0,0,0,0, 69185 27 ,,3,8,7,2,0,0,0,0, 83702 28 >'3,8,7,3Ao,o,o, 98220 29 > ^3)8,7,4,0,0,0,0, r-45212740 30 \'3,8,7,5,o,o,o,o. 27261 31 > '3,8,7,6,0,0,0,0, 41784 32 > '3,8,7,7,0,0,0,0, 56308 33 > '3,8,7,8,0,0,0,0, 70834 34 >l'3,8,7,9,o,o,o,o, 85296 37352918, 4,3,8,8,0,0,0,0,0, 99825 S6 ,,3,8,8,1,0,0,0,0, i'453i4355 37 ,,3,8,8,2,0,0,0,0, 28886 38 "3,8,8,3,0,0,0,0, 43419 39 \1'3, 8,8,4,0,0,0,0, 57953 40 >'3,8,8,5,o,o,o,o. 72489 41 ,,3,8,8,6,0,0,0,0, 87026 42 > '3,8,8,7,0,0,0,0, 1-45401565 43 ',,3,8,8,8,0,0,0,0, 16105 44 ,,3,8,8,9,0,0,0,0, 30581 37452868, X '3,8,9,0,0,0,0,0, 45124 46 ^ '3,8,9, 1,0,0,0,0, 59669 47 V '3,8,9,2,0,0,0,0, 74215 48 >'3,8,9,3,o,o,o,o. 88762 49 n1^3,8,9,4,o,o,o,o. I '455033 1 1 SO > '3,8,9,5,0,0,0,0, 17861 51 > '3,8,9,6,0,0,0,0, 32413 52 > '3,8,9,7,0,0,0,0, 46966 53 "3,8,9,8,0,0,0,0, 61521 54 J'S, 8,9,9,0,0,0,0, Multiples of Differences. 144 1 2882 1442 2884 4323 5764 4326 5768 7205 8646 7210 8652 10087 II528 12969 10094 1 1536 12978 1444 I44S 2888 2890 4332 4335 5776 57«o 7220 7225 8664 8670 IOI08 10115 IISS2 1 1560 12996 13005 1447 14481 2894 2896 4341 434+ 57«« 5792 72.^'; 7240 8682 8688 10129 10136 11576 11584 13023 13032 1443 2886 4329 5772 72IS 8658 lOIOI "544 12987 1446 2892 4338 5784 7230 8676 11122 1 1568 13014 1449 4347 5796 7245 1450 I45I 2900 2902 4350 4353 5800 5804 7250 7255 8700 8706 IOI50 10157 II600 1 1 608 13050 13059 1453 1454 2906 2908 4359 4362 5812, 5816 7265 7270 8718 8724 10171. 10178 1 1 624 11632 13077 13086 IOI43 1 1 592 13041 1452 2904 4356 5808 7260 8712 IOI64 II6I6 13068 1455 2910 .4365 5820 7275 8730 10185 1 1640 1309s Dual Logarithms of |, 2 = 69314718, 4,, 10 = 230258509, >„ 4 = 138629437, I, io2 = 460517019, V, 8 = 207944154, I, io3 = 690775528, powers of 2 and 10. 4,, 10* = 921034037, 4,, io5 = 1 15 1292546, 4,, io'5 = 1381551056, L io7 = 1611809565, L 10^ =- 1842068074, [, 10^ = 2072326584, 40] Nat. No. r4556 to r4691 D. Log. 3754.... to 3853.... D. No. 13,9,0,0, to 4'3,9,9,9, Natural Numbers. i'45569509 84066 98624 1-45613184 27745 42308 56872 71438 86005 i"457ooS74 15079 29651 44224 58798 73374 87951 1-45802530 17110 31692 46275 60794 75380 89968 1*45904557 19147 33739 48332 62927 77523 92121 1-46006655 21256 35858 50462 65067 79674 94282 1-46108891 23502 38114 52662 67277 81894 96512 I-462III32 25753 40375 54999 69624 84251 Dual Logarithms. 37548351- 55 56 57 58 59 60 61 62 37648301, 65 66 67 68 69 70 71 72 73 37748251, 75 76 77 78 79 80 81 82 83 37848201, 85 86 87 90 91 92 93 37948151 95 96 97 98 99 3800 01 02 03 Dual Numbers. 13,9,0,0,0,0,0,0, i3»9»o, 1,0,0,0,0, l3»9)0,2,o,o,o,o, \|'3, 9)0,3,0,0,0,0, i3)9>o,4,o,o,o,o, >I'3)9,o,5, 0,0,0,0, i3>9,o,6,o,o,o,o, >I'3j9,o,7, 0,0,0,0, >1'3, 9,0,8,0,0,0,0, i3)9>o,9,o,o,o,o, >I'3,9)i>o,o,o,o,o, \i'3,9> I) 1,0,0,0,0, i3, 9,1)2, 0,0,0,0, >i'3)9, 1)3)0,0,0,0, i3)9)i)4)0,o,o,o, \I'3)9) 1)5)0,0,0,0, i3)9,i)6,o,o,o,o, >1'3)9) 1)7,0,0,0,0, >i,3,9, 1,8,0,0,0,0, ^3)9) 1)9)0,0,0,0, >I'3)9) 2,0,0,0,0,0, N^3)9)2, 1,0,0,0,0, j/3, 9,2, 2, 0,0,0,0, 13,9,2,3,0,0,0,0, \k3, 9)2,4,0,0,0,0, >1'3, 9, 2,5,0,0,0,0, 43)9)2,6,0,0,0,0, 13)9)2,7,0,0,0,0, >l'3)9)2,8,o,o,o,o, >1^3)9)2,9)0,o,o,o, 13,9,3)0,0,0,0,0, >l/3)9)3, 1)0,0,0,0, >l'3)9)3)2,o,o,o,o, n1'3)9)3)3)0,o,o,o, \l'3)9)3)4)0,o,o,o, >I'3)9)3)5)0,o,o,o, >l'3)9)3)6,o,o,o,o, N'3)9)3,7)0,o,o,o, >'3)9)3)8,o,o,o,o, 43)9,3)9)0,0,0,0, 43)9)4)0,0,0,0,0, 43)9,4)1)0,0,0,0, 43)9)4)2,0,0,0,0, 43)9)4,3)0,0,0,0, 43)9)4)4)0,0,0,0, 43,9)4)5)0,0,0,0, 43,9,4,6,0,0,0,0, 43)9,4)7,0,0,0,0, 43,9)4,8,0,0,0,0, 43)9)4)9)0,0,0,0, Natural Dual Dual Numbers. Logarithms. Numbers. I'462988i5 38048101, 43)9,5)0,0,0,0,0, 1-46313445 05 ^ '3)9)5)1)0,0,0,0, 28076 06 >'3)9)5)2,o,o,o,o, 42709 07 > '3)9)5)3)0,0,0,0, 57343 08 > '3)9)5)4)0,0,0,0, 71979 09 43)9)5)5)0,0,0,0, 86616 10 > '3)9)5)6,0,0,0,0, 1-46401255 II >'3,9)5)7)0,o,o,o. 15895 12 > '3)9)5)8,0,0,0,0, 30537 13 43)9)5)9)0,0,0,0, 45114 38148051, 43)9)6,0,0,0,0,0, 59759 15 > '3)9)6, 1,0,0,0,0, 74405 16 ,,3,9,6,2,0,0,0,0, 89052 17 w3,9,6,3,o,o,o,o. 1-46503701 18 w3,9)6,4,o,o,o,o, 18351 19 43)9)6)5)0)0,0,0, ,,3,9,6,6,0,0,0,0, 33003 20 47656 21 > '3)9)6,7)0,0,0,0, ,,3,9,6,8,0,0,0,0, 62311 22 76967 23 43)9)6,9)0,0,0,0, 91559 38248001, ^ '3)9)7)0,0,0,0,0, 1-46606218 25 > '3)9)7) 1)0,0,0,0, 20879 26 ^ '3)9)7)2,0,0,0,0, 35541 27 > '3)9,7)3)0,0,0,0, 50205 28 ^ '3)9)7)4)0,0,0,0, 64870 29 w3)9,7)5)0,o,o,o, 79536 30 >'3)9)7)6,o,o,o,o, 94204 31 >'3)9)7,7)0,o,o,o, 1-46708873 32 > '3)9)7)8,0,0,0,0, > '3)9)7)9)0,0,0,0, 23544 2>Z 38151 3834795I) 43)9)8)0,0,0,0,0, 52825 35 > '3)9)8) 1)0,0,0,0, > '3)9)8,2,0,0,0,0, 67500 36 82177 37 > '3,9)8,3)0,0,0,0, 96855 38 43)9)8,4,0,0,0,0, 1-46811535 39 43)9)8)5)0,0,0,0, 26216 40 > '3)9)8,6,0,0,0,0, 40899 41 43)9)8,7)0,0,0,0, ,,3,9,8,8,0,0,0,0, 55583 42 70269 43 .'3)9)8,9)0,0,0,0, 84889 38447901, 43,9,9)0,0,0,0,0, 99577 45 43)9)9)1)0,0,0,0, 1-46914267 46 43,9)9)2,0,0,0,0, 28958 47 43,9,9,3)0,0,0,0, 43651 48 43)9)9)4)0,0,0,0, 58345 49 43)9)9)5)0,0,0,0, 73041 50 w3, 9)9,6,0,0,0,0, 87738 51 43,9)9)7)0,0,0,0, 1-47002437 52 43)9,9)8,0,0,0,0, 17137 53 43)9)9)9)0,0,0,0, Multiples of Differences. 145 5 1456 2910 2912 4365 4368 5820 5824 7275 7280 «73o «736 1018S 10192 II 640 1 1 648 13095 13 104 1458 1459 2916 2918 4374 4377 5«32 5«36 7290 7295 8748 «7S4 10206 10213 1 1 664 11672 13122 13131 146 1 1462 2922 2924 43«3 4386 5844 5848 7305 7310 8766 8772 10227 10234 1 1688 1 1696 13149 13158 1464 1465 2928 2930 4392 4395 5856 5860 7320 7325 8784 8790 10248 10255 11712 1 1 720 13176 1318S 1467 1468 2934 2936 4401 4404 5868 5872 7335 7340 8802 8808 10269 10276 1 1 736 1 1744 13203 13212 1470 2940 4410 5880 7350 8820 10290 II760 13230 Dual Logarithms of powers of 2 and 10. 4> 2 = 69314718, 4') 10 = 230258509, \, 10* = 921034037, 4') 10'^ = 1611809565, 4, 4 = 138629437, i, lo^ = 460517019, 4) lo^ = 1151292546, 4) ^o" = 1842068074, ^, 4) I03 4, 8 = 207944154, 690775528, 4. 10^ = 1381551056, 4) io9 = 2072326584, Nat. No. 1-4641 to 1*4786 D. Log. 3812.... to 3911.... D. No. 44,0,0,0, to U,0,9,9, [41 Natural Dual Dual Number?. Logarithms. Numbers. I •46410000 38124072, ,4,0,0,0,0,0,0,0, 24641 13 ,,4,0,0,1,0,0,0,0, 39283 14 > 4,0,0,2,0,0,0,0, 53927 15 > 4,0,0,3,0,0,0,0, 68572 16 \ 4,0,0,4,0,0,0,0, 83219 17 ^ 4,0,0,5,0,0,0,0, 97867 18 ,4,0,0,6,0,0,0,0, 1-46512517 19 ,4,0,0,7,0,0,0,0, 27168 20 ,4,0,0,8,0,0,0,0, 41821 21 4,4,0,0,9,0,0,0,0, 56410 38224022, ,4,0,1,0,0,0,0,0, 71066 23 ,4,0,1,1,0,0,0,0, 85723 24 ,4,0,1,2,0,0,0,0, 1*46600382 25 > 4,0, 1,3,0,0,0,0, 15042 26 > 4,0, 1,4,0,0,0,0, 29704 27 ,4,0,1,5,0,0,0,0, 44367 28 ,4,0,1,6,0,0,0,0, 5903^ 29 > 4,0, 1,7,0,0,0,0, 73697 30 ,4,0,1,8,0,0,0,0, 88364 31 ,4,0,1,9,0,0,0,0, i'46702966 38323972, ,4,0,2,0,0,0,0,0, 17636 33 ,4,0,2,1,0,0,0,0, 32308 34 ,4,0,2,2,0,0,0,0, 46981 35 '4,0,2,3,0,0,0,0, 61656 36 ,4,0.2,4,0,0,0,0, 76332 37 '4,0,2,5,0,0,0,0, 91010 38 ,4,0,2,6,0,0,0,0, I '46805689 39 ,4,0,2,7,0,0,0,0, 20370 40 ,4,0,2,8,0,0,0,0, 35052 41 ,4,0,2,9,0,0,0,0, 49669 38423922, '4,0,3,0,0,0,0,0, 64354 43 '4,0,3,1,0,0,0,0, 79041 44 ,4,0,3,2,0,0,0,0, 93729 45 ,4,0,3,3,0,0,0,0, I '46908418 46 '4,0,3,4,0,0,0,0, 23109 47 '^4,0,3,5,0,0,0,0, 37801 48 'I'4,o,3, 6,0,0,0,0, 52495 49 14,0,3,7,0,0,0,0, 67190 50 '1^4,0,3,8,0,0,0,0, 81887 51 14,0,3,9,0,0,0,0, 96519 38523872, ,4,0,4,0,0,0,0,0, i"47oii2i9 53 4,4,0,4,1,0,0,0,0, 25920 54 4,4,0,4,2,0,0,0,0, 40623 55 '4,0,4,3,0,0,0,0, 55327 56 4^4,0,4, 4,0,0,0,0, 70033 57 4'4,o,4,5>o,o,o,o, 84740 58 ,,4,0,4,6,0,0,0,0, 99448 59 '4,0,4,7,0,0,0,0, 1-47114158 60 ,,4,0,4,8,0,0,0,0, 28869 61 14,0,4,9,0,0,0,0, Natural Dual Dual Numbers. Logarithms. Numbers. I -47 1435 16 38623822, ,,4,0,5,0,0,0,0,0, 58230 63 ,,4,0,5,1,0,0,0,0, 72946 64 '4,0,5,2,0,0,0,0, 87663 65 '4,0,5,3,0,0,0,0, 1*47202382 66 '4,0,5,4,0,0,0,0, 17102 67 '4,0,5,5,0,0,0,0, 31824 68 ,,4,0,5,6,0,0,0,0, 46547 69 '4,0,5,7,0,0,0,0, 61272 70 '4,0,5,8,0,0,0,0, 75998 71 '4,0,5,9,0,0,0,0, 90660 38723772, ,,4,0,6,0,0,0,0,0, 147305389 73 ,,4,0,6,1,0,0,0,0, 20120 74 ,,4,0,6,2,0,0,0,0, 34852 75 ,,4,0,6,3,0,0,0,0, 49585 76 ,,4,0,6,4,0,0,0,0, 64320 77 ,,4,0,6,5,0,0,0,0, 79056 78 ,,4,0,6,6,0,0,0,0, 93794 79 ,,4,0,6,7,0,0,0,0, 147408533 80 ,,4,0,6,8,0,0,0,0, 23274 81 ,,4,0,6,9,0,0,0,0, 37951 38823722, ,,4,0,7,0,0,0,0,0, 52695 83 ,,4,0,7,1,0,0,0,0, 67440 84 ,,4,0,7,2,0,0,0,0, 82187 85 ,,4,0,7,3,0,0,0,0, 96935 86 ,,4,0,7,4,0,0,0,0, 1-47511685 87 '4,0,7,5,0,0,0,0, 26436 88 ,,4,0,7,6,0,0,0,0, 41189 89 ,,4,0,7,7,0,0,0,0, 55943 90 ,,4,0,7,8,0,0,0,0, 70699 91 ,,4,0,7,9,0,0,0,0, 85389 38923672, ,,4,0,8,0,0,0,0,0, 1-47600148 93 ,,4,0,8,1,0,0,0,0, 14908 94 ,,4,0,8,2,0,0,0,0, 29669 95 '4,0,8,3,0,0,0,0, 44432 96 ' 4,0,8,4,0,0,0,0, 59196 97 ,,4,0,8,5,0,0,0,0, 73962 98 ,,4,0,8,6,0,0,0,0, 88729 99 ,,4,0,8,7,0,0,0,0, 147703498 3900 ,,4,0,8,8,0,0,0,0, 18268 01 , ,4,0,8,9,0,0,0,0, 32974 39023622, , ,4,0,9,0,0,0,0,0, 47747 03 ,,4,0,9,1,0,0,0,0, 62522 04 ,,4,0,9,2,0,0,0,0, 77298 05 '4,0,9,3,0,0,0,0, 92076 06 4^4,0,9,4,0,0,0,0, 1-47806855 07 4'4,o,9,5»o,o,o,o, 21636 08 4,4,0,9,6,0,0,0,0, 36418 09 '14,0,9,7,0,0,0,0, 51202 10 ,,4,0,9,8,0,0,0,0, 65987 II 4'4,o,9,9,o,o,o,o, Multiples of DifiFerences. 1464 1465 2928 2930 4392 4395 5«56 5860 7320 7325 8784 8790 10248 10255 11712 II 720 13 1 76 i3i«5 1467 1468 2934 2936 4401 4404 5868 5«72 733') 7340 8802 8808 10269 10276 1 1 736 11744 13203 13212 1470 147 1 2940 2942 4410 4413 5880 5884 7350 73 IS 8820 8826 10290 10297 1 1 760 1 1 768 13230 13239 1466 2932 4398 5864 733« 8796 10262 1 1 728 13194 1469 2938 4407 5876 7345 8814 10283 11752 13221 1472 2944 4416 1473 1474 2946 2948 4419 4422 5892 5896 7365 7370 8838 8844 103 1 1 103 1 8 1 1 784 1 1 792 13257 13266 1476 1477 2952 2954 4428 4431 5904 5908 7380 7385 8856 8862 10332 10339 1 1808 n8i6 13284 13293 7360 8832 10304 II776 13248 1475 2950 4425 5900 7375 8850 10325 11800 13275 1478 2956 4434 5912 7390 10346 1 1 824 13302 Dual Logarithms of powers of 2 and 10. J,, 2 = 69314718, J,, 10 = 230258509, L 10* = 921034037, L lo^ = 1611809565, 4,, 4 = 138629437, ,„ lo^ = 460517019, ,„ lo^ = 1151292546, ^, 10^ = 1842068074, 4,, 8 = 207944154, J, 10' ^ — 690775528, 4,, 106 = 1381551056^ 4,, io9 = 2072326584, G 42] Nat. No. 1-4787 to 1-4934 D. Log. 3911.... to 4010..,. D. No. ^1,0,0, to W,l,9,9, Natural Numbers. i"47874ioo 1-47903676 18466 33258 48051 62846 77642 92440 1*48007239 21974 36776 51580 66385 81192 96000 I '481 108 10 25621 40434 55248 69996 84813 99631 1-48214451 29272 44095 58919 73745 88572 i '4830340 1 18166 32998 47831 62666 77502 92340 I -48407 1 79 22020 36862 51706 66484 81331 96179 I -485 1 1029 25880 40733 55587 70443 85300 I -486001 59 Dual Logarithms. 39119105, 12 13 14 15 16 17 18 19 20 39219055, 22 23 24 25 26 27 28 29 30 39319005, 32 33 34 35 Z^ 37 38 39 40 39418955, 42 43 44 45 46 47 48 49 50 39518905, 52 53 54 55 56 57 58 59 60 Dual Numbers, 4,4,1,0,0 v|,4,i,o,i >j,4, 1,0,2 i4, 1,0,3 >l'4,i,o,5 ,,4,1,0,6 v4,i,o,7 ,,4,1,0,8 4r4, 1,0,9 >I'4,i,i,5 J,4,i,i,6 > 4, 1, 1,7 ,,4,1,1,8. ,1,4,1,1,9 > 4,1, 2,5 > 4, 1,2,6, > 4,1, 2,7 ^4,I,2,8 4,4,1,2,9 4,1,3,°: 4,1,3,1 4,1,3,2 .4,1,3,3 i4,i,3,4; J4,i,3,5 > 4,1, 3, 6 > 4,1,3,7 > 4,1,3, 8 >|^4, 1,3,9 I4, 1,4,0 4,1,4,1 4,1,4,2 .4,1,4,3 ^4,1,4,4 4,1,4,5 4,1,4,6 4,1,4,7 4,1,4,8 4,1,4,9 0,0,0,0, 0,0,0,0 0,0,0,0 0,0,0,0 0,0,0,0 0,0,0,0 0,0,0,0 0,0,0,0 0,0,0,0 0,0,0,0, 0,0,0,0, 0,0,0,0, 0,0,0,0, 0,0,0,0 0,0,0,0 0,0,0,0 0,0,0,0 0,0,0,0 0,0,0,0 0,0,0,0 0,0,0,0 0,0,0,0, 0,0,0,0, 0,0,0,0 0,0,0,0, 0,0,0,0 0,0,0,0, 0,0,0,0, 0,0,0,0 0,0,0,0 0,0,0,0, 0,0,0,0 0,0,0,0 0,0,0,0 0,0,0,0 0,0,0,0, 0,0,0,0 0,0,0,0, 0,0,0,0 0,0,0,0 0,0,0,0 0,0,0,0 0,0,0,0 0,0,0,0 0,0,0,0 0,0,0,0 0,0,0,0, 0,0,0,0, 0,0,0,0 0,0,0,0 Natural Numbers. 1-48614951 39618855, 29812 62 44675 ^S 59539 64 74405 65 89272 66 1-48704141 67 1 90 1 1 68 33883 69 48756 70 63566 39718805, 78442 72 93320 73 1-48808199 74 23080 75 37962 76 52846 77 67731 78 82618 79 97506 80 1-48912329 3981875s, 27220 82 42113 83 57007 84 71903 85 8<)8oo 86 I -49001699 1 87 16599; 88 31501I 89 46404 90 ' 61241 39918705, 76147' 92 9105s 93 1-49105964 94 20875 95 35787 96 50701 97 65616 98 80533 99 95451 4000 1-49210302 40018655, 25223 1 02 40146 1 03 55070! 04 69996 05 Dual Logarithms. Dual Numbers. 84923 99851 1-49314781 06 07 08 29712 44645 09 10 5,0,0 5,i'0 5,2 5,3 5,4 5,5 5,6 5,7 5,8 5,9 6,0, 6,1 6,2 6,3 6,4 6,5 6,6 6,7 6,8 6,9 7,0 7,1 7,2 7,3 7,4, 7,5 7,6: 7,7 7,8 7,9 8,a 8,1 8,2 8,3 8,4 8,5 8,6 8,7 8,8 8,9 9,0 9,1 9,2 9,3 9,4 9,5 9,6 9,7 9,8 9,9 Multiples of DifTerences. 1478 1479! 2956 2958 j 4434 4437 5912 5916 7390 7395 8868 8874 10346 10353 1 1 824 1 1832 13302 133" ! 1480 2960 4440 5920 7400 I48I 1482 2962 2964 4443 4446 5924 5928 7405 7410 8886 8892 10367 10374 II 848 1 1856 13329 i333« 10360 1 1 840 13320 1483 2966 4449 5932 7415 I 1484 1485 2 2968 2970 3 4452 4455 4 593t> 5940 5 7420 7425 6 8904 8910 7 10388 10395 8 1 1872 11880 9 13356 13365 10381 1 1864 13347 i486 2972 4458 5944 7430 8916 10402 1 1888 ^3374 1487 1488 1489 2974 2976 2978 4461 4464 4467 6948 6952 5956 7435 7440 7445 8922 8928 8934 10409 10416 10423 1 1 896 1 1904 11912 13383 13392 13401 1490 2980 149 1 2982 4470 5960 4473 5964 7450 8940 7455 8946 10430 1 1920 10437 11928 13410 13419 1492 2984 4476 5968 7460 8952 10444 1 1936 13428 1493 2986 4479 5972 7465 8958 10451 "944 13437 Dual Logarithms of powers of 2 and 10. , 2 = 69314718, X, 10 = 230258509, L 10* = 921034037, J,, lo^ = 1611809565, ,, 4 = 138629437, ,„ lo^ = 460517019, ,„ 10^ = 1 151292546, J,, 10*^ = 1842068074, ; - 207944154, 4, lo-"^ = 690775528, 4,, lo'' = 1381551056, \, 10'' = 2072326584, Nat No. 1-4935 to 1-5083 D. Log. 4011.... to 4110.... D. No. ,1^4,2,0,0, to >H,2,9,9, [43 Natural Dual Dual Numbers. Logarithms, Numbers. 1-49352841 40I14138, 4,4,2,0,0,0,0,0,0, 67776 12 r, 4,2,0, 1, 0,0,0,0, 82713 13 v[,4, 2,0, 2,0,0,0,0, 97651 14 \1'4, 2,0,3,0,0,0,0, 1-49412591 15 4,4,2,0,4,0,0,0,0, 27532 16 >I'4,2,o,5,o,o,o,o, 42475 17 4,4,2,0,6,0,0,0,0, 57419 18 ,4,2,0,7,0,0,0,0, 72365 19 ,4,2,0,8,0,0,0,0, 87312 20 ,4,2,0,9,0,0,0,0, 1-49502194 40214088, > 4,2, 1,0,0,0,0,0, 1 7 144 22 ,,4,2,1,1,0,0,0,0, 32096 23 ,4,2,1,2,0,0,0,0, 47049 24 >4,2,i,3,o,o,o,o. 62004 25 ,4,2,1,4,0,0,0,0, 76960 26 > '4,2, 1,5,0,0,0,0, 91918 27 ,4,2,1,6,0,0,0,0, 1-49606877 28 ,4,2,1,7,0,0,0,0, 21838 29 ,4,2,1,8,0,0,0,0, 36800 30 4,4,2,1,9,0,0,0,0, 51696 403T4038, ,4,2,2,0,0,0,0,0, 66661 32 ,4,2,2,1,0,0,0,0, 81628 33 4,4,2,2,2,0,0,0,0, 96596 34 ,4,2,2,3,0,0,0,0, 1-49711566 35 ,4,2,2,4,0,0,0,0, 26537 36 ,4,2,2,5,0,0,0,0, 41510 37 ,4,2,2,6,0,0,0,0, 56484 38 ,4,2,2,7,0,0,0,0, 71460 S9 ,4,2,2,8,0,0,0,0, 86437 40 4,4,2,2,9,0,0,0,0, 1-49801348 40413988, 4'4, 2,3,0,0,0,0,0, 16328 42 ,4,2,3,1,0,0,0,0, 31310 43 > 4,2,3,2,0,0,0,0, 46293 44 w4,2,3,3,o,o,o,o. 61278 45 > 4,2,3,4,0,0,0,0, 76264 46 > 4,2,3,5,0,0,0,0, 91252 47 ,,4,2,3,6,0,0,0,0, I -49906241 48 >4,2,3,7,o,o,o,o. 21232 49 "4,2,3,8,0,0,0,0, 36224 50 ,,4,2,3,9,0,0,0,0, 5 1 149 40513938, ,,4,2,4,0,0,0,0,0, 66144 52 ,,4,3,4,1,0,0,0,0, 81141 53 ,,4,2,4,2,0,0,0,0, 96139 54 > 4,2,4,3,0,0,0,0, 1-50011139 55 ,,4,2,4,4,0,0,0,0, 26140 56 w4,2,4,5,o,o,o,o. 41 143 57 ,,4,2,4,6,0,0,0,0, 56147 58 •4,2,4,7,0,0,0,0, 71153 59 ,,4,2,4,8,0,0,0,0, 86160 60 4,4,2,4,9,0,0,0,0, Natural Numbers, 1-50101100 i6iio 31122 46135 61150 76166 91184 1-50206203 21224 36246 51201 66226 81253 96281 1*50311311 26342 41375 56409 71445 86482 1-50401452 16492 31534 46577 61622 76668 91716 1-50506765 2i8i6 36868 51853 66908 81965 97023 1*50612083 27144 42207 57271 72337 87404 1-50702405 17475 32547 47620 62695 77771 92849 1-50807928 23009 38091 Dual Logarithms, 4061 62 63 64 65 66 67 68 69 70 40713838, 72 73 74 75 76 77 78 79 80 40813788, 82 83 84 85 86 87 88 89 90 40913738, 92 93 94 95 96 97 98 99 4100 41013688, 02' 03 04 05 06 07 08 09 10 Dual Numbers. 4'4,2,5,O,0,0,0,0; 4^4,2,5,1,0,0,0,0 4^4,2,5,2,0,0,0,0 14,2,5,3,0,0,0,0 14,2,5,4,0,0,0,0 4'4,2,5, 5, 0,0,0,0, > 4,2, 5, 6,0,0,0,0 w4,2,5, 7,0,0,0,0 v4,2,5, 8,0,0,0,0 4^4,2,5,9,0,0,0,0, 4,4,2,6,0,0,0,0,0, > 4,2,6, 1,0,0,0,0 ,,4,2,6,2,0,0,0,0 V 4, 2,6,3,0, 0,0,0 4,4,2,6,4,0,0,0,0, > 4,2,6,5,0,0,0,0, ,,4,2,6,6,0,0,0,0 > 4,2,6,7,0,0,0,0 ,,4,2,6,8,0,0,0,0 4'4,2,6,9,o,o,o,o {4,2,7,0,0,0,0,0 4,2,7,1,0,0,0,0 4,2,7,2,0,0,0,0 4,2,7,3>o,o,o,o 4,2,7,4,0,0,0,0 > 4,2,7,5,0,0,0,0, ,,4,2,7,6,0,0,0,0, > 4,2,7,7,0,0,0,0 4,4,2,7,8,0,0,0,0, >l'4,2,7,9>o>o>o,o 4,4,2,8,0,0,0,0,0, J,4,2, 8, 1,0,0,0,0, 4,4,2,8,2,0,0,0,0 14,2,8,3,0,0,0,0 4,4,2,8,4,0,0,0,0, > 4,2,8,5,0,0,0,0 ,,4,2,8,6,0,0,0,0, ,,4,2,8,7,0,0,0,0, ,,4,2,8,8,0,0,0,0, ,,4,2,8,9,0,0,0,0 4,4,2,9,0,0,0,0,0 i4, 2, 9,^0,0,0,0 4,4,2,9,2,0,0,0,0, 4^4,2,9,3,0,0,0,0 4^4,2,9,4,0,0,0,0 {4,2,9,5,0,0,0,0 4,4,2,9,6,0,0,0,0, {4,2,9,7,0,0,0,0 {4,2,9,8,0,0,0,0 {4,2,9,9,0,0,0,0 Multiples of Differences. 1493 1494 2986 2988 4479 4482 5972 5976 74^S 7470 8958 8964 10451 10458 1 1944 11952 13437 13446 1496 M97 2992 2994 4488 4491 5984 S988 7480 74«S 8976 8982 10472 I0479 11968 1 1976 13464 13473 I49S 2990 4485 5980 7475 8970 10465 1 1960 1345s 1498 2996 4494 5992 7490 1499 1500 2998 3000 4497 4500 5996 6000 7495 7500 8994 9000 10493 10500 1 1992 12000 13491 13500 1502 1503 3004 3006 4506 4509 6008 6012 7510 75IS 9012 9018 10514 I052I I20l6 12024 13518 13527 1505 1506 3010 3012 4515 4518 6020 6024 7525 7530 9030 9036 10535 10542 12040 12048 13545 13554 10486 1 1984 13482 I50I 3002 4503 6004 7505 9006 10507 12008 13509 1504 3008 4512 6016 7520 9024 10528 12032 1353^ 1507 3014 452.1 602S 7535 9042 10549 12056 1356^3 1508 3016 4524 6032 7540 9048 10556 12064 13522- Dual Logarithms of powers of 2 and 10. 4,, 2 = 69314718, 4,, 10 = 230258509, 4^ 10" = 921034037, 4,, io7 = 161 1809565, i, 4 = 138629437, {, io2 = 460517019, {, 10^ = 1151292546, {, lo*' = 1842068074, {, 8 = 207944154, {, io3 = 690775528, {, loO = 138155J056, {, ro'^ = 2072326584, ii] Nat. No. 1-5084 to r5234 D. Log. 4110.... to 4209.... D. No. >^4,3,0,0, to |4,3,9,9, Natural Dual 1 Dual Numbers. Logarithms. Numbers. 1-50846369 41109171, 4,4,3,0,0,0,0,0,0, 61454 II 4'4>3.o, 1,0,0,0,0, 76540 12 4,4,3,0,2,0,0,0,0, 91628 13 ' 4,3)0,3,0,0,0,0, 1-50906717 14 > 4,3,0,4,0,0,0,0, 21808 15 > 4,3,0,5,0,0,0,0, 36900 16 > 4,3,0,6,0,0,0,0, 51993 17 v4,3,o,7,o,o,o,o. 67088 18 ' 4,3,0,8,0,0,0,0, 82185 19 v4,3>o,9,o,o,o,o. 97215 4120912I, '4,3,1,0,0,0,0,0, 1-51012315 21 ,4,3,1,1,0,0,0,0, 27416 22 > 4,3,1,2,0,0,0,0, 42518 23 > 4,3, ^,3,0,0,0,0, > 4,3,1,4,0,0,0,0, 57622 24 72728 25 w4,3,i, 5,0,0,0,0, 87835 26 > 4,3, 1,6,0,0,0,0, I -5 1 102944 27 > 4,3, 1,7,0,0,0,0, > 4,3, ^,8,0,0,0,0, 18054 28 33166 29 > 4,3,1,9,0,0,0,0, 48212 41309071, > 4,3,2,0,0,0,0,0, 63327 31 ,4,3,2,1,0,0,0,0, 78443 32 ,4,3,2,2,0,0,0,0, 93561 33 > 4,3,2,3,0,0,0,0, 1-51208680 34 > 4,3,2,4,0,0,0,0, 23801 35 ,4,3,2,5,0,0,0,0, 38923 36 ,4,3,2,6,0,0,0,0, 54047 37 w4,3,2,7,o,o,o,o. 69172 38 > 4,3,2,8,0,0,0,0, > 4,3,2,9,0,0,0,0, 84299 39 99360 41409021, > 4,3,3,0,0,0,0,0, ' 4,3,3, 1,0,0,0,0, 1-51314490 41 29621 42 > 4,3,3,2,0,0,0,0, 44754 43 > 4,3,3,3,0,0,0,0, 59888 44 > 4,3,3,4,0,0,0,0, 75024 45 w4,3,3, 5,0,0,0,0, 90162 46 > 4,3,3,6,0,0,0,0, 1-51405301 47 ^4,3,3,7,0,0,0,0, 20442 48 > 4,3,3,8,0,0,0,0, 35584 49 " 4,3,3,9,0,0,0,0, 50659 41508971, > 4,3,4,0,0,0,0,0, 65804 51 > 4,3,4, 1,0,0,0,0, 80951 52 '4,3,4,2,0,0,0,0, 96099 53 > 4,3,4,3,0,0,0,0, 1-51511249 54 55 '4,3,4,4,0,0,0,0, 26400 > 4,3,4,5,0,0,0,0, 41553 56 ,4,3,4,6,0,0,0,0, 56707 57 > 4,3,4,7,0,0,0,0, 71863 58 >I'4,3, 4,8,0,0,0,0, 87020 59 4^4,3,4,9,0,0,0,0, Natural Numbers. I-51602110 17270 32432 47595 62760 77926 93094 1-51708263 23434 38606 53712 84064 99242 1-51814422 29603 44786 59970 75^56 90344 1-51905466 20657 35849 51043 66238 81435 96633 1-52011833 27034 42237 57371 72577 87784 1-52102992 18202 33414 48627 63842 79058 94276 1-52209428 24649 39871 55095 70321 85548 1-52300777 16007 31239 46472 Dual Logarithms. 41608921, 61 62 63 64 65 66 67 68 69 41708871, 71 72 73 74 75 76 77 78 79 41808821, 81 82 83 84 85 86 87 88 89 41908771, 91 92 93 94 95 96 97 98 99 42008721, 01 02 03 04 05 06 07 08 09 Dual Numbers. >^4,3 |4,3 h^3 |4,3 |4,3 >|'4,3 |4,3 {4,3 4'4,3 |4,3 |4,3 U,3 ^4,3 U,3 |4,3 {4,3 4,3 4,3 4,3 4,3 4,3 4,3 4,3 4'4,3 |4,3 |4,3 {4,3 |4,3 14,3 |4,3 |4,3 U,3 >4,3 w4,3 4'4,3 |4,3 i4,3 i4,3 4'4,3 vl'4,3 |4,3 H3 U^3 ^4,3 i4,3 >!'4,3 {4,3 4'4,3 |4,3 5,0 5,1 5,2 5,3 5,4: 5,5 5,6 5,7 5,8 5,9 6,0, 6,1 6,2 6,3 6,4 6,5 6,6 6,7 6,8 6,9 7,0 7,1 7,2 7,3 7,4: 7,5 7,6 7,7 7,8 7,9 8,0 8,1 8,2 8,3 8,4 8,5 8,6 8,7 8,8 8,9 9,0 9,1 9,2 9,3 9,4 9,5 9,6 9,7 9,8 9,9 Multiples of Differences. I 1508 1509 1510 2 3016 3018 3020 3 4524 4527 4530 4 6032 6036 6040 5 7540 7545 7550 6 9048 9054 9060 7 10556 10563 10570 8 12064 12072 12080 9 13572 13581 13590 I 1511 1512 1513 2 3022 3024 3026 3 4533 4536 4539 4 6044 6048 6052 5 7555 7560 7565 6 9066 9072 9078 7 10577 10584 10591 8 12088 12096 1 2 104 9 I3S99 13608 13617 I 1514 1515 1516 2 3028 3030 3032 3 4542 4545 4548 4 6056 6060 6064 5 7570 7575 7580 6 9084 9090 9096 7 10598 10605 10612 8 12112 12120 12128 9 13626 13635 13644 I 1517 1518 1519 2 3034 3036 3038 3 4551 4554 4557 4 6068 6072 6076 5 7585 7590 7595 6 9102 9108 91 14 7 10619 10626 10633 8 12136 12 144 12152 9 13653 13662 13671 I 1520 1521 1522 2 3040 3042 3044 3 4560 4563 4566 4 6080 6084 6088 5 7600 7605 7610 6 9120 9126 9x32 7 1064.0 10647 10654 8 12160 12168 12176 9 13680 13689 13698 I 1523 2 3046 3 4569 4 6092 5 76^5 6 9138 7 10661 8 12184 9 13707 Dual Logarithms of powers of 2 and 10. 4,, 2 = 69314718, I, 10 -» 230258509, 4,, 10* = 921034037, L lo^ = 1611809565, 4^, 4 = 138629437, 4^, lo^ = 460517019, 4, lo^ =2: 1151292546, 1, 10^ — 1842068074, 4r, 8 = 207944154, 4,, I03 ^ 690775528, I, IO« = I38155IO56, I, lO^ = 2072326584, Nat. No. 1"5235 to 1'5386 D. Log. 4210.... to 4309.... D. No. >I4,4,0,0, to >I4,4,9,9, [45 Natural Dual Natural Number?. Logarithms. Numbers. i'52354833 42104204, ,4,4,0,0,0,0,0,0, ,4,4,0,1,0,0,0,0, 70068 II 85305 12 ,4,4,0,2,0,0,0,0, 1-52400544 13 > 4,4,0,3,0,0,0,0, , 15784 14 ,4,4,0,4,0,0,0,0, 31026 15 w4,4,o,5,o,o,o,o, 46269 16 ,4,4,0,6,0,0,0,0, 61514 17 ,4,4,0,7,0,0,0,0, 76760 18 > 4,4,0,8,0,0,0,0, > 4,4,0,9,0,0,0,0, 92008 19 ■1-52507188 42204154, ,4,4,1,0,0,0,0,0, 22439 21 >j,4,4, 1, 1,0,0,0,0, 37691 22 ,4,4,1,2,0,0,0,0, 52945 23 w4,4, 1,3,0,0,0,0, 68200 24 4'4,4ji>4,o,o,o,o, 83457 25 ,4,4,1,5,0,0,0,0, 98715 26 ,4,4,1,6,0,0,0,0, 1-52613975 27 > 4,4, 1,7,0,0,0,0, 29236 28 ,4,4,1,8,0,0,0,0, 44499 29 ,4,4,1,9,0,0,0,0, 59695 42304104, ,4,4,2,0,0,0,0,0, ,4,4,2,1,0,0,0,0, 74961 31 90228 32 ,4,4,2,2,0,0,0,0, i'527o5497 33 > 4,4,2,3,0,0,0,0, 2076S 34 > 4,4,2,4,0,0,0,0, 36040 35 ,4,4,2,5,0,0,0,0, ,4,4,2,6,0,0,0,0, 51314 36 66589 37 '4,4,2,7,0,0,0,0, 81866 38 ,44,2,8,0,0,0,0, 97144 39 ,4,4,2,9,0,0,0,0, X-52812355 42404054, J,4,4,3,o,o,o,o,o, > 4,4,3, 1,0,0,0,0, 27636 41 42919 42 > 4,4,3,2,0,0,0,0, > 4,4,3,3,0,0,0,0, 58203 43 73489 44 N 4,4,3,4,0,0,0,0, 88776 45 > 4,4,3,5,0,0,0,0, > 4,4,3,6,0,0,0,0, 1-52904065 46 19356 47 .4,4,3,7,0,0,0,0, 34648 48 > 4,4,3,8,0,0,0,0, w4,4,3,9,o,o,o,o, 49941 49 65167 42504004, ,4,4,4,0,0,0,0,0, 80464 51 ,4,4,4,1,0,0,0,0, 95762 52 ,4,4,4,2,0,0,0,0, 1-53011062 53 > 4,4,4,3,0,0,0,0, 26363 54 > 4,4,4,4,0,0,0,0, 41666 55 '4,4,4,5,0,0,0,0, 56970 56 ,4,4,4,6,0,0,0,0, 72276 57 '4,4,4,7,0,0,0,0, 87583 58 ,4,4,4,8,0,0,0,0, 1-53102892 59 '4,4,4,9,0,0,0,0, Natnral Numbers. I"531l8l32 33444 48757 64072 79389 94707 1-53210027 25348 40671 55995 71250 86577 i"533oi9o6 17236 32568 47901 63236 78572 93910 1*53409249 24521 39863 55207 70553 85900 1-53501249 16599 31951 47304 62659 77946 93304 1-53608663 24024 39386 54750 70115 85482 i"537oo85i 16221 31524 46897 62272 77648 93026 1-53808405 23786 39168 54552 69937 Dual Logarithms. 42603954 61 62 63 64 65 66 67 68 69 42703904, 71 72 73 74 75 76 77 78 79 42803854, 81 82 83 84 85 86 87 88 89 42903804, 91 92 93 94 95 96 97 98 99 43003754, 01 02 03 04 05 06 07 08 09 Dual Numbers. >^4,4,5>o,o,o,o,o, 4'4,4,5, 1,0,0,0,0 >I'4,4,5, 2,0,0,0,0 >i'4,4,5, 3,0,0,0,0 i4,4,5,4,o,o,o,o |4,4,5,5,o,o,o,o >^4,4,5, 6,0,0,0,0 4'4,4,5, 7,0,0,0,0, >l'4,4,5,8,o,o,o,o 4'4, 4, 5, 9,0,0,0,0 J4,4,6,o,o,o,o,o 4,4,4,6, 1,0,0,0,0 4,4,4,6,2,0,0,0,0 14,4,6,3,0,0,0,0 >I^4,4,6,4,o,o,o,o 14,4,6,5,0,0,0,0 4,4,4,6,6,0,0,0,0, 4,4,6,7,0,0,0,0 4,4,6,8,0,0,0,0 4,4,6,9,0,0,0,0 \^4,4,7, 0,0,0,0,0 \1^4,4,7, 1,0,0,0,0 > 4,4,7,2,0,0,0,0 > 4,4,7,3,0,0,0,0 I4, 4, 7, 4, 0,0, 0,0 >Ir4,4,7,5,o 0,0,0 ^4,4,7, 6,0,0,0,0 44,4,7 7,0,0,0,0^ ^4,4,7,8,0,0,0,0 i4,4,7, 9,0,0,0,0 ,4,4,8,0,0,0,0,0, > 4,4,8, 1,0,0,0,0 ,,4,4,8,2,0,0,0,0, > 4,4,8,3,0,0,0,0, |4,4,8,4,o,o,o,o k,4,8,5,o, 0,0,0 14,4,8,6,0,0,0,0 U,4,8,7, 0,0,0,0 [4,4,8,8,0,0,0,0 k4,8,9,o,o,o,o 44,4,9,0,0,0,0,0, N 4,4,9, 1,0,0,0,0 > 4,4,9, 2,0,0,0,0, > 4,4,9,3, 0,0, 0,0 44,4,9,4,0,0,0,0 44,4,9,5,0,0,0,0 > 4,4,9,6,0,0,0,0, > 4,4,9,7,0,0,0,0 > 4,4,9,8,0,0,0,0 44,4,9,9,0,0,0,0 Multiples of Differences. i';23 1524 3046 3048 4569 4572 6092 6096 7615 7620 9138 9144 10661 10668 12184 12192 13707 13716 1526 1527 30-52 3054 4^7« 4581 6104 6108 7630 763 s 9156 9162 10682 10689 12208 12216 13734 13743 I 1529 i';3o 2 3058 3060 3 4587 4590 4 6116 6120 5 7645 7650 6 9174 9180 7 10703 10710 8 12232 12240 9 i37(Ji 13770 I i';32 i,';33 2 3064 3066 3 4,S9(> 4599 4 6128 6132 5 7660 766 s 6 9192 9198 7 10724 1073 1 8 12256 12264 9 13788 13797 I IS35 1536 2 3070 3072 3 4605 4608 # 6140 6144 5 7675 7680 b 9210 9216 7 1074 ■; I07S2 8 12280 12288 9 13815 13824 1525 3050 4575 6100 7625 9150 10675 12200 13725 1528 3056 4584 6112 7640 9168 10696 12224 13752 1531 3062 4593 6124 7655 9186 107 1 7 12248 13779 1534 3068 4602 6136 7670 9204 10738 12272 13806 1537 3074 461 1 6148 7685 9222 10759 12296 13833 1538 3076 4614 6152 7690 9228 10766 12304 13842 Dual Logarichms of powers of 2 and 10. J,, 2 = 693147 18, L 10 = 230258509, I, 10* = 921034037, 14= 138629437, ,„ io2 = 460517019, ,,, lo'^ = 1151292546, 4, 8 = 207944154, 4» 10^ = 690775528, 4> 10" = 1381551056, 10" = 1611809565, 10* = 1842068074, 10^ = 2072326584, 46] Nat. No. 1-5387 to 1-5540 D. Log. 4309.... to 4408.... D. No. K5,0,0, to ^5,9^, Natural Numbers, 1-53878381 93769 i"53909i58 24549 39941 55335 70731 86128 i'54ooi527 16927 32259 47662 63067 78473 93881 i"54io929o 24701 401 13 55527 70943 86292 1-54201711 17131 32553 47976 63401 78827 94255 i "54309684 25115 40478 55912 7^348 86785 1*54402224 17664 33106 48549 63994 79440 94818 1-54510267 25718 41171 56625 72081 87538 1-54602997 18457 33919 Dual Logarithms. 43099237. 10 II 12 13 14 15 16 17 18 43I99187, 20 21 22 23 24 25 26 27 28 43299137, 30 31 32 33 34 35 ^6 37 38 43399087, 40 41 42 43 ^^ 46 47 48 43499037, 50 51 52 53 54 55 56 57 58 Dual Numbers. \'A,S 0,0, w4,5 0,1, \'A,S 0,2, >'4,5 0,3, H,5 0,4, >'4,5 0,5, ^'4,5 0,6, w4,5 0,7, |4,5 0,8, >!'4,5 0,9, >'4»5 1,0, w4,5, 1,1, >4,5 1,2, >'4,5 1,3, |4,5 1,4, w4,5, 1,5, >'4,5 1,6, •4,5 1,7, \4,5 1,8, 14,5 1,9, '4,5 2,0, >4,5 2,1, >4,5 2,2, x4,5 2,3, |4,5 2,4, >4,5 n4,5 2,5, 2,6, >4,5 >4,5 2,7, 2,8, >4,5 2,9, >4,5 3,0, >4,5 3,1, -4,5 3,2, >4,5 Z,h |4,5 3,4, >4,5 3,5, >4,5 3,6, ^4,5 3,7, >4,5 w4,5 3,8, 3,9, ^4,5 4,0, \4,5 4,1, >4,5 4,2, >4,5 4,3, 4'4,5 4,4, >4,5 4,5, >l'4,5 4,6 >4,5 ,4,7 >4,5 ,4,8 |4,5 ,4,9 Natural Numbers. I '546493 14 64779 80245 95713 I-54711183 26654 42127 57601 73077 88554 1-54803963 19443 34925 50409 65894 81381 96769 1-54912259 27750 43243 58767 74263 89760 I '55005259 20760 36262 51766 67271 82778 98286 1*55113726 29237 44750 60264 75780 91298 I-55206817 22338 37860 53384 68840 84367 99895 i'553i5425 30957 46490 62025 77561 93099 1*55408638 Dual Logarithms. 43598987, 60 61 62 64 65 66 67 68 43698937, 70 71 72 73 74 75 76 77 78 43798887, 80 81 82 83 84 85 86 87 88 43898837, 90 91 92 93 94 95 96 97 98 43998787, 4400 01 02 03 04 05 06 07 08 Dual Numbers. 5,0 5,1 5,2 5,3 5,4; 5,5 5,6 5,7 5,8 5,9 6,0 6,1 6,2 6,4: 6,5 6,6 6,7 6,8 6,9 7,0 7,1 7,2 7,3 7,4 7,5 7,6 7,7 7,8 7,9 8,0 8,1 8,2 8,3 8,4 8,5 8,6 8,7 8,8 8,9 9,0 9,1 9,2 9,3 9,4: 9,5 9,6 9,7 9,8 9,9 Multiples of Differences. 1538 IW 3076 .307« 4614 4617 6152 61S6 7690 769s 9228 9234 10766 10773 12304 12312 i3«42 i3«5i 1541 1542 3082 3084 4623 4626 6164 6168 7705 7710 9246 9252 10787 10794 12328 12336 i3«69 13878 I i';44 i$A^ 2 3088 3090 3 4632 4635 4 6176 6180 5 7720 772s 6 9264 9270 7 10808 108 1 5 8 I23S2 12360 9 I3«96 13905 iW 1548 3094 3096 4641 4644 6188 6192 773"; 7740 9282 9288 10829 10836 12376 12384 13923 13932 1550 1551 3100 3102 4650 46 S3 6200 6204 7750 7755 9300 9306 10850 io8s7 12400 12408 13950 1395'' 1540 3080 4620 6i6o 7700 9240 10780 12320 13860 1543 3086 4629 6172 7715 9258 10801 12344 13887 1546 3092 4638 6184 7730 9276 10822 12368 '3914 1549 3098 4647 6196 7745 9294 10843 12392 J13941 1552 3104 4656 6208 7760 9312 10864 1 2416 13968 1553 3106 4659 6212 7765 9318 10871 12424 13977 1554 3108 4662 6216 7770 9324 10878 12432 13986 X, 2 = 693147 18, V, 4 = 138629437, 4,, 8 - 207944154, Dual Logarithms of powers of 2 and 10. J,, 10 = 230258509, L 10* = 921034037, V, lo^ = 460517019, ,„ lo^ = 1151292546, \, io3 = 690775528, I, io« = 1381551056, I, lo^ = 161 1809565, ,„ lo** = 1842068074, 10'' = 2072326584, Nat. No. 1-5541 to 1-5696 D. Log Natural Dual Dual Numbers. Logarithms. Numbers. i'S54i7i65 44094270, ^, 4,6,0,0,0,0,0,0, 32707 10 > '4)6,0,1,0,0,0,0, 48250 II ,4,6,0,2,0,0,0,0, 63795 12 ,,4,6,0,3,0,0,0,0, 79341 13 ,,4,6,0,4,0,0,0,0, 94889 14 > '4)6,0,5,0,0,0,0, 1-55510438 15 ,,4,6,0,6,0,0,0,0, 25989 16 ,,4,6,0,7,0,0,0,0, 41542 17 ,,4,6,0,8,0,0,0,0, 57096 18 ,,4,6,0,9,0,0,0,0, 72582 44194220, ,,4,6,1,0,0,0,0,0, 88139 20 ,.4,6,1,1,0,0,0,0, 1-55603698 21 ,,4,6,1,2,0,0,0,0, 19258 22 ,,4,6,1,3,0,0,0,0, 34820 23 ,,4,6,1,4,0,0,0,0, 50383 24 > '4)6, 1,5,0,0,0,0, 65948 25 ,4,6,1,6,0,0,0,0, 81515 26 ,,4,6,1,7,0,0,0,0, 97083 27 ,,4,6,1,8,0,0,0,0, 1-55712653 28 ,4,6,1,9,0,0,0,0, 28155 44294170, ,,4,6,2,0,0,0,0,0, 43728 30 ,,4,6,2,1,0,0,0,0, 59302 3t ,,4,6,2,2,0,0,0,0, 74878 32 ,,4,6,2,3,0,0,0,0, 90455 33 ,,4,6,2,4,0,0,0,0, 1-55806034 34 ,,4,6,2,5,0,0,0,0, 21615 35 ,,4,6,2,6,0,0,0,0, 37197 36 w4)6,2,7, 0,0,0,0, 52781 37 ,,4,6,2,8,0,0,0,0, 68366 38 ,,4,6,2,9,0,0,0,0, 83883 44394120, ,,4,6,3,0,0,0,0,0, 99471 40 >'4)6,3,i)0,o,o,o, 1-55915061 41 > '4)6,3)2,0,0,0,0, 30653 42 > '4)6,3)3)0,0,0,0, 46246 43 |4,6,3,4,o,o,o,o. 61841 44 ^ '4,6,3)5)0,0,0,0, 77437 45 ,,4,6,3,6,0,0,0,0, 93035 46 ^ '4)6,3)7)0,0,0,0, 1-56008634 47 ,,4,6,3,8,0,0,0,0, 24235 48 ' '4)6,3)9)0,0,0,0, 39767 44494070, ,,4,6,4,0,0,0,0,0, 55371 50 ,,4,6,4,1,0,0,0,0, 70977 51 ,,4,6,4,2,0,0,0,0, 86584 52 > '4)6,4,3)0)0,0,0, 1-56102193 53 N '4)6,4)4)0,0,0,0, 17803 54 |4,6,4)5)0)0,o,o. 33415 55 |4,6,4,6,o,o,o,o. 49028 56 > '4)6,4)7)0,0,0,0, 64643 57 4,4,6,4,8,0,0,0,0, 80259 58 >l'4,6,4,9,o,o,o,o. D. Log. 4409.... to 4508.... D. No. W,6,0,0, to H6,9,9, [^7 Natural Dual Dual Numbers. Logarithms. Numbers. I-56195807 44594020, 4'4)6,5)0,o,o,o,o, I-56211427 60 > '4,6,5, 1)0,0,0,0, 27048 61 ,,4,6,5,2,0,0,0,0, 42671 62 ,,4,6,5,3,0,0,0,0, 58295 63 4'4) 6, 5, 4) 0,0, 0,0, 73921 64 > '4,6,5)5)0)0,0,0, 89548 65 > '4)6,5,6,0,0,0,0, 1-56305177 66 w4,6,5,7,o,o,o,o. 20808 67 > '4,6,5,8,0,0,0,0, 36440 68 ,,4,6,5,9,0,0,0,0, 52003 44693970, ,,4,6,6,0,0,0,0,0, 67638 70 ,,4,6,6,1,0,0,0,0, 83275 71 ,,4,6,6,2,0,0,0,0, 98913 72 ,,4,6,6,3,0,0,0,0, 1-56414553 73 ,,4,6,6,4,0,0,0,0, 30194 74 ,,4,6,6,5,0,0,0,0, 45837 75 ,,4,6,6,6,0,0,0,0, 61482 76 ,4,6,6,7,0,0,0,0, 77128 77 ,,4,6,6,8,0,0,0,0, 92776 78 ,,4,6,6,9,0,0,0,0, 1-56508355 44793920, ,,4,6,7,0,0,0,0,0, 24006 80 ,,4,6,7,1,0,0,0,0, 39658 81 ,,4,6,7,2,0,0,0,0, 55313 82 > '4,6,7)3)0)0,0,0, 70968 83 v4,6,7)4)0,o,o,o. 86625 84 w4,6,7, 5)0)0,0,0, 1*56602284 85 ,,4,6,7,6,0,0,0,0, 17944 86 >l'4,6,7,7)0,o,o,o. 33^°^ 87 ,,4,6,7,8,0,0,0,0, 49269 88 ,,4,6,7,9,0,0,0,0, 64863 44893870, ,4,6,8,0,0,0,0,0, 80529 90 ,,4,6,8,1,0,0,0,0, 96197 91 ,,4,6,8,2,0,0,0,0, 1-56711867 92 ,,4,6,8,3,0,0,0,0, 27538 93 ^4,6,8,4,0,0,0,0, 43211 94 |4)6,8,5,o,o,o,o. 58885 95 |4)6,8,6,o,o,o,o. 74561 96 ,,4,6,8,7,0,0,0,0, 90238 97 ,,4,6,8,8,0,0,0,0, 1-56805917 98 1,4,6,8,9,0,0,0,0, 21528 44993820, |4,6,9,o,o,o,o,o. 37210 4500 4,4,6,9,1,0,0,0,0, 52894 01 v4)6,9,2,o,o,o,o. 68579 02 >I'4)6,9)3)0)0,o,o, 84266 03 4,4,6,9,4,0,0,0,0, 99954 04 ^1^4)6,9,5,0,0,0,0, 1-56915644 05 4,4,6,9,6,0,0,0,0, 3^336 06 |4)6,9)7)0,o,o,o. 47029 07 J,4,6,9,8,o,o,o,o, 62724 08 4,4,6,9,9,0,0,0,0, Multiples of Differences. I5S4 !.■;';=; S108 3110 4662 4665 6216 6220 7770 7775 9324 9330 10878 10885 12432 12440 i39«6 1399s 1557 1558 3"4 3116 4671 4674 6228 6232 77«5 7790 9342 9348 10899 10906 12456 12464 14013 14022 1560 1561 3120 3122 4680 6240 7800 9360 4683 6244 7805 9366 10920 12480 10927 12488 14040 14049 1563 1564 3126 3128 4689 4692 6252 6256 7815 7820 9378 9384 10941 10948 12504 12512 14067 14076 1566 1567 3132 3134 4698 4701 6264 6268 7830 7835 9396 9402 10962 10969 12528 12536 14094 14103 1569 3138 4707 6276 784s 9414 10983 12552 I412I 1556 3II2 4668 6224 7780 9336 10892 12448 14004 1559 3118 4677 6236 7795 9354 10913 12472 1403 1 1562 3124 4686 6248 7810 9372 10934 12496 14058 1565 3130 4695 6260 7825 9390 10955 12520 14085 1568 3136 4704 6272 7840 9408 10976 12544 14112 Dual Logarithms of powers of 2 and 10. 4,, 10 = 230258509, 4,, lo* = 921034037, 4 = 138629437, X, io2 = 460517019, 4,, 10^ = 1151292546, 8 = 207944154, 4,, 10' = 690775528, 4,, io« = 1381551056, ,„ 2 = 693 147 1 , ,, 4 10'^ = 1611809565, lo** = 1842068074, 4,, 10" = 2072326584, 48] Nat. No. 1-5697 to 1"5853 D. Log. 4508.... to 4607.... D. No. 44,7,0,0, to >I4,7,9,9, Natural Dual Dual Numbers. Logarithms. Numbers. i"5697i337 45089303, X4,7,o,o,o,o,o,o, 4,4,7,0,1,0,0,0,0, 87034 09 1-57002733 10 4,4,7,0,2,0,0,0,0, 18433 II \^4,7,o,3,o,o,o,o. 3413s 12 U^7, 0,4,0,0,0,0, 49838 13 14,7,0,5,0,0,0,0, 65543 14 ^I,4,7, 0,6,0,0,0,0, 81250 15 i4,7>o,7,o,o,o,o. 96958 16 4,4,7,0,8,0,0,0,0, i'57ii2668 17 >l'4>7,o,9,o,o,o,o, 28308 45i89253> X4,7, 1,0,0,0,0,0, 44021 19 ,4,7,1,1,0,0,0,0, 59735 20 ^, 4,7,1, 2,0,0,0,0, 75451 21 >'4,7,i,3>o,o,o,o, 91169 22 w4,7, 1,4,0,0,0,0, 1-57206888 23 "4,7,1,5,0,0,0,0, 22609 24 ,,4,7,1,6,0,0,0,0, 38331 25 > '4,7, 1,7,0,0,0,0, 54055 26 ,,4,7,1,8,0,0,0,0, 69780 27 4^4,7,1,9,0,0,0,0, 85436 45289203, ,,4,7,2,0,0,0,0,0, 1-5730^165 29 ,,4,7,2,1,0,0,0,0, 16895 30 ,,4,7,2,2,0,0,0,0, 32627 31 w4,7,2,3,o,o,o,o. 48360 32 ,,4,7,2,4,0,0,0,0, 64095 33 > 4,7,2,5,0,0,0,0, 79831 34 ,,4,7,2,6,0,0,0,0, 95569 35 > 4,7,2,7,0,0,0,0, X-57411309 36 ,,4,7,2,8,0,0,0,0, 27050 37 ,,4, 7, 2-, 9, 0,0, 0,0, 42721 45389i53> > 4,7,3,0,0,0,0,0, '4,7,3,1,0,0,0,0, 58465 39 74211 40 > 4,7,3,2,0,0,0,0, 89958 41 v4,7,3,3,o,o,o,o, 1*57505707 42 "4,7,3,4,0,0,0,0, 21458 43 >I4,7, 3, 5,0,0,0,0, 37210 44 ,,4,7,3,6,0,0,0,0, 52964 45 > 4,7,3,7,0,0,0,0, 68719 46 w4,7,3,8,o,o,o,o, >1'4,7, 3, 9,0,0,0,0, 84476 47 I -5 7 600 1 64 45489103, ,,4,7,4,0,0,0,0,0, 15924 49 ,,4,7,4,1,0,0,0,0, 31686 50 > 4,7,4,2,0,0,0,0, 47449 51 >I/4,7,4,3,o,o,o,o, 63214 52 >I'4,7,4,4,o,o,o,o, 78980 53 >j'4,7, 4,5, 0,0,0,0, 94748 54 ,,4,7,4,6,0,0,0,0, i'577io5i7 55 >4,7,4,7, 0,0,0,0, 26288 56 > 4,7,4,8,0,0,0,0, 42061 57 >l'4,7,4,9,o,o,o,o. Natural Numbers. 1*57757764 73540 89317 1-57805096 20877 36659 52443 68228 84015 99803 i"579i5522 3^314 47107 62902 78698 94496 1-58010295 26096 41899 57703 73438 89245 i'58io5o54 20865 36677 52491 68306 84123 99941 1-58215761 31511 47334 63159 78985 94813 1-58310642 26473 42306 58140 73976 89743 i"584o5582 21423 37265 53109 68954 84801 1-58500649 16499 32351 Dual Logarithms. 45589053, 59 60 61 62 63 64 65 66 67 45689003, 69 70 71 72 73 74 75 76 77 45788953, 79 80 81 82 83 84 85 86 87 45888903, 89 90 91 92 93 94 95 96 97 45988853, 99 4600 01 02 03 04 05 06 07 Dual Numbers. 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, Multiples of Differences. 1569 1570 3i3« 3140 4707 4710 6276 6280 7«45 7«5o 9414 9420 10983 10990 12552 12560 14121 14130 1572 1573 3144 3146 471b 4719 6288 6292 7860 7B(>.S 9432 9438 11004 IIOII 12576 12584 j 14148 14157. I 1575 1576 2 3150 3152 3 4725 4728 4 6300 6304 ■; 7«75 7880 6 9450 9456 7 1 1025 11032 8 12600 12608 9 1417s 14 1 84 I 1578 1579 2 3i5f> 3158 3 4734 4737 4 6312 6316 S 7890 7895 6 9468 9474 7 1 1046 1 1053 8 12624 12632 9 14202 14211 1581 1582 3162 3164 4743 4746 6324 6328 7905 7910 9486 9492 1 1067 1 1074 12648 12656 14229 14238 I57I 3142 4713 6284 7855 9426 10997 12568 I4I39 1574 3148 4722 6296 7870 9444 11018 12592 14166 1577 3154 4731 6308 7885 9462 11039 12616 14193 1580 3160 4740 6320 7900 9480 11060 12640 14220 1583 3166 4749 6332 7915 9498 11081 12664 14247 1584 3168 4752 6336 7920 9504 1 1088 12672 14256 158S 3170 4755 6340 7925 9510 11095 12680 14265 4,, 2 = 69314718, I, 4 = 138629437, L 10 ^, 8 — 207944154, I, 10' Dual Logarithms of powers of 2 and 10. 4,, io_ = 230258509, I, 10* = 921034037, ,I„ lo^ = 161 1809565, 460517019, I, lo^ = 115x292 ,2 — 3 2546, L 10^ = 1842068074, 690775528, I, io« = 1381551056, I, io» = 2072326584, Nat. No. 1-5854 to 1-6011 D. Log. 4608.... to 4707..., D. No. ^I4,8,0,0, to H8,9,9, [49 Natural Numbers. 1-58541050 56904 72760 88617 1*58604476 20336 36198 52062 67927 83794 99591 1-58715461 31333 47206 63081 78957 94835 1*58810714 2659s 42478 58291 74177 90064 i"589o5953 21844 37736 53630 69525 85422 1-59001321 17149 33051 48954 64859 80765 96673 1-59112583 28494 44407 60321 76166 92084 1-59208003 23924 39846 55770 71696 87623 ^•59303552 19483 Dual Logarithms. 46084336, 09 10 II 12 13 14 15 16 1.7 46184286, 19 20 21 22 23 24 25 26 27 46284236, 29 30 31 32 33 34 35 36 37 46384186, 39 40 41 42 43 44 45 46 47 46484136, 49 50 51 52 53 54 55 56 57 Dual Numbers. >4 \'4j \'4, >'4) ^4) >'4) \4) >4) >'4) y4) >I'4, i4, i4, xI/4,1 ^4,< >4>' >4>< \f4,' >4,< w 4,i 4,^ u,^ l4,i |4,^ i4,^ 4.4,^ U,^ W u,^ u,^ u,^ i4,g \4)S \4,8 >4)8 U8 8,0,0,0,0,0,0, 8,0,1,0,0,0,0, 8,0,2,0,0,0,0, 8,0,3,0,0,0,0, 8,0,4,0,0,0,0, 8,0,5,0,0,0,0, 8,0,6,0,0,0,0, 8,0,7,0,0,0,0, 8,0,8,0,0,0,0, 8,0,9,0,0,0,0, 8,1,0,0,0,0,0, 8,1,1,0,0,0,0, 8,1,2,0,0,0,0, 8,i,3>o,o,o,o, 8,1,4,0,0,0,0, 8,1,5,0,0,0,0, 3,1,6,0,0,0,0, 3,1,7,0,0,0,0, 3,1,8,0,0,0,0, 3,1,9,0,0,0,0, 3,2,0,0,0,0,0, 3,2,1,0,0,0,0, 3,2,2,0,0,0,0, 5,2,3,0,0,0,0, 3,2,4,0,0,0,0, 5,2,5,0,0,0,0, 5,2,6,0,0,0,0, 5,2,7,0,0,0,0, 5,2,8,0,0,0,0, 5,2,9,0,0,0,0, 5,350,0,0,0,0, 5,3» 1)0,0,0,0, 5,3»2, 0,0,0,0, 5,3)3>o,o,o,o, ^34,0,0,0,0, 5,3,5,0,0,0,0, i,3»6,o,o,o,o, >,3)7,o,o,o,o, 1,3,8,0,0,0,0, >>3>9>o,o,o,o, ',4,0,0,0,0,0, ',4,1,0,0,0,0, ',4,2,0,0,0,0, '4,3)0,0,0,0, ',4,4,0,0,0,0, ',4,5)0,0,0,0, 1,4,6,0,0,0,0, U,7)0,o,o,o, 1,4,8,0,0,0,0, ■4)9)0,0,0,0, Natural Numbers. i'59335342 51276 67211 83148 99086 1-59415026 30968 469 1 1 62856 78802 94677 1-59510626 26577 42530 58484 74440 90397 1-59606356 22317 38279 54172 70137 86104 1-59702073 18043 34015 49988 65963 81940 97918 1-59813826 29807 45790 61775 77761 93749 i'59909738 25729 41722 57716 73640 , 89637 I 1-560056361 21637 : 37639 I 53643 69648 85655 I-60IO1664 17674 Dual Logarithms. Dual Numbers. 46584086, 59 60 61 62 63 64 65 66 67 46684036 69 70 71 72 73 74 75 76 77 46783986, 79 80 81 82 83 84 85 86 87 46883936, 89 90 91 92 93 94 95 96 97 f4 >i'4 {4 >4, \'4 >4) >4: V4; 8,5)0,0,0,0,0, 8,5)1)0,0,0,0, 8,5)2,0,0,0,0, 8,5)3)0)0,0,0, 8,5)4)0,0,0,0, 8,5)5)0)0,0,0, 8,5)6,0,0,0,0, 8)5)7)0,0,0,0, 8,5)8,0,0,0,0, 8)5)9)0,0,0,0, w4,8 >4) >4)8 >4)8 v4,8; w4) >4) >4)' >4)' \4)' 6,0,0,0,0,0, ,6,1,0,0,0,0, ,6,2,0,0,0,0, ,6,3,0,0,0,0, ,6,4,0,0,0,0, 5,6,5,0,0,0,0, 3,6,6,0,0,0,0, 5,6,7,0,0,0,0, 5,6,8,0,0,0,0, 5,6,9,0,0,0,0, w w 4,i 4,i i4,^ >4,^ >4, >4> >I'4) >4) \'4j v4, >4, \4) 1,7,0,0,0,0,0, 1,7,1,0,0,0,0, 1,7,2,0,0,0,0, 3,7)3)0,0,0,0, 5)7)4)0,0,0,0, 5,7)5)0)0,0,0, 3,7,6,0,0,0,0, 3,7)7,0,0,0,0, 3,7,8,0,0,0,0, 3,7,9,0,0,0,0, 3,8,0,0,0,0,0, 3,8,1,0,0,0,0, 3,8,2,0,0,0,0, 3,8,3,0,0,0,0, 3,8,4,0,0,0,0, 3,8,5,0,0,0,0, 3,8,6,0,0,0,0, 3,8,7,0,0,0,0, 3,8,8,0,0,0,0, 5,8,9,0,0,0,0, 99 4700 01 02 46983886,1 J4,8,9,o,o,o,o,o, I > 4)8,9, 1)0,0,0,0, K 4,8,9)2,0,0,0,0, n 4,8,9)3)0,0,0,0, >I'4)8,9,4,o,o,o,o, 03 04 05 06 07 >4)' >4)' \'4y I >4,' 5)9)5)0)0,0,0, 5,9,6,0,0,0,0, 5,9)7)0)0,0,0, 5,9,8,0,0,0,0, 5,9)9)0)0,0,0, Multiples of DifiFerences. 158S 3170 47SS 6340 7925 9510 11095 12680 14265 1586 3172 4758 6344 7930 9516 11102 12688 14274 1^88 1589 3176 .3178 4764 4767 (>3S2 6356 7940 7945 9528 9534 11116 11123 12704 12712 14292 14301 1591 1592 3182 3184 4773 4776 6364 6368 7955 7960 9546 9552 11137 11144 12728 12736 14319 14328 1594 3188 4782 6376 7970 9564 11158 12752 14346 1595 3190 4785 6380 7975 9570 H165 12760 14355 1597 1598 3194 3196 4791 4794 6388 6392 7985 7990 9582 9588 III79 rii86 12776 12784 14373 14382 1587 3174 4761 6348 7935 9522 11109 12696 14283 1590 3180 4770 6360 7950 9540 II 130 12720 14310 1593 3186 4779 6372 7965 9558 U151 12744 14337 1596 3192 4788 6384 7980 9576 IX 1 72 [12768 1599 3198 4797 6396 7995 9594 II 193 12792 14391 I 1600 2 3200 3 4800 4 6400 S 8000 6 9600 7 1 1200 8 12800 9 14400 I60I 3202 4803 6404 8005 9606 II 207 12808 14409 Dual Logarithms of powers of 2 and 10. 4" 2 = 69314718, J,, 10 = 230258509, 1, lo"^ = 921034037, ^. lo^ = 1611809565, |: 4 = 13S629437, V, io2 = 460517019, 1, lo^ = 1151292546, I, 10^ = 1842068074, ■l,S = 207944154, j, 10^ = 690775528, I, io<5 = 1381551056, I, lo' = 2072326584, II 50] Nat. No. r6012 to r6171 D. Log. 4707.... to 4806.... D. No. >^4,9,0,0, to >I4,9,9,9, Natural Dual Dual Numbers. Logarithms. Numbers. i'6oi2646i 47079369, \l'4>9)0,o,o,o,o,o, 42474 08 v4,9)0, 1,0,0,0,0, 58488 09 ,,4,9,0,2,0,0,0,0, 74504 10 w4,9>o,3,o,o,o,o. 90521 II v4,9jO,4jO,o,o,o, i'6o2o654o 12 w459>o,5)0,o,o,o. 22561 13 ,,4,9,0,6,0,0,0,0, 38583 14 ^ '4,9.0,7,0,0,0,0, 54607 15 ,,4,9,0,8,0,0,0,0, 70632 16 ,,4,9,0,9,0,0,0,0, 86587 47i793i9> V, 4,9, 1,0,0,0,0,0, i*6o3026i6 18 ,,4,9,1,1,0,0,0,0, 18646 19 ,,4,9,1,2,0,0,0,0, 34678 20 > 4,9, 1,3,0,0,0,0, 50711 21 ,,4,9,1,4,0,0,0,0, 66746 22 ^ 4,9,1,5,0,0,0,0, 82783 23 ,,4,9,1,6,0,0,0,0, 98821 24 > 4,9, 1,7,0,0,0,0, £•60414861 25 4,4,9,1,8,0,0,0,0, 30902 26 ,,4,9,1,9,0,0,0,0, 46874 47279269, ,,4,9,2,0,0,0,0,0, 62919 28 ,,4,9,2,1,0,0,0,0, 78965 29 ,,4,9,2,2,0,0,0,0, 95013 30 4^4,9,2,3,0,0,0,0, I •605 1 1063 31 '4,9,2,4,0,0,0,0, 27114 32 > 4,9,2,5,0,0,0,0, 43167 33 ,,4,9,2,6,0,0,0,0, 59221 34 v4,9,2,7,o,o,o,o. 75277 35 ,,4,9,2,8,0,0,0,0, 91335 36 ,,4,9,2,9,0,0,0,0, 1*60607321 473792i9> 4,4,9,3,0,0,0,0,0, 23382 38 ,{,4,9,3, 1,0,0,0,0, 1 39444 39 4^4,9,3,2,0,0,0,0, 55508 40 4/4,9,3,3,0,0,0,0, 71574 41 4'4,9,3,4,o,o,o,o, 87641 42 4^4,9,3,5,0,0,0,0, 1*60703710 43 k;9j3j6,o,o,o,o, 19780 44 >4, 9,3,7,0,0,0,0, 35852 45 > 4,9,3,8,0,0,0,0, 51926 46 v4,9,3, 9,0,0,0,0, 67928 47479169, V 4,9,4,0,0,0,0,0, 84005 48 ,,4,9,4,1,0,0,0,0, 1*60800083 49 4,4,9,4,2,0,0,0,0, 16163 50 4/4,9,4,3,0,0,0,0, 32245 51 4/4,9,4,4,0,0,0,0, 48328 52 4/4,9,4,5,0,0,0,0, 64413 53 4.4,9,4,6,0,0,0,0, 80499 54 v/4,9,4,7, 0,0,0,0, 96587 55 4,4,9,4,8,0,0,0,0, 1*60912677 56 4'4,9,4,9>o,o,o,o, Natural Dual Dual Numbers. Logarithms. Numbers. 1*60928696 475791^9, > 4,9,5,0,0,0,0,0, 44789 58 > 4,9,5, 1,0,0,0,0, 60883 59 ,,4,9,5,2,0,0,0,0, 76979 60 > 4,9,5,3,0,0,0,0, 93077 61 ' 4,9,5,4,0,0,0,0, 1*61009176 62 4/4,9,5,5,0,0,0,0, 25277 63 > 4,9,5,6,0,0,0,0, 41380 64 ' 4,9,5,7,0,0,0,0, 57484 65 > 4,9,5,8,0,0,0,0, 73590 66 > 4,9,5,9,0,0,0,0, 89625 47679069, 4,4,9,6,0,0,0,0,0, 1*61105734 68 4,4,9,6,1,0,0,0,0, 21845 69 ,,4,9,6,2,0,0,0,0, 37957 70 ,,4,9,6,3,0,0,0,0, 54071 71 ,,4,9,6,4,0,0,0,0, 70186 72 w4,9,6,5,o,o,o,o. 86303 73 ,,4,9,6,6,0,0,0,0, 1*61202422 74 > 4,9,6,7,0,0,0,0, 18542 75 ,,4,9,6,8,0,0,0,0, v4,9,6,9,o,o,o,o, 34664 76 507^5 47779019, ,,4,9,7,0,0,0,0,0, 66840 78 >/4,9,7, 1,0,0,0,0, 82967 79 >/4,9,7, 2, 0,0,0,0, 99095 80 N 4,9,7,3,0,0,0,0, 1*61315225 81 > 4,9,7,4,0,0,0,0, 31357 82 4'4,9,7, 5, 0,0,0,0, 47490 83 4/4,9,7,6,0,0,0,0, 63625 84 > 4,9,7,7,0,0,0,0, 79761 85 ,,4,9,7,8,0,0,0,0, 95899 86 4/4,9,7,9,0,0,0,0, 1*61411966 47878969, ,,4,9,8,0,0,0,0,0, 28107 88 > 4,9,8, 1,0,0,0,0, 44250 89 4,4,9,8,2,0,0,0,0, 60394 90 ^ 4,9,8,3,0,0,0,0, 76540 91 > 4,9,8,4,0,0,0,0, 92688 92 4/4,9,8,5,0.0,0,0, 1*61508837 93 ,,4,9,8,6,0,0,0,0, 24988 94 4/4,9,8,7,0,0,0,0, 41 140 95 ,,4,9,8,8,0,0,0,0, 4,4,9,8,9,0,0,0,0, 57294 96 73378 47978919, 4,4,9,9,0,0,0,0,0, 89535 98 4/4,9,9,1,0,0,0,0, 1*61605694 99 4/4,9,9,2,0,0,0,0, 21855 4800 > '4,9,9,3,0,0,0,0, 38017 CI 4/4,9,9,4,0,0,0,0, 54181 02 4/4,9,9,5,0,0,0,0, 70346 03 4,4,9,9,6,0,0,0,0, 86513 04 4/4,9,9,7,0,0,0,0, 4,4,9,9,8,0,0,0,0, 1*61702682 05 18852 06 14,9,9,9,0,0,0,0, Multiples of Differences. I60I 1602 3202 3204 4803 4806 6404 6408 8005 8010 9606 9612 1 1207 II2I4 12808 I28I6 14409 I44I8 1604 1605 3208 3210 4812 481"; 6416 6420 8020 8025 9624 9630 II 228 "235 12832 12840 14436 1444s 1607 1608 3214 3216 4821 4824 6428 6432 8os>; 8040 9642 9648 1 1 249 11256 12856 12864 14463 14472 1610 1611 3220 3222 4830 4«33 6440 6444 8050 «055 9660 9666 1 1270 11277 12880 12888 14490 14499 1603 3206 4809 6412 8015 9618 II22I 12824 14427 1606 3212 4818 6424 8030 9636 1 1242 12848 I44S4 1609 3218 4827 6436 8045 9654 1 1263 12872 14481 1612 3224 4836 6448 8060 9672 II 284 12896 14508 I6I3 1614 1615 3226 .^28 3230 4839 4842 4845 6452 6456 6460 8065 8070 807 s 9678 9684 9690 II29I 1 1298 "305 12904 12912 12920 145 1 7 14526 14535 I6I6 3232 4848 6464 8080 9696 II3I2 8 112928 9 Ih544 1617 3234 4851 6468 8085 9702 11319 12936 I45S3 X, 2 = 69314718, I, 10 = 230258509, 4/, 4 = 138629437, I, io2 = 460517019, 4/, 8 = 207944154, 4,, 10^ = 690775528, Dual Logarithms of powers of 2 and 10. I, J. 921034037, 1151292546, 4,, 10'^ = 161 1809565, 4,, 10^ =- 1842068074, 4,, 10" = 1381551056, 4,, 10^ = 2072326584, Nat. No. 1-6105 to r6265 D. Log. 4765.... to 4864.... D. No. >I4,0,0,0, to H,0,9,9, [M Natural Dual Dual Numbers. Logarithms. Numbers. l'6lo5iooo 47655090, X, 5, 0,0,0,0,0,0,0, 67105 66 ,,5,0,0,1,0,0,0,0, 83211 67 ,,5,0,0,2,0,0,0,0, 99319 68 >'5»o,o,3,o,o,o,o. 1-61115429 69 ,,5,0,0,4,0,0,0,0, 31541 70 >'5>°>°»550»0)°)0; 47654 71 ,,5,0,0,6,0,0,0,0, 63769 72 ^'5^0)0,7, 0,0,0,0, 79885 73 ,,5,0,0,8,0,0,0,0, 96003 74 4,5,0,0,9,0,0,0,0, I'6l2I205l 47755040, ,,5,0,1,0,0,0,0,0, 28172 76 1 ,1,5,0,1,1,0,0,0,0, 4429s 77 ,,5,0,1,2,0,0,0,0, 60419 78 ^'5>Oji)3)050>050) 76545 79 ,,5,0,1,4,0,0,0,0, 92673 80 iSjOji^S'O'OjOjO* i"6i3o88o2 81 ,,5,0,1,6,0,0,0,0, 24933 82 >'5>Oji>7,o,o,o,o, 41065 83 ,,5,0,1,8,0,0,0,0, 57199 84 ,,5,0,1,9,0,0,0,0, 73263 47854990, ,,5,0,2,0,0,0,0,0, 89400 86 ,,5,0,2,1,0,0,0,0, 1-61405539 87 ,1,5,0,2,2,0,0,0,0, 21680 88 ,,5,0,2,3,0,0,0,0, 37822 89 ,,5,0,2,4,0,0,0,0, 53966 90 >'5'°)2,5, 0,0,0,0, 70111 91 ,,5,0,2,6,0,0,0,0, 86258 92 >'5)0>2,7,o,o,o,o. 1-61502407 93 ,,5,0,2,8,0,0,0,0, 18557 94 ,,5,0,2,9,0,0,0,0, 34636 47954940, >l5>0)3)050,o,o,o, 50789 96 ,,5,0,3,1,0,0,0,0, 66944 97 >'5>o»3>2,o,o,o,o, 83101 98 >'5>o>3;3>o,o,o,o, 99259 99 >'5>053)4,o,o,o,o. 1-61615419 4800 >'5>o>3>5)0)0»OjO) 31581 01 ,,5,0,3,6,0,0,0,0, 47744 02 <'5>o.3>7>o,o,o,o. 63909 03 ,,5,0,3,8,0,0,0,0, 80075 04 ,,5,0,3,9,0,0,0,0, 96171 48054890, >l'5>o>4,o,o,o,o,o, 1-61712341 06 ,,5,0,4,1,0,0,0,0, 28512 07 ,,5,0,4,2,0,0,0,0, 44685 08 "5,0,4,3,0,0,0,0, 60859 09 w5,o,4,4,o,o,o,o. 77035 10 v5,o,4,5>o>o>o.o> 93213 II >'5>o>4,6,o,o,o,o, 1-61809392 12 >'5»o.4,7,o,o,o,o. 25573 13 ,,5,0,4,8,0,0,0,0, 41756 14 vk5.o>4,9)0>o>o>o> Natural Dual Dual Numbers. Logarithms. Numbers. 1-61857867 48154840, ,,5,0,5,0,0,0,0,0, 74053 16 ,,5,0,5,1,0,0,0,0, 90240 17 ,,5,0,5,2,0,0,0,0, I-61906429 18 >'5)0>5;3)0,o,o,o, 22620 19 >'5>o,5,4,o,o,o,o. 38812 20 > '5^0,5,5,0,0,0,0, 55006 21 ,,5,0,5,6,0,0,0,0, 71201 22 >'5'0,5, 7, 0,0,0,0, 87398 23 \ '5)0,5,8,0,0,0,0, 1-62003597 24 >'5jO,S,9jO,o,o,o, 19725 48254790, ,,5,0,6,0,0,0,0,0, 35927 26 ,,5,0,6,1,0,0,0,0, 52131 27 ,,5,0,6,2,0,0,0,0, 68336 28 "5,0,6,3,0,0,0,0, 84543 29 4,5,0,6,4,0,0,0,0, I-62100751 30 X5, 0,6,5, 0,0,0,0, 16961 31 ,,5,0,6,6,0,0,0,0, 33173 32 ,,5,0,6,7,0,0,0,0, 49386 33 ,,5,0,6,8,0,0,0,0, 65601 34 ,,5,0,6,9,0,0,0,0, 81745 48354740, ,,5,0,7,0,0,0,0,0, 97963 36 ,,5,0,7,1,0,0,0,0, 1-62214x83 37 ,,5,0,7,2,0,0,0,0, 30404 38 w5)0,7,3>o,o,o,o. 46627 39 4,5,0,7,4,0,0,0,0, 62852 40 v5,o,7,5>o,o,o,o. 79078 41 ,,5,0,7,6,0,0,0,0, 95306 42 ,,5,0,7,7,0,0,0,0, I-62311536 43 ,,5,0,7,8,0,0,0,0, 27767 44 ,,5,0,7,9,0,0,0,0, 43927 48454690, ,,5,0,8,0,0,0,0,0, 6016 1 46 ,,5,0,8,1,0,0,0,0, 76397 47 ,,5,0,8,2,0,0,0,0, 92635 48 ,,5,0,8,3,0,0,0,0, 1-62408874 49 ,,5,0,8,4,0,0,0,0, 25115 50 4,5,0,8,5,0,0,0,0, 41358 51 ,,5,0,8,6,0,0,0,0, 57602 52 ,,5,0,8,7,0,0,0,0, 73848 53 ,,5,0,8,8,0,0,0,0, 90095 54 ,,5,0,8,9,0,0,0,0, 1-62506271 48554640, ,,5,0,9,0,0,0,0,0, 22522 56 ,,5,0,9,1,0,0,0,0, 38774 57 ,,5,0,9,2,0,0,0,0, 55028 58 >'5»o,9,3,o,o,o,o. 71284 59 4,5,0,9,4,0,0,0,0, 87541 60 N'5>o,9)5»o,o,o,o, 1-62603800 61 ,,5,0,9,6,0,0,0,0, 20060 62 ^5)0,9,7)0,0,0,0, 36322 63 ,,5,0,9,8,0,0,0,0, 52586 64 4,5,0,9,9,0,0,0,0, Multiples of Differences. I6IO 16II 3220 3222 4830 4«.1S 6440 6444 8050 80SS 9660 9666 1 1270 U277 12880 12888 14490 14499 1613 1614 3226 3228 4839 4842 6452 6456 806;; 8070 9678 9684 11291 11298 12904 12912 HSi7 14526 1616 1617 3232 3234 4848 48=; I 6464 6468 8080 8085 9696 9702 11312 11319 12928 12936 14544 14553 1619 1620 3238 3240 4«';7 4860 6476 6480 8095 8100 9714 9720 "333 1 1340 12952 12960 14571 i45«o 1622 1623 3244 3246 4866 4869 6488 6492 8110 8115 9732 973« "354 11361 12976 12984 i459« 14607 i I6I2 3224 4836 6448 8060 9672 1 1284 12896 14508 I6I5 3230 4845 6460 8075 9690 11305 12920 14535 I6I8 3236 4854 6472 8090 9708 1 1326 12944 14562 I62I 3242 4863 6484 8105 9726 "347 12968 14589 1624 3248 4872 6496 8120 9744 II 368 12992 1461,6 1625 3250 4875 6500 8125 9750 "375 13000 14625 1626 3252 4878 6504 8130 9756 1 1382 13008 14634 Dual Logarithms of powers of 2 and 10. , 2 = 69314718, 4,, 10 = 230258509, 4,, lo* = 921034037 , 4 = 138629437, 4^) lo^ = 460517019, 4') 'fo^ = 1151292546, J,, lo*' = 1842068074, , 8 = 207944154, 4,, io3 = 690775528, 4,, lo^ = 1381551056, 4,, lo^ = 2072326584, 4,, 10'^ = 1611809565, 52] Nat. No. 1-6266 to 1-6427 D. Log. 4865.... to 4964.... D. No. >I.5,1,0,0, to i5,l,9,9, Natural Dual Dual Numbers. Logarithms. Numbers. 1-62661510 48650123, v^5, 1,0,0,0,0,0,0, 17776 66 >r5, 1,0,1,0,0,0,0, 94044 67 ,,5,1,0,2,0,0,0,0, 1-62710313 68 w5, 1,0,3,0,0,0,0, 26584 69 ^^,5, 1,0,4,0,0,0,0, 42857 70 4,5,1,0,5,0,0,0,0, 59131 71 V, 5, 1, 0,6,0,0,0,0, 75407 72 w5, 1,0,7,0,0,0,0, 91685 73 ^, 5, 1, 0,8,0,0,0,0, 1*62807964 74 ,,5,1,0,9,0,0,0,0, 24172 48750073. ,,5,1,1,0,0,0,0,0, 40454 76 ,,5,1,1,1,0,0,0,0, 56738 77 ,,5,1,1,2,0,0,0,0, 73024 78 ,,5,1,1,3,0,0,0,0, 893 1 1 79 ,,5,1,1,4,0,0,0,0, 1-62905600 80 ,,5,1,1,5,0,0,0,0, 21891 81 ,,5,1,1,6,0,0,0,0, 38183 82 > '5,1,1,7,0,0,0,0, 54477 83 ,,5,1,1,8,0,0,0,0, 70772 84 ,,5,1,1,9,0,0,0,0, 86996 48850023, ,,5,1,2,0,0,0,0,0, 1-63003295 86 ,,5,1,2,1,0,0,0,0, 19595 87 ,,5,1,2,2,0,0,0,0, 35897 88 ,,5,1,2,3,0,0,0,0, 52201 89 4,5,1,2,4,0,0,0,0, 68506 90 X5,i, 2,5,0,0,0,0, 84813 91 ,,5,1,2,6,0,0,0,0, 1-63101121 92 ,,5,1,2,7,0,0,0,0, 1 743 1 93 ,,5,1,2,8,0,0,0,0, 33743 94 ,,5,1,2,9,0,0,0,0, 49983 48949973. >'5,i,3,o,o,o,o,o. 66298 95 >'5,i,3,i,o,o,o,o. 82615 96 ,,5,1,3,2,0,0,0,0, 98933 97 w5, 1,3,3,0,0,0,0, ^'5,1,3,4,0,0,0,0, 1-63215253 98 31575 4899 >'5, ^,3,5,0,0,0,0, 47898 4900 >'5,i>3,6,o,o,o,o, 64223 01 N '5, 1,3,7,0,0,0,0, 80549 02 ,,5,1,3,8,0,0,0,0, 96877 03 w5,i,3,9,o,o,o,o. ^•633^3^33 49049923, ,,5,1,4,0,0,0,0,0, 29464 05 > '5, 1.4,1,0,0,0,0, 45797 06 ,,5,1,4,2,0,0,0,0, 62132 07 > '5,1,4,3,0,0,0,0, 78468 08 ,,5,1,4,4,0,0,0,0, 94806 09 >I'5, 1,4,5,0,0,0,0, I -6341 1 145 10 4,5,1,4,6,0,0,0,0, 27486 II ^ '5,1,4,7,0,0,0,0, 43829 12 ,,5,1,4,8,0,0,0,0, 60173 13 > '5, 1.4,9,0,0,0,0, Natural Dual Dual Numbers. Logarithms. 49149873, Numbers. 1-63476446 \ '5. 1,5,0,0,0,0,0, 92794 15 ,,5,1,5,1,0,0,0,0, 1-63509143 16 > '5.1,5,2,0,0,0,0, 25494 17 >'5. 1. 5. 3.0,0,0,0, 41847 18 4'5, 1,5,4,0,0,0,0, 58201 19 v'5,T,5,5.o,o,o,o, 74557 20 4'5, 1.5.6,0,0,0,0, 90914 21 w5,i, 5,7.0,0,0,0, 1-63607273 22 y, 5, 1,5,8,0,0,0,0, 23634 23 4^5.1.5.9,0,0,0,0, 39922 49249823, ,,5,1,6,0,0,0,0,0, 56286 25 ,,5,1,6,1,0,0,0,0, 72652 26 ,,5,1,6,2,0,0,0,0, 89019 27 >'5. 1, 6,3. 0,0,0,0, 1-63705388 28 ,,5,1,6,4,0,0,0,0, 21759 29 4'5, 1,6,5,0,0,0,0, 38131 30 X5, 1,6,6,0,0,0,0, 54505 31 ,,5,1,6,7,0,0,0,0, 70880 32 \ '5. 1,6,8,0,0,0,0, 87257 33 > '5. ij6, 9,0,0,0,0, 1-63803562 45349773, > '5. 1,7,0,0,0,0,0, 19942 35 >'5, 1. 7, 1, 0,0,0,0, 36324 36 ,,5,1,7,2,0,0,0,0, 52708 37 ^ '5. 1.7,3,0,0,0,0, 69093 38 v5, 1,7,4,0,0,0,0, 85480 39 > '5.1.7,5.0,0,0,0, 1*63901869 40 ,,5,1,7,6,0,0,0,0, 18259 41 > '5.1.7.7.0,0,0,0, 34651 43 ,,5,1,7,8,0,0,0,0, 51044 43 > '5.1.7.9.0,0,0,0, 67365 49449723, ,,5,1,8,0,0,0,0,0, 83762 45 ,,5,1,8,1,0,0,0,0, I -640001 6 1 46 ,,5,1,8,2,0,0,0,0, 16561 47 > '5. 1.8,3.0,0,0,0, 32963 48 \ '5. 1.8,4,0,0,0,0, 49366 49 > '5,1.8,5,0,0,0,0, 65771 50 >'5. 1. 8.6,0,0,0,0, 82178 51 ,,5,1,8,7,0,0,0,0, 98586 52 > '5. 1.8,8,0,0,0,0, I -641 14996 53 v5,i, 8,9,0,0,0,0, 31332 49549673, v5, 1,9,0,0,0,0,0, 47745 55 w5, 1,9,1,0,0,0,0, 64160 56 ,,5,1,9,2,0,0,0,0, 80576 57 > '5. 1.9.3,0,0,0,0, 96994 58 > '5.1.9.4.0,0,0,0, 1-64213414 59 v5, 1,9.5.0,0,0,0, 29835 60 ,'5,1.9.6,0,0,0,0, 46258 61 >'5.i. 9.7.0,0,0,0, 62683 62 > '5, 1.9.8,0,0,0,0, 79110 63 > '5. 1.9,9.0,0,0,0, Multiples of Differences. 1626 1627 3252 3254 4878 4881 6504 6508 8130 813s 9756 9762 II 382 11389 13008 I30I6 14634 14643 1629 1630 32'?8 3260 4887 4890 6516 6520 8145 8150 9774 9780 1 1403 11410 13032 13040 1 466 1 14670 1632 1633 3264 3266 4896 4899 6528 6532 8160 8165 9792 9798 1 1424 11431 13056 13064 14688 14697 1635 1636 3270 4905 6540 8175 3272 4908 6544 8180 9810 9816! "445 13080 11452 ! 13088 1 14715 14724 , 1638 3276 4914 6552 8190 1 1466 13 104 14742 I64I 3282 4923 6564 8205 9846 11487 I3I28 14769 1639 3278 4917 6556 8195 9834 "473 13112 14751 1642 3284 4926 6568 8210 9852 "494 13136 14778 1628 3256 4884 6512 8140 9768 11396 13024 14652 1631 3262 4893 6524 8155 9786 11417 13048 14679 1634 3268 4902 6536 8170 9804 1 1438 13072 14706 1637 3274 49" 6548 8185 9822 "459 13096 14733 1640 3280 4920 6560 8200 9840 11480 13120 14760 Dual Logarithms of powers of 2 and 10. 4,, 2 = 69314718, I, 10 = 230258509, L 10* = 921034037, 4,, 10'^ = 161 44=138629437, ,,,10^ = 460517019, 4,, io5 = 1151292546, 110^=184 ^,S- 207944154, 4,, io3 = 690775528, 4^. 106 = 1381551056, 4,, io9 = 207 1611809565, 2068074, 2326584, Nat. No. 1-6428 to 1-6592 D. Log. 4964.... to 5063.... D. No. >^5,2,0,0, to |5,2,9,9, [53 Natural Dual Dual Kumbers. . Logarithms. Numbers. 1-64288125 49645156, ,,5,2,0,0,0,0,0,0, i"643045S4 65 ,,5,2,0,1,0,0,0,0, 20984 66 ,,5,2,0,2,0,0,0,0, 37416 67 >'5j2,o,3,0,0,o,o. 53850 68 ,,5,2,0,4,0,0,0,0, 70285 69 >'5;2,o,5,o,o,o,o. 86722 70 ,,5,2,0,6,0,0,0,0, £•64403161 71 ,,5,2,0,7,0,0,0,0, 19601 72 ,,5,2,0,8,0,0,0,0, 36043 73 ,,5,2,0,9,0,0,0,0, 52413 49745106, ,,5,2,1,0,0,0,0,0, 68858 75 ,,5,2,1,1,0,0,0,0, 85305 76 ,,5,2,1,2,0,0,0,0, 1-64501754 77 >'5>2,i,3,o,o,o,o. 18204 78 >'5>2,i,4,o,o,o,o. 34656 79 v5,2,i, 5,0,0,0,0, 51109 80 ,,5,2,1,6,0,0,0,0, 67564 81 ,,5,2,1,7,0,0,0,0, 84021 82 -,5,2,1,8,0,0,0,0, 1-64600479 83 ,,5,2,1,9,0,0,0,0, 16865 49845056, ,,5,2,2,0,0,0,0,0, 33327 85 ,,5,2,2,1,0,0,0,0, 49790 86 ,,5,2,2,2,0,0,0,0, 66255 87 >'5j2,2,3,0,0,0,0. 82722 88 > '5)2,2,4,0,0,0,0, 99190 89 ,,5,2,2,5,0,0,0,0, 1-64715660 90 ,,5,2,2,6,0,0,0,0, 32132 91 > '5)2,2,7,0,0,0,0, 48605 92 ,,5,2,2,8,0,0,0,0, 65080 93 ,,5,2,2,9,0,0,0,0, 81482 49945006, w5,2,3,o,o,o,o,o, 97960 95 ,,5,2,3,1,0,0,0,0, I -648 1 4440 96 > '5)2,3)2,0,0,0,0, 30921 97 > '5)2,3)3)0)0,0,0, 47404 98 \!'5)2,3)4)0,o,o,o. 63889 99 >!'5)2, 3)5)0,0,0,0, 80375 5000 ,,5,2,3,6,0,0,0,0, 96863 01 > '5)2,3)7)0,0,0,0, i"649i3353 02 ,,5,2,3,8,0,0,0,0, 29844 03 > '5)2,3)9)0,0,0,0, 46263 50044956, ,,5,2,4,0,0,0,0,0, 62758 05 >'5)2,4)I)O,0,O,O, 79254 06 ,,5,2,4,2,0,0,0,0, 95752 07 > '5)2,4)3)0,0,0,0, 1-65012252 08 ^^5) 2,4,4,0,0,0,0, 28753 09 >I'5)2,4,5)0,o,o,o, 45256 10 ^I'5) 2,4)6,0,0,0,0, 61761 II 15)2,4,7,0,0,0,0, 78267 12 >'5)2, 4,8,0,0,0,0, 94775 13 n1'5.2,4,9)0,o,o,o. Natural Numbers. I-65111210 27721 44234 60748 77264 93782 I-65210301 26822 43345 59869 76320 92848 1*65309377 25908 42441 58975 7551^ 92049 1-65408588 25129 41596 58140 74686 91233 1-65507782 24333 40885 57439 73995 90552 1-65607037 23598 40160 56724 73290 89857 1-65706426 22997 39569 56143 72644 89221 1-65805800 22381 38963 55547 72133 88720 i"659o5309 21900 Dual Logarithms. 50144906, 15 16 17 18 19 20 21 22 23 50244856, 25 26 27 28 29 30 31 32 33 50344806, 35 36 37 38 39 40 41 42 43 50444756, 45 46 47 48 49 50 51 52 53 50544706, 55 56 57 58 59 60 61 62 (>3 Dual Numbers. 5,0; 5)1 5)2 5)3 5)4: 5)5 5,6 5)7 5,8 5,9 6,0, 6,1 6,2 6,3 6,4 6,5 6,6 6,7 6,8 6,9 7,0 7,1 7)2 7)3 7,4 7,5 7,6 7)7 7,8 7,9 8,0 8,1 8,2 8,3 8,4 8,5 8,6 8,7 8,8 8,9 9,0 9)1 9)2 9,3 9,4; 9,5 9,6 9,7 9,8 9,9 Multiples of Differences. 1642 3284 4926 6568 8210 9852 1149-^ 14778 1643 3286 4929 6572 8215 9858 11501 13144 14787 1645 1646 3290 3292 4935 4938 6580 6584 822s 8230 9870 9876 11515 11522 13160 13168 14805 14814 1648 1649 3296 3298 4944 4947 6S92 6596 8240 8245 9888 9894 1 1 536 1 1543 13184 13192 14832 14841 i 165 1 1652 3302 3304 4953 4956 6604 6608 8255 8260 9906 9912 "557 1 1564 13208 13216 14859 14868 1654 3308 4962 6616 1655 3310 4965 6620 8270 8275 9924 11578 9930 "585 13232 14886 13240 14895 1657 1658 3314 3316 4971 4974 6628 6632 8285 8290 9942 9948 "599 1 1606 13256 13264 14913 14922 1044 3288 4932 6576 8220 9864 1 1508 I3I52 14796 1647 3294 4941 6588 823s 9882 1 1529 13176 14823 1650 3300 4950 6600 8250 9900 "550 13200 14850 1653 3306 4959 6612 826S 9918 11571 13224 14877 1656 3312 4968 6624 8280 9936 1 1592 13248 14904 1659 3318 4977 6636 8295 9954 11613 13272 i493» Dual Logarithms of powers of 2 and 10. |, 2 = 69314718, ^, 10 = 230258509, ^, lo^ = 921034037, I, io7 = 1611809565, >!', 4 = 138629437, 4, lo^ = 460517019, X, 10^ = 1151292546, ,„ 10^ — 1842068074, i, 8 = 207944154, I, io3 = 690775528, I, lo'^ = 1381551056, 4,, 10'' = 2072326584, 54] Nat. No. r6593 to 1-6758 D. Log. 5064.... to 5162.... D. No. 4.5,3,0,0, to |5,3,9,9, Natural Numbers. I •65931006 47599 64194 80790 97388 i'66oi3988 30589 47192 63797 80403 96937 1-66113547 30158 46771 63386 80002 96620 i"662i3239 29860 46483 63034 79660 96288 I"663i29i8 29549 46182 62817 79453 96091 i'664i273i 29297 45940 62585 79231 95878 i"665i2528 29179 45832 62487 79143 95726 1*66612386 29047 45710 62375 79041 95709 I •66712379 29050 45723 Dual Logarithms. Dual Numbers. 50640189, 15,3,0,0,0,0,0,0, 65 66 67 68 69 70 71 72 73 50740139, 75 76 77 78 79 80 8i 82 83 50840089, 85 86 87 89 90 91 92 93 50940039, 95 96 97 98 99 5100 01 02 03 51039989, 04 05 06 07 08 09 10 II 12 4'5'3)0, 1,0,0,0,0, l5»3>o,2,o,o,o,o, > '5)350,3,0,0,0,0, >1'5»3.o,4jO,o,o,o, l5)3)0,5'0,o,o,o, l5'3)0,6,o,o,o,o, 15)3)0,7,0,0,0,0, \|'5)3)0,8,o,o,o,o, 4^5)3)0,9)0,0,0,0, \I'5)3) 1)0,0,0,0,0, |5)3) I) 1)0,0,0,0, >l'5)3) 1)2,0,0,0,0, 15)3)1)3)0,0,0,0, i5)3) 1)4)0,0,0,0, 15)3)1)5)0,0,0,0, 5)3)1)6,0,0,0,0, 5,3,1,7,0,0,0,0, 5)3)1)8,0,0,0,0, 5)3)1)9)0,0,0,0, >I'5)3) 2,0,0,0,0,0, >I'5)3) 2, 1,0,0,0,0, >'5)3)2, 2, 0,0,0,0, > '5)3)2,3)0,0,0,0, >I'5)3)2,4)0,o,o,o, >1'5)3)2, 5)0,0,0,0, >l'5)3) 2,6,0,0,0,0, >'5)3)2,7)0,o,o,o, ^'5)3)2,8,0,0,0,0, 4'5)3)2,9)0,o,o,o, 4'5)3)3)0,o,o,o,o, >'5)3)3)i)0,o,o,o, v5)3)3)2,o,o,o,o, >I'5)3)3)3)0,o,o,o, ^^5)3)3)4,o,o,o,o, >I'5)3)3)5)0,o,o,o, >'5)3)3)6,o,o,o,o, -'5)3)3)7)0,0,0,0, ^5)3)3)8,0,0,0,0, >l'5)3)3)9)0,o,o,o, i 5)3)4)0,0,0,0,0, 5)3)4)1,0,0,0,0, >}'5)3)4) 2,0,0,0,0, >l'5)3)4)3)0,o,o,o, >!'5)3?4)4)0,o,o,o, 3)4)5)0,0,0,0, 3,4,6,0,0,0,0, |5)3)4,7)0,o,o,o, >l'5)3)4,8,o,o,o,o, >l'5)3)4)9)0,o,o,o, Natural Numbers. 1*66762322 78998 95676 i"668i2356 29037 45720 62405 79091 95779 1*66912469 29084 45777 62472 79168 95866 i*67oi2566 29267 45970 62675 79381 96013 1*67112723 29434 46147 62862 79578 96296 1*67213016 29737 46460 63109 79835 96563 1*67313293 30024 46757 63492 80228 96966 1*67413706 30372 47115 63860 80606 97354 1*67514104 30855 47608 64363 81119 Dual Logarithms. 5II39939) 14 15 16 17 18 19 20 21 22 51239889, 24 25 26 27 28 29 30 31 32 51339839) 34 35 36 31 38 39 40 41 42 51439789 44 45 46 47 48 49 50 51 52 5^539739) 54 55 56 57 58 59 60 61 62 Dual Numbers. >I'5)3)5)0,o,o,o,o, \|'5)3)5) 1)0,0,0,0, >1'S)3)5)2, 0,0,0,0, ^5)3)5)3)0,0,0,0, 15)3)5)4,0,0,0,0, J5)3)5)5)0,o,o,o, i5)3)5)6)0,o,o,o, >l'5)3)5)7)0,o,o,o, >l'5)3)5)8,o,o,o,o, i5)3»5)9,o,o,o,o, \l'5)3)6,o,o,o,o,o, i5)3)6, 1,0,0,0,0, ,1,5,3, 6,2,0,0,0,0, i5)3)6,3)0,o,o,o, 4'5)3>6,4,o,o,o,o, 4^5)3)6)5)0,0,0,0, 4'5)3)6,6,o,o,o,o, 15)3)6,7)0,0,0,0, 4'5)3)6,8,o,o,o,o, 4'5)3)6,9,o,o,o,o, \I'5)3)7)0,o,o,o,o, >1'5)3)7) 1)0,0,0,0, >'5)3)7)2,o,o,o,o,| 4'5)3)7)370,o,o,o, >I'5)3)7)4)0,o,o,o, >j'5)3)7)5)0,o,o,o, > '5)3)7)6,0,0,0,0, >'5)3)7)7)0,o,o,o, > '5)3)7)8,0,0,0,0, \l'5,3)7,9,o,o,o,o, i5)3)8,o,o,o,o,o, > '5)3)8) 1,0,0,0,0, > '5,3)8,2,0,0,0,0, v5, 3)8,3, 0,0,0,0, 4'5,3, 8,4,0,0,0,0, J'5,3, 8,5, 0,0,0,0, w5, 3,8,6,0,0,0,0, > '5,3)8,7,0,0,0,0, >'5,3, 8,8,0,0,0,0, 4'5,3, 8,9,0,0,0,0, 15,3,9,0,0,0,0,0, > .5)3)9) 1,0,0,0,0, >'5)3)9)2,o,o,o,o, v5)3)9)3)0,o,o,o, 4.5,3,9)4)0,0,0,0, 15)3)9)5)0,0,0,0, w5, 3, 9,6,0,0,0,0, w5,3, 9)7)0,0,0,0, > '5)3,9,8)0,0,0,0, 4'5)3)9)9)0,o,o,o, Multiples 0/ Differences. 1659 1660 .33 1 « 3320 4977 4980 6636 6640 8295 8300 9954 9960 11613 11620 13272 13280 1493 1 14940 1662 3324 4986 6648 8310 9972 11634 13296 14958 1663 3326 4989 6652 8315 9978 1I64I 13304 14967 1665 1666 3330 3332 4995 4998 6660 6664 8325 8330 9990 9996 ii6s«; 11662 13320 1.3328 14985 14994 1668 1669 3336 3338 5004 5007 6672 6676 8340 834s 10008 10014 11676 11683 13344 13352 15012 15021 1671 1672 3342 3344 5013 5016 6684 6688 8355 8360 10026 10032 II 697 11704 13368 13376 15039 15048 1661 3322 4983 6644 8305 9966 1 1627 13288 14949 1664 3328 4992 6656 8320 9984 11648 I33IZ 14976 1667 3334 5001 6668 8335 10002 1 1669 13336 15003 1670 3340 5010 6680 8350 10020 11690 13360 15030 1673 3346 5019 6692 8365 10038 11711 13384 15057 1674 3348 5022 6696 8370 10044 11718 13392 15066 1675 3350 5025 6700 8375 10050 11725 13400 1507s J, 2 = 69314718, , 4 = 138629437, , 8 = 207944154, Dual Logarithms of powers of 2 and 10. ., 10 = 230258509, X, 10* = 921034037, 460517019, 690775528, L io7 = 1611809565, lo^ = 1151292546, \, 10^ = 1842068074, 10'' = 1381551056, }, lo^ = 2072326584, Nat. No. r6759 to r6925 D. Log. 5163.... to 5262.... D. No. 15,4,0,0, to >^5,4,9,9, [55 Natural Duals. Dual Numbers. Logarithms. Numbers. 1-67590316 51635222, i5'4,o,o,o,o,o,o. 1-67607075 64 >'5>4,o, 1,0,0,0,0, 23836 65 ,,5,4,0,2,0,0,0,0, 40598 66 hA,o,3iO,o,o,o, 57362 67 >^5»4,o,4,o,o,o,o. 74128 68 >I'5)4,o,5,o,o,o,o, 90895 69 >1^5.4,o,6,o,o,o,o. 1-67707664 70 > '5^4,0,7,0,0,0,0, 24435 71 >'5'4,o,8,o,o,o,o, 41207 72 l5>4,o,9,o,o,o,o, 57906 51735172, "S»4, 1,0,0,0,0,0, 74682 74 ,.5,4,1,1,0,0,0,0, 91459 75 ^'5»4, 1,2,0,0,0,0, 1-67808238 76 >'5>4,i,3>o,o,o,o. 25019 77 >'5>4, 1,4,0,0,0,0, 41802 78 > '5,4, 1,5,0,0,0,0, 58586 79 \ '5,4, 1,6,0,0,0,0, 75372 80 > '5,4, 1,7,0,0,0,0, 92160 81 ,,5,4,1,8,0,0,0,0, 1-67908949 82 > '5,4, 1,9,0,0,0,0, 25664 51835122, > '5,4,2,0,0,0,0,0, 42457 84 ,,5,4,2,1,0,0,0,0, 59251 85 ,,5,4,2,2,0,0,0,0, 76047 86 v5,4,2,3,o,o,o,o. 92845 87 ,,5,4,2,4,0,0,0,0, 1-68009644 88 > '5,4,2,5,0,0,0,0, 26445 89 w5, 4,2, 6,0,0,0,0, 43248 90 N '5,4,2,7,0,0,0,0, 60052 91 >'5, 4,2, 8,0,0,0,0, 76858 92 > '5,4,2,9,0,0,0,0, 93590 51935072, > '5,4,3,0,0,0,0,0, 1-68110399 94 w5, 4,3, 1,0,0,0,0, 27210 95 "5,4,3,2,0,0,0,0, 44023 96 > '5,4,3,3,0,0,0,0, 60837 97 > '5,4,3,4,0,0,0,0, 77653 98 > '5,4,3,5,0,0,0,0, 94471 99 > '5,4,3,6,0,0,0,0, I-68211290 5200 > '5,4,3,7,0,0,0,0, 28111 01 "5,4,3,8,0,0,0,0, 44933 02 "5,4,3,9,0,0,0,0, 61684 52035022, ,,5,4,4,0,0,0,0,0, 78510 04 > '5,4,4, 1,0,0,0,0, 95338 05 "5,4,4,2,0,0,0,0, 1-68312168 06 ^ '5,4,4,3,0,0,0,0, 28999 07 "5,4,4,4,0,0,0,0, 45832 08 > '5,4,4,5,0,0,0,0, 62667 09 > '5,4,4,6,0,0,0,0, 79503 10 > '5,4,4,7,0,0,0,0, 96341 II "5,4,4,8,0,0,0,0, X-684i3i8i 12 >'5,4,4,9'0,o,o,o, Natural Numbers. 1-68429946 46789 63634 80480 97328 1-68514178 31029 47882 64737 81593 98376 1-68615236 32098 48961 65826 82693 99561 1*68716431 33303 50176 66974 83851 1-68800729 17609 34492 51374 68259 85146 1-68902035 18925 35741 52635 69530 86427 1*69003326 20226 37128 54032 70937 87844 1-69104677 21587 38499 55413 72329 89246 I-69206165 23086 40008 56932 Dual Logarithms. Dual Numbers. 52134972, 14 15 16 17 18 19 20 21 22 52234922, 24 25 26 27 28 29 30 31 32 52334872, 34 35 36 37 38 39 40 41 42 52434822, 44 45 46 47 48 49 SO 51 52 52534772, 54 55 56 57 58 59 60 61 62 >1'5, 4,5, 0,0,0,0,0 j^5, 4,5, 1,0,0,0,0 \|'5,4,5, 2,0,0,0,0 45,4,5,3,0,0,0,0 >1'5, 4,5,4,0,0,0,0 15,4,5,5,0,0,0,0 >^5,4,5, 6,0,0,0,0 i 5,4,5, 7,0,0,0,0. 5,4,5,8,0,0,0,0 >I'5,4,5,9,o,o,o,o 4'5,4,6,o,o,o,o,o > '5,4,6, 1, 0,0,0,0 > '5, 4,6,2,0,0,0,0 > '5, 4,6,3,0,0,0,0 is, 4,6,4,0,0,0,0. i 5,4,6,5, 0,0,0,0 5,4,6,6,0,0,0,0 |5, 4,6,7, 0,0,0,0 \1^5, 4,6,8,0,0,0,0 15,4,6,9,0,0,0,0 > '5, 4,7,0,0,0,0,0 > '5,4,7, 1,0,0,0,0, >'5, 4,7, 2, 0,0,0,0, > '5,4,7,3,0,0,0,0, >I'5,4,7,4,o,o,o,o 15,4,7,5,0,0,0,0 |5,4,7,6,o,o,o,o ^^5,4,7,7,o,o,o,o ^5,4,7, 8,0,0,0,0 15,4,7,9,0,0,0,0 5,4,8,0,0,0,0,0 5,4,8,1,0,0,0,0 5,4,8,2,0,0,0,0 .5,4,8,3,0,0,0,0 ^5,4,8,4,0,0,0,0 > '5,4,8,5,0,0,0,0 > '5, 4,8,6,0,0,0,0 ^ '5,4,8,7, 0,0,0,0 ^ '5, 4,8,8,0,0,0,0 ^'5,4,8,9,0,0,0,0, >1'5, 4,9,0,0,0,0,0 is, 4,9, 1, 0,0,0,0 i 5,4,9,2, 0,0,0,0 5,4,9,3,0,0,0,0, is, 4,9,4,0,0,0,0, iS,4,9,5,o,o,o,o is, 4,9,6,0,0,0,0, is, 4,9,7, 0,0,0,0 is, 4,9,8,0,0,0,0 is>4,9,9,o,o,o,o Multiples of Differences. 1675 1676 3350 3352 5025 5028 6700 6704 «375 8380 10050 10056 11725 11732 13400 13408 15075 15084 1678 3356 5034 6712 8390 10068 11746 13424 I5I02 1679 3358 5037 6716 8395 10074 "753 13432 15111 I68I 1682 3362 3364 5043 5046 6724 6728 8405 8410 10086 10092 II 767 1 1774 13448 13456 15129 *5i38 1684 3368 1685 3370 5052 6736 8420 5055 6740 8425 10104 lOIIO 11788 13472 15156 "795 13480 15165 1687 1688 3374 3376 5061 5064 6748 6752 8435 8440 10122 10128 11809 11816 13496 13504 15183 15192 1690 1691 3380 3382 5070 5073 6760 6764 8450 8455 10140 10146 1 1 830 "837 13520 13528 15210 15219 1677 3354 5031 6708 8385 10062 "739 13416 15093 1680 3360 5040 6720 8400 10080 1 1 760 13440 15120 1683 3366 5049 6732 8415 10098 1 1 781 13464 15147 1686 3372 5058 6744 8430 10116 11802 13488 15174 1689 3378 5067 6756 8445 10134 11823 13512 15201 1692 3384 5076 6768 8460 10152 1 1844 13536 1522S Dual Logarithms of powers of 2 and 10. i, 10 = 230258509, i, 10* = 921034037, X, 10^ = 1611809565, ,,, 10^ = 1151292546, i, lo** = 1842068074, i, 10" = 1381551056, I, io9 = 2072326584, ", 2 = 6931471 ,,, 4 = 138629437, L Io2 = 4605170I9, i, 8 = 207944154, i, io3 = 690775528, 56] Nat. No. 1-6926 to 17094 D. Log. 5263.... to 5361.... D. No. >1.5,5,0,0, to |5,5,9,9, Natural Dual Dual Numbers. Logarithms. Numbers. i*692662i9 52630255, >'5.5»o,o,o,o,o,o. 83146 64 ,,5,5,0,1,0,0,0,0, i'693ooo74 65 ,,5,5,0,2,0,0,0,0, 17004 66 >'5>5>o,3,o,o,o,o. 33936 67 >'5»5>o,4>o,o,o,o. ■ 50869 68 >I'5>5.o,5,o,o,o,o, 67804 69 v5,5>o,6,o,o,o,o, 84741 70 ^'5>5.o,7,o,o,o,o, i'694oi679 71 ,,5,5,0,8,0,0,0,0, 18619 72 \'5.5jO,9,o,o,o,o, 35485 52730205, >'5'5»i>o,o,o,o,o. 52428 74 ,'5»5'^)i;0,o,o,o, 69373 75 ,,5,5,1,2,0,0,0,0, 86320 76 >'S,5»i,3>o,o,o,o, 1-69503269 77 \'5»5.i>4,o,o,o,o. 20219 78 >'5>5>i»5,o,o,o,o. 37171 79 >'5'5»i>6,o,o,o,o, 54125 80 >'5.5>i>7,o,o,o,o. 71080 8t >'5>5'i>8,o,o,o,o, ■ 88037 82 >'5>5»i>9»o,o,o,o, 1*69604920 52830155, ,,5,5,2,0,0,0,0,0, 21880 84 >'5»5»2,I,0,0,0,0, 38842 85 >'S»5. 2, 2,0,0,0,0, 55806 86 >'5>5.2,3,o,o,o,o, 72772 87 4'5>5.2,4>o,o,o,o, 89739 88 >'5>5>2,5,o,o,o,o, 1*69706708 89 >'5>5)2,6,o,o,o,o, 23679 90 {5>5^2,7,o,o,o,o, 40651 91 > '5^5.2)8,0,0,0,0, 57625 92 \^5.5> 2,9,0,0,0,0, 74525 52930105, v'S.5)3>o,o,o,o,o, 91502 94 >'5.5>3>i.o,o,o,o. 1*69808481 95 >'5.5>3.2,o,o,o,o, 25462 96 >'5.5>3>3.o,o,o,o, 42445 97 ^'5>5.3.4,o,o,o,o, 59429 98 w5>5.3)5>o,o,o,o. 76415 99 >'5»5>3.6,o,o,o,o. 93403 5300 >'5.5.3,7>o,o,o,o, 1*69910392 01 > '5.5.3.8,0,0,0,0, 27383 02 > '5.5.3.9,0,0,0,0, 44300 53030055, ^5.5.4,0,0,0,0,0, 61294 04 > '5.5,4, 1,0,0,0,0, 78290 05 > '5.5.4,2,0,0,0,0, 95288 06 N '5.5.4.3.0,0,0,0, 1*70012288 07 > '5,5.4,4,0,0,0,0, 29289 08 15,5,4,5,0,0,0,0, 46292 09 Is, 5. 4.6,0,0,0,0, 63297 10 >'5. 5. 4,7. 0,0,0,0, 80303 II ^ '5,5,4,8,0,0,0,0, 97311 12 >'5, 5,4,9,0,0,0,0, Natural Dual Dual Numbers. Logarithms. Numbers. 1*70114244 53130005, > '5.5,5,0,0,0,0,0, 31255 14 >'5.5.5.i.o,o,o,o, 48268 15 >'5.5. 5. 2,0,0,0,0, 65283 16 >'5.5.5.3.o,o,o,o. 82300 17 >'5. 5. 5.4,0,0,0,0, 99318 18 > '5.5.5.5.0.0,0,0, 1*70216338 19 \'5.5, 5, 6,0,0,0,0, 33360 20 >'5. 5.5,7,0,0,0,0, 50383 21 > '5,5,5,8,0,0,0,0, 67408 22 \'5,5.5,9,o,o,o,o. 84358 53229955, > '5,5,6,0,0,0,0,0, 1-70301386 23 >'5,5, 6,1, 0,0,0,0, 18416 24 ,,5,5,6,2,0,0,0,0, 35448 25 > '5.5.6.3.0.0,0,0, 52482 26 > '5.5.6,4.0,0,0,0, 69517 27 > '5.5.6,5.0,0,0,0, 86554 28 > '5.5.6.6,0,0,0,0, 170403593 29 w5,5, 6,7,0,0,0,0, 20633 30 ^ '5.5.6,8,0,0,0,0, 37675 31 > '5,5.6,9.0,0,0,0, 54642 53329905, > '5.5,7,0,0,0,0,0, 71687 Zi v5,5. 7. 1.0,0,0,0, 88734 34 v5.5.7.2,o,o,o,o. 1*70505783 35 > '5.5.7.3.0,0,0,0, 22834 36 v5,5,7.4,o,o,o,o, 39886 37 > '5.5.7.5.0,0,0,0, 56940 38 > '5.5.7.6,0,0,0,0, 73996 39 > '5.5,7.7.0,0,0,0, 91053 40 .'5.5.7.8,0,0,0,0, 1*70608112 41 v5,5.7>9,o,o,o,o, 25096 53429855. ,,5,5,8,0,0,0,0,0, 42159 43 w5. 5.8,1,0,0,0,0, 59223 44 ,,5,5,8,2,0,0,0,0, 76289 45 v5. 5.8,3.0.0,0,0, 93357 46 ,,5,5,8,4,0,0,0,0, 1*70710426 47 > '5.5.8,5,0,0,0,0, 27497 48 >'5. 5.8.6,0,0,0,0, 44570 49 >'5. 5, 8,7,0,0,0,0, 61644 50 "5,5,8,8,0,0,0,0, 78720 51 v5.5.8,9,o,o,o,o, 95721 53529805, w5,5,9,o,o,o,o,o. 1*70812801 53 "5,5,9,1,0,0,0,0, 29882 54 "5,5,9,2,0,0,0,0, 46965 55 > '5.5.9.3.0,0,0,0, 64050 56 > '5.5.9.4.0,0,0,0, 81136 57 "5.5.9,5,0,0,0,0, 98224 58 "5.5.9.6.0,0,0,0, 1*70915314 59 > '5.5.9.7.0,0,0,0, 32406 60 > '5.5,9,8,0,0,0,0, 49499 61 "5,5,9,9.0,0,0,0, Multiples of Differences. 1692 1693 3.3«4 .33«6 5076 5079 6768 6772 8460 846s 10152 10158 1 1844 11851 1.IS.S6 13544 15228 15237 1695 3390 5085 6780 8475 IOI70 II 865 13560 15255 1696 3392 5088 6784 1694 3388 5082 6776 8470 IOI64 11858 13552 15246 1697 3394 5091 6788 10176 10182 11872 1 1879 13568 13576 15264,15273 1698 1699 1700 3396 3398 3400 5094 5097 5100 6792 6796 6800 8490 8495 8500 IOI88 10194 I0200 1 1 886 1 1893 1 1900 13584 13592 13600 15282 15291 15300 1 701 1702 3402 3404 5103 5106 6804 6808 8505 8510 10206 I02I2 1 1907 II9I4 13608 I3616 15309 I5318 1704 1705 3408 3410 5112 5"5 6816 6820 8520 8525 10224 10230 1 1928 "935 13632 13640 15336 15345 I 1707 1708 2 3414 3416 3 5121 5124 4 6828 6832 5 8535 8540 6 10242 10248 7 "949 11956 8 13656 13664 9 15363 15372 1703 3406 5109 6812 85IS I02l8 II92I 13624 15327 1706 3412 5II8 6824 8530 10236 1 1942 13648 15354 1709 3418 5127 6S36 8545 10254 1 1963 13672 I538I ^. 2 = 69314718, I,, 4 = 138629437, Dual Logarithms of powers of 2 and 10. 10 = 230258509, L 10* = 921034037, L lo^ = 1611809565, lo^ = 460517019, X, 10^ = 1151292546, ,„ 10^ = 1842068074, \,2>- 207944154, J,, io3 = 690775528, \, io« = 1381551056, I, io» = 2072326584, Nat. No. 17095 to 17265 D. Log. 5362.... to 5461.... D. No. >1.5,6,0,0, to |5,6,9,9, [57 Natural Numbers, Dual Logarithms. 170958881 75977 93075 1*71010174 27275 44378 61482 78588 95696 171112806 29840 46953 64068 81184 98302 171215422 32544 49667 66792 83919 171300970 18100 35232 52366 69501 86638 171403777 20917 38059 55203 72271 89418 171506567 23718 40870 58024 75180 92338 171609497 26658 43743 60907 78073 95241 171712411 29582 46755 63930 81106 08284 53625288, 63 64 65 66 67 68 69 70 71 53725238, 73 74 75 76 77 78 79 80 5382518 83 84 85 86 87 88 89 90 91 53925138, 93 94 95 96 97 98 99 5400 01 54025088, 03 04 OS 06 07 08 09 10 II Dual Numbers. 15.6,0,0,0,0,0,0 \|/5. 6,0, 1,0,0,0,0 4^5,6,0,2,0,0,0,0 i5>6,o,3,o,o,o,o, 15,6,0,4,0,0,0,0, >1'5. 6,0,5,0,0,0,0, >l,5,6,o,6,o,o,o,o, i5'6,o,7, 0,0,0,0 >i'5)6,o,8,o,o,o,o i5>6,o,9,o,o,o,o, 15,6,1,0,0,0,0,0 15)6,1,1,0,0,0,0 5,6,1,2,0,0,0,0 5»6,T, 3, 0,0,0,0 5,6,1,4,0,0,0,0 ^1'5»6,1, 5, 0,0,0,0, 5,6,1,6,0,0,0,0, 5,6,1,7,0,0,0,0 5,6,1,8,0,0,0,0 is. 6, 1, 9,0,0,0,0 -5,6,2,0,0,0,0,0 .5,6,2,1,0,0,0,0 .5,6,2,2,0,0,0,0 .5,6,2,3,0,0,0,0 is. 6,2,4,0,0,0,0 is. 6.2, 5, 0,0,0,0 is. 6,2,6,0,0,0,0 is. 6.2, 7, 0,0,0,0 is. 6,2,8,0,0,0,0 i5.6,2,9,o,o,o,o is. 6,3. 0,0,0,0,0 is. 6,3.1.0,0,0,0 ^'5)6,3. 2, 0,0,0,0 v'S. 6,3. 3. 0,0,0,0 is. 6,3. 4.0,0,0,0 S.6,3.5.0.0.0.0 5. 6,3. 6,0,0,0,0 5.6,3)7.0,0,0,0 5,6,3,8,0,0,0,0 iS.6,3.9.0.0.0,0 iS)6,4)0,o,o,o,o iS)6,4)i)0,o,o,o ,,5,6,4,2,0,0,0,0, >'5. 6,4,3. 0,0,0,0 i5)6,4.4,o,o,o,o iS.6,4,5. 0,0,0,0 is. 6,4,6,0,0,0,0 is. 6,4.7. 0,0,0,0 is.6,4.8,0,0,0,0 i5.6.4,9)0,o,o,o Natural Numbers. 171815387 32569 49752 66937 84124 171901312 18502 35694 52888 70083 87202 17200440X 21601 38803 56007 73213 90420 172107629 24840 42052 59189 76405 93623 172210842 28063 45286 62511 79737 96965 172314195 31348 48581 65816 83053 172400291 17531 34773 52016 69261 86508 172503679 20929 38181 55435 72691 89948 172607207 24468 41730 58994 Dual Logarithms. 54125038, 13 14 IS 16 17 18 19 20 21 5422 23 24 25 26 27 28 29 30 31 54324938, 35 34 35 36 37 38 39 40 41 5442 43 44 45 46 47 48 49 50 51 54524838, 53 54 55 56 57 58 59 60 61 Dual Numbers. i5)6.5. 0,0,0,0,0 is. 6,5. 1.0.0,0,0 is. 6,5)2,0,0,0,0 iS)6,5.3.o,o,o,o iS)6,S. 4,0,0,0,0 5.6,5,5,0,0,0,0 5.6,5.6,0,0,0,0 5)6,5,7)0,0,0,0 5,6,5,8,0,0,0,0 iS)6)S)9.o,o,o,o iS.6,6,0,0,0,0,0 5.6.6,1,0,0,0,0 5,6,6,2,0,0,0,0 5. 6,6,3, 0,0,0,0 i5, 6,6,4,0,0,0,0 S. 6,6,5,0,0,0,0 5,6,6,6,0,0,0,0 5. 6,6,7, 0,0,0,0 5,6,6,8,0,0,0,0 5,6,6,9,0,0,0,0 iS)6,7)0,o,o,o,o, i5.6,7. 1.0,0,0,0 i 5)6,7.2, 0,0,0,0 5.6,7.3.0,0,0,0 iS.6,7)4.o,o,o,o is. 6.7.5.0,0,0,0 iS)6,7.6,o,o,o,o is. 6,7)7)0,0,0,0 i5)6,7)8,o,o,o,o is. 6,7.9)0,0,0,0 iS)6,8,o,o,o,o,o 5,6,8,1,0,0,0,0 5.6,8,2,0,0,0,0 .5,6,8,3,0,0,0,0 5,6,8,4,0,0,0,0, is. 6.8,5,0,0,0,0 ,,5,6,8,6,0,0,0,0 > '5)6.8,7, 0,0,0,0 w5. 6,8,8,0,0,0,0 i5)6,8,9,o,o,o,o iS)6,9.o,o,o,o,o is. 6,9. 1.0,0,0,0 is.6,9.2,0,0,0,0 is. 6,9.3)0,0,0,0 is. 6,9.4,0,0,0,0 i5)6.9)5.o,o,o,o >'5. 6.9.6.0,0,0,0 is. 6,9.7. 0,0,0,0 iS.6,9)8,o,o,o,o iS.6.9)9.o,o,o,o, Multiples of Differences. 1709 1710 34i« 3420 5127 5130 6836 6840 «=;45 «S,So 10254 10260 11963 1 1970 13672 13680 iS3«i 15390 1712 1713 3424 3426 5136 5139 6848 6852 8560 «56S 10272 10278 II 984 11991 13696 13704 15408 15417 171S 1716 3430 3432 5145 5i4« 6860 6864 8.'57.'? 8580 10290 10296 12005 I20I2 13720 13728 15435 15444 I7I8 3436 5154 6872 8590 10308 12026 13744 15462 I7I9 3438 5157 6876 8595 I03I4 12033 13752 15471 17x1 3422 5133 6844 8555 10266 "977 13688 15399 1714 3428 5142 6856 8570 10284 1 1998 13712 15426 1717 3434 5151 6868 8585 10302 12019 13736 15453 1720 3440 5160 6880 8600 10320 12040 13760 15480 I72I 1722 1723 3442 3444 3446 5163 i;i66 5169 6884 6888 6892 8605 8610 861-; 10326 10332 10338 12047 I20S'V 1 206 1 13768 13776 13784 15489 15498 15507 I 1724 1725 2 3448 3450 3 5172 5i7,S 4 6896 6900 5 8620 8625 6 10344 10350 7 12068 12075 8 13792 13800 9 15516 15525 1726 3452 5178 6904 8630 10356 12082 13808 15534 Dual Logarithms of powers of 2 and 10. J,, 2 = 69314718, I, 10 = 230258509, ^, 10* =: 92..1 034037, X, 10'^ = 161 1809565, i, 4 = 138629437, i, lo^ = 460517019, i, lo^ = 1151292546, i, 10^ — 1842068074, i, 8 = 207944154, i, io3 = 690775528, i, 10" = 1381551056, i, io9 = 2072326584, I 60] Nat. No. 17613 to 1*7789 D. Log. 5661.... to 5759.... D. No. >I.5,9,0,0, to >I.5,9,9,9, Natural Dual Dual Numbers. Logarithms. Numbers. 176139107 56610387, vl,5, 9,0,0,0,0,0,0, 56721 62 vl'5'9> 0,1,0,0,0,0, 74337 ^2, >I'5>9>0,2,0,0,0,0, 91954 64 >'5)9>o,3, 0,0,0,0, 176209573 65 >I'5'9>o,4,o,o,o,o, 27194 66 4'5'9>o,5.o,o,o,o, 44817 67 \^5>9>o,6,o,o,o,o. 62441 68 l5»9.o,7,o,o,o,o. 80067 69 w5, 9,0,8,0,0,0,0, 97"695 70 >^5)9,o,9,o,o,o,o. 1 763 1 5 246 56710337, .r5, 9, 1,0,0,0,0,0, 32878 72 >'5>9.i^i>o,o,o,o. 505 1 1 73 "5'9>i>2,o,o,o,o, 68146 74 >'5)9>i>3>o,o,o,o. 85783 75 >'5>9)i>4,o,o,o,o. 176403422 76 >'5»9>Ij5»o,o,o,o, 21062 77 v'5>9) 1)6,0,0,0,0, 38704 78 > '5)9) 1)7)0,0,0,0, 56348 79 w5, 9, 1,8,0,0,0,0, 73994 80 >'5)9)i)9)0,o,o,o. 91561 56810287, ,1,5,9,2,0,0,0,0,0, 176509210 82 v'5)9)2, 1, 0,0,0,0, 26861 83 xl,5, 9,2, 2, 0,0,0,0, 44514 84 > '5)9)2,3)0,0,0,0, 62168 85 >, 5,9,2,4,0,0,0,0, 79824 86 w5)9)2,5)0,o,o,o. 97482 87 > '5)9)2,6,0,0,0,0, 17661-5142 88 v'5)9)2)7)0,o,o,o. 32804 89 > '5)9.2,8,0,0,0,0, 50467 90 >^5)9)2,9)0,o,o,o. 68052 56910237, >'5.9)3).o»o,o,o,o, 85719 92 ^ '5)9)3)1)0,0,0,0, 176703388 93 > '5)9.3)2,0,0,0,0, 21058 94 > '5)9)3)3)0,0,0,0, 38730 95 w5, 9)3)4)0,0,0,0, 56404 96 vl'5)9.3. 5.0,0,0,0, 74080 97 vl'5)9.3)6,o,o,o,o, 91757 98 >l'5)9.3)7.o,o,o,o. 176809436 99 "5)9.3)8,0,0,0,0, 27117 5700 "5.9)3)9.0,0,0,0, 44720 57010187, > '5.9)4)0,0,0,0,0, 62404 02 v'S)9)4)i,o,o,o,o, 80090 03 "5.9)4)2,0,0,0,0, 97778 04 > '5)9)4)3)0)0,0,0, 176915468 05 > '5.9)4,4.0,0,0,0, 33160 06 ^ '5.9)4.5)0,0,0,0, 50853 07 > '5)9)4)6,0,0,0,0, 68548 08 > '5.9)4,7)0,0,0,0, 86245 09 "5)9)4)8,0,0,0,0, 177003944 10 > '5.9.4,9.0)0,0,0, Natural Numbers. 177021565 39267 56971 74677 92384 1 77 1 10093 27804 45517 63232 80948 98587 177216307 34029 51752 69477 87204 177304933 22653 4039s 58129 75786 93524 177411263 29004 46747 64492 82238 99986 177517735 35487 53162 70917 88674 177606433 24194 41956 59720 77486 95254 177713024 30715 66263 84040 177801818 19598 37380 55164 72950 90737 Dual Logarithms. 57110137, 12 13 14 15 16 17 18 19 20 57210087, 22 23 24 25 26 27 28 29 30 57310037, 32 34 35 36 37 38 39 40 57409987, 41 42 43 44 45 46 47 48 49 57509937) 51 52 53 54 55 56 57 58 59 Dual Numbers. ^I'5)9)5.0,0,0,0,0, 5.9.5)1)0,0,0,0, 5,9,5,2,0,0,0,0, 5.9.5.3)0.0,0,0, 4'5>9.5)4.o,o,o,o, >I'5.9.5)5.o,o,o,o, >I'5)9)5)6,o,o,o,o, \l'5)9)5)7.o,o,o,o, \I'5.9.5)8)0,o,o,o, 15.9,5.9.0,0,0,0, 1,5,9,6,0,0,0,0,0, ,5,9,6,1,0,0,0,0, [,5,9,6,2,0,0,0,0, 1'5, 9.6.3.0,0,0,0, ['5.9)6,4.0,0,0,0, ^S. 9.6.5.0,0,0,0, > '5.9.6,6,0,0,0,0, > '5.9)6,7.0,0,0,0, > '5)9.6)8,0,0,0,0, i5. 9.6,9.0,0,0,0, ^ '5.9.7.0,0,0,0,0, >'5)9.7. 1)0,0,0,0, >'5)9.7)2, 0,0,0,0, "5)9.7)3)0,0,0,0, Is ) 9) 7. 4. 0,0, 0,0, 5.9.7.5)0,0,0,0, 5.9.7.6,0,0,0,0, 5.9.7.7)0,0,0,0, 5.9)7)8,0,0,0,0, 15.9,7)9)0,0,0,0, > '5,9.8)0,0,0,0,0, > '5.9.8, 1.0,0,0,0, > '5.9)8.2,0,0,0,0, > '5)9)8,3.0,0,0,0, >I'5. 9.8,4.0,0,0,0, 5)9.8,5.0.0,0,0, 5,9,8,6,0,0,0,0, 5,9,8,7,0,0,0,0, 5,9,8,8,0,0,0,0, 15.9.8,9.0.0,0,0, 15.9.9.0.0,0,0,0, 15.9.9.1.0,0,0,0, > '5)9.9.2.0,0,0,0, "5.9.9)3.0,0,0,0, >I'5. 9.9,4,0,0,0,0, 'I'S. 9)9.5. 0,0,0,0, 15.9.9)6.0,0,0,0, 15)9)9)7)0,0,0,0, \|/5)9)9.8,o,o,o,o, 15.9.9)9.0,0,0,0, Multiples of Differences. 1761 1762 3522 3524 5283 5286 7044 7048 8805 8810 10566 10572 12327 12334 14088 14096 i5«49 15858 1764 1765 352« 3530 5292 S295 7056 7060 8820 8825 10584 10590 12348 12355 I14112 14120 li5«76 15885 1763 3526 5289 7052 88IS 10578 I234I I4I04 15867 1766 3532 5298 7064 1767 1768 3534 3536 5301 5304 7068 7072 8835 8840 10602 10608 12369 12376 14136 14144 15903 15912 1770 1771 3540 3542 5310 5313 7080 7084 8850 »«55 10620 10626 12390 12397 14160 14168 15930 15939 10596 I236Z 14128 15894 1769 3538 5307 7676 8845 I06I4 12383 14152 1 592 1 1772 3544 5316 8860 10632 12404 14176 15948 1773 1774 it;.") 3546 3548 3550 5319 5322 5325 7092 7096 7100 8865 8870 8875 10638 10644 10650 I24II 12418 12425 I4I84 I4I92 14200 15957 15966 1597s 1776 1777 3552 3554 S328 5.331 7104 7108 8880 8885 10656 10662 12432 12439 14208 142 1 6 15984 15993 I "78 3556 5334 7112 8890 10668 12446 14224 16002 Dual Logarithms of powers of 2 and 10. ^, 10 = 230258509, \, 10* = 921034037, 10^ = 1611809565, 4,, 2 = 693 147 18, 4'. 4 = 138629437, 4 lo^ = 460517019, \, lo^ = 1 15 1292546, 1, 10^ = 1842068074, 4,, 8 = 207944154, i, io3 = 690775528, 4,, io« = 1381551056, 4,, lo^ = 2072326584, Nat. No. r7715 to 17891 D. Log. 5718.... to 5817.... D. No. 4^6,0,0,0. to >I:6,0,9,9, [^1 Natural Numbers. 177156100 73816 91533 177209252 26973 44696 62420 80146 97874 177315604 33256 50989 68724 86461 177404200 21940 39682 57426 75172 92920 177510589 28340 46093 63848 81604 Dual Logarithms. 99362 I776I7I22 34884 52647 43 44 45 46 70412 47 88100 177705869 23640 57485958, 49 50 4I4I2 59186 51 52 76962 94740 I778I25I9 30300 48083 65788 83575 I7790I363 I9I53 36945 54739 72534 9033 1 178008130 25931 57186108, 19 20 21 22 23 24 25 26 27 57286058, 29 30 31 32 33 34 35 36 37 57386008, 39 40 41 42 Dual Numbers. 53 54 55 56 57 i 6,0,0,0,0,0,0,0 6,0,0,1,0,0,0,0 ^j^6, 0,0, 2,0,0,0,0, \i'6,o,o,3,o,o,o,o >j,6, 0,0,4,0,0,0,0 \I'6,o,o,5,o,o,o,o v,6, 0,0, 6, 0,0,0,0 >'6,o,o,7, 0,0,0,0 >,6, 0,0,8, 0,0,0,0 >j,6,o,o,9,o,o,o,o t 6,0, 1,0,0,0,0,0 6,0,1,1,0,0,0,0 xj,6, 0,1,2,0,0,0,0, '16,0,1,3,0,0,0,0 \j^6, 0,1,4,0,0,0,0 >I'6,o,i,5,x>,o,o,o, >I,6,o, 1,6,0,0,0,0 J,6,o, 1, 7,0,0,0,0 >{,6,o, 1,8,0,0,0,0 >i,6, 0,1,9,0,0,0,0, >I^6, 0,2, 0,0,0,0,0 >,6, 0,2, 1, 0,0,0,0 >,6, 0,2, 2, 0,0,0,0 ^,6,0,2, 3, 0,0,0,0 |6,o, 2,4, 0,0,0,0 X6,o,2, 5,0,0,0,0 >I^6, 0,2, 6,0,0,0,0 ^6,0,2,7,0,0,0,0 j,6, 0,2, 8, 0,0, 0,0 vj^6,o,2, 9, 0,0,0,0 |6,o,3, 0,0,0,0,0, 4,6,0,3,1,0,0,0,0 >l6,o,3,2,o,o,o,o >l'6,o,3,3,o,o,o,o \l'6,o,3,4,o,o,o,o ['6,0,3,5,0,0,0,0 ^6,0,3,6,0,0,0,0 ^6,0,3,7, 0,0,0,0 ^6,o,3, 8,0,0,0,0 [^6,0,3, 9,0,0,0,0 57585908, "6,0,4,0,0,0,0,0 59 >,6,o,4,i,o,o,o,o 60 > '6,0,4,2,0,0,0,0 61 ,,6,0,4,3,0,0,0,0 62 ,,6,0,4,4,0,0,0,0 63 N '6,0,4,5,0,0,0,0 64 ,,6,0,4,6,0,0,0,0 65 >'6,o,4,7, 0,0,0,0 66 ,,6,0,4,8,0,0,0,0 67 > '6,0,4,9,0,0,0,0 Natural Numbers. 178043654 61458 79264 97072 178114882 32693 50506 68321 86138 178203957 21698 39520 57344 75170 92998 178310827 28658 46491 64326 82162 99920 178417760 35602 53446 71291 89138 178506987 24838 42690 60544 78320 96178 178614038 31899 49762 67627 85494 178703363 21233 39105 56898 74774 92651 178810530 28411 46294 64179 82065 99953 178917843 Dual Logarithms., 57685858 69 70 71 72 73 74 75 76 77 57785808, 79 80 8i 82 83 84 85 86 87 57885758, 89 90 91 92 93 94 95 96 97 57985708, 99 5800 01 02 03 04 05 06 07 58085658, 09 10 II 12 13 14 15 16 17 Dual Numbers. ,,6,0,5,0,0,0,0,0, ^ '6,0,5, 1,0,0,0,0, ,,6,0,5,2,0,0,0,0, >'6,o,5, 3, 0,0,0,0, \I'6,o,5,4,o,o,o,o, 16,0,5,5,0,0,0,0, 4,6,0,5,6,0,0,0,0, 4'6,o,5, 7,0,0,0,0, 4,6,0,5,8,0,0,0,0, 16,0,5,9,0,0,0,0, ,,6,0,6,0,0,0,0,0, ,,6,0,6,1,0,0,0,0, 4,6,0,6,2,0,0,0,0, ,16,0,6,3,0,0,0,0, 4,6,0,6,4,0,0,0,0, 4,6,0,6,5,0,0,0,0, 4,6,0,6,6,0,0,0,0, 4,6,0,6,7,0,0,0,0, 4,6,0,6,8,0,0,0,0, 4,6,0,6,9,0,0,0,0, 4,6,0,7,0,0,0,0,0, 4,6,0,7,1,0,0,0,0, 4,6,0,7,2,0,0,0,0, 16,0,7,3,0,0,0,0, 4,6,0,7,4,0,0,0,0, 16,0,7,5,0,0,0,0, ,,6,0,7,6,0,0,0,0, ,,6,0,7,7,0,0,0,0, ,,6,0,7,8,0,0,0,0, 4,6,0,7,9,0,0,0,0, 6,0,8,0,0,0,0,0, 6,0,8,1,0,0,0,0, 6,0,8,2,0,0,0,0, .6,0,8,3,0,0,0,0, 4,6,0,8,4,0,0,0,0, [,6,0,8,5,0,0,0,0, ',6,0,8,6,0,0,0,0, 16,0,8,7,0,0,0,0, L6, 0,8, 8, 0,0, 0,0, 1,6,0,8,9,0,0,0,0, 4,6,0,9,0,0,0,0,0, 6,0,9,1,0,0,0,0, 6,0,9,2,0,0,0,0, 6,0,9,3,0,0,0,0, 6,0,9,4,0,0,0,0, i 6,0,9,5,0,0,0,0, 6,0,9,6,0,0,0,0, 4/6,0,9,7,0,0,0,0, 4,6,0,9,8,0,0,0,0, 4,6,0,9,9,0,0,0,0, I77I 1772 3542 3544 5313 5316 7084 7088 «HS^ 8860 10626 10632 12397 12404 14168 14176 15939 15948 1774 177=; 3548 3550 5322 5325 7096 7100 8870 887s 10644 X0650 X2418 12425 14192 14200 15966 15075 1777 3554 5331 7108 Multiples of ' ' ' DifiFerences, 1773 3546 5319 7092 8865 10638 1 241 1 14184 15957 1776 3552 5328 7104 8880 10656 12432 14208 15^84 1779 3558 5337 7116 8895 10674 12453 14232 16011 1782 3564 5346 7128 8910 10692 12474 14256 16038 1785 3570 5355 7140 8925 10710 12495 14280 16065 1788 3576 5364 7152 8940 10728 12516 114304 1x6092 10662 12439 X42X6 15993 ' 1778 3556 5334 7112 8890 X0668 X2446 X4224 16002 1780 I78X 3560 3562 5340 5343 7120 7X2*4 8900 890=; 10680 X0686 X2460 12467 X4240 X4248 X6020 X6029 1783 1784 3566 3568 5349 5352 7132 7136 89x5 8520 X0698 10704 X2481 X2488 14264 X4272 X6047 i6o§6 1786 3572 5358 7144 8930 X07X6 X2502 14288 X6074 1789 3578 5367 7156 8945 10734 12523 X43I2 x6xoi 1787 3574 5361 7148 8935 X0722 12509 14296 X6083 ,,, 2 = 69314718, >', 4 Vj 8 Dual Logarithms of powers of 2 and 10. = 69314718, X, 10 = 230258509, 4,, lo^ = 921034037, = 138629437, 4', io2 = 460517019, J,, io5 = 1151292546, = 207944154, 4,, 10' = 690775528, 4,, lo'' = 1381551056, 1, lo"^ = 161 1809565, ,„ 10^ = 1842068074, I, 10^ = 2072326584, G2j 'Nat. No. 17892 to r8070 D. Log. 5818.... to 5917.... D. No. >^6,1,0,0, to >I.6,1,9,9, Natural Dual Dual Numbers. Logarithms. Nurnbers. 178927661 58181141, ,1,6,1,0,0,0,0,0,0, 45554 19 >,6,i,o,i, 0,0,0,0, 63449 20 >,6,I,0,2,0,0,0,0, 81345 21 ,,6,1,0,3,0,0,0,0, 99243 22 J,6, 1,0,4,0,0,0,0, 179017143 23 ,,6,1,0,5,0,0,0,0, 35045 24 ,,6,1,0,6,0,0,0,0, 52949 25 ,,6,1,0,7,0,0,0,0, 70854 26 ,,6,1,0,8,0,0,0,0, . 88761 27 ,,6,1,0,9,0,0,0,0, 179106589 5828109I, ,1,6, X, 1,0,0,0,0,0, 24500 29 ,,6,1,1,1,0,0,0,0, 42412 30 ,1,6,1,1,2,0,0,0,0, 60326 31 ,, 6,1, 1,3,0,0,0,0, 78242 32 ,,6,1,1,4,0,0,0,0, 96160 33 >'6,i, 1, 5,0,0,0,0, 1 792 14080 34 ,,6,1,1,6,0,0,0,0, 32001 35 ,,6,1,1,7,0,0,0,0, 49924 36 ,,6,1,1,8,0,0,0,0, 67849 37 |6,i, I, 9,0,0,0,0, 85696 58381041, 4,6,1,2,0,0,0,0,0, 179303625 39 ,,6,1,2,1,0,0,0,0, 21555 40 ,,6,1,2,2,0,0,0,0, 39487 41 ,,6,1,2,3,0,0,0,0, 57421 42 ,,6,1,2,4,0,0,0,0, 75357 43 ,,6,1,2,5,0,0,0,0, 93295 44 ,,6,1,2,6,0,0,0,0, 179411234 45 ,,6,1,2,7,0,0,0,0, 29175 46 ,,6,1,2,8,0,0,0,0, 47118 47 ,,6,1,2,9,0,0,0,0, - 64982 58480991, ,,6,1,3,0,0,0,0,0, 82928 49 ,,6,1,3,1,0,0,0,0, 179500876 50 ,,6,1,3,2,0,0,0,0, 18826 51 \>6,i,3,3^o,o,o,o, 36778 52 ,,6,1,3,4,0,0,0,0, 54732 53 > '6,1,3, 5>o,o,o,o, 72687 54 ,,6,1,3,6,0,0,0,0, 90644 55 46,1,3,7,0,0,0,0, 179608603 56 ^'6,1,3,8,0,0,0,0, 26564 57 4'6,i,3j9>o,o,o,o, 44447 58580941, 4,6,1,4,0,0,0,0,0, 62411 59 \^6, 1,4,1,0,0,0,0, 80377 60 X6, 1,4,2,0,0,0,0, 98345 61 |6,i, 4,3)0,0,0,0, 179716315 62 4,6,1,4,4,0,0,0,0, 34287 63 4,6,1,4,5,0,0,0,0, 52260 64 4,6,1,4,6,0,0,0,0, 70235 65 4,6,1,4,7,0,0,0,0, 88212 66 4,6,1,4,8,0,0,0,0, 179806191 67 4,6,1,4,9,0,0,0,0, Natural Numbers. 179824091 42073 60057 78043 - 96031 179914021 32012 50005 68000 85997 1-80003915 21915 39917 57921 75927 93935 i"8oiii944 29955 47968 65983 83919 i'8o2oi937 19957 37979 56003 74029 92056 1*80310085 28116 46149 64103 82139 i*8o4ooi77 18217 36259 54303 72348 90395 1*80508444 26495 44467 62521 80577 98635 1*80616695 34757 52820 70885 88952 1*80707021 Dual Logarithms. 58680891, 69 70 71 72 73 74 75 76 77 58780841, 79 80 81 82 83 84 85 86 87 58880791 89 90 91 92 93 94 95 96 97 58980741, 99 5900 01 02 03 04 05 06 07 59080691, 09 10 II 12 13 14 15 16 17 Dual Numbei-s. 4,6,1,5,0,0,0,0,0, 4'6, 1,5, 1,0,0,0,0, 4.6,1,5,2,0,0,0,0, 4'6, 1,5,3,0,0,0,0, 16,1,5,4,0,0,0,0, vl'6, 1,5,5,0,0,0,0, 4,6,1,5,6,0,0,0,0, 16,1,5,7,0,0,0,0, j'6,1, 5, 8,0,0,0,0, |6,i,5,9>o,o,o,o, 4,6,1,6,0,0,0,0,0, 4.6,1,6,1,0,0,0,0, 4,6,1,6,2,0,0,0,0, 4.6,1,6,3,0,0,0,0, 4.6,1,6,4,0,0,0,0, 4.6,1,6,5,0,0,0,0, 4.6,1,6,6,0,0,0,0, 4.6,1,6,7,0,0,0,0, ,.6,1,6,8,0,0,0,0, 4.6,1,6,9,0,0,0,0, 4.6,1,7,0,0,0,0,0, 4.6,1,7,1,0,0,0,0, 4.6,1,7,2,0,0,0,0, 46,1,7,3,0,0,0,0, 4.6,1,7,4,0,0,0,0, >I'6,i,755>o,o,o,o, 4.6,1,7,6,0,0,0,0, 16, 1,7,7,0,0,0,0, 4,6,1,7,8,0,0,0,0, 4.6,1,7,9,0,0,0,0, 4.6,1,8,0,0,0,0,0, 4.6,1,8,1,0,0,0,0, 4.6,1,8,2,0,0,0,0, 4.6,1,8,3,0,0,0,0, 4.6,1,8,4,0,0,0,0, 4.6,1,8,5,0,0,0,0, i 6,1, 8,6, 0,0,0,0, 6,1,8,7,0,0,0,0, 4.6,1,8,8,0,0,0,0, 4.6,1,8,9,0,0,0,0, 4.6,1,9,0,0,0,0,0, 4.6,1,9,1,0,0,0,0, 4.6,1,9,2,0,0,0,0, 16, 1,9,3,0,0,0,0, 4,6,1,9,4,0,0,0,0, |6,i, 9,5, 0,0,0,0, 4,6,1,9,6,0,0,0,0, 4.6,1,9,7,0,0,0,0, ,,6,1,9,8,0,0,0,0, 4.6,1,9,9,0,0,0,0, Multiples of Differences. 1789 1790 35 7« 3S8o 5367 5370 7156 7160 8945 8950 10734 10740 12523 12530 14312 14320 16101 16110 1792 3584 5376 7168 8960 10752 12544 14336 16128 1795 3590 5385 7180 8975 10770 12565 14360 I6I55 1793 3586 5379 7172 8965 10758 12551 14344 16137 1796 3592 5388 7184 8980 10776 12572 14368 16164 1798 1799 3596 3598 5394 5397 7192 7196 8990 8995 10788 10794 12586 12593 14384 14392 16182 16191 1801 1802 3602 5403 7204 3604 5406 7208 9005 10806 9010 10812 12607 14408 16209 1261^ 14416 16218 1804 1805 3608 3610 5412 5415 7216 7220 9020 9025 10824 10830 12628 12635 14432 14440 1 16236 1624s I I79I 3582 5373 7164 8955 10746 12537 14328 16119 1794 358S 5382 7176 8970 10764 1255S 14352 16146 1797 3594 5391 7188 8985 10782 12579 14376 16173 i8co 3600 5400 7200 9000 10800 12600 14400 16200 1803 3606 5409 7212 9015 10818 12621 14424 16227 1806 3612 5418 7224 9030 10836 12642 14448 16254 1807 3614 5421 7228 903s 10842 12649 14456 16263 4., 2 = 693 147 1 8, I, 4 = 138629437, 4., 8 = 207944154, Dual Logarithms of powers of 2 and 10. 4., 10 = 230258509, 4., lo* =: 921034037, 4., io2 = 460517019, 4,, lo^ = 1151292546, 4,, io3 = 690775528, i> lo*^ = 1381551056, 10'^ = 1611809565, 10^ =■ 1842068074, 10^ = 2072326584, Nat. No. 1-8071 to 1-8251 D. Log. 5917.... to 6016.... D. No. |6,2,0,0, to >I.6,2,9,9, [63 Natural Numbers. Dual Logarithms. 1-80716938 35010 53084 71159 89236 1-80807315 25396 43479 61563 79649 97655 1-80915745 33837 51930 70025 88122 1-81006221 24322 42424 60528 78553 96661 1-81114771 32882 50995 69110 87227 1-81205346 23467 41589 '59632 77758 95886 1-81314016 32147 50280 68415 86552 1-81404691 22831 40892 59036 77182 95330 1-81513480 3I63I 62 49784 63 67939 64 86096 65 1-81604255 66 59I76I74, 18 19 20 21 22 23 24 25 26 59276124, 28 29 30 31 32 33 34 35 Z^ 59376074, 38 39 40 41 42 43 44 45 46 59476024, 48 49 50 5t 52 53 54 55 56 59575974, 58 59 60 61 Dual Numbers. ,2,0,0,0,0,0,0 ,0,1,0,0,0,0 ,0,2,0,0,0,0 ,0,3,0,0,0,0 ,0,4,0,0,0,0 ,0,5,0,0,0,0 ,0,6,0,0,0,0 ,0,7,0,0,0,0 ,0,8,0,0,0,0 ,0,9,0,0,0,0 ,1,0,0,0,0,0 ,1,1,0,0,0,0 ,1,2,0,0,0,0 ,1,3,0,0,0,0 ,1 4,0,0,0,0 ,1,5,0,0,0,0 ,1,6,0,0,0,0 ,1,7,0,0,0,0, ,1,8,0,0,0,0 ,1,9,0,0,0,0 ,2,0,0,0,0,0 ,2,1,0,0,0,0 ,2,2,0,0,0,0 ,2,3,0,0,0,0 ,2,4,0,0,0,0 ,2,5,0,0,0,0 ,2,6,0,0,0,0 ,2,7,0,0,0,0 ,2,8,0,0,0,0 ,2,9,0,0,0,0 ,3,0,0,0,0,0 ,3,1,0,0,0,0 ,3,2,0,0,0,0, ,3,3,0,0,0,0 ,3,4,0,0,0,0 ,3,5,0,0,0,0 ,3,6,0,0,0,0 ,3,7,0,0,0,0 ,3,8,0,0,0,0 ,3,9,0,0,0,0 ,4,0,0,0,0,0 ,4,1,0,0,0,0 ,4,2,0,0,0,0 ,4,3,0,0,0,0 ,4,4,0,0,0,0, ,4,5,0,0,0,0 ,4,6,0,0,0,0 ,4,7,0,0,0,0 ,4,8,0,0,0,0^ ;,4,9,o,o,o,o Natural Numbers. 1-81622333 40495 58659 76825 94992 1-81713161 31332 49505 67680 85857 1-81803955 22135 403^7 58501 76687 94875 i-8i9i3o64 31255 49448 67643 85759 1-82003958 22158 40360 58564 76770 94978 1-82113187 31398 4961 1 67745 85962 1-82204181 22401 40623 58847 77073 95301 i"823i353i 31762 49913 68148 86385 1-82404624 22864 41106 59350 77596 95844 1-82514094 Dual Logarithms, 59675924, 68 69 70 71 72 73 74 75 76 59775874, 78 79 80 81 82 83 84 85 86 59875824, 88 89 90 91 92 93 94 95 96 59975774, 98 99 6000 02 03 04 05 06 60075724, 08 09 10 II 12 13 14 15 16 Dual Numbers. 1,0,0,0,0 ,0,0,0,0 ,0,0,0,0 ,0,0,0,0 ,0,0,0,0 ,0,0,0,0, ,0,0,0,0, ,0,0,0,0 ,0,0,0,0 ,0,0,0,0 ,0,0,0,0 ,0,0,0,0 ,0,0,0,0. ,0,0,0,0, ,0,0,0,0 ,0,0,0,0 ,0,0,0,0 ,0,0,0,0 ,0,0,0,0, ,0,0,0,0 ,0,0,0,0, ,0,0,0,0, ,0,0,0,0, ,0,0,0,0 ,0,0,0,0 ,0,0,0,0 ,0,0,0,0 ,0,0,0,0 ,0,0,0,0 ,0,0,0,0 ,0,0,0,0 ,0,0,0,0 ,0,0,0,0 ,0,0,0,0 ,0,0,0,0, ,0,0,0,0 ,0,0,0,0 ,0,0,0,0, ,o,o,"t),o ,0,0,0,0 ,0,0,0,0 ,0,0,0,0 ,0,0,0,0 ,0,0,0,0 ,0,0,0,0 ,0,0,0,0 ,0,0,0,0 ,0,0,0,0 ,0,0,0,0, ,0,0,0,0, Multiples of Differences. 1807 1808 1 3614 3616 1 5421 5424 7228 7232 903'; 9040 10842 10848 12649 12656 14456 14464 16263 16272 I8I0 1811 3620 3622 S430 5433 7240 7244 9050 9055 10860 10866 12670 12677 14480 14488 16290 16299 1813 1814 3626 3628 5439 5442 7252 7256 9065 9070 10878 10884 12691 12698 14504 14512 163 1 7 16326 1816' 1817 3632' 3634 544« ,S45i 7264 7268 9080 9085 10896 10902 12712 12719 14528 14536 16344 16353 1819 1820 3638 3640 5457 5460 7276 7280 9095 9100 10914 10920 12733 12740 14552 14560 16371 16380 1822 1823 3644 3646 5466 5469 7288 7292 9110 9115 10932 10938 12754 12761 14576 14584 16398 16407 1825 3650 5475 7300 9125 10950 12775 14600 16425 1809 3618 5427 7236 9045 10854 12663 14472 16281 1812 3624 5436 7248 9060 10872 12684 14496 16308 1815 3630 5445 7260 9075 10890 12705 14520 16335 1818 3636 5454 7272 9090 10908 12726 14544 16362 1821 3642 5463 7284 9105 10926 12747 14568 16389 1824 3648 5472 7296 9120 10944 12768 14592 16416 X, 2 = 693 147 1 8, I, 4 = 138629437, I, 8 =^ 207944154, Dual Logarithms of powers of 2 and 10. L 10 = 230258509, I, io2 = - 460517019, 690775528, lo* = 921034037, ,„ 10^ = II5I292546, 4,, 10''' = I38I55I056, 10'' = I6II809565, lo** = 1842068074, 10^ = 2072326584, 64] Nat. No. 1-8252 to 1-8433 D. Log. 6Q17.... to 6116..,. D. No. 16,3,0,0, to |6,3,9,9, Natural Dual Dual Numbers. Logarithms. Numbers. 1-82524107 60171207, ,,6,3,0,0,0,0,0,0, 42359 18 ,,6,3,0,1,0,0,0,0, 60613 19 ,,6,3,0,2,0,0,0,0, 78869 20 > '6,3,0,3,0,0,0,0, 97127 21 |6,3,o,4,o,o,o,o, I-826I5387 22 > '6,3,0,5,0,0,0,0, 33649 23 \l'6,3, 0,6,0,0,0,0, 51912 24 ,,6,3,0,7,0,0,0,0, 70177 25 ,,6,3,0,8,0,0,0,0, 88444 26 ,,6,3,0,9,0,0,0,0, 1-82706631 60271157, "6,3,1,0,0,0,0,0, 24902 28 ,.6,3,1,1,0,0,0,0, 43174 29 ,,6,3,1,2,0,0,0,0, 61448 30 ,,6,3,1,3,0,0,0,0, 79724 31 > '6,3, 1,4,0,0,0,0, 98002 32 >I'6,3, 1,5,0,0,0,0, 1-82816282 33 ,,6,3,1,6,0,0,0,0, 34564 34 > '6,3, 1,7,0,0,0,0, 52847 35 ,,6,3,1,8,0,0,0,0, 71132 36 ,,6,3,1,9,0,0,0,0, 89338 60371107, ,,6,3,2,0,0,0,0,0, 1-82907627 38 V'6,3,2,I,0,0,0,0, 25918 39 ,,6,3,2,2,0,0,0,0, 442 1 1 40 > '6,3,2,3,0,0,0,0, 62505 41 \ '6,3,2,4,0,0,0,0, 80801 42 > '6,3, 2,5,0,0,0,0, 99099 43 ,,6,3,2,6,0,0,0,0, 1-83017399 44 > '6,3,2,7,0,0,0,0, 35701 45 ,,6,3,2,8,0,0,0,0, 54005 46 > '6,3,2,9,0,0,0,0, 72227 60471057, > '6,3,3,0,0,0,0,0, 90534 48 ,,6,3,3,1,0,0,0,0, 1-83108843 49 >^6,3,3,2,o,o,o,o. 27154 50 > '6,3,3,3,0,0,0,0, > '6,3,3,4,0,0,0,0, 45467 51 63782 52 > '6,3,3,5,0,0,0,0, 82098 53 > '6,3,3,6,0,0,0,0, 1-83200416 54 > '6,3,3,7,0,0,0,0, 18736 55 - ^ '6,3,3,8,0,0,0,0, 37058 56 ^ '6,3,3,9,0,0,0,0, 55299 60571007, ^ '6,3,4,0,0,0,0,0, 73625 58 > '6,3,4, 1,0,0,0,0, 91952 59 ,,6,3,4,2,0,0,0,0, > '6,3,4,3,0,0,0,0, 1-83310281 60 28612 61 > '6,3,4,4,0,0,0,0, 46945 62 > '6,3,4,5,0,0,0,0, 65280 63 |6,3,4,6,o,o,o,o. 83617 64 {6,3,4,7,0,0,0,0, 1-83401955 65 4'6,3,4,8,o,o,o,o, 20295 66 14,6,3,4,9,0,0,0,0, Natural Numbers. i"83438554 56898 75244 93592 1-83511941 30292 48645 67000 85357 1-83603716 21993 40355 58719 77085 95453 1-83713823 32194 50567 68942 87319 1-83805615 23996 42378 60762 79148 97536 1-83915926 34318 52711 71106 89421 1-84007820 26221 44624 63028 81434 99842 1-84118252 36664 55078 73410 91827 1-84210246 28667 47090 65515 83942 1-84302370 20800 39232 Dual Logarithms. 60670957, 68 69 70 71 72 73 74 75 76 60770907, 78 79 80 81 82 83 84 85 86 60870857, 88 89 90 91 92 93 94 95 96 60970807, 98 99 6100 03 04 05 06 •1070757, 08 09 10 II 12 13 14 15 16 Dual Numbers. 5,0 I Multiples of Differences. 1825 1826 .3650 3652 5475 5478 7300 7304 9125 9130 10950 10956 12775 12782 14600 14608 16425 16434 1828 1829 3656 3658 5484 5487 7312 7316 9140 9145 10968 10974 12796 12803 14624 14632 16452 1 646 1 1831 1832 3662 3664 5493 5496 7324 7328 9155 9160 10986 10992 12817 12824 14648 14656 16479 16488 1834 1835 1 3668 3670 1 5502 5505 7336 7340 9170 9175 1 1 1004 IIOIO i 12838 12845 14672 14680 16506 16515 1837 1838 3674 3676 55" 5514 7348 7352 9185 9190 11022 1 1028 12859 12866 14696 14704 16533 16542 1840 1841 3680 3682 5520 5523 7360 7364 9200 9205 1 1040 1 1046 12880 12887 14720 14728 16560 16569 1843 3686 5529 7372 9215 1 1058 I290I 14744 16587 Dual Logarithms of powers of 2 and 10. 4,, 10 = 230258509, 4,, 10* = 921034037, L lo^ = 1611809565, , 4', ^°^ = 1842068074, ^ — 1381551056, I, Io9 = 2072326584, , 2 = 69314718, , 4 = 138629437, 4', 10^ = 460517019, X, lo^ = 1151292546 , 8 = 207944154, 4,, lo^ = 690775528, 4,, 10'' Nat. No. 1-8434 to 1-8618 D. Log. 6116.... to 6215.... D. No. ^6,4,0,0, to 16,4,9,9, [65 Natural Numbers. 1-84349348 67783 86220 1-84404659 23099 41541 59985 78431 96879 1-84515329 33697 52150 70605 89062 i-846o752i 25982 44445 62909 81375 99843 1-84718231 36703 55177 73653 92130 1-84810609 29090 47573 66058 84545 1*84902949 2T439 39931 58425 76921 95419 1-85013919 32420 50923 69428 87852 1-85106361 24872 43384 61898 80414 98^32 1-85217452 35974 54498 Dual Logarithms. 61166240, 17 18 19 20 21 22 23 24 25 6126619O, 27 28 29 30 31 32 S3 34 35 61366140, 37 38 39 40 41 42 43 44 45 61466090, 47 48 49 50 51 52 53 54 55 61566040, 57 58 59 60 61 62 65 64 65 Dual Numbers. i 6,4,0,0,0,0,0, 6,4,0,1,0,0,0, v|/6, 4,0, 2,0,0,0,0, >l'6,4,o,3,o,o,o,o v^6, 4,0,4,0,0,0,0 >l'6,4,o,5, 0,0,0,0 ,,6,4,0,6,0,0,0,0, ,,6,4,0,7,0,0,0,0 ,,6,4,0,8,0,0,0,0 >l,6,4,o,9,o,o,o,o vl,6,4, 1,0,0,0,0,0 ^6,4, 1, 1, 0,0,0,0 ,{,6,4, 1,2,0,0,0,0 |6,4,i,3»o,o,o,o i6,4>i>4>o,o,o,o \^6,4, 1,5,0,0,0,0 vj,6,4, 1,6,0,6,0,0 J,6,4, 1,7,0,0,0,0 ,,6,4,1,8,0,0,0,0 ,1,6,4,1,9,0,0,0,0 4,6,4,2,0,0,0,0,0 4,6,4,2,1,0,0,0,0 ,1,6,4,2,2,0,0,0,0, 16,4,2,3,0,0,0,0, ,1,6,4,2,4,0,0,0,0 4,6,4,2,5,0,0,0,0 \1'6,4, 2,6,0,0,0,0 j6,4,2, 7, 0,0,0,0 ,1,6,4,2,8,0,0,0,0 4,6,4,2,9,0,0,0,0 J,6,4,3, 0,0,0,0,0 4^6,4,3, i>o,o,o,o 4'6,4,3»2,o,o,o,o 4/6,4,3,3,0,0,0,0 16,4,3.4,0,0,0,0 |6,4,3.S.o,o,o,o, 4'6,4,3)6,o,o,o,o 16,4,3,7,0,0,0,0 i6,4,3,8,o,o,o,o 4'6,4,3.9>o,o,o,o i 6, 4,4, 0,0, 0,0,0 6,4,4,1,0,0,0,0 J,6, 4, 4, 2, 0,0, 0,0 4'6,4,4,3)0,o,o,o 4^6,4,4,4,0,0,0,0 > '6,4,4,5,0,0,0,0 ,,6,4,4,6,0,0,0,0 ,,6,4,4,7,0,0,0,0 ,,6,4,4,8,0,0,0,0, 16,4,4,9.0,0,0,0 Natural Numbers. 1-85272940 91467 I '85309996 28527 47060 65595 84132 1-85402670 2I2IO 39752 58213 76759 95307 1-85513857 32408 50961 69516 88073 1-85606632 25193 43671 62235 80801 99369 i"857i7939 36511 55085 73661 92238 1-85810817 29315 47898 66483 85070 1-85903659 22249 40841 59435 78031 96629 1-86015144 33746 52349 70954 89561 1-86108170 26781 45394 64009 82625 Dual Logarithms. 61665990 67 68 69 70 71 72 73 74 75 61765940, 77 78 79 80 81 82 83 84 85 61865890, 87 88 89 90 91 92 93 94 95 61965840, 97 98 99 6200 01 02 03 04 05 62065790, 07 08 09 II 12 13 14 15 Dual Numbers. 4'6, 4. 5. 0,0, 0,0,0 4/6,4,5. 1.0,0,0,0 ^6,4,5.2,0,0,0,0 \l'6,4,5.3.o,o,o,o, \l'6,4,5)4.o,o,o,o 4'6,4.5.5.o,o,o,o 4/6,4,5.6,0,0,0,0 4/6,4,5.7.0,0,0,0, 4/6,4,5.8.0,0,0,0 4/6,4.5.9.0,0,0,0, 4,6,4,6,0,0,0,0,0 4,6,4,6,1,0,0,0,0, 4,6,4,6,2,0,0,0,0, 4'6,4,6,3, 0,0,0,0 4,6,4,6,4,0,0,0,0 4/6,4,6,5,0,0,0,0 4,6,4,6,6,0,0,0,0 4,6,4,6,7,0,0,0,0 i 6,4,6,8,0,0,0,0 6,4.6,9,0,0,0,0 4/6,4,7.0.0,0,0,0 4,6,4,7,1,0,0,0,0 4,6,4,7,2,0,0,0,0 4/6,4,7.3.0,0,0,0 4/6,4,7.4.0,0,0,0 6,4,7.5.0,0,0,0^ 6,4,7.6,0,0,0,0 6,4,7.7.0,0,0,0 4/6,4,7.8,0,0,0,0 4/6,4.7.9.0.0,0,0 ,,6,4,8,0,0,0,0,0 ,,6,4,8,1,0,0,0,0 ,,6,4,8,2,0,0,0,0 >/6,4.8,3,o,o,o,o 4,6,4,8,4,0,0,0,0 4/6,4,8,5,0,0,0,0 ,,6,4,8,6,0,0,0,0 ,,6,4,8,7,0,0,0,0 ,,6,4,8,8,0,0,0,0 4,6,4,8,9,0,0,0,0 [,6,4,9,0,0,0,0,0 16,4,9,1,0,0,0,0, 16,4,9,2,0,0,0,0, 1/6,4.9.3.0.0,0,0, ^6,4,9,4,0,0,0,0, 4/6,4,9.5.0.0,0,0 ,,6,4,9,6,0,0,0,0 >/6,4.9.7. 0.0,0,0 ,,6,4,9,8,0,0,0,0, 4,6,4,9,9,0,0,0,0 Multiples of Differences. 1843 3686 5529 7372 921S 1 1058 12901 14744 16587 1844 36S8 5532 7376 9220 1 1064 12908 14752 16596 1846 1847 3692 3694 5538 5541 7384 7388 9230 9235 11076 1 1082 12922 12929 14768 14776 1 66 14 16623 1849 3698 5547 7396 924s 11 094 12943 14792 1 664 1 1850 3700 5550 7400 9250 IIIQO 12950 14800 16650 I 1845 3690 5535 7380 9225 11070 12915 14760 16(05 1848 3696 5544 7392 9240 1 1088 12936 14784 16632 1851 3702 5553 7404 9255 1 1 106 12957 1852 1853 3704 3706 5556 5559 7408 7412 6260 9265 IIII2 11118 12964 12971 14816 14824 16668 16677 1855 1856 3710 3712 5565 5568 7420 7424 9275 9280 1 1 130 1 1 136 12985 12992 14840 14848 16695 16704 1858 1859! 371b 3718 5574 5577 7432 7436 9290 9295 11148 11154 13006 13013 14864 14872 16722 16731 16659 1854, 3708 5562 7416 9270 III24 12978 14832 16686 1857 3714 5571 7428 9285 1 1 142 12999 14856 I67I3 i860 3720 5580 7440 9300 1 1 160 13020 14880 16740 I86I 3722 5583 7444 9305 1 1 166 13027 14888 16749 L 2 = 693147 18, ,„ 4 = 138629437, 4,, 8 = 207944154, Dual Logarithms of powers of 2 and 10. , 10 = 230258509, I, 10* = 921034037, , io2 = 460517019, L io5 = 1151292546, . lo^ = 690775528, 4,, lo" = 1381551056, , 10'^ = 1611809565, , 10^ = 1842068074, 10^ = 2072326584, K col Nat. No. 1-8619 to r8304 D. Log. 6216.... to 6315.... D. No. |6,5,0,0, to 4.6,5,9,9, Natural Numbers. Dual Logarithms. i'86i92S4i 1*86211460 30081 48704 67329 85956 1-86304585 23215 41847 60481 79034 97672 i'864i63i2 34954 53597 722-42 90889 I "86509538 28189 46842 65413 84070 •1-86602728 21388 40050 58714 77380 96048 1-86714718 33389 51978 70653 89330 1-86808009 26690 45373 64058 82744 1-86901432 20122 38730 57424 76120 94818 1-87013517 32218 50921 69626 88333 i'87io7042 62161273, 17 18 19 20 21 22 23 24 25 62261223, 27 28 29 30 31 32 33 34 35 '62361173, 37 38 39 40 41 42 43 44 45 62461123, 47 48 49 50 51 52 53 54 55 62561073, 57 58 59 60 61 62 ^Z 64 65 Dual Nuuibers. ,1,6,5,0,0,0,0,0,0, >!^6, 5, 0,1,0,0,0,0, 4,6,5,0,2,0,0,0,0, 4'6,S»o,3, 0,0,0,0, ^6,5, 0,4,0,0,0,0, 4.6,5,0,5,0,0,0,0, 4,6,5,0,6,0,0,0,0, 4'6,5>o,7, 0,0,0,0, 4,6,5,0,8,0,0,0,0, 4.6,5,0,9,0,0,0,0, 4,6,5,1,0,0,0,0,0, 4'6,5:i)i>o,o,o,o, 4,6,5,1,2,0,0,0,0, 4'6,5>i,3>o,o,o,o, 4'6,5>i>4> 0,0,0,0, 4'6,55i»550,o,o,o, 4,6,5,1,6,0,0,0,0, 16,551, 7>o,o,o,o, 4,6,5,1,8,0,0,0,0, 4^6,5,1,9,0,0,0,0, 4,6,5,2,0,0,0,0,0, 4,6,5,2,1,0,0,0,0, 4,6,5,2,2,0,0,0,0, 4^6, 5, 2, 3, 0,0,0,0, i6,5j2, 4,0,0,0,0, 4^6,5, 2, 5, 0,0,0,0, 4,6,5,2,6,0,0,0,0, >'6,5,2,7,o,o,o,o, ,,.6,5,2,8,0,0,0,0, 4'6,5;2, 9,0,0,0,0, 4'6,5, 3, 0,0,0,0,0, 4'6,5'3,i, 0,0,0,0, 4'6,5,3,2,o,o,o,o, 4'6,5,3'3,o,o,o,o, 4'6,5,3j4,o,o,o,o, 4'6,5,3,5»o»o,o,o, 16,5,3,6,0,0,0,0, ^6,5,3,7,0,0,0,0, 4^6,5,3,8,0,0,0,0, 4-6,5)3,9,0,0,0,0, 4^6,5,4,0,0,0,0,0, 4^6,5,4, 1,0,0,0,0, 4'6,5, 4,2, 0,0,0,0, 4.6,5,4,3,0,0,0,0, i6,5, 4,4,0,0,0,0, 4^6,5,4,5,0,0,0,0, 4^6,5,4,6,0,0,0,0, 4'6,5, 4,7,0,0,0,0, 4^6,5,4,8,0,0,0,0, 4^6,5,4,9,0,0,0,0, Natural Numbers. i"87i25669 44382 63096 81812 1-87200530 19250 37972 56696 75422 94150 1-87312795 31526 50259 68994 87731 1-87406470 25211 43954 62698 81444 1-87500108 18858 37610 56364 75120 93878 1-87612637 31398 50161 68926 87608 1-87706377 25148 43921 62695 81471 1-87800249 19029 37811 56595 75296 94084 1-87912873 31664 50457 69252 88049 1-88006848 25649 44452 Dual Logarithms. Dual Numbers. 62661023, 67 68 69 70 71 72 73 74 75 62760973, 77 78 79 80 8a 82 83 84 85 62860923, 87 88 89 90 91 92 9Z 94 95 62960873, 97 98 99 6300 01 02 03 04 05 63060823, 07 08 09 10 II 12 13 14 15 4-6,5,5,0,0,0,0,0, 4^6,5,5,1,0,0,0,0, 4^6,5,5,2,0,0,0,0, 4'6,5, 5, 3,0,0,0,0, 4'6,5,5i4,o,o,o,o, 4'6,5, 5)5, 0,0,0,0, 4^6,5,5,6,0,0,0,0, |6,5, 5,7,0,0,0,0, 4'6,5,5,8,o,o,o,o, 4'6,5)5)9>o,o,o,o, 4'6,5, 6,0,0,0,0,0, i 6,5, 6,1, 0,0,0,0, 6,5,6,2,0,0,0,0, 4^6,5,6,3,0,0,0,0, 4'6,5)6,4,o,o,o,o, 4.6,5,6,5,0,0,0,0, 4.6,5,6,6,0,0,0,0, 4'6,5, 6,7,0,0,0,0, 4.6,5,6,8,0,0,0,0, i6,5)6,9,o,o,o,o, 4^6,5,7,0,0,0,0,0, 4'6,5, 7) 1,0,0,0,0, 6,5,7,2,0,0,0,0, 6,5,7,3,0,0,0,0, 6,5,7)4,0,0,0,0, > '6,5,7,5)0)0)0,0, > '6,5,7,6,0,0,0,0, 4'6,5)7)7)0,o,o,o, 4'6,5, 7,8,0,0,0,0, 4'6,5)7)9)0,o,o,o, 4'6,5)8,o,o,o,o,o, 4,6,5,8,1,0,0,0,0, 4.6,5,8,2,0,0,0,0, 4'6,5)8,3)0,o,o,o, 4'6,5)8,4,o,o,o,o, 16,5)8,5)0,0,0,0, ,,6,5,8,6,0,0,0,0, >'6,5, 8,7, 0,0,0,0, ,,6,5,8,8,0,0,0,0, 4'6,5)8)9)0,o,o,o, 4.65„9)0,o,o,o,o, 4'6,5, 9) 1)0,0,0,0, 4^6,5)9)2,0,0,0,0, 4'6,5, 9)3)0,0,0,0, 4'6,5)9)4,o,o,o,o, 4.6,5)9)5)0,0,0,0, >. 6,5, 9,6,0,0,0,0, 4/6,5,9)7)0,0,0,0, 4.6,5,9,8,0,0,0,0, 4'6,5)9)9,o,o,o,o, Multiples of Differences I 1861 1862 2 3722 3724 3 5SH3 SS86 4 7444 7448 5 9.305 9310 6 1 1 166 11172 7 13027 13034 8 14888 14896 9 16749 i675«, 1864: 1865 3728 3730 5595 7460 9325 - ■ 5592 4j 7456 5 1 9320 6 111184 I II 190 7 13048 13055 8 14912 1I4920 9 I16776 J16785 ij 1867 2 i 3734 3 5^^ 4! 7468 5 j 9335 6 I 1202 7 1 1 3069 8 14936 9 16803 1870 3740 5610 7480 9350 1 1 220 13090 8 : 14960 9 1 1 6830 1873 3746 5619 7492 9365 1 1238 13111 14984 9)16857 1868 3736 5604 7472 9340 1 1208 13076 14944 16812 1871 3742 5613 7484 9355 111226 13097 14968 : 16839 1874 3748 5622 7596 9370 1 1244 1863 3726 5589 7452 9315 11178 1 3041 14904 16767 1866 3732 5598 7464 9330 II 196 13062 14928 16794 1869 3738 5607 7476 9345 11214 13083 14952 16821 1872 3744 5616 7488 9360 1 1232 13104 14976 116848 1875 3750 5625 7500 9375 1 1250 13118 13125 14992 15000 16866 ,16875 1876 3752 5628 7504 9380 1 1256 13132 8 15008 9 16884 1877 3754 5631 7508 9385 j 1 1262 13139 15016 '16893 i878i 375^. 5634' 7512 9390 1 1268 13146 15024 16902 1879! 1880 3758 j 3760 56371 5640 7516 7520 9395 . 9400 11274 11280 13153 13160 15032 15040 16911 16920 4., 2 = 693 147 18, 4,, ^, 4 = 138629437, 4.) 4., 8 = 207944154, ,1., Dual Logarithms of ]-)Owers of 2 and 10, 10^ = 230258509, io2 = 460517019, 921034037, 4,, 10" = 1611809565, lo^ = 690775528, 4,, lo^ = 1 15 1292546, 4/) 10^ = 1842068074, 4,, 10" = 1381551056, 4., 10^ = 2072326584, Nat. No. 1-8805 lo r8992 D. Log. 6315.... to 6414.... D. No. >1.6,6,0,0, to >^6,6,9,9, [67 Natural Dual Dual Numbers. Logarithms. Numbers. 1-88054769 63156306, v6, 6, 0,0, 0,0, 0,0, 73574 16 >,6, 6, 0,1, 0,0,0,0, 92381 17 >, 6, 6, 0,2, 0,0,0,0, i'88iiii9o 18 >'6,6,o,3, 0,0,0,0, 30001 19 16,6,0,4,0,0,0,0, 48814 20 4,6,6,0,5,0,0,0,0, 67629 21 \, 6, 6, 0,6, 0,0, 0,0, 86446 22 ,,6,6,0,7,0,0,0,0, i'88205265 23 ,,6,6,0,8,0,0,0,0, 24086 24 ^I,6, 6,0,9,0,0,0,0, 42824 63256256, 4,6,6,1,0,0,0,0,0, 61648 26 ,,6,6,1,1,0,0,0,0, 80474 27 v6, 6, 1,2,0,0,0,0, 99302 28 ,,6,6,1,3,0,0,0,0, 1-88318132 29 xl,6,6,i 4,0,0,0,0, 36964 30 ,,6,6,1,5,0,0,0,0, 55798 31 ,,6,6,1,6,0,0,0,0, 74634 32 ,,6,6,1,7,0,0,0,0, 93471 33 x,6,6,i, 8, 0,0,0,0, 1-88412310 34 ,,6,6,1,9,0,0,0,0, 31067 63356206, ,,6,6,2,0,0,0,0,0, ,,6,6,2,1,0,0,0,0, 49910 36 68755 37 ,,6,6,2,2,0,0,0,0, ,,6,6,2,3,0,0,0,0, 87602 38 1-88506451 39 ,,6,6,2,4,0,0,0,0, 25302 40 J,6,6,2,5,o,o,o,o, ,,6,6,2,6,0,0,0,0, 44155 41 63009 42 J,6,6,2, 7,0,0,0,0, ,,6,6,2,8,0,0,0,0, 81865 43 1-88600723 44 4,6,6,2,9,0,0,0,0, 19498 63456156, ,,6,6,3,0,0,0,0,0, 38360 46 ,,6,6,3,1,0,0,0,0, 57224 47 ,,6,6,3,2,0,0,0,0, 76090 48 < '6,6,3,3,0,0,0,0, ,'6,6,3,4,0,0,0,0, 94958 49 1-88713827 50 > '6,6,3,5,0,0,0,0, 32698 51 ,,6,6,3,6,0,0,0,0, ,,6,6,3,7,0,0,0,0, S1571 52 70446 53 ,,6,6,3,8,0,0,0,0, 89323 54 ,,6,6,3,9,0,0,0,0, 1-88808117 63556106, ,,6,6,4,0,0,0,0,0, 26998 56 ,1,6,6,4,1,0,0,0,0, ,,6,6,4,2,0,0,0,0, 45881 57 64766 58 16,6,4,3,0,0,0,0, 83652 59 ,,6,6,4,4,0,0,0,0, 1-88902540 60 ,,6,6,4,5,0,0,0,0, ,,6,6,4,6,0,0,0,0, 21430 61 40322 62 ,,6,6,4,7,0,0,0,0, 59216 63 ,,6,6,4,8,0,0,0,0, 78112 64 ^6,6,4,9,0,0,0,0, Natural Dual Dual Numbers. Logarithms. Numbers. 1-88996925 63656056, vl,6,6,5, 0,0,0,0,0, 1-89015825 66 ,,6,6,5,1 0,0,0,0, 34727 67 ^!/6,6,5,2 0,0,0,0, 53630 68 vl'6,6,5,3 0,0,0,0, 72535 69 >!'6,6,5,4 0,0,0,0, 91442 70 >'6,6,5,5 0,0,0,0, I-89110351 71 \1'6,6,5,6 0,0,0,0, 29262 72 > '6,6,5,7 0,0,0,0, 48175 73 ,,6,6,5,8 V '6,6,5,9 0,0,0,0, 67089 74 0,0,0,0, 85922 63756006, ,,6,6,6,0 0,0,0,0, I-89204841 76 16,6,6,1 0,0,0,0, 23761 77 ,,6,6,6,2 0,0,0,0, 42683 78 ,,6,6,6,3 0,0,0,0, 61607 79 ,{,6,6,6,4 0,0,0,0, 80533 80 ,,6,6,6,5 ,,6,6,6,6 0,0,0,0, 99461 81 0,0,0,0, i'893i839i 82 4/6,6,6,7 0,0,0,0, 37323 83 ,,6,6,6,8 0,0,0,0, 56257 84 ,,6,6,6,9 0,0,0,0, 75108 63855956, ,,6,6,7,0 0,0,0,0, 94046 86 ,,6,6,7,1 0,0,0,0, 1-89412985 87 ,,6,6,7,2 0,0,0,0, 31926 88 v'6,6,7,3 0,0,0,0, 50869 89 > '6,6,7,4 0,0,0,0, 69814 90 > '6,6,7,5 0,0,0,0, 88761 91 ,,6,6,7,6 0,0,0,0, 1-89507710 92 > '6,6,7,7 0,0,0,0, 26661 93 ,'6,6,7,8 0,0,0,0, 45614 94 4^6,6,7,9 0,0,0,0, 64483 63955906, J,6, 6,8,0 0,0,0,0, 83439 96 ,,6,6,8,1 0,0,0,0, 1-89602397 97 >, 6,6,8,2 0,0,0,0, 21357 98 ,,6,6,8,3 ,,6,6,8,4 0,0,0,0, 403^9 99 0,0,0,0, 59283 6400 ,,6,6,8,5 0,0,0,0, 78249 01 ,,6,6,8,6 0,0,0,0, 97217 02 ,,6,6,8,7 0,0,0,0, 1-89716187 03 ,,6,6,8,8 0,0,0,0, 35159 04 w6,6,8,9 0,0,0,0, 54047 64055856, ,,6,6,9,0 0,0,0,0, 73022 06 ,,6,6,9,1 0,0,0,0, 91999 07 ,,6,6,9,2 0,0,0,0, 1-89810978 08 ^ '6,6,9,3 0,0,0,0, 29959 09 ,,6,6,9,4 0,0,0,0, 48942 10 4'6,6,9,5 0,0,0,0, 67927 II ,'6,6,9,6 0,0,0,0, 86914 12 |6,6,9,7 0,0,0,0, 1-89905903 13 4,6,6,9,8 0,0,0,0, 24894 14 4.6,6,9,9 0,0,0,0, Multiples of Differences. 1880 I88I 3760 3762 5640 5643 7520 7524 9400 9405 1 1280 II286 I3I60 13167 15040 15048 16920 16929 1883 1884 3766 3768 5649 56=12 7532 7536 9415 9420 II 298 1 1 304 13181 13188 15064 15072 16947 16956 1886 1887 3772 3774 565« 5661 7544 7S4« 9430 9435 11316 1 1322 13202 13209 15088 15096 16974 16983 1889 1890 377B 3780 5667 5670 7556 7560 9445 9450 "334 11340 13223 13230 15112 15120 1 7001 17010 1892 3784 5676 7568 9460 1 1352 13244 8115136 9 1 1 7028 1893 3786 5679 7572 9465 11358 13251 15144- 17037 1895 1896 3790 3792 5685 5688 7580 7584 9475 9480 11370 11376 13265 13272 15160 15168 17055 1 7064 1882 3764 5646 7528 9410 1 1292 13174 15056 16938 IS85 3770 565s 7540 9425 II3I0 1319s 15080 16965 1888 3776 5664 7552 9440 II328 1 32 1 6 1 5 104 16992 1891 3782 5673 7564 945S 1 1 346 13237 15128 1 7019 1894 378». 5682> 7576 9470 11364 13258 15152 17046 1897 3794 5691 7588 9485 1 1382 13279 15176 17073 X89« 3796 5694 7592 9490 11388 7 j 13286 8 15184 15192 9 [17082 :i709l 1899 3798 5697 7596 9495 11394 13293 Dual Logarithms of powers of 2 and 10, |, 2 = 69314718, 4,, 10 = 230258509, 4,, 10* = 921034037, 4,, 10" = 1611809565, I, 4 = 138629437, I, io2 = 460517019, 4,, io5 = 1151292546, 4„ io« = 1842068074, ^,8- 207944154, ^, io3 = 690775528, 4', 10''' = 1381551056, 4,, io» = 2072326584, 68] Nat. No. 1-8993 to 1-9182 D. Log. 6415.... to 6514.... D. No. J^,7,0,0, to >^6,7,9,9, Natural Numbers. i"899353i7 543 1 1 73306 92303 i*9ooii302 3^ 3° 3 49306 683 1 1 87318 i"9oio6327 25252 44265 63279 82295 i'902oi3i3 20333 39355 58378 77404 96432 i"903T5377 34409 53442 • 72477 91514 i'904io553 29594 48637 67682 86729 1-90505692 24743 43795 62849 ■ 81905 I '90600963 20023 39085 58149 77215 96198 I '90715268 34340 53413 72488 91565 1*90810644 29725 48808 67893 Dual Logarithms. 64151339. 16 17 l8 19 20 21 22 23 24 64251289, 26 27 28 29 30 31 32 33 34 64351239, 36 3.7 38 39 40 41 42 43 44 64451 189, 46 47 48 49 50 51 52 53 54 64551139. 56 57 58 59 60 61 62 63 64 Dual Numbers. 4-6,7,0,0,0,0,0,0 46,7,0, 1,0,0,0,0 4-6,7,0,2,0,0,0,0 4'6,7)0,3,o,o,o,o 4-6,7,0,4,0,0,0,0 4,6,7,0,5,0,0,0,0 4-6,7,0,6,0,0,0,0 4-6,7,0,7,0,0,0,0 4-6,7,0,8,0,0,0,0 4-6,7,0,9,0,0,0,0 4-6,7,1,0,0,0,0,0 4-6,7,1,1,0,0,0,0 4-6,7,1,2,0,0,0,0, i6,7,i, 3,0,0,0,0 4-6,7,1,4,0,0,0,0 4'6,7.i>5>0)0)0.o 4,6,7,1,6,0,0,0,0, 46,7,1, 7>o>OjO,o 4,6,7,1,8,0,0,0,0 4-6,7,1,9,0,0,0,0 4,6,7,2,0,0,0,0,0 4,6,7,2,1,0,0,0,0 4,6,7,2,2,0,0,0,0 46,7,2,3,0,0,0,0 4-6,7,2,4,0,0,0,0 4,6,7,2,5,0,0,0,0 4,6,7,2,6,0,0,0,0 46,7,2,7,0,0,0,0 46,7,2,8,0,0,0,0 46,7,2,9,0,0,0,0 46,7,3,0,0,0,0,0; 46,7,3,1,0,0,0,0 46,7,3,2,0,0,0,0 46,7,3,3jO,o,o,o 46,7,3>4,o,o,o,o, 46,7,3,5,0,0,0,0 46,7,3,6,0,0,0,0 46,7,3,7,0,0,0,0 46,7,3,8,0,0,0,0 46,7,3,9,0,0,0,0 46,7,4,0,0,0,0,0 46,7,4,1,0,0,0,0 46,7,4,2,0,0,0,0 46,7,4,3,0,0,0,0 46,7,4,4,0,0,0,0, 46,7,4,5,0,0,0,0 46,7,4,6,0,0,0,0, 46,7,4,7,0,0,0,0, 46,7,4,8,0,0,0,0 46,7,4,9,0,0,0,0, Natural Numbers. 1-90905983 25074 44167 63261 82357 1-91001455 20555 39657 58761 77781 1-91115999 35111 54225 73340 92457 I-91211576 30697 49820 68859 87986 1-91307115 26246 45379 64514 83650 1-91402788 21928 41070 60128 79274 98422 1*91517572 36724 55878 75034 94192 i'9i6i335i 32512 51588 70753 89920 1-91709089 28260 47433 66608 85785 I -91804964 24144 Dual Logarithms, 64651089 66 67 68 69 70 71 72 73 74 64751039, 76 77 78 79 80 81 82 83 84 64850989, 86 87 Dual Numbers. 46,7,5,0,0,0,0,0 46,7,5,1,0,0,0,0 46,7,5,2,0,0,0,0 46,7,5,3,0,0,0,0 46,7,5,4,0,0,0,0 46,7-5-5'0,o,o,o 46,7.5.6,0.0,0,0 46,7,5-7,0,0,0,0 46,7,5,8,0,0,0,0 46,7,5,9,0,0,0,0 46,7,6,0,0,0,0,0 46,7,6,1,0,0,0,0, 46,7,6,2,0,0,0,0 46,7,6,3,0,0,0,0 46,7,6,4,0,0,0,0 46,7,6,5,0,0,0,0 46,7,6,6,0,0,0,0 46,7,6,7,0,0,0,0 46,7,6,8,0,0,0,0 46,7,6,9,0,0,0,0 46,7,7,0,0,0,0,0 46,7,7,1,0,0,0,0 46,7,7,2,0,0,0,0, 46,7,7,3,0,0,0,0 46,7,7,4,0,0,0,0 46,7,7,5>o,o,o,o > '6,7, 7, 6,0,0,0,0 46,7,7,7,0,0,0,0 46,7,7,8,0,0,0,0 46,7,7,9,0,0,0,0 ■6,7,8,0,0,0,0,0 6,7,8,1,0,0,0,0 .6,7,8,2,0,0,0,0; 6,7,8,3,0,0,0,0 46,7,8,4,0,0,0,0 [,6,7,8,5,0,0,0,0 [,6,7,8,6,0,0,0,0 i 6,7, 8,7,0,0,0,0 6,7,8,8,0,0,0,0 6,7,8,9,0,0,0,0 46,7,9,0,0,0,0,0 6,7,9,1,0,0,0,0 ■6,7,9,2,0,0,0,0 ■6,7,9,3,0,0,0,0 ■6,7,9,4,0,0,0,0, 46,7,9,5,0,0,0,0 46,7,9,6,0,0,0,0 46,7,9,7,0,0,0,0 46,7,9,8,0,0,0,0 46,7,9,9,0,0,0,0 Multiples of Differences. 1899 3798 5697 7596 9495 "394 13293 15192 1 7091 1902 3804 5706 7608 9510 U412 13314 8 jiS2i6 9I17118 1905 3810 5715 7620 9525 1 1430 1333s 15240 1 7 145 1900 3800 5700 7600 9500 1 1400 13300 15200 17100 1903 3806 5709 7612 9515 11418 13321 15224 17127 ' 1906 3812 5718 7624 9530 1 1436 13342 15248 17154 1908 1909 3816 3818 5724 5727 7632 7636 9540 954S 1 1448 "454 I33.S6 13363 15264 15272 I7I72 17181 I9II 3822 5733 7644 9555 1 1466 13377 15288 1 7199 1912 3824 5736 7648 9560 1 1472 13384 15296 17208 I9I4 i9i';l 3828 3830 5742 5745 7656 7660 9570 9575 1 1484 1 1490 13398 13405 15312 15320 , 17226 1723s 1901 3802 5703 7604 9505 1 1406 13307 15208 17109 1904 3808 5712 7616 9520 1 1424 13328 15232 I7I36 1907 3814 5721 7628 9535 1 1442 13349 15256 17163 1910 3820 5730 7640 9550 1 1460 13370 15280 17190 1913 3826 5739 7652 9565 1 1478 13391 15304 17217 1916 3832 5748 7664 9580 1 1496 13412 15328 17244 1917 3834 5751 7668 9585 1 1 502 13419 15336 17253 1918 3836 5754 7672 9590 1 1 508 13426 IS344 17262 Dual Logarithms of powers of 2 and 10. 2 = 69314718, 4> 10 = 230258509, 4, 10* = 921034037, 4 = 138629437, 8 = 207941154, 4, 10^ = 460517019, 4, 10^ = 1151292546, 4, io3 = 690775528, 4, 106 = 1381551056, 10" = 1611809565, 10^ = 1842068074, lo^ = 2072326584, Nat. No. 1'9183 to 1-9374 D. Log. 6514.... to 6613.... D. No. >I.6,8,0,0, to 16,8,9,9, [69 Natural Dual Dual Numbers. Logarithms. Numbers. 1-91834670 65146372, >I,6,8, 0,0,0,0,0,0, 53853 15 >f6, 8, 0,1, 0,0,0,0, 73038 16 ,-6,8,0,2,0,0,0,0, 92225 17 ,,6,8,0,3,0,0,0,0, I'9i9ii4i4 18 >j,6, 8,0,4,0,0,0,0, 30605 19 >16, 8,0,5, 0,0,0,0, 49798 20 X, 6, 8,0,6,0,0,0,0, 68993 21 X, 6, 8,0,7, 0,0,0,0, 88190 22 ,,6,8,0,8,0,0,0,0, i'92oo7389 23 >|^6,8,o,9, 0,0,0,0, 26505 65246322, >, 6, 8, 1, 0,0,0,0,0, 45708 25 ,r6, 8,1, 1, 0,0,0,0, 64913 26 ,,6,8,1,2,0,0,0,0, 84119 27 ,,6,8,1,3,0,0,0,0, 1-92103327 28 ,,6,8,1,4,0,0,0,0, 22537 29 ,,6,8,1,5,0,0,0,0, 41749 30 ,,6,8,1,6,0,0,0,0, 60963 31 ,,6,8,1,7,0,0,0,0, 80179 32 ,,6,8,1,8,0,0,0,0, 99397 33 ,[,6, 8, 1,9,0,0,0,0, i'922i8532 65346272, ,,6,8,2,0,0,0,0,0, 37754 35 ,,6,8,2,1,0,0,0,0,- 56978 36 ,,6,8,2,2,0,0,0,0, 76204 37 ,,6,8,2,3,0,0,0,0, 95432 38 ,,6,8,2,4,0,0,0,0, i'923i4662 39 4,6,8,2,5,0,0,0,0, 33893 40 ,,6,8,2,6,0,0,0,0, 53126 41 ,,6,8,2,7,0,0,0,0, 72361 42 ,,6,8,2,8,0,0,0,0, 91598 43 ,,6,8,2,9,0,0,0,0, 1-92410751 65446222, ,1,6,8,3,0,0,0,0,0, 29992 45 ,,6,8,3,1,0,0,0,0, 49235 46 ,,6,8,3,2,0,0,0,0, 68480 47 > '6,8,3,3,0,0,0,0, 87727 48 ,,6,8,3,4,0,0,0,0, 1-92506976 49 w6,8,3,5,o,o,o,o, 26227 50 ,,6,8,3,6,0,0,0,0, 45480 51 ,,6,8,3,7,0,0,0,0, 64735 52 ,,6,8,3,8,0,0,0,0, 83992 53 "6,8,3,9,0,0,0,0, i-925o3i62 65546172, , ,6, 8, 4,0,0,0, 0,0, 22422 55 ,,6,8,4,1,0,0,0,0, 41684 56 ,,6,8,4,2,0,0,0,0, 60948 57 "6,8,4,3,0,0,0,0, 80214 58 ,,6,8,4,4,0,0,0,0, 99482 59 ,,6,8,4,5,0,0,0,0, 1-92718752 60 ,,6,8,4,6,0,0,0,0, 38024 61 ,,6,8,4,7,0,0,0,0, 57298 62 ,,6,8,4,8,0,0,0,0, 76574 63 4,6,8,4,9,0,0,0,0, Natural Numbers. 1-92795765 I-92815045 34327 S3610 72895 92182 i*929ii47i 30762 50055 69350 88561 1-93007860 27160 46463 65768 85075 1-93104384 23694 43006 62320 81550 1-93200868 20188 39510 58834 78160 97488 1*93316818 36150 55484 74732 94069 I -93413408 32749 52092 71437 90784 1*93510133 29484 48837 68107 87464 1-93606823 26184 45547 64912 , 84278 1-93703646 23016 42388 Dual Logarithms. 65646122, 65 66 67 68 69 70 71 72 73 65746072, 75 76 77 78 79 80 81 82 83 65846022, 85 86 87 88 89 90 91 92 93 65945972, 95 96 97 99 6600 01 02 03 66045922, 05 06 07 08 09 10 II 12 13 Dual Numbers. ,8,5,0,0,0,0,0 ,8,5,1,0,0,0,0 ,8,5,2,0,0,0,0 ,8,5,3,0,0,0,0 ,8,5,4,0,0,0,0 ,8,5,5,0,0,0,0 ,8,5,6,0,0,0,0 ,8,5,7,0,0,0,0 ,8,5,8,0,0,0,0 ,8,5,9,0,0,0,0, ,8,6,0,0,0,0,0. ,8,6,1,0,0,0,0 ,8,6,2,0,0,0,0 ,8,6,3,0,0,0,0 ,8,6,4,0,0,0,0 ,8,6,5,0,0,0,0. ,8,6,6,0,0,0,0, ,8,6,7,0,0,0,0 ,8,6,8,0,0,0,0 ,8,6,9,0,0,0,0 ,8,7,0,0,0,0,0 18,7,1,0,0,0,0, ,8,7,2,0,0,0,0, .8,7,3,0,0,0,0, 18,7,4,0,0,0,0 ,8,7,5,0,0,0,0 ,8,7,6,0,0,0,0 ,8,7,7,0,0,0,0 ,8,7,8,0,0,0,0, ,8,7,9,0,0,0,0, ,8,8,0,0,0,0,0 ,8,8,1,0,0,0,0 ,8,8,2,0,0,0,0 ,8,8,3,0,0,0,0 ,8,8,4,0,0,0,0 ,8,8,5,0,0,0,0 ,8,8,6,0,0,0,0 ,8,8,7,0,0,0,0 ,8,8,8,0,0,0,0 ,8,8,9,0,0,0,0 ,8,9,0,0,0,0,0 ,8,9,1,0,0,0,0 ,8,9,2,0,0,0,0 ,8,9,3,0,0,0,0 .8,9,4,0,0,0,0 .8,9,5,0,0,0,0 ,8,9,6,0,0,0,0 ,8,9,7,0,0,0,0 ,8,9,8,0,0,0,0 ,8,9,9,0,0,0,0 Multiples of Diflferences. I9I8 1919 3«36 3«3« 5754 5757 7672 7676 9590 9595 1 1 508 11514 13426 13433 15344 I. 5352 17262 17271 1921 1922 3842 3844 5763 5766 7684 7688 9605 9610 II 526 "532 13447 1 3454 15368 15376 17289 17298 1924 IQ2S 3848 3850 5772 5775 7696 7700 9620 9625 "544 "550 13468 13475 15392 15400 17316 17325 1927 1928 3854 .S8S6 5781 5784 7708 7712 9635 9640 11562 1 1568 13489 13496 15416 I54M 17343 17352 1930 193 1 3860 3862 5790 5793 7720 7724 9650 9655 I1580 II 586 13510 13517 15440 15448 17370 17379 1933 1934 3866 3868 5799 5802 7732 7736 9665 9670 11598 1 1604 13531 13538 15464 15472 17397 17406 1920 3840 5760 7680 9600 11520 13440 15360 17280 1923 3846 5769 7692 9615 1 1538 13461 15384 17307 1926 3852 5778 7704 9630 11556 13482 15408 17334 1929 3858 5787 7716 9645 11574 13503 15432 17361 1932 3864 5796 7728 9660 11592 13524 15456 17388 193s 3870 5805 7740 9675 I16IO 13545 15480 17415 1936 3872 5808 7744 9680 11616 13552 15488 17424 1937 3874 5811 7748 9685 1 1622 13559 15496 17433 Dual Logarithms of powers of 2 and 10. |, 2 = 69314718, I, 10 = 230258509, ,1,, 10* = 921034037, I, 10^ = 1611809565, V' 4 = 138629437, L io2 = 460517019, L 10^ = 1151292546, 4', 10^ = 1842068074, 4^, 8 = 207944154, I, io3 = 690775528, I, 10^ = 1381551056, I, io5> = 2072326584, 70] Nat. No. r9375 to 1*9567 D. Log. 6614.... to 6713.... D. No. >I,6,9,0A to >^6,9,9,g, Natural Dual Dual Numbers. Logarithms. Numbers. i"93753oi7 66141405, >l,6,9,o,o,o,o,o,o, 72392 15 > '6,9,0,1,0,0,0,0, 91769 16 V, 6,9,0,2,0,0,0,0, i'938iii48 17 ,,6,9,0,3,0,0,0,0, 30529 18 ,,6,9,0,4,0,0,0,0, 49912 19 ,1,6,9,0,5,0,0,0,0, 69297 20 \!'6,9,o,6,o,o,o,o, 88684 21 ,1,6,9,0,7,0,0,0,0, 1-93908073 22 4,6,9,0,8,0,0,0,0, 27464 n 16, 9, 0,9, 0,0, 0,0, 46770 66241355, ^, 6, 9, 1, 0,0,0,0,0, 66165 25 ,,6,9,1,1,0,0,0,0, 85562 26 ,,6,9,1,2,0,0,0,0, I "94004961 27 > '6,9,1,3,0,0,0,0, 24361 28 xl,6, 9, 1,4,0,0,0,0, 43763 29 ,,6,9,1,5,0,0,0,0, 63167 30 ,,6,9,1,6,0,0,0,0, 82573 31 v6,9,i, 7, 0,0,0,0, i'94ioi98i 32 ,,6,9,1,8,0,0,0,0, 21391 33 V '6,9, 1,9,0,0,0,0, 40717 66341305, ,,6,9,2,0,0,0,0,0, 60131 35 ,,6,9,2,1,0,0,0,0, 79547 36 ,,6,9,2,2,0,0,0,0, 98965 37 \1'6, 9, 2,3,0,0,0,0, 1-94218385 38 ,1,6,9,2,4,0,0,0,0, 37807 39 > '6,9,2,5,0,0,0,0, 57231 40 ,,6,9,2,6,0,0,0,0, 76657 41 ,,6,9,2,7,0,0,0,0, 96085 42 ,.6,9,2,8,0,0,0,0, 1:94315515 43 ,,6,9,2,9,0,0,0,0, 34858 66441255, ,,6,9,3,0,0,0,0,0, 54291 45 > '6,9,3, 1,0,0,0,0, 73726 46 ,,6,9,3,2,0,0,0,0, 93163 47 >'6,9,3, 3, 0,0,0,0, i'944i26o2 48 > '6,9,3,4,0,0,0,0, 32043 49 '1'6,9,3, 5, 0,0,0,0, 51486 50 46,9,3,6,0,0,0,0, 70931 51 >'6,9,3,7,o,o,o,o. 90378 52 ,,6,9,3,8,0,0,0,0, 1-94509827 53 > '6,9,3,9,0,0,0,0, 29193 66541205, 4,6,9,4,0,0,0,0,0, 48646 55 ,,6,9,4,1,0,0,0,0, 68101 56 ,,6,9,4,2,0,0,0,0, 87558 57 v'6,9,4,3,o,o,o,o. 1-94607017 58 ,,6,9,4,4,0,0,0,0, 26478 59 > '6,9,4,5,0,0,0,0, 45941 60 ,,6,9,4,6,0,0,0,0, 65406 61 "6,9,4,7,0,0,0,0, 84873 62 ,,6,9,4,8,0,0,0,0, I "94704341 ^z |6,9,4,9,o,o,o,o. Natural Dual Dual .Numbers. Logarithms. Numbers. 1-94723722 66641155, >l'6,9,5, 0,0,0,0,0, 43194 65 \1'6,9,5, 1,0,0,0,0, 62668 66 ,,6,9,5,2,0,0,0,0, 82144 67 4^6,9,5,3,0,0,0,0, I-94801622 68 \ '6,9,5,4,0,0,0,0, 21102 69 ' '6,9,5,5,0,0,0,0, 40584 70 ,,6,9,5,6,0,0,0,0, 60068 71 > '6,9,5,7,0,0,0,0, 79554 72 |6,9,5,8,o,o,Q,o, 99042 73 > '6,9,5,9,0,0,0,0, 1-94918446 66741105, 4,6,9,6,0,0,0,0,0, 37938 75 ,,6,9,6,1,0,0,0,0, 57432 76 ,1,6,9,6,2,0,0,0,0, 76928 77 ,,6,9,6,3,0,0,0,0, 96426 78 4^6,9,6,4,0,0,0,0, i"95oi5926 79 > '6,9,6,5,0,0,0,0, 35428 80 ,,6,9,6,6,0,0,0,0, 54932 81 ,,6,9,6,7,0,0,0,0, 74437 82 ,,6,9,6,8,0,0,0,0, 93944 83 |6,9,6,9,o,o,o,o. 1-95113364 66841055, ,,6,9,7,0,0,0,0,0, 32875 85" ,,6,9,7,1,0,0,0,0, 52388 86 w6,9,7, 2, 0,0,0,0, 71903 87 > '6,9,7,3,0,0,0,0, 91421 88 \ '6,9,7,4,0,0,0,0, 1-95210940 89 > '6,9,7,5,0,0,0,0, 30461 90 ,,6,9,7,6,0,0,0,0, 49984 91 V '6,9,7,7,0,0,0,0, 69509 92 ,,6,9,7,8,0,0,0,0, 89036 9Z ,,6,9,7,9,0,0,0,0, 1*95308477 66941005, ,,6,9,8,0,0,0,0,0, 28008 95 ,,6,9,8,1,0,0,0,0, 47541 96 ,,6,9,8,2,0,0,0,0, 67076 97 ,,6,9,8,3,0,0,0,0, 86613 98 ,,6,9,8,4,0,0,0,0, 1-95406152 99 4^6,9,8,5,0,0,0,0, 25693 6700 4,6,9,8,6,0,0,0,0, 45236 01 ,,6,9,8,7,0,0,0,0, 64781 02 ,,6,9,8,8,0,0,0,0, 84327 03 4,6,9,8,9,0,0,0,0, 1-95503785 67040955, ,,6,9,9,0,0,0,0,0, 2333s 05 ,,6,9,9,1,0,0,0,0, 42887 06 ,,6,9,9,2,0,0,0,0, 62441 07 ^ '6,9,9,3,0,0,0,0, 81997 08 V '6,9,9,4,0,0,0,0, 1-95601555 09 > '6,9,9,5,0,0,0,0, 21115 10 ,,6,9,9,6,0,0,0,0, 40677 II "6,9,9,7,0,0,0,0, 60241 12 ,,6,9,9,8,0,0,0,0, 79807 13 ,,6,9,9,9,0,0,0,0, Multiples of Differences. 1955 3910 5865 7820 9775 II 730 1368s 15640 17595 Dual Logarithms of powers of 2 and 10. |, 2 = 69314718, 4,, 10 = 230258509, 4,, 10* = 921034037, 4,, io7 = 161 1809565, 4/, 4 = 138629437, I, lo^ = 460517019, ]f, io5 = 1151292546, 4', lo^ — 1842068074, 4,, 8 = 207944154, i, io3 = 690775528, 4,, io« = 1381551056, 4,, lo^ = 2072326584, 1937 1938 3874 3876 58II 5814 7748 7752 968s 9690 II 622 1 1628 13559 13566 15496 15404 17433 17442 1940 3880 5820 7760 9700 1 1 640 13580 15520 17460 I94I 3882 5823 7764 9705 1 1 646 13587 15528 17469 1943 1944 3886 3888 5829 5832 7772 7776 9715 9720 11658 II 664 I360I 13608 15544 15552 17487 17496 1 1946 1947 3892 3894 5838 5841 7784 7788 9730 9735 1 1676 1 1682 13622 13629 15568 15576 ^17514 17523 1949 1950 3898 3900 5847 5850 7796 78CXD 9745 9750 II 694 1 1 700 13643 13650 15592 15600 17541 17550 1952 1953 3904 3906 5856 5859 7808 7812 9760 9765 11712 11718 13664 13671 15616 15624 17568 17577 1939 3878 5817 7756 9695 1 1 634 13573 15512 17451 1942 3884 5826 7768 9710 II652 13594 15536 17478 1945 3890 5835 7780 9725 11670 13615 15560 17505 1948 3896 5844 7792 9740 1 1688 13636 15584 17532 1951 3902 5853 7804 9755 1 1 706 13657 15608 17559 1954 3908 5862 7816 9770 11724 13678 15632 17586 1956 3912 5868 7824 9780 11736 13692 15648 17604 Nat. No. 1-9487 to 1-9680 D. Log. 6671.... to 6770.... D. No. ^^7,0,0,0, to |7,0,9,9, [n Natural Dual Dual N umbeis. Logarithms. Numbers. 1-94871710 66717126, >I,7, 0,0,0,0,0,0,0, 91198 72 ^,7, 0,0,1, 0,0,0,0, i"949io687 73 ,,7,0,0,2,0,0,0,0, 30178 74 > ,7,0,0,3,0,0,0,0, 49671 75 y|,7,o,o,4,0,o,o,o, 69166 76 ,1,7,0,0,5,0,0,0,0, 88663 77 4,7,0,0,6,0,0,0,0, i"95oo8i62 78 ,|,7, 0,0,7, 0,0,0,0, 27663 79 ,,7,0,0,8,0,0,0,0, 47166 80 v^7, 0,0, 9, 0,0, 0,0, 66582 66817076, ,,7,0,1,0,0,0,0,0, 86089 82 ,,7,0,1,1,0,0,0,0, i"95ioS598 83 ,,7,0,1,2,0,0,0,0, 25109 84 ,,7,0,1,3,0,0,0,0, 44622 85 4,7,0,1,4,0,0,0,0, 64136 86 ,[,7,0, 1, 5,0,0,0,0, 83652 87 ,,7,0,1,6,0,0,0,0, 1-95203170 88 ,,7,0,1,7,0,0,0,0, 22690 89 ,,7,0,1,8,0,0,0,0, 42212 90 ,,7,0,1,9,0,0,0,0, 61649 66917026, ,,7,0,2,0,0,0,0,0, 81174 92 ,,7,0,2,1,0,0,0,0, 1-95300702 93 ,,7,0,2,2,0,0,0,0, 20232 94 ,,7,0,2,3,0,0,0,0, 39764 95 ,,7,0,2,4,0,0,0,0, 59298 96 ,,7,0,2,5,0,0,0,0, 78834 97 ,,7,0,2,6,0,0,0,0, 98372 98 ,,7,0,2,7,0,0,0,0, 1-95417912 99 ,.7,0,2,8,0,0,0,0, 37454 6700 ,,7,0,2,9,0,0,0,0, 56911 67016976, J,7)0?3)0)0,o,o,o, 76457 02 ,,7,0,3,1,0,0,0,0, 96005 03 ,,7,0,3,2,0,0,0,0, 1-95515555 04 > '7,0,3,3,0,0,0,0, 35107 05 ,,7,0,3,4,0,0,0,0, 54661 06 >'7>o>3,5>o,o,o,o. 74216 07 ,,7,0,3,6,0,0,0,0, 93773 08 ,,7,0,3,7,0,0,0,0, i"956i3332 09 ,,7,0,3,8,0,0,0,0, 32893 10 vl'7, 0,3, 9,0,0,0,0, 52368 67116926, 4,7,0,4,0,0,0,0,0, 71933 12 j 17,0,4,1,0,0,0,0, 1 91500 13 4,7,0,4,2,0,0,0,0, 1-95711069 14 l7,o,4,3,o>o,o,o. 30640 15 4^7)0,4,4,0,0,0,0, 50213 16 "7,0,4,5,0,0,0,0, 69788 17 ,,7,0,4,6,0,0,0,0, 89365 18 >'7,o,4,7,o,o,o,o. 1-95808944 19 ,,7,0,4,8,0,0,0,0, 28525 20 4^7,0,4,9,0,0,0,0, Natural Numbers. 1-95848020 67605 87192 I-95906781 26372 45965 65560 85157 1-96004756 24356 43868 63472 83078 1-96102686 22296 41908 61522 81138 1-96200756 20376 39912 59536 79162 98790 1-96318420 38052 57686 77322 96960 I-96416599 36152 55796 75442 95090 I "965 14740 34391 54044 73699 93356 I-96613015 32588 52251 71916 91583 1-96711252 30923 50596 70271 1-96809627 Dual Logarithms. ! Dual Numbers. 67216876, 22 23 24 25 26 27 28 29 30 67316826, 32 33 34 35 36 37 38 39 40 67416776, 42 43 44 45 46 47 48 49 50 67516726, 52 53 54 55 56 57 58 59 60 67616676, 62 63 64 65 66 67 68 69 70 Multiples of Differences, 1948 1949 3896 3898 5844 5847 7792 7796 9740 9745 1 1688 1 1 694 13636 13643 15584 15592 17532 1 7541 1 1951 1952 3902 3904 5853 S8^6 7804 7808 9755 9760 1 1 706 11712 13657 13664 15608 15616 17559 17568 1954 1955 3908 3910 5862 S86S 7816 7820 9770 9775 1 1 724 1 1 730 13678 13685 15632 15640 17586 17595 1950 3900 5850 7800 9750 1 1 700 13650 15600 17550 1953 3906 5859 7812 9765 II7I8 I367I 15624 17577 1956 3912 1957 3914 5871 7828 9785 1 1 742 13699 8115656 9 !i76i3 1958 3916 5874 7832 9790 1 1 748 13706 15664 17622 i960 I96I 3920 5880 7840 9800 1 1 760 3922 5883 7844 9805 11766 13720 15680 17640 13727 15688 17649 7824 9780 1 1 736 13692 15648 17604 1959 3918 5877 7836 9795 "754 13713 15672 1 763 1 1962 3924 1963 1964 3926 3928 S889 5892 7852 78S6 981^ 9820 1 1 778 1 1784 I374I 13748 15704 I57I2 17667 17676, 1966 1967 3932 3934 5898 5901 7864 7868 9830 9835 1 1 796 1 1802 13762 13769 15728 15736 [17694 17703 7848 9810 1 1 772 13734 15696 17658 1965 3930 5895 7860 9825 1 1 790 13755 15720 17685 1968 3936 5904 7872 9840 1 1808 13776 15744 I77U Dual Logarithms of powers of 2 and 10. j, 2 = 69314718, 4,, 10 =230258509, 4,, lo* =: 921034037, 4,, io7 = 161 1809565, |, 4 = 138629437, 4,, io2 = 460517019, 4^, io5 = 1151292546, 1 108 =- 1842068074, 4., 8 = 207944154, 4,, Io3 = 690775528, i> IO« = 1381551056, I, Io9 = 2072326584, 72] Nat, No. 1*9682 to 1-9877 D. Log. 6771.... to 6870.... D. No. W,0,0, to >^7,1,9,9, Nahiral Numbers. I "96820427 40109 59793 79479 99167 1-96918857 38549 58243 77939 97637 1-97017247 36949 56653 76359 96067 i*97ii5777 35489 55203 74919 94636 1-97214264 33985 53708 73433 93160 1-97312889 32620 52353 72088 91825 1-97411478 31219 50962 70707 90454 1-97510203 29954 49706 69461 89218 1-97608889 28650 48413 68178 87945 1-97707714 27485 47258 67033 86810 ■Dual Lojjarithms. 67712159 72 73 74 75 76 77 78 79 80 67812109, 82 83 84 85 86 87 88 89 90 67912059, 92 93 94 95 96 97 98 99 6800 68012009, 02 03 04 05 06 07 08 09 10 68111959, 12 13 14 15 16 17 18 19 20 Dual Numbers. >I'7) 1)0,0,0,0,0,0, 4,7,1,0,1,0,0,0,0, i7, 1,0,2,0,0,0,0, >i'7) 1)0,3,0,0,0,0, vl,7, 1,0,4,0,0,0,0, \I'7) 1)0,5,0,0,0,0, |7, 1,0,6,0,0,0,0, >I'7) 1)0,7)0,0,0,0, >, 7, 1, 0,8,0,0,0,0, vj,7, 1,0,9,0,0,0,0, xl,7, 1, 1,0,0,0,0,0, ,,7,1,1,1,0,0,0,0, >, 7, 1, 1, 2,0,0,0,0, ^ '7) I) 1)3)0,0,0,0, 4'7>i>i>4,o, 0,0,0, >I'7) I) 1)5)0)0,0,0, i7, 1, 1,6,0,0,0,0, 4'7) I) 1)7)0)0,0,0, >|,7, 1, 1,8,0,0,0,0, >I'7) I) 1)9)0,0,0,0, ,1,7,1,2,0,0,0,0,0, 47)1)2,1,0,0,0,0, 7,1,2,2,0,0,0,0, 7,1)2,3)0,0,0,0, 7,1,2,4,0,0,0,0, vl'7'I,2,5,0,0,0,0, J7,i, 2,6,0,0,0,0, |7) 1)2)7,0,0,0,0, 4,7,1,2,8,0,0,0,0, |7)i)2, 9,0,0,0,0, nI'7, 1)3)0,0,0,0,0, 17)1)3)1,0,0,0,0, xi'7) 1)3)2,0,0,0,0, >1'7) 1)3)3)0,0,0,0, >1'7) 1)3)4)0,0,0,0, |7) 1)3,5)0,0,0,0, \|^7) 1)3)6,0,0,0,0, >l'7)i)3)7)0,o,o,o, >'7) 1,3)8,0,0,0,0, 47)1)3)9)0,0,0,0, i 7, 1,4,0,0,0,0,0, 7,1,4,1,0,0,0,0, 47)1)4)2,0,0,0,0, 47)1)4)3)0)0,0,0, 47)1)4)4)0,0,0,0, 47)1)4)5)0)0,0,0, 47)^)4,6,0,0,0,0, 47)1)4,7)0,0,0,0, 47,1)4,8,0,0,0,0, 47)1)4)9)0,0,0,0, Natural Numbers. 1-97806498 26279 46062 65847 85634 1-97905423 25214 45007 64802 84598 1-98004304 24104 43906 63710 83516 1-98103324 23134 42946 62760 82576 I-9S202308 22128 41950 - 61774 81600 1*98301428 21258 41090 60924 80760 I-98400510 20350 40192 60036 79882 99730 I-98519580 39432 59286 79142 9891 1 I-98618771 38633 58497 78363 Dual Logarithms. 68211909, 22 98231 66 -987I810I 67 37973 68 57847 69 77722 70 23 24 25 26 27 28 29 30 683II859, 32 33 34 35 36 37 38 39 40 68411809, 42 43 44 45 46 47 48 49 50 68511759, 52 53 54 55 56 57 58 59 60 68611709, 62 63 64 65 Dual Numbers. 47)1)5)0)0,0,0,0, 47)1)5)1)0,0,0,0, 47,1)5)2)0,0,0,0, 47)1)5)3)0,0,0,0, 47)1)5)4)0,0,0,0, 47)1)5)5)0)0,0,0, 47)1)5)6)0,0,0,0, 47)1)5)7)0,0,0,0, 47)^)5)8,0,0,0,0, 47)1)5)9)0,0,0,0, 4,7,1,6,0,0,0,0,0, 47)1)6,1,0,0,0,0, 47)1)6,2,0,0,0,0, 47,1)6)3)0,0,0,0, 47,1,6,4,0,0,0,0, 47)1)6,5)0,0,0,0, 47,1,6,6,0,0,0,0, 47)1)6,7)0,0,0,0, ,,7,1,6,8,0,0,0,0, 47,1,6,9,0,0,0,0, 47)1)7)0,0,0,0,0, 47)1)7)1)0,0,0,0, 47,1)7)2)0,0,0,0, 47)1)7)3)0)0,0,0, '47)i>7)4iO,o,o,o, 47)1)7)5)0)0)0)0) 47)T)7)6,o,o,o,o, 47)1)7)7)0,0,0,0, 47)1)7)8,0,0,0,0, 47)1)7)9)0,0,0,0, /7) 1)8)0,0,0,0,0, ^7,1,8,1,0,0,0,0, ^7,1,8,2,0,0,0,0, ['7)1)8)3)0)0,0,0, 1,7,1,8,4,0,0,0,0, 47)1)8,5,0,0,0,0, 47,1)8,6,0,0,0,0, ! 7, 1,8,7,0,0,0,0, 7,1,8,8,0,0,0,0, 7,1,8,9,0,0,0,0, 4,7,1,9,0,0,0,0,0, 7)1)9)1)0)0,0,0, 7,1,9,2,0,0,0,0, 7)1)9)3)0,0,0,0, 7)1)9)4)0,0,0,0, 47)^)9)5)0)0,0,0, 4,7,1,9,6,0,0,0,0, >'7)i)9)7)0)0,o,o, ,,7,1,9,8,0,0,0,0, 47)1)9)9)0,0,0,0, Multiples of Differences. 1968 3936 5904 7872 9840 1 1808 13776 15744 17712 1971 3942 5913 7884 9855 1 1826 X3797 15768 9 17739 1974 3948 5922 7896 9870 1 1844 13818 8 15792 9I17766 1977 3954 5931 7908 9885 1 1 862 13839 15816 17793 1969 3938 5907 7876 9845 11814 13783 15752 17721 1972 3944 5916 7888 9860 1 1832 13804 15776 17748 1975 3950 5925 7900 9875 1 1 850 13825 15800 17775 1978 3956 5934 7912 9890 1 1 868 13846 15824 17802 1980 1981 3960 3962 5940 5943 7920 7924 9900 9905 11880 1 1886 13860 13867 15840 15848 17820 17829 IQ83 1984 3966 3968 5949 5952 7932 7936 9915 9920 1 1 898 11904 13881 13888 15864 15872 17847 17856 1970 3940 5910 7880 9850 1 1 820 13790 15760 17730 1973 3946 5919 7892 9865 118^8 I38II 15784 17757 ' 1976 3952 5928 7904 9880 1 1856 13832 15808 17784 1979 3958 5937 7916 9895 1 1874 13853 15832 1 781 1 1982 3964 5946 7928 9910 1 1892 13874 15856 17838 198S 3970 5955 7940 9925 11910 1389s 15880 17865 I9»6 3972 5958 7944 9930 11916 13902 8 ; 1 5888 9 17874 1987 3974 5961 7948 9935 11922 13909 15896 17883 Dual Logarithms of powers of 2 and 10. X, 2 = 69314718, I, 10 = 230258509, I, 10* = 921034037, L lo"!^ = 1611809565, >') 4 = 138629437, ^,, io2 = 460517019, ,„ io5 = 1151292546, ,„ lo^ = 1842068074, 4, 3 = 207944154, 4. 10=^ = 690775528, 4) 106 = 1381551056, 4. io» = 20723265S4, Nat. No. 1-9878 to 2'0076 D. Log. 6870.... to 6969.... D. No. >I/7,2,0,0, to i7,2,9,9, [73 Natural Dual Numbers. Logarithms. 1-98788631 68707192, 1-98808510 71 28391 72 48274 73 68159 74 88046 1-98907935 27826 47719 67614 87420 1-99007319 27220 47123 67028 86935 I-99I06845 26756 46669 66584 86407 1-99206326 26247 46170 66095 86022 i"993o595i 25882 45815 65750 85593 69007042, i'99405532 01 25473 02 45416 03 65361 04 85308 •i'995o5256 25207 45160 65115 84978 ^-99604936 24896 44858 64822 84788 i'997o4756 24726 44698 64672 75 76 77 78 79 68807142, 8i 82 83 84 85 86 87 88 89 68907092, 91 92 93 94 95 96 97 98 99 Dual Numbers. 05 06 07 08 09 69106992, II 12 13 14 15 16 17 18 19 X7, 2,0,0,0,0,0,0, ,1,7, 2, 0,1,0,0,0,0, 4,7,2,0,2,0,0,0,0, >l/7 5 2,0,3,0,0,0,0, >i'7> 2,0,4,0,0,0,0, >I'7)2, 0,5, 0,0,0,0, 7,2,0,6,0,0,0,0, 7,2,0,7,0,0,0,0, 7,2,0,8,0,0,0,0, 7,2,0,9,0,0,0,0, 7,2,1,0,0,0,0,0, 7,2,1,1,0,0,0,0, 7,2,1,2,0,0,0,0, 7,2,1,3,0,0,0,0, i7,2,i 4,0,0,0,0, i7>2,i,5,o,o,o,o, 7,2,1,6,0,0,0,0, 7,2,1,7,0,0,0,0, 7,2,1,8,0,0,0,0, 7,2,1,9,0,0,0,0, 17,2,2,0,0,0,0,0, ,,7,2,2,1,0,0,0,0, ,,7,2,2,2,0,0,0,0, >'7, 2,2, 3,0,0,0,0, 4,7,2,2,4,0,0,0,0, ['7,2,2,5,0,0,0,0, 1,7,2,2,6,0,0,0,0, ^7, 2, 2, 7,0,0,0,0, [,7,2,2,8,0,0,0,0, ^7, 2,2,9,0,0,0,0, |7, 2,3,0,0,0,0,0, >'7, 2,3,1, 0,0,0,0, >'7, 2, 3, 2,0,0,0,0, ^^7, 2, 3, 3, 0,0,0,0, >^7, 2,3,4,0,0,0,0, 7,2,3,5,0,0,0,0, 7,2,3,6,0,0,0,0, 7,2,3,7,0,0,0,0, 7,2,3,8,0,0,0,0, >^7, 2,3,9,0,0,0,0, |7, 2,4,0,0,0,0,0, >'7, 2, 4,1,0,0,0,0, ,,7,2,4,2,0,0,0,0, > '7,2,4,3,0,0,0,0, \I'7, 2,4,4,0,0,0,0, >j'7,'2,4,5, 0,0,0,0, ,,7,2,4,6,0,0,0,0, w7, 2,4,7,0,0,0,0, ,,7,2,4,8,0,0,0,0, 4^7, 2,4,9,0,0,0,0, Natural Numbers. 1-99784563 1-99804541 24521 44503 64487 84473 I -99904461 24451 44443 64437 84348 2-00004346 24346 44348 64352 84358 2-00104366 24376 44388 64402 84332 2-00204350 24370 44392 64416 84442 2-00304470 24500 44532 64566 84516 2-00404554 24594 44636 64680 84726 2-00504774 24824 44876 64930 84901 2-00604959 25019 45082 65147 85214 2-00705283 25354 45427 65502 Dual Logarithms. 69206942, 21 22 23 24 25 26 27 28 29 69306892, 31 32 33 34 35 36 37 38 39 69406842, 41 42 ■ 43 44 45 46 47 48 49 69506792, 51 52 53 54 55 56 57 58 59 69606742, 61 62 63 64 65 66 67 68 Dual Numbers. 4'7, 2,5, 0,0,0,0,0, >^7, 2, 5, 1,0,0,0,0, ,,7,2,5,2,0,0,0,0, >'7, 2, 5,3, 0,0,0,0, 4'7, 2,5,4,0,0,0,0, J7,2,5,5,o,o,o,o, 4'7, 2,5,6,0,0,0,0, xi?, 2, 5, 7, 0,0,0,0, i7, 2,5,8,0,0,0,0, 4'7, 2, 5, 9,0,0,0,0, 7,2,6,0,0,0,0,0, 7,2,6,1,0,0,0,0, 7,2,6,2,0,0,0,0, 7,2,6,3,0,0,0,0, 7,2,6,4,0,0,0,0, i 7, 2,6,5,0,0,0,0, 7,2,6,6,0,0,0,0, 4,7,2,6,7,0,0,0,0, i 7, 2,6,8,0,0,0,0, 7,2,6,9,0,0,0,0, 4^7, 2, 7, 0,0,0,0,0, >'7, 2, 7, 1, 0,0,0,0, >'7, 2, 7, 2, 0,0,0,0, >'7,2,7, 3, 0,0,0,0, 4'7, 2, 7,4,0,0,0,0, 1^7,2,7,5,0,0,0,0, 17,2,7,6,0,0,0,0, ['7,2,7,7,0,0,0,0, /7, 2, 7,8,0,0,0,0, /7,2,7, 9,0,0,0,0, ^7,2,8,0,0,0,0,0, ^7,2,8,1,0,0,0,0, ^7, 2,8,2,0,0,0,0, ^7,2,8,3,o,o,o,o, [,7,2,8,4,0,0,0,0, ^7, 2, 8,5, 0,0,0,0, ,,7,2,8,6,0,0,0,0, |7, 2,8,7,0,0,0,0, ,,7,2,8,8,0,0,0,0, 4,7,2,8,9,0,0,0,0, 4,7,2,9,0,0,0,0,0, ,,7,2,9,1,0,0,0,0, ,,7,2,9,2,0,0,0,0, \'7, 2, 9,3, 0,0,0,0, 17,2,9,4,0,0,0,0, 4'7,2, 9,5,0,0,0,0, ,,7,2,9,6,0,0,0,0, >'7, 2, 9,7, 0,0,0,0, ,,7,2,9,8,0,0,0,0, 4^7,2,9,9,0,0,0,0, Multiples of Differences. 1987 1988 3974 3976 5961 5964 7948 7952 9935 9940 1 1922 11928 13909 13916 15896 15904 17883 17892 1990 1991 3980 3982 5970 5973 7960 7964 9950 9955 1 1940 1 1946 13930 13937! 15920 15928 1 79 10 17919I 1989 3978 5967 7956 9945 1 1934 13923 15912 1 790 1 1992 39^4 5976 1993 1994 3986 3988 5979 5982 7972 7976 9965 9970 11958 11964 i3$5i 13958 15944 15952 17937 17946 1996 1997 3992 3994 5988 5991 7984 7988 9980 9985 1 1976 II 982 13972 13979 15968 15976 17964 17973 1999 3998 5997 7996 2000 4000 6000 8000 9995 lOOOO "994 12000 13993 15992 17991 14000 16000 18000 2002 4004 6006 8008 2003 4006 6009 8012 lOOlO IOOI5 I20I2 I2018 14014 16016 18018 14021 16024 18027 2005 2006 4010 4012 6015 6018 8020 8024 10025 10030 12030 12036 14035 14042 16040 16048 18045 18054 9960 1 1952 13944 '5936 17928 1995 3990 5985 7980 9975 1 1970 13965 15960 1795s 1998 3996 5994 7992 9990 11988 13986 15984 17982 2001 4002 6003 8004 10005 12006 14007 16008 18009 2004 4008 6012 8016 10020 12024 14028 16032 18036 2007 4014 6021 8028 10035 12042 14049 16056 18063 J,, 2 = 693 147 18, 4,, 4 = 138629437, 4,, 8 ^ 207944154, Dual Logarithms of powers of 2 and 10. , 10 = 230258509, 921034037, 4,, 10^ = 1611809565, , lO^ = 460517019, ,„ 10^ =: II51292546, ,„ 10^ = 1842068074, I03 = 690775528, I, I06 = I38155IO56, I, IO» = 2072726584, L 74] Nat. No. 20078 to 2-0116 D. Log. 6970 .... to 6989 .... D. No. >!.,7,3,0,0, to nI',7,3,1,9, Natural Numbers. 2-00785486 2-06805565 25646 45729 65814 85901 2*00905990 26081 46174 66269 §1^271 e'oioo637o 26471 46574 66679 86786 2"oiio6895 27006 47119 67234 Dual Logarithms. 69702225, 71 72 73 74 75 76 77 78 79 69802175, 81 82 83 84 85 86 87 88 89 Dual Numbers. \!'753»o.o,o,o,o,o t 7,3,0, 1,0,0,0,0, 7,3,0,2,0,0,0,0, |7»3>o,3.o>o»0;0 >I'7>3>0;4,o,o,o,o, >'7)3>0)6,o,o„o,o, >'7)350)7jO>0)0,o >'7;3)0>8,o,o,o,o l7>3)0»9>OjO>o,o i7j3)I.O>0;0)0)0: >'7>35 1) 1)0^0)0, o, >'7)3»i>2,o,o,o,o >'7)3.ij3>OjO>o>o h>3yh4,°>o,o,0: >I'7>3)i>5)0;0>o>o w7)3>i'6,o, 0,0,0 \I'7>3)i>8,o,o,o,o 4'7»3>i>9j0.o>o>o Multiples of Differences. 2007 2008 4014 4016 6021 6024 8028 8032 1003s 10040 12042 12048 14049 14056 16056 16064 18063 18072 2009 4018 6027 8036 10045 12054 14063 16072 18081 2010 2011 4020 6030 8040 4022 6033 8044 10050 12060 10055 12066 14070 16080 14077 16088 18090 18099 With >^,(^°*) ^^^ 4'j(2*) the dual logarithm of any natural number may be obtained from this Hmited table ; but, if it was continued to ^,(2-99161136) = ^'j ",4,7.6,0, 2,3,9, = 109581215, and a table of the descending branch from 4r,('299i6ii36) = '11'4'7'6'0'2'3'9'f = '120677293 added, then the use of ^,(2-) would not be required and >^,(^°') would seldom have to be involved. An abridgment of these complete tables are given in the " Young Dual Arithmetician.*' THE END. TABLE II, DUAL LOGARITHMS AND DUAL NUMBERS, CORRESPONDING NATURAL NUMBKRS. DESCENDING BRANCH. Nat. No. "9999 to -9901 D. Log. 1.... to '99,... D. No. '0'0'Olt to '0'0'9'9t (i; Natural Dual Dual Numbers. . Logarithms. Numbers. •99990000 'lOOOI '0'0'0'i'o'o'o'of 80001 '20001 00020000'^ 70003 '30002 00030000'^ 60006 '40002 'O'O'O'4'O'O'O'O^ ' 50010 '50003 'O'O'O'5'O'O'O'O' ' 40015 '60003 'o'o'o'6'o'o'o'o^ 30021 '70004 'o'o'o'7'o'o'o'o'* 20028 '80004 'o'o'o'8'o'o'o'o' ^ 10036 '90005 '0'0'0'9'o'o'o'of 00000 '100050 'o'o'i'o'o'o'o'of •99890010 '110051 'o'o'i'i'o'o'o'o" 80021 '120051 'o'o'l'2'o'o'o'o'^ 70033 '130052 . '0'0'1'3'0'o'o'o'j^ 60046 '140052 '0'0'1'4'o'o'o'of 50060 '150053 '0'0'1'5'0'o'o'of 40075 '160053 'o'o'i'6'o'o'o'of 30091 '170054 'o'o'i'7'o'o'o'of 20108 '180054 'o'o'i'8'o'o'o'o'^ IOI26 '190055 'o'o'l'9'o'o'o'o'' 00 1 00 '200100 '0'0'2'0'o'o'o'of •99790120 '210101 'o'o'2'l'o'o'o'o'^ 80141 '220101 '0'0'2'2'0'0'0'of 70163 '230102 'o'o'2'3'o'o'o'o' * 60186 '240102 'o'o'2'4'o'o'o'o' ^ 50210 '250103 '0'0'2'5'o'o'o'ot 40235 '260103 'o'o'2'6'o'o'o'o'^ 30261 '270104 '0'0'2'7'o'o'o'of 20288 '280104 '0'0'2'8'o'o'o'ot 10316 '290105 '0'0'2'9'0'0'o'of 00300 '300150 'o'o'3'o'o'o'o'ol^ •99690330 '310^51 '0'0'3'l'o'o'o'of 80361 '320151 'o'o'3'2'o'o'o'o" 70393 '330152 'o'o'3'3'o'o'o'o' ' 60426 '340152 '0'0'3'4'0'0'0'of 50460 '350153 'o'o'3'5'o'o'o'o>f 40495 '360153 'o'o'3'6'o'o'o'o' ^ 30531 '370154 'o'o'3'7'o'o'o'o' ^ 20568 '380154 'o'o'3'8'o'o'o'o'^ 10606 '390155 'o'o'3'9'o'o'o'o'[' 00600 '400200 0040000 ol* •99590640 '410201 'o'o'4'l'o'o'o'o'^ 80681 '420201 'o'o'4'2'o'o'o'o'^ 70723 '430202 'o'o'4'3'o'o'o'o' ^ 60766 '440202 'o'o'4'4'o'o'o'o' ^ 50810 '450203 '0'0'4'5'o'o'o'of 40855 '460203 'o'o'4'6'o'o'o'o' ' 30901 '470204 '0'0'4'7'0'0'o'ot 20948 '480204 '0'0'4'8'0'o'o'ot 10996 '490205 'o'o'4'9'o'o'o'o'j^ Natural Dual Dual Numbers. Logarithms. Numbers. ■99500999 '500250 '0'0'5'0'0'0'o'of •99491049 '510251 'o'o'5'i'o'o'o'o'^ 81 100 '520251 'o'o'5'2'o'o'o'o' ^ 71152 '530252 'o'o'5'3'o'o'o'o' ^ 61205 '540252 'o'o'5'4'o'o'o'o' ' 51259 '550253 '0'0'5'5'o'o'o'ot 41314 '560253 'o'o'5'6'o'o'o'o' ^ 31370 '570254 'o'o'5'7'o'o'o'o' ' 21427 '580254 'o'o'5'8'o'o'o'o' ^ 1 1485 '590255 'o'o'5'9'o'o'o'o' ^ 01498 '600300 'o'o'6'o'o'o'o'o'h •99391558 '6 1 030 1 '0'0'6'i'o'o'o'of 81619 '620301 'o'o'6'2'o'o'o'o' ^ 71681 '630302 'o'o'6'3'o'o'o'o' ' 61744 '640302 'o'o'6'4'o'o'o'o' ' 51808 '650303 'o'o'6'5'o'o'o'o^ 41873 '660303 '0'0'6'6'0'0'0'of 31939 '670304 'o'o'6'7'o'o'o'o' ' 22006 '680304 'o'o'6'8'o'o'o'o' ^ 12074 '690305 'o'o'6'9'o'o'o'o' ' 02097 '700350 00700000^ •99292167 '710351 'o'o'7'l'o'o'o'o'^ 82238 '720351 'o'o'7'2'o'o'o'o' ^ 72310 '730352 '0'0'7'3'o'o'o'of 62383 '740352 '0'0'7'4'o'o'o'of 52457 '750353 'o'o'7'5'o'o'o'o'|^ 42532 '760353 'o'o'7'6'o'o'o'oI^ 32608 '770354 '0'0'7'7'o'o'o'of 22685 '780354 'o'o'7'8'o'o'o'o' ' 12763 '790355 '0'0'7'9'0'o'o'of 02794 '800400 'o'o'8'o'o'o'o'o'J •99192874 '8 1 040 1 'o'o'8'i'o'o'o'o" 82955 '820401 'o'o'8'2'o'o'o'o' ' 73037 '830402 'o'o'8'3'o'o'o'o' ^ 63120 '840402 'o'o'8'4'o'o'o'o' ^ 53204 '850403 '0'0'8'5'0'oVof 43289 '860403 '0'0'8'6'o'o'o'of 33375 '870404 '0'0'8'7'0'0'0'of 23462 '880404 '0'0'8'8'0'o'o'o'r^ 13550 '890405 '0'0'8'9'0'o'o'of 03592 '900450 'o'o'9'o'o'o'o'o| •99093682 '91045 1 'o'o'9'i'o'o'o'o" 83773 '920451 'o'o'9'2'o'o'o'o'' 73865 '930452 'o'o'9'3'o'o'o'o' ^ 63958 '940452 '0'0'9'4'0'0'0'of 54052 '950453 'o'o'9'5Vo'o'o^ 44147 '960453 'o'o'9'6'o'o'o'o' ' 34243 '970454 'o'o'9'7'o'o'o'o' ' 24340 '980454 '0'0'9'8'0'0'0'a^ ' 14438 '990455 'o'o'9'9'o'o'o'o'|' Multiples of Differences. I 999 998 997 2 1998 1996 1994 3 2997 2994 2991 4 399<> 3992 3988 5 499 S 4990 4985 6 5994 S988 598a 7 (>993 6986 6979 8 7992 7984 7976 9 8991 8982 «973 I 996 995 994 2 1992 1990 198S 3 2988 2985 2982 4 39«4 3980 3976 ■; 4980 4975 4970 6 5976 5970 5964 7 6972 6965 6958 8 7968 7960 7952 9 8964 «9SS 8946 993 992 1986 1984 2979 2976 3972 3968 4965 4960 5958 5952 6951 6944 7944 793<> «937 8928 991 1982 2973 3964 4955 5946 6937 7928 8919 990 1980 2970 3960 4950 5940 6930 7920 8910 (2) Nat. No. -9900 to '9302 D. Log. '100.... to '199.... D. No. 'O'l'O'Of to '0'l'9'9t Natural Dual Dual Numbers. Logarithms. Numbers. •99000000 '1005034 'o'l'o'o'o'o'o'o'l^ •98990100 '1015035 'o'l'o'i'o'o'o'o'^ 80201 '1025035 'o'l'o'2'o'o'o'o'^ 70303 '1035036 'o'l'o'3'o'o'o'o" 60406 '1045036 '0'1'0'4'o'o'o'of 50510 '1055037 '0'1'0'5'o'o'o'oj 40615 '1065037 'o'i'o'6'o'o'o'o'^ 30721 '1075038 'o'i'o'7'o'o'o'o'^ 20828 '1085038 'o'i'o'8'o'o'o'o'* 10936 '1095039 'o'l'o'9'o'o'o'o^ OIOOO '1105084 'o'l'i'o'o'o'o'o'I^ •98891 1 10 '1115085 'o'l'i'i'o'o'o'o'* 8I22I '1125085 'o'l'l'2'o'o'o'o'' 71333 '1135086 'o'l'l'3'o'o'o'o'^ 61446 '1145086 'o'l'l'4'o'o'o'o'l' 51560 '1155087 'o'i'i'5'o'o'o'o4^ 41675 '1165087 'o'i'i'6'o'o'o'o'^ 3I79I '1175088 'o'l'l'7'o'o'o'o'^ 21908 '1185088 '0'1'1'8'0'0'0'of 12026 '1195089 '0'1'1'9'0'o'o'of 02099 '1205134 'o'l'2'o'o'o'o'o| •98792219 '1215135 'o'l'2'l'o'o'o'o'^ 82340 '1225x35 '0'1'2'2'0'0'0'of 01 23000 ol* 7.2462 '1235136 62585 '1245136 'o'i'2'4'o'o'o'o'^ 52709 '1255137 '0'1'2'5'o'o'o'o'f 42834 '1265137 'o'i'2'6'o'o'o'o'' 32960 '1275138 'o'i'2'7'o'o'o'o'^ 23087 '1285138 'o'i'2'8'o'o'o'o'^ 13215 '1295139 '0'1'2'9'0'0'o'of 03297 '1305184 'o'i'3'o'o'o'o'o4^ •98693427 '1315185 'o'l'3'l'o'o'o'o'^ 83558 '1325185 'o'i'3'2'o'o'o'o'^ 73690 '1335186 'o'i'3'3'o'o'o'o'^ 63823 '1345186 '0'1'3'4'0'0'0'of 53957 '1355187 0135000 oy 44092 '1365187 'o'i'3'6'o'o'o'o'^ 34228 '1375188 'o'i'3'7'o'o'o'o'^ 24365 '1385188 'o'i'3'8'o'o'o'o'^ 14503 '1395189 '0'1'3'9'o'o'o'of 04594 '1405234 '0'1'4'0'o'o'o'of •98594734 '1415235 'o'l'4'l'o'o'o'o" 84875 '1425235 'o'i'4'2'o'o'o'o'^ 75017 '1435236 'o'i'4'3'o'o'o'o'' 65159 '1445236 '0'1'4'4'0'0'0'of 55302 '1455237 'o'i'4'5'o'o'o'o'I^ 45446 '1465237 'o'i'4'6'o'o'o'o'' 35591 '1475238 'o*i'4'7'o'o'o'o'^ 25737 '148523S 'o'i'4'8'6'o'o'o'* 15884 '1495239 'o'i'4'9'o'o'o'o'^ Natural Dual Dual Numbers. Logarithms. Numbers. •98505989 '1505284 '0'1'5'0'o'o'o'of •98496138 '1515285 '0'1'5'l'o'o'o'of 86288 '1525285 'o'l'5'2'o'o'o'o'^ 76439 '1535286 'o'i'5'3'o'o'o'o'^ 'o'i'5'4'o'o'o'o'^ 66591 '1545286 56744 '1555287 'o'i'5'5'o'o'o'o| 'o'i'5'6'o'o'o'o^ 46898 '1565287 37053 '1575288 '0'1'5'7'0'0'o'of 27209 '1585288 '0'1'5'8'0'0'0'of 17366 '1595289 '0'1'5'9'0'0'0'o'j^ 07483 '1605334 'o'i'6'o'o'o'o'o4^ •98397642 '1615335 'o'i'6'i'o'o'o'o'* 87802 '1625335 'o'i'6'2'o'o'o'o'^ 77973 '1635336 '0'1'6'3'0'0'0'of 68135 '1645336 'o'i'6'4'o'o'o'o'^ 58298 '1655337 '0'1'6'5'0'0'0'of 48462 '1665337 'o'i'6'6'o'o'o'o'^ 38627 '1675338 'o'i'6'7'o'o'o'o'^ 28793 '1685338 'o'i'6'8'o'o'o'o" 'o'x'6'9'o'o'o'of 18960 '1695339 09076 '1705384 '0'1'7'o'o'o'o'of •98299245 '1715385 'o'i'7'i'o'o'o'o'' 89415 '1725385 'o'i'7'2'o'o'o'o'^ 79586 '1735386 'o'i'7'3'o'o'o'o''^ 69758 '1745386 '0'1'7'4'0'0'0'o'j^ 59931 '1755387 '0'1'7'5'0'0'0'of '0'1'7'6'0'0'0'of 50105 '1765387 40280 '1775388 'o'i'7'7'o'o'o'o'^ 30456 '1785388 'o'i'7'8'o'o'o'o'' 20633 '1795389 '0'1'7'9'0'0'0'of 10767 '1805434 'o'i'8'o'o'o'o'of 00946 '1815435 'o'i'8'i'o'o'o'o'^ •98191 126 '1825435 'o'i'8'2'o'o'o'o'^ 81307 '1835436 'o'i'8'3'o'o'o'o'' 71488 '1845436 '0'1'8'4'0'0'0'of 61671 '1855437 'o'i'8'5'o'o'o'ot 51855 '1865437 'o'i'8'6'o'o'o'o" 42040 '1875438 'o'i'8'7'o'o'o'o'^ 32226 '1885438 'o'i'8'8'o'o'o'o'^ 22413 '1895439 '0'1'8'9'0'0'0'of 12556 '1905484 'o'i'9'o'o'o'o'o| 02745 '1915485 'o'i'9'i'o'o'o'o'' •98092935 '1925485 'o'i'9'2'o'o'o'o^^ 83126 '1935486 'o'i'9'3'o'o'o'o" 73318 '1945486 'o'i'9'4'o'o'o'o" 63511 '1955487 'o'i'9'5'o'o'o'o4^ 53705 '1965487 'o'i'9'6'o'o'o'o" 43900 •1975488 'o'i'9'7'o'o'o'o'^ 34096 '19854S8 'o'i'9'8'o'o'o'o'' 24392 '1995489 'o'i'9'9'o'o'o'o'" Multiples of Differences. 990 1980 2970 3960 4950 5940 6930 7920 8910 9891 988 1978 I 1976 2967 I 20! 3956139 4945 5934 6923 7912 8901 987 986 9S5 1974 1972 1970 1 2961 2958 29s S 394« 3944 39-V 4935 493D 49- 5922 ,S9it) S9i 6909 6902 bh 7896 7888 7.V' 8883 8874 88( ; 984 1968 2952 3936 4920 5904 6888 7872 8856 981 1962 2943 3924 4905 5886 6867 7848 8829 1966 2949 3932 4915 5898 688 1 7864 8847 980 i960 2940 3920 4900 5880 6860 7840 8820 Nat. No. '9801 to -9704 D. Log. '201.... to '300.... D. No. '0'2'0'Ot to '0'2'9'9t (3) Natural Dual Dual Natural Dual Dual Numbers. Logarithms Numbers. Numbers. Logarithms. Numl^ers. iviuitipies 01 Differences. •98010000 '2010067 'o'2'o'o'o'o'o'o'^ •97520929 '23I03I7 'o'2'5'o'o'o'o'o'* 00199 •97990399 '2020068 '2030068 'o'2'o'l'o'o'o'o'^ '0'2'0'2'0'0'0'0'^ III77 01426 '2520318 '2530318 'o'2'5'i'o'o'o'o'* '0'2'5'2'0'0'0''0' ' I 2 980 i960 979 1958 978 1956 80600 '2040069 'o'2'o'3'o'o'o'o'' •97491676 '2540319 'o'2'5'3'o'o'o'o'* 3 2940 2937 2934 70802 '2050069 'o'2'o'4'o'o'o'o' ^ 81927 '2550319 'o'2'5'4'o'o'o'o' * 4 5 3920 4900 3916 4895 3912 4890 61C05 '2060070 'o'2'o'5'o'o'o'o>^ 72179 '2560320 'o'2'5'5'o'o'o'o'* 6 5880 5874 5868 51209 '2070070 'o'2'o'6'o'o'o'o' ^ 62432 '2570320 'o'2'5'6'o'o'o'o' ^ 7 8 9 6860 7840 8820 6853 7832 881 1 6846 7824 8802 41414 '2080071 'o'2'o'7'o'o'o'o" 52686 '2580321 'o'2'5'7'o'o'o'o'^ 31620 '2090071 'o'2'o'8'o'o'o'o'^ 42941 '2590321 'o'2'5'8'o'o'o'o'^ 21827 '2100072 'o'2'o'9'o'o'o'o' ' 33197 '2600322 'o'2'5'9'o'o'o'o'' 11990 '2110117 02100000'* 23408 '2610367 'o'2'6'o'o'o'o'o' ' I 977 976 975 02199 '2120118 'O'2'l'l'o'o'o'o'* 13666 '2620368 'o'2'6'i'o'o'o'o'* 2 1954 1952 1950 97892409 '2130118 '0'2'l'2'0'0'0'0'* 03925 '2630368 'o'2'6'2'o'o'o'o'^ 3 4 5 2931 3908 4885 2928 3904 4880 2925 3900 4875 82620 '2140119 'o'2'i'3'o'o'o'o'* •97394185 '2640369 'o'2'6'3'o'o'o'o' ' 72832 '2150119 02 14000 ol* 84445 '2650369 'o'2'6'4'o'o'o'o" 6 7 5862 6839 5856 6832 5850 6825 63045 '2160120 'o'2'i'5'o'o'o'o'* 74707 '2660370 '0'2'6'5'0'0'0'of 8 7816 7808 7800 53259 '2170120 'o'2'i'6'o'o'o'o'* 64970 '2670370 'o'2'6'6'o'o'o'o'' 9 8793 8784 8775 43474 '2180121 'o'2'i'7'o'o'o'o'* 55234 '2680371 'o'2'6'7'o'o'o'o'' 33690 '2190121 'o'2'i'8'o'o'o'o'^ 45498 '2690371 'o'2'6'8'o'o'o'o' * 23907 '2200122 '0'2'1'9'0'0'0'ot 35763 '2700372 'o'2'6'9'o'o'o'o' * I 974 973 972 14078 '2210167 '0'2'2'0'0'0'o'of 25985 '2710417 'o'2'7'o'o'o'o'o'* 2 3 1948 2922 1946 2919 1944 2916 04297 '2220168 '0'2'2'l'0'0'0'0" 16252 '2720418 'o'2'7'i'o'o'o'o'* 4 3896 3892 3888 •97794517 '2230168 'o'2'2'2'o'o'o'o'* 06520 '2730418 'o'2'7'2'o'o'o'o'^ 5 4870 4865 4860 84738 74960 '2240169 '2250169 '0'2'2'3'0'0'0'of 0224000 o'p •97296789 87059 '2740419 '2750419 'o'2'7'3'o'o'o'o' ' 'o'2'7'4'o'o'o'o'' 6 7 8 5844 6818 7792 5838 6Su 7784 5832 6804 7776 65183 '2260170 '0'2'2'5'0'0'0'of 77330 '2760420 0275000 OY 9 8766 8757 8748 55406 '2270170 '0'2'2'6'0'0'0'0'* 67602 '2770420 'o'2'7'6'o'o'o'o" 45630 '2280171 '0'2'2'7'0'0'0'0'* 57875 '2780421 'o'2'7'7'o'o'o'o'' 35855 '2290171 '0'2'2'8'0'0'0'0'* 48149 '2790421 'o'2'7'8'o'o'o'o' ■ I 971 970 26081 '2300172 '0'2'2'9'0'0'0'of 38424 '2800422 'o'2'7'9'o'o'o'o'* 2 3 1942 2913 1940 2910 16264 06492 '2310217 '2320218 '0'2'3'0'0'0'o'of '0'2'3'l'o'o'o'of 28659 18936 '2810467 '2820468 'o'2'8'o'o'o'o'o' ^ '0'2'8'ro'o'o'o" 4 5 6 3884 4855 5826 3880 4850 5820 •97696721 '2330218 0232000 o'p 09214 '2830468 'o'2'8'2'o'o'o'0'' 7 6797 6790 86951 '2340219 '0'2'3'3'0'0'0'of •97199493 '2840469 'o'2'8'3'o'o'o'o'* 8 7768 7760 77182 '2350219 '0'2'3'4'o'o'o'of 89773 '2850469 'o'2'8'4'o'o'o'o'* 9 »739 8730 67414 '2360220 '0'2'3'5'o'o'o'ot 80054 '2860470 'o'2'8'5'o'o'o'o>' 57647 '2370220 'o'2'3'6'o'o'o'of 70336 '2870470 'o'2'8'6'o'o'o'o' ' 47881 '2380221 'o'2'3'7'o'o'o'o| 60619 '2880471 'o'2'8'7'o'o'o'o'* 38116 '2390221 'o'2'3'8'o'o'o'o'* 50903 '2890471 'o'2'8'8'o'o'o'o'' 'o'2'8'9'o'o'o'o'* 28352 '2400222 '0'2'3'9'0'0'0'of 41188 '2900472 18548 '2410267 '0'2'4'0'0'0'o'of 31430 '2910517 'o'2'9'o'o'o'o'o" 08786 '2420268 'o'2'4'i'o'o'o'o'* 21717 '2920518 '0'2'9'l'o'o'o'of ■97599025 '2430268 'o'2'4'2'o'o'o'o'* 12005 '2930518 '0'2'9'2'0'0'0'ot 89265 '2440269 'o'2'4'3'o'o'o'o' ' 02294 '2940519 'o'2'9'3'o'o'o'o" 79506 '2450269 'o'2'4'4'o'o'o'o' * •97092584 '2950519 'o'2'9'4'o'o'o'o' ' 69748 '2460270 '0'2'4'5'o'o'o'ot 82875 '2960520 'o'2'9'5'o'o'o'o' ^ 59991 '2470270 '0'2'4'6'0'0'0'o'f 73167 '2970520 'o'2'9'6'o'o'o'o'' 50235 '2480271 'o'2'4'7'o'o'o'o" 63460 '2980521 'o'2'9'7'o'o'o'o'* 40480 '2490271 'o'2'4'8'o'o'o'o'^ 53754 '2990521 '0'2'9'8'0'0'0'o'f 30726 '2500272 'o'2'4'9'o'o'o'o| 44049 '3000522 'o'2'9'9'o'o'o'o" (4) Nat. No. -9702 to -9607 D. Log. '301.... to '400.... D. No. '0'3'0'Ot to '0'3'9'9f Natural Numbers. •97029900 20197 1049s 00794 •96991094 81395 71697 62000 ; 52304 42609 32870 23177 13485 03794 •96894104 84415 74727 65040 55353 •■. 45667 35937 26253 16570 06888 •96797207 87527 77848 68170 58493 48819 39101 29427 19754 10082 0041 1 •96690741 81072 71404 61737 52071 42362 32698 23035 13373 03712 •96594052 84393 74735 65078 55421 Dual Logarithms, '3015101 '3025102 '3035102 '3045103 '3055103 '3065104 '3075104 '3085105 '3095105 '3105106 '3115151 '3125152 '3135152 '3145153 '3155153 '3165154 '3175154 '318515s '3195155 '3205156 '3215201 '3225202 '3235202 '3245203 '3255203 '3265204 '3275204 '3285205 '3295205 '3305206 '3315251 '3325252 '3335252 '3345253 '3355253 '3365254 '3375254 '3385255 '3395255 '3405256 '3415301 '3425302 '3435302 '3445303 '3455303 '3465304 '3475304 '3485305 '3495305 '3505306 Dual Numbers. 0300000 Of 0301000 o'p '0'3'0'2'0'0'0'of '0'3'0'3'0'0'0'cf 0304000 cp 'o'3'o'5'o'o'o'of '0'3'0'6'0'0'0'oj 'o'3'o'7'o'o'o'o 'o'3'o'8'o'o'o'o 03090000 03100000'' 03 I 1000 O'^ 03120000'' 03 13000 ol* 0314000 o'p '0'3'1'5'o'o'o'ot '0'3'1'6'O'O'O'OJ 0317000 o'p '0'3'1'8'o'o'o'of '0'3'1'9'o'o'o'ot 0320000 o'p 032 1000 O'l* 0322000 o'p 0323000 o'p 0324000 o'p 03250000 0320000 O' 'o'3'2'7'o'o'o'o' '0'3'2'8'0'0'0'of 0329000 o'p 0330000 Of 'o'3'3'i'o'o'o'o| 0332000 of 0333000 of 0334000 Of 03350000 03300000 'o'3'3'7'o'o'o'o '0'3'3'8'0'0'0'ot '0'3'3'9'0'o'o'of 0340000 Of '0'3'4'l'o'o'o'of 'o'3'4'2'o'o'o'o'|' '0'3'4'3'0'0'0'of '0'3'4'4'0'0'0'ot 0345000 of '0'3'4'6'0'0'0'of '0'3'4'7'0'0'0'ot 'o'3'4'8'o'o'o'o| '0'3'4'9'0'0'0'ot Natural Numbers. '96545720 . 36065 26411 16758 07106 ■96497455 87805 78156 68508 58861 49^74 39529 ■ 29885 20242 10600 00959 •96391219 81680 72042 62405 52725 43090 33456 23823 14191 04560 •96294930 85301 75672 66044 56372 46746 37I2I 27497 17874 08252 •96198631 8901 1 79392 69774 60x16 50500 40885 31271 21658 12046 02435 •96092825 83215 73607 Dual Logarithms. 3515351 '3525352 '3535352 '3545353 '3555353 '3565354 '3575354 '3585355 '3595355 '3605356 '3615401 '3625402 '3635402 '3645403 '3655403 '3665404 '3675404 '3685405 '3695405 '3705406 '37T5451 '3725452 '3735452 '3745453 '3755453 '3765454 '3775454 '3785455 '3795455 '3805456 '3815501 '3825502 '3835502 '3845503 '3855503 '3865504 '3875504 '3885505 '3895505 '3905506 '3915551 '3925552 '3935552 '3945553 '3955553 '3965554 '3975554 '3985555 '3995555 '4005556 Dual Numbers. '0'3'5'0'0'o'o'oj' '0'3'5'l'o'o'o'of 'o'3'5'2'o'o'o'o" '0'3'5'3'0'o'o'of '0'3'5'4'0'0'0'of '0'3'5'5'0'0'0'of 'o'3'5'6'o'o'o'o'' '0'3'5'7'0'0'0'of '0'3'5'8'o'o'o'of '0'3'5'9'0'0'0'of '0'3'6'0'0'0'o'o'f '0'3'6'i'o'o'o'o'J' 'o'3'6'2'o'o'o'o| '0'3'6'3'0'0'0'of 'o'3'6'4'o'o'o'o'|' '0'3'6'5'0'0'0'ot '0'3'6'6'0'0'0'of '0'3'6'7'0'0'0'oj 'o'3'6'8'o'o'o'o| '0'3'6'9'0'0'0'of '0'3'7'0'0'0'o'of '0'3'7'i'o'o'o'of '0'3'7'2'0'0'0'of 'o'3'7'3'o'o'o'o| 0374000 of '0'3'7'5'o'o'o'of 'o'3 7'6'0'0'0'of '0'3'7'7'0'0'o'of '0'3'7'8'o'o'o'oj 'o'3'7'9'o'o'o'o| '0'3'8'o'o'o'o'ot '0'3'8'i'o'o'o'of 'o'3'8'2'o'o'o'o| '0'3'8'3'0'0'0'of '0'3'8'4'0'0'0'of '0'3'8'5'0'0'0'of 'o'3'8' 'o'3'°' o b'3'8'6'o'o'o'o'f 7'o'o'o'o| 'o'3'8' 'o'3'8' 'o'3'8' '0'3'8'8'0'0'0'of '9'0'0'0'oj 0390000 Of 0391000 Of 0392000 Of 0393000 of 0394000 of 0395000 Of 'o'3'9'6'o'o'o'o' ' 0397000 Of 0390000 O' 'o'3'9'9'o'o'o'o Multiples of Differences. 970 1940 2910 3880 4850 5820 6790 7760 9 1 8730 969 1938 2907 3876 4845 5814 6783 7752 8721 96S 1936 2904 3872 4840 5808 6776 7744 8712 967 1934 2901 3868 483s 5802 6769 7736 8703 964 1928 2892 3856 4820 5784 6748 7712 8676 961 1922 2883 3844 4805 5766 6727 7688 8649 966' 965 1932 1930 2898 3864 4830 5796 6762 7728 8694 963 1926 2889 3852 481 s 5778 6741 7704 8667 960 1920 2880 3840 4800 5760 6720 7680 8640 2895 3860 4825 5790 6755 7720 8685 962 1924 2886 3848 4810 5772 6734 7696 8658 I Nat. No. -9605 to 9511 D. Log. '402.... to '501.... D. No. '0'4'0'Ot to •0'4'9'9t (5) Natural Numbers. •96059601 49995 40390 30786 21183 I1581 01980 •95992380 82781 73183 63541 53945 44350 34756 25163 15570 05978 •95896387 86797 77208 67578 57991 48405 38820 29236 19653 10071 00490 •95790910 81331 71710 62133 52557 42982 33408 23835 14263 04692 •95695122 85552 75939 66371 56804 47238 37673 28109 18546 08984 ■95599423 89863 Dual Logarithms. '4020134 '4030135 '4040135 '4050136 '4060136 '4070137 '4080137 '4090138 '4100138 '4110139 '4120184 '4130185 '4140185 '4150186 '4160186 '4170187 '4180187 '4190188 '4200188 '4210189 '4220234 '4230235 '4240235 '4250236 '4260236 '4270237 '4280237 '4290238 '4300238 '4310239 '4320284 '4330285 '4340285 '4350286 '4360286 •4370287 '4380287 '4390288 '4400288 '4410289 '4420334 '4430335 '4440335 '4450336 '4460336 '4470337 '4480337 '4490338 '4500338 '4510339 Dual Numbers. o 4 O O O O O I 04010000'^ 0402000 01 0403000 o^j 0404000 01 '0'4'0'5'0'0'0'of 'o'4'o'6'o'o'o'o>^ 04070000 O4O0OOOO'* 0409000 0*1* 04 I 0000 O'^ 041 1000 O'* 041 20000^^ 'o'4'i'3'o'o'o'o'^ •0'4'1'4'0'0'0'oj '0'4'1'5'0'0'0'of 'o'4'i'6'o'o'o'o'^ 041 7000 C 'o'4'i'8'o'o'o'o'^ •0'4'1'9'0'0'0'of 04200000'' 'o'4'2'i'o'o'o'o'' '0'4'2'2'0'0'0'0'' 04230000" 04240000" 042 50000" 04200000" 042 70000" O42OOOOO" 0429000 o'p 04300000" 04310000" 04320000" 'o'4'3'3'o'o'o'o" 'o'4'3'4'o'o'o'of 04350000" 04300000" 04370000" 04300000" 0439000 o'p 0440000 01^ 04410000" 04420000" 04430000" 0444000 o'p 04450000" 04400000" 'o'4'4'7'o'o'o'o" 'o'4'4'8'o'o'o'o" 'o'4'4'9'o'o'o'o" Natural Numbers. •95580263 70705 61148 51592 42037 32483 22930 13378 03827 •95494277 - 84683 .' 75135 65587 56040 • 46494 . 36949 27405 17862 08320 •95398779 89198 79659 70121 60584 51048 41513 31979 22446 12914 03383 •95293809 84280 74752 65225 55698 46172 36647 27123 17600 08078 •95198515 88995 79476 69958 60441 50925 41410 31896 22383 12871 Dual Logarithms. '4520384 '4530385 '4540385 '4550386 '4560386 '4570387 '4580387 '4590388 '4600388 '4610389 '4620434 '4630435 '4640435 '4650436 '4660436 '4670437 '4680437 '4690438 '4700438 '4710439 '4720484 '4730485 '4740485 '4750486 '4760486 '4770487 '4780487 '4790488 '4800488 '48x0489 '4820534 '4830535 '4840535 '4850536 '4860536 '4870537 '4880537 '4890538 '4900538 '4910539 •4920584 '4930585 '4940585 •4950586 '4960586 '4970587 '4980587 '4990588 '5000588 '5010589 Dual Numbers. 0450000 O' 045 1000 O''* 0452000 O' 0453000 O' 0454000 O"* 'o'4'5'5'o'o'o'o'|^ 04500000" 'o'4'5'7'o'o'o'o' ' O450OOOO" 0459000 cp 04000000" 'o'4'6'i'o'o'o'o" •o'4'6'2'o'o'o'o" 04030000" 'o'4'6'4'o'o'o'o" '0'4'6'5'0'0'0'of 'o'4'6'6'o'o'o'o" 'o'4'6'7'o'o'o'o'' 'o'4^6^8^o^o'o'o" 0409000 oy 04700000" 047 1000 O" 047 20000" 04730000" 0474000 oy '0'4'7'5'o'o'o'of 'o'4'7'6'o'o'o'o" 04770000" 'o'4'7'8'o'o'o'o" 'o'4'7'9'o'o'o'o" '0'4'8'0'0'0'o'of 'o'4'8'i'o'o'o'o" •o'4'8'2'o'o'o'o" '0'4'8'3'0'0'0'of '0'4'8'4'0'0'0'of 'o'4'8'5'o'o'o'o" 'o'4'8'6'o'o'o'o" 'o'4'8'7'o'o'o'o" 'o'4'8'8'o'o'o'o" 'o'4'8'9'o'o'o'ot '0'4'9'o'o'o'o'of 04910000" 'o'4'9^2^o'o'o'o" 'o'4'9'3'o'o'o'o" 04940000" '0'4'9'5'0'0'0'of 'o'4'9'6'o'o'o'o' ' 'o'4'9'7'o'o'o'o" •o'4'9'8'o'o'o'o" 'o'4'9'9'o'o'o'o" Multiples if Differences. I 960 959 958 2 1920 1918 1916 .s 2880 2877 2874 4 3840 3«36 3832 S 4800 4795 4790 6 S76o 5754 5748 7 6720 6713 6706 8 7680 7672 7664 9 8640 8631 8622 I 957 956 955 2 1914 1912 1910 3 2871 2868 2861; 4 3828 3824 3820 5 47«.$ 4780 4775 6 5742 573<' 5730 7 6699 6692 668«; 8 76 S6 7648 7640 9 8613 8604 8595 I 954 953 952 2 1908 1906 1904 3 2862 28S9 28i;6 4 3816 3812 3808 5 4770 4765 4760 6 5724 5718 5712 7 6678 6671 6664 8 7632 7624 7616 9 8586 8577 8568 I 951 2 1902 3 2853 4 3804 ■; 4755 6 5706 7 6657 8 7608 9 8559 (6) Nat. No. "9509 to -9416 D. Log. '502.... to '601.... D. No. '0'5'0'Ot to '0'5'9'9t Natural Dual Du.-xl Numbers. Logarithms. Numbers. •95099005 '5025168 'o'5'o'o'o'o'o'o'l^ •0'5'o'l'o'o'o'ot 89495 '5035169 79986 '5045169 'o'5'o'2'o'o'o'o'^ 70478 '5055170 'o'5'o'3'o'o'o'o4^ 60971 '5065170 '0'5'0'4'o'o'o'of 51465 '5075171 05050000'^ 41960 '5085 17 1 'o'5'o'6'o'o'o'o'^ 32456 '5095172 'o'5'o'7'o'o'o'o'' 22953 '5105172 'o'5'o'8'o'o'o'o'^ 13451 '5115173 '0'5'0'9'0'o'o'of 03906 '5125218 'o'5'i'o'o'o'o'o| •94994406 '5135219 'o'5'i'i'o'o'o'o'^ 84907 '5145219 'o'5'i'2'o'o'o'o'^ 75409 '5155220 'o'5'i'3'o'o'o'o'^ . 6591 1 '5165220 '0'5'1'4'o'o'o'of 56414 •5175221 05150000'^ 46918 '5185221 'o'5'i'6'o'o'o'o" 37423 '5195222 'o'5'i'7'o'o'o'o'^ 27929 '5205222 'o'5'i'8'o'o'o'o^ 18436 '5215223 '0'5'1'9'0'0'0'of 08902 '5225268 05200000'^ •9489941 1 '5235269 'o'5'2'i'o'o'o'o'^ 89920 '5245269 '0'5'2'2'0'0'0'of '0'5'2'3'0'0'0'of 80431 '5255270 70943 '5265270 '0'5'2'4'0'0'0'of 61456 '5275271 '0'5'2'5'0'0'0'of 51970 '5285271 •o'5'2'6'o'o'o'o' ^ 42485 '5295272 'o'5'2'7'o'o'o'o'' 33001 '5305272 '0'5'2'8'0'0'0'of 23518 '5315273 '0'5'2'9'0'0'o'of 13993 '5325318 'o'5'3'o'o'o'o'o| 04512 '5335319 'o'5'3'i'o'o'o'o'^ ■94795032 '5345319 'o'5'3'2'o'o'o'o" 85552 '5355320 'o'5'3'3'o'o'o'o| 76073 '5365320 '0'5'3'4'0'0'0'of 66595 '5375521 '0'5'3'5'0'0'0'ot 57119 '5385321 'o'5'3'6'o'o'o'o'' 47643 '5395322 'o'5'3'7'o'o'o'o'^ 38168 '5405322 'o'5'3'8'o'o'o'o'^ 28694 '5415323 '0'5'3'9'o'o'o'o'j^ 19179 '5425368 '0'5'4'o'o'o'o'ot 09707 '5435369 'o'5'4'i'o'o'o'o| 00236 '5445369 'o'5'4'2'o'o'o'o'^ •94690766 '5455370 'o'5'4'3'o'o'o'o'^ 81297 '5465370 'o'5'4'4'o'o'o'o' ^ 71829 '5475371 'o'5'4'5'o'o'o'o1^ 62362 '5485371 '0'5'4'6'0'o'o'o'J^ 52896 '5495372 'o'5'4'7'o'o'o'o'^ 43431 '5505372 'o'5'4'8'o'o'o'o' ^ '0'5'4'9'0'0'o'of 33967 '5515373 Natural Dual Dual Numbers. Logarithms. Numbers. •94624460 '5525418 0550000 o'j^ 14998 '5535419 'o'5'5'i'o'o'o'o'^ 05537 '5545419 'o'5'5'2'o'o'o'o'* 'o'5'5'3'o'o'o'o'^ •94596076 '5555420 86616 '5565420 '0'5'5'4'0'0'0'of 77157 '5575421 '0'5'5'5'0'0'0'of 67699 '5585421 'o'5'5'6'o'o'o'o' ' 58242 '5595422 'o'5'5'7'o'o'o'o'^ 48786 '5605422 '0'5'5'8'0'0'0'of '0'5'5'9'0'0'o'of S933T^ '5615423 29836 '5625468 '0'5'6'0'0'0'o'ot 20383 '5635469 'o'5'6'i'o'o'o'o'^ 10931 '5645469 'o'5'6'2'o'o'o'o" 01480 '5655470 'o'5'6'3'o'o'o'o'^ •94492030 '5665470 'o'5'6'4'o'o'o'o' ^ 82581 '5675471 0505000 o'p 73133 '5685471 'o'5'6'6'o'o'o'o'' 63686 '5695472 '0'5'6'7'0'0'0'ot 54240 '5705472 '0'5'6'8'0'0'o'of '0'5'6'9'0'0'0'of 44795 '5715473 35306 '5725518 '0'5'7'0'0'0'o'of 25862 '5735519 05710000'^ 16419 '5745519 'o'5'7'2'o'o'o'o'^ 06977 '5755520 'o'5'7'3'o'o'o''of •94397536 '5765520 0574000 o'p 88096 '5775521 05750000'' '0'5'7'6'o'o'o'of 78657 '5785521 69219 '5795522 'o'5'7'7'o'o'o'o'l^ 59782 '5805522 'o'5'7'8'o'o'o'o" 50346 '5815523 '0'5'7'9'0'0'0'of 40870 '5825568 '0'5'8'0'0'0'o'ot 31436 '5835569 'o'5'8'i'o'o'o'o| 22003 '5845569 'o'5'8'2'o'o'o'o' ' 12571 '5855570 'o'5'8'3'o'o'o'o'' 03140 '5865570 '0'5'8'4'0'0'0'of •94293710 '5875571 '0'5'8'5'0'0'0'of 84281 '5^85571 'o'5'8'6'o'o'o'o'' 74853 '5895572 '0'5'8'7'0'0'0'of 65426 '5905572 '0'5'8'8'0'0'0'of 55999 '5915573 •o'5'8'9'o'o'o'o'^ 46530 '5925618 05900000" 'o'5'9'i'o'o'o'o" 37105 '5935619 27681 '5945619 'o'5'9'2'o'o'o'o" 18258 '5955620 'o'5'9'3'o'o'o'o' ' 08836 '5965620 '0'5'9'4'0'0'0'of ■94199415 '5975621 '0'5'9'5'0'0'0'o'f 89995 '5985621 'o'5'9'6'o'o'o'o' ' 80576 '5995622 '0'5'9'7'0'0'0'of 71158 '6005622 'o'5'9'8'o'o'o'o' ' 'o'5'9'9'o'o'o'o| 61741 '6015623 Multiples of Differences. 950 1900 2850 3800 4750 6 ! 5700 7 I 6650 8 I 7600 9 8550 1 947 2 1894 3 ! 2841 413788 5 4735 6 5682 7 j 6629 8 I 7576 9 • 8523 949 1898 2847 3796 4745 94S 1896 2844 3792 4740 5694 i S(>^>i 6643 ; 6636 7592 8541 :75i^4 8532 946 945 1892 1890 2838 2i^'; 3784 3780 4730 4725 Sb76 S670 6622 661 <; 7568 7560 8514 8505 944 1888 2832 3776 4720 5664 6608 7552 8496 941 1882 2823 3764 4705 5646 6587 7528 8469 ' 943 1886 2829 3772 4715 5658 6601 7544 8487 942 18S4 2826 3768 4710 5652 6594 7536 8478 Nat. No. -9414 to '9322 D. Log. '603.... to '702.... D. No. '0'600t to '0'6'9'9t (7) Natural Dual Dual Numbers. Logarithms. Numbers. •94148015 '6030202 'o'6'o'o'o'o'o'oi 38600 '6040203 'o'6'o'i'o'o'o'o 29186 '6050203 'o'6'o'2'o'o'o'o' ^ 19773 '6060204 'o'6'o'3'o'o'o'o'^ IO361 '6070204 'o'6'o'4'o'o'o'o' ^ 00950 '6080205 '0'6'0'5'0'0'0'of •94091540 '6090205 'o'6'o'6'o'o'o'o'^ 82131 '6100206 '0'6'0'7'0'0'0'of 72723 '6110206 'o'6'o'8'o'o'o'o'^ 63316 '6120207 'o'6'o'9'o'o'o'o'^ . 53867 '6130252 'o'6'i'o'o'o'o'o'^ 44462 '6140253 'o'6'i'i'o'o'o'o'^ 35058 '6150253 'o'6'i'2'o'o'o'o'^ 25654 '6160254 'o'6'i'3'o'o'o'o'^ 16251 '6170254 'o'6'i'4'o'o'o'o'^ 06849 '6180255 '0'6'1'5'0'oVo'^ •93997448 '6190255 'o'6'i'6'o'o'o'o'' 88048 '6200256 'o'6'i'7'o'o'o'o'^ 78649 '6210256 'o'6'i'8'o'o'o'o'^ 69251 '6220257 'o'6:i'9'o'o'o'o'^ 59813 '6230302 '0'6'2'0'0'0'o'of 50417 '6240303 'o'6'2'i'o'o'o'o'^ 41022 '6250303 'o'6'2'2'o'o'o'o'^ 31628 '6260304 'o'6'2'3'o'o'o'o' ' 22235 '6270304 'o'6'2'4'o'o'o'o' ^ 12843 '6280305 'o'6'2'5'o'o'o'o' ^ 03452 '6290305 'o'6'2'6'o'o'o'o'* •93894062 '6300306 'o'6'2'7'o'o'o'o'^ 'o'6'2'8'o'o'o'o'' 84673 '6310306 75285 '6320307 'o'6'2'9'o'o'o'o'^ 65853 '6330352 'o'6'3'o'o'o'o'o'' 56466 '6340353 'o'6'3'i'o'o'o'o'^ 47080 '6350353 'o'6'3'2'o'o'o'o'^ 37695 '6360354 'o'6'3'3'o'o'o'o'' 28311 '6370354 'o'6'3'4'o'o'o'o- 18928 '6380355 'o'6'3'5'o'o'o'o' ' 09546 '6390355 'o'6'3'6'o'o'o'o' ^ 00165 '6400356 'o'6'3'7'o'o'o'o'^ ■93790785 '6410356 '0'6'3'8'0'0'o'of 'o'6'3'9'o'o'o'o'' 81405 '6420357 71987 '6430402 'o'6'4'o'o'o'o'o'^ 62610 '6440403 'o'6'4'i'o'o'o'o'^ 53234 '6450403 'o'6'4'2'o'o'o'o' ^ 43859 '6460404 'o'6'4'3'o'o'o'o' ' 34485 '6470404 'o'6'4'4'o'o'o'o'^ 25112 '6480405 '0'6'4's'o'o'o'of 15739 '6490405 'o'6'4'6'o'o'o'o'^ 06367 '6500406 'o'6'4'7'o'o'o'o'^ •93696996 '6510406 'o'6'4'8'o'o'o'o' ' 87626 '6520407 'o'6'4'9'o'o'o'o'' Natural Numbers. •93678215 68847 59480 50114 40749 31385 22022 12660 03299 ■93593939 84537 ■ 75179 65821 56464 47108 37753 28399 19046 09694 00343 ■93490953 81604 72256 62909 J 53563 44218 34874 25531 16188 06846 •93397462 88122 78783 . 69445 60108 50772 41437 32103 22770 13438 04064 •93294734 85405 76076 66748 57421 48095 38770 29446 20123 Dual Logarithms. '6530452 '6540453 '6550453 '6560454 '6570454 '6580455 '6590455 '6600456 '6610456 '6620457 '6630502 '6640503 '6650503 '6660504 '6670504 '6680505 '6690505 '6700506 '6710506 '6720507 '6730552 '6740553 '6750553 '6760554 '6770554 '6780555 '6790555 '6800556 '6810556 '6820557 '6830602 '6840603 '6850603 '6860604 '6870604 '6880605 '6890605 '6900606 '6910606 '6920607 '6930652 '6940653 '6950653 '6960654 '6970654 '6980655 '6990655 '7000656 '7010656 '7020657 Dual Numbers. '0'6'5'0'0'o'o'of '0'6'5'i'o'o'o'o'^ 'o'6'5'2'o'o'o'o'^ 'o'6'5'3'o'o'o'o'^ '0'6'5'4'0'o'o'of 'o'6'5'5"'o'o'o'o>| '0'6'5'6'o'o'o'o'j 'o'6'5'7'o'o'o'o'^ 'o'6'5'8'o'o'o'o'^ 'o'6'5'9'o'o'o'o'| '0'6'6'0'0'0'o'o'f '0'6'6'i'o'o'o'of '0'6'6'2'0'0'0'of 'o'6'6'3'o'o'o'o' o'o'o'o4^ b'o'o'of 'o'6'6'4'' '0'6'6'5'0'0'0'of '0'6'6'6'0'0'0'of 'o'6'6'7'o'o'o'o 'o'6'6'8'o'o'o'o '0'6'6'9'0'0'0'a '0'6'7'0'o'o'o'of '0'6'7'i'o'o'o'of 'o'6'7'2'o'o'o'o4^ '0'6'7'3'0'0'0'of '0'6'7'4'o'o'o'of '0'6'7'5'0'0'0'of '0'6'7'6'0'0'0'of 'o'6'7'7'o'o'o'o'^ 'o'6'7'8'o'o'o'o'^ 'o'6'7'9'o'o'o'o'I^ '0'6'8'0'0'0'o'o'f 'o'6'8'i'o'o'o'o'' '0'6'8'2'0'0'0'of 'o'6'8'3'o'o'o'o'^ 'o'6'8'4'o'o'o'o' ^ '0'6'8'5'0'0'0'of 'o'6'8'6'o'o'o'o'^ 'o'6'8'7'o'o'o'o| '0'6'8'8'0'0'0'o'j^ 'o'6'8'9'o'o'o'o'^ 'o'6'9'o'o'o'o'o 'o'6'9'i'o'o'o'o 'o'6'9'-2'o'o'o'o '0'6'9'3'0'0'0'of '0'6'9'4'0'0'o'ot '0'6'9'5'0'0'0'ot '0'6'9'6'0'0'o'of •o'6'9'7'o'o'o'o^ 'o'6'9'8'o'o'o'o'^ 'o'6'9'9'o'o'o'o'^ Multiples of Differences. 941 940 1882 1880 2823 2820 3764 3760 4705 4700 S646 5640 6,S«7 6580 7=128 7S20 8469 8460 938 1876 2814 3752 4690 5628 6566 7504 8442 93=; 934 1870 1868 2805 2802 3740 3736 4(575 4670 5610 S604 6545 6.S3« 7480 7472 «4i5 8406 939 1878 2817 3756 4695 5634 6573 7513 8451 937' 936 1874 1872 2811 2808 3748 3744 4685 4680 5622 5616 6559 6553 7496 7488 8433 I 8424 933 1866 2799 3732 4665 5598 6531 7464 8397 932 1864 2796 3728 4660 5592 6524 7456 8388 (8) Nat. No. '9320 to '9228 D. Log. 703.... to '802.... D. No; 'OTO'Ot to 'OTg'gf Natural Dual Dual Niunbers. Logarithms. Numbers. •93206535 '7035235 '0'7'0'0'0'o'o'of •93197214 '7045236 'o'7'o'l'o'o'o'o'I* 87894 '7055236 'o'7'o'2'o'o'o'o'* 78575 '7065237 'o'7'o'3'o'o'o'o| '0'7'0'4'0'o'o'of 69257 '7075237 59940 '7085238 '0'7'0'5'o'o'o'oj^ 50624 '7095238 '0'7'0'6'0'0'0'of 41309 '7105239 'o'7'o'7'o'o'o'o'^ 31995 '7115239 'o'7'o'8'o'o'o'o'^ 22682 '7125240 '0'7'0'9'o'o'o'o'j^ 13329 '7135285 '0'7'i'o'o'o'o'of 04018 '7145286 'o'7'i'i'o'o'o'o" •93094708 '7155286 'o'7'i'2'o'o'o'o" 85399 '7165287 'o'7'i'3'o'o'o'o" 'o'7'i'4'o'o'o'o'^ 76090 '7175287 66782 '7185288 '0'7'1'5'o'o'o'of 57475 '7195288 '0'7'1'6'o'o'o'ot 48169 '7205289 'o'7'i'7'o'o'o'o'^ 38864 '7215289 'o'7'i'8'o'o'o'o'^ 29560 '7225290 'o'7'i'9'o'o'o'o'^ 20215 '7235335 'o'7'2'o'o'o'o'o'I^ 10913 '7245336 'o'7'2'i'o'o'o'o" 01612 '7255336 'o'7'2'2'o'o'o'o" •92992312 '7265337 'o'7'2'3'o'o'o'o' ^ 83013 '7275337 'o'7'2'4'o'o'o'o' ' 73715 '7285338 '0'7'2'5'o'o'o'of 64418 '7295338 'o'7'2'6'o'o'o'o'|^ 5SI22 '7305339 'o'7'2'7'o'o'o'o'* 45826 '7315339 '0'7'2'8'o'o'o'of 36531 '7325340 'o'7'2'9'o'o'o'o'I^ 27195 '7335385 '0'7'3'0'0'0'o'of 17902 '7345386 'o'7'3'i'o'o'o'o" 08610 '7355386 'o'7'3'2'o'o'o'o" •92899319 '7365387 'o'7'3'3'o'o'o'o" 90029 '7375387 'o'7'3'4'o'o'o'o'|^ 80740 '7385388 'o'7'3'5'o'o'o'o4^ 'o'7'3'6'o'o'o'o' ^ 71452 '7395388 62165 '7405389 'o'7'3'7'o'o'o'o'|^ 52879 '7415389 'o'7'3'8'o'o'o'o' ' 43594 '7425390 'o'7'3'9'o'o'o'o' ' 34268 '7435435 '0'7'4'0'0'0'o'oj^ 24985 '7445436 'o'7'4'i'o'o'o'o'^ 15703 '7455436 'o'7'4'2'o'o'o'o'^ 'o'7'4'3'o'o'o'o' ^ 06421 '7465437 •92797140 '7475437 'o'7'4'4'o'o'o'o'^ 87860 '7485438 '0'7'4'5'0'o'o'of 78581 '7495438 'o'7'4'6'o'o'o'o' ' 69303 '7505439 'o'7'4'7'o'o'o'o' ^ 60026 '7515439 'o'7'4'8'o'o'o'o' ^ 50749 '7525440 '0'7'4'9'0'0'0'o't^ Natural Dual Dual Numbers. Logarithms. Numbers. •92741434 '7535485 '0'7'5'0'0'0'o'of 32160 '7545486 'o'7'5'i'o'o'o'o'^ 22887 '7555486 'o'7'5'2'o'o'o'o'^ 13615 '7565487 'o'7'5'3'o'o'o'o' ' 04344 '7575487 '0'7'5'4'0'0'0'of •92695074 '7585488 '0'7'5'5'0'0'0'o'f 85804 '7595488 'o'7'5'6'o'o'o'o'^ 76535 '7605489 'o'7'5'7'o'o'o'o'' 67267 '7615489 'o'7'5'8'o'o'o'o' ' 58000 '7625490 '0'7'5'9'0'0'0'of • 48692 '7635535 '0'7'6'0'0'0'o'o't^ 39427 '7645536 'o'7'6'i'o'o'o'o'^ 30163 '7655536 'o'7'6'2'o'o'o'o' ^ 20900 '7665537 'o'7'6'3'o'o'o'o" I1637 '7675537 '0'7'6'4'0'o'o'o'j^ 02376 '7685538 'o.'7'6'5'o'o'o'of '0'7'6'6'0'0'0'ot •92593116 '7695538 83857 '7705539 'o'7'6'7'o'o'o'o' ' 74599 '7715539 'o'7'6'8'o'o'o'o'^ 65342 '7725540 'o'7'6'9'o'o'o'o' ' ■ 56043 '7735585 07700000^^ 'o'7'7'i'o'o'o'o'^ ■ 46787 '7745586 37532 '7755586 'o'7'7'2'o'o'o'o' ^ 'o'7'7'3'o'o'o'o'' 28278 '7765587 19025 '7775587 'o'7'7'4'o'o'o'o'I^ 09773 '7785588 '0'7'7'5'0'0'0'of 00522 '7795588 'o'7'7'6'o'o'o'o ' •92491272 '7805589 'o'7'7'7'o'o'o'o' ' 82023 '7815589 'o'7'7'8'o'o'o'o' ^ 72775 '7825590 'o'7'7'9'o'o'o'o' ^ 63487 '7835635 '0'7'8'0'0'0'o'of 54241 '7845636 'o'7'8'i'o'o'o'o'" 44996 '7855636 'o'7'8'2'o'o'o'o' ' 35752 '7865637 'o'7'8'3'o'o'o'o' ^ 26508 '7875637 'o'7'8'4'o'o'o'o" 17265 '7885638 'o'7'8'5'o'o'o'o4^ 08023 '7895638 'o'7'8'6'o'o'o'o' ' •92398782 '7905639 'o'7'8'7'o'o'o'o' ^ 89542 '7915639 'o'7'8'8'o'o'o'o1^ 80303 '7925640 '0'7'8'9'0'0'0'of 71024 '7935685 '0'7'9'0'0'o'o'o'j^ 'o'7'9'i'o'o'o'o" 61787 '7945686 52551 '7955686 'o'7'9'2'o'o'o'o' ^ 43316 '7965687 'o'7'9'3'o'o'o'o' ' 34082 '7975687 '0'7'9'4'o'o'o'o'j^ 24849 '7985688 ■ '0'7'9'5'0'0'0'of 15617 '7995688 'o'7'9'6'o'o'o'o^' 06385 '8005689 'o*7'9'7'o'o'o'o' ^ •92297154 '8015689 'o'7'9'8'o'o'o'o' ' 87924 '8025690 'o'7'9'9'o'o'o'o'|' Multiples of Differences. 932 1864 2796 3728 4660 SS92 6524 7456 931 1862 2793 3724 4655 5586 6517 7448 8379 930 i860 2790 3720 4650 5580 6510 7440 8370 929 928 927 i8!;8 i8s6 18^4 2787 2784 2781 3716 3712 3708 4^4,'; 4640 4f>35 S.S74 .SS68 SS' 78161 '9895705 'o'9'8'5'o'o'o'o" 'o'9'8'6'o'o'o'o' ' 23311 '9405455 'o'9'3'6'o'o'o'o'' 69103 '9905705 14209 '9415456 'o'9'3'7'o'o'o'o' ' 60046 '9915706 'o'9'8'7'o'o'o'o'^ 05108 '9425456 'o'9'3'8'o'o'o'o' ^ 50990 '9925706 'o'9'8'8'o'o'o'o'' •90996007 '9435457 '0'9'3'9'o'o'o'of 41935 '9935707 '0'9'8'9'0'0'0'of 86866 '9445502 'o'9'4'o'o'o'o'o" 32841 '9945752 'o'9'9'o'o'o'o'o" 77767 '9455503 'o'9'4'i'o'o'o'o'' 23788 '9955753 'o'9'9'i'o'o'o'o'' ' 68669 '9465503 'o'9'4'2'o'o'o'o'^ 14736 '9965753 'o'9'9'2'o'o'o'o" 59572 '9475504 'o'9'4'3'o'o'o'o' ^ 05685 '9975754 'o'9'9'3'o'o'o'o'* 50476 '9485504 '0'9'4'4'o'o'o'of •90496634 '9985754 'o'9'9'4'o'o'o'o' 41381 '9495505 'o'9'4'5'o'o'o'o'* 87584 '9995755 '0'9'9'5'0'0'0'of 32287 '9505505 'o'9'4'6'o'o'o'o' ^ 78535 '10005755 'o'9'9'6'o'o'o'o' 23194 '9515506 'o'9'4'7'o'o'o'o'^ 69487 '10015756 •o'9'9'7'o'o'o'o' 14102 '9525506 'o'9'4'8'o'o'o'o4^ 60440 '10025756 'o'9'9'8'o'o'o'o' 1 05011 '9535507 '0'9'4'9'0'0'0'of 51394 ■10035757 'o'9'9'9'o'o'o'o' Nat. No. -9000 to '8911 D. Log. '1053.... to 1152.... D. No. TO'O'Ot to T0'9'9t (") Natural Dual Dual 1 Numbers. Logarithms. Numbers. •90000000 '10536052 'I'o'o'o'o'o'o'o t •89991000 '10546053 I I o'p 82001 '10556053 '1'0'0'2'o'o'o'of 73003 '10566054 '1'0'0'3'o'o'o'cf 64006 '10576054 '1'0'0'4'o'o'o'of 55010 '10586055 10050000" 46014 '10596055 'i'o'o'6'o'o'o'of 37019 '10606056 'i'o'o'7'o'o'o'of 28025 '10616056 'i'o'o'8'o'o'o'of 19032 '10626057 10090000'* 1 0000 '10636102 •I'o'i'o'o'o'o'of 01009 '10646103 'I'o'l'i'o'o'o'of •89892019 '10656103 'l'o'l'2'o'o'o'o'^ 83030 '10666104 '1'0'1'3'0'o'o'of 74042 '10676104 10140000'P 65055 '10686105 'i'o'i'5'.o'o'o'ot 56068 '10696105 'i'o'i'6'o'o'o'of 47082 '10706106 'l'o'l'7'o'o'o'o'' .38097 '10716106 'i'o'i'8'o'o'o'of 29113 '10726107 '1'0'1'9'0'o'o'of 20090 '10736152 'l'o'2'o'o'o-oV i 1 1 108 '10746153 102 1000 0' i 02127 '10756153 'l'0'2'2'0'0'0'0' V •89793147 '10766154 'i'o'2'3'o'o'o'o' V 84168 '10776154 'i'o'2'4'o'o'o'o' V 75190 '10786155 '1'0'2'5'0'0'0'oi V 66212 '10796155 10200000' k 57235 '10806156 'i'o'2'7'o'o'o'o' k 48259 '10816156 I0200000' I 39284 '10826157 'i'o'2'9'o'o'o'o' k 30270 '10836202 '1'0'3'0'0'0'o'of 21297 '10846203 'i'o'3'i'o'o'o'o'^ 12325 '10856203 'i'o'3'2'o'o'o'o'^ 03354 '10866204 'i'o'3'3'o'o'o'o'^ •89694384 '10876204 'i'o'3'4'o'o'o'o'} 854IS '10886205 'i'o'3'5'o'o'o'o'| k 76446 '10896205 'i'o'3'6'o'o'o'o' i 67478 '10906206 'i'o'3'7'o'o'o'o' \ 58511 '10916206 10300000' i 49545 '10926207 'i'o'3'9'o'o'o'o' i 40540 '10936252 '1'0'4'0'0'0'o'ot 31576 '10946253 '1'0'4'i'o'o'o'of 22613 '10956253 'i'o'4'2'o'o'o'o'h 13651 '10966254 '1'0'4'3'0'0'0'of 04690 '10976254 '1'0'4'4'0'0'o'ot •89595730 '10986255 '1'0'4'5'0'0'o'of 86770 '10996255 'i'o'4'6'o'o'o'o1^ 77811 'l 1006256 'i'o'4'7'o'o'o'o'^ 68853 '11016256 'i'o'4'8'o'o'o'o'^ 59896 '11026257 'i'o'4'9'o'o'o'o" Natural Dual Dual Numbers. Logarithms. Numbers. •89550899 'l 1036302 1 'l'o'5'o'o'o'o'o'l* 1 41944 'l 1046303 105 1000 o'p 32990 'l 1056303 'i'o'5'2'o'o'o'o" 24037 'l 1066304 'i'o'5'3'o'o'o'o'* 15085 'l 1076304 '1'0'5'4'0'0'0'of 06133 'l 1086305 10550000'^ •89497182 'l 1096305 '1'0'5'6'O'O'O'O'J^ 88232 '11106306 'i'o'5'7'o'o'o'o" 79283 '11116306 'i'o'5'8'o'o'o'o'' 7033s '11126307 'i'o'5'9'o'o'o'o'I* 61348 '11136352 'i'o'6'o'o'o'o'of 52402 '11 146353 'i'o'6'i'o'o'o'o'^ 43457 '11156353 'i'o'6'2'o'o'o'o'I* 34513 '11166354 '1'0'6'3'0'0'0'of • 25570 '11176354 '1'0'6'4'0'0'o'of 16627 '11186355 'i'o'6'5'o'o'o'o1^ 07685 '1 1 196355 'i'o'6'6'o'o'o'o'* •89398744 '11206356 'i'o'6'7'o'o'o'o'* 89804 '11216356 'i'o'6'8'o'o'o'o'f 80865 '11226357 'i'o'6'9'o'o'o'o'l^ 71887 'l 1236402 '1'0'7'o'o'o'o'of 62950 'l 1246403 '1'0'7'1'0'0'o'of 54014 '11256403 1072000 01* 45079 'l 1266404 'i'o'7'3'o'o'o'o'j* 36144 'l 1276404 1074000 o'p 27210 '11286405 1075000 01* 18277 'l 1296405 'i'o'7'6'o'o'o'o'l^ 09345 '11306406 'i'o'7'7'o'o'o'o'|^ 00414 '11316406 '1'0'7'8'0'0'0'of •89291484 '11326407 'i'o'7'9'o'o'o'o'^ 82515 '11336452 '1'0'8'0'0'0'o'ot 73587 'l 1346453 '1'0'8'1'o'o'o'o'f 64660 '11356454 'i'o'8'2'o'o'o'o" 55734 '11366454 '1'0'8'3'0'0'o'oj 46808 '11376454 '1'0'8'4'0'0'o'of 37883 '11386455 1005000 01* 28959 'l 1396455 'i'o'8'6'o'o'o'o'^ 20036 'l 1406456 '1'0'8'7'0'0'0'o'j* 1H14 '11416456 'i'o'8'8'o'o'o'o' ' 02193 '11426457 'i'o'8'9'o'o'o'o' ' •89193233 '11436502 '1'0'9'o'o'o'o'of 84314 '11446503 '1'0'9'1'0'0'o'of 75396 '11456503 'i'o'9'2'o'o'o'o'I^ 66478 '11466504 '1'0'9'3'0'0'0'o'j^ ■ 57561 'l 1476504 'i'o'9'4'o'o'o'o'I^ 48645 '11486505 '1'0'9'5'o'o'o'of 39730 '11496505 '1'0'9'6'0'0'0'ot 30816 '11506506 'i'o'9'7'o'o'o'o'^ 21903 '11516506 'i'o'9'8'o'o'o'o'} 12991 '11526507 'i'o'9'9'o'o'o'o'[* Multiples of Differences. 901 1802 2703 3604 4505 5406 6307 7208 8109 1796 2694 3592 4490 5388 6286 7184 8082 89s 1790 2685 3580 4475 5370 6265 7160 9 i 8055 900 180Q 2700 3600 4500 5400 6300 899 1798 2697 3596 4495 5394 6293 7200. 7192 8100 1 8091 897 1794 2691 3588 4485 5382 6279 7176 1792 2688 3584 4480 5376 6272 7168 8073 j 8064 I 892 2 1784 3 2676 4 3568 5 4460 6 53 S2 7 6244 8 7136 9 8028 894 1788 2682 3576 4470 5364 6258 7152 8046 891 1782 2673 3564 4455 5346 6237 7128 8019 893 1786 2679 3572 4465 5358 6251 7144 8037 (12) Nat. No. -8910 to -8822 D. Log. 1154.... to '1253.... D. No. ITO'Ot to 'ITQ'Ot Natural Numbers, •89100000 •89091090 82181 73273 64366 55460 46554 37649 28745 19842 10900 01999 •88993099 84200 75302 66404 57507 48611 39716 30822 21889 12997 04106 •88895216 86326 77437 68549 59662 50776 41891 32967 24084 15202 06320 •88797439 88559 79680 70802 61925 53049 44134 35260 26386 17513 08641 •88699770 90900 82031 73163 64296 Dual Logarithms, '11541086 '11551087 '11561087 '11571088 '11581088 '11591089 '11601089 '11611090 '11621090 '11631091 '11641136 '11651137 '11661137 '11671138 '11681138 '11691139 '11701139 '11711140 '11721140 '11731141 '11741186 '11751187 '11761187 '11771188 '11781188 '11791189 '11801189 '11811190 '11821190 '11831191 '11841236 '11851237 '11861237 '1T871238 '11881238 '11891239 '11901239 '11911240 '11921240 '11931241 '11941286 '11951287 '11961287 '11971288 '11981288 '11991289 '12001289 '12011290 '12021290 '12031291 Dual Numbers. I lOOOOOOT I I o I o o o o'p I 102000 o'p I 103000 o'p I 104000 o'p I 105000 OT I loooooo'p I 1070000 I lOOOOOO 'i'i'o'9'o'o'o'o 'I'l'i'o'o'oVof I I I I o o O O'l' I I I 2 O O O O'p I I 13000 oY '1'1'1'4'0'0'o'of 'i'i'i'5'o'o'o'of 'i'i'i'6'o'o'o'of I I 17000 ol* 'i'i'i'8'o'o'o'of '1'1'1'9'0'0'0'of '»'■,'«», «'_', I'I'2'O'O'O'O'O'I^ 11210000'^ '1'1'2'2'0'0'0'of I 1230000'* I 124000 o*]* I 125000 o^j^ I 120000 o'p '1'1'2'7'o'o'o'of '1'1'2'8'0'0'0'of I 129000 o'p I 1300000'* I 13 1000 O'* I 132000 O'* I 133000 O'* I 1340000'* I 1350000'* I 1300000'* I 137000 o^ 'i'i'3'8'o'o'o'o'^ '1'1'3'9'0'0'o'ot I 1400000']* I 14100001* I 142000 o'j* I 143000 ol* I 144000 O'P I 145000 o'j* I 140000 o^* I 1470000'* I I 400000'* 'i'i'4'9'o'o'o'o'^ Natural Numbers. •88655390 46524 37659 28795 19932 II070 02209 •88593349 84490 75632 66735 57878 49022 40167 3 13 13 22460 13608 04757 •88495907 87057 78168 69320 60473 51628 42783 33939 25096 16253 074II •88398570 89690 80851 72013 63176 54340 45505 36670 27836 19003 IOI7I 01300 •88292470 83641 74813 65986 57159 48333 39508 30684 2I86I Dual Logarithms. 12041336 12051337 12061337 12071338 12081338 12091339 12101339 12 1 1 1340 12121340 12131341 12141386 12151387 12161387 12171388 12181388 12191389 12201389 12211390 12221390 12231391 12241436 12251437 12261437 12271438 12281438 12291439 12301439 12311440 12321440 12331441 12341486 12351487 12361487 12371488 12381488 12391489 12401489 12411490 I 242 1490 12431491 12441536 12451537 12461537 12471538 12481538 12491538 12501538 12511539 12521539 12531540 Dual Numbers. 'i'i'5'o'o'o'o'o1^ 'i'i'5'i'o'o'o'o'I^ 'i'i'5'2'o'o'o'o'l* 'i'i'5'3'o'o'o'o'l^ I 154000 o'j* 'i'i'5'5'o'o'o'. 'i'i'5'6'o'o'o'o '1'1'5'7'0'0'0'of 'i'i'5'8'o'o'o'o'I^ '1'1'5'9'0'0'o'o'lv 'i'i'6'o'o'o'o'o1^ 'i'i'6'i'o'o'o'o'I^ 'i'i'6'2'o'o'o'o'I^ 'i'i'6'3'o'o'o'o'I^ '1'1'6'4'o'o'o'o'f 'i'i'6'5'o'o'o'o1^ 'i'i'6'6'o'o'o'o'I* '1'1'6'7'0'0'0'of 'i'i'6'8'o'o'o'o1* 'i'i'6'9'o'o'o'of 'i'i'7'o'o'o'o'o'I^ 'i'i'7'i'o'o'o'o'I* '1'1'7'2'0'0'0'o'f 11730000'j* 'i'i'7'4'o'o'o'o'I^ 'i'i'7'5'o'o'o'o'I^ 'i'i'7'6'o'o'o'o'f 'i'i'7'7'o'o'o'o'I^ 'i'i'7'8'o'o'o'o'} '1'1'7'9'o'o'o'o'i* 'i'i'8'o'o'o'o'o'I^ iioioooo'p 'i'i'8'2'o'o'o'o'} 'i'i'8'3'o'o'o'o'f 'i'i'8'4'o'o'o'o'|^ 'i'i'8'5'o'o'o'o'I^ 'I'I'8'6'o'o'o'o'^ 'i'i'8'7'o'o'o'o'f 'I'I'8'8'o'o'o'o'^ 'i'i'8'9'o'o'o'o'I* 'i'i'9Vo'o'o'o'Iv 'i'i'9'i'o'o'o'o'I^ 'i'i'9'2'o'o'o'o'I* I 193000 o'j* *i'i'9'4'o'o'o'of 'i'i'9'5'o'o'o'o'^ 'i'i'9'6'o'o'o'o'} '1'1'9'7'o'o'o'o'i* 'i'i'9'8'o'o'o'o'^ 'i'i'9'9'o'o'o'o'i* Multiples of Differences. 891 890 1782 1780 2673 2670 3564 3560 4455 4450 5346 5340 6237 6230 7128 7120 8019 8010 888 887 1776 1774 2664 2661 3552 3548 4440 4435 5328 5322 6216 6209 7104 7096 7992 79«3; I 88s 884 2 1770 1768 3 2655 2652 4 3540 3536 5 4425 4420 b 5310 5304 7 6195 6188 8 7080 7072 9 7965 7956 I 882 2 1764 3 2646 4 3528 5 4410 b 5292 7 bi74 8 7056 . 9 793« Nat. No. '8820 to -8733 D. Log. 1254.... to 1353.... D. No. T2'0'0t to T2'9'9t (13) ■Natural Numbers. •88209000 00179 •88191359 82540 73722 64905 56089 47273 38458 29644 20791 I1979 03168 •88094358 85549 76740 67932 59125 50319 41514 32670 23867 15065 06263 •87997462 88662 79863 71065 62268 53472 44638 35844 27050 18257 09465 00674 •87891884 83095 74307 65520 56693 47907 39122 30338 21555 12773 03992 •87795212 86432 77653 Dual Logarithms. 2546119 2556120 2566120 2576121 2586121 2596122 2606122 2616123 2626123 2636124 2646169 2656170 2666170 2676171 2686171 2696172 2706172 2716173 2726173 2736174 2746219 2756220 2766220 2776221 2786221 2796222 2806222 2816223 2826223 2836224 2846269 2856270 2866270 2876271 2886271 2896272 2906272 2916273 2926273 2936274 2946319 2956320 2966320 2976321 2986321 2996322 3006322 3016323 3026323 3036324 Dual Numbers. 2'0'0'0'o'o'of 2'0'l'o'o'o'of 2'0'2'0'0'o'of 2'o'3'o'o'o'o' 2'o'4'o'o'o'o' 2'0'5'ovo'o 2'o'6'o'o'o'o 2070000' 2'0'8'0'o'o'of 2'0'9'0'0'0'of 2 I O O O O O'P 2 I I O O O O' 2 I 2 O O O O' 2 130000' 2'1'5'ovo'of 2'1'6'0'0'ov^ 2'i'7'o'o'o'o'^ 2'i'8'o'o'o'o'^ 2 190000'^ 2 200000'' 2210000'^ 222000 oT 2 2 3 O O O O' 2 2 4 O O O O' 2'2'5'o'o'o'of 2'2'6'o'o'o'o'^ 2 2 70000'' 2'2'8'0'0'0'0'^ 2'2'9'o'o'o'o'|^ 2 3 O O O O O' 2 3 I O O O O' 2'3'2'o'o'o'0' 2'3'3'o'o'o'o' 2'3'4'o'o'o'o' 2'3'5'0'0'0'of 2'3'6'o'o'o'o'^ 2370000" 2'3'8'o'o'o'o'' 2'3'9'0'0'0'of 240000 O'P 2410000' 2420000 2430000' 2440000 2'4'5'o'o'o'o'I^ 2'4'6'o'o'o'o 2'4'7'o'o'o'o 2'4'8'o'o'o'o' 2'4'9'0'o'o'of Natural Dual Dual Numbers. Logarithms. Numbers. •87768836 '13046369 'l'2'5'o'o'o'o'ot 60059 '13056370 '1'2'5'i'o'o'o'of SI283 '13066370 'l'2'5'2'0'0'0'0- 42508 '13076371 '1'2'5'3'0'ovo'^ 33734 '13086371 'i'2'5'4'o'o'o'o'^ 24961 '13096372 'i'2'5'5'o'o'o'o'l^ 'i'2'5'6'o'o'o'o'I^ 16189 '13106372 07417 '13116373 '1'2'5'7'0'0'0'of •87698646 '13126373 I 250000 O'' 89876 '13136374 'i'2'5'9'o'o'o'o" 81068 '13146419 '1'2'6'0'0'0'o'of 72300 '13156420 'j'2'6'1'0'0'0'0'^ 63533 '13166420 '1'2'6'2'0'0'0'o'f 54767 '13176421 'i'2'6'3'o'o'o'o1^ 46002 '13186421 'i'2'6'4'o'o'o'o'^ 37237 '13196422 'i'2'6'5'o'o'o'o'I^ 28473 '13206422 'i'2'6'6'o'o'o'o'^ 19710 '13216423 'i'2'6'7'o'o'o'o" 10948 '13226423 'i'2'6'8'o'o'o'o'^ 02187 '13236424 'i'2'6'9'o'o'o'ot •87593386 '13246469 '1'2'7'o'o'o'o'of 84627 '13256470 'i'2'7'i'o'o'o'o'' 75868 '13266470 12720000'* 67110 '13276471 1273000 O'P 58353 '13286471 '1'2'7'4'o'o'o'of 49597 '13296472 '1'2'7'5'o'o'o'ot 40842 '13306472 'i'2'7'6'o'o'o'o'^ 32088 '13316473 12770000'^ 23335 '13326473 'i'2'7'8'o'o'o'o" 14582 '13^36474 '1'2'7'9'0'0'0'o'lv 05793 '13346519 I 2000000" •87497042 '13356520 'i'2'8'i'o'o'o'o" 88292 '13366520 I 2020000'' 79543 '1337652I 'i'2'8'3'o'o'o'o" 70795 '1338652I 'i'2'8'4'o'o'o'o'^ 62048 '13396522 'i'2'8'5'o'o'o'o'j^ 53302 '13406522 'i'2'8'6'o'o'o'o'^ 44557 '13416523 'i'2'8'7'o'o'o'o'^ 35813 '13426523 'i'2'8'8'o'o'o'o'^ 27069 '13436524 'i'2'8'9'o'o'o'o| 18287 '13446569 'i'2'9'o'o'o'o'o'l^ 09545 '13456570 '1'2'9'l'ovo'o" 00804 '13466570 'l'2'9'2'o'o'o'o" •87392064 '13476571 'i'2'9'3'o'o'o'o" 83325 '13486571 'i'2'9'4'o'o'o'o'f 74587 '13496572 '1'2'9'5'o'o'o'of 65850 '13506572 'i'2'9'6'o'o'o'o" 57113 '13516573 'i'2'9'7'o'o'o'o" 48377 '13526573 'i'2'9'8'o'o'o'o'* 39642 '13536574 '1'2'9'9'o'o'o'of Multiples of Differences. 882 881 1764 1762 2646 2643 3528 3524 4410 440,'; 5292 5286 6174 6167 7056 7048 793« 7929 879 1758 2637 3516 4395 5274 6153 7032 791 1 876 1752 2628 3504 4380 5256 6132 7008 7884 873 1746 2619 3492 4365 5238 61 1 1 6984 7857 878 1756 2634 3512 4390 5268 6146 7024 7902 875 1750 2625 3500 4375 5250 6125 7000 7875 880 1760 2640 3520 4400 5280 6160 7040 7920 877 1754 263 < 3508 4385 5262 6139 7016 7893 874 1748 2622 3496 4370 5244 6118 6992 7866 (m) Nat. No. '8732 to "8646 D. Log. '1355.... to '1454.... D. No. T3'0'0t to T3'9'9t Natural Dual Dual Numbers. Logarithms. Numbers. •87326910 '13551153 'l'3'o'o'o'o'o'o'l^ 18177 '13561154 '1'3'0'i'o'o'o'o'f* 09444 '13571154 '1'3'0'2'o'o'o'o'j^ 00714 '13581155 'i'3'o'3'o'o'o'o'^ •87291984 '13591155 'i'3'o'4'o'o'o'o^^ 83255 '13601156 '1'3'0'5'0'0'0'of 74527 '13611156 'i'3'o'6'o'o'o'o'^ 65800 '13621157 *i'3'o'7'o'o'o'o'^ 57073 '13631^57 'i'3'o'8'o'o'o'o'|^ 48347 '13641158 '1'3'0'9'o'o'o'of 39583 '13651203 'i'3'i'o'c3'o'o'o| 30859 '13661204 'i*3'i'i'o'o'o'o4^ 22136 '13671204 'T'3'1'2'0'0'0'0'^ 13414 '13681205 'i'3'i'3'o'o'o'o'* 04693 '13691205 'i'3'i'4'o'o'o'o'^ •87195973 '13701206 'i'3'i'5'o'o'o'o'|^ 87253 '13711206 '1'3'1'6'0'0'0'of 78534 '13721207 'i'3'i'7'o'o'o'o'^ 69816 '13731207 'i'3'i'8'o'o'o'o'^ 61099 '13741208 '1'3'1'9'0'0'0'of 52344 '13751253 'i'3'2'o'o'o'o'o'|^ 43629 '13761254 'i'3'2'i'o'o'o'o'* 34915 '13771254 'l'3'2'2'o'o'o'o'^ 26202 '13781255 'i'3'2'3'o'o'o'o'* 17489 '13791255 'i'3'2'4'o'o'o'of 08777 '13801256 '1'3'2'5'o'o'o'of 00066 '13811256 'i'3'2'6'o'o'o'o'|^ •87091356 '13821257 'i'3'2'7'o'o'o'o'I^ 82647 '13831257 '1'3'2'8'0'0'0'ot 73939 '13841258 'i'3'2'9'o'o'o'o1^ 65191 '13851303 '1'3'3'0'0'0'o'ot 56484 '13861304 'i'3'3'i'o'o'o'o^' 47778 '13871304 'i'3'3'2'o'o'o'o'^ 39073 '13881305 'i'3'3'3'o'o'o'o'^ 30369 '13891305 'i'3'3'4'o'o'o'o'' 21666 '13901306 '1'3'3'5'0'0'0'ot 12964 '13911306 'i'3'3'6'o'o'o'o'^ 04263 '13921307 '1'3'3'7'0'0'0'of •86995563 '13931307 'i'3'3'8'o'o'o'o'' 86863 '13941308 '1'3'3'9'0'0'0'of 78126 '13951353 '1'3'4'0'0'oVof 69428 '13961354 'i'3'4'i'o'o'o'o'^ 60731 '13971354 'i'3'4'2'o'o'o'o'' 52035 '13981355 'i'3'4'3'o'o'o'o" 43340 '13991355 '1'3'4'4'0'0'o'of 34646 '14001356 '1'3'4'5'0'0'0'o'j^ 'i'3'4'6'o'o'o'o" 25953 '14011356 17260 '14021357 'i'3'4'7'o'o'o'o'^ 08568 '14031357 '1'3'4'8'0'0'o'of •86899877 '14041358 '1'3'4'9'o'o'o'of Natural Dual Dual Numbers: Logarithms. Numbers. •86891 148 '1405 1403 '1'3'5'0'0'0'o'of 82459 '14061404 'i'3'5'i'o'o'o'o'^ 73771 '14071404 'i'3'5'2'o'o'o'o'^ 65084 '14081405 '1'3'5'3'0'0'o'of 56397 '14091405 '1'3'5'4'o'o'o'of 477 1 1 '14101406 '1'3'5'5'0'0'0'of 39026 '14111406 'i'3'5'6'o'o'o'o" 30342 '14121407 '1'3'5'7'0'0'o'of 21659 '14131407 '1'3'5'8'0'0'o'of 12977 '14141408 '1'3'5'9'0'0'0'of 04257 '14151453 'i'3'6'o'o'o'o'o4^ •86795577 '14161454 'i'3'6'i'o'o'o'o'^ 86897 '14171454 'i'3'6'2'o'o'o'o'^ 'i'3'6'3'o'o'o'o'^ 78218 '14181455 69540 '14191455 '1'3'6'4'o'o'o'o'j^ 60863 '14201456 'i'3'6'5'o'o'o'o| 52187 '14211456 'i'3'6'6'o'o'o'o'^ 43512 '14221457 'i'3'6'7'o'o'o'o'^ 34838 '14231457 'i'3'6'8'o'o'o'o"- 26165 '14241458 'i'3'6'9'o'o'o'o'^ 17453 '14251503 '1'3'7'o'o'o'o'of 08781 '14261504 'i'3'7'i'o'o'o'o'^ OOIIO '14271504 'I'^'fi'o'o'd'o^ •86691440 '14281505 'i'3'7'3'o'o'o'o'^ 82771 '14291505 'i'3'7'4'o'o'o'o" 74103 '14301506 '1'3'7'5'0'0'o'o'j^ 65436 '14311506 'i'3'7'6'o'o'o'o '' 56769 '14321507 'i'3'7'7'o'o'o'o" 48103 '14331507 'i'3'7'8'o'o'o'o'^ 39438 '14341S08 '1'3'7'9'0'o'o'C 30735 '14351553 '1'3'8'0'0'0'o'o'j^ 22072 '14361554 'i'3'8'i'o'o'o'o'^ I34IO '14371554 'i'3'8'2'o'o'o'o'^ 04749 '14381555 'i'3'8'3'o'o'o'o'^ •86596089 '14391555- 'i'3'8'4'o'o'o'o'* 87429 '14401556 '1'3'8'5'0'o'o'of 78770 '14411556 'i'3'8'6'o'o'o'o'^ 70II2 '14421557 '1'3'8'7'0'0'0'of 61455 '14431557 '1'3'8'8'0'0'0'ot 52799 '14441558 '1'3'8'9'0'0'0'of 44104 '1445 1603 '1'3'9'0'0'0'o'of 35450 '1446 1 604 'i'3'9'i'o'o'o'o'^ 26796 '1447 1 604 'i'3'9'2'o'o'o'o'^ I8I43 '1448 1605 '1'3'9'3'0'0'0'of 09491 '14491605 'i'3'9'4'o'o'o'o^ 00840 '14501606 '1'3'9'5'0'0'0'ot •86492190 '14511606 '1'3'9'6'0'0'o'of 83541 '14521607 'i'3'9'7'o'o'o'o'' 74893 '14531607 'i'3'9'8'o'o'o'o'^ 66246 '14541608 'i'3'9'9'o'o'o'o'| Multiples of Differences. 873 1746 2619 3492 4365 5238 6111 6984 7857 872 1744 2616 3488 4360 5232 6104 6976 871 1742 2613 34^4 4355 5226 6fi. 6( 7848 J7^ 870 869 1740 17.38 2610 2607 3480 3476 4350 4345 5220 5214 6090 6083 6960 6952 1 7830 7821 i 867 1734 2601 3468 4335 5202 6069 6936 7803 864 1728 2592 3456 4320 5184 6048 6912 7776 868 1736 2604 3472 4340 5208 6076 6944 7812 8661 8651 1732I1730I 2598 I 2595 3464 j 3460. 4330 4325: 5196 51901 6062 1 6055 6928 [6920' 779417785. Nat. No. -8645 to "8560 D. Log. 1455.... to 1554.... D. No. 1'4'0'Ot to l'4'9'9t (»5) Natural Numbers. •S6453641 44996 36352 27708 19065 10423 01782 •86393142 84503 75865 67187 58550 49914 41279 32645 24012 15380 06748 •86298117 89487 80S20 72192 63565 54939 46314 37689 29065 20442 11S20 03199 ■86194539 85920 77301 68683 60066 51450 42835 34221 25608 16995 08345 •86099734 91124 82515 73907 65300 56693 48087 39482 30878 Dual Logarithms. '14556186 '*4566i87 '14576187 '14586188 '14596188 '14606189 '14616189 '14626190 '14636190 '14646191 '14656236 '14666237 '14676237 '14686238 '14696238 '14706239 '14716239 j'14726240 |'i473624o ri474624i j'14756286 '14766287 '14776287 '14786288 '14796288 '14806289 '14816289 '14826290 '14836290 '14846291 '14856336 '14866337 '14876337 '14886338 '14896338 '14906339 '14916339 '14926340 '14936340 '14946341 '14956386 '14966387 '14976387 '14986388 '14996388 '15006389 '15016389 '15026390 '15036390 '15046391 Dual Numbers. 1400000 O'* 'l'4'o'l'o'o'o'o'^ '1'4'0'2'o'o'o'of 'i'4'o'3'o'o'o'oj> 'i'4'o'4'o'o'o'o'f 'i'4'o'5'o'o'o'o 'i'4'o'6'o'o'o'o 14070000 'i'4'o'8'o'o'o'of 'i'4'o'9'o'o'o'of 'i'4'i'o'o'o'o'o'l^ 'i'4'i'i'o'o'o'o'^ '1'4'1'2'0'o'o'of 'i'4'i'3'o'o'o'o'^ 'l'4'i'4'o'o'o'of '1'4'1'5'0'0'0'of 'i'4'i'6'o'o'o'o'^ 'i'4'i'7'o'o'o'o''^ 'i'4'i'8'o'o'o'o| 'i'4'i'9'o'o'o'o'^ 14200000'* 'i'4'2'i'o'o'o'o'^ 'l'4'2'2'o'o'o'o'^ 'i'4'2'3'o'o'o'o'^ 14240000'^ 1425000 or 'i'4'2'6'o'o'o'o'^ 'i'4'2'7'o'o'o'o'^ I 4 2 o o o o o f '1'4'2'9'o'o'o'of 'i'4'3'o'o'o'o'o^ 'i'4'3'i'o'o'o'o' 'i'4'3'2'o'o'o'o' 14330000 14340000' '1'4'3'5'0'0'0'of 'i'4'3'6'o'o'o'of 'i'4'3'7'o'o'o'o' 'i'4'3'8'o'o'o'o' 1439000 O'j^ 1440000 O' I44IOOOO' '1'4'4'2'0'o'o'o'j 1443000 O'j^ '1'4'4'4'o'o'o'of '1'4'4'5'o'o'o'ot '1'4'4'6'o'o'o'of I 4470000" I 4400000'* 'i'4'4'9'o'o'o'o'^ Natural Numbers. •86022237 13635 05034 •85996433 79234 70636 62039 53443 44848 36214 27620 19027 10435 01844 •85893254 84665 76077 67489 58902 50278 41693 33109 24526 .15944 07362 •85798781 90201 81622 73044 64428 55852 47276 38701 30127 21554 129S2 0441 1 •85695841 87271 78663 70095 61528 52962 44397 35833 27269 18706 10144 01583 Dual Lotrarithms. 15056436 15066437 15076437 15086438 15096438 15 106439 15 1 16439 15 126440 15 136440 15146441 15156486 15 166487 15176487 15 186488 15196488 15206489 15216489 15226490 15236490 15246491 15256536 15266537 15276537 15286538 15296538 15306539 15316539 15326540 15336540 15346541 15356586 15366587 15376587 15386588 15396588 15406589 15416589 15426590 15436590 15446591 15456636 15466637 15476637 1548663S 15496638 15506639 15516639 15526640 15536640 15546641 Dual Numbers. 1450000 o'p '1'4'5'l'o'o'o'of 1452000 of I 4 5 3 o o o of 14540000']^ 'iV5'5'o'o'o'of 'i'4'5'6'o'o'o'o'|^ '1'4'5'7'0'o'o'of '1'4'5'8'o'o'o'of '1'4'5'9'0'o'o'of '1'4'6'o'o'o'o'ot 14010000^ '1'4'6'2'o'o'o'o'j^ 'i'4'6'3'o'o'o'o| 'i'4'6'4'o'o'o'o'|^ •1'4'6'5'0'0'0'ot '1'4'6'6'0'0'0'oA '1'4'6'7'0'0'0'ot '1'4'6'8'0'0'o'of 'i'4'6'9'o'o'o'o'I^ I 4 7 o o o o o'p 147 1000 O' 14720000 I 4 7 3 o o o o'j I 4 7 4 o o o o'p 1475000 o'p I 4 7 o o o o O'j* 1477000 o'p I 4 7 o o o o O'j 'i'4'7'9'o'o'o'o| '1'4'8'0'0'o'o'of '1'4'8'i'o'o'o'of 'i'4'8'2'o'o'o'o'|^ 'i'4'8'3'o'o'o'o' 'i'4'8'4'o'o'o'o '1'4'8'5'0'0'0'of 'i'4'8'6'o'o'o'o'^ 'r4'8'7'o'o'o'ot •1'4'8'8'o'o'o'of I 4090000'* 1490000 o'r '1'4'9'i'o'o'o'o'j* 'i'4'9'2'o'o'o'o^ 1493000 OT 1494000 O'J' 14950000'* 1 4900000'* 'i'4'9'7'o'o'o'o'' 'i'4'9'8'o'o'o'o'* 'i'4'9'9'o'o'o'o" 1 Multiples of Differences. 864 1728 2592 3456 4320 S184 6048 8 I 6912 9 I 7776 861 1722 2583 3444 4305 5166 6027 9 i 7749 863 1726 2589 3452 431S S17S j 6041 6904 17767 860 1720 2580 3440 4300 5160 6020 862 1724 2586 3448 4310 6034 6896 7758 859 1718 2577 3436 4295 5154 6013 I 858 857 2 1716 1714 3 2574 2571 4 3432 3428 5 4290 4285 b 5148 S142 7 6006 5999 8 6864 6S56I 9 7722 7713 6880 i 6S72 7740 1 773* 856 1712 2568 3424 4280 5136 5992 684S 77^4 (i6) Nat. No. -8558 to *8474 D. Log. 1556.... to 1655,... D. No. T5'0'0t to T5'9'9t Natural Dual Dual Numbers. •8558910S Logarithms. Numbers. '15561220 '1'5'0'0'0'o'o'of 80546 '15571221 'l'5'o'l'o'o'o'o|' 71988 '15581221 'i'5'o'2'o'o'o'o'^ 63431 '15591222 'i'5'o'3'o'o'o'o| 'i'5'o'4'o'o'o'o'^ 54875 '15601222 46320 '15611223 'I'S'o's'o'o'o'o'f 37765 '15621223 'i'5'o'6'o'o'o'o'^ 292II '15631224 'i'5'o'7'o'o'o'o'^ 20658 '15641224 'i'5'o'8'o'o'o'o'^ 12106 '15651225 'i'5'o'9'o'o'o'o'|^ 03516 '15661270 15100000'P •83494866 '15671271 15 1 1000 o'p 86317 '15681271 '1'5'1'2'o'o'o'of 77768 '15691272 'i'5'i'3'o'o'o'o'^ 69220 '15701272 'i'5'i'4'o'o'o'of 60673 '15711273 'i'5'i'5'o'o'o'ot 52127 '15721273 '1'5'1'6'0'0'0'of 43682 '15731274 'i'5'i'7'o'o'o'o| 35138 '15741274 'i'5'i'8'o'o'o'o" 26594 '15751275 'i'5'i'9'o'o'o'o'^ 18012 '15761320 '1'5'2'0'0'0'o'of 09470 '15771321 'i'5'2'i'o'o'o'o'^ 00929 '15781321 'l'5'2'2'o'o'o'o'^ •85392389 '15791322 'i'5'2'3'o'o'o'o'^ 83850 '15801322 'i'5'2'4'o'o'o'o'^ 75312 '15811323 V5^2'5'o'o'o'ot 66774 '15821323 '1'5'2'6'0'o'o'c 58237 '15831324 '1'5'2'7'0'0'0'o't^ 49701 '15841324 1520000 o'p 41166 '15851325 'i'5'2'9'o'o'o'o'I^ 32594 '15861370 '1'5'3'0'o'o'o'of 24061 '15871371 '1'5'3'i'o'o'o'of 15529 '15881371 'i'5'3'2'o'o'o'ot C6997 '15891372 '1'5'3'3'0'0'0'ot •85298466 '15901372 'i'5-3'4'o'o'o'ot 89936 81407 '15911373 '15921373 '1'5'3'5'0'0'0'of 'i'5'3'6'o'o'o'o" 72879 '1593^374 '1'5'3'7'0'0'0'of 64352 '15941374 '1'5'3'8'0'o'o'of 55826 '15951375 '1'5'3'9'0'0'0'ot 47262 '15961420 'i'5'4'o'o'oVo| 'i'5'4'i'o'o'o'o'^ 38737 '15971421 30213 '15981421 'i'5'4'2'o'o'o'o'^ 21690 '15991422 'i'5'4'3'o'o'o'o'' I3168 '16001422 'i'5'4'4'o'o'o'o'^ 04647 '16011423 '1'5'4'5'0'0'0'o't^ •85196127 '16021423 'i'5'4'6'o'o'o'o^' 87607 '16031424 '1'5'4'7'o'o'o'of 79088 '16041424 'i'5'4'8'o'o'o'o'^ 70570 '16051425 '1'5'4'9'o'o'o'of Natural Dual Dual Numbers. Logarithms. Numbers. •85162015 '16061470 '1'5'5'0'0'0'o'of 53499 '16071471 'i'5'5'i'o'o'o'o'^ 44984 '16081471 'i'5'5'2'o'o'o'o'^ 36470 '16091472 'i'5'5'3'o'o'o'o4' '1 '5'5'4'0'0'0'of 27956 '16101472 19443 '16111473 'i'5'5'5'o'o'o'o| 1 093 1 '16121473 '1'5'5'6'o'o'o'of 02420 '16131474 'i'5'5'7'o'o'o'o" 'i'5'5'8'o'o'o'o'^ '85093910 '16141474 85401 '16151475 '1'5'5'9'0'0'0'of 76853 '1616x520 '1'5'6'0'0'o'o'of 68345 '16171521 'i'5'6'i'o'o'o'o'^ 59838 '16181521 '1'5'6'2'0'o'o'of 51332 '16191522 '1'5'6'3'0'0'0'of 42827 '16201522 '1'5'6'4'0'0'0'of 34323 '16211523 'i'5'6'5'o'o'o'o| 25820 '16221523 'i'5'6'6'o'o'o'o" 17317 '16231524 'i'5'6'7'o'o'o'o'' 08815 '16241524 'i'5'6'8'o'o'o'o'^ 00315 '16251525 'i'5'6'9'o'o'o'o'^ •84991776 '16261570 '1'5'7'o'o'o'o'of 83278 '16271571 'i'5'7'i'o'o'o'o'^ 74780 '16281571 'i'5'7'2'o'o'o'o'^ 66283 '16291572 '1'5'7'3'0'0'0'of 57786 '16301572 'i'5'7'4'o'o'o'of 49290 '16311573 '1'5'7'5'0'o'o'of 40795 '16321573 'i'5'7'6'o'o'o'o ^ 'i'5'7'7'o'o'o'o" 32301 '16331574 23808 '16341574 'i'5'7'8'o'o'o'o'^ 15316 '16351575 '1'5'7'9'0'0'0'c'' 06784 '16361620 'i'5'8'o'o'o'o'o4^ •84898293 '16371621 'i'5'8'i'o'o'o'o'' 89803 '16381621 'i'5'8'2'o'o'o'o'* 81314 '1639x622 'i'5'8'3'o'o'o'o'^ 72826 '16401622 'i'5'8'4'o'o'o'o'^ 64338 '164x1623 '1'5'8'5'0'oVof 55852 '16421623 'i'5'8'6'o'o'o'o'^ 47366 '1643x624 '1'5'8'7'o'o'o'of 38881 '1644x624 'i'5'8'8'o'o'o'o'|^ 'i'5'8'9'o'o'o'o"' 30397 '16451625 21877 '16461670 '1'5'9'0'0'0'o'of 13395 '16471671 '1'5'9'x'o'o'o'o'^ 04914 '16481671 'i'5'9'2'o"o'o'of •84796434 '1649x672 'i'5'9'3'o'o'o'o| 87954 'X6501672 'x'5'9'4'0'0'0'0'*^ 79475 '16511673 'i'5'9'5'o'o'o'o'|J 70997 '16521673 'i'5'9'6'o'o'o'o" 62520 '16531674 'i'5'9'7'o'o'o'o'' 54044 '16541674 'i'5'9'8'o'o'o'o'* 45569 '16551675 'x'5'9'9'0'0'0'0'* Multiples «if iJiffercnces. 1710 2565 3420 4275 5130 ,598s 8 6840 9 ! 7<^9S 852 851 1704 1702 2SS6 25 S3 3408 3404 4260 4255 S112 5106 5964 SQS7 6816 6808 7668 7659 I 849 848 1 2 1698 169') ' 3 2.S47 2S44; 4 339(> 3392 S 424s 4240 6 5094 5088' 7 5943 S93() 8 6792 6784 9 7641 7632 Nat. No. -8473 to -8389 D. Log. 15 j6.... to '1755.... D. No. TB'O'Of to T6'9'9t (i7) Natural Numbers. •84733214 24741 16269 07797 •84699326 90856 82387 73919 65452 569^5 48481 40016 31552 23089 14627 06166 •84597705 89245 80786 72328 63832 55376 46920 38465 30011 21558 13106 04654 ■84496203 87753 79269 70821 62374 53928 45483 37038 28594 20151 11709 03268 ■84394789 86350 77911 69473 61036 52600 44165 35731 27297 18864 Dual Logarithms. 6566254 6576255 6586255 6596256 6606256 6616257 6626257 6636258 6646258 6656259 6666304 6676305 6686305 6696306 6706306 6716307 6726307 6736308 6746308 6756309 6766354 6776355 0786355 6796356 6806356 6816357 6826357 6836358 6846358 6856359 6866404 6876405 6886405 6896406 6906406 6916407 6926407 6936408 6946408 6956409 6966454 6976455 6986455 6996456 7006456 7016457 7026457 7036458 7046458 7056459 Dual Numbers. '6'o'o'o'o'o'o^ '6'0'i'o'o'o'of '6'0'2'0'0'0'of '6'0'3'0'0'0'cf '6'0'4'o'o'o'of '6'0'5'0'0'0'of '6'0'6'0'0'0'of 6 o 7 o o o OT '6'o'8'o'o'o'o| '6'0'9'o'o'o'of O I o O O O O' I I o o o o '6'i'2'o'o'o'o o 130000' '6'1'4'o'o'o'of '6'1'5'ovo'ot •6'1'6'0'0'0'ot '6'1'7'0'0'0'of '6'i'8'o'o'o'ot '6'1'9'0'0'o'of '6'2Vo'o'o'o| '6'2'i'o'o'o'o'f '6'2'2'0'0'0'of '6'2'3'0'0'0'of 0240000']^ '6'2'5'o'o'o'ot '6'2'6'0'0'0'of '6'2'7'o'o'o'o'^ '6'2'8'0'0'0'o'f '6'2'9'0'0'o'of 030000 o'r 0310000^ '6'3'2'0'0'0'of '6'3'3'0'0'0'of '6'3'4'0'0'0'of '6'3'5'o'o'o'o'f '6'3'6'0'0'0'of '6'3'7'0'0'o'of '6'3'8'0'0'0'ot '6'3'9'0'o'o'ot '6'4'0'0'0'o'ot '6'4'l'o'o'o'of '6'4'2'0'0'0'ot '6'4'3'0'0'0'of '6'4'4'0'0'o'of '6'4'5'o'o'o'o>^ '6'4'6'o'o'o'o' '6'4'7'o'o'o'o' '6'4'8'o'o'o'o' '6'4'9'o'o'o'o' Natural Dual Dual Numbers. Logarithms. Numbers. •84310394 '17066504 'i'6'5'o'o'o'o'o1^ 01963 •17076505 'i'6'5'i'o'o'o^of •84293533 '17086505 'i'6'5'2'o'o'o'o'' 85104 '17096506 'i'6'5'3'o'o'o'o'' 76675 '17106506 '1'6'5'4'0'0'0'of 68247 '17116507 '1'6'5'5'0'0'0'of '1'6'5'6'0'0'0'of 59820 '17126507 5^394 '17136508 '1'6'5'7'0'0'0'of 42969 '17 146508 'i'6'5'8'o'o'o'o1^ 34545 •17156509 'i'6'5'9'o'o'o'of 26084 '17166554 ' I '6'6'o'o'o'o'of 'i'6'6'i'o'o'o'of 17661 '17176555 09239 '17186555 '1'6'6'2'0'0'0'of 00818 '17196556 '1'6'6'3'0'0'0'ot •84192398 '17206556 '1'6'6'4'0'0'o'ot 83979 '17216557 '1'6'6'5'o'o'o'ot 75561 '17226557 'i'6'6'6'o'o'o'ot 67M3 '17236558 '1'6'6'7'0'0'0'of 58726 '17246558 'x'6'6'8'o'o'o'of 50310 '17256559 '1'6'6'9'0'0'0'ot 41858 '17266604 '1'6'7'0'0'0'o'of 33444 '17276605 '1'6'7'i'o'o'o'of '1'6'7'2'0'o'o'oj 25031 '17286605 16618 '17296606 '1'6'7'3'0'0'0'of 08206 '17306606 '1'6'7'4'0'0'0'of •84099795 '17316607 '1'6'7'5'0'0'0'ot 91385 '17326607 '1'6'7'6'0'0'0'of 82976 '17336608 »»'<'..'-'«'— '-.'—A 1077000 o'p 74568 '17346608 '1'6'7'8'o'o'o'of '1'6'7'9'o'o'o'of 66161 '17356609 577^6 '17366654 '1'6'8'o'o'o'o'o'f 'i'6'8'i'o'o'o'o" 49310 '17376655 40905 '17386655 '1'6'8'2'0'0'0'ot 32501 '17396656 '1'6'8'3'0'0'0'of ' I '6'8'4'0'0'0'of 24098 '17406656 15696 '17416657 '1'6'8'5'0'0'0'of 07294 '17426657 'i'6'8'6'o'o'o'of •83998893 '17436658 •i'6'8'7'o'o'o'o'^ 90493 '17446658 'i'6'8'8'o'o'o'o'^ 82094 '17456659 'i'6'8'9'o'o'o'of 73658 '17466704 '1'6'9'0'o'o'o'of 65261 •17476705 'i'6'9'i'o'o'o'of 56865 '17486705 '1'6'9'2'0'0'0'of 48469 •17496706 '1'6'9'3'0'0'0'of 40074 '17506706 'i'6'9'4'o'o'o'of 31680 '17516707 '1'6'9'5'oVo'of 23287 •17526707 'i'6'9'6'o'o'o'of 14895 •17536708 'i'6'9'7'o'o'o'o'* 06504 '17546708 'i'6'9'8'o'o'o'of •838981 13 '17556709 '1'6'9'9'o'o'o'of Multiples of Differences. 847 1694 2541 3388 423s 5082 5929 6776 7623 846 1692 2538 3384 4230 5076 5922 6768 7614 844 84-? 1688 1686 2532 2529 SS?^ 3372 4220 421 <; 5064 5058 5908 .sgoi <>7.S2 6744 I7596 7587 841 ' 840 1682 i68o 2523 2520 33(54 3360 4205 4200 504b 5040 5887 5880 5728 6720 7569 7560 838 1676 2514 3352 4190 5028 5866 6704 7542 845 1690 2S3S 3380 4225 5070 5915 6760 7605 843 1684 2526 3368 4210 5052 5894 6736 7578 i539 1678 2517 3356 4195 5034 5873 6712 755* (i8) Nat. No. "8388 to -8305 D. Log. 1757.... to 1856.... D. No. ITO'Ot to T7'9'9t N.itural Dual Dual Numbers. •33885881 Logarithms. Numbers. '17571287 'l'7'o'o'o'o'o'o4^ 77492 '17581288 'l'7'o'l'o'o'o'o'^ 69104 '17591288 '1'7'0'2'0'o'o'of 60717 '17601289 '1'7'0'3'0'o'o'of 52331 '17611289 'i'7'o'4'o'o'o'o]^ 43946 '17621290 '1'7'0'5'o'o'o'oj 35562 '17631290 'i'7'o'6'o'o'o'o" 27179 '17641291 '1'7'0'7'0'o'o'of 18796 '17651291 'i'7'o'8'o'o'o'o" 10414 '17661292 'i'7'o'9'o'o'o'of 01995 '17671337 '1'7'i'o'o'o'o'of •83793615 '17681338 '1'7'i'i'o'o'o'ot 85236 '17691338 'i'7'i'2'o'o'o'o| 76857 '17701339 '1'7'1'3'0'0'0'of 68479 '17711339 '1'7'1'4'0'0'o'of 60102 '17721340 '1'7'1'5'0'0'0'of '1'7'1'6'0'0'0'ot 5.1726 '17731340 43351 '17741341 'i'7'i'7'o'o'o'o'^ 34977 '17751341 '1'7'1'8'0'0'0'of 26604 '17761342 '1'7'1'9'0'0'0'of 18193 '17771387 'i'7'2'o'o'o'o'o'h 'i'7'2'i'o'o'o'o'^ 09821 '17781388 01450 '17791388 'l'7'2'2'o'o'o'o'^ 'i'7'2'3'o'o'o'o'^ •83693080 '17801389 84711 '17811389 'i'7'2'4'o'o'o'o'^ 76343 '17821590 '1'7'2'5'0'0'0'of • 67975 '17831390 'i'7'2'6'o'o'o'o'^ 59608 '17841391 'i'7'2'7'o'o'o'o'^ 51242 '17851391 '1'7'2'8'0'o'o'of 42877 '17861392 'i'7'2'9'o'o'o'o'^ 34475 '17871437 I 7300000'^ 26112 '17881438 17310000'' 17749 '17891438 'i'7'3'2'o'o'o'o'' 09387 '17901439 'i'7'3'3'o'o'o'o'' 'i'7'3'4'o'o'o'o'^ 01026 '17911439 •03592666 '17921440 'i'7'3'5'o'o'o'o]> 84307 '17931440 'i'7'3'6'o'o'o'o'' 75949 '17941441 'i'7'3'7'o'o'o'o'^ 67592 '17951441 17300000'^ 59235 '17961442 'i'7'3'9'o'o'o'o" 50840 '17971487 I 740000 O^*, ,42485 '17981488 '1'7'4'l'o'o'o'ot '1'7'4'2'o'o'o'ot 34131 '17991488 25778 '18001489 '1'7'4'3'o'o'o'of '1'7'4'4'o'o'o'of 17425 '18011489 09073 '18021490 '1'7'4'5'o'o'o'of 00722 '18031490 'i'7'4'6'o'o'o'o| 'i'7'4'7'o'o'o'o| 'i'7'4'8'o'o'o'o" 'i'7'4'9'o'o'o'o'* ■83492372 '1804149I 84023 '18051491 75675 '18061492 Natural Dual Dual Numbers. Logarithms. Numbers. •83467290 '18071537 '1'7'5'0'0'0'o'of 58943 '18081538 'i'7'5'i'o'o'o'o" 50597 '18091538 '1'7'5'2'0'o'o'of 42252 '18101539 '1'7'5'3'o'o'o'of 33908 '18111539 '1'7'5'4'o'o'o'of 25565 '18121540 '1'7'5'5'o'o'o'of 17222 '18131540 'L'7'5'6'o'o'o'of 08880 '18141541 '1'7'5'7'0'o'o'of 00539 '18151541 '1'7'5'8'o'o'o'of •83392199 '18161542 '1'7'5'9'o'o'o'of 83822 '18171587 '1'7'6'0'o'o'o'ot 75484 '18181588 17010000'' 67146 '18191588 'i'7'6'2'o'o'o'o" 58809 '18201589 'i'7'6'3'o'o'o'o'^ 50473 • '182I1589 '1'7'6'4'0'0'0'of 42138 '18221590 '1'7'6'5'o'o'o'of 33804 '18231590 'i'7'6'6'o'o'o'o'' 25471 '18241591 'i'7'6'7'o'o'o'o'^ 17138 '18251591 'i'7'6'8'o'o'o'o'^ 08806 '18261592 'i'7'6'9'o'o'o'o" 00439 '18271637 '1'7'7'o'o'o'o'ot •83292109 '18281638 'i'7'7'i'o'o'o'o" 83780 '18291638 'i'7'7'2'o'o'o'o" 75452 '18301639 'i'7'7'3'o'o'o'o'^ 67124 '18311639 '1'7'7'4'o'o'o'of 58797 '18321640 'i'7'7'5'o'o'o'o4^ 50471 '18331640 'i'7'7'6'o'o'o'o'^ 42146 '18341641 'i'7'7'7'o'o'o'o| 33822 '18351641 'i'7'7'8'o'o'o'o'^ 25499 '1S361642 '1'7'7'9'o'o'o'of 17138 '18371687 'i'7'8'o'o'o'o'o| 08816 '18381688 '1'7'8'i'o'o'o'of 00495 '18391688 '1'7'8'2'0'o'o'of •83192175 '18401689 '1'7'8'3'0'0'0'of 83856 '184116S9 '1'7'8'4'0'0'o'of 75538 '18421690 '1'7'8'5'o'o'o'of 67220 '18431690 '1'7'8'6'o'o'o'of 58903 '18441691 'i'7'8'7'o'o'o'o| 50587 '18451691 'i'7'8'8'o'o'o'o>^ 42272 '18461692 'i'7'8'9'o'o'o'o| 33921 '18471737 '1'7'9'o'o'o'o'o'f 25608 '18481738 'i'7'9'i'o'o'o'o'^ 17295 '18491738 'i'7'9'2'o'o'o'o'' 08983 '18501739 'i'7'9'3'o'o'o'o'^ 00672 '18511739 'i'7'9'4'o'o'o'o'^ •83092362 '18521740 'i'7'9'5'o'o'o'o| 84053 '18531740 'i'7'9'6'o'o'o'o'' 75745 '18541741 'i'7'9'7'o'o'o'o" 67437 '1855174I 'i'7'9'8'o'o'o'o'' 59130 '18561742 'i'7'9'9'o'o'o'o" Multiples of Differences. 1676 2514 3352 4190 5028 5866 6704 7543 83s 834 1670 1668 2505 2502 3340 333^ 4175 4170 5010 5004 S«4S S83« ! 6&80 •66721 75'S 7506: 832 1664 2496 3328 4160 4992 5824 6656 7488 Nat. No. -8304 to '8222 D. Log. '1857.... to 1956.... D. No. T8'0'0t to T8'9'9t (^9) Natural Dual Dhal Numbers. Logarithms. Numbers. •83047023 '18576321 'i'8'o'o'o'o'o'of 38718 '18586322 'l'8'o'i'o'o'o'o'N 30414 '18596322 '1'8'0'2'0'0'0'of 22III '18606323 'i'8'o'3'o'o'o'o'^ 13809 '18616323 'i'8'o'4'o'o'o'o| 05508 '18626324 'i'8'o'5'o'o'o'o| •82997207 '18636324 'i'8'o'6'o'o'o'o'^ 88907 '18646325 '1'8'0'7'o'o'o'of 80608 '18656325 'I'S'o'S'o'o'o'o'^ 72310 '18666326 '1'8'0'9'0'0'o'of 63976 '18676371 'r'S'i'o'o'o'o'of 55680 '18686372 'i'8'i' I 'o'o'o'of 47384 '18696372 'i'8'i'2'o'o'o'o| 39089 '18706373 'i'8'i'3'o'o'o'o'' 30795 '18716373 '1'8'1'4'0'o'o'of 22502 '18726374 '1'8'1'5'0'0'o'of 'i'8'i'6'o'o'o'of 142 10 '18736374 05919 '18746375 'i'8'i'7'o'o'o'o| •S2897628 '18756375 'i'8'i'8'o'o'o'of 89338 '18766376 '1'8'1'9'0'o'o'of 81OI2 '18776421 'i'8'2'o'o'o'o'o| '1'8'2'i'o'o'o'ot 72724 '18786422 64437 '18796422 10220000'* 'i'8'2'3'o'o'o'o'^ '1'8'2'4'0'0'0'of 5615I '18806423 47865 '18816423 39580 '18826424 '1'8'2'5'0'o'o'of 31296 '18836424 'i'8'2'6'o'o'o'o'^ 23013 '18846425 'i'8'2'7'o'o'o'o'^ 14731 '18856425 'i'8'2'8'o'o'o'o'* 06450 '18866426 '1'8'2'9'o'o'o'of S2798131 '18876471 '1'8'3'o'o'o'o'of ' I '8'3' I 'o'o'o'of 89S5I '18886472 81572 '18896472 '1'8'3'2'0'0'0'of 73294 '18906473 '1'8'3'3'0'0'0'of 'i'8'3'4'o'o'o'of 65017 '18916473 56740 '18926474 ' w'O'- '»'—'-. »_'_A 1035000 ol^ 48464 '18936474 '1'8'3'6'o'o'o'of 40189 '18946475 'i'8'3'7'o'o'o'o" 3I915 '18956475 '1'8'3'8'0'0'0'of 23642 '18966476 '1'8'3'9'0'o'o'of 15333 '18976521 '1'8'4'0'o'o'o'of 07062 '18986522 'i'8'4'i'o'o'o'o- •82698792 '18996522 'i'8'4'2'o'o'o'o'* 90522 '19006523 'i'8'4'3'o'o'o'o'* '1'8'4'4'0'o'o'of 82253 '19016523 73985 '19026524 '1'8'4'5'0'o'o'of 65718 '19036524 '1'8'4'6'0'0'0'of 57452 '19046525 '1'8'4'7'o'o'o'of 49186 '19056525 'i'8'4'8'o'o'o'o'* 40921 '19066526 'i'8'4'9'o'o'o'o'* ■Natural Dual Dual Numbers. Logarithms. Numbers. •82632618 '19076571 'i'8'5'o'o'o'o'o'* 24355 '19086572 'i'8'5'i'o'o'o'o'' 16093 '19096572 '1'8'5'2'o'o'o'of 07831 '19106573 I 5 3 o'j^ •82599570 '19116573 'i'8'5'4'o'o'o'of 91310 '19126574 'i'8'5'5'o'o'o'o" 83051 '19136574 '1'8'5'6'0'o'o'of 74793 '19146575 1057000 O^j^ 66536 '19156575 'i'8'5'8'o'o'o'o'^ 'i'8'5'9'o'o'o'o- 58279 '19166576 49985 '19176621 •i'8'6'o'o'o'o'o'' 41730 '19186622 'i'8'6'i'o'o'o'o'* 33476 '19196622 'i'8'6'2'o'o'o'o'* 25223 '19206623 '1'8'6'3'0'o'o'of 16970 '19216623 'i'8'6'4'o'o'o'o- 08718 '19226624 'i'8'6'5'o'6'o'o'^ 00467 '19236624 'i'8'6'6'o'o'o'o'^ •82492217 '19246625 'i'8'6'7'o'o'o'o'* 83968 '19256625 'i'8'6'8'o'o'o'o'* 75720 '19266626 'i'8'6'9'o'o'o'o'* 67435 '19276671 'i'8'7'o'o'o'o'of 59188 '19286672 'i'8'7'i'o'o'o'o>^ 50942 '19296672 'i'8'7'2'o'o'o'o" 42697 '19306673 'i'8'7'3 'o'o'o'of 34453 '19316673 1074000 o'p 26210 '19326674 '1'8'7'svo'o'of • 17967 '19336674 'i'8'7'6'o'o'o'o'* 09725 '19346675 '1'8'7'7'0'0'0'of 01484 '19356675 'i'8'7'8'o'o'o'o" •82393244 '19366676 'i'8'7'9'o'o'o'o'* 84968 '19376721 'i'8'8'o'o'o'o'o'^ 76730 '19386722 'i'8!8'i'o'o'o'o>^ 68492 '19396722 'i'8'8'2'o'o'o'o'^ 60255 '19406723 'i'8'8'3'o'o'o'o'^ 52019 '19416723 'i'8'8'4'o'o'o'o'> 43784 '19426724 'i'8'8'5'o'o'o'o'' 35550 '19436724 •t'8'8'6'o'o'o'o'» 'i'8'8'7'o'o'o'o'*^ 27316 '19446725 19083 '19456725 'i'8'8'8'o'o'o'o'^ 10851 '19466726 'i'8'8'9'o'o'o'o'^ 02583 '19476771 'i'8'9'o'o'o'o'o'^ 1091000 ol* •82294353 '19486772 S6124 '19496772 '1'8'9'2'o'o'o'of 77895 '19506773 1093000 oy 69667 '19516773 'i'8'9'4'o'o'o'o" 61440 '19526774 '1'8'9'5'0'0'0'of 'i'8'9'6'o'o'o'o'^ 53214 '19536774 44989 '19546775 'i'8'9'7'o'o'o'o'> 36765 '19556775 '1'8'9'8'o'o'o'of 28541 '19566776 'i'8'9'9'o'o'o'o" Multiples of Differences. 830; 829 1660 1^158 2490 3320 4150 4980 5810 24s 7 3316 4145 4974 5803 6640 j 663: 7470 i 7461 827 826 1654 1652 2481 2478 3308 3304 413.'; 41.30 4962 49=; (> S789 5782 6616 6608 7443 7434 1 j 824 2 1648 3 2472 4 ! 3296 5 4120 6! 4944 7 5768 8 j 6592 9 I 7416 823 1646 2469 3292 411S 4938 5761 6584 7407 828 1656 24S4 3312 4140 4968 5796 6624 7452 825 1650 2475 3300 4125 4950 5775 6600 7425 822 1644 2466 3288 4110 4932 5754 6576 739S (»o) Nat. No. -8221 to -8140 D.iog. 1958.... to '2057.... D. No. T9'0'0t to T9'9'9t Natural Dual Dual Numbers. I^ogarithms. Nwrnbers. •82216552 '19581354 'l'9'o'o'o'o'o'o^ 08330 'i959'355 'l'9'o'l'o'o'o'o'^ 00 log '19601355 'l'9'o'2'o'o'o'o" •82191889 '19611356 '1'9'0'3'o'o'o'c'j^ 83670 '19621356 'i'9'o'4'o'o'o'o^ 75452 '19631357 I 9050000' 'i'9'o'6'o'o'o'o'' 67234 '19641357 59017 '^9651358 'i'9'o'7'o'o'o'o" 'I'g'o'S'o'o'o'o'^ 50802 '19661358 42587 '19671359 '1'9'0'9'o'o'o'of 34335 '19681404 I 9 I oy 26122 '19691405 'i'9'i'i'o'o'o'o'^ 17909 '19701405 '1'9'1'2'0'o'o'of 09697 '19711406 'i'9'i'3'o'o'o'o'^ 01486 '19721406 'i'9'i'4'o'o'o'o| •82093276 '19731407 '1'9'1'5'0'0'0'of 85067 '19741407 'i'9'i'6'o'o'o'o'^ 76858 '19751408 '1'9'1'7'0'0'0'of 68650 '19761408 'i'9'i'8'o'o'o'o'I^ 60443 '19771400 'i'9'i'9'o'o'o'of 52201 '19781454 I 920000 O'j* 43996 '19791455 'i'9'2'i'o'o'o'o'* 35792 '19801455 'l'9'2'2'o'o'o'o'* 27588 '19811456 'i'9'2'3'o'o'o'o" 19385 '19821456 '1'9'2'4'o'o'o'of IH83 '19831457 'i'9'2'5'o'o'o'o'I^ 02982 '19841457 '1'9'2'6'0'0'0'of •81994782 '19851458 'i'9'2'7'o'o'o'o'' 86583 '19861458 'i'9'2'8'o'o'o'o" 78384 '19871459 'i'9'2'9'o'o'o'o" 70149 '19881504 1930000 o'p 61952 '19891505 '1'9'3'l'o'o'o'of 53756 '19901505 'i'9'3'2'o'o'o'o" 45561 '19911506 '1'9'3'3'0'0'0'of 'x'9'3'4'o'o'o'of 37366 '19921506 29172 '19931507 '1'9'3'5'0'0'0'of 20979 '19941507 1930000 o'p 12787 '19951508 'i'9'3'7'o'o'o'o'^ 04596 '19961508 '1'9'3'8'0'0'0'of •81896406 •19971509 '1'9'3'9'0'0'0'of 88179 '19981554 '1'9'4'0'0'0'o'ot 79990 '19991555 'i'9'4'i'o'o'o'o'^ 71802 '20001555 'i'9'4'2'o'o'o'o'^ 63615 '20011556 '1'9'4'3'0'0'0'of 55429 '20021556 '1'9'4'4'0'0'0'of 47243 '20031557 '1'9'4'5'0'oVof 39058 '20041557 '1'9'4'6'0'0'0'of 30874 '20051558 'i'9'4'7'o'o'o'o'I^ 22691 '20061558 'i'9'4'8'o'o'o'o'1^ '1'9'4'9'0'0'0'of 14509 '20071559 Natural Dual Dual Numbers. Logarithms. Numbers. •81806291 '20081604 'i'9'5'o'o'o'o'o'{^ •81798110 '20091605 'i'9'5'i'o'o'o'o'^ 89930 '20101605 'i'9'5'2'o'o'o'o" 81751 '20111606 '1'9'5'3'0'0'0'ot 73573 '20121606 '1'9'5'4'0'o'o'o'j^ 65396 '20131607 19550000" 57219 '20141607 'i'9'5'6'o'o'o'o'* 49043 '20151608 'i'9'5'7'o'o'o'o'^ 40868 '20161608 'i'9'5'8'o'o'o'o'^ 32694 '20171609 '1'9'5'9'0'o'o'o'j^ 24484 '20181654 '1'9'6'0'o'o'o'of 16312 '20191655 'i'9'6'i'o'o'o'of 08140 '20201655 '1'9'6'2'0'0'0'o'j^ •81699969 '20211656 '1'9'6'3'0'0'0'of 91799 '20221656 '1'9'6'4'0'0'0'o'i^ 83630 '20231657 '1'9'6'5'0'0'0'ot 75462 '20241657 '1'9'6'6'0'0'0'of 67294 '20251658 'i'9'6'7'o'o'o'o" 59^27 '20261658 'i'9'6'8'o'o'o'of 50961 '20271659 'i'9'6'9'o'o'o'o'I^ 42760 '20281704 '»'„♦..»-.'_>— '-.'-.A 1970000 01* 34596 '20291705 'i'9'7'i'o'o'o'o'' 26433 '20301705 19720000'* 18270 '203 1 1 706 'i'9'7'3'o'o'o'o'|* loioS '20321706 1974000 o'p 01947 '20331707 '1'9'7'5'0'0'0'of •81593787 '20341707 'i'9'7'6'o'o'o'o'* 85628 '20351708 '1'9'7'7'0'0'0'of 77469 '20361708 'i'9'7'8'o'o'o'o'' 693 1 1 '20371709 'i'9'7'9'o'o'o'o'* 61117 '20381754 'i'9'8'o'o'o'o'o'*^ 52961 '20391755 '1'9'8'i'o'o'o'of 44806 '20401755 '1'9'8'2'0'0'0'of 36652 '20411756 'i'9'8'3'o'o'o'o'' 28498 '20421756 'i'9'8'4'o'o'o'o'|^ 20345 '20431757 '1'9'8'5'0'0'0'of 12193 '20441757 '1'9'8'6'0'0'0'oj 04042 '20451758 'i'9'8'7'o'o'o'o'' •81495892 '20461758 'i'9'8'8'o'o'o'o'* 87742 '20471759 'i'9'8'9'o'o'o'o'I* 79556 '20481804 'i'9'9'o'o'o'o'o| 71408 '20491805 'i'9'9'i'o'o'o'o" 63261 '20501805 '1'9'9'2'0'0'0'of 55115 '20511806 'i'9'9'3'o'o'o'o" 46969 '20521806 '1'9'9'4'0'o'o'of 38824 '20531807 '1'9'9'5'0'0'0'ot 30680 '20541807 '1'9'9'6'0'0'0'of 22537 '20551808 1997000 OJ 14395 '20561808 'I'g'g'S'o'o'o'o'' 06254 '20571809 'i'9'9'9'o'o'o'o'I» Multiples of Differences. 822 1644 2466 3288 41 10 4932 5754 6576 821 1642 2463 3284 4105 4926 5747 I6568 9 739817389 819 1638 2457 3276 4095 4914 5733 6552 7371 816 1632 2448 3264 4080 4896 5712 6528 7344 818 1636 2454 3272 4090 4908 5726 6544 7362 820 1640 2460 32S0 41CX) 4920 5740 6560 73S0 817 1634 245 » 3268 4085 4902 '5719 6536 735i 8151 814 1630 1 1628 2445 , 2443 3260 4075 4890 5705 6520 3256 4070 4884 5698 6512 7335 ; 7326 ' Nat. No. -8100 to '8020 D.Log. Natural Dual Dual Numbers, Logarithms. Numbers. *8ioooooo 21072103 '2'0'0'0'o'o'o'oj^ •80991900 '21082104 '2'0'0'l'o'o'o'of 83801 '21092104 '2'o'o'2'o'o'o'o'' 75703 '21102105 '2'o'o'3'o'o'o'o' ' 67605 '21II2105 '2'o'o'4'o'o'o'o' ^ 59508 '21122106 '2'0'0'5'o'o'o'of 51412 '2II32106 *2'o'o'6'o'o'o'o" 433*7 '21142107 '2'0'0'7'0'0'0'of 35223 '21152107 '2'0'0'8'o'o'o'of 27129 '21162108 '2'o'o'9'o'o'o'o'|^ 19000 '21172153 '2'0'l'o'o'o'o'of 10908 '21182154 '2'o'l'l'o'o'o'o'' 02817 '21192154 '2'o'l'2'o'o'o'o'' •80894727 '21202155 '2'o'i'3'o'o'o'o'^ 86638 '21212155 '2'o'i'4'o'o'o'o'^ 78549 '21222156 '2'0'1'5'o'o'o'of 70461 '21232156 '2'0'1'6'0'0'o'of 62374 '21242157 '2'0'1'7'o'o'o'of 54288 '21252157 '2'o'i'8'oo'o'o''* 46203 '21262x58 '2'o'i'9'o'o'o'o'^ 38081 '21272203 '2'0'2'0'o'o'o'of 29997 '21282204 '2'o'2'l'o'o'o'o'^ 21915 '21292204 '2'o'2'2'o'o'o'o'^ 13833 '21302205 '2'o'2'3'o'o'o'o'^ 05752 '21312205 '2'o'2'4'o'o'o'o'^ •80797671 '21322206 '2'0'2'5'o'o'o'of 89591 '21332206 '2'o'2'6'o'o'o'o'I^ 81512 '21342207 '2'o'2'7'o'o'o'o'^ 73434 '21352207 '2'0'2'8'o'o'o'of 65357 '21362208 '2'o'2'9'o'o'o'o'I* 57243 '21372253 '2'o'3'o'o'o'o'o'|^ 49167 '21382254 '2'o'3'i'o'o'o'o" 41092 '21392254 '2'o'3'2'o'o'o'o'^ 33018 '21402255 '2'0'3'3'o'o'o'of 24945 '21412255 2034000 o'p 16873 '21422256 '2'o'3'5'o'o'o'o4^ 08801 '21432256 '2'o'3'6'o'o'o'o'^ 00730 '21442257 '2'o'3'7'o'o'o'o' ' •80692660 '21452257 '2'0'3'8'0'0'0'of 84591 '21462258 '2'o'3'9'o'o'o'o^' 76486 •21472303 '2'o'4'o'o'o'o'o'|^ 68418 '21482304 '2'0'4'1'0'0'c'o" 60351 '21492304 '2'o'4'2'o'o'o'o'^ 52285 '21502305 '2'o'4'3'o'o'o'o" 44220 '21512305 '2'o'4'4'o'o'o'o'^ 36156 '21522306 '2'o'4'5'o'o'o'ot 28092 '21532306 '2'o'4'6'o'o'o'o' ' 20029 '21542307 '2'o'4'7'o'o'o'o' ' 11967 '21552307 '2'o'4'8'o'o'o'o>^ 03906 '21562308 '2*o'4'9'o'o'o*of Natural Dual Dual Numbers. Logarithms. Numbers. •80595809 '21572353 •2'o^5'o'o'o'o'o' ' 87749 '21582354 '2'o'5'i'o'o'o'o'^ 79690 '21592354 '2'o'5'2'o'o'o'o'^ 71632 '21602355 '2'o'5'3'o'o'o'o'^ 63575 '2I6I2355 '2'o'5'4'o'o'o'o'^ 55519 '21622356 '2'o'5'5'o'o'o'o4^ 47463 '21632356 '2'o'5'6'o'o'o'o'^ 39408 '21642357 •2'o'5'7'o'o'o'o'^ 31354 '21652357 '2'o'5'8'o'o'o'o'^ 23301 '21662358 '2'o'5'9'o'o'o'o'{^ I52I3 '21672403 '2'o'6'o'o'o'o'o'^ 07I6I '21682404 '2'o'6'i'o'o'o'o'^ •804991 10 '21692404 *2'o'6'2'o'o'o'o'* 91060 '21702405 •2'o'6'3'o'o'o'o'' 83011 '21712405 '2'o'6'4'o'o'o'o' ' 74963 '21722406 '2'o'6'5'o'o'o'o4^ 66916 '21732406 '2'o'6'6'o'o'o'o'^ 58869 '21742407 '2'o'6'7'o'o'o'o" 5^823 '21752407 '2'o'6'8'o'o'o'o'^ 42778 '21762408 •2'o'6'9'o'o'o'o^^ 34698 '21772453 •2'o'7'o'o'o'o'of 26655 '21782454 '2'o'7'i'o'o'o'o'|^ 18612 '21792454 '2'0'7'2'0'0'0'o'j^ 10570 '21802455 '2'o'7'3'o'o'o'o'^ 02529 '2I8I2455 '2'o'7'4'o'o'o'o^ •80394489 '21822456 '2'o'7'5'o'o'o'o' ' 86450 '21832456 •2'o'7'6'o'o'o'o ^ 784II '21842457 '2'o'7'7'o'o'o'o' > 70373 '21852457 '2'o'7'8'o'o'o'o'* 62336 '21862458 •2'0'7'9'0'o'o'c' ^ 54264 '21872503 '2'o'8'o'o'o'o'o'^ 46229 '21882304 '2'o'8'i'o'o'o'o" 38194 '21892304 '2'o'8'2'o'o'o'o'* 30160 '21902305 •2'o'8'3'o'o'o'o' ' 22127 •21912305 '2'o'8'4'o'o'o'o'^ 14095 •21922306 •2'o'8'5'o^o'o'o'^ 06064 '21932306 '2'o'8'6'o'o'o'o'^ •80298033 '21942307 '2'o'8'7'o'o'o'o'^ 90003 '21952307 •2'o'8'8'o'o'o'o' ^ 8x974 '21962308 •2'o'8'9'o'o'o'o^ ' 73909 '21972553 '2'o*9'o'o'o'6'o' ^ 65882 '21982554 '2'o'9"i'o'o'o'o" 57855 '21992554 •2'o'9'2'o'o'o'o' ' 49829 '22002555 '2'o'9'3'o'o'o'o' ^ 41804 '22012555 '2'0'9'4'o'o'o'of 33780 '22022556 '2'o'9'5'o'o'o'o' ' 25757 '22032556 '2'o'9'6'o'o'o'o' ' 17734 '22042557 '2'o'9'7^o'o'o'o' ' 09712 '22052557 '2'o'9'8'o'o'o'o'^ 01691 '22062558 •2'o'9'9'o'o'o'o'^ Multiples of Differences, 810 1620 2430 3240 4050 4860 5670 6480 7290 809 1618 2427 3236 4045 4854 5663 6472 7281 807 806 I6I4 I6I2 2421 2418 3228 3224 403.S 4030 4842 4836 5649 S642 64S6 6448 7263 7254 r I 804 2 1608 3 2412 4 3216 5 I 4020 6 j 4824 7 1 5628 8 I 6432 9 I 7236 803 1606 2409 3212 401 5 4818 5621 6424 7227 808 1616 2424 3232 4040 4848 5656 6464 7272 80s 1610 2415 3220 4025 4830 5635 6440 7245 802 1604 2406 3208 4010 4812 5614 6416 7218 {22) Nat No. -8019 to 7939 D. Log. '2207.... to '2306.... D. No. '2'rO'Ot to •2'r9'9t Natural Dual Dual Numbers. Logarithms. Numbers. •80190000 '22077137 '2'1'o'o'o'o'o'of 81981 '220^138 '2'1'o'l'o'o'o'of 73963 '22097138 '2'l'o'2'o'o'o'o'^ 65946 '22107139 '2"i'o'3'o'o'o'o'J^ 57929 '22117140 '2'i'o'4'o'o'o'o']^ 49913 '22127140 •2'l'o'5'o'o'o'o't^ 41898 '22137140 '2'i'o'6'o'o'o'o'' 33884 '22147141 '2'1'0'7'0'o'o'of 25871 '22157141 '2'L'o'8'o'o'o'ot 17858 '22167142 '2'i'o'9'o'o'o'o'|^ 09810 '22177187 '2'1'l'o'o'o'o'of 01799 '22187188 '2'1'l'l'o'o'o'of •80093789 '22197188 '2'l'l'2'o'o'o'o^ 85780 '22207189 '2'i'i'3'o'o'o'o'^ 77771 '22217189 '2'1'1'4'0'0'o'of 69763 '22227190 '2'1'1'5'0'o'o'ot 61756 '22237190 '2'1'1'6'o'o'o'of 53750 '22247191 '2'1'1'7'o'o'o'of 45745 '22257191 '2'i'i'8'o'o'o'of 37740 '22267192 '2'1'1'9'o'o'o'of 29700 '22277237 '2'x'2'o'o'o'o'of 21697 '22287238 '2'1'2'l'o'o'o'of 13695 '22297238 '2'1'2'2'o'o'o'of 05694 '22307239 '2'1'2'3'o'o'o'of •79997693 '22317239 '2'1'2'4'o'o'o'o'i^ 89693 '22327240 '2'1'2'5'o'o'o'of 81694 '22337240 '2'1'2'6'o'o'o'of 73696 '22347241 '2'l'2'7'o'o'o'o'*^ 65699 '22357241 '2'1'2'8'o'o'o'of 57702 '22367242 '2'1'2'9'o'o'o'of 49671 '22377287 2 1300000'^ 41676 '22387288 '2'i'3'i'o'o'o'o'' 33682 '22397288 '2'l'3'2'o'o'o'o'^ 25689 '22407289 '2'i'3'3'o'o'o'o'^ 17696 '22417289 '2'1'3'4'0'0'0'of 09704 '22427290 '2'i'3'5'o'o'o'ot 01713 '22437290 '2'1'3'6'0'0'0'ot •79893723 '22447291 '2'r'3'7'o'o'o'o'^ 85734 '22457291 '2'i'3'3'o'o'o'o" 77745 '22467292 '2'i'3'9'o'o'o'o'^ 69721 '22477337 2 140000 O'P 61734 '22487338 '2'i'4'i'o'o'o'o'^ 53748 '22497338 '2'l'4'2'o'o'o'o'^ 45763 '22507339 '2'i'4'3'o'o'o'o" 37778 '22517339 '2'1'4'4'o'o'o'of 29794 •22527340 '2'1'4'5'o'o'o'ot 21811 '22537340 '2'i'4'6'o'o'o'o'' 13829 '22547341 '2'i'4'7'o'o'o'o'> 05848 '22557341 '2'i'4'8'o'o'o'o^* •79797867 '22567342 '2'i'4'9'o'o'o'o| Natural Dual Dual Numbers. Logarithms. Numbers. 79789851 '22577387 •2^l'5'o'o'o'o^of 81872 '22587388 '2'i'5'i'o'o'o'o'^ 73894 '22597388 '2'l'5'2'o'o'o'o'^ 65917 '22607389 '2'1'5'3'o'o'o'of 57940 '22617389 '2'i'5'4'o'o'o'o'|^ 49964 '22627390 '2'i'5'5'o'o'o'o4^ 41989 '22637390 '2'i'5'6'o'o'o'o'' 34015 '22647391 '2'i'5'7'o'o'o'o'^ '2'i^5'8'o'o'o'o'' 26042 '22657391 18069 '22667392 •2^i'5'9'o'o'o'o'* 1 006 1 '22677437 '2'i'6'o'o'o'o'o| 02090 '22687438 '2'i'6'i'o'o'o'o'^ •79694120 '22697438 '2'l'6'2'o'o'o'o'^ 86I5I '22707439 '2'i'6'3'o'o'o'o'^ 78182 '22717439 '2'1'6'4'0'o'o'of 70214 '22727440 '2'i'6'5'o'o'o'o4^ 62247 '22737440 '2'i'6'6'o'o'o'o" 54281 '22747441 '2'i'6'7'o'o^o'o'^ 46316 '22757441 '2'1'6's'o'o'o'o'^ 38351 '22767442 '2'i'6'9'o'o'o'o'^ 30351 '22777487 '2'i'7'o'o'o'o'o4^ 22388 '22787488 '2'i'7'i'o'o'o'o'^ 14426 '22797488 '2'l'7'2^o'o'o'o'^ '2'1'7'3'0'0'o'o'p 06465 '22807489 •79598504 '22817489 '2'1'7'4'0'0'0'o'j^ 90544 '22827490 '2'r7'5'o'o'o'o4^ 82585 '22837490 '2'i'7'6'o'o'o'o'^ 74627 •22847491 '2'i'7'7'o'o'o'o'* '2'i'7'8'o'o'o'o'^ •2'i'7'9'o'o'o'o" 66670 '22857491 58713 '22867492 50721 '22877537 '2'i'8'o'o'o'o'o'1^ 42766 '22887538 '2'i'8'i'o'o'o'o'^ 34812 •22897538 '2'l'8'2'o'o'o'o'^ 26859 '22907539 '2'i'8'3'o'o'o'o'^ 18906 '22917539 '2'i'S'4'o'o'o'o'|' 10954 '22927540 '2'i'8'5'o'o'o'oj^ 03003 •22937540 '2'i^8'6'o^o^o'o'' •79495053 •22947541 '2'i'S'7'o'o'o'o'^ 87103 •22957541 '2'i'8'8'o'o'o'o'j' 79^54 •22967542 '2'i'8'9'o^o'o'o'^ 7II70 '22977587 *2'i'9'o'o'o'o'o^ 63223 '22987588 '2'i'9^i'o^o'o^o'^ 55277 '22997588 •2'l'9'2'o'o'o'o'^ 47331 •23007589 '2'i'9'3^o'o'o'o'^ 39386 '23017589 '2'i'9^4^o'o'o'o'^ 31442 '23027590 '2'i'9'5'o'o'o'o4^ 23499 '23037590 '2'i'9'6'o'o'o'o'^ 15557 '23047591 '2'i'9'7'o^o'o'o'^ 07615 '23057591 '2'i'9'8'o'o'o'o'^ 79399674 •23067592 '2'i'9'9'o^o'o'o'' Multiples of Differtii. 1 I 801 2 I 1602 3 I 2403 4 ! 3204 5 1 4005 614806 5607 6408 7209 r 798 7':-; 2 159^ 159^ 3 2394 2391 4 3192 318S S 3990 398s 6 4788 4782 7 SS86 5579 8 6384 6376 9 7182 7'73 7951 794; 7 1590 ! 1588 ■ i; 2385 I 2382 : 2- ; 3180 3'76 31 3975 3970 ! 3" 4770 476-: - ■5565 55? 6360 635 7155 7M Nat. No. 7938 to 7860 D. Log. '2308.... to '2407.... D. No. •2'2'0'Ot to •2'2'9'9t (^i) Natural Numbers. •79388100 80161 72223 64286 56350 48414 40479 32545 24612 16680 08712 00781 ■79292851 84922 76994 69066 61139 53213 45288 37363 29403 21480 13558 05637 •79197716 89796 81877 73959 66c 42 58125 50174 42259 34345 26432 18519 10607 02696 •79094786 86877 78968 71024 63117 55211 47305 39400 31496 23593 15691 07789 •78999888 Dual Logarithms. '23082170 '23092171 '23102171 '23112172 '23122172 '23132173 '23142173 '23152174 '23162174 '23172175 '23182220 '23192221 '23202221 '23212222 '23222222 '23232223 '23242223 '23252224 '23262224 '23272225 '23282270 '23292271 '23302271 '23312272 '23322272 I, j 23332273 '23342273 1*23352274 |'23362274 |'23372275 '23382320 '23392321 |'23402321 {•23412322 '23422322 '23432323 '23442323 '23452324 '23462324 '23472325 '23482370 '23492371 '23502371 '23512372 '23522372 '23532373 '23542373 '23552374 '23562374 '23572375 Dual Numbers. '2'2'0'0'0'o'o'of '2'2'0'l'o'o'o'of '2'2'0'2'o'o'o'o'f '2'2'o'3'o'o'o'o| '2'2'0'4'o'o'o'of 22000000 22070000' '2'2'0'8'o'o'o'of '2'2'0'9'o'o'o'of 2210000 OT 22110000 '2'2'l'2'o'o'o'o '2'2'l'3'o'o'o'o '2'2'l'4'o'o'o'o 22150000'' '2'2'l'6'o'o'o'o'^ '2'2'l'7'0'0'0'0'^ '2'2'1'8'O'O'OV '2'2'l'9'o'o'o'o'' '2'2'2'o'o'o'o'0' '2'2'2'l'o'o'o'0' '2'2'2'2'o'o'o'0' '2'2'2'3'o'o'o'of 2224000 o'p 22250000'' 22200000'' >_>_)_)„)_ 22270000 2 2200000" '2'2'2'9'o'o'o'o' 2 2300000" '2'2'3'l'o'o'o'o'^ 22320000" 22330000" 2234000 o'p 2 2 3 5 o O O ' 2 230000 O' '2'2'3'7'o'o'o'o 22300000 '2'2'3'9'o'o'o'o'|' 2 240000 O' '2'2'4'l'o'o'o'o '2'2'4'2'o'o'o'o '2'2'4'3'o'o'o'o '2'2'4'4'o'o'o'o 2245000 O'P '2'2'4'6'0'0'0'of '2'2'4'7'o'o'o'o" 22400000" *2'2'4'9'o'o'o'o" Natural Dual Dual Numbers. Logarithms. Numbers. ■78991953 '23582420 •2'2^5'o'o'o'o'o'f' 84054 '23592421 '2'2^5'l'o'o'o'o" 76156 '23602421 '2'2'5'2'o'o'o'o" 68258 '23612422 '2'2'5'3'o'o'o'o" 60361 '23622422 '2'2'5'4'o'o'o'ot 52465 '23632423 '2'2'5'5'o'o'o'o| 44570 '23642423 '2'2'5'6'o'o'o'o' ' 36676 '23652424 •2'2'5'7'o'o'o'o" 28782 '23662424 '2'2'5'8'o'o'o'o" 20889 '23672425 '2'2'5'9'ovo'o' ' I2961 '23682470 '2'2'6'o'o'o'o'o'|' 05070 •23692471 '2'2'6'l'0'0'0'0" •78897179 '23702471 '2'2'6'2'o'o'o'o" 89289 '23712472 '2'2'6'3'o'o'o'o" 81400 '23722472 '2'2'6'4'o'o'o'o' ' 73512 '23732473 '2'2'6'5'o'o'o'o'[' 65625 '23742473 '2'2'6'6'o'o'o'o' ' 57738 ! '23752474 '2'2'6'7'o'o'o'o'^ 49852 '23762474 •2'2'6'8'o'o'o'o" 41967 '23772475 '2'2'6'9'o'o'o'o{ 34048 ^23782520 '2'2'7'0'o'0'0'0^ 26165 '23792521 '2'2'7'l'o'o'o'o" 18282 •23802521 '2'2'7'2'0'0'0'0" 10400 '23812522 '2'2'7'3'0'0'0'of 02519 '23822522 '2'2'7'4'0'0'0^0'|^ •78794639 '23832523 '2'2'7'5'0'0'0'of 86760 '23842523 22700000'^ 78881 '23852524 '2'2'7'7'o'o'o'o'j' 71003 '23862524 '2'2'7'8'o'o'o'o1' 63126 '23872525 '2'2'7'9'o'o'o'o'|' 55214 '23882570 '2'2'8'o'o'o'o'o'^ 47338 '23892571 '2'2'8'l'o'o'o'o" 39463 '23902571 '2'2'8'2'o'o'o'o" 31589 '23912572 '2'2'8'3'o'o'o'o" 23716 '23922572 '2'2'8'4'o'o'o'o" 15844 '23932573 '2'2'8'5'o'o'o'o4' 07972 '23942573 '2'2'8'6'o'o'o'o" ooioi ! '23952574 '2'2'8'7'o'o'o'o" •78692231 '23962574 '2'2'8'8'o'o'o'o" 84362 '23972575 '2'2'8'9'o'o'o'o" 76458 •23982620 '2'2'9'0'0'0'o'o'f 68590 '23992621 '2'2'9'l'o'o'o'o" 60723 '24002621 '2'2'9'2'o'o'o'o" 52857 '24012622 '2'2'9'3'o'o'o'o" 44992 '24022622 '2'2'9'4'0'0'0'o'f 37128 '24032623 '2'2'9'5'o'o'o'o'^ 29264 '24042623 '2'2'9'6'o'o'o'o" 21401 '24052624 '2'2'9'7'o^o'o'o" 13539 '2406262^ '2'2'9'8'o'o'o'o'' 05678 "24072625 '2'2'9'9'o'o'o'o'' Multiples of Differences. 793 792 i5«6 1584 2379 2376 3172 3168 3965 3960 475« 4752 5551 5S44 t>.344 6336 7137 7128 790 1580 2370 3160 3950 4740 5530 6320 7II0 787 1574 2361 3148 3935 4722 5509 8 ; 6296 9 7083 789 1578 2367 3156 3945 4734 5523 6312 7101 I 786 ■ «572 235S '3144 !3930 14716 '5502 ;6288 17074 791 1582 2373 31H 3955 4746 5537 6328 7119 788 1576 2364 3152 3940 472S 5516 6304 7092 (24) Nat No. 7859 to '7781 D. Log. '2408.... to '2507.... D. No. '2'3'0'Ot to '2'3'9'9t Natural . Dual Dual Numbers. Logarithms. Numbers. 78594219 '24087204 *2*3*o'o*o'o'o*of 86360 '24097205 *2*3'o*i'o'o'o'o| 78501 '24107205 '2'3'o'2'o*o'o*0'^ 70643 '24117206 '2'3'o'3*o'o*o'o'' 62786 '24127206 '2'3'o'4'o*o'o'o'^ 54930 '24137207 '2'3*o'5'o'o'o'of 47074 '24147207 '2'3'o*6'o'o'o*o'^ 39219 '24157208 '2*3'o'7*o*o'o'o'^ 31^365 '24167208 '2'3'o'8*o'o*o'o'^ 23512 '24177209 '2'3*o'9'o*o'o'o'^ 15625 '24187254 *2'3'i'o'o'o'o*o^ 07773 '24197255 '2'3'i*i*o*o*o'o'^ •78499922 '24207255 '2'3*l'2*0*0*0*0'^ 92072 '24217256 '2*3'i'3*o'o'o'o'^ 84223 '24227256 '2'3*i*4'o'o'o'o'^ 76375 '24237257 '2'3'i'5'o'o'o'o'I^ 68527 '24247257 '2'3'i*6'o'o'o*of 60680 '24257258 '2'3'i'7*o'o*o'o'^ 52834 '24267258 '2'3'i'8'o'o'o'o'^ 44989 '24277259 '2'3'i'9'o*o*o'o" 37109 '24287304 '2*3'2'o'o*o'o'o'|^ 29265 '24297305 '2'3'2*l'o'o'o*0^' 21422 '24307305 '2'3'2'2'o'o*o'o" 13580 '24317306 '2'3'2'3*o'o'o'o'* 05739 '24327306 '2"3'2'4'o*o'o*o' ^ •78397898 '24337307 *2'3'2'5'o'o'o'of 90058 '24347307 '2'3'2*6'o'o'o'o" 82219 '24357308 '2'3*2'7'o'o'o*o'* 74381 '24367308 *2'3'2'8*o*o*o'of 66544 '24377309 '2'3*2'9*o*o'o'o1^ 58672 '24387354 '2'3'3'0'0'0'o'of 50836 '24397355 '2*3*3' i'o*o'o*o" 43001 '24407355 '2'3*3'2'o'o'o*o'' 35167 '24417356 '2'3'3'3'o'o'o*o'' 27333 '24427356 '2'33'4'0'0'0'of 19500 '24437357 '2*3'3'5'o'o*o'o4* 1 1668 '24447357 '2*3*3*6*0*0*0*0'^ 03837 '24457358 '2*3'3*7'o*o*o*o' ^ •78296007 '24467358 '2'3'3'8*o'o'o*o' ' '2'3*3'9'o'o*o'of 88177 '24477359 80313 '24487404 '2*3'4'o'o'o'o'o'j^ ' 2*3*4* i'o*o'o'o'^ 72485 '24497405 64658 '24507405 *2'3*4'2'o*0*0*0'^ 56832 *245i74o6 *2*3'4'3'o*o'o*o'^ 49006 '24527406 *2'3'4*4'o'o'o'o^ 41181 '24537407 '2'3'4'5Vo'o'o| 33357 '24547407 '2'3'4'6*o*o'o'o'> 25534 '24557408 '2'3*4'7'o'o'o*o'^ 17711 '24567408 *2*3'4*8'o'o*o'o'' 09889 '24577409 *2'3'4'9'o'o'o'of Natural Numbers. •78202033 78194213 86394 78575 70757 62940 55124 47308 39493 31679 23831 16019 08207 00396 •78092586 84777 76969 . 69161 61354 53548 45707 37902 30098 22295 1 4493 06692 •77998891 91091 83292 75494 67662 59865 52069 44274 36480 28686 20893 13101 05310 77897519 89694 81905 74117 66330 58543 50757 42972 35188 27404 19621 Dual Logarithms, 24587454 24597455 24607455 24617456 24627456 24637457 24647457 24657458 24667458 24677459 24687504 24697505 24707505 24717506 24727506 24737507 24747507 24757508 24767508 24777508 24787554 24797555 24807555 24817556 24827556 24837557 24847557 24857558 24867558 24877559 24887604 24897605 24907605 24917606 24927606 24937607 24947607 24957608 24967608 24977609 24987654 24997655 25007655 25017656 25027656 25037657 25047657 25057658 25067658 25077659 Dual Numbers. 2'3'5*o'o*o*o■o'^ 2'3*5'i*o'o'o'o 2'3'5'2'o'o*o'o 2'3*5'3'o'o'o'o 2*3*5*4* o'o'o*o 2'3'5'5]o'o*o'of 2*3'5*6'o'o*o*o'|^ 2'3*5*7'o*o*o*o'|^ 2'3'5'8'o'o'o'of 2'3*5'9'o'o*o*oj^ 2'3'6*o'o'o'o'o'j^ 2'3*6'i'o'o'o'oT^ 2*3'6*2*o*o'o'oj^ 23 6'3'o'o'o*o'I^ 2*3'6'4'o*o'o'o'I^ 2*3*6*5*o'o'o'o 2'3'6*6'o*o*o' 2'3'6'7'o*o'o'o' 2*3*6*8'o'o*o'o' 2*3'6'9'o'o'o'o' 2'3'7'oo'o'o'o'|^ 2'3'7*i*o'o*o'o'p 2'3'7'2*o*o'o*of 2'3'7'3'0'o'o'o'j^ 2'3*7'4'o'o'o'o^ 2'3*7'5*o'o'o'o'I^ 2*3*7*6'o'o'o'o 2'3'7'7'o*o'o'o' 2'3'7'8'o*o*o*o' 2'3'7'9'o'o'o*o' 2'3'8'o*o'o'o'of 2*3*8*1*0*0*0*0' 2'3*8'2'o*o*o'o' 2*3'8'3*o*o*o'o' 2*3*8*4'o'o*o'o' .»_»o'-'- 2 30 5 O O O O' 2'3*8'6*o*o'o'o' 2'3'8*7'o'o'o' *3'8'8'o'o'o*o| *3'8*9*o*o'o'of 2 39 00000' 2'3'9*i*o'o*o'o' 2'3'9*2*o'o'o'o' 2'3*9'3'o'o'o'o' 2'3'9'4'o'o'o'of 2'3'9*5'o'o'o'o' 2'3'9*6'o'o'o'( 2397000 2*3'9*8'o'o'o'o' 2'3'9'9'o'o*o'o'j^ Multiples of Differences. 785 1570 2355 3140 3925 47IO 5495 6280 7065 782 1564 2346 3128 3910 4692 5474 6256 7038 784! 7S3 1568' 1566 2352 3136 3920 4704 5488 6272 7056 781 1562 2343 3124 3905 4686 5467 2349 3132 3915 469S 54S1 6264 7047 780 1560 2340 3120 390J 4680 5460 1 1 779 2 , 1558 3 2337 4 3"6 5 3895 6 1 4674 7 I 5453 8 I 6232 9 ! 701 1 6248 j 6240 7029 I 7020 778 »556 2334 3112 3890 4668 5446 6224 7002 Nat. No. 7780 to 7704 D. Log. '2509.... to '2608.... D. No. '2'4'0'Ot to '2'4'9'9t (^5) Natural Numbers. 77808277 00496 •77792716 84937 77159 69381 61604 53828 46053 38278 30469 22696 14924 07153 •77699382 91612 83843 7607s 68307 60540 52738 44973 37209 29445 21682 13920 06159 98399 •77590639 82880 75086 67328 59571 51815 44060 36306 28552 20799 13047 05296 •77497510 89760 82011 74263 66516 58769 51023 43278 35534 27790 Dual Logarithms. 25092237 '25102238 '25112238 '25122239 '25132239 '25142240 '25152240 '25162241 '25172241 '25182242 '25x92287 '25202288 '25212288 '25222289 '25232289 '25242290 '25252290 '25262291 '25272291 '25282292 '25292337 '25302338 '25312338 25322339 25332339 '25342340 '25352340 '25362341 '25372341 '25382342 '25392387 '25402388 '25412388 '25422389 '25432389 '25442390 '25452390 '25462391 '25472391 '25482392 '25492437 '25502438 '25512438 '25522439 '25532439 '25542440 '25552440 '25562441 '25572441 '25582442 Dual Numbers. 24000000 2'4'o'i'o'o'o'o' 2'4'o'2'o'o'o'o 2403000 o'p 24040000^ 24050000 2'4'o'6'o'o'o'o 2'4'o'7'o'o'o'o' 2'4'0'8'0'ob'of 2'4'0'9'0'0'0'of 2410000 O''* 241 1000 O' 2'4'l'2'o'o'o'0' 2'4'i'3'o'o'o'o' 2'4'i'4'o'o'o'o' 2'4'i'5'o'o'o'o' 24100000'^ 2'4'1'7'0'0'0'of 2'4'i'8'o'o'o'o' 2'4'i'9'o'o'o'o- 24200000''^ 2'4'2'l'o'o'o'0' 2'4'2'2'o'o'o'0' 2'4'2'3'o'o'o'o' 2'4'2'4'o'o'o'o' 24250000'* 24200000'* 2'4'2'7'o'o'o'o'* 24200000'* 2429000 o'p 2430000 o''* 243 1000 O' 243 2000 O' 2'4'3'3'o'o'o'o' 2'4'3'4'o'o'o'o' 24350000' 2'4'3'6'o'o'o'o' 2'4'3'7'o'o'o'o' 24300000' 2'4'3'9'o'o'o'o'I* 2440000 O' 2441000 O' 2'4'4'2'o'o'o'o' 2'4'4'3'o'o'o'o' 2'4'4'4'o'o'o'o' w 2445000 o'p 2'4'4'6'o'o'o'o' 2'4'4'7'o'o'o'o' 2'4'4'8'o'o'o'o' 2'4'4'9'o'o'o'o' Natural Dual Dual Numbers. Logarithms. Numbers. •77420013 '25592487 '2'4'5'o'o'o'o'o' * 12271 '25602488 '2'4'5'i'o'o'o'o'' 04530 '25612488 '2'4'5'2'o'o'o'o" •77396790 '25622489 '2'4'5'3'o'o'o'o'* 89050 '25632489 '2'4'5'4'o'o'o'o' * 81311 '25642490 '..' .'-'-'— '—'—'—A 24550000'* 73573 '25652490 '2'4'5'6'o'o'o'o'* 65836 '25662491 '2'4'5'7'o'o'o'o" '2'4'5'8'o'o'o'o'* 58099 '25672491 50363 '25682492 '2'4'5'9'o'o'o'of 42593 '25692537 '2'4'6'o'o'o'o'o'* 34859 '25702538 '2'4'6'i'o'o'o'o'* 27126 '25712538 '2'4'6'2'o'o'o'o' ' 19393 '25722539 '2'4'6'3'o'o'o'o" '2'4'6'4'o'o'o'o' * 11661 '25732539 03930 '25742540 '2'4'6'5'o'o'o'o" •77296200 '25752540 '2'4'6'6'o'o'o'o' ' 88470 '25762541 '2'4'6'7'o'o'o'o'' 80741 '25772541 '2'4'6'8'o'o'o'o' ^ 73013 '25782542 '2'4'6'9'o'o'o'o' * 65250 '25792587 '2'4'7'o'o'o'o'o" 57523 '25802588 '2'4'7'i'o'o'o'o" 49797 '25812588 '2'4'7'2'o'o'o'o" 42072 '25822589 '2'4'7'3'o'o'o'o'* 34348 '25832589 '2'4'7'4'o'o'o'o'I* 26625 '25842590 '2'4'7'5'0'0'0'o'j* 18902 '25852590 '2'4'7'6'o'o'o'o' ' 11180 '25862591 '2'4'7'7'o'o'o'o'* 03459 '25872591 '2'4'7'8'o'o'o'o'* •77195739 '25882592 '2'4'7'9'o'o'o'o'I^ 87985 '25892637 '2'4'8'o'o'o'o'o" '2'4'8'i'o'o'o'o'^ 80266 '25902638 72548 '25912638 '2'4'8'2'o'o'o'o'* '2'4'8'3'o'o'o'o' * 64831 '25922639 57115 '25932639 '2'4'8'4'o'o'o'o' * 49399 '25942640 '2'4'8'5'o'o'o'o'^ 41684 '25952640 '2'4'8'6'o'o'o'o'* '2'4'8'7'o'o'o'o't* 33970 '25962641 26257 '25972641 '2'4'8'8'0'0'o'of 18544 '25982642 '2'4'8'9'o'o'o'o'|* 10797 '25992687 '2'4'9'o'o'o'o'o' ^ 03086 '26002688 '2'4'9'i'ob'o'o'* •77095376 '26012688 '2'4'9'2'o'o'o'o'* 87666 '26022689 '2'4'9'3'o'o'o'o'' 79957 '26032689 '2'4'9'4'o'o'o'o' * 72249 '26042690 24950000'* 64542 '26052690 '2'4'9'6'o'o'o'o' * 56836 '26062691 24970000'* 49130 '26072691 '2'4'9'8'o'o'o'o' ' 41425 '26082692 '2'4'9'9'o'o'o'o' ' Muiltiples of Dfferences. 778 777 iSS^J 1554 2334 2331 3U2 3108 3890 388s 4668 4662 =144^ 5439 6224 6216 7002 6993 775 774 1550 1548 2325 2322 3100 3096 3875 3870 4650 4644 5425 5418 6200 6192 6975 6966 772 1544 2316 30S8 3860 4632 5404 6176 6948 771 1542 2313 3084 3855 4626 5397 6168 6939 776 1553 2328 3104 3880 4656 5432 6208 6984 1546 2319 3092 3865 4638 5411 6184 6957 770 1540 2310 3080 3850 4620 5390 6160 6930 (26) Nat. No. 7703 to 7627 D. Log. '2609.... to '2708.... D. No. '2'5'0'Ot to '2'5'9'9t Natural Numbers. L 77030194 22491 14789 07088 •76999387 91687 83988 76290 68592 60895 53164 45469 37774 30080 22387 14695 07004 •76899313 91623 83934 76211 68523 60836 53150 45465 37780 30096 22413 14731 07050 •76799334 91654 83975 76297 68619 60942 53266 45591 37916 30242 22535 14863 07192 •76699521 91851 84182 76514 68846 61179 53513 Dual Logarithms. '26097271 '26107272 '26117272 '26127273 '26137273 '26147274 '26157274 '26167275 '26177275 '26187276 '26197321 '26207322 '26217322 '26227323 j'26237324 1 26247325 I 26257325 1*26267326 '26277326 '26287327 '26297371 '26307372 '26317372 '26327373 '26337373 '26347374 '26357374 '26367375 '26377375 '26387376 '26397421 '26407422 '26417422 '26427423 '26437423 '26447424 '26457424 '26467425 '26477425 '26487426 '26497471 '26507472 '26517472 '26527473 '26537473 '26547474 '26557474 '26567475 '26577475 '26587476 Dual Numbers. '2'5'o'o'o'o'o'of 2501000 O'j* 2502000 o'v '2'5'0'3'0'0'0'cf '2'5'0'4'0'0'0'of 2505000 ol* '2'5'0'6'o'o'o'of '2'5'0'7'o'o'b'ot '2'5'o'S'o'o'o'of 2509000 oT 25 lOOOOO'^ '2'5'i'i'o'o'o'o''^ 25 1 20000'^ 25 130000" 25 14000 o'p 2515000 OY '2'5'1'6'0'0'o'of '2'5'1'7'o'o'o'of '2'5'1'8'0'0'0'of '2'5'1'9'0'0'o'of '2'5'2'o'o'o'o'o'I^ '2'5'2'i'o'o'o'of '2'5'2'2'o'o'o'of '2'5'2'3'o'o'o'of 2 5 2 4 o o o oy 25 250000'^ 25200000'* 25270000'* '2'5'2'8'o'o'o'o'^ '2'5'2'9'0'0'0'of '->-'«»_>„' 2 5 300000'* '2'5'3'i'o'o'o'o'^ '2'5'3'2'o'o'o'o'^ '2'5'3'3'o'o'o'o'* '2'5'3'4'0'o'o'o'p '2'5'3'5'o'o'o'o '2'5'3'6'o'o'o'o '2'5'3'7'o'o'o'o '2'5'3'8'0'0'o'ot '2'5'3'9'0'o'o'o'i* 25400000'* 25410000'* 25420000'* 25430000']* '2'5'4'4'o'c'o'ot '2'5'4'5'0'0'0'o'i^ '2'5'4'6'o'o'o'o'^ '2'5'4'7'0'0'0'of 2 5 4 0.0 o o o'J* '2'5'4'9'o'o'o'o'}' Natural Numbers. •76645813 38148 30484 22821 15159 07497 •76599836 92176 84517 76859 69167 61510 53854 46199 38544 30890 23237 15585 07933 00282 •76492598 84949 77301 69653 62006 54360 46715 39070 31426 23783 16105 08463 00822 •76393182 85543 77904 70266 62629 54993 47358 39689 32055 24422 16790 09158 01527 •76293897 86268 78639 71011 Dual Logarithms, '26597521 '26607522 '26617522 '26627523 '26637523 '26647524 '26657524 '26667525 '26677525 '26687526 '26697571 '26707572 '26717572 6727573 '26737573 '26747574 '26757574 '26767575 '26777575 '26787576 '26797621 '26807622 '26817622 ['26827623 '26837623 '26847624 '26857624 '26867625 '26877625 '26887626 '26897671 '26907672 '26917672 '26927673 '26937673 '26947674 '26957674 '26967675 '26977675 '26987676 '26997721 '27007722 '27017722 '27027723 '27037723 '27047724 '27057724 '27067725 '27077725 '27087726 Dual Numbers. '2'5'5'o'o'o'c'o'}^ '2'5'5'i'o'o'o'o'I^ '2'5'5'2'o'o'o'o'I^ '2'5'5'3'o'o'o'o'j^ '2'5'5'4'o'o'o'o'|* '2'5'5'5'o'o'o' 25500000 '2'5'5'7'o'o'o'o'| '2'5'5'8'o'o'o'o'I^ '2'5'5'9'o'o'o'o| '2'5'6'o'o'o'o'o'|^ '2'5'6'i'o'o'o'o'j* '2'5'6'2'0'0'0'o'f '2'5'6'3'o'o'o'o'j^ '2'5'6'4'o'o'o'o'} '2'5'6'5'o'o'o'of' '2'5'6'6'o'o'o'o'I* '2'5'6'7'o'o'o'o '2'5'6'8'o'o'o'o '2'5'6'9'o'o'o'o I : '2'5'7'o'o'o'o'o'I^ i '2'5'7'i'o'o'o'o' I '2'5'7'2'o'o'o'o i '2'5'7'3'o'o'o'o I '2'5'7'4'0'0'0'of '2'5'7'5'o'o'o'o'I^ '2'5'7'6'0'0'0'of '2'5'7'7'o'o'o'o'[ '2'5'7'8'0'0'o'of '2'5'7'9'0'0'o'o'j^ '2'5'8'o'o'o'o'o' '2'5'8'i'o'o'o'o' 2502000 O' '2'5'8'3'o'o'o'o' '2'5'8'4'0'0'0'of '2'5'8'5'o'o'o'o'[* '2'5'8'6'0'0'o'of '2'5'8'7'0'0'o'o'f '2'5'8'8'0'0'0'o'i^ '2'5'8'9'o'o'o'o| '2'5'9'o'o'o'o'o'I^ '2'5'9'i'o'o'o'c'^ '2'5'9'2'o'o'o'o'I^ '2'5'9'3'o'o'o'o'} '2'5'9'4'o'o'o'o'|* '2'5'9'5'o'o'o'o'I* '2'5'9'6'0'0'0'o'f '2'5'9'7'0'0'0'of '2'5'9'8'o'o'o'o'I* '2'5'9'9'o'o'o'ot Multiples of Differences. 770 j 769 1540; 1538 2310 2307 3080 3076 3850 3845 4620 4614 5390 5383 6160 j 6152 6930 1 6921 767 766 1534 1532 2301 2298 3068 3064 3835 .38301 4602 4596 1 5369 S362 j 6136 6128 1 6903 6894! 76S 153^ 2304 3072 3840 460S 5376 6144 6912 765 »530 2295 3060 3825 4590 5355 6120 6885 764 1528 2292 3056 3820 4584 5348 6112 6876 763 762 1526 1524 2289 2286 3052 3048 3815 j 3S10 4578 4572 5341 5334 6104 6096 6867 1 6858 Nat. No. 7625 to 7553 D. Log. '2710.... to '2809.... D. No. •2'6'0'Ot to '2W9t (27) Natural Numbers. 76259892 52266 44641 37017 29393 21770 14148 06527 •76198906 91286 83632 76014 68396 60779 53163 45548 37933 30319 22706 15094 07449 •76099838 92228 84619 77011 69403 61796 54190 46585 38980 31341 23738 16136 08534 00933 '75993333 85734 78135 70537 62940 55310 47714 40119 32525 24932 17340 09748 02157 •75894567 86978 Dual Logarithms. 27103305 '271 12306 '27122306 '27132307 '27142307 '27152308 '27162308 '27172309 '27182309 '27192310 '27202355 '27212356 '27222356 '27232357 '27242357 '27252358 '27262358 '27272359 '27282359 '27292360 '27302405 '27312406 ■'27322406 i'27332407 '27342407 '27352408 '27362408 '27372409 '27382409 '27392410 '27402455 '27412456 '27422456 '27432457 '27442457 '27452458 '27462458 '27472459 '27482459 '27492460 '27502505 '27512506 '27522506 '27532507 '27542507 '27552508 '27562508 '27572509 '27582509 '27592510 Dual Numbers. '2'6'o'o'o'o'o'of '2'6'o'l'o'o'o'of '2'6'0'2'o'o'o'ot '2'6'0'3'0'o'o'of '2'6'0'4'o'o'o'of '2'6'0'5'o'o'o'of '2'6'0'6'o'o'o'of '2'6'0'7'0'o'o'of '2'6'0'8'o'o'o'of '2'6'o'9'o'o'o'o'|^ '2'6'i'o'o'o'o'of '2'6'i'i'o'o'o'o| '2'6'l'2'o'6'o'o^ '2'6'1'3'o'o'o'of '2'6'1'4'0'0'o'of '2'6'1'5'o'o'o'ot *2'6'i'6'o'o'o'of '2'6'1'7'0'0'0'of '2'6'i'8'o'o'o'of '2'6'1'9'0'o'o'of '2'6'2'o'o'o'o'of '2'6'2'l'o'o'o'o'^ '2'6'2'2'o'o'o'o'^ '2'6'2'3'o'o'o'o'^ '2'6'2'4'o'o'o'o'^ '2'6'2'5'o'o'o'of '2"6'2'6'o'o'o'o'I^ '2'6'2'7'0'o'o'ot '2'6'2'8'0'0'0'of '2'6'2'9'o'o'o'o'I^ ^2'6'3'o'o'o'o'of '2'6'3'i'o'o'o'o| '2'6'3'2'o'o'o'of '2'6'3*3'o'oVof '2'6'3'4'o'o'o'of '2'6'3'5'o'o'o'o'j^ '2'6'3'6'0'o'o'of '2'6*3'7'o'o'o'o| '2'6'3'8'0'0'o'of '2'6'3'9'0'0'0'o'j' '2'6'4'0'0'oo'of '2'6'4'i'o'o'o'o'^ '2'6'4'2'o'o'o'o'^ '2'6'4'3'o'o'o'o' ^ '2'6'4'4'o'o'o'o'^ '2'6'4'5'o'o'o'o '2'6'4'6'o'o'o'o '2'6'4'7'o'o'o'o' '2'6'4'8'0'0'0'of '2'6'4'9'0'0'o'of Natural Numbers. •75879355 71767 64180 56594 49008 41423 33839 26256 18673 11091 03475 •75795895 88315 80736 73158 65581 58004 50428 42853 35279 27672 20099 12527 04956 •75697386 89816 82247 74679 67112 59545 51944 44379 36S14 29250 21687 14125 06563 •75599002 91442 83883 76292 68734 61177 53621 46066 38511 30957 23404 15852 08300 Dual Logarithms. '27602555 '27612556 '27622556 '27632557 '27642557 '27652558 '27662558 '27672559 '27682559 '27692560 '27702605 '27712606 '27722606 '27732607 '27742607 '27752608 '27762608 '27772609 '27782609 '27792610 '27802655 '27812656 '27822656 '27832657 '27842657 '27852658 '27862658! '27872659 I '27882659 I '27892660 j |'27902705 i ;'279i27o6 !'279227o6 j'27932707 ;'27942707' j'27952708 i'27962708 '27972709 '27982709 '27992710 '28002755 '28012756 '28022756 '28032757 '28042757 '28052758 '28062758 '28072759 '28082759 '28092760 Dual Numbers. 2'6'5'o'o'o'o'of 2'6'5'i'o'o'o'o4^ 2'6'5'2'0'0'o'of 2'6'5'3'o'o'o'o| 2'6'5'4'0'0'0'of 2'6'5'5'0'0'0'o'f 2'6'5'6'o'o'o'o'^ 2'6'5'7'o'o'o'o'» 2'6'5'8'o'o'o'o'^ 2'6'5'9'o'o'o'o| 2'6'6'o'o'o'o'o' 2'6'6'x'o'o'o'o' 2'6'6'2'o'o'o'o' 2'6'6'3'o'o'o'o' 2'6'6'4'0'0'0'of 2'6'6'5'0'0'o'ot 2'6'6'6'o'o'o'o'^ 2'6'6'7'6'o'o'o'^ 2'6'6'8'o'o'o'o'^ 2'6'6'9'o'o'o'o'^ 2'6'7'o'o'o"o'o4^ 2'6'7'i'o'o'o'o]^ 2'6'7'2'o'o'o'o'f 2'6'7'3'0'0'0'of 2'6'7'4'o'o'o'o'i* 2'6'7'5'0'0'0'of 2'6'7'6'0'o'o'oj^ 2'6'7'7'0'0'0'of 2'6'7'8'o'o'o'o| 2'6'7'9'0'0'0'oj' 2'6'8'o'o'o'o'o'| 2'6'8'i'o'o'o'o'^ 2'6'8'2'o'o'o'o'^ 2'6'8'3'o'o'o'o'^ 2'6'8'4'o'o'o'o^ 2'6'8'5'0'0'0'of 2'6'8'6'o'o'o'o'^ 2'6'8'7'0'o'o'of 2'6'8'8'0'0'0'of 2'6'8'9'o'o'o'o'^ 2'6'9'o'o'o'o"o'|* 2'6'9'i'o'o'o'o| 2'6'9'2'o'o'o'o'^ 2'6'9'3'o'o'o'o^ 2'6'9'4'o'o'o'o'|^ 2'6'9'5Vo'o'o'^ 2'6'9'6'o'o'o'o' ^ 2'6'9'7'o'o'o'o'^ 2'6'9'8'o'o'o'o'^ 2'6'9'9'o'o'o'o" ^tultiples of Differences. 1 762 761 i 1524 1522 2286 2283 3048 3044 3810 3«o.S 4572 4566 5.134 S.327 6096 6088 6858 6849 759 1518 2277 3036 3795 4554 5313 6072 6831 I 756 2 1512 3 2268 4 1 3024 3780 4536 7 8 9 5292 6048 6804 758 I5I6 2274 3032 3790 4548 5306 6064 6822 755 1510 2265 3020 3775 4530 5285 6040 6795 760 1520 2280 3040 3800 4660 5320 6080 6840 757 1514 2271 302S 3785 4542 5299 6056 6813 (28) Nat. No. 7549 to 7475 D. Log. '2810.... to '2939.... D. No. '2T0*0t to '2T9'9t Natural Numbers. ■75497293 89743 82194 74646 67099 59552 52006 44401 36917 29373 21796 14254 06713 •75399172 91632 84093 76554 69016 61479 53943 46374 38839 31305 23772 16240 08708 01177 75293647 86118 78589 71027 63500 55974 48448 40923 33399 25876 18353 1 083 1 03310 ■75195757 88237 80718 73200 65683 58166 50650 43135 35621 28107 Dual Logarithms, '28107338 '28117339 '28127339 '28137340 '28147340 '28157341 '28167341 '28177342 '28187342 '28197343 '28207388 '28217389 '28227389 '28237390 '28247390 '28257391 '28267391 '28277392 '28287392 |'28297393 '28307438 '28317439 '28327439 '28337440 '28347440 '28357441 '28367441 '28377442 '28387442 '28397443 '28407488 '28417489 '28427489 '28437490 '28447490 '28457491 '28467491 '28477492 '28487492 '28497493 '28507538 '28517539 '28527539 '28537540 '28547540 '28557541 '28567541 '28577542 '28587542 '28597543 Dual Numbers. '2'7'0'0'0'o'o'ot '2'7'0'l'o'o'o'of '2'7'o'2'o'o'o'o'f '2'7'o'3'o'o'o'o| '2'7'0'4'0'0'0'of '2'7'o'5'o'o'o'o'| '2'7'o'6'o'o'o'o 2707000 O' '2'7'o'8'o'o'o'o' '2'7'0'9'0'0'0'of '2'7'l'o'o'o'o'of '2'7'i'i'o'o'o'o'^ '2'7'l'2'o'o'o'o'^ '2'7'i'3'o'o'o'o'^ '2'7'i'4'o'o'o'o'^ 27 150000'* '^'7'i'6'o'o'o'o'* '2'7'i'7'o'o'o'o'* '2'7'i'8'o'o'o'o'* '2'7'1'9'o'o'o'of '2'7'2'0'0'o'o'of '2'7'2'l'0'0'0'0'* '2'7'2'2'o'o'o'o'* '2'7'2'3'o'o'o'o'* '2'7'2'4'o'o'o'o'* '2'7'2'5'0'0'0'of '2'7'2'6'o'o'o'o'* 2727000 O'' '2'7'2'8'o'o'o'o'* '2'7'2'9'0'0'o'of 27300000'* 273 1000 o'* 27320000'* '2'7'3'3'o'o'o'o'^ '2'7'3'4'o'o'o'o'I* '2'7'3'5'0'0'0'ot '2'7'3'6'0'0'0'o'f '2'7'3'7'o'o'o'o'* 27300000'* 27390000'* 27400000'* 27410000'* 27420000'* 27430000'* 27440000']^ 2745000 OT* 27400000' 27470000' 2 7400000' '2'7'4'9'o'o'o'o' Natural Numbers. Dual I Logarithms. I Dual Numbers. •75I2056I 13049 05538 •75098027 90517 83008 75500 67992 60485 52979 45440 37935 30431 22928 15426 07924 00423 •74992923 85424 77925 70396 62899 55403 47907 40412 32918 25425 17932 10440 02950 •74895425 87935 80446 72958 65471 57984 50498 43013 35529 28045 20530 13048 05567 •74798086 90606 83127 75649 68171 60695 53-^19 ('28607588 '28617589 '28627589 '28637590 '28647590 '28657591 '28667591 '28677592 '28687592 '28697593 '28707638 '28717639 '28727639 '28737640 '28747640 '28757641 '28767641 '28777642 '28787642 '28797643 '28807688 '28817689 '28827689 '28837690 '28847690 '28857691 '28867691 '28877692 '28887692 '28897693 '28907738 '28917739 '28927739 '28937740 '28947740 '28957741 '28967741 '28977742 '28987742 '28997743 '29007788 '29017789 '29027789 '29037790 '29047790 '29057791 '2906779X '29077792 '29087792 •29097793 '2'7'5'o'o'o'o'o'I^ '2'7^5'i'o'o'o'o'^ '2'7'5'2'0'0'0'o'f '2'7'5'3'0'0'0'o'p '2'7'5'4'o'o'o'o'I^ 27550000'* '2'7'5'6'o'o'o'o'^ '2'7'5'7'o'o'o'o'^ '2'7'5'8'o'o'o'o'* '2'7'5'9'o'o'o'o" '2'7'6'o'o'o'o'o '2'7'6'i'o'o'o'o '2'7'6'2'o'o'o'o '2'7'6'3'o'o'o'o' '2'7'6'4'0'0'0'of '2'7'6'5'o'o'o'o'|* '2'7'6'6'o'o'o'o'* '2'7'6'7'o'o'o'o'* '2'7'6'8'0'0'0'of '2'7'6'9'0'0'0'o'j* 2770000 o'p '2'7'7'l'oVo'o'}^ '2'7'7'2'o'o'o'o' Multiples of Differences. 2773 0000 '2'7'7'4'0'0'o'o'j* 2775000 OI* '2'7'7'6'o'o'o'o'|^ '2'7'7'7'0'0'0'oi '2'7'7'8'o'o'o'o'f '2'7'7'9'0'0'0'o'j^ 27000000'* '2'7'8'i'o'o'o'o'* '2'7'8'2'o'o'o'o'* '2'7'8'3'o'o'o'o'* 27040000'* '2'7'8'5'o'o'o'O'f '2'7'8'6'o'o'o'o'* '2'7'8'7'o'o'o'o" '2'7'8'8'o'o'o'o'^ '2'7'8'9'o'o'o'o'* 27900000' )->_>„» _»_)_>_!_ 27910000 '2'7'9'2'o'o'o'o '2'7'9'3'o'o'o'o' '2'7'9'4'0'0'0'of 2795000 c 2790000 O' '2'7'9'7'o'o'o'o' '2'7'9'8'0'0'o'o'J* '2'7'9'9'o'o'o'o' 754 1508 2262 3016 3770 4524 5278 6032 6786 I 751 1502 2253 3004 3755 4506 5257 6008 6759 748 1496 2244 2992 3740 4488 5236 5984 6732 753] 75 1506 150 2259 225 3012 300 3765 I 376 4518 451 5271 526 6024 601 6777 i 676 750 1500 2250 3000 3750 4500 5250 6000 6750 747 1494 .2241 2988 373S 4482 5229 5976 6723 Nat. No. 7474 to 7400 D. Log. '2911.... to '3010.... D. No. '2'8'0'Ot to '2'8'9'9t (^9) Natural Numbers. •74742320 34846 27373 19900 12428 04957 •74697487 90017 82548 75080 67578 601 1 1 52645 45180 37715 30251 22788 15326 07864 00403 •74592910 85451 77992 70534 63077 55621 48165 40710 33256 25803 18317 10865 03414 ■74495964 88514 81065 73617 66170 58723 51277 43799 36355 28911 21468 14026 06585 ■74399144 91704 84265 76827 Dual Logarithms, 29112372 '29122373 '29132373 '29142374 '29152374 '29162375 '29172375 '29182376 '29192376 '29202377 '29212422 '29222423 '29232423 '29242424 '29252424 '29262425 '29272425 '29282426 '29292426 '29302427 '29312472 '29322473 '29332473 '29342474 '29352474 '29362475 '29372475 '29382476 '29392476 29402477 29412522 29422523 29432523 '29442524 29452524 '29462525 '29472525 '29482526 '29492526 29502527 29512572 29522573 29532573 29542574 29552574 '29562575 29572575 '29582576 '29592576 '29602577 Dual Numbers. '2'8'0'0'o'o'o'ot '2'8'o'i'o'o'o'o'^ '2'8'0'2'0'0'0'0'^ '2'8'o'3'o'o'o'o'^ '2'8'0'4'0'0'0'oj '2'8'0'5'0'o'o'of '2'8'o'6'o'o'o'o'' '2'8'o'7'o'o'o'o'* '2'8'o'8'o'o'o'o| '2'8'0'9'0'0'0'of 20IOOOOO'' 2 O I 1000 O'P '2'8'l'2'o'o'o'o'^ '2'8'i'3'o'o'o'o'^ '2'8'1'4'o'o'o'of •2'8'i'5Vo'o'of '2'8'i'6'o'o'o'o'^ '2'8'i'7'o'o'o'o'^ '2'8'i'8'o'o'o'o'^ '2'8'1'9'o'o'o'of '2'8'2'o'o'o'o'ot '2'8'2'l'0'0'0'0' '2'8'2'2'o'o'o'o'h 2023000 O' '2'8'2'4'o'o'o'o' '2'8'2'5'o'o'o'o1 '2'8'2'6'o'o'o'o'^ 3027000 O'j '2'8'2'8'o'o'o'o'^ '2'8'2'9'o'o'o'o'| '2'8'3'o'o'o'o'of 203 1000 o'* '2'8'3'2'o'o'o'o'^ 20330000'* '2'8'3'4'o'o'o'of '2'8'3'5'0'0'0'of '2'8'3'6'o'o'o'o' '2'8'3'7'o'o'o'o' '2'8'3'8'o'o'o'o' '2'8'3'9'o'o'o'o' 20400000'* 2041000 O'' 20420000'* 20430000'* '2'8'4'4'o'o'o'o'I^ '2'8'4'5'o'o'o'o'] '2'8'4'6'o'o'o'oj '2V4'7'o'o'o'o'^ '2"i'4 8'o'o'o'o'^ '2'8'4'9'o'o'o'o'^ Natural Numbers. •74369355 61918 54482 47047 39612 32177 24744 I73I2 09880 02449 ■74294986 87557 80128 72700 65273 57846 50420 42995 35571 28147 20691 13269 05828 •74198427 91007 83588 76170 68752 61335 53919 46470 39055 3I64I 24228 I68I6 09404 01993 •74094583 87174 79766 72324 64917 575" 50105 42700 35296 27892 20489 13087 05686 Dual Logarithms. '29612622 '29622623 '29632623 '29642624 '29652624 '29662625 '29672625 '29682626 '29692626 '29702627 '29712672 '29722673 '29732673 '29742674 '29752674 '29762675 '29772675 '29782676 '29792676 '29802677 '29812722 '29822723 '29832723 '29842724 '29852724 '29862725 '29872725 '29882726 '29892726 '29902727 '29912772 '29922773 '29932773 '29942774 '29952774 '29962775 '29972775 '29982776 '29992776 '30002777 '30012822 '30022823 '30032823 '30042824 '30052824 '30062825 '30072825 '30082826 '30092826 '30102827 Dual Numbers. 2050000 01 205 1000 o*^ '2'8'5'2'o'o'o'o'| '2'8'5'3'o'o'o'o4 '2'8'5'4'o'o'o'o'j '2'8'5'5'o'o'o'o'] '2'8'5'6'o'o'o'o'^ 20570000'^ '2'8'5'8'0'0'0'oj '2'8'5'9'o'o'o'o'| '2'8'6'o'o'o'o'o'I^ '2'8'6'I'o'o'o'o'^ '2'8'6'2'0'o'o'o'j* '2'8'6'3'o'o'o'o'|* '2'8'6'4'o'o'o'o'I* '2'8'6'5'o'o'o'o' '2'8'6'6'o'o'o'o' '2'8'6'7'o'o'o'o' '2'8'6'8'o'o'o'o' '2'8'6'9'o'o'o'o' 20700000'* 207 1000 o'* 20720000'* '2'8'7'3'o'o'o'o'* '2'8'7'4'0'0'0'o'i* '2'8'7'5'0'o'o'o'j^ '2'8'7'6'o'o'o'o'* '2'8'7'7'o'o'o'o'^ '2'8'7'8'0'Q'o'o'* '2'8'7'9'0'o'o'o'j^ '2'8'8'o'o'o'o'o| '2'8'8'i'o'o'o'o'* '2'8'8'2'o'o'o'o'* '2'8'8'3'o'o'o'o'* •2'8'8'4'o'o'o'o| '2'8'8'5'0'o'o'of '2'8'8'6'o'o'o'o'* '2'8'8'7'o'o'o'o'^ '2'8'8'8'o'o'o'o'^ '2'8'8'9'o'o'o'o'|^ 20900000'* '2'8'9'i'o'o'o'o'* '2'8'9'2'o'o'o'o'* '2'8'9'3'o'o'o'o'* '2'8'9'4'0'0'0'o'i* '2'8'9'5'o'o'o'o'| '2'8'9'6'o'o'o'o'^ 20970000'^ 20900000'^ 20990000'] Multiples of Differences. 747 1494 2241 2988 3735 4482 5229 5976 6723 746 1492 2238 2984 3730 4476 5222 5968 6714 744 743 1488 i486 2232 2229 2976 2972 3720 371"; 4464 44,S« 5208 5201 S952 5944 6696 6687 741 1482 2223 2964 3705 4446 5187 5928 66691 740 1480 2220 2960 3700 4440 5180 5920 6600 745 1490 223s 2980 3725 4470 5215 5960 6705 742 1484 2226 2968 37IO 4452 5194 5936 6678 (3o) Nat. No. 7399 to 7326 D. Log. '3011 .... to '3110 .... D. No. '2'9'0'Ot to '2'9'9'9t Natural Dual Dual Numbers, Logarithms. Numbers. •73994897 '301 17405 '2'9'o'o'o'o'o'o| 87498 '30127406 '2'9'o'i'o'o'o'o'* 80099 '30137406 '2'9'0'2'0'0'0'o'f 72701 '30147407 '2'9'0'3'0'0'0'c'' 65304 '30157407 '2'9'0'4'0'0'0'of 57907 '30167408 '2'9'0'5'0'0'0'ojJ 505 1 1 '30177408 '2'9'o'6'o'o'o'o' ' 43116 '30187409 '2'9'o'7'o'o'o'o" 35722 '30197409 '2'9'o'8'o'o'o'o' ' 28328 '30207410 '2'9'o'9'o'o'o'o' ' 20902 '3021745s • 29100000'^ 13510 '30227456 29110000'^ 06119 '30237456 '2'9'l'2'o'o'o'o'^ •73898728 '30247457 '2'9'1'3'0'0'0'of 91338 '30257457 '2'9'i'4'o'o'o'o'|^ 83949 '30267458 '2'9'1'5'0'0'0'of 76561 '30277458 29160000^ 69173 '30287459 291 7000 0^ 61786 '30297459 '2'9'i'8'o'o'o'o'^ 54400 '30307460 '2'9'1'9'0'0'0'of 46981 '30317505 2920000 01* 39596 '30327506 '2'9'2'l'o'o'o'c 32212 '30337506 '2'9'2'2'o'o'o'o'» 24829 '30347507 '2'9'2'3'o'o'o'o'* '2'9'2'4'0'0'o'of 17447 '30357507 10065 '30367508 2925000 o'p 02684 '30377508 '2'9'2'6'o'o'o'o' ' •73795304 '30387509 '2'9'2'7'o'o'o'of 87924 '30397509 '2'9'2'8'0'0'0'of 80545 '30407510 '2'9'2'9'o'o'o'o' ' 73134 '30417555 29300000'' 65757 '30427556 '2'9'3'i'o'o'o'o'' 583S0 '30437556 '2'9'3'2'0'0'0'of 51004 '30447557 '2'9'3'3'o'o'o'o" 43629 '30457557 '2'9'3'4'o'o'o'o' ' 36255 '30467558 2935000 o'p 28881 '30477558 '2'9'3'6'o'o'o'o' ' 2937000 o'p 21508 '30487559 14136 '30497559 '2'9'3'8'0'0'0'of 06765 '30507560 '2'9'3'9'0'0'0'of •73699361 '30517605 2940000 cp 91991 '30527606 '2'9'4'i'o'o'o'o| 84622 '30537606 '2'9'4'2'o'o'o'o' ' 77254 '30547607 '2'9'4'3'o'o'o'o" 69886 '30557607 '2'9'4'4'o'o'o'of 62519 '30567608 '2'9'4'5'o'o'o'ot 55153 •30577608 '2'9'4'6'o'o'o'o| 47787 '30587609 '2'9'4'7'o'o'o'o' ' 40422 '30597609 '2'9'4'8'o'o'o'o' ' 33058 '30607610 '2'9'4'9'o'o'o'o' ' Natural Numbers. •73625662 18299 10937 03576 •73596216 88856 81497 74139 66782 59425 52036 44681 37327 29973 22620 15268 07916 00565 '73493215 85866 78484 71136 63789 56443 49097 41752 34408 27065 19722 12380 05006 •73397665 90325 82986 75648 68310 60973 53637 46302 38967 3160I 24268 16936 09604 02273 •73294943 87614 80285 72957 65630 Dual Logarithms. Dual Numbers. '30617655 '30627656 '30637656 '30647657 '30657657 '30667658 i '30677658 I '30687659 I '30697659 I '30707660 I '30717705! '30727706! '307377061 '30747707 ! '30757707 1 '30767708 1 '30777708 j '307877091 '307977091 '30807710 i '30817755 '30827756 '30837756 '30847757 '30857757 '30867758 '30877758 '30887759 '30897759 '30907760 '30917805 '30927806 '30937806 '30947807 '30957807 '30967808 '30977808 '30987809 '30997809 '31007810 '31017855 '31027856 '31037856 '31047857 '31057857 '31067858 '31077858 '31087859 •31097859 '31107860! 2'9'5'0'0'0'o'of 2'9'5'i'o'o'o'o>' 2'9'5'2'o'o'o'o'' 2'9'5'3'o'o'o'o'* 2'9'5'4'o'o'o"o'I^ 2'9'5'5'o'o'o'o| 2'9'5'6'0'0'o'o'j^ 2'9'5'7'0'0'0'oj^ 2'9'5'8'o'o'o'o'j^ 2'9'5'9'o'o'o'o'|^ 2'9'6'o'o'o'o'o^ 2'9'6'i'o'o'o'o'' 2'9'6'2'0'o'o'C 2'9'6'3'o'o'o'o'' 2'9'6'4'o'o'o'o'j^ 2*9'6'5'o'o'o'of 2'9'6'6'o'o'o'o'' 2'9'6'7'o'o'o'o'* 2'9'6'8'o'o'o'of 2'9'6'9'o'o'o'o'' 2'9'7'o'o'o'o'of 2'9'7'i'o'o^o^o'j^ 2'9'7'2'o'o'o'o'I' 2'9'7'3'o'o'o'o4' 2'9'7'4'o'o'o'o^ 2'9'7'5'o'o'o'ot 2'9'7^6'o'o'o'of 2'9'7'7'o'o'o'o'i' 29700000 b'o4' b'o'j' 2'9'7'9'0'o'i 2 9 O o o o o< 2'9'8'i'o'o'o'o' 2'9'8'2'o'o'o'o' 2'9'8'3'o'o^o'o' 2'9'S'4'o'o'o'of 2'9'8'5'0'0'0'of 2'9'8'6'0'0'0'oj 2'9'8'7'o'o'o'of 2'9'8'8'0'0'0'of 2'9'8'9'o'o^o^of 2'9'9'o'o'o'o'of 2'9'9'i'o'o'o'of 2'9'9'2'o'o'o'of 2'9'9'3'0'o'o'of 2'9'9'4'o'o'o'o'}' 2'9'9'5'0'0'0'of 2'9'9'6'0'0'0'of 2'9'9'7'o'o'o'o| 2'9'9'8'o'o'o'o'|* 2'9'9'9'0'0'0'of Multiples of Differences. 1 739 2 1478 3 2217 4 I 2956 5 3695 6 I 4434 7IS173 8 5912 916651 ! 738 1 1476 12214 1 2952 13690 1 4428 5166 73: 147- 221! 294J 368f 442: 5i5< 5904 ;S9( 6642 . 6^- 736 1472 2208 2944 3680 735! 73 1470 1 I 2205 j 2 2940 , 3675 441614410 5152 5145 5888 5880 662416615 660 733 i 732 1466 i 1464 367 440 SI 587 2199 2932 3665 4398 5131 5864 6597 2196 292S 3660 4392 5«24 5856 6588 Nat. No. 7290 to 7218 D.Log. '3160.... to '3259.... D. No. 'S'O'O'Ot to '30'9'9t (ji) Natural Dual Dual Numbers. •72900000 Logarithms. '31608155 Numbers. '3'o'o'o'o'o'o'o'j^ •72892710 '31618156 '3'o'o'i'o'o'o'o" 85421 '31628156 '3'0'0'2'0'0'0'o'f' 78132 '31638157 '3'0'0'3'0'o'o'o'j^ 70844 '31648157 '3'0'0'4'0'0'0'of 63557 '31658158 '3'o'o'5'o'o'o'o4^ 56271 '31668158 '3'o'o'6'o'o'o'o'^ 48985 •31678159 '3'0'0'7'0'0'o'of 41700 '31688159 '3'o'o'8'o'o'o'o'^ 34416 '31698160 '3'0'0'9'o'o'o'of 27100 '31708205 '3'0'i'o'o'o'o'of 19817 '31718206 '3'o'i'i'o'o'o'o'^ 12535 '31728206 '3'o'i'2'o'o'o'o'^ 05254 '3173820;^ '3'o'i'3'o'o'o'o'* •72797973 '31748207 '3'o'i'4'o'o'o'o'^ 90693 '31758208 '3'0'1'5'0'0'0'of 83414 '31768208 '3'0'1'6'0'0'0'of 76136 '31778209 '3'0'1'7'0'0'0'of 68858 '31788209 '3'0'1'8'o'o'o'o'j^ 61581 '31798210 '3'o'i'9'o'o'oo'|^ 54273 '31808255 '3'o'2'o'o'o'o*of 46998 •31818256 '3'o'2'i'o'o'o'o'^ 39723 '31828256 '3'o'2'2'o'o'o'o" 32449 '31838257 '3'o'2'3'o'o'o"o" 25176 '31848257 '3'0'2'4'0'0'o'of 17903 '31858258 '3'0'2'5'0'0'0'of 1063 1 '31868258 '3'o'2'6'o'o'o'o'' 03360 '31878259 '3'o'2'7'o'o'o'o' ' '3'0'2'8'o'o'o'ot •72696090 [31888259 88820 '31898260 '3'o'2'9'o'o'o'o'[' 81519 '31908305 '3'o'3'o'o'o'o'o^ ■ 74251 '31918306 '3'o'3'i'o'o'o'o'' 66984 '31928306 '3'o'3'2'o'o'o'o' ^ 59717 '31938307 '3'0'3'3'0'0'o'of 52451 '31948307 '3'0'3'4'0'0'o'o'J^ 45186 |'3i9583o8 '3'o'3'5'o'o'o'o4^ 37921 :'3i9683o8 '3'o'3'6'o'o'o'o' ^ 30657 '31978309 ^3'o'3'7'o'o'o'o'^ 23394 '31988309 '3'o'3'8'o'o'o'o'[' 16132 '31998310 '3'o'3'9'o'o'o'o' ' 08837 ,'32008355 30400000'^ 01576 |'32oi8356 '3'o'4'i'o'o'o'o'' ■72594316 '32028356 '3'o'4'2'o'o'o'o'^ 87057 '32038357 '3'o'4'3'o'o'o'o' ^ 79798 '32048357 '3'0'4'4'0'0'0'of 72540 '32058358 '3'o'4'5'o'o*o'o'h 65283 '32068358 '3'o'4'6'o'o'o'o' ^ 58026 '32078359 '3'o'4'7'o'o'o'o'^ 50770 '32088359 '3'o'4'8'o'o'o'o'^ 43515 '32098360 '3'o'4'9'o'o'o'o| Natural 1 Dual Dual Numbers. Logarithms. Numbers. •72536228 '32108305 '3'0'5'0'0'0'o'of 28974 '32118306 '3'o'5'i'o'o'o'o'^ 21721 '32128306 '3'o'5'2'o'o'o'o'* 14469 '32138307 '3'o'5'3'o'o'o'o" 07218 '32148307 '3'0'5'4'0'o'o'of •72499967 '32158308 '3'o'5'5'o'o'o'o>f 92717 '32168308 '3'o'5'6'o'o'o'o' ' 85468 '32178309 '3'o'5'7'o'o'o'o'^ 78219 '32188309 '3'o'5'8'o'o'o'o' ' 70971 '32198310 '3'0'5'9'0'0'0'of 63692 '32208355 '3'o'6'o'o'o'o'o4' 56446 '32218356 '3'o'6'i'o'o'o'o'^ 49200 '32228356 '3'o'6'2'o'o'o'o{ 41955 '32238357 '3'o'6'3'o'o'o'o' ^ 347 1 1 '32248357 '3'0'6'4'o'o'o'o'J^ 27468 '32258358 '3'o'6'5'o'o'o'o^ 20225 '32268358 '3'o'6'6'o'o'o'o' * 12983 '32278359 '3'o'6'7'o'o'o'o'|^ 05742 '32288359 1 '3'0'6'8'0'0'0'of •72398501 '32298360 '3'0'6'9'0'0'o'of 91228 '32308405 '3'0'7'0'0'0'o'of 83989 '32318406 '3'o'7'i'o'o'o'o'^ 76751 '32328406 { '3'o'7'2'o'o'o'o" 69513 '32338407 1 '3'0'7'3'o'o'o'o'j^ 62276 '32348407 '3'0'7'4'o'o'o'of 55040 '32358408 '3'0'7'5'0'0'0'of 47804 '32368408 '3'o'7'6'o'o'o'o ^ 40569 '32378409 '3'o'7'7'o'o'o'o' ' 33335 '32388409 '3'o'7'8'o'o'o'o' ^ 26102 '32398410 '3'o'7'9'o'o'o'o' ^ 18837 '32408455 •3'o'8'o'o'o'o'o| '3'o'8'i'o'o'o'o^ 1 1605 '32418456 04374 '32428456 '3'o'8'2'oyo'o| J •72297144 '32438457 3 8 3 ot 89914 '32448457 '3'o'8'4'o"o o'of 82685 '32458458 '3'o'8'5'o'o'o'o'h 75457 '32468458 '3'o'8'6'o'o'o'o' * 68229 '32478459 '3'o'8'7'o'o'o'o'*^ 61002 '32488459 '3'0'3'8'o'o'o'of 1 53776 '32498460 '3*0 89000 of 46518 '32508505 '3'o'9'o'o"o'c'o'J^ 39293 •32518506 '3'o'9'i'o'o'o'o'^ '3'o'9'2'o'o'o'o'^ 32069 '32528506 24846 '32538507 '3*o'9'3'o'o'o'of 17624 '32548507 '3'0'9'4'0'0'o'o'j^ 10402 '32558508 '3*o'9*5'o'o'o'o'|^ '3'o'9'6'o'o'o'o'^ 03181 '32568508 •72195961 '32578509 '3'o'9'7'o'o'o'o'^ 88741 '32588509 '3'o'9'8'o'o'o'o" '3'o'9'9'o'o'o'o^ 81522 '32598510 Multiples of Differences. 729 1458 2187 2916 364s 4374 5103 5832 6561 728 1456 2184 2912 3640 4368 5096 5824 6552 726 725 1452 1450 2178 2175 2904 2900 3(^30 3625 43.S(> 43';o 5082 507 s 5808 5800 6534 6525 723 1446 2169 2892 3615 4338 5061 5784 6507 722: 1444 2166 2888 3610 4332 5054 5776 6498 727 »454 2181 2908 3635 4362 5089 5816 6543 724 1448 2172 2896 3620 4344 5068 5792 6516 721 1442 2163 2884 3605 4326 5047 5768 6489 (52) Nat. No. 7217 to 7145 D. Log. '3261.... to '3360.... D. No. '3'1'0'Ot to '3'l'9•9'^ Natural Dual Dual Natural Dual Dual Numbers. Logarithms Numbers. Numbers. Logarithms '33113439 Numbers, Multiples ol Diffeieiices. •72 1 71000 '32613189 '3'i'o'o'o'o'o'o- •71810866 '3'i'5'o'o'o'o'o'^ 63783 '32623190 '3'i'o'i'o'o'o'o'^ 03685 '33123440 '3'i'5'i'o'o'o'o'^ 1 721 1442 n-^rt , .. r.* 56567 '32633190 '3'i'o'2'o'o'o'o" •71796505 '33133440 '3'i'5'2'o'o'o'o'^ 2 720 1440 1438 49351 '32643191 '3'i'o'3'o'o'o'o'' 89325 '33 143441 '3'i'5'3'o'o'o'o' ^ 3 2163 2160 2157 42136 '32653191 '3'i'o'4'o'o'o'o'^ 82146 '33153441 '3'i'5'4'o'o'o'o'^ 4 5 2884 360^ 2880 3600 2S76 3595 34922 '32663192 '3'i'o'5'o'o'o'o'I^ 74968 '33163442 '3'i'5'5'o'o'o'o| '3'i'5'6'o'o'o'o'^ '3'i'5'7'o'®'o'o'^ 6 4326 4320 4314 27709 '32673192 '3'i'o'6'o'o'o'o'^ 67791 '33173442 7 8 9 5047 5768 6480 5040 5760 6a8o 5033 20496 '32683193 '3'i'o'7'o'o'o'o'^ 60614 '33183443 5752 6.171 13284 '32693193 '3'1'0'8'o'o'o'of 53438 '33193443 '3'1'5'8'0'o'o'of 06073 '32703194 '3'1'0'9'o'o'o'of 46263 '33203444 '3'i'5'9'o'o'o'o" •72098829 '32713239 '3'i'i'o'o'o'o'o4^ 39055 '33213489 '3'i'6'o'o'o'o'o'^ I 718 717 716 91619 '32723240 '3'i'i'i'o'o'o'o'^ 31881 '33223490 '3'i'6'i'o'o'o'o'' 2 1436 1434 1432 84410 '32733240 '3'i'i'2'o'o'o'o" 24708 '33233490 '3'i'6'2'o'o'o'o" 3 4 2154 2872 2I5I 2868 2148 2864 77202 '32743241 31130000'^ 17536 '33243491 '3'i'6'3'o'o'o'o'^ 5 3590 3585 3580 69994 '32753241 '3'i'i'4'o'o'o'o" 10364 '33253491 '3'i'6'4'o'o'o'ot 6 7 4308 5026 4302 5019 4296 5012 62787 '32763242 31150000'^ 03193 '33263492 '3'1'6'5'o'o'o'of 8 5744 5736 5728 55581 '32773242 '3'i'i'6'o'o'o'o'' •71696023 '33273492 '3'i'6'6'o'o'o'o" '3'i'6'7'o'o'o'o" 9 6462 6453 64.H 48375 '32783243 '3'i'i'7'o'o'o'o" 88854 '33283493 41170 '32793243 '3'i'i'8'o'o'o'o'^ 81685 '33293493 '3'1'6'S'o'o'o'o" 33966 '32803244 '3'i'i'9'o'o'o'o'^ 74517 '33303494 '3'i'6'9'o'o'o'o'^ I 1 71SI 714 26730 '32813289 '3'i'2'o'o'o'o'o'^ 67316 '33313539 '3'i'7'o'o'o'o'o'I^ 2 ' 3i 1430 2145 1428 2142 19527 '32823290 '3'i'2'i'o'o'o'o" 60149 '33323540 317100001' 4 2860 2856 12325 '32833290 '3'l'2'2'o'o'o'o'^ '3'i'2'3'o'o'o'o'^ 52983 '33333540 '3'i'7'2'o'o'o'o'^ '3'i'7'3'o'o'o'o'^ 5 6 7I 3575 4290 SOQi; 3570 4284 4998 5712 05124 '32843291 45818 '33343541 •71997923 '32853291 '3'1'2'4'0'0'0'of 38653 '33353541 '3'1'7'4'o'o'o'o'J^ 8i 5720 90723 '32863292 '3'1'2'5'0'0'o'of 31489 '33363542 3175000 oy 91 6435 6426 83524 '32873292 '3'i'2'6'o'o'o'o- 24326 '33373542 '3'1'7'6'o'o'o'of 76326 '32883293 '3'i'2'7'o'o'o'o'^ 17164 '33383543 '3'i'7'7'o'o'o'o'I^ 69128 '32893293 '3'i'2'8'o'o'o'o'^ 10002 '33393543 '3'i'7'8'o'o'o'o'' '3'i'7'9'o'o'o'ot 6193I '32903294 '3'1'2'9'0'0'0'of 02841 '33403544 54704 '32913339 '3'1'3'0'0'0'o'of •71595649 '33413589' '3'1'8'0'0'0'o'of 47509 '32923340 3I3IOOOOY 88489 '33423590 1 '3'1'8'l'o'o'o'o'P 40314 '32933340 '3'i'3'2'o'o'o'o" 81330 '33433590 !'3'i'8'2'o'o'o'o- 33120 '32943341 '3'1'3'3'0'0'0'o'f '3'1'3'4'0'o'o'of 74172 '33443591 i '3'1'8'3'0'0'0'of 25927 '32953341 67015 '33453591 3184 0000^ 18734 '32963342 '3'1'3'5'0'0'o'of 59858 '33463592 3 105000 o^p II542 '32973342 '3'i'3'6'o'o'o'o'' 52702 '33473592 '3'i'8'6'o'o'o'o| '3't'8'7'o'o'o'o''^ 04351 '32983343 '3'i'3'7'o'o'o'o'^ 45547 '33483593 71897161 '32993343 '3'1'3'8'0'0'0'of 38392 '33493593 '3'1'8'8'0'0'0'ot 89971 '33003344 '3'i'3'9'o'o'o'of 31238 '33503594 '3'1'8'9'o'o'o'of 82749 '33013389 '3'1'4'0'0'0'o'o'f 24053 '33513639 '3'i'9'o'o'o'o'o4^ 75561 '33023390 '3'i'4'i'o'o'o'o'^ 16901 '33523640 '3'i'9'i'o'o'o'o" 68373 '33033390 '3'i'4'2'o'o'o'o'* 09749 '33533640 '3'i'9'2'o'o'o'o" 61186 '33043391 '3'i'4'3'o'o'o'o^' 02598 '33543641 '3'i'9'3'o'o'o'o'^ '3'i'9'4'o'o'o'o" 54000 '33053391 '3'i'4'4'o'o'o'ot •71495448 '33553641 46815 '33063392 '3'iVs'o'o'o'ot 88298 '33563642 '3'1'9'5'0'0'0'o'f 39630 '33073392 '3'i'4'6'o'o'o'o4' 81150 '33573642 '3'i'9'6'o'o'o'o'' 32446 '33083393 '3'i'4'7'o'o'o'o'' 74002 '33583643 '3'i'9'7'o'o'o'o'' 25263 '33093393 '3'i'4'8'o'o'o'o'> 66855 '33593643 '3'1'9'8'o'o'o'o'f li;o8o '33103394 1 '3'i'4'9'o'o'o'o'^ 59708 •33603644 1 '3'i'9'9'o'o'o'o" Nat. No. 7144 to 7074 D.Los?. '3361.... to '3460.... D. No. '3'2'0'Ot to '3'2'9*9t (22) Natural Dual Dual Numbers. Logarithms. Numl-)cr-5. •71449290 '33618222 '3'2'o'o'o'd'o'ot '3'2'o'i'o'o'o'o'^ 42145 '33628223 35001 '33638223 '3'2'o'2'o'o'o'o'^ 27857 '33648224 '3'2'0'3'0'0'0'c'^ 20714 '33658224 '3'2'0'4'0'0'0'of 13572 '33668225 '3'2'o-'5'o'o'o'o'^ 06431 '33678225 '3'2'o'6'o'o'o'o" •71399290 '33688226 '3'2'o'7'o'o'o'o" 92150 '33698226 '3'2'o'8'o'o'o'o" '3'2'0'9'0'o'o'of 85011 '33708227 77841 '33718272 '3'2'l'o'o'o'o'of 70703 '33728273 '3'2'i'i'o'o'o'o'^ 63566 '33738273 '3'2'l'2'o'o'o'o'^ '3'2'i'3'o'o'o'o" 56430 '33748274 49294 '33758274 '3'2'1'4'0'0'0'of 42159 '33768275 3215000 ol* 35025 '33778275 3210000 o'p 27891 '33788276 '3'2'i'7'o'o'o'o'^ 20758 '33798276 '3'2'1'8'0'0'0'of 13626 '33808277 32 19000 o'p 06463 '33818322 32200000'* •71299332 '33828323 322 1000 cp 92202 '33838323 '3'2'2'2'0'0'0'of 85073 '33848324 3223000 oy 77944 '33858324 '3'2'2'4'o'o'o'o'I* 70816 '33868325 3225000 ol* 63689 '33878325 32200000'* '3'2'2'7'o'o'o'o" 56563 '33888326 49437 '33898326 '3'2'2'8'o'o'o'o" 3229000 o'p 42312 '33908327 35^57 '33918372 3230000 o'p 28033 '33928373 323 1000 01* • 20910 '33938373 '3'2'3'2'o'o'o'o'I* 13788 '33948374 '3'2'3'3'o'o'o'o' * '3'2'3'4'o'o'o'o'I* 06667 '33958374 •71199546 '33968375 '3'2'3'5'0'0'o'ot 92426 '33978375 '3'2'3'6'0'0'0'o'f '3'2'3'7'o'o'o'o'i^ 85307 '33988376 78189 '33998376 '3'2'3'8'o'o'o'o'^ 71071 '34008377 '3'2'3'9'o'o'o'o'I^ 63921 '34018422 '3'2'4'o'o'o'o'ot 56805 '34028423 '3'2'4'i'o'o'o'o'|^ 49689 '34038423 32420000'* '3'2'4'3'o'o'o'o'* 42574 '34048424 35460 '34058424 '3'2'4'4'o'o'o'o'I* 28346 '34068425 3245000 01* 21233 '34078425 '3'2'4'6'o'o'o'o'* 14121 '34088426 '3'2'4'7'o'o'o'o" 07010 '34098426 '3'2'4'8'o'o'o'o'|* ■71099899 '34108427 '3'2'4'9'o'o'o'o'* N'atural Nximbers. •71092757 85648 78539 71431 64324 57218 50112 43007 35903 28799 21665 14563 07462 00361 •70993261 86162 79063 71965 64868 57772 50643 43548 36454 29360 22267 15175 08083 00992 •70893902 86813 79692 72604 65517 58430 51344 44259 37175 30091 23008 15926 08813 01732 •70794652 87573 80494 73416 66339 59262 52186 45111 Dual Lo"rarithms. '34118472 '34128473 '34138473 '34148474 '34158474 '34168475 '34178475 '34188476 '34198476 '34208477 '34218522 '34228523 '34238523 '34248524 '34258524 '34268525 '34278525 '34288526 '34298526 '34308527 '34318572 '34328573 '34338573 '34348574 '34358574 '34368575 '34378575 '34388576 '34398576 '34408577 '34418622 '34428623 '34438623 '34448624 '34458624 '34468625 '34478625 '34488626 '34498626 '34508627 '34518672 '34528673 '34538673 '34548674 '34558674 '34568675 '34578675 '34588676 '34598676 '34608677 Dual Numbers. 32500000''^ 325 1000 O' 3252000 O''* '3'2'5'3'o'o'o'o'I^ '3'2'5'4'o'o'o'o'^ '3'2'5'5'o'o'o'o'|* '3'2'5'6'o'o'o'o'* '3'2'5'7'o'o'o'o'^ '3'2'5'8'o'o'o'o'* '3'2'5'9'o'o'o'o'I* '3'2'6'o'o'o'o'of '3'2'6'i'o'o'o'o'^ '3'2'6'2'0'0'0'o'f '3'2'6'3'o'o'o'o'j* '3'2'6'4'o'o'o'o'l* '3'2'6'5'o'o'o'o'l^ '3'2'6'6'o'o'o'o'I* '3'2'6'7'0'0'o'of '3'2'6'8'o'o'o'o'I* '3'2'6'9'o'o'o'o'I* 3270000 ol* 32710000'? '3'2'7'2'o'o'o'o'}^ '3'2'7'3'o'o'o'o'I^ '3'2'7'4'0'0'0'o'J* '3'2'7'5'o'o'o'of '3'2'7'6'o'o'o'o'f 3277000 O'? 32 '7'8'o'o'o'of '7'9'o'o'o'O'f 320OOOOO'* 32010000'* 3 2020000'* 3203000 O'Y '3'2'8'4'o'o'o'of '3'2'8'5'o'o'o'o'(* '3'2'8'6'0'0'0'of '3'2'8'7'o'o'o'o{ '3'2'8'8'o'o'o'o'I* '3'2'8'9'o'o'o'o'I* 5'2'9'o'o'o'o'o'|* 5'2'9'i'o'o'o'o'|^ '3'2'9'2'0'0'0'of '3'2'9'3'o'o'o'o'j* '3'2'9'4'o'o'o'o'I^ '3'2'9'5'o'o'o'o'I* '3'2'9'6'0'0'0'o'j^ '3'2'9'7'0'0'0'of '3'2'9'8'o'o'o'o'j* '3'2'9'9'o'o'o'o'I* Multiples of Differences. 714 1428 2142 2156 3570 4284 4998 5712 6426 713 1426 2139 2852 3565 712 1424 2136 2848 3560 4278 4272 4991 14984 5704 I 5696 6417 640S I • 711 1422 2133 2844 3555 4266 7 1 4977 8 I 5688 9 I 6399 708 1416 2124 2832 3540 4248 4956 8 1 5664 9 I 6372 710 1420 2130 2840 3550 4260 4970 5680 6390 707 1414 2121 2828 3535 4242 4949 5656 6363 709 1418 2127 2836 3545 4254 4963 5672 6381 (34) Nat. No. 7073 to 7003 D.Log. '3162.... to '3561.... D. No; '3'3'0'Ot to '3'3'9'9t Natural Numbers, 70734797 27724 20651 I3S79 06508 •70699437 92367 85298 78229 71161 64062 56996 49930 42865 35801 28737 21674 14612 07551 •70600491 93398 86339 79280 72222 65165 58108 51052 43997 3-6943 29889 22805 15753 08701 01650 •70494600 8755X 80502 73454 66407 59360 52282 45237 38192 31148 24105 17063 10021 02980 •70395940 88900 Dual Lorarithms. •34623256 '34633257 '34643257 '34653258 '34663258 '34673259 '34683259 '34693260 '34703260 '34713265 '34723306 '34733307 '34743307 '34753308 '34763308 '34773309 '34783309 '34793310 '34803310 '34813311 '34823356 '34833357 '34843357 '34853358 '34863358 '34873359 '34883359 '34893360 '34903360 '34913361 '34923406 34933407 34943407 '34953408 '34963408 34973409 '34983409 '34993410 '35003410 '35013411 '35023456 '35033457 '35043457 '35053458 '35063458 '35073459 '35083459 '35093460 '35103460 '35113461 Dual Numbers. '3'3'0'0'0'o'o'of '3'3'0'l'o'o'o'of '3'3'o'2'o'o'o'o'I^ •3'3'o'3'o'o'o'o| '3'3'o'4'o'o'o'o'|^ '3'3'o'5'o'o[o'o'jJ '3'3'0'6'0'o'o'o'p '3'3'0'7'0'0'0'of '3'3'0'8'0'o'o'of '3'3'0'9'0'0'o'of 33 looooo'p '3'3'i'i'o'o'o'oi '3'3'1'2'0'o'o'of '3'3'1'3'0'0'0'of '3'3'1'4'o'o'o'ot '3'3'1'5'o'o'o'ot '3'3'1'6'o'o'o'of '3'3'1'7'0'0'0'of '3'3'1'8'0'o'o'of 3 3 19000 o'p 33200000 '3'3'2'i'o'o'o'o '3'3'2'2'o'o'o'o '3'3'2'3'0'0'0'of '3'3'2'4'0'0'0'of '3'3'2'5'0'0'0'ot '3'3'2'6'o'o"o'o''^ '3'3'2'7'0'c'o'o'^ '3'3'2'8'o o'of '3'3'2'9'o'o'o'o'J^ 3330000 of '3'3'3'l'o'o'o'of '3'3'3'2'o'o'o'of '3'3'3'3'o'o'o'of '3'3'3'4'o'o'o'of '3'3'3'5'o'oVof '3'3'3'6'o'o'o'of '3'3'3'7'o'o'o'ot '3'3'3'8'o'o'o'of '3'3'3'9'o'o'o'o'^ 3341000 O' '3'3'4'2'o'o'o'o' 33430000^ '3'3'4'4'o'o'o'o '3'3'4'5'o'o'o'of '3'3'4'6'o'o'o'o'^ '3'3'4'7'o'o'o'o'^ 3340000 oy 3349000 of Natural Numbers. •70381830 74792 67755 60718 53682 46647 39612 32578 25545 18512 1 1 448 04417 •70297387 90357 83328 76300 69272 62245 55219 48x93 41136 34112 27089 20066 13044 06023 •70199002 91982 84963 77944 70895 63878 56862 49846 42831 35817 28803 21790 14778 07767 00724 •70093714 86705 79696 72688 65681 58674 51668 44663 37659 Dual Logarithms. '35123506 '35133507 '35143507 '35153508 '35163508 '35173509 '35183509 '35193510 '35203510 '35213511 '35223556 '35233557 '35243557 '35253558 '35263558 '35273559 '35283559 '35293560 '35303560 '35313561 '35323606 '35333607 '35343607 '35353608 '35363608 '35373609 '35383609 '35393610 '35403610 '35413611 '35423656 '35433657 '35443657 '35453658 '35463658 '35473659 '35483659 '35493660 '35503660 '35513661 '35523706 '35533707 '35543707 '35553708 '35563708 '35573709 '35583709 '355937*0 '35603710 '356137" Dual Numbers. '3'3'5'0'0'0'o'of '3'3'5'l'o'o'o'of '3'3'5'2'o'o'o'o^ '3'3'5'3'0'0'0'of 3354000 of 3355000 of '3'3'5'6'0'0'0'oj^ '3'3'5'7'0'0'o'of '3'3'5'8'0'0'0'of '3'3'5'9'0'0'0'of '3'3'6'0'0'0'o'of '3'3'6'l'o'o'o'of '3'3'6'2'0'0'0'of '3'3'6'3'0'0'0'of '3'3'6'4'0'0'0'of '3'3'6'5'o'o'o'o| '3'3'6'6'0'0'0'of '3'3'6'7'o'o'o'o4^ '3'3'6'8'0'0'0'of '3'3'6'9'o'o'o'of '3'3'7'0'0'0'o'of '3'3'7'i'o'o'o'of '3'3'7'2'o'o'o'o| '3'3'7'3'0'0'o'of '3'3'7'4'0'0'0'of 3375000 of '3'3'7'6'o'o'o'o '3'3'7'7'o'o'o'o' '3'3'7'8'o'o'o'o' '3'3'7'9'o'o'o'o' '3'3'8'0'0'0'o'ot '3'3'8'i'o'o'c '3'3'8'2'0'0'0'of '3'3'8'3'o'o'o'o '3'3'8'4'o'o'o'o '3'3'8'5'o'o'o'o' '3'3'8'6'o'o'o'o '3'3'8'7'o'o'o'o' '3'3'8'8'o'o'o'o'^ '3'3'8'9'o'o'o'of> '3'3'9'o'o'o'o'o '3'3'9'i'o'o'o'o' '3'3'9'2'o'o'o'o '3'3'9'3'0'0'0'of '3'3'9'4'0'0'0'of 33950000'^ 33900000'^ '3'3'9'7'o'o'o'o'^ '3'3'9'8'o'o'o'o^^ '3'3'9'9'0'0'0'of Multiples of Differences. 707 1414 2I2I 2828 3535 4242 4949 5656 6363 706 1412 2118 2824 3530 4236 4942 5648 6354 704 703 1408 1406 2II2 2109 2826 2812 3520 3515 4224 4218 4928 4921 S632 5('24 6336 6327 » 701 700 2 1402 1400 3 2103 2100 4 2S04 2800 5 3505 3500 b 4206 4200 7 4907 4900 8 S()o8 5600 9 6309 6300 Nat. No. 7002 to '6933 D. Log I Natural Dual i Dual | Numbers. Logarithms. 4» Numbers. j 70027449 '35628289 '3'4'o'o'o'o'o'o'? '3'4'o'i'o'o'o'o'^ 20446 '35638290 13444 '35648290 '3'4'o'2'o'o'o'o'* 06443 '35658291 '3'4'0'3'0'0'0'o'j^ •69999442 '35668291 '3'4'0'4'0'0'0'of 92442 '35678292 '3'4'0's'o'o'o'o'U 85443 '35688292 '3'4'o'6'o'o'o'o'' 78444 '35698293 '3'4'0'7'o'o'o'of 71446 '35708293 '3'4'o'8'o'o'o'o'f 64449 '35718294 '3'4'0'9'0'0'0'of 57422 '35728339 '3'4'i'o'o'o'o'ot 50426 '35738340 '3'4'i'i'o'o'o'o'' 43431 '35748340 '3'4'i'2'o'o'o'o'^ 36437 '35758341 '3'4'i'3'o'o'o'o'* 29443 '35768341 '3'4'1'4'0'0'0'of 22450 '35778342 '3'4'i'5'o'o'o'ojJ 15458 '35788342 '3'4'i'6'o'o'o'o'* 08466 '35798343 '3'4'i'7'o'o'o'o'^ 01475 •35808343 '3'4'i'8'o'o'o'of ■69894485 '35818344 '3'4'1'9'0'0'0'oj^ 87465 '35828389 34200000'* '3'4'2'i'o'o'o'o'* 80476 '35838390 7348S '35848390 '3'4'2'2'o'o'o'o'* 66501 '35858391 '3'4'2'3'o'o'o'o" 59514 '35868391 '3'4'2'4'o'o'o'o' ' 52528 '35878392 •3'4'2'5'o'o'o'o'I* 45543 '35888392 '3'4'2'6'o'o'o'o' ' 38558 '35898393 '3'4'2'7'o'o'o'o'* 31574 '35908393 '3'4'2'8'o'o'o'o" 24591 '35918394 3429000 o'p 17578 '35928439 34300000" '3'4'3'i'o'o'o'o'** '3'4'3'2'0'0'0'of 10596 '35938440 03615 '35948440 •69796635 '35958441 '3'4'3'3'o'o'o'o'* '3'4'3'4'0'o'o'of 89655 '35968441 82676 '35978442 '3'4'3'5'0'o'o'ot 75698 '35988442 '3'4'3'6'0'o'o'of 3437000 o'J* 58720 '35998443 61743 '36008443 '3'4'3'8'o'o'o'o'? '3'4'3'9'0'0'0'o'i* 54767 '36018444 47760 '36028489 '3'4'4'o'o'o'o'o'|* 40785 '36038490 '3'4'4'i'o'o'o'o" '3'4'4'2'o'o'o'o'* 33811 '36048490 26838 '36058491 '3'4'4'3'o'o'o'o'? '3'4'4'4'o'o'o'of 19865 '36068491 12893 '36078492 3445000 of 05922 '36088492 '3'4'4'6'0'0'0'of •69698951 '36098493 '3'4'4'7'o'o'o'o- 91981 '36108493 '3'4'4'8'o'o'o'o' ' 85012 '361 18494 '3'4'4'9'o'o'o'o'* D. No. '3'4'0'Ot to '3*4'9'9t (35) Natural Dual Dual Numbers. Logarithms. Numbers. •69678012 '36128539 '3'4'5'0'0'0'o'of 71044 '36138540 '3'4'5'i'o'o'o'o'* 64077 '36148540 '3'4'5'2'o'o'o'o" 57111 '36158541 '3'4'5'3'o'o'o'o'' 50145 '3616S541 '3'4'5'4'0'0'0'of 43180 '36178542 '3'4'5'5'o'o'o'o|' '3'4'5'6'o'o'o'o'[> 36216 '36188542 29252 '36198543 '3'4'5'7'0'0'0'ot '3'4'5'8'o'o'o'o'j^ 22289 '36208543 15327 '36218544 '3'4'5'9'o'o'o'o'|* 08334 '36228589 34000000'' 01373 '36238590 34010000'* •69594413 '36248590 '3'4'6'2'o'o'o'of 87454 '36258591 '3'4'6'3'o'o'o'o'> 80495 '36268591 '3'4'6'4'o'o'o'o' ' 73537 '36278592 '3'4'6'5'o'o'o'o'* 66580 '36288592 '3'4'6'6'o'o'o'o'* 59623 '36298593 '3'4'6'7'o'o'o'o" 52667 '36308593 '3'4'6'8'o'o'o'o' * 45712 '36318594 '3'4'6'9'o'o'o'o' * 38726 '36328639 '3'4'7'o'o'o'o'o'* 31772 '36338640 '3'4'7'i'o'o'o'o" 24819 '36348640 '3'4'7'2'o'o'o'o" 17867 '36358641 '3'4'7'3'o'o'o'o" 10915 '36368641 '3'4'7'4'o'o'o'o'* . 03964 '36378642 34750000'* '3'4'7'6'o'o'o'o'* •69497014 '36388642 90064 '36398643 '3'4'7'7'o'o'o'o'* 83^15 '36408643 '3'4'7'8'o'o'o'o' ' 76167 '36418644 '3'4'7'9'o'o'o'o' * 69187 '36428689 34000000" 62240 '36438690 '3'4'8'i'o'o'o'o" 55294 '36448690 '3'4'8'2'o'o'o'o' * 48348 '36458691 '3'4'8'3'o'o'o'o' • 41403 '36468691 '3'4'8'4'o'o'o'o'* 34459 '36478692 '3'4'8'5'o'o'o'o'^ 27516 '36488692 '3'4'8'6'o'o'o'o'* '3'4'8'7'o'o'o'o' * 20573 '36498693 13631 '36508693 '3'4'8'8'o'o'o'o' ^ 06690 '36518694 '3'4'8'9'o'o'o'o'i^ •69399718 '36528739 '3'4'9'o'o'o'o'o4*. '3'4'9'i'o'o'o'o'i^' 92778 '36538740 85839 '36548740 '3'4'9'2'o'o'o'o1^ 78900 '36558741 '3'4'9'3'o'o'o'o'* 71962 '36568741 '3'4'9'4'o'o'o'o'^ 65025 '36578742 '3'4'9'5'o'o'o'o'* 58087 •36588742 '3'4'9'6'o'o'o'o'^ S"5i '36598743 '3'4'9'7'o'o'o'o" 44216 '36608743 '3'4'9'8'o'o'o'o' * 37282 36618744 '3'4'9'9'o'o'o'o' ' Multiples of Differences. 700 699 1400 I39« 2IOO 2097 2800 2796 3400 3495 4200 4194 4900 4^93 5600 ,SS92 6300 6291 697 1394 2091 2788 348s 4182 4879 5576 6273 .694 1388 2082 2776 3470 4164 4858 5552 6246 696 1392 2088 2784 3480 4176 4872 5568 6264 693 1386 2079 2772 3465 4158 4851 5544 6237 69S 1396 2094 2792 3490 41S8 4886 5584 6282 69s 1390 2085 2780 3475 4170 4865 5560 625s (36) Nat. No. -6932 to -6864 D. Log. '3663.... to '3762.... D. No. '3'5'0'Ot to •3'5'9'9t Natural Numbers. •69327175 20242 13310 06379 •69299448 92518 85589 78660 71731 64803 57848 50922 43997 37073 30149 23226 16304 09382 02461 •69195541 88590 81671 74753 67836 60919 . 54003 47088 40173 33259 26346 1 940 1 12489 05578 •69098667 91757 84848 77940 71032 64125 57219 50282 43377 36473 29569 22666 15764 08862 01961 ■68995061 88161 Dual Logarithms. Dual Numbers. '36^33323 '36643324 '36653324 '36663325 '36673325 '36683326 '36693326 '36703327 '36713327 '36723328 '36733373 '36743374 '36753374 '36763375 '36773375 '36783376 '36793376 '36803377 '36813377 '36823378 '36833423 '36843424 '36853424 '36863425 '36873425 '36883426 '36893426 '36903427 '36913427 '36923428 '36933473 '36943474 '36953474 '36963475 '36973475 '36983476 '36993476 '37003477 '37013477 '37023478 '37033523 '37043524 '37053524 '37063525 '37073525 '37083526 '37093526 '37103527 '37113527 •37123528 '3'5'o'o'o'o'o'o'^ '3'5'o'i'o'o'o'o'|^ '3'5'0'2'0'0'o'of '3'5'0'3'0'0'0'of '3'5'0'4'0'o'o'of 35050000 '3'5'o'6'o'o'o'o '3'5'o'7'o'o'o'o' '3'5'0'8'0'0'0'of '3'5'0'9'0'0'0'of 35 looooo'^ 35 I 1000 o" '3'5'i'2'o'o'o'o'^ '3'5'i'3'o'o'o'o'* '3'5'1'4'0'o'o'of '3'5'1'5'0'0'0'ot '3'5'1'6'0'0'0'of '3'5'i'7'o'o'o'o' '3'5'i'8'o'o'o'o '3'5'i'9'o'o'o'o 3520000 o'p '3'5'2'i'o'o'o'o'|^ '3'5'2'2'0'0'0'o'j^ '3'5'2'3'0'o'o'o'p '3'5'2'4'0'o'o'of 3525000 O' '3'5'2'6'o'o'o'o' '3'5'2'7'o'o'o'o' '3'5'2'8'o'o'o'o' '3'5'2'9'0'0'0'of 3530000 of 3531000 of '3'5'3'2'0'o'o'of '3'5'3'3'0'0'0'of '3'5'3'4'0'0'0'of '^' ..'^»,-» 3535000 of '3'5'3'6'0'0'0'of '3'5'3'7'o'o'o'o'^ '3'5'3'8'0'0'0'of '3'5'3'9'0'0'0'of '3'5'4'o'o'o'o'o| '3'5'4'i'o'o'o'of '3'5'4'2'o'o'o'of '3'5'4'3'0'0'0'ot '3'5'4'4'0'o'o'of 3545000 of '3'5'4'6'o'o'o'of 35470000" '3'5'4'8'o'o'o'o" '3'5'4'9'0'0'0'of Natural Numbers. •68981232 74334 67437 60540 53644 46749 39854 32960 26067 19174 12251 05360 •68898469 91580 84691 77803 70915 64028 57142 50256 43339 36455 29571 22688 15806 08924 02043* ■68795163 88283 81404 74496 67619 60742 53866 46991 401 16 33242 26369 19496 12624 05722 •68698851 9 1 98 1 85112 78243 71375 64508 57642 50776 439^1 Dual Logarithms. Dual Njumbers. 37133573 '37143574 '37153574 '37163575 '37173575 '37183576 '37193576 '37203577 '37213577 '37223578 '37233623 '37243624 '37253624 '37263625 '37273625 '37283626 '37293626 '37303627 '37313627 '37323628 '37333673 '37343674 '37353674 '37363675 '37373675 '37383676 '37393676 '37403677 '37413677 '37423678 '37433723 '37443724 '37453724 '37463725 '37473725 '37483726 '37493726 '37503727 '37513727 '37523728 '37533773 '37543774 '37553774 '37563775 '37573775 '37583776 '37593776 '37603777 '37613777 •37623778 '3'5'5'0'0'0'o'ot '3'5'5'l'o'o'o'of '3'5'5'2'0'0'0'o'f '3'5'5'3'0'0'0'of '3'5'5'4'o'o'o'oi '3'5'5'5'o'o'o'of '3'5'5'6'0'0'0'of '3'5'5'7'0'0'0'of '3'5'5'8'0'0'o'oi '3'5'5'9'0'0'0'of '3'5'6'0'0'0'o'ot '3'5'6'i'o'o'o'o'f '3'5'6'2'o'o'o'o'^ '3'5'6'3'o'o'o'o'^ '3'5'6'4'o'o'o'o'^ '3'5'6'5'0'0'0'ot '3'5'6'6'0'0'0'of '3'5'6'7'0'0'0'of '3'5'6'8'o'o'o'o'f '3'5'6'9'o'o'o'of 35700000' 35710000' '3'5'7'2'o'o'o'o' '3'5'7'3'o'o'o'o' '3'5'7'4'0'0'0'of 3575000 Of '3'5'7'6'o'o'o'of '3'5'7'7'o'o'o'of '3'5'7'8'o'o'o'of '3'5'7'9'o'o'o'o'i^ 35000000'^ 350 I 0000" '3'5'8'2'o'o'o'o'^ 35830000'^ '3'5'8'4'o'o'o'of '•3'5'8'5'o'o'o'o'^ '3'5'8'6'0'0'0'of '3'5'8'7'0'o'o'of '3'5'8'8'o'o'o'oi '3'5'8'9'o'o'o'ot '3'5'9'o'o'o'o'o'^ '3'5'9'i'o'o'o'o '3'5'9'2'o'o'o'o' '3'5'9'3'o'o'o'o '3'5'9'4'o'o'o'o '3'5'9'5'o'o'o'o '3'5'9'6'o'o'o'o '3'5'9'7'o'o'o'o '3'5'9'8'o'o'o'o| '3'5'9'9'0'o'o'oj Multiples of Differences. 69.1 692 1386 I3«4 2079 2076 2772 276S 3465 3460 41 s« 4152 4S5I 4844 5544 5S.>6 0237 6228 690 1380 2070 2760 3450 4140 4830 8 i 5520 9 j O210 689 1378 2067 2756 3445 4«34 4823 S5I2 6201 1 1 6S7I 686 2 I 137411372 3 I 2061 1 2058 4 ! 2748 2744 5 i 3435 3430 6;4i22 4116 7 '■ 4809 4802 8 i 5496 5488 9 1 6183 1 6174 Nat. No. -6863 to -6795 D. Log. '3763.... to '3862.... D. No. •3'6'0'Ot to '3'6'9'9t (37) Natural Numbers. •68633903 27040 20177 133 15 06454 I '68599593 92733 85874 79015 72158 65269 58412 51556 44701 37847 30993 24140 17288 10436 03585 •68496704 89854 83005 76157 69309 62462 55616 48770 41925 35081 28207 21364 14522 07681 00840 •68394000 87161 80322 73484 66647 59779 52943 46108 39273 32439 25606 18773 11941 05110 •68298279 Dual Logarithms. '37638357 '37648358 '37658358 '37668359 '37678359 '37688360 '37698360 '37708361 '37718361 '37728362 '37738407 '37748408 '37758408 '37768409 '37778409 '37788410 '377984^0 '378084H '37818411 '37828412 '37838457 '37848458 '37858458 '37868459 '37878459 '37888460 '37898460 '37908461 '37918461 '37928462 '37938507 '37948508 '37958508 '37968509 '37978509 '37988510 '37998510 '380085 1 1 '38018511 '38028512 '38038557 •38048558 '38058558 '38068559 '38078559 '38088560 '38098560 '38108561 '38118561 '38128562 Dual Numbers. 3000000 cp '3'6'o'i'o'o'o'o'^ '3'6'o'2'o'o'o'o'^ '3'6'0'3'o'o'o'cf '3'6'0'4'0'0'0'of '3'6'0'5'0'o'o'of '3'6'0'6'0'0'0'of '3'6'o'7'o'o'o'o| '3'6'0'8'0'0'o'of '3'6'o'9'o'o'o'o| '3'6'i'o'o'o'o'of '3'6'i'i'o'o'o'of '3'6'1'2'0'0'0'of '3'6'1'3'0'0'o'ot '3'6'1'4'0'0'0'of '3'6'1'5'o'o'o'ot '3'6'1'6'0'0'0'of '3'6'1'7'0'0'0'ot '3'6'1'8'0'0'0'of '3'6'1'9'o'o'o'of 3020000 oy '3'6'2'l'o'o'o'of '3'6'2'2'o'o'o'o| '3'6'2'3'0'0'0'ot '3'6'2'4'0'0'0'o'i^ '3'6'2'5'o'o'o'of '3'6'2'£'o'o'o'of '3'6'2'7'o'o'o'of '3'6'2'8'o'o'o'of '3'6'2'9'0'0'0'of '3'6'3'0'o'o'o'of '3'6'3'i'o'o'o'o| '3'6'3'2'0'o'o'of '3'6'3'3'0'0'0'of '3'6'3'4'0'0'o'of '3'6'3'5'0'0'0'of '3'6'3'6'0'o'o'of '3'6'3'7'o'o'o'of '3'6'3'8'0'0'0'ot '3'6'3'9'0'0'0'o'i' '3'6'4'0'0'0'o'o'j^ '3*6*4' I'o'o'o'of '3*6'4*2*o'o'o'o'j^ '3'6'4'3'0'0'0'o'p '3'6'4'4*o*o*o'oj '3'6'4'5'o'o'o'ot '3'6'4*6'o'o'o'ot '3'6'4'7'0'0'0'of '3'6'4'8'o'o'o'of '3'6'4'9'0'o'o'of Natural Numbers. ■68291419 84590 77762 70934 64107 57281 50455 43630 36806 29982 23128 16306 09484 02663 •68195843 89023 82204 75386 68568 61751 54905 48090 41275 34461 27648 20835 » 14023 07211 00399 •68093589 86750 79941 73133 66326 59519 52713 45908 39105 32301 25498 18663 ii86i •67905060 98259 91459 84660 77862 71064 64267 57471 Dual Lotrarithms. '38138607 '38148608 '38158608 '38168609 '38178609 '38188610 '38198610 '3820861 1 '38218611 '38228612 '38238657 '38248658 '38258658 '38268659 '38278659 '38288660 '38298660 '38308661 '38318661 '38328662 '38338707 '3834870.8 '38358708 '38368709 '38378709 '38388710 '38398710 '384087 1 1 '38418711 '38428712 '38438757 '38448758 '38458758 '38468759 '38478759 '38488760 '38498760 '38508761 '38518761 '38528762 '38538807 '38548808 '38558808 '38568809 '38578809 '38588810 '38598810 '38608811 '38618811 '38628812 Dual Numbers. '3'6'5'0'0'0'o'of '3'6'5'l'o'o'o'o'^ '3'6'5'2'0'0'0'of '3'6'5'3'0'0'0'of '3'6'5'4'0'0'0'of '3'6'5'5'o'o'o'o '3'6'5'6'o'o'o'o' '3'6'5'7'o'o'o'o '3'6'5'8'0'0'0'of '3'6'5'9'0'o'o'of '3'6'6'0'o'o'o'of '3'6'6'i'o'o'o'o| '3'6'6'2'o'o'o'of '3'6'6'3'0'0'o'of '3'6'6'4'0'0'o'of '3'6'6'5'0'0'0'ot '3'6'6'6'o'o'o'of '3'6'6'7'0'0'0'of '3'6'6'8'o'o'o'of '3'6'6'9'o'o'o'ot '3'6'7'0'0'0'o'of '3'6'7'i'o'o'o'o'I^ '3'6'7'2'0'0'0'of '3'6'7'3'0'0'0'of '3'6'7'4'0'o'o'of '3'6'7'5'0'0'o'of '3'6'7'6'0'0'0'of '3'6'7'7'o'o'o'of '3'6'7'8'0'o'o'of '3'6'7'9'0'0'0'o'j^ '3'6'8'0'0'0'o'of '3'6'8'i'o'o'o'o| '3'6'8'2'0'0'0'of '3'6'8'3'0'0'0'of '3'6'8'4'o'o'o'of '3'6'8'5'o'o'o'of '3'6'8'6'0'0'0'of '3'6'8'7'0'0'0'of '3'6'8'8'0'o'o'of '3'6'8'9'o'o'o'o'* '3'6'9'o'o'o'o'o'|^ '3'6'9'i'o'o'o'of '3'6'9'2'o'o'o'o'|^ '3'6'9'3'0'0'0'of '3'6'9'4'o'o'o'of '3'6'9'5'o'o'o'o| '3'6'9'6'o'o'o'of '3'6'9'7'o'o'o'o '3'6'9'8'o'o'o'o •3'6'9'9'o'o'o'o Multiples of Differences. 686 1372 2058 2744 3430 4116 4802 5488 6174 683 1366 2049 2732 3415 4098 4781 S464 6147 I 680 2 1360 3 2040 4 2720 5 3400 6 4080 7 4760 8 5440 9 6120 685 1370 2055 2740 3425 41 10 4795 5480 6165 682 1364 2046 2728 3410 4092 4774 5456 6138 679 1358 2037 2716 3395 4074 4753 5432 6111 684 1368 2052 2736 3420 4104 4788 5472 6156 681 1362 2043 2724 3405 4086 4767 5448 6129 (38) Nat. No. -6794 to -6727 D. Log. '3864.... to '3963.... D. No. '3'7'0'Ot to '3T9'9t Natural Numbers. ■67947564 40769 33975 27182 20389 13597 06806 00015 •67893225 86436 79616 72828 66041 59254 52468 45683 38898 32114 25331 18548 11736 04955 •67798175 91395 84616 77838 71060 64283 57507 50731 43924 37150 30376 23603 1 683 1 10059 03288 •67696518 89748 82979 76180 69412 62645 55879 49113 42348 35584 28820 22057 15295 Dual IvOgarithms. '38643390 '38653391 '38663391 '38673392 '38683392 '38693393 '38703393 '38713394 '38723394 '38733395 '38743440 '38753441 '38763441 '38773442 '38783442 '38793443 '38803443 '38813444 '38823444 '38833445 '38843490 '38853491 '38863491 '38873492 •38883492 •38893493 '38903493 '38913494 •38923494 '38933495 '38943540 '38953541 '38963541 '38973542 '38983542 '38993543 '39003543 '39013544 '39023544 '39033545 '39043590 '39053591 '39063591 '39073592 '39083592 '39093593 '39103593 '39113594 '39123594 '39133595 Dual Numbers. '3'7'0'0'0'o'o'of '3'7'0'l'o'o'o'of '3'7'o'2'o'o'o'o'|^ '3'7'0'3'0'o'o'o'J^ '3'7'0'4'0'o'o'of '3'7'o'5'o'o^o'ot '3'7'o'6'o^o'o'of '3'7'o'7'o'o'o'o| •3'7^o'8'o'o'o'of '3'7'0'9'0'0'0'of 37100000'* 3 7 I I o o o Op •3'7*i'2'o'o'o'o| '3'7'i'3'o'o'o'o'^ '3'7'1'4'0'0'0'of 37150000^ '3'7'i^6'o'o'o'o'j^ '3'7'i'7'o'o'o'o' •3'7'i'8'o'o'o'o •3'7'i'9'o'o'o'o' 3720000 O'j* '3'7'2'l'o'o'o'of '3'7'2'2'o'o'o'of '3'7'2'3'o'o'o'of '3'7'2'4'o'o'o'of 37250000^* '3'7'2'6'o'o'o'of '3'7'2'7'o'o'o-'of '3'7'2'8'o'o'o'o'f '3'7'2'9'0'0'0'of '3'7'3'o'o^o^o^ot '3'7'3'i'o'o'o'o'f '3'7'3'2'0'0'0'of '3'7'3'3'0'0'0'oj '3'7'3'4'0'0'0'of 37350000-]^ '3'7'3'6'o'o'o'o| '3'7'3'7'0'0'0'of '3'7'3'8'o'o'o'o| '3'7'3'9'0'0'o'of •3'7'4'o'o^o'o'o'I* '3'7'4'I'o'o'o'o'^ '3'7'4'2'0'0'0'of '3'7'4'3'0'0'0'of .»_» .1,1 37'4'400'0'0'p '3'7'4'5'o'o'o'ot '3'7'4'6'0'0'0'o'i' '3'7'4'7'0'0'0'o'f '3'7'4'8'0'00'of '3'7'4'9'0'0'0'of Natural Numbers. •67608504 01743 •67594983 82223 81464 74706 67949 61192 54436 47681 40895 34141 27388 20635 13883 Dual Logarithms. '39143640 '39153641 '39163641 '39173642 '39183642 '39193643 '39203643 '39213644 •39223644 '39233645 '39243690 '39253691 j'39263691 '39273692 '39283692 07132 00381 •67493631 '39293693 '39303693 '39313694 86882 |'39323694 80133 '39333695 73354 i'39343740 66607 i'39353741 5:"'^6o I '39363741 53114 i'39373742 46369 '39383742 39624 32880, 26137 29394 12652 05881 •67399140 92400 85661 78922 72184 65447 58710 51974 45239 38475 31741 25008 18276 "544 04813 •67298083 91353 84624 77805 '39393743 '39403743 '39413744 '39423744 .'39433745 1*39443790 ! '39453791 j '39463791 '39473792 '39483792 '39493793 '39503793 '39513794 '39523794 '39533795 '39543840 '39553841 '39563841 '39573842 '39583842 '39593843 '39603843 '39613844 '39623844 '39633845 Dual Numbers. '37'5'0'0'0'o'ot '3'7'5'l'o'o'o'oi '3'7'S'2'o'o'o'of '3'7'5'3'0'0'o'of '3'7'5'4'o'o'o'o| •3'7'5'5'0'0'0'of '3^7'5'6'o^o'o'of '3'7'5'7'o'o'o'o •3'7'5'8'o'o'o'o '3'7'5'9'0'0'0'a •3^7'6'o^o'o'o'o' •3'7'6'i'o'o'o'o '3'7'6'2'o'o'o'o' '3'7'6'3'o'o'o'ot '3'7'6'4'o'o'o'of •3'7'6'5'o'o^o'of •3^7.'6'6'o'o'o'of '3'7'6'7'o'o'o'of •3'7'6'8'o'o'o'o| '3'7'6'9'0'0'0'of 3770000 OI* 3 7 7 1000 o'r '3'7'7'2'0'0'0'oj^ '3'7'7'3'0'0'0'af '3'7'7'4'o'o'o'of 3 7 7 5 oooo'^ '3'7'7'6'o'o'o'o'\ '3'7'7'7'o'o'o'o'^ '3'7'7'8'o'o'o'o'* •3'7'7'9'o'o'o'o'^ 370OOOOO '3'7'8'i'o'o'o'o' '3'7'8'2'o'o'o^o' '3'7'8'3'0'0'0'of '3'7'8'4'o'o'o'of 3705000 OT 37000000' '3'7'8'7'o'o'o'o' •3'7'8'8'o'o^o'o' 3709000 O' 37900000' '3'7'9'i'o'o'o'o' '3'7'9'2'o'o'o'o' 37930000' '3'7'9'4'0'0'0'of 37950000'^ '3'7'9'6'o'o'o'o'* '3'7'9'7'o'o'o'o" 37900000" 37990000^ Multiples of Differences. 679 678 i35» 135^ 2037 2034 2716 2712 3395 3390 4074 4068 4753 4746 5432 5424 6111 6102 676 675 1352 1350 2028 2025 2704 2700 33«o 3375 4056 4050 4732 4725 5408 5400 6084 6075 673 1346 2019 2692 3365 4038 471 1 5384 6057 TABLE III. ANGULAR MAGNITUDES AND TRIGONOMETIMCAL LINES. I Degree, Difference for Seconds, [1 M. Sine. M. 10" 20" 30" 40" SO" 60" 70" 80" „ 90 Arc. o I 3 4 OCXXXXX) 2909 5818 8727 001 1636 60 59 58 57 56 485 485 485 485 485 970 970 970 970 970 H5S H5S 1455 1455 H55 1940 1940 1940 1940 1940 2424 2424 2424 2424 2424 2909 2909 2909 2909 2909 3394 3394 3394 3394 3394 3879 3879 3879 3879 3879 4364 4364 4364 4364 4364 0000000 2909 5818 8727 001 1636 Arc Sec. Diff. 10 20 30 40 50 60 70 80 90 48s 5 6 7 8 9 4544 7453 0020362 3271 6180 55 54 53 52 51 485 .485 485 485 485 970 970 970 970 970 1455 H5S 1455 1455 1455 1940 1940 1940 1940 1940 2424 2424 2424 2424 2424 2909 2909 2909 2909 2909 3394 3394 3394 3394 3394 3879 3879 3879 3879 3879 4364 4364 4364 4364 4364 4364 4364 4364 4364 4364 4545 7454 0020363 3272 6181 9089 0031998 4907 7816 0040725 970 1454 1939 2424 2909 3394 3878 4363 lO II 12 13 14 9089 0031998 4907 7815 0040724 50 49 48 47 46 485 485 485 485 485 970 970 970 970 970 1455 H55 1455 1455 1455 1940 1940 1940 1940 1940 2424 2424 2424 2424 2424 2909 2909 2909 2909 2909 3394 3394 3394 3394 3394 3879 3879 3879 3879 3879 15 i6 17 i8 19 3633 6542 9451 0052360 5268 45 44 43 42 41 485 485 485 485 485 970 970 970 970 970 1455 1455 1455 1455 1455 1940 1940 1940 1940 1940 2424 2424 2424 2424 2424 2909 2909 2909 2909 2909 3394 3394 3394 3394 3394 3879 3879 3879 3879 3878 4364 4364 4364 4363 4363 3634 6543 9452 0052361 5270 20 21 22 23 24 8177 0061086 3995 6904 9813 40 39 38 37 36 485 485 485 485 485 970 970 970 970 970 H55 1455 1455 H5S 1455 1940 1940 1940 1940 1940 2424 2424 2424 2424 2424 2909 2909 2909 2909 2909 3394 3394 3394 3394 3394, 3394 3394 3394 3394 3394 3878 3878 3878 3878 3878 4363 4363 4363 4363 4363 8178 0061086 3995 6904 9813 25 26 27 28 29 0072721 5630 8539 0081448 4357 35 34 33 32 31 485 485 485 485 485 970 970 970 970 970 1455 1455 H55 1455 1455 1940 1940 1940 1940 1940 2424 2424 2424 2424 2424 2909 2909 2909 2909 2909 3878 3878 3878 3878 3878 4363 4363 4363 4363 4363 0072722 5631 8540 0081449 4358 30 31 32 33 34 7265 0090174 3083 5992 8900 30 29 28 27 26 485 48s 485 485 485 970 970 970 970 970 1455 1455 1455 145 5 1455 1940 1940 1940 1940 1940 2424 2424 2424 2424 2424 2909 2909 2909 2909 2909 3394 3394 3394 3394 3394 3878 3878 3878 3878 3878 4363 4363 4363 4363 4363 7266 0090175 3084 5993 8902 35 36 37 38 39 0101809 4718 7627 011053s 3444 25 24 23 22 21 20 19 18 17 16 485 485 485 48s 485 970 970 970 970 970 1455 1455 1455 1454 1454 1940 1940 1940 1939 1939 2424 2424 2424 2424 2424 2424 2424 2424 2424 2424 2909 2909 2909 2909 2909 3394 3394 3394 3394 3394 3878 3878 3878 3878 3878 4363 4363 4363 4363 4363 0101811 4720 7629 0110538 3447 40 41 42 43 44 6353 9261 0122170 5079 7987 485 485 485 485 485 970 970 970 970 970 1454 1454 1454 1454 1454 1939 1939 1939 1939 1939 2909 2909 2909 2909 2909 2909 2909 2909 2909 2909 3394 3394 3394 3394 3394 3394 3394 3394 3394 3394 3878 3878 3878 3878 3878 4363 4363 4363 4363 4363 6355 9264 0122173 5082 7991 45 46 47 48 49 50 51 52 53 54 0130896 3805 6713 9622 0142530 15 14 13 12 II 485 485 485 485 485 970 970 970 970 970 1454 1454 1454 1454 1454 1939 1939 1939 1939 1939 2424 2424 2424 2424 2424 3878 3878 3878 3878 3878 4363 4363 4363 4363 4363 0130900 3809 6718 9627 0142536 5439 8348 0151256 4165 7073 10 9 8 7 6 485 48s 485 485 485 970 970 970 970 970 1454 1454 1454 1454 1454 1939 1939 1939 1939 1939 2424 2424 2424 2424 2424 2909 2909 2909 2909 2909 3394 3394 3394 3394 3394 3878 3878 3878 3878 3878 4363 4363 4363 4363 4363 5444 8353 0151262 4171 7080 55 56 57 58 59 60 M. 9982 0162890 5799 8707 0171616 4524 5 4 3 2 I 485 485 485 485 485 485 970 970 969 969 969 969 1454 1454 1454 1454 1454 1454 1939 1939 1939 1939 1939 1939 2424 2423 2423 .2423 2423 2423 2909 2909 2908 2908 2908 2908 3394 3393 3393 3393 3393 3393 3878 3878 3878 3878 3878 3878 4363 4363 4363 4362 4362 4362 9989 0162898 5807 8716 0171625 4533 Cosine. M. 10" 20" 30" 40" j so" 60" 70' 80" 90" Arc. 89 Degrees. 2] 1 Degree. Difference for Seconds. M. Sine. M. 10" 20" 30" 40" SO" 60" 70" 80" 90" Arc. Arc. o I 2 3 4 I 7 8 9 0174524 7432 01 8034 I 3249 6158 60 59 58 'A 485 485 485 485 485 969 969 969 969 969 1454 1454 1454 1454 1454 1938 1938 1938 1938 1938 2423 2423 2423 2423 2423 2908 2908 2908 2908 2908 3393 3393 3393 3393 3393 3878 3878 3878 3878 3878 4363 4362 4362 4362 4362 0174533 7442 018035 1 3260 6169 Sec. DiflF. 10 485 9066 0191974 4883 7791 0200699 55 54 53 52 51 485 485 485 485 485 969 969 969 969 969 1454 1454 1454 1454 H54 1938 1938 1938 1938 1938 1938 1938 1938 1938 1938 2423 2423 2423 2423 2423 2908 2908 2908 2908 2908 3393 3393 3393 3393 3393 3878 3878 3878 3878 3878 4362 4362 4362 4362 4362 9078 0191987 4896 7805 0200714 30 40 50 60 70 80 90 970 1454 1939 2424 2909 3394 lO II 12 13 3608 6516 9424 0212332 5241 50 49 48 47 46 485 485 485 485 485 969 969 969 969 969 1454 1454 1454 1454 1454 2423 2423 2423 2423 2423 2908 2908 2908 2908 2908 3393 3393 3393 3393 3393 3878 3878 3877 3877 3877 4362 4362 4362 4362 4362 3622 6530 9440 0212349 5258 3878 4363 15 i6 17 i8 19 8149 0221057 3965 6873 9781 45 44 43 42 41 485 485 485 485 485 969 969 969 969 969 1454 1454 H54 1454 1454 1938 1938 1938 1938 1938 2423 2423 2423 2423 2423 2008 2908 2908 2908 2908 3393 3393 3393 3393 3393 3877 3877 3877 3877 3877 4362 4362 4362 4362 4362 8167 0221076 3985 6894 9803 20 21 22 23 24 0232690 5598 8506 0241414 4322 40 39 38 37 36 485 485 485 485 485 969 969 969 969 969 1454 1454 1454 1454 1454 1938 1938 1938 1938 1938 1938 1938 1938 1938 1938 2423 2423 2423 2423 2423 2908 2908 2908 2908 2908 3393 3393 3393 3393 3393 3877 3877 3877 3877 3877 4362 4362 4362 4362 4362 023271 1 5620 8529 0241438 4347 25 26 27 28 11 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 7230 0250138 3046 5954 8862 35 34 33 32 31 485 485 485 485 485 485 485 485 485 485 969 969 969 969 969 1454 1454 1454 1454 1454 2423 2423 2423 2423 2423 2908 2908 2908 2908 2908 3393 3393 3392 3392 3392 3877 3877 3877 3877 3877 4362 4362 4362 4362 4362 7256 0250165 3074 5983 8891 , 0261769 4677 7585 0270493 3401 30 29 28 27 26 969 969 969 969 969 1454 1454 1454 1454 1454 1938 1938 1938 1938 1938 2423 2422 2422 2422 2422 2907 2907 2907 2907 2907 3392 3392 3392 3392 3392 3877 3877 3877 3876 3876 4362 4362 4362 4362 4362 0261799 4708 7617 0270527 3435 6309 9216 0282124 5032 7940 25 24 23 22 21 485 485 485 485 485 969 969 969 969 969 969 969 969 969 969 969 969 969 969 969 1454 1454 1454 1454 1454 1938 1938 1938 1938 1938 2422 2422 2422 2422 2422 2907 2907 2907 2907 2907 3392 3392 3392 3392 3392 3876 3876 3876 3876 3876 4362 4361 4361 4361 4361 6344 9253 0282162 5071 7981 0290847 3755 6662 9570 0302478 20 19 18 17 16 485 485 485 485 485 485 485 485 485 485 1454 1454 1454 1454 1454 1938 1938 1938 1938 1938 2422 2422 2422 2422 2422 2907 2907 2907 2907 2907 3392 3392 3392 3392 3392 3876 3876 3876 3876 3876 4361 4361 4361 4361 4361 0290888 3797 6706 9615 0302524 45 46 47 48 49 50 51 52 53 54 5385 8293 031 1200 4108 7015 15 14 13 12 II 1454 1454 1454 1454 1454 1938 1938 1938 1938 1938 2422 2422 2422 2422 2422 2907 2907 2907 2907 2907 3392 3392 3392 3392 3392 3876 3876 3876 3876 3876 4361 4361 4361 4361 4361 5433 8342 0311251 4160 7069 9922 0322830 5737 8644 0331552 10 9 8 7 6 485 485 485 485 485 969 969 969 969 969 1454 1454 1454 H54 1454 1938 1938 1938 1938 1938 2422 2422 2422 2422 2422 2907 2907 2907 2907 2907 3392 3392 3392 3392 3392 3876 3876 3876 3876 3876 4361 4361 4361 4361 4361 9977 0322886 5795 8704 0331513 55 56 57 58 59 60 4459 7366 0340274 3181 6088 8995 5 4 3 2 I M. 485 485 485 485 485 485 969 969 969 969 969 969 1454 1454 1454 1454 1454 1454 1938 1938 1938 1938 1938 1938 2422 2422 2422 2422 2422 2422 2907 2907 2907 2907 2907 2907 3392 3392 3392 3392 3392 3392 3876 3876 3876 3876 3876 3876 4361 4361 4361 4361 4361 4361 4522 7431 0340340 3249 6158 9066 M. Cosine. 10" 20" 30- 40" 50" 60" 70" 80" 90" Arc. 88 Degrees. 2 Degi ees. Difference for Seconds [3 M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o 0348995 60 485 969 1454 1938 2423 2907 3392 3876 4361 0349066 Arc I 2 0351902 4809 59 58 485 485 969 969 1454 1454 1938 1938 2423 2423 2907 2907 3392 3392 3876 3876 4361 4361 0351975 4884 Sec Diff 3 4 7716 0360623 57 56 55 485 485 969 969 1454 1454 1938 1938 2423 2423 2907 2907 3392 3392 3876 3876 4361 4361 7793 0360702 10 20 485 970 1454 5 3530 485 969 1454 1938 2423 2907 3392 3876 4361 361 1 6 6437 54 485 969 1454 1938 2423 2907 3392 3876 4361 6520 30 7 9344 53 485 969 1454 1938 2423 2907 3392 3876 4361 9429 40 1939 2424 8 0372251 52 485 969 1454 1938 2423 2907 3392 3876 4361 0372338 50 9 5158 51 485 969 1454 1938 2423 2423 2907 3392 3876 4361 5247 60 70 2909 10 8065 50 485 969 1454 1938 2907 3392 3876 4361 8155 3394 II 0380971 49 485 969 1454 1938 2423 2907 3392 3876 4361 0381064 80 3878 12 3878 48 485 969 1454 1938 2423 2907 3392 3876 4361 3973 90 4363 13 6785 47 485 969 1454 1938 2423 2907 3392 3876 4361 6882 H 9692 46 485 969 1454 1453 1938 2423 2907 3392 3876 4361 9791 IS 0392598 45 484 969 1937 2422 2906 3391 3875 4360 0392700 16 5505 44 484 969 1453 1937 2422 2906 3391 3875 4360 5609 17 841 1 43 484 969 1453 1937 2422 2906 3391 3875 4360 8518 i8 0401318 42 484 969 1453 1937 2422 2906 3391 3875 4360 0401427 19 4224 41 484 969 1453 1937 2422 2906 3391 3875 4360 4336 20 7131 40 484 969 1453 1937 2422 2906 3391 3875 4360 7244 21 0410037 39 484 969 1453 1^37 2422 2906 3391 3875 4360 041 1053 22 2944 38 484 969 1453 1937 2422 2906 3391 3875 4360 3062 23 5850 37 484 969 1453 1937 2422 2906 3391 .3875 4360 5971 24 25 8757 36 484 969 1453 1937 2422 2906 3391 3391 3875 3875 4360 8880 0421663 35 484 969 1453 1937 2422 2906 4360 0421789 2b 4569 34 484 969 1453 1937 2422 2906 3391 3875 4360 4698 27 7475 33 484 969 1453 1937 2422 2906 3391 3875 4360 7607 28 0430382 32 484 969 1453 1937 2422 2906 3391 3875 4359 0430516 2^ 30 3288 31 484 969 H53 1937 2422 2906 3391 3875 4359 3425 6194 30 484 969 1453 1937 2422 2906 3391 3875 4359 6332 31 9100 29 484 969 1453 1937 2422 2906 3391 3875 4359 9241 32 0442006 28 484 969 1453 1937 2422 2906 3391 3874 4359 0442150 33 4912 27 484 969 1453 1937 2422 2906 3391 3874 4359 5059 34 7818 26 484 969 1453 1937 2422 2906 3391 3874 4359 7968 35 0450724 25 484 969 1453 1937 2422 2906 3391 3874 4359 0450877 3b 3630 24 484 969 1453 1937 2422 2906 3391 3874 4359 3786 37 6536 23 484 969 1453 1937 2422 2906 3391 3874 4359 6695 3ii 9442 22 484 969 1453 1937 2422 2906 3391 3874 4359 9604 39 0462347 21 •484 969 1453 1937 2422 2906 3391 3874 4359 0462513 40 i 5253 20 484 968 1452 1936 2422 2905 3390 3873 4358 5421 41 8159 19 484 968 1452 1936 2421 2905 3390 3873 4358 8330 42 0471065 18 484 968 1452 1936 2421 2905 3390 3873 4358 0471239 43 3970 17 484 968 1452 1936 1 2421 2905 3390 3873 4358 4148 44 6876 16 484 968 1452 1936 2421 2421 2905 2905 3390 3873 4358 7057 45 9781 15 484 968 1452 1936 3390 3873 4358 9966 4b 0482687 14 484 968 1452 1936 2421 2905 3390 3873 4358 0482875 47 5592 13 484 968 1452 1936 2421 2905 3390 3873 4358 5784 48 8498 12 484 968 1452 1936 2421 2905 3390 3873 4357 8693 49 0491403 II 484 968 1452 1936 2421 2905 3390 3873 4357 0491602 SO 4308 10 484 968 1452 1936 2421 2905 3390 3873 4357 4510 SI 7214 9 484 968 1452 1936 2421 2905 3390 3873 4357 7419 52 0500119 8 484 968 1452 1936 2421 2905 3390 3873 4357 0500328 S3 3024 7 484 968 1452 1936 2421 2905 3390 3873 4357 3237 54 5929 6 484 968 1452 1936 2421 2905 3390 3873 4357 6146 55 8835 5 484 968 1452 1936 2421 2905 3390 3873 4357 9055 56 05 1 1 740 4 484 968 1452 1936 2421 2905 3390 3873 4357 05 1 1 964 57 4645 3 484 968 1452 1936 2421 2905 3390 3873 4357 4873 58 1 7SSO 2 484 968 1452 1936 2421 2905 3390 3873 4357 7782 59 1 0520455 I 484 968 1452 1936 2421 2905 3390 3873 4357 0520691 60 3360 484 963 1452 1936 2421 2905 3390 3873 4357 3599 M. Cosine. M. 10" 20" 30" 40" SO" 60" 70' 80" 90" Arc. 87 Degrees. 4] 3 Degrees. Difference for Seconds. M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. Arc. A X o I 2 3 4 0523360 6264 9169 0532074 4979 60 58 56 484 484 484 484 484 968 968 968 968 968 1452 1452 1452 1452 1452 1936 1936 1936 1936 1936 2420 2420 2420 2420 2420 2904 2904 2904 2904 2904 3388 3388 3388 3388 3388 3872 3872 3872 3872 3872 4356 4356 4356 4356 4356 0523599 6508 9417 0532326 5235 Sec. Did 10 20 30 40 50 60 70 80 90 48^ 970 1454 1939^ 2424 2909 3394 3878 4363 i S 6 7 8 9 7883 0540788 3693 6597 9502 55 54 53 52 51 484 484 484 484 484 968 968 968 968 968 1452 1452 1452 1452 1452 1936 1936 1936 1936 1936 2420 2420 2420 2420 2420 2904 2904 2904 2904 2904 3388 3388 3388 3388 3388 3388 3388 3388 3388 3388 3872 3872 3872 3872 3872 4356 4356 4356 4356 4356 8144 0541053 3962 6871 9780 lO II 12 13 14 0552406 5311 8215 0561 I 19 4024 50 49 48 47 46 484 484 484 484 484 968 968 968 968 968 1452 1452 1452 1452 1452 1936 1936 1936 1936 1936 2420 2420 2420 2420 2420 2904 2904 2904 2904 2904 3872 3872 3872 3872 3872 4356 4356 4356 4356 4356 0552688 5597 8506 0561415 4324 15 i6 17 i8 19 6928 9832 0572736 5640 8544 45 44 43 42 41 484 484 484 484 484 968 968 968 968 968 1452 1452 1452 1452 1452 1936 1936 1936 1936 1936 2420 2420 2420 2420 2420 2904 2904 2904 2904 2904 3388 3388 3388 3388 3388 3872 3872 3872 3872 3872 4356 4356 4356 4356 4356 7233 0570142 3051 5960 8869 1 ! 20 21 22 23 24 0581448 4352 7256 0590160 3064 40 39 38 37 36 484 484 484 484 484 968 968 968 968 968 1452 1452 1452 1452 1452 1936 1936 1936 1936 1936 2420 2420 2420 2420 2420 2904 2904 2904 2904 2904 3388 3388 3388 3388 3872 3872 3872 3872 3872 4356 4356 4356 4356 4356 0581777 4686 7595 0590504 3413 25 26 27 28 29 5967 8871 0601775 4678 7582 35 34 33 32 -IL 30 29 28 27 26 484 484 484 484 484 968 968 968 968 968 1452 1452 1452 1452 145 1 1936 1936 1936 1936 1936 2420 2420 2420 2420 2419 2904 2904 2904 2904 2903 3388 3388 3388 3388 3387 3872 3872 3872 3872 3871 4356 4356 4356 4355 4355 6322 9231 0602140 5049 7958 30 31 32 33 34 0610485 3389 6292 9196 0622099 484 484 484 484 484 968 968 968 968 968 145 1 145 1 1451 145 1 145 1 1936 1935 1935 1935 1935 2419 2419 2419 2419 2419 2903 2903 2903 2903 2903 3387 3387 3387 3387 3387 3871 3871 3871 3871 3871 4355 4355 4355 4354 4354 0610865 3774 6683 9592 0622501 ■35 36 37 38 39 5002 7905 0630808 3711 6614 25 24 23 22 21 484 484 484 484 484 968 968 968 968 968 145 1 145 1 145 1 145: 145 1 1935 1935 1935 1935 1935 2419 2419 2419 2419 2419 2903 2903 2903 2903 2903 3387 3387 3387 3387 3387 3870 3870 3870 3870 3870 4354 4354 4354 4354 4354 5410 8319 0631228 4137 7046 40 41 42 43 44 45 46 47 48 49 9517 0642420 5323 8226 0651129 20 19 18 17 16 484 484 484 484 484 968 968 968 968 968 145 1 145 1 145 1 145 1 145 1 1935 1935 1935 1935 1935 2419 2419 2419 2419 2419 2903 2903 2903 2903 2903 3387 3387 3387 3387 3387 3870 3870 3870 3870 3870 4354 4354 4354 4354 4354 9954 0642863 5772 8681 0651590 4031 6934 9836 0662739 5641 15 14 13 12 II 484 484 484 484 484 968 968 968 968 968 145 1 145 1 145 1 145 1 145 1 1935 1935 1935 1935 1935 2419 2419 2419 2419 2419 2903 2903 2903 2903 2903 3387 3387 3387 3387 3387 3870 3870 3870 3870 3870 4354 4354 4354 4354 4354 4499 7408 0660317 3226 6135 50 51 52 53 54 8544 0671446 4349 7251 0680153 10 9 8 7 6 484 484 484 484 484 968 968 968 968 968 145 1 145 1 145 1 1451 145 1 1935 1935 1935 1935 1935 2419 2419 2419 2419 2419 2903 2903 2903 2903 2903 3387 3387 3387 3387 3387 3870 3870 3870 3870 3870 4354 4354 4354 4354 4354 9043 0671952 4861 7770 0680679 M 57 58 59 60 305 s 5957 8859 0691761 4663 7565 5 4 3 2 I 484 484 484 484 484 484 968 968 968 968 968 967 145 1 145 1 1451 145 1 1451 145 1 1935 1935 1935 1935 1934 1934 2419 2419 2419 2419 2418 2418 2903 2903 2903 2903 2902 2902 3387 3387 3387 3387 3386 3386 3870 3870 3870 3870 3870 3870 4354 4354 4354 4354 4353 4353 3588 6497 9406 0692315 5224 8132 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 86 Degrees. \ 4 Degrees. Difference for Seconds. [5 ' M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o I 2 3 4 5 6 7 8 9 0697565 0700467 3368 6270 9171 60 59 58 57 56 484 484 484 484 484 967 967 967 967 967 145 1 145 1 145 1 145 1 1451 1934 1934 1934 1934 1934 2418 2418 2418 2417 2417 2902 2902 2902 2901 2901 3385 3385 3385 3385 3385 3869 3869 3869 3868 3868 4352 4352 4352 4352 4352 0698132 070 I 04 I 3950 6859 9768 Arc. Sec. DiflF. 10 20 30 40 50 60 70 80 90 485 0712073 4974 7876 0720777 3678 55 54 53 52 51 484 484 484 484 484 967 967 967 967 967 145 1 145 1 1451 145 1 145 1 1934 1934 1934 1934 1934 2417 2417 2417 2417 2417 2901 2901 2901 2901 2901 3385 3385 3385 3385 3385 3868 3868 3868 3868 3868 4352 4352 4352 4352 4352 0712677 5586 8495 0721404 4313 970 1454 1939 2424 2909 3394 3878 4363 lO II 12 13 14 6580 9481 0732382 5283 8184 50 49 48 47 46 484 484 484 484 484 967 967 967 967 967 145 1 1451 145 1 145 1 145 1 1934 1934 1934 1934 1934 2417 2417 2417 2417 2417 2901 2901 2901 2901 2901 3385 3385 3385 3385 3385 3868 3868 3868 3868 3868 4352 4352 4352 4352 4352 7221 0730130 3039 5948 8857 17 i8 19 0741085 3986 6887 9787 0752688 45 44 43 42 41 484 484 484 484 484 967 967 967 967 967 145 1 145 1 1451 145 1 145 1 1934 1934 1934 1934 1934 2417 2417 2417 2417 2417 2901 2901 2901 2901 2901 338s 3385 338s 3385 3385 3868 3868 3868 3868 3868 4352 4352 4352 4352 4352 0741766 4675 7584 0750493 3402 20 21 22 23 24 5589 8489 0761390 4290 7190 40 39 38 37 36 484 484 483 483 483 967 967 967 967 967 145 1 145 1 1450 1450 1450 1934 1934 1934 1934 1934 2417 2417 2416 2416 2416 2901 2901 2900 2900 2900 3385 3385 3384 3384 3384 3868 3868 3867 3867 3867 4352 4352 4351 4351 4351 6310 9219 0762128 5037 7946 26 27 28 29 30 31 32 33 34 35 36 37 38 39 0770091 2991 5891 8791 078 1 69 1 35 34 33 32 31 483 483 483 483 483 967 967 967 1450 1450 1450 1450 1450 1934 1934 1934 1934 1934 2416 2416 2416 2416 2416 2900 2900 2900 2900 2900 3384 3384 3384 3384 3384 3867 3867 3867 3867 3867 4351 4351 4351 4351 4351 0770855 3764 6673 9582 0782490 4591 7491 0790391 3290 6190 30 29 28 27 26 483 483 483 483 483 967 967 967 967 967 1450 1450 1450 1450 1450 1934 1934 1934 1934 1934 2416 2416 2416 2416 2416 2900 2900 2900 2900 2900 3384 3384 3384 3384 3384 3867 3867 3867 3867 3867 4351 4351 4351 4351 4351 5398 8307 0791 2 16 4125 7034 9090 0801989 4889 7788 0810687 25 24 23 22 21 483 483 483 483 483 967 966 966 966 966 1450 1450 1450 1450 1450 1934 1933 1933 1933 1933 2416 2416 2416 2416 2416 2900 2899 2899 2899 2899 3384 3383 3383 3383 3383 3867 3866 3866 3866 3866 4351 4351 4351 4350 4350 9943 0802852 5761 8670 081 1579 40 41 42 43 44 3587 6486 9385 0822284 5183 20 19 18 17 16 483 483 483 483 483 966 966 966 966 966 1450 1450 1450 1450 1450 1933 1933 1933 1933 1933 2416 2416 2416 2416 2416 2899 2899 2899 2899 2899 3383 3383 3382 3382 3382 3866 3866 3866 3866 3866 4350 4350 4350 4350 4350 4487 7396 0820305 3214 6123 45 46 47 48 49 8082 0830981 3880 6778 9677 15 14 13 12 II 483 483 483 483 483 966 966 966 966 966 1450 1450 1450 1450 1450 1933 1933 1933 1933 1933 2416 2416 2416 2416 2416 2899 2899 2899 2899 2899 3382 3382 3382 3382 3382 3866 3866 3866 3866 3866 4350 4350 4350 4350 4350 9032 083 1 94 1 4850 7759 0840668 50 51 52 53 54 11 S7 58 59 60 0842576 5474 8373 085 1 27 1 4169 10 9 8 7 6 483 483 483 483 483 966 966 966 966 966 1450 1450 1450 1450 1450 1932 1932 1932 1932 1932 2415 2415 2415 2415 2415 2898 2898 2898 2898 2898 3381 3381 3381 3381 3381 3865 3865 3865 3865 3864 4349 4349 4349 4349 4349 3576 6485 9394 0852303 5212 7067 9966 0862864 5762 8660 0871557 5 4 3 2 I 483 483 483 483 483 483 966 966 966 966 966 966 1450 1450 1450 1450 1450 1450 1932 1932 1932 1932 1932 1932 2415 2415 2415 2415 2415 2415 2898 2898 2898 2898 2898 2898 3381 3381 3381 3381 3381 3381 3864 3864 3864 3864 3864 3864 4349 4349 4349 4349 4349 4349 8121 0861030 3939 6848 9757 0872665 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 85 Degrees. 6] 5 Deg rees. Difference for Seconds. M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o I 2 3 4 0871557 4455 7353 0880251 3148 60 59 58 57 56 483 483 483 483 483 966 966 966 966 966 1449 1449 1449 1449 1449 1932 1932 1932 1932 1932 2415 2415 2415 2415 2415 2898 2898 2898 2897 2898 3381 3381 3381 3381 3381 3864 3864 3864 3864 3864 4347 4347 4347 4347 4347 0872665 5574 8483 0881392 4301 Arc. Sec. Diff. 10 20 30 40 50 60 70 80 90 485 5 6 7 8 9 lO II 12 13 6046 8943 0891840 4738 7635 55 54 53 52 51 483 483 483 483 483 966 966 966 966 966 1449 1449 1449 1449 1449 1932 1932 1932 1932 1932 2415 2415 2415 2415 2415 2897 2897 2898 2897 2897 3381 3381 3381 3380 3380 3864 3864 3864 3864 3863 4347 4347 4347 4346 4346 7210 08901 19 3028 5937 8846 970 1454 1939 2424 2909 3394 3878 4363 0900532 3429 6326 9223 0912119 50 49 48 47 46 483 483 483 483 483 966 966 966 966 966 1449 1449 1448 1448 1448 1932 1932 193 1 193 1 1931 2415 2415 2414 2414 2414 2897 2897 2897 2896 2897 3380 3380 3380 3380 3380 3863 3862 3862 3862 3862 3862 3862 3862 3862 3862 4345 4345 4345 4345 4345 0901754 4663 7572 0910481 3390 17 i8 19 5016 7913 0920809 3706 6602 45 44 43 42 41 483 483 483 483 483 966 966 966 966 966 1448 1448 1448 1448 1448 193 1 1931 1931 1931 193 1 2414 2414 2414 2414 2414 2897 2896 2897 2896 2897 3380 3380 3380 3380 3380 4345 4345 4345 4345 4345 6299 9208 0922117 5026 7935 20 21 22 23 24 9499 0932395 5291 8187 0941083 40 39 38 37 36 483 483 483 483 483 965 965 965 965 965 1448 1448 1448 1448 1448 1930 1930 1930 1930 1930 2413 2413 2413 2413 2413 2896 2896 2896 2896 2896 3379 3379 3379 3379 3379 3861 3861 3861 3861 3861 4344 4344 4344 4344 4343 0930843 3752 6661 9570 0942479 25 26 27 28 29 30 31 32 33 34 3979 6875 9771 0952666 5562 35 34 33 32 31 483 483 483 483 483 965 965 965 965 965 1448 1448 1448 1448 1448 1930 1930 1930 1930 1930 2413 2413 2413 2413 2413 2896 2896 2895 2896 2896 3378 3378 3378 3378 3378 3861 3861 3861 3861 3861 4343 4343 4343 4343 4343 5388 8297 0951206 4115 7024 8458 0961353 4248 7144 0970039 30 29 28 27 26 483 483 483 483 483 965 965 96s 965 965 1448 1448 1448 1448 1448 1930 1930 1930 1930 1930 2413 2413 2413 2412 2412 2895 2895 2896 2895 2895 3378 3378 3378 3378 3378 3861 3861 3861 3860 3860 4343 4343 4343 4343 4343 9931 0962840 5749 8658 0971567 37 38 39 2934 5829 8724 0981619 4514 25 24 23 22 21 483 483 483 483 483 965 965 965 965 965 1448 1448 1448 1448 1448 1930 1930 1930 1930 1930 2412 2412 2412 2412 2412 2895 2895 2895 2895 2894 3378 3378 3378 3377 3377 3860 3860 3860 3860 3860 4343 4343 4343 4343 4343 4476 7385 0980294 3203 6112 40 41 42 43 44 7408 0990303 3197 6092 8986 20 19 18 17 16 15 14 13 12 II 483 483 483 483 483 482 482 482 482 482 965 965 965 965 965 1448 1448 1448 1448 1448 1930 1930 1930 1930 1930 1929 1929 1929 1929 1929 2412 2412 2412 2412 2412 2895 2894 2895 2894 2895 3377 3377 3377 3377 3377 3859 3859 3859 3859 3859 4342 4342 4342 4342 4342 9019 0991928 4837 7746 1000655 45 46 47 48 49 50 51 52 53 54 11 57 58 60 1001881 4775 7669 1010563 3457 965 965 965 965 965 1447 1447 1447 1447 1447 241 1 2411 241 1 241 1 2411 2894 2894 2894 2894 2894 3376 3376 3376 3376 3376 3858 3858 3858 3858 3858 4341 4341 4341 4341 4341 3564 6473 9382 1012291 5200 6351 9245 1022138 5032 7925 10 9 8 7 6 482 482 482 482 482 965 965 965 965 965 1447 1447 1447 1447 1447 1929 1929 1929 1929 1929 241 1 2411 2411 241 1 241 1 2894 2893 2894 2893 2894 3376 3376 3376 3376 3376 3858 3858 3858 3858 3858 4341 4341 4341 4341 4341 8108 1021017 3926 6835 9744 I 0308 I 9 3712 6605 9499 1042392 5285 5 4 3 2 I 482 482 482 482 482 482 965 965 965 964 964 964 1447 1447 1447 1446 1446 1446 1929 1929 1929 1928 1928 1928 241 1 2411 241 1 2410 2410 2410 2893 2893 2894 2893 2893 2893 3376 3376 3376 3375 3375 3375 3858 3858 3858 3857 3857 3857 4341 4341 4341 4339 4339 4339 1032653 5562 8471 I 04 I 380 4289 7198 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 1 80" 90" Arc. 84 Degrees. 6 Degrees. Difference for Seconds. [7 M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o I 1045285 8178 60 59 482 482 964 964 1446 1446 1928 1928 2410 2410 2893 2892 3375 3375 3857 3857 4339 4339 I 047 I 98 1050107 Arc. c;„~ r\;ff 2 105 1070 3963 5« 57 482 482 964 964 1446 1446 1928 1928 2410 2410 2893 2893 3375 3375 3857 3857 4339 4339 3016 5925 485 970 1454 4 6856 56 482 964 1446 1928 2410 2892 3375 3857 4339 8834 20 3<^ S 9748 55 482 964 1446 1928 2410 2893 3375 3857 4339 1061743 6 I 06264 I 54 482 964 1446 1928 2410 2892 3375 3857 4339 4652 40 1939 2424 7 5533 53 482 964 1446 1928 2410 2892 3375 3857 4339 7561 Sfi 8 8425 52 482 964 1446 1928 2410 2893 3375 3857 4339 1070470 60 2909 3394 9 1071318 51 482 964 1446 1928 2410 2892 3375 3857 4339 3379 70 80 lO 4210 50 482 964 1446 1928 2410 2892 3375 3857 4339 6287 3878 II 7102 49 482 964 1446 1928 2410 2892 3375 3857 4339 9196 90 4363 12 9994 48 482 964 1446 1928 2410 2891 3375 3857 4339 1082 105 n 1082885 47 482 964 1446 1928 2409 2892 3373 3855 4337 5014 5777 46 45 482 482 964 1446 1928 2409 2892 3373 3855 4337 4337 7923 8669 964 1446 1928 2409 2891 3373 385s 1090832 i6 1091560 44 482 964 1446 1928 2409 2892 3373 3855 4337 3741 17 4452 43 482 964 1446 1928 2409 2891 3373 385s 4337 6650 i8 7343 42 482 964 1446 1928 2409 2891 3373 3855 4337 9559 19 1 100234 41 482 964 1446 1928 2409 2892 3373 3855 4337 1 102468 20 3126 40 482 964 1445 1927 2409 2891 3373 3854 4336 5376 21 6017 39 482 964 1445 1927 2409 2891 3373 3854 4336 8285 22 8908 3« 482 964 1445 1927 2409 2891 3373 3854 4336 1111194 2^ 1111799 37 482 964 1445 1927 2409 2890 3373 3854 4336 4103 24 21? 4689 36 482 964 1445 1927 2409 2891 2891 3373 3854 4336 7012 7580 35 482 964 1445 1927 2409 3373 3854 4336 9921 26 1 1 2047 1 34 482 964 . 1445 1927 2409 2890 3373 3854 4336 II 22830 27 3361 33 482 964 1445 1927 2409 2891 3373 3854 4336 5739 28 6252 32 482 963 1445 1927 2408 2890 3372 3853 4335 8648 29 9142 1 132032 31 482 963 1445 1927 2408 2408 2890 3372 3853 4335 1131557 30 482 963 1445 1926 2890 3372 3853 4335 4464 11 4922 29 482 963 1445 1926 2408 2890 3372 3853 4335 7373 32 7812 28 482 963 1445 1926 2408 2890 3372 3853 4335 1 140282 33 1 140702 27 482 963 1445 1926 2408 2890 3372 3853 4335 3191 34 3S 3592 6482 26 482 963 1445 1926 1926 2408 2408 2890 3371 3853 4334 6100 25 482 963 1445 2890 3371 3853 4334 9009 36 9372 24 482 963 1445 1926 2408 2889 3371 3853 4334 1151918 37 1152261 23 482 963 1445 1926 2408 2890 3371 3853 4334 4827 38 5151 22 482 963 1445 1926 2407 2889 3371 3852 4334 7736 -39 40 8040 21 482 963 1445 1926 2407 2889 2889 3371 3852 4334 1 160645 1 160929 20 482 963 1445 1926 2407 3371 3852 4334 3553 41 3818 19 482 963 1445 1926 2407 2889 3371 3852 4334 6462 42 6707 18 482 963 1445 1926 2407 2889 3371 .3852 4334 9371 43 9596 17 482 963 1445 1926 2407 2889 3371 .3852 4334 1 172280 44 4S 1 1 72485 16 482 482 963 1445 1926 2407 2889 3371 3852 4334 5189 5374 15 963 1445 1926 2407 2889 3371 3852 4334 8098 46 8263 14 482 963 1445 1926 2407 2888 3371 3852 4334 1181007 47 1181151 13 482 963 1445 1926 2407 2889 3371 3852 4334 3916 48 4040 12 482 963 1445 1926 2407 2888 3371 3852 4334 6825 49 SO 6928 II 482 963 1445 1926 2407 2407 2888 3371 3852 3852 4334 9734 9816 10 482 963 1445 1926 2888 3370 4334 I 192642 51 1 192704 9 482 963 1445 1926 2407 2889 3370 3852 4334 5551 52 5593 8 482 963 1445 1926 2407 2888 3369 3851 4333 8460 S3 8481 7 482 963 1445 1926 2407 2887 3369 3850 4332 1 20 1 369 54 1 201 368 6 481 962 1444 1925 2406 2888 3369 3850 4332 4278 55 4256 5 481 962 1444 1924 2406 2888 3368 3849 4331 7187 56 7144 4 481 962 1443 1924 2405 2887 3368 3849 4330 I 2 10096 57 I 2 1003 I 3 481 962 1443 1924 2405 2888 3368 3849 4330 3005 5« 2919 2 481 962 1443 1924 2405 2887 3368 3849 4330 5914 59 5806 I 481 962 1443 1924 2405 2887 3368 3849 4330 8823 bo 1 218693 481 962 1443 1924 2405 2888 3368 70" 3849 4330 1221730 M. Cosine. M. 10" 20" 30" 40" 50" 60" 80" 90" Arc. 83 De grees. 8] 7 Degrees. Difference for Seconds. M. Sine. M. 10" 20" 30" 40" 50" 60" 70' 80" 90" Arc. o 121 8693 60 481 963 1444 1926 2406 2888 3369 3850 4332 1221730 Arc. I 1221581 59 481 963 1444 1926 2406 2887 3368 3849 4330 4639 . * ^ 2 4468 58 481 481 481 963 963 963 1444 1443 1443 1926 2406 2405 2405 2405 2887 98R6 3368 3367 3367 3849 3848 3848 4330 7548 Sec. Diff. 3 4 7355 I 23024 I 57 56 1924 1924 2887 2887 4329 4329 1230457 3366 10 20 485 3128 55 481 963 1443 1924 3367 3848 4329 6275 970 6 6015 54 481 963 1443 1924 2405 2886 3367 3848 4329 9184 3^ 1454 7 8901 53 481 963 1443 1924 2405 2887 3367 3848 4329 1242093 40 1939 8 1241788 52 481 963 1443 1924 2405 2886 3367 3848 4329 5002 60 70 80 2424 9 4674 51 481 963 1443 1924 2405 2886 3367 3848 4329 791 1 2909 lo 7560 50 481 963 1443 1924 2405 2886 3367 3848 4329 1250819 3394 3878 A •! fit's II 1250446 49 481 963 1443 1924 2405 2886 3367 3848 4329 3728 QO 12 3332 48 481 963 1443 1924 2405 2886 3367 3848 4329 6637 13 6218 47 481 963 1443 1924 2405 2886 3367 3848 4329 9546 H 9104 46 481 963 1443 1924 2405 2886 3367 3848 4329 1262455 15 I 261 990 45 481 963 1443 1924 2405 2885 3367 3848 4329 5364 i6 4875 44 481 963 1443 1924 2405 2886 3367 3848 4329 8273 17 7761 43 481 963 1443 1924 2405 2885 3367 3848 4329 1271182 i8 1270646 42 481 963 1443 1924 2405 2885 3367 3848 4329 4091 19 3531 41 481 963 1443 1924 2405 2885 3367 3848 4329 7000 20 6416 40 481 963 1443 1924 2405 2886 3367 3848 4329 9908 21 9302 39 481 963 1443 1924 2405 2884 3367 3848 4329 1282817 22 1282186 38 481 963 1443 1924 2405 2885 3367 3848 4329 5726 23 5071 37 481 963 1443 1924 2405 2885 3367 3848 4329 8635 24 7956 36 481 963 1443 1924 2405 2885 3367 3848 4329 1291544 25 I 290841 35 481 963 1443 1924 2405 2884 3367 3848 4329 4453 26 3725 34 481 963 1443 1924 2405 2884 3367 3848 4329 7362 27 6609 33 481 963 1443 1924 2405 2885 3367 3848 4329 I 30027 I 28 9494 32 481 962 1442 1923 2403 2884 3365 3846 4326 3180 29 1302378 31 30 481 962 1442 1923 2403 2884 3365 3846 4326 6089 30 5262 481 962 1442 1923 2403 2884 3365 3846 4326 8996 31 8146 29 481 962 1442 1923 2403 2884 3365 3846 4326 131 1905 32 1311030 28 481 962 1442 1923 2403 2883 3365 3846 4326 4814 33 3913 27 481 961 1442 1923 2403 2884 3365 3846 4326 7723 34 6797 26 481 961 1442 1923 2403 2884 3365 3846 4326 1320632 35 9681 25 481 961 1442 1922 2402 2883 3364 3844 4325 3541 36 1322564 24 481 961 1442 1922 2402 2883 3364 3844 4325 6450 37 5447 23 481 961 1442 1922 2402 2883 3364 3844 4325 9359 3« 8330 22 481 961 1442 1922 2402 2883 3364 3844 4325 1332268 39 1331213 21 481 961 1442 1922 2402 2883 3364 3844 4325 5177 40 4096 20 481 961 1442 1922 2402 2883 3364 3844 4325 8085 41 6979 19 481 961 1442 1922 2402 2883 3364 3844 4325 1340994 42 9862 18 481 961 1442 1922 2402 2882 3364 3844 4325 3903 43 1342744 17 481 961 1442 1922 2402 2883 3364 3844 4325 6812 44 5627 16 481 961 1442 1922 2402 2882 3364 3844 4325 9721 45 8509 15 481 961 1442 1922 2402 2883 3364 3844 4325 1352630 46 1351392 14 481 961 1441 1921 2401 2882 3363 3843 4324 5539 47 4274 13 481 961 1441 1921 2401 2882 3363 3843 4324 8448 48 7156 12 481 961 1441 1921 2401 2882 3363 3843 4324 1361357 49 1360038 II 481 961 1441 1921 2401 2881 3363 3843 4324 4266 50 2919 10 481 961 1441 1921 2401 2882 3363 3843 4324 7174 51 i^' 9 481 961 1441 1921 2401 2882 3363 3843 4324 1370083 52 8683 8 481 961 1441 1921 2401 2881 3363 3843 4324 2992 53 I 37 I 564 7 481 961 1441 1921 2401 2881 3363 3843 4324 5901 54 4445 6 480 960 1441 1921 2401 2882 3363 3843 4324 8810 55 0^327 5 480 960 1440 1920 2400 2881 3361 3841 4321 1381719 50 1380208 4 480 960 1440 1920 2400 2881 3361 3841 4321 4628 57 3089 3 480 960 1440 1920 2400 2881 3361 3841 4321 7537 S« 5970 2 480 960 1440 1920 2400 2880 3361 384r 4321 1390446 59 8850 I 480 960 1440 1920 2400 2881 3361 3841 4321 3355 bo 1391731 480 960 1440 1920 2400 2881 3361 3841 4321 6263 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 8 2 Deg frees. 8 Degr ees. Difference for Seconds [1 M. Sine. M. 10" 20" 30" 40" so" 60" 70" 80" 90" Arc. o 1391731 60 480 960 1441 1921 2401 2881 3361 3842 4322 1396263 Arc. I 4612 59 480 960 1440 1920 2400 2880 3360 3841 4321 9172 2 7492 58 480 960 1440 1920 2400 2880 3360 3841 4321 I 40208 I Diff h3 1400372 3252 57 56 480 480 960 960 1440 1440 1920 1920 2400 2400 2880 2880 3360 3360 3841 3840 4321 4320 4320 4990 7899 1410808 ■4 10 20 48s 970 ■5 6132 55 480 960 1440 1920 2400 2880 3360 3840 B6 9012 54 480 960 1440 1920 2400 2880 3360 3840 4320 3717 30 I4'>4 ■7 1411892 S3 480 960 1440 1920 2400 2880 3360 3840 4320 6626 40 1939 ■8 4772 52 480 960 1440 1920 2400 2880 3360 3840 4320 9535 50 2424 9 7651 51 480 960 1440 1920 2400 2880 3360 3840 4320 1422444 60 70 2909 10 142053 I 50 480 960 1440 1920 2400 2880 3360 3840 4320 5352 3394 II 3410 49 480 960 1440 1920 2400 2880 3360 3840 4320 8261 80 3878 12 6289 48 480 960 1440 1920 2399 2879 3359 3839 4319 143 1 1 70 90 4363 13 9168 47 480 960 1440 1920 2399 2879 3359 3839 4319 4079 H 1432047 46 480 960 1440 1920 2399 2879 3359 3839 4319 6988 15 4926 45 480 960 1440 1920 2399 2879 3359 3839 4319 9897 16 7805 44 480 960 1440 1920 2399 2879 3359 3839 4319 1442806 17 1440684 43 480 959 1439 1919 2398 2878 3358 3838 4318 5715 18 3562 42 480 959 1439 1919 2398 2878 3358 3838 4318 8624 19 20 6440 41 480 959 1439 1919 2398 2878 3358 3838 4318 H51533 4441 9319 40 480 959 1439 1919 2398 2878 3358 3838 4318 21 1452197 39 480 959 1439 1919 2398 2878 3358 3838 4318 7350 22 5075 38 480 959 1439 1919 2398 2878 3358 3838 4318 1460259 23 7953 7>1 480 959 1439 1919 2398 2878 3358 3838 4318 3168 24 1460830 36 480 959 1439 1919 2398 2878 3358 3838 4318 6077 25 3708 35 480 959 1439 1919 2398 2878 3358 3838 4318 8986 26 6585 34 480 959 1439 1919 2398 2878 3358 3838 4318 147 1 895 27 9463 33 480 959 H39 1918 2397 2877 3357 3837 4317 4804 28 1472340 32 480 959 H39 1918 2397 2877 3357 3837 4317 7713 29 30 5217 31 480 959 1439 1918 2397 2877 3357 3836 4317 1480622 8094 30 480 959 1439 1918 2397 2877 3357 3836 4316 3529 31 I 48097 I 29 480 959 1439 1918 2397 2877 3357 3836 4316 6438 32 3848 28 480 959 1439 1918 2397 2877 3357 3836 4316 9347 33 6724 27 480 959 1439 1918 2397 2877 3357 3836 4316 1492256 34 9601 26 25 480 959 1439 1918 2397 2876 3356 3835 4315 5165 35 1492477 479 959 1438 1918 2397 2876 3356 3835 4315 8076 36 5353 24 479 959 1438 1918 2397 2876 3356 3835 4315 1500983 37 8230 23 479 959 1438 1918 2397 2876 3356 3835 4315 3892 3« 1501106 22 479 959 1438 1918 2397 2876 3356 3835 4315 6801 J9. 40 3981 21 479 959 1438 1918 2397 2876 3356 3835 4315 9710 6857 20 479 959 1438 1918 2397 2876 3356 3835 4315 1512618 41 9733 19 479 959 1438 1918 2397 2876 3356 3835 4315 5527 42 15 1 2608 18 479 958 1438 1917 2396 2875 3355 3834 4314 8436 43 5484 17 479 958 1438 1917 2396 2875 3355 3834 4314 1521345 44 8359 16 479 958 1438 1917 2396 2875 3355 3834 4314 4254 45 1521234 15 479 958 1438 1917 2396 2875 3354 3834 4313 7163 46 4109 14 479 958 1438 1917 2396 2875 3354 3834 4313 1530072 47 6984 13 479 958 1438 1917 2396 2875 3354 3834 4313 2981 48 9858 12 479 958 1438 1917 2396 2875 3354 3834 4313 5890 49 1532733 II 479 958 1438 1917 2396 2875 3354 3834 4313 8799 50 5607 10 479 958 1438 1917 2396 2875 3354 3834 4313 1541707 51 8482 9 479 958 1438 1917 2396 2875 3354 3834 4313 4616 52 1541356 8 479 958 1437 1916 2395 2874 3353 3833 4312 7525 S3 4230 7 479 958 1437 1916 2395 2874 3353 3833 4312 1550434 55 7104 6 479 958 1437 1916 2395 2874 3353 3832 4312 3343 9978 5 479 958 1437 1916 2395 2874 3353 3832 431 1 6252 5(5 1552851 4 479 958 1437 1916 2395 2874 3353 3832 431 1 9161 57 5725 3 479 958 1437 1916 2395 2874 3353 3832 431 1 1562070 5« 8598 2 479 958 1437 1916 2395 2874 3353 3832 431 1 4979 59 1561472 I 479 958 1436 1915 2394 2873 3352 3831 4310 7888 60 1 4345 479 958 1436 1915 2394 2873 3352 3831 4310 1570796 M. ' Cosine. M. 10" 20" 30" 40" SO" 60" 70" 80" 90" Arc. 81 Degrees. 10] 9 Degrees. Difference for Seconds. ! M. Sine. M. 10" 20" 30" 40" SO" 60" 70" 80" 90" Arc. Arc, o I 2 3 4 1564345 7218 1570091 2963 5836 60 59 58 57 56 479 479 479 479 479 958 958 958 958 958 1437 1437 1437 1437 1437 1916 1916 1916 1916 1916 2394 2394 2394 2394 2394 2873 2873 2873 2873 2873 3352 3352 3352 3352 3352 3831 3831 3831 3831 3831 4310 4310 4310 4310 4310 1570796 3705 6614 9523 1582432 Sec. Diff. 10 20 30 40 50 60 70 80 90 485 970 1454 1939 2424 2909 3394 3878 4363 I 7 8 9 8708 1581581 4453 7325 1 590 1 97 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 479 479 479 479 479 479 479 479 479 479 958 957 957 957 957 1437 1437 1436 1436 1436 1916 1915 191S 1915 191S 2394 2393 2393 2393 2393 2873 2872 2872 2872 2872 3352 3351 3351 3351 3351 3831 3830 3830 3830 3830 4310 4309 4309 4308 4308 5341 8250 1591159 4068 6977 lO II 12 13 H 15 i6 I? i8 19 3069 5940 8812 I 60 I 683 4555 7426 1610297 3167 6038 8909 957 957 957 957 957 1436 1436 1436 1436 1436 1915 1915 19IS 1915 1914 2393 2393 2393 2393 2392 2872 2872 2872 2872 2871 3351 3351 3351 3351 3350 3830 3830 3830 3830 3829 3829 3829 3828 3828 3828 4308 4308 4308 4308 4307 1599885 1602794 5703 8612 1611521 479 479 479 479 479 957 957 957 957 957 1436 1436 1436 1436 1436 1914 1914 1914 1914 1914 2392 2392 2392 2392 2392 2871 2871 2871 2871 2871 3350 3350 3350 3350 3350 4307 4307 4307 4307 4307 4430 7339 1620248 3157 6066 20 21 22 23 24 1 62 1 779 4650 7520 1630390 3260 479 478 478 478 478 957 957 957 957 957 1436 1435 1435 1435 1435 1914 1914 1914 1914 1914 2392 2392 2392 2392 2392 2871 2870 2870 2870 2870 3350 3349 3349 3349 3349 3828 3827 3827 3827 3827 4307 4306 4306 4306 4306 1628974 163 1 883 4792 7701 I 6406 10 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 6129 8999 1641868 4738 7607 35 34 33 32 31 478 478 478 478 478 957 957 957 956 956 1435 1435 1435 1435 1435 1914 1914 1914 1913 1913 2392 2392 2392 2391 2391 2870 2870 2870 2869 2869 3349 3349 3349 3348 3348 3827 3827 3827 3826 3826 4306 4306 4306 4305 4305 3519 6428 9337 1652246 5155 1650476 3345 6214 9082 1661951 30 29 28 27 26 478 478 478 478 478 956 956 956 956 956 1435 1435 1434 1434 1434 1913 1913 1912 1912 1912 2391 2391 2390 2390 2390 2869 2869 2868 2868 2868 3347 3347 3346 3346 3346 3826 3826 3825 3824 3824 4304 4304 4303 4303 4302 1658062 1660971 3880 6789 9698 4819 7687 1670556 3423 6291 25 24 23 22 21 20 19 18 17 16 478 478 478 478 478 956 956 956 956 956 1434 1434 1434 1434 1434 1912 1912 1912 1912 1912 2390 2390 2390 2390 2390 2389 2389 2389 2389 2389 2868 2868 2868 2868 2868 2867 2867 2867 2867 2867 2867 2867 2867 2866 2866 3346 3346 3346 3346 3346 3824 3824 3824 3824 3824 4302 4302 4302 4302 4302 1672607 5516 8425 1681334 4243 • 40 41 42 43 44 9159 1682026 4894 7761 1690628 478 478 478 478 478 956 956 956 956 956 1433 1433 1433 1433 1433 1911 1911 1911 1911 1911 3345 3345 3345 3345 3345 3345 3345 3345 3344 3344 3823 3823 3822 3822 3822 4301 4301 4301 4300 4300 1687151 1690060 2969 5878 8787 45 46 47 48 49 50 SI 52 53 54 55 56 57 58 59 60 M. 3495 6362 9228 1702095 4961 15 14 13 12 II 478 478 478 478 478 956 956 956 955 955 1433 1433 1433 1433 1433 1911 1911 1911 1910 1910 2389 2389 2389 2388 2388 3822 3822 3822 3821 3821 4300 4300 4300 4299 4299 1 701696 4605 7514 1 7 10423 3332 7828 1 7 10694 3560 6425 9291 10 9 8 7 6 478 478 478 478 478 955 955 955 955 955 1433 H33 H33 1433 1433 1910 1910 1910 1910 1910 2388 2388 2388 2388 2388 2866 2866 2866 2866 2866 3344 3343 3343 3343 3343 3821 3821 3821 3821 3821 4299 4298 4298 4298 4298 6240 9149 1722058 4967 7876 1722156 5022 7887 1730752 3617 6482 5 4 3 2 I 478 478 478 478 478 478 955 955 955 955 955 955 1433 1433 1433 1433 1433 1433 1910 1910 1910 1910 1910 1910 2388 2387 2387 2387 2387 2387 2866 2865 2865 2865 2865 2865 3343 3343 3343 3343 3343 3343 3821 3820 3820 3820 3820 3820 4298 4298 4298 4298 4298 4298 1730785 3694 6603 9512 1 74242 1 5329 Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 80 Degrees. 10 Degrees. Difference for Seconds. [11 M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 1736482 9346 1742211 5075 60 59 58 57 477 477 477 477 955 955 955 955 1432 1432 1432 1432 1910 1910 1910 1910 2387 2387 2387 2387 2864 2865 2864 2864 3342 3342 3342 3342 3819 3819 3819 3819 4297 4297 4297 4297 1745329 8238 1 75 1147 4056 Arc. I 2 Sec. Diff. 3 485 970 1454 4 7939 56 55 477 955 1432 1910 2387 2864 3342 3819 4297 6965 20 30 1 1750803 477 955 1432 1910 2387 2864 3342 3819 4297 9874 6 3667 54 477 955 1432 1910 2387 2864 3342 3819 4297 1762783 40 1030 7 6531 53 477 955 1432 1910 2387 2864 3342 3819 4297 5692 50 2424 8 9395 52 477 955 1432 1910 2387 2863 3342 3819 4297 8601 60 2909 9 1762258 51 477 955 1432 1910 2387 2863 3342 3819 4297 1771510 70 80 3394 lO 5121 SO 477 955 1432 1910 2387 2863 3342 3819 4297 4418 3878 II 7984 49 477 955 1432 1910 2387 2863 3342 3819 4297 7327 90 4363. 12 1770847 48 477 955 1432 1910 2387 2863 3342 3819 4297 1780236 n 3710 47 477 955 1432 1910 2387 2863 3342 3819 4297 3145 H IS 6573 9435 46 45 477 954 1432 1909 2386 2862 3341 3818 J.296 4296 6054 477 954 1432 1909 2386 2863 3341 3818 8963 i6 1782298 44 477 954 1432 1909 2386 2862 3341 3818 4296 1791872 17 5160 43 477 954 1432 1909 2386 2862 3341 3818 4296 4781 i8 8022 42 477 954 1432 1909 2386 2862 3341 3818 4296 7690 19 1790884 41 477 954 1432 1909 2386 2862 3341 3818 4296 1800599 20 3746 40 477 954 1432 1909 2386 2861 3341 3818 4296 3507 21 6607 39 477 954 1432 1909 2386 2862 3341 3818 4296 6416 22 9469 38 477 954 1432 1909 2386 2861 3341 3818 4296 9325 23 1802330 37 477 953 1430 1907 2384 2861 3338 3816 4294 1812234 ,24 5191 3<> 477 953 1430 1907 2384 2861 3338 3816 4294 5143 21 8052 35 477 953 1430 1907 2384 2861 3338 3816 4294 8052 26 1810913 34 477 953 1430 1907 2384 2861 3338 3816 4294 I 82096 I 27 3774 33 477 953 1430 1907 2384 2861 3338 3816 4294 3870 28 6635 32 477 953 1430 1906 2383 2860 3356 3814 4291 6778 (29 9495 31 477 953 1430 1906 2383 2860 3336 3814 4291 9687 30 1822355 30 477 953 1430 1906 2383 2860 3336 3814 4291 1832595 ■31 5215 29 477 953 1430 1906 2383 2860 3336 3814 4291 5504 I32 8075 28 477 953 1430 1906 2383 2860 3336 3814 4291 8413 33 183093s 27 477 953 1430 1906 2383 2860 3336 3814 4291 1841322 34 3795 26 477 953 1430 1906 1906 2383 2859 3336 3814 4291 4231 3? 6654 25 477 953 1430 2383 2860 3336 3814 4291 7140 36 9514 24 477 953 1430 1906 2382 2859 3336 3812 4289 1850049 37 1842373 23 477 953 1430 1906 2382 2859 3336 3812 4289 2958 138 5232 22 477 953 1430 1906 2382 2859 3336 3812 4289 5867 J39 8091 21 477 953 1430 1906 2382 2858 3336 3812 4289 8775 i40 1850949 20 477 953 1430 1906 2382 2859 3336 3812 4289 1861684 41 3808 19 476 953 1429 1905 2381 2858 3334 3810 4287 4593 ,42 6666 18 476 953 1429 1905 2381 2858 3334 3810 4287 7502 143 9524 17 476 953 1429 1905 2381 2858 3334 3810 4287 1 87041 1 44 1862382 16 IS 476 953 1429 1905 1 2381 2858 3334 3810 4287 3320 6229 '45 5240 476 953 1429 1905 2381 2858 3334 3810 4287 46 8098 14 476 953 1429 1905 2381 2858 3334 3810 4287 9138 147 1870956 13 476 953 1429 1905 2381 2857 3334 3810 4287 1882047 i48 3813 12 476 953 1429 1905 2381 ,2857 3334 3810 4287 4956 49 6670 II 476 953 1429 1905 2381 2858 3334 3810 4287 7865 ISO 9528 10 476 952 1428 1904 2380 2857 3333 3809 4285 1890773 !Si 1882385 9 476 952 1428 1904 2380 2856 3333 3809 4285 3682 52 5241 8 476 952 1428 1904 2380 2857 3333 3809 4285 6591 53 8098 7 476 952 1428 1904 2380 2856 3333 3809 4285 9500 i-5* 1890954 6 476 952 1428 1904 2380 2857 3333 3809 4285 1902409 !ss 3811 5 476 952 1428 1904 2380 2856 3332 3808 4284 5318 56 6667 4 476 952 1428 1904 2380 2856 3332 3808 4284 8227 57 9523 3 476 952 1428 1904 2380 2856 3332 380S 4284 1911136 58 1902379 2 476 952 1428 1904 2380 2855 3332 3808 4284 4045 !59 5234 I 476 952 1428 1904 2380 2856 3332 3808 4284 6954 bo 8090 476 952 1428 1904 2380 2855 3332 3808 4284 9862 M. Cosine. M. 10" 20" 30" 40" so" 60" 70" -, 1 „ 80' 1 90 Arc. 79 De grees. • 12] 11 Degrees. Difference for Seconds. M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o 1908090 60 476 476 952 1427 1903 2379 2379 2855 2856 3331 3806 3806 4282 4282 1919862 Arc. I 1910945 S9 952 1427 1903 3331 1922771 2 3801 58 476 952 1427 1903 2379 2855 3331 3806 4282 5680 Sec. DifiF. ^ 6656 57 476 952 1427 1903 2379 2854 3331 3806 4282 8589 4 9510 56 476 952 1427 1903 2379 2855 3331 3806 4282 1 93 1 498 10 20 485 S 1922365 55 476 952 1427 1903 2379 2855 3331 3806 4282 4407 970 6 5220 54 476 951 1427 1902 2378 2854 3329 380s 4280 7316 i*-* 1454 7 8074 53 476 951 1427 1902 2378 2854 3329 3805 4280 1940225 4u 1939 8 1930928 52 476 951 1427 1902 2378 2854 3329 3805 4280 3134 5^ 60 70 80 2424 9 3782 51 476 951 1427 1902 2378 2854 3329 3805 4280 6043 2909 lO 6636 50 476 951 1427 1902 2378 2854 3329 3805 4280 8951 3394 3878 n 9490 49 476 951 1427 1902 2378 2854 3329 3805 4280 1951860 QO 12 1942344 48 476 951 1427 1902 2377 2853 3329 1 3804 4280 4769 n 5197 47 476 951 1427 1902 2377 2853 3329 3804 4280 7678 14 8050 46 476 951 1427 1902 2377 2853 3329 3804 4280 1960587 M 1950903 45 476 951 1427 1902 2377 2853 3329 3804 4280 3496 i6 3756 44 476 951 1427 1902 2377 2853 3329 3804 4280 6405 17 6609 43 476 951 1427 1902 2377 2852 3329 3804 4280 9314 i8 9461 42 476 951 1427 1902 2377 2853 3329 3804 4280 1972223 19 1962314 41 475 951 1426 1901 2376 2852 3327 3803 4279 5132 20 5166 40 475 951 1426 1 901 2376 2852 3327 3803 4279 8040 21 8018 39 475 951 1426 1901 2376 2852 3327 3803 4279 1980949 22 1970870 38 475 951 1426 1901 2376 2852 3327 3803 4279 3858 23 3722 37 475 950 1425 1900 2375 2851 3326 3801 4276 6767 24 6573 36 475 950 950 1425 1900 2375 2852 3326 3801 4276 9676 25 9425 35 475 1425 1900 2375 2851 3326 3801 4276 1992585 26 1982276 34 475 950 1425 1900 2375 2851 3326 3801 4276 5494 27 5127 33 475 950 1425 1900 2375 2851 3326 3801 4276 8403 28 7978 32 475 950 1425 1900 2375 2851 3326 3801 4276 2001312 29 1990829 31 475 950 1425 1900 2375 2850 3326 3801 4276 4220 30 3679 30 475 950 1425 1900 2375 2851 3326 3801 4276 7128 31 6530 29 475 950 1425 1900 2375 2850 3325 3800 4276 2010037 32 9380 28 475 950 1425 1900 2375 2850 3325 3800 4276 2946 33 2002230 27 475 950 1425 1900 2375 2850 3325 3800 4276 5855 34 5080 2b 475 950 1425 1900 2375 2850 3325 3800 3799 4276 8764 35 7930 25 475 950 1425 1900 2374 2849 3324 4274 2021673 3<5 2010779 24 475 950 1425 1900 2374 2850 3324 3799 4274 4582 37 3629 23 475 950 1425 1900 2374 2849 3324 3799 4274 7491 3« 6478 22 475 950 1425 1900 2374 2849 3324 3799 4274 2030400 39 9327 21 475 950 1425 1900 2374 2849 3324 3799 4274 3309 40 2022176 20 475 950 1425 1900 2374 2848 3324 3799 4274 6217 41 5024 19 475 950 1425 1900 2374 2849 3324 3799 4274 9126 42 7873 18 475 949 1424 1899 2373 2848 3323 3798 4272 2042035 43 2030721 17 475 949 1424 1899 2373 2848 3323 3798 4272 4944 44 3569 16 475 949 1424 1899 2373 2849 3323 3798 4272 7853 45 6418 15 475 949 1424 1899 2373 2847 3323 3798 4272 2050762 4b 9265 14 475 949 1424 1899 2373 2848 3323 3798 4272 3671 47 2042113 13 475 949 1424 1899 2373 2848 3323 3798 4272 6580 48 4961 12 475 949 1424 1898 2372 2847 3321 3795 4270 9489 49 7808 11 475 949 1424 1898 2372 2847 3321 3795 4270 2062398 50 2050655 10 475 949 1424 1898 2372 2847 3321 3795 4270 5306 51 3502 9 475 949 1424 1898 2372 2847 3321 3795 4270 8215 52 6349 8 474 949 1423 1897 2371 2846 3320 3794 4269 207 I I 24 53 919s 7 474 949 1423 1897 2371 2847 3320 3794 4269 4033 54 2062042 6 474 949 1423 1423 1897 2371 2846 2846 3320 3794 4269 6942 55 4888 5 474 949 1897 2371 3320 3794 4269 9851 5b 7734 4 474 949 1423 1897 2371 2846 3320 3794 4269 2082760 H 2070580 3 474 949 1423 1897 2371 2846 3320 3794 4269 5669 5« 3426 2 474 949 1423 1897 2371 2846 3320 3794 4269 8578 59 6272 1 474 948 1422 1896 2370 2845 3319 3793 4267 2091487 bo 9117 474 948 1422 1896 2370 2845 3319 3793 4267 4395 M. Cosine. M. 10" 20" 30" 40" so" 60" 70" j 80" 1 90" Arc. 7 8 Def tXQQS. 12 Degrees. Difference for Seconds. [13 M. 9 lO II 12 13 JA_ 15 i6 17 i8 i9. 20 21 22 23 24 25 26 27 28 30 31 32 33 34 35 36 37 38 -39 40 41 42 43 44 45 46 47 48 49 SO 51 52 53 Sine. 2079 1 1 7 2081962 4807 7652 2090497 3341 6186 9030 2101874 4718 7561 21 10405 3248 6091 8934 2121777 4619 7462 2130304 3146 5988 8829 2141671 4512 7353 2150194 3035 5876 8716 2161556 4396 7236 2170076 2915 5754 8593 2181432 4271 7110 9948 2192786 5624 8462 2201300 4137 6974 981 1 2212648 5485 8321 2221158 3994 6830 9666 54 I 2232501 55 56 5337 8172 57 I 2241007 58 I 3842 59 6676 60 j 95 II M. ! Conine. M. 60 59 58 57 56 55 54 53 52 11 50 49 48 47 10 20 30 474 474 474 474 474 474 474 474 474 _474^ 474 474 474 474 474 474 474 474 474 474 474 474 474 474 474 474 474 473 473 473 473 473 473 473 473 473 473 473 473 -473. 473 473 473 473 473 473 473 473 473 473 473 10" 948 948 948 948 948 948 948 948 948 948 948 948 948 948 948 947 947 947 947 947 947 947 947 947 947 947 947 947 947 947 946 946 946 946 946 946 946 946 "946 946 946 946 946 946 946 946 946 946 945 945 945 945 945 945 945 945 945 945 945 1422 1422 1422 1422 1422 40 1422 1422 1422 1422 1422 1422 1422 1422 1422 1422 1422 1422 1421 142 1 142 1 1421 1421 1421 1421 142 1 1421 1421 1420 1420 1420 1420 1420 1419 1419 1419 1419 1419 1419 1419 1419 1419 1419 1419 1418 1418 1412 I4i{ 141^ 1415 141! 141; I4i{ 141^ 141? 141^ I4ii I4i{ 1415 I4i{ 141? 141J "1^ 896 896 896 896 896 896 895 894 894 894 894 894 894 894 894 894 893 893 893 893 893 892 892 892 892 892 892 892 892 892 892 892 890 890 890 890 890 890 "4^ 50" 2370 2370 2370 2370 2370 60" 2370 2370 2370 2370 2370 2370 2369 2369 2369 2369 2369 2369 2368 2368 2368 2368 2368 2367 2367 2367 2367 2367 2366 2366 2366 2366 2366 2365 2365 2365 2365 2365 2365 2365 2365 2365 2365 2365 2364 2364 2364 2364 2364 2364 2364 2363 2363 2363 2363 2363 2362 2362 2362 2362 2362 2362 2844 2843 2843 2843 2843 2842 2843 2842 2842 2842 2841 2842 2841 2841 2841 2841 2841 2840 2840 2840 2840 2840 2839 2839 2839 2839 2839 2839 2838 2838 2838 2838 2838 2837 2837 2837 2837 2837 2836 2837 2836 2836 2836 2835 2836 2835 2835 2835 2834 2835 2834 60" 70" 3309 3309 3309 3309 3309 3308 3308 3308 3308 3308 3308 ~7^ 80" 3793 3793 3793 3793 3793 3793 3792 3792 3792 3792 3792 3791 3791 3791 3791 3791 3791 3790 3790 3790 3790 3790 3788 3788 3788 3788 3788 3787 3787 3787 3787 3787 3785 3785 3785 3785 3785 3785 3784 3784 3784 3784 3784 3783 3783 3783 3782 3782 3782 3782 3782 3782 3782 3782 3782 3780 3780 3780 3780 3780 3780 80" 90 4267 4267 4267 4267 4267 4267 4266 4266 4266 4266 4266 4265 4265 4265 4265 4265 4265 4263 4263 4263 4263 4263 4262 4262 4262 4262 4262 4261 4261 4261 4261 4261 4258 4258 4258 4258 4258 4258 4257 4257 4257 4257 4257 4256 4256 4256 4255 4255 4255 4255 4254 4254 4254 4254 4254 4253 4253 4253 4253 4253 4253 ~9^ Arc. 2094395 7304 2100213 3122 6031 8940 2 II 1 849 4758 7667 2120576 3484 6393 9302 2132211 5120 8029 2140938 3847 6756 9665 2152573 5482 8391 2161300 4209 7118 2170027 2936 5845 8754 2181662 4571 7480 2190389 3298 6207 9116 2202025 4934 7843 2210750 3659 6568 9477 2222386 5295 8204 2231113 4022 6931 9839 2242748 5657 8566 2251475 4384 7293 2260202 3111 6020 8928 Arc. Arc. . . ,.A. Sec. Diff 10 485 20 970 30 1454 40 1939 50 60 2424 2C09 70 80 90 3394 3878 4363 77 Degrees. 14] 13 Degrees • Difference for Seconds. M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o I 22495 1 1 2252345 60 59 472 472 945 945 1417 1417 1889 1889 2361 2361 2834 2834 3306 3306 3778 3778 4251 4251 2268928 2271837 Arc. A 2 5179 58 472 945 1417 1889 1889 2361 2361 2834 2833 3306 3306 3778 4251 4746 Sec JJitt. 3 8013 57 472 945 1417 3778 4251 7655 4 2260846 56 472 945 1417 1889 2361 2834 3306 3778 4251 2280564 10 20 30 40 50 60 485 5 3680 55 472 944 1416 1889 2360 2833 3305 3777 4249 3473 970 US4 1939 2424 2909 3394 3878 6 6513 54 472 944 1416 1889 2360 2833 3305 3777 4249 6382 7 9346 53 472 944 1416 1889 2360 2833 3305 3777 4249 9291 8 2272179 52 472 944 1416 1889 2360 2833 3305 3777 4249 2292200 9 5012 51 472 944 1416 1889 2360 2832 3305 3777 4249 5109 70 80 lO 7844 50 472 944 1416 1889 2360 2833 3305 3777 4249 8017 II 2280677 49 472 944 1416 1888 2360 2832 3304 3776 4248 2300926 90 A■^6■^ 12 3509 48 472 944 1416 1888 2360 2832 3304 3776 4248 3835 n 6341 47 472 944 1416 1888 2360 2831 3304 3776 4248 6744 14 9172 46 472 944 1416 1888 2360 2832 3304 3776 4248 9653 I"? 2292004 45 472 944 1416 1888 2359 2831 3303 3775 4247 2312562 i6 4835 44 472 944 1416 1888 2359 2831 3303 3775 4247 5471 17 7666 43 472 944 1415 1888 2359 2831 3303 3774 4246 8380 i8 2300497 42 472 944 1415 1888 2359 2831 3303 3774 4246 2321289 19 20 3328 41 472 944 1415 1887 2359 2831 3303 3774 4246 4198 6159 40 472 943 1415 1887 2358 2830 3302 3774 4245 7106 21 8989 39 472 943 1415 1887 2358 2830 3302 3773 4245 2330015 22 2311819 38 472 943 1415 1886 2358 2830 3301 3773 4244 2924 23 4649 37 472 943 1415 1886 2358 2830 3301 3773 4244 5833 24 2"; 7479 36 472 943 1415 1886 2358 2830 3301 3773 4244 8742 2320309 35 472 943 141S 1886 2357 2829 3301 3772 4244 234165 1 26 3138 34 472 943 1415 1886 2357 2829 3301 3772 4244 4560 27 5967 33 472 943 1415 1886 2357 2829 3301 3772 4244 7469 28 8796 32 472 943 1415 1886 2357 2829 3301 3772 4244 2350378 29 30 2331625 31 30 472 472 943 1415 1886 2357 2829 3301 3772 4244 3287 4454 943 1414 1886 2357 2828 3300 3771 4243 6194 31 7282 29 472 943 1414 1886 2357 2828 3300 3771 4243 9103 32 2340 II 28 472 943 1414 1886 2356 2828 3300 3771 4243 2362012 ^^ 2938 27 472 943 1414 1885 2356 2828 3299 3770 4242 4921 34 3S 5766 26 472 943 1414 1885 2356 2828 3299 3770 4242 7830 8594 25 471 942 1414 1884 2356 2827 3298 3770 4241 2370739 36 2351421 24 471 942 1413 1884 2355 2827 3298 3769 4241 3648 37 4248 23 471 942 1413 1884 2355 2827 3298 3769 4240 6557 3« 7075 22 471 942 1413 1884 2355 2827 3298 3769 4240 9466 39 40 9902 21 471 942 1413 1884 2355 2355 2827 3298 3769 4240 2382375 2362729 20 471 942 1413 1884 2826 3297 3768 4239 5283 41 5555 19 471 942 1413 1884 2355 2826 3297 3768 4239 8192 42 8381 18 471 942 1413 1884 2355 2826 3297 3768 4239 2391 lOI 43 2371207 17 471 942 1413 1884 2355 2826 3297 3768 4239 4010 44 45 4033 6859 16 471 942 1413 1884 2355 2826 2825 3297 3297 3768 4239 6919 15 471 942 1413 1884 2355 3768 4239 9828 46 9684 H 471 942 1413 1884 2355 2826 3297 3768 4239 2402737 47 2382510 13 471 942 1412 1884 2354 2825 3296 3767 4238 5646 48 5335 12 471 942 1412 1883 2354 2824 3296 3767 4238 8555 49 50 8159 II 471 942 1412 1883 2354 2825 3296 3766 4237 241 1464 2390984 10 471 942 1412 1883 2354 2824 3296 3766 4237 4372 51 3808 9 471 942 1412 1883 2354 2825 3296 3766 4237 7281 52 6633 8 471 941 1412 1883 2353 2824 3295 3766 4236 2420190 53 9457 7 471 941 1412 1882 2353 2823 3295 3765 4236 3099 54 55 2402280 6 471 941 1412 1882 2353 2824 3294 3765 4235 6008 5104 5 471 941 1412 1882 2353 2823 3294 3765 4235 8917 5<> 7927 4 471 941 1412 1882 2352 2824 3294 3765 4235 2431826 57 241075 1 3 471 941 1412 1882 2352 2823 3294 3764 4235 4735 5« 3574 2 471 941 1412 1882 2352 2822 3294 3764 4234 7644 59 6396 I 471 941 1412 1882 2352 2823 3294 3764 4234 2440553 bo M. 9219 471 941 1412 1882 2352 2822 3294 3764 4234 3461 Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 76 Degrees. 14 Degrees. Difference for Seconds. [15 M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" ' 90" Arc. o I 2419219 2422041 60 59 470 470 941 941 1411 1411 1881 1881 2351 2351 2822 2822 3292 3292 3762 3762 4233 4233 2443461 6370 Arc. 2 4863 7685 58 57 470 470 941 94 c 1411 1411 1881 1881 2351 2351 2822 2822 3292 3292 3762 3762 4233 4233 9279 2452188 485 970 1454 1939 2424. 4 2430507 56 470 941 141 1 1881 2351 2822 3292 3762 4233 5097 20 30 40 3329 55 470 940 1410 1880 2350 2821 3291 3762 4232 8006 6 6150 54 470 940 1410 1880 2350 2821 3291 3761 4232 2460915 7 8971 S3 470 940 1410 1880 2350 2821 3291 3761 4231 3824 S 8 2441792 52 470 940 1410 1880 2350 2821 3291 3761 4231 6733 2909 3394 9 4613 SI 470 940 1410 1880 2350 2820 3291 3761 4231 9642 70 80 lO 7433 50 470 940 1410 1880 2350 2821 3291 3761 4231 2472550 3878 II 2450254 49 470 940 1410 1880 2350 2820 3290 3760 4230 5459 90 4363 12 3074 48 470 940 1410 1880 2350 2820 3290 3760 4230 8368 n 5894 47 470 940 1410 1880 2349 2819 3290 3760 4230 2481277 IS 8713 46 470 940 1410 1880 2349 2820 3290 3760 4230^ 4229 4186 2461533 45 470 940 1409 1879 2349 2819 3289 3759 7095 i6 4352 44 470 940 1409 1879 2349 2819 3289 3759 4229 2490004 17 7171 43 470 940 1409 1879 2349 2819 3289 3758 4228 2913 i8 9990 42 470 940 1409 1879 2349 2819 3289 3758 4228 5822 19 2472809 41 470 939 1409 1878 2348 2818 3288 3758 4227 8731 20 5627 40 470 939 1409 1878 2348 2818 3288 3757 4227 2501639 21 8445 39 470 939 1409 1878 2348 2818 3287 3757 4226 4548 22 2481263 38 470 939 1409 1878 2348 2818 3287 3757 4226 7457 2^ 4081 37 470 939 1409 1878 2348 2818 3287 3757 4226 2510366 24 6899 36 35 470 470 939 939 1409 1409 1878 2347 2817 3287 3756 4226 3275 2=; 9716 1878 2347 2817 3287 3756 4226 6184 26 2492533 34 470 939 1409 1878 2347 2817 3287 3756 4226 9093 27 5350 33 470 939 1409 1878 2347 2817 3287 3756 4226 2522002 28 8167 32 470 939 1409 1878 2347 2817 3287 3756 4226 4911 29 30 2500984 31 469 939 1408 1878 2347 2816 3286 3755 4225 7820 3800 30 469 939 1408 1877 2346 2816 3286 3755 4225 2530727 11 6616 29 469 939 1408 1877 2346 2816 3286 3755 4225 3636 32 9432 28 469 939 1408 1877 2346 2816 3286 3755 4225 6545 33 2512248 27 469 938 1408 1877 2346 2815 3285 3754 4223 9454 34 3S 5063 26 469 938 1408 1877 2346 2816 3285 3754 4223 2542363 7879 25 469 938 1407 1876 2345 2815 3284 3753 4222 5272 36 2520694 24 469 938 1407 1876 2345 2814 3284 3753 4222 8181 37 3508 23 469 938 1407 1876 2345 2815 3284 3753 4222 2551090 38 6323 22 469 938 1407 1876 2345 2814 3284 3753 4222 3999 39 40 9137 21 469 938 1407 1876 2345 2815 3284 3753 4222 6908 2531952 20 469 938 1407 1876 2345 2814 3283 3752 4221 9816 41 4766 19 469 938 1407 1876 2344 2813 3283 3752 4221 2562725 42 7579 18 469 938 1406 1875 2344 2814 3283 3752 4221 5634 43 2540393 17 469 938 1406 1875 2344 2813 3282 3751 4220 8543 44 3206 16 469 938 1406 1875 2344 2813 3282 3751 4220 2571452 ■ l45 6019 15 469 938 1406 1875 2344 2813 3282 3751 4220 4361 |46 8832 14 469 938 1406 1875 2344 2813 3282 3751 4220 7270 IP47 2551645 13 469 938 1406 1875 2344 2813 3282 3751 4220 2580179 48 4458 12 469 937 1406 1874 2343 2812 3281 3750 4219 3088 49 SO 7270 II 10 469 937 1406 1874 2343 2812 3281 3749 4218 5997 2560082 469 937 1406 1874 2343 2812 3281 3749 4218 8906 51 2894 9 469 937 1406 1874 2343 281 1 3280 3748 4218 2591815 52 5705 8 469 937 1406 1874 2343 2812 3280 3747 4217 4724 53 8517 7 469 937 1406 1874 2342 281 1 3280 3747 4217 7633 54 2571328 6 469 937 1406 1874 2342 281 1 3280 3747 4217 2600542 55 4139 5 469 937 1406 1874 2342 2811 3280 3747 4217 3451 56 6950 4 468 937 1405 1874 2342 2810 3279 3747 4216 6360 57 9760 3 468 937 1405 1874 2341 2810 3279 3746 4216 9269 5ii 2582570 2 468 937 1405 1874 2341 2811 3279 3746 4215 2612178 19 5381 I 468 936 1405 1873 2341 2809 3278 3746 4215 5087 60 8190 468 936 1405 1873 2341 2810 3278 3745 4214 7994 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 75 Degrees. 16] Ifi > Degrees. Difference for Seconds. M. Sine. M. 10" 20" 30" 40" so" 60" 70" 80" 90" Arc. o 2588190 60 468 937 1405 1873 2341 2810 3278 3746 4215 2617994 Arc. I 2591000 59 468 937 1405 1873 2341 2810 3278 3746 4215 2620903 A 2 3810 6619 58 468 468 936 936 1404 1872 1872 2340 2340 2809 2809 3277 3746 3746 4214 3812 6721 Sec. Diff. 3 S"/ 1404 3277 4214 4 9428 56 55 468 936 1404 1872 2340 2340 2809 2808 3277 3746 4214 9630 10 20 485 S 2602237 468 936 1404 1872 3277 3746 4214 2632539 970 6 5045 54 468 936 1404 1872 2340 2808 3277 3746 4214 5448 3^ 1454 7 7853 53 468 936 1404 1872 2340 2809 3277 3746 4214 8357 40 1939 8 2610662 52 468 936 1404 1872 2340 2807 3276 3744 4212 2641266 5^ 60 70 80 2424 9 3469 51 468 936 1404 1872 2340 2340 2808 3276 3744 4212 4175 2909 lO 6277 50 468 936 1404 1872 2808 3276 3744 4212 7083 3394 3878 II 9085 49 468 936 1403 1871 2339 2807 3276 3744 4212 9992 QO 12 2621892 48 468 936 1403 1871 2339 2807 3275 3743 421 1 2652901 13 4699 47 468 936 1403 1871 2339 2807 3275 3743 421 1 5810 H 7506 46 468 936 1403 1871 2339 2806 3275 3743 4211 8719 15 2630312 45 468 936 1403 1871 2339 2806 327s 3743 421 1 2661628 i6 3118 44 468 936 1403 1871 2339 2807 3275 3743 421 1 4537 17 5925 43 468 935 1403 1870 2338 2805 3273 3741 4208 7446 1 i8 8730 42 468 935 1403 1870 2338 2806 3273 3741 4208 2670355 1 19 2641536 41 468 935 1403 1870 2338 2806 3273 3741 4208 3264 1 20 4342 40 468 935 1403 1870 2338 2805 3273 3740 4208 6172 21 7147 39 468 935 1403 1870 2338 2805 3273 3740 4208 9081 22 9952 38 468 935 1403 1870 2338 2805 3273 3740 4208 2681990 23 2652757 37 468 935 1403 1870 2338 2804 3273 3740 4208 4899 24 5561 36 468 935 1403 1870 2338 2805 3273 3740 4208 7808 2S 8366 35 467 935 1402 1869 2337 2804 3271 3738 4206 26907 1 7 26 2661 170 34 467 935 1402 1869 2337 2803 3271 3738 4206 3626 27 3973 33 467 935 1402 1869 2337 2804 3271 3738 4206 6535 28 6777 32 467 935 1402 1869 2337 2804 3271 3738 4206 9444 29 9581 31 467 934 1 401 1868 2336 2803 3270 3737 4204 2702353 ^ 30 2672384 30 467 934 1401 1868 2336 2803 3270 3737 4204 5260 31 5187 29 467 934 1401 1868 2336 2802 3270 3737 4204 8169 32 7989 28 467 934 1401 1868 2336 2803 3270 3737 4204 271 1078 33 2680792 27 467 934 1401 1868 2335 2802 3269 3736 4203 3987 34 3594 26 467 934 1401 1868 2335 2802 3269 3736 4203 6896 35 6396 25 467 934 1 401 1868 2335 2802 3269 3736 4203 9805 36 9198 24 467 934 1401 1868 2335 2802 3269 3736 4203 2722714 37 2692000 23 467 934 1400 1867 2334 2801 3268 3734 4201 5623 3« 4801 22 467 934 1400 1867 2334 2801 3268 3734 4201 8532 39 7602 21 467 934 1400 1867 2334 2801 3268 3734 4201 2731441 40 2700403 20 467 934 1400 1867 2334 2801 3268 3734 4201 4349 41 3204 19 467 934 1400 1867 2334 280c 3268 3734 4201 7258 42 6004 18 467 934 1400 1867 2334 2801 3268 3734 4201 2740167 43 8805 17 467 933 1400 1866 2333 2800 3266 3733 4199 3076 44 45 27 II 605 16 467 933 1400 1866 2333 2799 3266 3733 3733 4199 5985 4404 15 467 933 1400 1866 2333 2800 3266 4199 8894 4b 7204 14 467 933 1400 1866 2333 2799 3266 3732 4199 2751803 47 2720003 13 467 933 1400 1866 2333 2799 3266 3732 4199 4712 48 2802 12 467 933 1400 1866 2333 2799 3266 3732 4199 7621 49 5601 II 467 933 1400 1866 2333 2799 3266 3732 4199 2760530 SO 8400 10 467 933 1400 1866 2333 2798 3266 3732 4199 3438 51 2731 198 9 467 933 1400 1866 2333 2799 3266 3732 4199 6347 52 3997 8 466 933 1399 1865 2332 2797 3264 3730 4197 9256 53 6794 7 466 933 1399 1865 2332 2798 3264 3730 4197 2772165 5^ 55 9592 6 466 933 1399 1865 2332 2798 3264 3730 4197 5074 2742390 5 466 932 1398 1864 2331 2797 3263 3729 4195 7983 5b 5187 4 466 932 1398 1864 2331 2797 3263 3729 4195 2780892 57 7984 3 466 932 1398 1864 2331 2797 3263 3729 4195 3801 5« 2750781 2 466 932 1398 1864 2331 2796 3263 3729 4195 6710 59 3577 I 466 932 1398 1864 2331 2797 3263 3729 4195 9619 60 6374 466 932 1398 1864 2331 2796 3263 3729 4195 2792527 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 74 Degrees. 16 Degrees. Difference for Seconds Ll^ M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o 2756374 60 466 932 1398 1864 2330 2796 3262 3728 4194 2792527 Arc, I 2 9170 2761965 59 S8 466 466 932 932 1398 1398 1864 1864 2330 2330 2795 2796 3262 3262 3728 3728 4194 4194 5436 8345 Sec. Diff. 3 4 4761 7556 57 56 466 466 932 932 1398 1398 1864 1864 2330 2330 2795 2796 3262 3262 3728 3728 4194 4194 4193 2801254 4163 7072 1 10 1 /i8e ^ 2770352 55 466 932 1398 1864 2330 2795 3261 3727 20 970 6 3147 54 466 932 1398 1864 2330 2794 3261 3727 4193 9981 30 1454 7 5941 53 466 932 1398 1864 2330 2795 3261 3727 4193 2812890 ^0 1939 8 8736 52 466 931 1397 1862 2329 2794 3259 3725 4190 5799 50 2424 9 lO 2781530 51 466 931 1397 1862 2329 2794 3259 3725 4190 8708 60 70 2909 4324 50 466 931 1397 1862 2329 2794 3259 3725 4190 2821616 3394 II 7118 49 466 931 1397 1862 2328 2793 3259 3724 4190 4525 80 3878 12 991 1 48 466 931 1397 1862 2328 2793 3259 3724 4190 7434 90 4363 n 2792704 47 466 931 1397 1862 2328 2793 3259 3724 4190 2830343 H 5497 46 466 931 1397 1862 2328 2793 3259 3724 4190 3252 IS 8290 45 466 931 1397 1862 2328 2793 3259 3724 4190 6161 i6 2801083 44 465 931 1397 1861 2327 2792 3257 3722 4188 9070 17 3875 43 465 931 1396 j86i 2327 2792 3257 3722 4188 2841979 i8 ■6667 42 465 931 1396 1 861 2327 2792 3257 3722 4188 4888 19 9459 41 40 465 931 1396 1861 2327 2792 3257 3722 4f88 7797 20 2812251 465 930 1395 i860 2326 2791 3256 3721 4186 2850705 21 5042 39 465 930 1395 i860 2326 2791 3256 3721 4186 3614 22 7833 38 465 930 1395 i860 2326 2791 3256 3721 4186 6523 23 2820624 37 465 930 1395 i860 2326 2791 3256 3721 4186 9432 24 3415 36 465 930 1395 i860 2325 2790 3255 3720 4185 2862341 6205 35 465 930 1395 i860 2325 2790 3255 3720 4185 5250 26 8995 34 465 930 1395 i860 2325 2790 3255 3720 4185 8159 27 2831785 33 465 930 1395 i860 2325 2790 3255 3720 4185 2871068 28 4575 32 465 930 1394 1859 2324 2789 3254 3718 4183 3977 29 7364 31 465 930 1394 1859 2324 2789 3254 3718 4183 6886 30 2840153 30 465 930 1394 1859 2324 2789 3254 3718 4183 00^793 31 2942 29 465 930 1394 1859 2324 2789 3254 3718 4183 2882702 32 5731 28 465 930 1394 1859 2324 2789 3254 3718 4183 561 1 S3 8520 27 465 929 1394 1858 2323 2788 3252 3717 4181 8520 34 2851308 26 465 929 1394 1858 2323 2788 3252 3717 4181 2891429 3"; 4096 25 465 929 1394 1858 2323 2788 3252 3717 4181 4338 36 6884 24 465 929 1394 1858 2323 2787 3252 3716 4181 7247 37 9671 23 465 929 1394 1858 2323 2787 3252 3716 4181 2900156 38 2862458 22 465 929 1394 1858 2323 2788 3252 3716 4181 3065 39 5246 21 465 929 1394 1858 2323 2786 3252 3716 4181 5974 40 8032 20 465 929 1394 1858 2323 2787 3252 3716 4181 8882 41 2870819 19 464 929 1393 1857 2322 2786 3250 3714 4179 2911791 42 3605 18 464 929 1393 1857 2322 2786 3250 3714 4179 4700 43 6391 17 464 929 1393 1857 2322 2786 3250 3714 4179 7609 44 9177 16 464 929 1393 1857 2322 2786 3250 3714 4179 2920518 4S 2881963 IS 464 928 1392 1856 2321 2785 3249 3713 4177 3427 46 4748 14 464 928 1392 1856 2321 2785 3249 3713 4177 6336 47 7533 13 464 928 1392 1856 2321 2785 3249 3713 4177 9245 48 2890318 12 464 928 1392 1856 2321 2785 3249 3713 4177 2932154 49 ! 3103 II 464 928 1392 1856 2320 2784 3248 3712 4176 5063 SO 5887 10 464 928 1392 1856 2320 2784 3248 3712 4176 7971 SI 8671 9 464 928 1392 1856 2320 2784 3248 3712 4176 2940880 S2 2901455 8 464 928 1392 1856 2320 2784 3248 3712 4176 3789 S3 4239 7 464 928 1391 1855 2319 2783 3247 3710 4174 6698 54 7022 6 464 928 1391 1855 2319 2783 3247 3710 4174 9607 SS 9805 S 464 928 1391 1855 2319 2783 3247 3710 4174 2952516 S6 2912588 4 464 928 1391 1855 2319 2783 3247 3710 4174 5425 S7 5371 3 464 927 1391 1854 2318 2782 3245 3709 4172 8334 S8 8153 2 464 927 1391 1854 2318 2782 3245 3709 4172 2961243 S9 2920935 I 464 927 1391 1854 2318 2782 3245 3709 4172 4152 60 3717 464 927 1391 1854 2318 2782 3245 3709 4172 7060 M. 1 Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 73 Degrees. 18] 17 !( 3grees • Difference "or Second.s. M. o I Sine. M. 10" 20" J 30" 40" 50" 60" 70" 80" 90" >^rc. 2923717 6499 60 59 464 464 927 927 1391 1391 1854 1854 2318 2318 2782 2781 3245 3245 3709 3708 4172 4172 2967060 9969 Arc. Sec. 2 3 9280 2932061 58 57 464 464 927 927 1391 1391 1854 1854 2318 2318 2781 2781 3245 3245 3708 3708 4172 4172 2972878 5787 Difif. 4 4842 56 464 927 1391 1854 2318 2781 3245 3708 4172 8696 20 30 40 50 60 485 S 7623 55 463 927 1390 1853 2317 2780 3243 3706 4170 2981605 970 1454 1939 2424 2909 3394 3878 6 2940403 54 463 927 1390 1853 2317 2780 3243 3706 4170 4514 7 3183 53 463 927 1390 1853 2317 2780 3243 3706 4170 7423 8 5963 52 463 927 1390 1853 2317 2780 3243 3706 4170 2990332 9 lO 8743 51 50 463 463 927 927 1390 1853 2317 2779 3243 3706 4170 3241 70 80 2951522 1390 1853 2317 2780 3243 3706 4170 6149 II 4302 49 463 926 1389 1852 2316 2779 3242 3705 4168 9058 90 4363 12 7081 48 463 926 1389 1852 2316 2778 3242 3705 4168 3001967 13 9859 47 463 926 1389 1852 2316 2779 3242 3705 4168 4876 H 2962638 46 45 463 926 1389 1852 2315 2778 3241 3704 3704 4167 7785 IS 5416 463 926 1389 1852 2315 2778 3241 4167 3010694 i6 8194 44 463 926 1389 1852 2315 2777 3241 3704 4167 . 3603 17 2970971 43 463 926 1389 1852 2315 2778 3241 3704 4167 6512 i8 3749 42 463 926 1388 1851 2314 2777 3240 3702 4165 9421 19 6526 41 463 926 1388 1851 2314 2777 3240 3702 4165 3022330 20 9303 40 463 926 1.388 185 1 2314 2776 3240 3702 4165 5238 21 2982079 39 463 926 1388 1851 2314 2777 3240 3702 4165 8147 22 4856 38 463 925 1388 1850 2313 2776 3238 3701 4163 3031056 27, 7632 37 463 925 1388 1850 2313 2776 3238 3701 4163 3965 24 2990408 36 463 925 1388 1850 2313 2776 3238 3701 4163 6874 2"; 3184 35 463 925 1388 1850 2313 2775 3238 3700 41*53 9783 26 5959 34 463 925 1.388 1850 2313 2775 3238 3700 4163 3042692 27 8734 33 463 925 1388 1850 2313 2775 3238 3700 4163 5601 28 3001509 32 463 925 1.388 1850 2313 2775 3238 3700 4163 8510 29 30 4284 31 462 925 1387 1849 2312 2774 3236 3698 4161 3051419 7058 30 462 925 1387 1849 2312 2774 3236 3698 4161 4327 31 9832 29 462 925 1.387 1849 2312 2774 3236 3698 4161 7236 32 3012606 28 462 925 1387 1849 2312 2774 3236 3698 4161 3060145 .3.3 5380 27 462 924 1386 1848 2311 2773 3235 3697 4159 3054 34 3S 8153 26 462 924 1386 1848 2311 2311 2773 3235 3697 4159 5963 3020926 25 462 924 1386 1848 2773 3235 3697 4159 8872 36 3699 24 462 924 1386 1848 2311 2772 3235 3697 4159 307 1 78 1 37 6471 23 462 924 1386 1848 23 1 1 2773 3235 3697 4159 4690 38 9244 22 462 924 1386 1848 2310 2772 3234 3696 4158 7599 39 40 3032016 4788 21 20 462 924 1386 1848 2310 2772 3234 3696 4158 3080408 462 924 1386 1848 2310 2771 3234 3696 4158 3415 41 7559 19 462 924 1386 1848 2310 2772 3234 3696 4158 6324 42 3040331 18 462 924 1385 1847 2309 2771 3233 3694 4156 9233 43 3102 17 462 924 1,385 1847 2309 2770 3233 3694 4156 3092142 4r 5872 16 462 924 1385 1847 2309 2771 3233 3694 4156 5051 8643 15 462 923 1385 1846 2308 2770 3231 3693 4154 7960 46 3051413 14 462 923 1.385 1846 2308 2770 3231 3693 4154 3100869 47 4183 13 462 923 1385 1846 2308 2770 3231 3693 4154 3778 48 6953 12 462 923 1.385 1846 2308 2770 3231 3693 4154 6687 49 9723 II 462 923 1385 1846 2308 2769 3231 3692 4154 9596 50 3062492 10 462 923 1,385 1846 2308 2769 3231 3692 4154 31 12504 51 5261 9 462 923 1385 1846 2308 2769 3231 3692 4154 5413 52 8030 8 461 923 1384 1845 2307 2768 3229 3690 4152 8322 53 3070798 7 461 923 1384 1845 2307 2768 3229 3690 4152 3121231 54 55 3566 6 461 923 1384 1384 1845 2307 2768 3229 3690 4152 4140 6334 5 461 923 1845 2307 2768 3229 3690 4152 7049 56 9102 4 461 922 1383 1844 2306 2767 3228 3689 4150 9958 57 3081869 3 461 922 1383 1844 2306 2767 3228 3689 4150 3132867 58 4636 2 461 922 1383 1844 2306 2767 3228 3689 4150 5776 59 7403 I 461 922 1,383 1844 2306 2767 3228 3689 4150 8685 60 3090170 461 922 1383 1844 2305 2766 3227 3688 4149 3141593 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 72 Decrees. 18 Decrees. Difference for Seconds. [19 M. Sine. M. 10" 20" [ 30" 40" so" 60" 70" 80" 90" Arc. o I 3090170 2936 60 59 461 461 922 922 1383 1383 1844 1844 2305 2305 2766 2766 3227 3227 3688 3688 4149 4149 3141593 4502 Arc. 2 3 5702 8468 5« 57 461 461 922 922 1383 1383 1844 1844 2305 2305 2766 2766 3227 3227 3688 3688 4149 4149 741 1 3150320 i^in. 485 4 5 3101234 56 461 922 1382 1843 2304 2765 3226 3687 4148 3229 10 20 30 40 50 60 3999 55 461 922 1382 1843 2304 2765 3226 3686 4147 6138 970 1454 1939 2424 2909 3394 3878 6 6764 54 461 922 1382 1843 2304 2765 3226 3686 4147 9047 7 9529 53 461 922 1382 1843 2304 2765 3226 3686 4147 3161956 8 31 12294 52 461 921 1382 1842 2303 2764 3224 3685 4145 4865 9 lO 5058 51 461 921 1382 1842 2303 2764 3224 3685 4145 7774 70 80 7822 50 461 921 1382 1842 2303 2764 3224 3685 4145 3170682 II 3120586 49 461 921 1382 1842 2303 2763 3224 3684 4145 3591 90 4363 12 3349 48 461 921 1382 1842 2303 2763 3224 3684 4145 6500 13 6112 47 461 921 1382 1842 2303 2763 3224 3684 4145 9409 14 8875 46 461 921 1382 1842 2303 2763 3224 3684 4145 3182318 IS 3131638 45 461 921 1382 1842 2303 2762 3224 3684 4145 5227 lb 4400 44 461 921 1382 1842 2303 2763 3224 3684 4145 8136 17 7163 43 461 921 1381 1 841 2302 2762 3222 3682 4143 3191045 i8 9925 42 461 921 1381 1 841 2302 2761 3222 3682 4143 3954 19 20 3142686 41 460 920 1380 1840 2302 2762 3222 3682 4143 6863 5448 40 460 920 1380 1840 2301 2761 3221 3681 4141 9771 21 8209 39 460 920 1380 1840 2301 2760 3221 3681 4141 3202680 22 3150969 38 460 920 1380 1840 2301 2761 3221 3681 4141 5589 23 3730 37 460 920 1380 1840 2300 2760 3220 3680 4140 8498 24 25 6490 36 460 920 1380 1840 2300 2760 3220 3680 4140 32 II 407 9250 35 460 920 1380 1840 2300 2760 3220 3680 4140 4316 26 3162010 34 460 920 1380 1840 2300 2760 3220 3680 4140 7225 27 4770 33 460 920 1380 1840 2300 2759 3219 3679 4139 3220134 28 7529 32 460 920 1380 1840 2299 2759 3219 3679 4139 3043 29 3170288 31 460 920 1379 1839 2299 2759 3219 3679 4139 5952 30 3047 30 460 920 1379 1839 2299 2758 3217 3677 4136 8860 31 5805 29 460 919 1379 1838 2298 2758 3217 3677 4136 3231769 32 8563 28 460 919 1379 1838 2298 2758 3217 3677 4136 4678 33 3181321 27 460 919 1379 1838 2298 2758 3217 3677 4136 7587 34 35 4079 26 460 919 1379 1838 2298 2757 3217 3676 4136 3240496 6836 25 460 919 1379 1838 2298 2757 3217 3676 4136 3405 36 9593 24 460 919 1379 1838 2298 2757 3217 3676 4136 6314 37 3192350 23 460 919 1379 1838 2298 2756 3217 3676 4136 9223 3« 5106 22 459 919 1379 1838 2298 2757 3217 3676 4136 3252132 39 7863 21 459 919 1378 1837 2297 2756 3215 3674 4134 5041 40 3200619 20 459 919 1378 1837 2297 2755 321S 3674 4134 7948 41 3374 19 459 919 1378 1837 2297 2756 3215 3674 4134 3260857 42 6130 18 459 918 1377 1836 2296 2755 3214 3673 4132 3766 43 8885 17 459 918 ^77 1836 2296 2755 3214 3673 4132 6675 44 32 1 1 640 16 459 918 n77 1836 2296 2755 3214 3673 4132 9584 45 4395 15 459 918 n77 1836 2295 2754 3213 3672 4131 3272493 4b 7149 14 459 918 ^2,77 1836 2295 2754 3213 3672 4131 5402 47 9903 13 459 918 ^2,77 183b 2295 2754 3213 3672 4131 8311 48 3222657 12 459 918 i?,77 1836 2295 2754 3213 3672 4131 3281220 49 50 5411 II 10 459 918 1376 1835 2294 2753 3212 3670 4129 4129 8164 459 918 1376 1835 2294 2753 3212 3670 4129 7037 51 3230917 9 459 918 1376 1835 2294 2753 3212 3670 4129 9946 52 3670 8 459 917 1376 1834 2293 2752 3210 3669 4127 3292855 S3 6422 7 459 917 1376 1834 2293 2752 3210 3669 4127 5764 54 9174 6 459 917 1376 1834 2293 2752 3210 3669 4127 8673 55 3241926 5 459 917 1376 1834 2293 2752 3210 3669 4127 3301582 56 4678 4 459 917 1376 1834 2293 2751 3210 3668 4127 4491 S7 7429 3 459 917 1376 1834 2293 2751 3210 3668 4127 7400 5« 3250180 2 459 917 1376 1834 2293 2751 3210 3668 4127 3310309 59 2931 I 459 917 1376 1834 2293 2751 3210 3668 4127 3218 60 5682 458 917 1375 1833 2292 2750 3208 3666 4125 6126 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70: 80" 90" Arc. 71 Degrees. 201 19 Degrees. Difference for Seconds. M. Sine. M. 10" 20" 30" 40" 50" 1 6o'' 70" 80" 90" Arc. o I 2 3 4 3255682 8432 3261182 3932 6681 60 59 58 11 458 458 458 458 458 917 917 917 916 916 1375 1375 1375 1374 1374 1833 1833 1833 1832 1832 2292 i 2750 3208 3208 3208 3207 3207 ^666 3666 3666 366s 3665 4x21; 4125 4125 4123. 4123 3316126 9035 3321944 4853 7762 Arc. 2292 2291 2291 2750 2749 2749 Sec. Diff. 10 20 30 40 50 60 70 80 90 485 5 6 7 8 9 9430 3272179 4928 7676 3280424 55 54 53 52 51 458 458 458 458 458 916 916 916 916 916 1374 1374 1374 1374 1374 1832 1832 1832 1832 1832 2291 2291 2290 2290 2290 2749 2749 2748 2748 2748 3207 3207 3206 3206 3206 3665 3665 3664 3664 3664 4123 4123 4122 4122 4122 3330671 -^580 6489 9398 3342307 970 1454 1939 2424 2909 3394 3878 4363 lO II 12 13 H 3172 5919 8666 3291413 4160 50 49 48 47 46 458 458 458 458 458 916 916 916 916 916 1373 1373 1373 1373 1373 1831 1831 1831 1831 1831 2289 2289 2289 2289 2289 2747 2747 2747 2747 2746 3205 3205 3205 3205 3205 3662 3662 3662 3662 3662 4120 4120 4120 4120 4120 5215 8124 3351033 3942 6851 15 i6 17 i8 19 6906 9653 3302398 5144 7889 45 44 43 42 41 458 458 458 458 458 916 915 915 915 915 1373 1373 1373 1373 1373 1831 1830 1830 1830 1830 2289 2288 2288 2288 2288 2747 2745 2746 2745 2745 3205 3203 3203 3203 3203 3662 3661 3661 3661 3661 4120 4118 4118 4118 4118 9760 3362669 5578 8487 3371396 20 21 22 23 24 3310634 3379 6123 8867 3321611 40 39 38 37 36 458 457 457 457 457 915 915 915 915 915 1373 1372 1372 1372 1372 1830 1829 1829 1829 1829 2288 2287 2287 2287 2287 2745 2744 2744 2744 2744 3203 3201 3201 3201 3201 3661 3658 3658 3658 3658 4118 4116 4116 4116 4116 4304 7213 3380122 3031 5940 25 26 27 28 29 4355 7098 9841 3332584 5326 35 34 33 32 31 30 29 28 27 26 457 457 457 457 457 914 914 914 914 914 1371 1371 1371 1371 1371 1828 1828 1828 1828 1828 2286 2286 2286 2286 2286 2743 2743 2743 2742 2743 3200 3200 3200 3200 3200 3657 3657 3657 3657 3657 41 14 4114 4114 41 14 4114 8849 3391758 4667 7576 3400485 30 31 32 33 34 8069 3340810 3552 6293 9034 457 457 457 457 457 914 914 914 914 914 1371 1371 1370 1370 1370 1828 1828 1827 1827 1827 2285 2285 2284 2284 2284 2741 2742 2741 2741 2741 3199 3199 3198 3198 3198 3656 3656 3654 3654 3654 4113 4113 4111 4111 4111 3392 6301 9210 3412119 5028 7937 3420846 3755 6664 9573 35 36 37 38 39 3351775 4516 7256 9996 3362735 25 24 23 22 21 457 457 457 457 457 914 913 913 913 913 1370 1370 1370 1370 1370 1827 1826 1826 1826 1826 2284 2283 2283 2283 2283 2741 2740 2740 2739 2740 3198 3196 3196 3196 3196 3654 3653 3653 3653 3653 41 1 1 4109 4109 4109 4109 40 41 42 43 44 5475 8214 3370953 3691 6429 20 19 18 17 16 457 456 456 456 913 913 913 913 913 1370 1370 1369 1369 1369 1826 1826 1825 1825 1825 2283 2283 2282 2282 2282 2739 2739 2738 2738 2738 3196 3196 3194 3194 3194 3652 3652 3650 3650 3650 4109 4109 4107 4107 4107 3432481 5390 8299 3441208 4117 45 46 47 48 49 9167 3381905 4642 7379 3390116 15 14 13 12 II 456 456 456 456 456 913 912 912 912 912 1369 1368 1368 1368 1368 1825 1824 1824 1824 1824 2282 2281 2281 2281 2281 2738 2737 2737 2737 2736 3194 3193 3193 3193 3193 3650 3649 3649 3649 3649 4107 4105 4105 4105 4105 7026 9935 3452844 5753 8662 50 51 52 53 54 2852 5589 8325 3401060 3796 10 9 8 7 6 456 456 456 456 456 912 912 912 912 912 1368 1368 1368 1368 1367 1824 1824 1824 1824 1823 2281 2280 2280 2280 2279 2737 2736 2735 2736 2735 3193 3192 3192 3192 3191 3649 3648 3648 3648 3646 4105 4104 4104 4104 4102 3461570 4479 7388 3470297 3206 55 56 57 58 59 60 6531 9265 3412000 4734 7468 3420201 5 4 3 2 I 456 456 456 456 456 456 912 912 911 911 911 911 1367 1367 1367 1367 1367 1367 1823 1823 1822 1822 1822 1822 2279 2279 2278 2278 2278 2278 2734 2735 2734 2734 2733 2734 3191 3191 3189 3189 3189 3189 3646 3646 3645 3645 3645 3645 4100 4100 4100 4100 4100 4100 6115 9024 3481933 4842 7751 3490659 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 70 Degrees. 2C Degrees. Difference for Seconds • L2 M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o 3420201 60 456 911 1367 1822 2278 2734 3189 3645 4100 3490659 Arc. I 2935 59 456 911 1367 1822 2278 2733 3189 3644 4100 3568 2 5668 58 456 91X 1367 1822 2278 2732 3189 3644 4100 6477 C^P 1 T'*;^: 3 4 8400 343 1 133 1? 456 455 911 911 1367 1366 1822 1821 2278 2277 2733 2732 3189 3187 3644 3642 4100 4098 9386 3502295 10 20 485 Q70 1 3865 55 455 9U 1366 1821 2277 2732 3187 3642 4098 5204 6 6597 54 455 911 1366 1821 2277 2732 3187 3642 '4098 8113 30 1454 1939 2424 7 9329 53 455 910 1365 1820 2276 2731 3186 3641 4096 3511022 40 8 3442060 52 455 910 1365 1820 2276 2731 3186 3641 4096 3931 50 9 4791 51 455 910 1365 1820 2276 2730 3186 3641 4096 6840 60 70 2909 lO 7521 50 455 910 1365 1820 2276 2731 3186 3641 4096 9748 3394 II 3450252 49 455 910 1365 1820 2275 2730 3185 3641 4096 3522657 80 3878 12 2982 48 455 910 1365 1820 2275 2730 3185 3641 4096 5566 90 4363 n 5712 47 455 910 1365 1820 2275 2729 3185 3641 4096 8475 H 8441 46 455 910 1365 1820 2275 2730 3185 3641 4096 3531384 15 3461171 45 455 910 1364 1819 2274 2729 3184 3638 4093 4293 i6 3900 44 455 910 1364 1819 2274 2728 3184 3638 4093 7202 17 6628 43 455 910 1364 1819 2274 2729 3184 3638 4093 35401 1 1 i8 9357 42 455 910 1364 1819 2273 2728 3182 3637 4091 3020 19 3472085 41 455 909 1364 1819 2273 2727 3182 3637 4091 5929 20 4812 40 455 909 1364 1819 2273 2728 3182 3637 4091 8837 21 7540 39 455 909 1364 1818 2273 2727 3182 3636 4091 3551746 22 3480267 38 455 909 1364 1818 2273 2727 3182 3636 4091 4655 23 2994 37 455 909 1364 1818 2273 2726 3182 3636 4091 7564 24 5720 36 455 909 1364 1818 2273 2727 3182 3636 4091 3560473 2? 8447 35 454 909 1363 1817 2272 2726 3180 3634 4089 3382 26 3491 173 34 454 909 1363 1817 2272 2725 3180 3634 4089 6291 27 3898 33 454 909 1363 1817 2272 2726 3180 3634 4089 9200 28 6624 32 454 908 1362 1816 2272 2725 3179 3633 4087 3572109 29 9349 31 454 908 1362 1816 2272 2725 3179 3633 4087 5018 30 3502074 30 454 908 1362 1816 2272 2724 3179 3633 4087 7926 31 4798 29 454 908 1362 1816 2272 2725 3179 3633 4087 3580835 32 7523 28 454 908 1362 1816 2270 2723 3178 3632 4086 3744 33 3510246 27 454 908 1362 1816 2270 2724 3178 3632 4086 6653 34 2970 26 454 908 1361 1815 2269 2723 3177 3630 4084 9562 3"; 5693 25 454 908 1361 1815 2269 2723 3177 3630 4084 3592471 36 8416 24 454 908 1361 1815 2269 2723 3177 3630 4084 5380 37 3521 139 23 454 908 1361 1815 2269 2723 3177 3630 4084 8289 38 3862 22 454 907 1361 1814 2268 2722 3175 3629 4082 360 II 98 39 6584 21 454 907 1361 1814 2268 2722 3175 3629 4082 4107 7015 40 9306 20 454 907 1361 1814 2268 2721 3175 3628 4082 41 3532027 19 454 907 1361 1814 2268 2721 3175 3628 4082 9924 42 4748 18 454 907 1361 1814 2268 2721 3175 3628 4082 3612833 43 7469 17 454 907 1361 1814 2268 2721 3175 3628 4082 5742 44 3540190 16 453 907 1360 1813 2267 2720 3173 3626 4080 8651 45 2910 15 453 907 1360 1813 2267 2720 3173 3626 4080 3621560 46 5630 14 453 907 1360 1813 2267 2720 3173 3626 4080 4469 47 8350 13 453 907 1360 1813 2267 2720 3173 3626 4080 7378 48 3551070 12 453 906 1359 1812 2266 2719 3172 3625 4078 3630287 49 3789 II 10 453 453 906 1359 1812 2266 2719 3172 3625 4078 3196 50 6508 906 1359 1812 2265 2718 3171 3624 4077 6104 SI 9226 9 453 906 1359 1812 2265 2718 3171 3624 4077 9013 52 3561944 8 453 906 1359 1812 2265 2718 3171 3624 4077 3641922 53 4662 7 453 906 1359 1812 2265 2718 3171 3624 4077 4831 54 7380 6 453 905 1358 1811 2264 2717 3170 3622 4075 7740 55 3570097 5 453 905 1358 1811 2264 2717 3170 3622 4075 3650649 56 2814 4 453 905 1358 1811 2264 2717 3170 3622 4075 3558 57 5531 3 453 905 1358 1811 2264 2717 3170 3622 4075 6467 5« 8248 2 453 905 1358 1810 2263 2716 3168 3621 4073 9376 59 3580964 I 453 905 1358 1810 2263 2715 3168 3621 4073 3662285 bo 3679 453 905 1358 1810 2263 2716 3168 3621 4073 5193 M. Cosine. M. 10" 20" 30" 40" so" 60" 70" 80" 90" Arc. 69 Degrees. 22] 21 Degrees • Difference for Seconds. M. o Sine. M. 10" 20" 30" 40" SO" 60" 70" 80" 90" Arc. 3583679 639s 60 453 905 1358 1358 1810 1810 2263 2263 2716 3168 3168 3621 3620 4073 3665 191 Arc. I S9 453 905 2715 4073 8100 ' "• 2 3 91 10 3591825 58 57 453 453 905 905 1358 1358 1810 1810 2263 2263 2715 2715 3168 3168 3620 3620 4073 4073 3671009 3918 Sec. Diff. 4 4540 56 452 905 1357 1809 2262 2714 3166 3618 4071 6827 10 20 48s ■; 7254 55 452 905 1357 1809 2262 2714 3166 3618 4071 9736 970 6 9968 54 452 905 1357 1809 2262 2714 3166 3618 4071 3682645 30 H54 7 3602682 53 452 904 1356 1808 2261 2713 3165 3617 4069 5554 40 50 60 70 80 1939 8 5395 52 452 904 1356 1808 2261 2713 3165 3617 4069 8463 2424 9 8108 51 452 904 1356 1808 2261 2713 3165 3617 4069 3691372 2909 3394 3878 4363 lO 36 I 082 I 50 452 904 1356 1808 2261 2713 3165 3617 4069 4280 II 3534 49 452 904 1356 1808 2260 2712 3164 3616 4068 7189 90 12 6246 48 452 904 1356 1808 2260 2712 3164 3616 4068 3700098 1,3 8958 47 452 904 1355 1807 2259 2711 3163 3614 ,4066 3007 H 3621669 46 452 904 1355 1807 2259 2711 3163 3614 3614 4066 5916 I? 4380 45 452 904 1355 1807 2259 271 1 3163 4066 8825 i6 7091 44 452 904 1355 1807 2259 2711 3163 3614 4066 3711734 17 9802 43 452 903 1355 1806 2258 2710 3161 3613 4064 4643 i8 3632512 42 452 903 1355 1806 2258 2710 3161 3613 4064 7552 19 5222 41 452 903 1355 1806 2258 2710 3161 3613 4064 3720461 20 7932 40 452 903 1355 1806 2258 2709 3161 3613 4064 3369 21 3640641 39 452 903 1355 1806 2258 2710 3161 3613 4064 6278 22 3351 38 452 903 1355 1806 2258 2708 3161 3612 4064 9187 23 6059 37 452 903 1355 1806 2258 2709 3161 3612 4064 3732096 24 8768 36 452 903 1355 1805 2257 2257 2708 3159 3610 4062 5005 2"; 3651476 35 451 903 1354 1805 2708 3159 3610 4062 7914 26 4184 34 451 903 1354 1805 2257 2707 3159 3610 4062 3740823 27 6891 33 451 903 1354 1805 2257 2708 3159 3610 4062 3732 28 9599 32 451 902 1353 1804 2256 2707 3158 3609 4060 6641 29 3662306 31 451 902 1353 1804 2256 2706 3158 3609 4060 9550 .30 5012 30 451 902 1353 1804 2256 2707 3158 3609 4060 3752458 31 7719 29 451 902 1353 1804 2255 2706 3157 3608 4059 5367 32 3670425 28 451 902 1353 1804 2255 2705 3157 3608 4059 8276 33 3130 27 451 902 1353 1804 2255 2706 3157 3608 4059 3761 185 34 5836 26 451 902 1352 1803 2254 2705 3156 3607 4057 4094 .3? 8541 25 451 902 1352 1803 2254 2705 3156 3606 4057 7003 36 3681246 24 451 901 1352 1802 2253 2704 3154 3605 4055 9912 .37 3950 23 451 901 1352 1802 2253 2704 3154 3605 4055 3772821 3« 6654 22 451 901 1352 1802 2253 2704 3154 3605 4055 5730 39 9358 21 20 451 901 1352 1802 2253 2253 2703 3154 3605 4055 4055 8639 40 3692061 451 901 1352 1802 2704 3154 3605 3781547 41 4765 19 451 901 s»i352 1802 2253 2703 3154 3604 4055 4456 . 42 7468 18 450 901 1351 1801 2252 2702 3152 3602 4053 7365 43 3700170 17 450 901 1351 1 801 2252 2702 3152 3602 4053 3790274 44 2872 16 450 901 1351 i8or 2252 2702 2702 3152 3152 3602 4053 3183 . 45 5574 15 450 901 1351 1801 2252 3602 4053 6092 46 8276 14 450 900 1350 1800 2251 2701 3151 3601 4051 9001 ' 47 3710977 13 450 900 1350 1800 2251 2701 3151 3601 4051 3801910 48 3678 12 450 900 1350 1800 2251 2701 3151 3601 4051 4819 49 6379 II 450 900 1350 1800 2251 2700 3150 3601 4051 7728 SO 9079 10 450 900 1350 1800 2251 2701 3150 3601 4051 3810636 51 3721780 9 450 900 1350 1800. 2250 2699 3150 3600 4050 3545 52 4479 8 450 900 1350 1800 2250 2700 3150 3600 4050 6454 53 7179 7 450 900 1349 1799 2249 2699 3149 3599 4048 9363 54 9878 6 450 900 1349 1799 2249 2699 3149 3599 4048 3822272 - 55 3732577 5 450 899 1349 1798 2248 2698 3147 3597 4046 5181 56 5275 4 450 899 1349 1798 2248 2698 3147 3597 4046 8090 57 7973 3 450 899 1349 1798 2248 2698 3147 3597 4046 3830999 5« 3740671 2 450 899 1349 1798 2248 2698 3147 3597 4046 3908 59 3369 I 450 899 1349 1798 2248 2697 3147 3596 4045 6817 60 6066 450 899 1349 1798 2248 2697 3147 3596 4045 9724 , M. Cosine. M. 10" 20" 30" 40". 50" 60" 70" 80" 90" Arc. 68 Degrees. 22' Degrees. DiffereiK :e for Seconds. [2 M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 3839724 3842633 o I •^746066 8763 60 59 450 450 899 899 1349 1349 1798 1798 2248 2248 2697 2696 3147 3147 3596 3596 4045 4045 Arc. 2 3 3751459 4156 58 57 450 449 899 899 1349 1348 1798 1797 2248 2247 2697 2696 3147 3145 3596 3594 4045 4044 5542 8451 um. 48s 970 1454 1939 2424 2909 3394 3878 4 5 6852 56 449 899 1348 1797 2247 2695 3145 3594 4044 3851360 10 20 30 40 50 60 9547 55 449 899 1348 1797 2247 2696 3145 3594 4044 4269 6 3762243 54 449 898 1347 1796 2246 2695 3144 3593 4042 7178 7 4938 53 449 898 1347 1796 2246 2694 3144 3593 4042 3860087 8 7632 52 449 898 1347 1796 1 2246 2695 3144 3593 4042 2996 9 3770327 51 449 898 1347 1796 2245 2694 3143 3592 4041 5905 70 80 lO 3021 50 449 898 1347 1796 2245 2693 3143 3592 4041 8813 II 5714 49 449 898 1347 1796 2245 2694 3143 3592 4041 3871722 90 4363 12 8408 48 449 898 1346 1795 2244 2693 3142 3590 4039 4631 13 3781 lOI 47 449 898 1346 1795 2244 2693 3142 3590 4039 7540 14 3794 46 449 897 1346 1794 2243 2692 3140 3589 4037 3880449 11 6486 45 449 897 1346 1794 2243 2692 3140 3589 4037 3358 i6 9178 44 449 897 1346 1794 2243 2692 3140 3589 4037 6267 17 3791870 43 449 897 1346 1794 2243 2692 3140 3589 4037 9176 i8 4562 42 449 897 1346 1794 2243 2691 3140 3588 4036 3892085 19 7253 41 449 897 1346 1794 2243 2691 3140 3588 4036 4994 20 9944 40 448 897 1345 1793 2242 2690 3138 3586 4035 7902 21 3802634 39 448 897 1345 1793 2242 2690 3138 3586 4035 39008 1 1 22 5324 38 448 897 1345 1793 2242 2690 3138 3586 4035 3720 23 8014 37 448 897 1345 1793 2242 2690 3138 3586 4035 6629 24 3810704 36 448 896 1344 1792 2241 2689 3137 3585 4033 9538 2S 3393 35 448 896 1344 1792 2241 2689 3137 3585 4033 3912447 26 6082 34 448 896 1344 1792 2241 2688 3137 3585 4033 5356 27 8770 33 448 896 1344 1792 2241 2689 3137 3585 4033 8265 28 3821459 32 448 896 1344 1792 2240 2688 3136 3584 4032 3921 174 29 4147 31 448 896 1344 1792 2240 2687 3136 3584 4032 4083 30 6834 30 448 896 1344 1792 2240 2688 3136 3584 4032 6991 31 9522 29 448 896 1343 1 791 2239 2687 3135 3582 4030 9900 32 3832209 28 448 896 1343 1791 2239 2686 3135 3582 4030 3932809 33 4895 27 448 896 1343 1791 2239 2687 3135 3582 4030 5718 34 3S 7582 26 448 895 1343 1790 2238 2686 3133 3581 4028 8627 3840268 25 448 895 1343 1790 2238 2685 3133 3581 4028 3941536 36 2953 24 448 895 1343 1790 2238 2686 3133 3581 4028 4445 37 5639 23 448 895 1343 1790 2238 2685 3133 3580 4028 7354 38 8324 22 448 895 1343 1790 2238 2684 3133 3580 4028 3950263 39 40 3851008 21 448 895 1343 1790 2238 2685 3133 3580 4028 3172 3693 20 447 895 1342 1789 2237 2684 3131 3578 4026 6079 41 6377 19 447 895 1342 1789 2237 2683 3131 3578 4026 8988 42 9060 18 447 895 1342 1789 2237 2684 3131 3578 4026 3961897 43 3861744 17 447 894 1 341 1788 2236 2683 3130 3577 4024 4806 44 4427 16 447 894 1341 1788 2236 2683 3130 3577 4024 7715 45 7110 15 447 894 1341 1788 2235 2682 3129 3576 4023 3970624 46 9792 14 447 894 1341 1788 2235 2682 3129 3576 4023 3533 47 3872474 13 447 894 1341 1788 2235 2682 3129 3576 4023 6442 48 5156 12 447 894 1340 1787 2234 2681 3128 3574 4021 9351 49 50 7837 3880518 II 10 447 894 1340 1787 1 2234 2681 3128 3574 4021 3982260 447 894 1340 1787 2234 2681 3128 3574 4021 5168 51 3199 9 447 894 1340 1787 2234 2681 3128 3574 4021 8077 52 5880 8 447 893 1340 1786 2233 2680 3126 3573 4019 3990986 53 8560 7 447 893 1340 1786 2233 2680 3126 3573 4019 3895 54 3891240 6 447 893 1340 1786 2233 2679 3126 3572 4019 6804 55 3919 5 447 893 1340 1786 2233 2679 3126 3572 4019 9713 56 6598 4 447 893 1340 1786 2233 2679 3126 3572 4019 4002622 57 9277 3 446 893 1339 1785 2232 2678 3124 3570 4017 5531 58 3901955 2 446 893 1339 1785 2232 2678 3124 3570 4017 8440 59 4633 I 446 893 1339 1785 2232 2678 3124 3570 4017 1349 60 7311 446 893 1339 1785 2232 2678 3124 3570 4017 4014257 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 1 90" Arc. 67 Degrees. 24J 23 Degrees. Difference for Seconds. M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o 39073 1 1 60 446 893 1339 1785 2232 2678 3124 3570 4017 4014257 Arc. I 2 9989 3912666 59 58 446 446 892 892 1338 1338 1784 1784 2231 2231 2677 2677 3123 3123 3569 3569 4015 4015 7166 4020075 Sec. Uiff 3 5343 57 446 892 1338 1784 2230 2676 3122 3568 4014 2984 4 8019 56 446 892 1338 1784 2230 2676 3122 3568 4014 5893 8802 10 20 48s 070 5 392069s 55 446 892 1338 1784 2230 2676 3122 3568 4014 6 3371 54 446 892 1338 1784 2230 2676 3122 3568 4014 4031711 ^0 IJ.sA 7 6047 53 446 892 1337 1783 2229 2675 3121 3566 4012 4620 40 1939 24.24. 8 8722 52 446 892 1337 1783 2229 2675 3121 3566 4012 7529 50 60 70 9 3931397 51 446 891 1337 1782 2228 2674 3119 3565 4010 4040438 2QOQ lO 4071 50 446 891 1337 1782 2228 2674 3119 3565 4010 3346 3394 II 6745 49 446 891 1337 1782 2228 2674 3119 3565 4010 6255 80 3878 12 9419 48 446 891 1337 1782 2228 2674 3119 3565 4010 9164 90 4363 13 3942093 47 446 891 1337 1782 2228 2673 3119 3564 4010 4052073 14 4766 46 445 891 1336 1782 2228 2673 3119 3564 4010 4982 15 7439 45 445 891 1336 1781 2227 2672 3117 3562 4008 7891 i6 39501 1 1 44 445 891 1336 1781 2227 2672 3117 3562 4008 4060800 17 2783 43 445 891 1336 1781 2227 2672 3117 3562 4008 3709 i8 5455 42 445 891 1336 1781 2227 2672 3117 3562 4008 6618 19 8127 41 445 890 1335 1780 2226 2671 3116 3561 4006 9527 20 3960798 40 445 890 1335 1780 2226 2670 3116 3561 4006 4072435 21 3468 39 445 890 1335 1780 2226 2671 3116 3561 4006 5344 22 6139 3« 445 890 1335 1780 2225 2670 3115 3560 4005 8253 23 8809 37 445 890 1335 1780 2225 2670 3115 3560 4005 4081162 24 3971479 36 445 890 1335 1780 2225 2669 3115 3560 4005 4071 2? 4148 35 445 890 1335 1780 2225 2670 3115 3560 4005 6980 26 6818 34 445 890 1335 1780 2225 2668 3114 3558 4003 9889 27 9486 33 445 890 1335 1780 2225 2669 31H 3558 4003 4092798 28 3982155 32 445 889 1334 1778 2223 2668 3112 3557 4001 5707 29 4823 31 445 889 1334 1778 2223 2668 3112 3557 4001 8616 30 7491 30 445 889 1334 1778 2223 2667 3112 3556 4001 4101523 31 3990158 29 445 889 1334 1778 2223 2667 3112 3556 4001 4432 32 2825 28 445 889 1334 1778 2223 2667 3112 3556 4001 7341 33 5492 27 445 889 1334 1778 2223 2666 3112 3556 4001 41 10250 34 8158 26 445 889 1334 1778 2223 2667 3112 3556 4001 3159 \ 35 4000825 25 444 889 1333 1777 2222 2665 3110 3554 3999 6068 36 3490 24 444 889 1333 1777 2222 2666 3110 3554 3999 8977 % 37 6156 23 444 888 1332 1776 2221 2665 3110 3554 3999 41 2 1 886 3« 8821 22 444 888 1332 1776 2221 2665 3110 3554 3999 4795 40 401 1486 21 444 888 1332 1776 2220 2664 3108 3552 3996 7704 4150 20 444 888 1332 1776 2220 2664 3108 3552 3996 4130612 41 6814 19 444 888 1332 1776 2220 2664 3108 3552 3996 3521 42 9478 18 444 888 1331 1775 2219 2663 3107 3550 3994 6430 43 4022 141 17 444 888 1331 1775 2219 2663 3107 3550 3994 9339 44 4804 16 444 888 ^331 1775 2219 2663 3107 3105 3550 3994 4142248 45 7467 15 444 887 1331 1774 2218 2662 3549 3992 5157 46 4030129 14 444 887 1331 1774 2218 2662 3105 3549 3992 8066 47 2791 13 444 887 1331 1774 2218 2662 3105 3549 3992 4150975 48 5453 12 444 887 1331 1774 2218 2661 3105 3548 3992 3884 49 8114 II 444 887 1331 1774 2218 2661 3105 3548 3992 6793 9701 50 4040775 10 444 887 1331 1774 2218 2661 3105 3548 3992 51 3436 9 443 887 1330 1773 2217 2660 3103 3546 3990 4162610 52 6096 8 443 887 1330 1773 2217 2660 3103 3546 3990 5519 53 8756 7 443 887 1330 1773 2217 2660 3103 3546 3990 8428 54 4051416 6 443 886 1329 1772 2216 2659 3102 3545 3988 4171337 55 4075 5 443 886 1329 1772 2216 2659 3102 3545 3988 4246 50 6734 4 443 886 1329 1772 2216 2659 3102 3545 3988 7155 57 9393 3 443 886 1329 1772 2215 2658 3101 3544 3987 4180064 58 406205 1 2 443 886 1329 1772 2215 2658 3101 3544 3987 2973 59 4709 I 443 886 1329 1772 2215 2657 3101 3544 3987 5882 60 7366 443 886 1329 1772 2215 2658 3101 3544 3987 8790 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 66 Degrees. 24 Degrees. Difference for Seconc Is. [£. M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o 4067366 4070024 60 59 443 443 886 886 1329 1328 1772 1771 2215 2214 2658 2657 3101 3544 3987 39S5 4188790 4191699 Arc. 3542 ' > 2 2681 58 443 885 1328 1770 2213 2656 3098 3541 3983 4608 Sec. Diff. 3 5337 SI 443 885 1328 1770 2213 2656 3098 3541 3983 7517 4 7993 S^ 443 885 1328 1770 2213 2656 3098 3541 39S3 4200426 10 20 485 S 4080649 55 443 885 1328 1770 2213 2656 3098 3541 3983 3335 970 6 3305 54 443 885 1328 1770 2213 2655 3098 3540 3983 6244 3^ H54 7 5960 53 443 885 1328 1770 2213 2655 3098 3540 3983 9153 40 1939 8 8615 52 442 885 1327 1769 2212 2654 3096 3538 3981 4212062 5^ 60 70 80 2424 9 4091269 51 442 885 1327 1769 2212 2654 3096 3538 3981 4971 2909 lO 3923 50 442 885 1327 1769 2212 2654 3096 3538 3981 7879 3394 3878 II 6577 49 442 884 1326 1768 2211 2653 3095 3537 3979 4220788 QO 12 9230 48 442 884 1326 1768 2211 2653 3095 3537 3979 3697 y" Tj-^j 1.3 4101883 47 442 884 1326 1768 221 1 2653 3095 3537 3979 6606 14 IS 4536 46 442 884 1326 1768 22 1 1 2653 3095 3537 3979 9515 7189 45 442 884 1326 1768 2210 2652 3094 3536 3978 4232424 i6 9841 44 442 884 1326 1768 2210 2651 3094 3536 3978 5333 17 41 12492 43 442 884 1326 1768 2210 2652 3094 3536 3978 8242 i8 5144 42 442 884 1325 1767 2209 2651 3093 3534 3976 4241 15 1 19 7795 41 442 884 1325 1767 22og 2650 3093 3534 3976 4060 20 4120445 40 442 884 1325 1767 2209 2651 3093 3534 3976 6968 21 3096 39 442 883 1325 1766 2208 2649 3091 3533 3974 9877 22 5745 38 442 883 1325 1766 2208 2650 3091 3533 3974 4252786 23 8395 7>1 442 883 1325 1766 2208 2649 3091 3532 3974 5695 24 4131044 36 442 883 1325 1766 2208 2649 3091 3532 3974 8604 2=; 3693 35 442 883 1325 1766 2208 2649 3091 3532 3974 4261 5 13 26 6342 34 441 883 1325 1766 2208 2648 3089 3530 3972 4422 27 8990 ■hZ 441 883 1325 1766 2208 2648 3089 3530 3972 7331 28 4141638 32 441 882 1323 1764 2206 2647 3088 3529 3970 4270240 29 4285 31 441 882 1323 1764 2206 2647 3088 3529 3970 3149 .30 6932 30 441 882 1323 1764 2206 2647 3088 3529 3970 6057 31 9579 29 441 882 1323 1764 2206 2647 3088 3529 3970 8966 32 4152226 28 441 882 1323 1764 2205 2646 3087 3528 3969 4281875 33 4872 27 441 882 1323 1764 2205 2646 3087 3528 3969 4784 34 7517 26 441 882 1323 1764 2205 2646 3087 3528 3969 7693 3"; 4160163 25 441 882 1322 1763 2204 2645 3086 3526 39<-9 4290602 ^6 2808 24 441 882 1322 1763 2204 2645 3086 3526 3969 3511 37 5453 23 441 881 1322 1762 2203 2644 3084 3525 3965 6420 3« 8097 22 441 881 1322 1762 2203 2644 3084 3525 3965 9329 39 4170741 21 441 881 1322 1762 2203 2644 3084 3525 3965 4302238 40 3385 20 441 881 1322 1762 2203 2643 3084 3524 3965 5146 41 6028 19 441 881 1322 1762 2203 2643 3084 3524 3965 8055 42 8671 18 441 881 1322 1762 2203 2642 3084 3524 3965 4310964 43 4181313 17 441 881 1322 1762 2203 2643 3084 3524 3965 3873 44 3956 16 440 881 1321 1761 2202 2641 3082 3522 3963 6782 45 6597 15 440 881 1321 1761 2202 2642 3082 3522 3963 9691 46 9239 14 440 880 1320 1760 2201 2641 3081 3521 3961 4322600 47 4191880 13 440 880 1320 1760 2201 2641 3081 3521 3961 5509 48 4521 12 440 880 1320 1760 2200 2640 3080 3520 3960 8418 49 7161 n 440 880 1320 1760 2200 2640 3080 3520 3960 4331327 50 9801 10 440 880 1320 1760 2200 2640 3080 3520 3960 4235 51 4202441 9 440 880 1319 1759 2199 2639 3079 3518 3958 7144 52 5080 8 440 880 1319 1759 2199 2639 3078 3518 3958 4340053 53 7719 7 440 880 1319 1759 2199 2639 3078 3518 3958 2962 54 4210358 6 440 879 1319 1758 2198 2638 3077 3077 3517 3956 5871 55 2996 5 440 879 1319 1758 2198 2638 3517 3956 8780 56 5634 4 440 879 1319 1758 2198 2638 3077 3517 3956 4351689 57 8272 3 440 879 1319 1758 2198 2637 3077 3516 3956 4598 58 4220909 2 440 879 1319 1758 2198 2637 3077 3516 3956 7507 59 3546 I 440 879 1319 1758 2198 2637 3077 3516 3956 4360416 bo 6183 439 879 1318 1757 2197 2636 3075 3514 3954 3324 M. Co<=ine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 65 Degrees. 26] 25 Degrees. Difference for Seconds. M Sine. M. 10" 20" 30" 40" 50" 60" 1 70" 80" 90" Arc. o I 4226183 8819 60 59 439 439 879 879 1318 1318 1757 1757 2197 2197 2636 2636 3075 3075 3514 3514 3954 3954 4363323 6232 Arc. A ■> 2 3 4231455 4090 58 57 439 439 878 878 1317 1317 1756 1756 2196 2196 2635 2635 3074 3074 3513 3513 3952 3952 9141 4372050 Sec. Diff. 4 56 55 439 439 878 1317 1756 2196 2635 3074 3513 3952 4959 10 20 485 -; 9360 878 1317 1756 2195 2634 3073 3512 3951 7868 970 6 4241994 54 439 878 1317 1756 2195 2634 3073 3512 3951 4380777 30 40 50 60 1 454 7 4628 53 439 878 1317 1756 2195 2634 3073 3512 3951 3686 1939 8 7262 52 439 878 1316 1755 2194 2633 3072 3510 3949 6595 2424 2909 3394 3878 9 9895 51 439 878 1316 1755 2194 2633 3072 3510 3949 9504 7n lO 4252528 50 439 878 1316 1755 2194 2633 3072 3510 3949 4392412 80 II 5161 49 439 877 1316 1754 2193 2632 3070 3509 3947 5321 90 4363 12 7793 48 439 877 1316 1754 2193 2632 3070 3509 3947 8230 1.3 4260425 47 439 877 1316 1754 2193 2631 3070 3508 3947 4401 139 H 3056 46 439 877 1316 1754 2193 2631 3070 3508 3508 3947 4048 I? 5687 45 439 877 1316 1754 2193 2631 3070 3947 6957 : i6 8318 44 439 877 1316 1754 2193 2631 3070 3508 3947 9866 17 4270949 43 438 877 1315 1753 2192 2630 3068 3506 3945 4412775 i8 3579 42 438 877 1315 1753 2192 2629 3068 3506 3945 5684 19 6208 41 438 877 1315 1753 2192 2630 3068 3506 3945 8593 20 8838 40 438 876 1314 1752 2191 2629 3067 3505 3943 4421501 21 4281467 39 438 876 1314 1752 2190 2628 3066 3504 3942 4410 22 4095 38 438 876 1314 1752 2190 2628 3066 3504 3942 7319 23 6723 yj 438 876 1314 1752 2190 2628 3066 3504 3942 4430228 24 9351 36 438 876 1314 1752 2190 2628 3066 3504 3942 i,m 2"; 4291979 35 438 876 1313 175 1 2189 2627 3065 3502 3940 6046 26 4606 34 438 876 1313 1751 2189 2627 3065 3502 3940 8955 27 7233 33 438 875 1313 1750 2188 2626 3063 3501 3938 4441864 28 9859 32 438 875 1313 1750 2188 2626 3063 3501 3938 4773 29 4302485 31 438 875 1313 1750 2188 2626 3063 3501 3938 7682 3° 5111 30 438 875 1313 1750 2188 2625 3063 3500 3938 4450589 31 7736 29 438 875 1313 1750 2188 2625 3063 3500 3938 3498 32 4310361 28 438 875 13 13 1750 2188 2625 3063 3500 3938 6407 33 2986 27 437 87? 1312 1749 2187 2624 3061 3498 3936 9316 34 5610 26 437 875 1312 1749 2187 2187 2624 3061 3498 3936 4462225 3? 8234 25 437 875 1312 J 749 2623 3061 3498 3936 5134 36 4320857 24 437 875 1312 1749 2187 2624 3061 3498 3936 8043 37 3481 23 437 874 1311 1748 2186 2622 3060 3497 3934 4470952 38 6103 22 437 874 1311 1748 2186 2623 3060 3497 3934 3861 39 8726 21 20 437 874 1311 1748 2185 2622 3059 3496 3933 6770 40 4331348 437 874 1311 1748 2185 2622 3059 3496 3933 9678 41 3970 19 437 874 1310 1747 2184 2621 3058 3494 3931 4482587 42 6591 18 437 874 1310 1747 2184 2621 3058 3494 3931 5496 43 9212 17 437 874 1310 1747 2184 2620 3058 3494 3931 8405 44 4341832 16 437 874 1310 1747 2184 2621 2619 3058 3056 3494 3493 3931 4491314 4? 4453 15 437 873 1310 1746 2183 3929 4223 46 7072 H 437 873 1310 1746 21S3 2620 3056 3493 3929 7132 47 9692 13 437 873 1310 1746 2183 2619 3056 3493 3929 4500041 48 435231 1 12 437 873 1310 1746 2183 2619 3056 3493 3929 2950 49 4930 II 436 873 1309 1745 2182 2618 3054 3490 3927 5859 SO 7548 10 436 873 1309 1745 2182 2618 3054 3490 3927 8767 51 4360166 9 436 873 1309 ^745 2182 2618 3054 3490 3927 451 1676 52 2784 8 436 872 1308 1744 2181 2617 3053 3489 3925 4585 53 5401 7 436 872 1308 1744 2181 2617 3053 3489 3925 7494 54 8018 6 436 872 1308 1308 1744 2181 2616 3053 3489 3925 4520403 55 4370634 5 436 872 1744 2181 2617 3053 3489 3925 3312 50 3251 4 436 872 1308 1744 2180 2615 3052 .3488 3924 6221 57 5866 3 436 872 1308 1744 2180 2616 3052 3488 3924 9130 5« 8482 2 436 872 1307 1743 2179 2615 3051 3486 3922 4532039 59 4381097 I 436 872 1307 1743 2179 2614 3051 3486 3922 4948 60 371 1 436 872 1307 1743 2179 2615 3051 ! 3486 80" 3922 7856 Arc M. Cosine, M. 10" 20" 30" 40" 50" 60" j 70" 90" 64 Decrees. 26 Degrees. Difference for Seconds. [2 M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o I 438371 1 6326 60 59 436 436 872 871 1307 1307 1743 1742 2179 2178 2615 2614 3058 3049 3486 3485 3922 3920 4537856 4540765 Arc. 2 3 8940 4391553 58 57 436 436 871 871 1307 1307 1742 1742 2178 2178 2613 2613 3049 3049 3484 3484 3920 3920 3674 6583 oec. um. 485 4 5 4166 56 436 871 1307 1742 2178 2613 3049 3484 3920 9492 20 30 40 50 60 6779 55 436 871 1307 1742 2178 2613 3049 3484 3920 4552401 970 H54 1939 2424 2909 3394 3878 6 9392 54 435 871 1306 1741 2177 2612 3047 3482 3918 5310 7 4402004 53 435 871 1306 1741 2177 261 1 3047 3482 3918 8219 8 4615 52 435 871 1306 1 741 2177 2612 3047 3482 3918 4561 128 9 7227 51 435 870 1305 1740 2176 261 1 3046 3481 3916 4037 70 80 lO 9838 50 435 870 1305 1740 2176 2610 3046 3481 3916 6945 II 4412448 49 435 870 1305 1740 2176 261 1 3046 3481 3916 9854 90 4361 12 5059 48 435 870 1305 1740 2175 2609 3045 3480 3915 4572763 13 7668 47 435 870 1305 1740 2175 2610 3045 3480 3915 5672 14 4420278 46 435 '870 1304 1739 2174 2609 3044 3478 3913 8581 15 2887 45 435 870 1304 1739 2174 2609 3044 3478 3913 4581490 16 5496 44 435 869 1304 1738 2173 2608 3042 3477 3911 4399 17 8104 43 435 869 1304 1738 2173 2608 3042 3477 391 1 7308 i8 4430712 42 435 869 1304 1738 2173 2607 3042 3477 391 1 4590217 19 3319 41 435 869 1304 1738 2173 2608 3042 3477 391 1 3126 20 5927 40 435 869 1304 1738 2173 2607 3042 3476 3911 6034 21 8534 39 434 869 1303 1737 2172 2606 3041 3474 3909 8943 22 444 II 40 38 434 869 1303 1737 2172 2606 3041 3474 3909 4601852 23 3746 37 434 869 1303 1737 2172 2606 3041 3474 3909 4761 24 6352 36 434 868 1302 1736 2171 2605 3039 3473 3907 7670 2S 8957 35 434 868 1302 1736 2171 2605 3039 3473 3907 4610579 26 4451562 34 434 868 1302 1736 2171 2605 3039 3473 3907 3488 27 4167 33 434 868 1302 1736 2170 2604 3038 3472 3906 6397 28 6771 32 434 868 1302 1736 2170 2604 3038 3472 3906 9306 29 9375 31 434 868 1 301 1735 2169 2603 3037 3470 3904 4622215 30 4461978 30 434 868 1 301 1735 2169 2603 3037 3470 3904 5123 31 4581 29 434 868 1 301 1735 2169 2603 3037 3470 3904 8032 32 7184 28 434 867 1301 1734 2168 2602 3035 3469 3902 4630941 33 9786 27 434 867 1301 1734 2168 2602 3035 3469 3902 3850 34 35 4472388 26 434 867 1301 1734 2168 2602 3035 3469 3902 6759 4990 25 434 867 1301 1734 2168 2601 3035 3468 3902 9668 36 7591 24 434 867 1301 1734 2168 2601 3035 3468 3902 4642577 37 4480192 23 433 867 1300 1733 2167 2600 3033 3466 3900 5486 3« 2792 22 433 867 1300 1733 2167 2600 3033 3466 3900 8395 39 40 5392 21 433 867 1300 1733 2167 2600 3033 3466 3900 4651304 7992 20 433 866 1299 1732 2166 2599 3032 3465 3898 421 1 41 4490591 19 433 866 1299 1732 2166 2599 3032 3465 3898 7120 42 3190 18 433 866 1299 1732 2166 2599 3032 3465 3898 4660029 43 5789 17 433 866 1299 1732 2165 2598 3031 3464 3897 2938 44 8387 16 433 866 1299 1732 2165 2597 3031 3464 3897 5847 45 4500984 15 433 866 1299 1732 2165 2598 3031 3464 3897 8756 46 3582 14 433 866 1298 1731 2164 2597 3030 3462 3895 4671665 47 6179 13 433 866 1298 1731 2164 2596 3030 3462 3895 4574 48 8775 12 433 866 1298 1731 2164 2597 3030 3462 3895 7483 49 50 45 II 372 II 433 865 1298 1730 2163 2595 3028 3461 3893 4680392 3967 10 433 865 1298 1730 2163 2596 3028 3461 3893 3300 SI 6563 9 433 865 1298 1730 2163 2595 3028 3460 3893 6209 52 9158 8 433 865 1298 1730 2163 2595 3028 3460 3893 9118 53 4521753 7 432 865 1297 1729 2162 2594 3026 3458 3891 4692027 54 55 4347 6 432 865 1297 1729 2162 2594 3026 3458 3891 4936 6941 5 432 865 1297 1729 2162 2594 3026 3458 3891 . 7845 56 9535 4 432 864 1296 1728 2161 2593 3025 3457 3889 4700754 57 4532128 3 432 864 1296 1728 2161 2593 3025 3457 3889 3663 5« 4721 2 432 864 1296 1728 2160 2592 3024 3456 3888 6572 59 7313 I 432 864 1296 1728 2160 2592 3024 3456 3888 9481 60 9905 432 864 1296 1728 2160 2592 3024 3456 3888 4712389 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 63 Degrees. 28] 27 Degrees. Difference for Second.s. M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o 4539905 60 432 864 1296 1728 2160 2592 3024 3456 3888 4712388 Arc 1 2 4542497 5088 59 58 432 432 864 864 1295 1295 1727 1727 2159 2159 2591 2591 3023 3023 3454 3454 3886 3886 5297 8206 A Sec Diff 3 4 7679 4550269 57 56 55 432 432 863 863 1295 1295 1726 1726 2159 2159 2590 2590 3021 3021 3453 3454 3884 3885 4721115 4024 10 20 485 970 S 2859 432 863 1295 1726 2159 2590 3021 3453 3885 6933 6 5449 54 432 863 1295 1726 2158 2589 3021 3452 3884 9842 30 1454 7 8038 53 432 863 1295 1726 2158 2589 3021 3452 3884 4732751 40 IQ3Q 8 4560627 52 432 863 1295 1726 2158 2589 3021 3452 3884 5660 50 2424 9 3216 51 431 863 1294 1726 2157 2588 3020 3451 3883 8569 60 70 2909 lO 5804 50 431 863 1294 1726 2157 2588 3020 3451 3883 4741477 3394 II 8392 49 431 862 1294 1725 2156 2587 3019 3450 3881 4386 80 3878 12 4570979 48 431 862 1294 1725 2156 2587 3019 3450 3881 7295 90 4363 1.3 3566 47 431 862 1294 1725 2156 2587 3018 3450 3881 4750204 .14 6153 46 431 862 1293 1724 2155 2586 3017 3448 3879 3113 IS 8739 45 431 862 1293 1724 2155 2586 3017 3448 3879 6022 i6 4581325 44 431 862 1293 1724 2155 2585 3017 3448 3879 8931 17 3910 43 431 862 1293 1724 2155 2586 3017 3448 3879 4761840 18 6496 42 431 862 1293 1724 2155 2584 3016 3447 3878 4749 19 9080 41 431 862 1293 1724 2155 2585 3016 3447 3878 7658 20 4591665 40 431 861 1292 1723 2154 2583 3015 3446 3876 4770566 21 4248 39 431 861 1292 1723 2154 2584 3015 3446 3876 3475 22 6832 38 431 861 1292 1722 2153 2583 3014 3444 .3875 6384 23 9415 37 431 861 1292 1722 2x53 2583 3014 3444 387 s 9293 i 24 4601998 36 430 861 1 291 1722 2152 2582 3013 3443 3874 4782202 25 4580 35 430 861 1 291 1722 2152 2582 3013 3443 3874 5111 26 7162 34 430 861 1291 1722 2152 2582 3013 3443 3874 8020 27 9744 33 430 860 1291 1721 2151 2581 301 1 3442 3872 4790929 28 4612325 32 430 860 1291 1721 2151 2581 301 1 3442 3872 3838 29 4906 31 430 860 1290 1720 2150 2580 3010 3440 3870 6747 30 7486 30 430 860 1290 1720 2150 2580 3010 3440 3870 9654 31 4620066 29 430 860 1290 1720 2150 2580 3010 3440 3870 4802563 32 2646 28 430 860 1289 1719 2149 2579 3009 3438 3868 5472 i 33 5225 27 430 860 1289 1719 2149 2579 3009 3438 3868 8381 i 34 7804 26 430 859 1289 1719 2149 2578 3008 3438 3867 48 1 1 290 35 4630382 25 430 859 1289 1719 2149 2578 3008 3438 3867 4199 36 2960 24 430 859 1289 1719 2149 2578 3008 3438 3867 7108 37 5538 23 430 859 1289 1718 2148 2577 3007 3436 3866 4820017 3« 8115 22 430 859 1289 1718 2148 2577 3007 3436 3866 2926 39 4640692 21 430 859 1289 1718 2148 2577 3007 3436 3866 5835 8743 40 3269 20 429 859 1288 1718 2147 2576 3006 3435 3865 41 5845 19 429 859 1288 1718 2147 2575 3006 3435 3865 4831652 42 8420 18 429 859 1288 1718 2147 2576 3006 3435 3865 4561 43 4650996 17 429 858 1287 1716 2146 2575 3004 3433 3862 7470 44 3571 16 429 858 1287 1716 2145 2574 3003 3432 3861 4840379 3288 45 6145 15 429 858 1287 1716 2145 2574 3003 3432 3861 46 8719 14 429 858 1287 1716 2145 2574 3003 3432 3861 6197 47 4661293 13 429 858 1287 1716 2145 2573 3002 3431 3860 9106 48 3866 12 429 858 1287 1716 2145 2573 3002 3431 3860 4852015 » 49 6439 II 429 858 1287 1716 2145 2573 3002 3431 3860 4924 50 9012 10 429 857 1286 1715 2144 2572 3001 3430 3858 7832 51 4671584 9 429 857 1286 1715 2144 2572 3001 3430 3858 4860741 52 4156 8 429 857 1286 1715 2144 2571 3001 3430 3858 3650 S3 6727 7 429 857 1286 1714 2143 2571 3000 3428 3857 6559 54 9298 6 429 857 1286 1714 2143 2571 3000 3428 3857 9468 55 4681869 5 428 857 1285 1714 2142 2570 2999 3427 3856 4872377 50 4439 4 4*28 857 1285 1714 2142 2570 2999 3427 .3856 5286 57 7009 3 428 856 1284 1713 2141 2569 2997 3426 .3854 8195 5« 9578 2 428 856 1284 1713 2141 2569 2997 3426 3854 488 II 04 , 59 4692147 I 428 856 1284 1712 2141 2569 2997 3425 3853 4013 60 4716 428 856 1284 1712 2140 2568 2996 3424 3852 6921 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. J 62 Degrees. 28 Degrees. Difference for Second s. [3: Arc. M. Sine. M. 10" 20" 30" 40" so" 60" 70" 80" 90" Arc. o 4694716 60 428 856 1284 1712 2140 2568 2996 3424 3852 4886922 I 7284 59 428 856 1284 1712 2140 2568 2996 3424 38=;2 9831 / "N 2 9852 58 428 428 856 856 1283 1283 1711 1711 2139 2139 2567 2567 2995 3422 3850 3850 4892740 5649 Sec. Diff. 3 4702419 57 2995 3422 4 4986 56 428 856 1283 1711 2139 2567 2995 3422 3850 8558 10 20 485 U 7553 55 428 855 1283 1710 2138 2566 2993 3421 3848 4901467 970 6 4710119 54 428 855 1283 1710 2138 2566 2993 3421 3848 4376 3^ 1454 7 2685 53 428 855 1283 1710 2138 2565 2993 3420 3848 7285 40 1939 8 5250 52 428 855 1283 1710 2138 2565 2993 3420 3848 4910194 50 60 70 80 2424 9 781S 51 428 855 1283 1710 2138 2137" 2565 2993 2991 3420 3418 3848 3846 3103 601 1 2909 lO 4720380 50 427 855 1282 1709 2564 3394 3878 II 2944 49 427 855 1282 1709 2137 2564 2991 3418 3846 8920 12 5508 48 427 854 1281 1708 2136 2563 2990 3417 3844 4921829 1.3 8071 47 427 854 1281 1708 2136 2563 2990 3417 3844 4738 14 4730634 46 427 427 854 1281 1708 2136 2563 2990 3417 3844 7647 IS 3197 45 854 1281 1708 2135 2562 2989 3416 3843 4930556 i6 5759 44 427 854 1281 1708 2135 2562 2989 3416 3843 3465 17 8321 43 427 854 1280 1707 2134 2561 2988 3414 3841 6374 i8 4740882 42 427 854 1280 1707 2134 2561 2988 3414 3841 9283 19 20 3443 41 427 854 1280 1707 2134 2561 2988 3414 3841 4942192 6004 40 427 853 1280 1706 2133 2560 2986 3413 3839 5100 21 8564 39 427 853 1280 1706 2133 2560 2986 3413 3839 8009 22 475 1 1 24 38- 427 853 1280 1706 2133 2559 2986 3412 3839 4950918 23 3683 37 427 853 1280 1706 2133 2559 2986 3412 3839 3827 24 6242 36 427 853 1280 1706 2133 2559 2986 3412 3839 6736 25 8801 35 426 853 1279 1705 2132 2558 2984 3410 3837 9645 26 4761359 34 426 853 1279 1705 2132 2558 2984 3410 3837 4962554 27 3917 33 426 8<;2 1278 1704 2131 2557 2983 3409 38^5 5463 28 6474 32 426 852 1278 1704 2131 2557 2983 3409 3835 8372 29 9031 31 426 852 1278 1704 2131 2557 2983 3409 3835 497 1 28 1 4189 30 4771588 30 426 8^2 1278 1704 2130 2556 2982 3408 3834 31 4144 29 426 8=52 1278 1704 2130 2556 2982 3408 3834 7098 32 6700 28 426 8c;2 1277 1703 2129 2555 2981 3406 3832 4980007 33 9255 27 426 8^2 1277 1703 2129 2555 2981 3406 3832 2916 34 4781810 26 426 852 1277 1703 2129 2554 2981 Ji"6_ 3406 3832 3832 5825 35 4364 25 426 852 1277 1703 2129 2555 2981 8734 3<3 6919 24 426 851 1277 1702 2128 2553 2979 3405 3830 4991643 37 9472 23 426 851 1277 1702 2128 2554 2979 3405 3830 4552 3« 4792026 22 426 851 1277 1702 2128 2553 2979 3404 3830 7461 39 4579 21 425 851 1276 1701 2127 2552 2977 3402 3828 5000370 40 7131 20 425 851 1276 1701 2127 2552 2977 3402 3828 3278 41 9683 19 425 851 1276 1 701 2127 2552 2977 3402 3828 6187 42 4802235 18 425 850 1275 1700 2126 2551 2976 3401 3826 9096 43 4786 17 425 850 1275 1700 2126 2551 2976 3401 3826 5012005 44 7337 16 425 850 1275 1700 2126 2551 2976 3401 3826 4914 45 9888 15 425 850 1275 1700 2125 2550 2975 3400 3825 7822 46 4812438 14 425 850 1275 1700 2125 2549 2975 3400 3825 5020731 47 4987 13 425 850 1275 1700 2125 2550 2975 3400 3825 3640 48 7537 12 425 850 1274 1699 2124 2549 2974 3398 3823 6549 49 50 4820086 II 425 849 1274 1698 2123 2548 2972 3397 3822 9458 2634 10 425 849 1274 1698 2123 2548 2972 3397 3822 5032366 SI 5182 9 425 849 1274 1698 2123 2548 2972 3397 3821 5275 52 7730 8 425 849 1274 1698 2123 2547 2972 3396 3821 8184 53 4830277 7 425 849 1274 1698 2123 2547 2972 3396 3821 5041093 54 2824 6 424 849 1273 1697 2122 2546 2970 3394 3819 4002 55 5370 5 424 849 1273 1697 2122 2546 2970 3394 3819 691 1 5b 7916 4 424 849 1273 1697 2122 2546 2970 3394 3819 9820 57 4840462 3 424 848 1272 1696 2121 2545 2969 3393 3817 5052729 SH 3007 2 424 848 1272 1696 2121 2545 2969 3393 3817 5638 59 5552 I 424 848 1272 1696 2120 2544 2968 3392 3816 8546 60 8096 424 848 1272 1696 2120 2544 2968 3392 3816 5061455 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 61 Degrees. 30] 29 Degrees • Difference for Seconds. M. o I Sine. M. 10" 20" .30" 40" 50" 60" 70" 80" 90" Arc. 4848096 4850640 60 59 424 424 848 848 1272 1272 1696 1696 2120 2120 2544 2544 2968 2968 3392 3392 3816 3816 5061455 4364 Arc, A Sec Diff 2 3 3184 5727 58 57 424 424 848 848 1271 1271 1695 1695 2119 2119 2543 2543 2967 2967 3390 3390 3814 3814 7273 5070182 485 970 1454 4 8270 56 424 847 1271 1694 2118 2542 2965 3389 3812 3091 20 30 ■; 4860812 55 424 847 1271 1694 2118 2542 2965 3389 3812 6000 6 3354 54 424 847 1271 1694 2118 2541 2965 3388 3812 8909 40 1939 7 5895 53 424 847 1271 1694 2118 2541 2965 3388 3812 5081818 50 2424 8 8436 52 424 847 1271 1694 2118 2541 2965 3388 3812 4727 60 2909 9 4870977 51 423 847 1270 1693 2117 2540 2963 3386 3810 7636 70 80 3394 3878 lO 3517 50 423 847 1270 1693 2117 2540 2963 3386 3810 5090544 II 6057 49 423 847 1270 1693 2117 2540 2963 3386 3810 3453 90 4.363- 12 8597 48 423 846 1269 1692 2116 2539 2962 .3385 3808 6362 n 4881 136 47 423 846 1269 1692 2115 2538 2961 3384 3807 9271 H 3674 46 423 846 1269 1692 2115 2538 2961 3384 3384 3807 5 102 1 80 ii 6212 45 423 846 1269 1692 2115 2538 2961 3807 5089 i6 8750 44 423 846 1269 1692 2115 2538 2961 3384 3807 7998 17 4891288 43 423 846 1268 1691 2114 2537 2960 3.382 380s 51 10907 i8 3825 42 423 845 1268 1690 2113 2536 2958 3.381 3803 3816 19 20 6361 41 423 845 1268 1690 2113 2536 2958 3381 3803 6725 8897 40 423 845 1268 1690 2113 2536 2958 .3.381 3803 9633 21 4901433 39 423 845 1268 1690 2113 2535 2958 3380 3803 5122542 22 3968 38 423 845 1268 1690 2113 2535 2958 3380 3803 •5451 2,3 6503 37 423 845 1268 1690 2113 2535 2958 3380 3803 8360 1 24 9038 36 422 845 1267 1689 2112 2534 2956 3378 3801 5131269 \ 2? 4911572 35 422 844 1266 1688 2111 2533 2955 3377 3799 4178 26 4105 34 422 844 1266 1688 2111 2533 2955 3377 3799 7087 27 6638 33 422 844 1266 1688 2111 2533 2955 ^zn 3799 9996 28 9171 32 422 844 1266 1688 2111 2533 2955 3377 3799 5142905 29 30 4921704 31 422 844 1266 1688 2110 2532 2954 3376 3798 5814 ■ 4236 30 422 844 1265 1687 2109 2531 2953 3374 3796 8722 31 6767 29 422 844 1265 1687 2109 2531 2953 3374 3796 5151631 32 9298 28 422 844 1265 1687 2109 2531 2953 3374 3796 4540 33 4931829 27 422 843 1265 1686 2108 2530 2951 3373 3794 7449 34 4359 26 422 843 1265 1686 2108 2530 2951 3373 3794 5160358 j 35 6889 25 422 843 1265 J 686 2108 2530 2951 3373 3794 3267 36 9419 24 422 843 1265 1686 2108 2529 2951 3372 3794 6176 37 4941948 23 422 843 1265 1686 2108 2528 2951 3372 3794 9085 3« 4476 22 422 843 1265 1686 2108 2529 2951 3372 3794 5171994 39 7005 21 421 843 1264 1685 2107 2107 2527 2949 3370 3792 4903 40 9532 20 421 843 1264 1685 2528 2949 3370 3792 781 1 41 4952060 19 421 842 1263 1684 2106 2527 2948 3369 3790 5,180720 42 4587 18 421 842 1263 1684 2105 2526 2947 3368 3789 3629 43 7113 17 421 842 1263 1684 2105 2526 2947 3368 3789 6538 44 9639 16 421 842 1263 1684 2105 2526 2525" 2947 2946 3368 3789 3787 9447 45 4962165 15 421 842 1262 1683 2104 3366 5192356 46 4690 14 421 842 1262 1683 2104 2525 2946 3366 3787 5265 47 7215 •13 421 842 1262 1683 2104 2525 2946 3366 3787 8174 48 9740 12 421 841 1262 1682 2103 2524 2944 3365 .3785 5201083 49 4972264 II 421 841 1262 1682 2103 2523 2944 3364 3785 3992 50 4787 10 421 841 1262 1682 2103 2523 2944 3364 3785 6899 51 7310 9 421 841 1262 1682 2103 2523 2944 3364 3785 9808 52 9833 8 420 841 1261 1681 2102 2522 2942 3362 3783 5212717 53 4982355 7 420 841 1261 1681 2102 2522 2942 3362 3783 5626 54 4877 6 420 841 1261 1681 2102 2522 2942 3362 3783 8535 55 7399 5 420 840 1260 1680 2101 2521 2941 3361 3781 5221444 56 9920 4 420 840 1260 1680 2101 2521 2941 3361 .3781 4353 57 4992441 3 420 840 1260 1680 2100 2520 2940 3360 3780 7262 5« 4961 2 420 840 1260 1680 2100 2520 2940 3360 3780 5230171 i 59 7481 I 420 840 1259 1679 2099 2519 2939 .3358 3778 3080 60 5000000 420 840 1259 1679 2099 2519 2939 3358 3778 5988 M. Cosine. M. ■ 10" 20'' 30" 40" 50" 60" 70" 80" 90" Arc. 60 Degrees. 30 Degrees. Difference for Seconds. [: M.' Sine. M. 10" 20" 30" 40" 50" " 60 70" 80" 90" Arc. o I 5CXD0000 2519 60 59 420 420 840 840 1259 1259 1679 1679 2099 2099 2519 2518 2939 2939 3358 3358 3778 3778 5235988 8897 Arc. 2 3 5037 7556 58 57 420 420 840 839 1259 1259 1679 1678 2099 2098 2519 2517 2939 2937 3358 3357 3778 3776 5241806 4715 hec. uin. 485 4 5010073 56 420 839 1259 1678 2098 2518 2937 3357 3776 7624 10 20 30 40 50 6n S 2591 55 420 839 1259 1678 2098 2516 2937 3356 3776 5250533 970 1454 1939 2424 2909 3394 3878 6 5107 54 420 839 1259 1678 2098 2517 2937 3356 3776 3442 7 7624 53 419 839 1258 1677 2097 2516 2935 3354 3774 6351 8 5020140 52 419 838 1257 1676 2096 2515 2934 3353 3772 9260 9 2655 51 419 838 1257 1676 2096 2515 2934 3353 3772 5262169 70 80 lO 5170 50 419 838 1257 1676 2096 2515 2934 3353 3772 5077 II 7685 49 419 838 1257 1676 2095 2514 2933 3352 3771 7986 90 4363 12 5030199 48 419 838 1257 1676 2095 2514 2933 3352 3771 5270895 13 2713 47 419 838 1257 1676 2095 2514 2933 3352 3771 3804 14 5227 46 419 838 1256 1676 2094 2513 2932 3350 3769 6713 15 7740 45 419 838 1256 1675 2094 2512 2932 3350 3769 9622 i6 5040252 44 419 838 1256 1675 2094 2513 2932 3350 3769 5282531 17 2765 43 419 837 1256 1674 2093 25 1 1 2930 3349 3767 5440 iS 5276 42 419 837 125b 1674 2093 2512 2930 3349 3767 8349 19 7788 41 419 837 1256 1674 2093 2510 2930 3348 3767 5291258 20 5050298 40 419 837 1256 1674 2093 25 1 1 2930 3348 3767 4166 21 2809 39 418 837 1255 1673 2092 2510 2928 3346 3765 7075 22 5319 38 418 837 1255 1673 2092 2509 2928 3346 3765 9984 23 7828 37 418 837 1255 1673 2092 2510 2928 3346 3765 5302893 24 5060338 36 418 835 1254 1672 2091 2508 2927 3345 3763 5802 25 2846 35 418 836 1254 1672 2091 2509 2927 3345 3763 871 1 26 5355 34 418 836 1254 1672 2090 2508 2926 3344 3762 5311620 27 7863 33 418 836 1253 1671 2089 2507 2925 3342 3760 4529 28 5070370 32 418 836 1253 1671 2089 2507 2925 3342 3760 7438 29 2877 31 418 83b 1253 1671 2089 2507 2925 3342 3760 5320347^ 3255 30 5384 30 418 835 1253 1670 2088 2506 2923 3341 3758 31 7890 29 418 835 1253 1670 2088 2506 2923 3341 3758 6164 32 5080396 28 418 835 1253 1670 2088 2505 2923 3340 3758 9073 33 2901 27 418 835 1253 1670 2088 2505 2923 3340 3758 5331982 34 35 5406 26 417 417 835 1252 1669 2087 2^87 2504 2504 2921 2921 3338 3756 4891 7910 25 83s 1252 1669 3338 3756 7800 3b 5090414 24 417 835 1252 1669 2087 2504 2921 3338 3756 5340709 37 2918 23 417 834 1251 1668 2086 2503 2920 3337 3754 3618 3« 5421 22 417 834 1251 1668 2086 2503 2920 3337 3754 6527 39 40 7924 21 417 834 1251 1668 2085 2502 2919 3336 3753 9436 5100426 20 417 834 1251 1668 2085 2502 2919 3336 3753 5352344 41 2928 19 417 834 1250 1667 2084 2501 2918 3334 3751 5253 42 5429 18 417 834 1250 1667 2084 2501 2918 3334 3751 8162 43 7930 17 417 834 1250 1667 2084 2501 2918 3334 3751 5361071 44 5 1 1043 1 lb 417 833 1250 1666 2083 2500 2916 3333 3749 3980 45 2931 15 417 833 1250 1666 2083 2500 2916 3333 3749 6889 4b 5431 14 417 833 1250 1666 2083 2499 2916 3332 3749 9798 47 7930 13 416 833 1250 1666 2083 2499 2916 3332 3749 5372707 48 5120429 12 416 833 1249 1665 2082 2498 2914 3330 3747 5616 49 50 2927 II 416 833 1249 1665 2082 2498 2914 3330 3747 8525 5425 10 416 833 1249 1665 2082 2498 2914 3330 3747 5381432 51 7923 9 416 832 1248 1664 2081 2497 2913 3329 3745 4341 52 5130420 8 416 832 1248 1664 2081 2496 2913 3329 3745 7250 S3 2916 7 416 832 1248 1664 2081 2497 2913 3329 3745 5390159 54 5413 6 416 832 1248 1664 2080 2495 2912 3328 3744 3068 55 7908 5 416 832 1248 1664 2080 2496 2912 3328 3744 5977 5b 5140404 4 416 832 1247 1663 2079 2495 291 1 3326 3742 8886 57 2899 3 416 831 1247 1663 2079 2494 2909 3325 3740 5401795 i,8 5393 2 416 831 1247 1662 2079 2494 2909 3325 3740 4704 59 7887 I 416 831 1247 1662 2078 2494 2909 3325 3740 7613 60 5 I 5038 I 416 831 1247 1662 2078 2493 2909 3324 3740 5410521 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 59 Degrees. 32] 31 Degrees. Difference for Seconds. M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o I 2 3 4 5 1 5038 1 2874 5367 7859 5 16035 1 60 59 58 S7 56 416 416 415 415 415 831 831 831 831 830 1247 1247 1246 1246 1245 1662 1662 1661 1 661 1660 2078 2078 2077 2077 2076 2493 2493 2492 2492 2491 2909 2909 2907 2907 2906 3324 3324 3322 3322 3321 3740 3740 3738 3738 3736 5410521 3430 6339 9248 5422157 Arc. Sec. Uift: 10 20 30 40 50 60 70 80 90 485 970 H54 1939 24.24 2909 5 6 7 8 9 2842 5333 7824 5 1703 14 2804 55 54 53 52 51 415 415 415 415 415 830 830 830 830 830 1245 1245 1245 1245 1244 1660 1660 1660 1660 1659 2076 2076 2075 2075 2074 2491 2491 2490 2490 2489 2906 2906 2905 2905 2904 3321 3321 3320 3320 3318 3736 3736 3735 3735 3733 5066 7975 5430884 3793 6702 lO II 12 13 14 5293 7782 5180270 2758 5246 50 49 48 47 46 415 415 415 415 415 830 829 829 829 829 1244 1244 1244 1244 1244 1659 1658 1658 1658 1658 2074 2073 2073 2073 2073 2489 2488 2488 2488 2487 2904 2902 2902 2902 2902 3318 3317 3317 3317 3316 3733 3731 3731 3731 3731 9610 5442519 5428 8337 5451246 3394 3878 4363 15 i6 17 1 8 19 7733 5190219 2705 5191 7676 45 44 43 42 41 414 414 414 414 414 829 829 829 828 828 1243 1243 1243 1242 1242 1657 1657 1657 1656 1656 2072 2072 2072 2071 2071 2486 2486 2486 2485 2485 2900 2900 2900 2899 2899 3314 3314 3314 3313 3313 3729 3729 3729 3727 3727 4155 7064 9973 5462882 5791 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 5200161 2646 5130 7613 5210096 40 39 38 37 36 414 414 414 414 414 828 828 828 828 828 1242 1242 1 241 1241 1241 1656 1656 1655 1655 1655 2071 2070 2069 2069 2069 2485 2484 2483 2483 2483 2899 2898 2897 2897 2897 3313 3312 3310 3310 3310 3727 3726 3724 3724 3724 8699 5471608 4517 7426 5480335 2579 5061 7543 5220024 2505 35 34 33 32 31 30 29 28 27 26 414 414 414 414 414 827 827 827 827 827 1 241 1 241 1241 1241 1241 1654 1654 1654 1654 1654 2068 2068 2068 2068 2068 2482 2482 2481 2481 2481 2895 2895 2895 2895 2895 3309 3309 3308 3308 3308 3722 3722 3722 3722 3722 3244 6153 9062 549 1 97 1 4880 4986 7466 9945 5232424 4903 413 413 413 413 413 827 826 826 826 826 1240 1239 1239 1239 1239 1653 1652 1652 1652 1652 2067 2066 2066 2066 2065 2480 2479 2479 2479 2478 2893 2892 2892 2892 2891 3306 3306 3306 3306 3304 3720 3719 3719 3719 3717 7788 5500697 3606 6515 9424 5512333 5242 8151 5521060 3969 35 37 38 39 7381 9859 5242336 4813 7290 25 24 23 22 21 413 413 413 413 413 826 826 826 826 825 1239 1238 1238 1238 1238 1652 165 1 165 1 1651 1650 2065 2064 2064 2064 2063 2478 2477 2477 2477 2476 2891 2890 2890 2890 2888 3304 3302 3302 3302 3301 3717 3715 3715 3715 3713 40 41 42 43 44 9766 5252241 4717 7191. 9665 20 19 18 17 16 413 413 412 412 412 825 825 825 825 825 1238 1238 1237 1237 1237 1650 1650 1649 1649 1649 2063 2063 2062 2062 2062 2475 2476 2474 2474 2474 2888 2888 2886 2886 2886 3301 3301 3298 3298 3298 3713 3713 3711 3711 3711 6877 9786 5532695 5604 8513 45 46 47 48 49 5262139 4613 7085 9558 5272030 15 14 13 12 II 10 9 8 7 6 412 412 412 412 412 412 412 412 412 412 825 824 824 824 824 1237 1236 1236 1236 1236 1649 1648 1648 1648 1648 2062 2061 2061 2060 2060 2474 2472 2473 2472 2472 2886 2885 2885 2884 2884 3298 3297 3297 3296 3296 3711 3709 3709 3708 3708 5541422 4331 7240 5550149 3058 50 51 52 53 54 57 58 59 60 4502 6973 9443 5281914 4383 824 824 824 823 823 1235 1235 1235 1235 1235 1647 1647 1647 1646 1646 2059 2059 2059 2058 2058 2471 2470 2471 2469 2470 2883 2883 2883 2881 2881 3294 3294 3294 3293 3293 3706 3706 3706 3704 3704 5966 8875 5561784 4693 7602 6»53 9322 5-91790 4258 6726 9193 5 4 3 2 I 412 411 411 411 411 411 823 823 823 823 822 822 1235 1234 1234 1234 1233 1233 1646 1645 1645 1645 1644 1644 2058 2057 2057 2057 2056 2056 2469 2468 2468 2468 2467 2466 2881 2879 2879 2879 2878 2878 3292 3290 3290 3290 3289 3289 3704 3702 3702 3702 3700 3700 557051 1 3420 6329 9237 5582145 5054 M. Cosine. M. 10" 20" 30" 40" „ 50" 6a" 70" 80" 90" Arc. 58 De:jree3. 32 Degrees. Difference for Seconds, [Zi M. Sine. M. 10" 20" 30" 40" so" 60" 70" 80" 90" Arc, o 5299193 60 411 822 1233 1644 2055 2466 2877 3288 3699 5585054 Arc. I 5301659 5Q 411 822 1233 1644 2055 2466 2877 3288 3699 7963 , ^ , 2 4125 6591 58 411 822 822 1233 1644 1644 2055 2055 2466 2466 2877 2877 3288 3288 3699 3699 5590872 3781 Sec. Diff. 3 S/ 411 1233 4 9057 J6 55 411 822 1232 1643 2054 2054 2464 2465 2876 3286 3697 6690 10 20 485 5311521 411 822 1232 1643 2876 3286 3697 9599 970 6 3986 54 411 821 1232 1642 2053 2464 2874 3285 3695 5602508 i"-" 1454 7 6450 53 411 821 1232 1642 2053 2463 2874 3284 3695 5417 40 1939 8 8913 52 411 821 1232 1642 2053 2463 2874 3284 3695 8326 50 60 70 80 2424 9 lO 5321376 51 411 821 1232 1 23 1 1642 2053 2052 2463 2874 2872 3284 3695 561 1235 2909 3394 3878 3839 50 410 821 1641 2462 3282 3693 4143 II 6301 49 410 821 1231 1641 2052 2462 2872 3282 3693 7052 90 12 8763 48 410 820 1230 1640 2051 2461 2871 3281 3691 9961 n 5331224 47 410 820 1230 1640 2051 2461 2871 3281 3691 5622870 14 3685 46 410 410 820 820 1230 1640 2050 2460 2870 3280 3690 5779 ii; 6145 45 1230 1640 2050 2460 2870 3280 3690 8688 i6 8605 44 410 820 1230 1640 2050 2460 2870 3280 3690 5631597 I? 5341065 43 410 820 1229 1639 2049 2458 2869 3278 3688 4506 i8 3523 42 410 820 1229 1639 2049 2459 2869 3278 3688 7415 19 20 5982 8440 41 40 410 819 1229 1638 2048 2458 2867 3277 3686 5640323 410 819 1229 1638 2048 2458 2867 3277 3686 3232 21 5350898 39 410 819 1229 1638 2048 2457 2867 3276 3686 6141 22 3355 38 410 819 1229 1638 2048 2457 2867 3276 3686 9050 2^ 5812 37 409 819 1228 1637 2047 2456 2865 3274 3684 5651959 24 8268 36 409 819 1228 1637 2047 2456 2865 3274 3684 4868 2S 5360724 35 409 818 1227 1636 2046 2455 2864 3273 3682 7777 26 3179 34 409 818 1227 1636 2046 2455 2864 3273 3682 5660686 27 5634 33 409 818 1227 1636 2046 245 s 2864 3273 3682 3595 28 8089 32 409 818 1227 1636 2045 2454 2863 3272 3681 6504 29 5370543 31 409 818 1226 1635 2044 2453 2862 3270 3679 9413 30 2996 30 409 818 1226 1635 2044 2453 2862 3270 3679 5672321 31 5449 29 409 818 1226 1635 2044 2453 2862 3270 3679 5230 32 7902 28 409 817 1226 1634 2043 2452 2860 3269 3677 8139 33 5380354 27 409 817 1226 1634 2043 2452 2860 3269 3677 5681048 34 2806 26 409 817 1226 1634 2043 2451 2860 3268 3677 3957 3=; 5257 25 409 817 1226 1634 2043 2451 2860 3268 3677 6866 36 7708 24 408 817 1225 1633 2042 2450 2858 3266 3675 9775 37 5390158 23 408 817 1225 1633 2042 2450 2858 3266 3675 5692684 38 2608 22 408 817 1225 1633 2042 2450 2858 3266 367s 5593 39 5058 21 408 816 1224 1632 2041 2449 2857 3266 3674 8502 40 7507 20 408 816 1224 1632 2040 2448 2856 3264 3672 5701410 41 9955 19 408 816 1224 1632 2040 2448 2856 3264 3672 4319 42 5402403 18 408 816 1224 1632 2040 2448 2856 3264 3672 7228 43 4851 17 408 816 1223 1631 2039 2447 .2855 3262 3670 5710137 44 7298 16 408 816 1223 1631 2039 2447 2855 3262 3670 3046 4? 9745 15 408 815 1223 1630 2038 2446 2853 3261 3668 5955 46 5412191 14 408 815 1223 1630 2038 2446 2853 3261 3668 8864 47 4637 13 408 815 1223 1630 2038 2445 2853 3260 3668 5721773 48 7082 12 408 815 1223 1630 2038 2445 2853 3260 3668 4682 49 9527 11 407 815 1222 1629 2037 2444 2851 3258 3666 7591 50 542 1 97 1 10 407 815 1222 1629 2037 2444 2851 3258 3666 5730499 ■51 4415 9 407 815 1222 1629 2037 2444 2851 3258 3666 3408 52 6859 8 407 814 1221 1628 2036 2443 2850 3257 3664 6317 53 9302 7 407 814 1221 1628 2036 2442 2849 3256 3663 9226 54 5431744 6 407 814 1221 1628 2036 2443 2849 3256 3663 5742135 55 4187 5 407 814 1220 1627 2034 2441 2848 3254 3661 5044 56 6628 4 407 814 1220 1627 2034 2441 2848 3254 3661 7953 57 9069 3 407 814 1220 1627 2034 2441 2848 3254 3661 5750862 58 5441 5 10 2 407 814 1220 1627 2034 2441 2848 3254 3661 3771 59 3951 I 407 813 1220 1626 2033 2439 2846 3253 3659 6680 60 6390 407 813 1220 1626 2033 2440 2846 3253 3659 9587 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 57 Degrees. 34] 33 Degrees • Difference for Seconds. M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o I 5446390 8830 60 59 407 407 813 813 1220 1220 1626 1626 2033 2033 2440 2439 2846 2846 3253 3252 3659 3659 5759587 5762496 Arc. Diff 2 5451269 3707 58 57 406 406 813 813 I2I9 I2I9 1625 1625 2032 2032 2438 2438 2844 2844 3250 3250 3657 3657 5405 8314 485 970 1454 4 6145 56 406 813 I2I9 1625 2032 2438 2844 3250 3657 5771223 20 30 S 8583 55 406 812 I2I8 1624 2031 2437 2843 3249 3655 4132 6 5461020 54 406 812 I2I8 1624 2030 2436 2842 3248 3654 7041 40 1939 7 3456 53 406 812 I2I8 1624 2030 2436 2842 3248 3654 9950 50 2424 8 5892 52 406 812 1218 1624 2030 2436 2842 3248 3654 5782859 60 2909 9 8328 51 406 8X2 I2I7 1623 2029 2435 2841 3246 3652 5768 70 80 3394 lO 5470763 50 406 812 I2r7 1623 2029 2435 2841 3246 3652 8676 3878 II 3198 49 406 811 1217 1622 2028 2434 2839 3245 3650 5791585 90 4363 12 5632 48 406 811 1217 1622 2028 2434 2839 3245 3650 4494 n 8066 47 406 811 1217 1622 2028 2433 2839 3244 3650 7403 14 5480499 46 406 811 1217 1622 2028 2433 2839 3244 3650 5800312 1=; 2932 45 406 811 1217 1622 2028 2433 2839 3244 3650 3221 i6 5365 44 405 811 1216 1621 2027 2432 2837 3242 3648 6130 17 7797 43 405 810 1215 1620 2026 2431 2836 3241 3646 9039 i8 5490228 42 405 810 1215 1620 2026 2431 2836 3241 3646 5811948 19 20 2659 41 405 810 1215 1620 2926 2431 2836 3241 3646 4857 5090 40 405 810 1215 1620 2025 2430 2835 3240 3645 7765 21 7520 39 405 810 1215 1620 2025 2430 2835 3240 3645 5820674 22 9950 38 405 810 1214 1619 2024 2429 2834 3239 3644 3583 2.3 5502379 37 405 810 1214 1619 2024 2428 2834 3239 3644 6492 24 4807 .36 405 810 1214 1619 2024 2429 2834 3239 3644 9401 2S 7236 35 405 809 1214 1618 2023 2427 2832 3237 3641 5832310 26 9663 34 405 809 1214 1618 2023 2428 2832 3237 3641 5219 27 5512091 33 405 809 1214 1618 2023 2427 2832 3236 3641 8128 28 4518 32 404 809 1213 1617 2022 2426 2830 3234 3639 5841037 29 30 6944 31 404 809 1213 1617 2022 2426 2830 3234 3639 3946 9370 30 404 808 1212 1616 2021 2425 2829 3233 3637 6854 31 5521795 29 404 808 1212 1616 2021 2425 2829 3233 3637 9763 32 4220 28 404 808 1212 1616 2021 2425 2829 3233 3637 5852672 33 6645 27 404 808 1212 1616 2020 2424 2828 3232 3636 5581 34 9069 26 404 808 1211 1615 2019 2423 2827 3230 3634 8490 35 5531492 25 404 808 1211 1615 2019 2423 2827 3230 3634 5861399 36 3915 24 404 808 1211 1615 2019 2423 2827 3230 3634 4308 37 6338 23 404 807 1211 1614 2018 2422 2825 3229 3632 7217 3« 8760 22 404 807 1211 1614 2018 2422 2825 3229 3632 5870126 39 5541182 21 404 807 1211 1614 2018 2421 2825 3228 3632 3035 40 3603 20 404 807 1211 1614 2018 2421 2825 3228 3632 5943 41 6024 19 403 807 1210 1613 2017 2420 2823 3226 3630 8852 42 8444 18 403 807 1210 1613 2017 2420 2823 3226 3630 5881761 43 5550864 17 403 806 1209 1612 2016 2419 ' 2822 3225 3628 4670 44 3283 16 403 806 1209 1612 2016 2419 ' 2822 3225 3628 7579 45 5702 15 403 806 1209 1612 2016 2419 2822 3225 3628 5890488 46 8121 H 403 806 1209 1612 2015 2418 2821 3224 3627 3397 47 5560539 13 403 806 1208 1611 2014 2417 2820 3222 3625 6306 48 2956 12 403 806 1208 1611 2014 2417 2820 3222 3625 9215 49 5373 II 403 806 1208 1611 2014 2417 2820 3222 3625 5902124 50 7790 10 403 805 1208 1610 2013 2416 2818 3221 3623 5032 51 5570206 9 403 805 1208 1610 2013 2415 2818 3220 3623 . 7941 52 2621 8 403 805 1208 1610 2013 2415 2818 3220 3623 5910850 53 5036 7 403 805 1208 1610 2013 2415 2818 3220 3623 3759 54 55 7451 6 402 805 120? 1609 2012 2414 2816 3218 3621 6668 9865 5 402 805 1207 1609 2012 2414 2816 3218 3621 9577 st> 5582279 4 402 804 1206 1608 201 1 2413 2815 3217 3619 5922486 57 4692 3 402 804 1206 1608 201 1 2413 2815 3217 3619 5395 5« 7105 2 402 804 1206 1608 2010 2412 2814 3216 3618 8304 59 9517 I 402 804 1206 1608 2010 2412 2814 3216 3618 5931213 bo M. 5591929 402 804 1205 1607 2009 241 1 2813 3214 3616 4119 Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 56 Decrees. 34 Degrees. Difference for Seconds. [c M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o I 2 3 4 5591929 4340 6751 9162 5601572 60 59 58 57 56 402 402 402 402 402 804 804 804 803 803 1205 1205 1205, 1205 1205 1607 1607 1607 1606 1606 2009 2009 2009 2008 2008 2411 '241 1 241 1 2410 2409 2813 2813 2813 2811 281 1 3214 3214 3214 3213 3212 3616 3616 3616 3614 3614 59341 19 7028 9937 5942846 5755 Arc. Sec. Difif. 10 20 30 40 50 60 70 80 90 485 5 6 7 8 9 3981 6390 8798 561 1206 3614 55 54 53 52 51 402 401 401 401 401 803 803 803 803 802 1205 1204 1204 1204 1203 1606 1605 1605 1605 1604 2008 2007 2007 2007 2006 2409 2408 2408 2408 2407 2811 2809 2809 2809 2808 3212 3210 3210 3210 3209 3614 3612 3612 3612 3610 8664 5951573 4482 7391 5960200 970 1454 1939 2424 2909 3394 3878 4363 lO II 12 13 H 15 16 17 18 19 6021 8428 5620834 3239 56-^5 50 49 48 47 46 401 401 401 401 401 802 802 802 802 801 1203 1203 J 203 1203 1202 1604 1604 1604 1604 1602 2006 2005 2005 2005 2003 2407 2406 2405 2406 2404 2808 2807 2807 2807 2804 3209 3208 3208 3208 3205 3610 3609 3609 3609 3605 3208 6117 9026 5971935 4844 8049 5630453 2857 5260 7663 45 44 43 42 41 401 401 401 401 401 801 801 801 801 801 1202 1202 1202 1202 1202 1602 1602 1602 1602 1602 2003 2003 2003 2003 2003 2404 2404 2403 2403 2403 2804 2804 2803 2803 2803 3205 3205 3204 3204 3204 3605 3605 3605 3605 3605 7753 5980662 3571 6480 9389 20 21 22 23 24 5640066 2467 4869 7270 9670 40 39 38 37 36 400 400 400 400 400 801 801 800 800 800 1 201 1 201 1200 1200 1200 1601 1601 1600 1600 1600 2002 2002 2001 2000 2000 2401 2402 2401 2400 2400 2802 2802 2801 2800 2800 3202 3202 3201 3200 3200 3603 3603 3601 3600 3600 5992297 5206 8115 6001024 3933 25 26 27 28 J9 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 5652070 4469 6868 9267 5661665 35 34 33 32 31 400 400 400 400 400 800 800 800 799 799 1199 1199 1199 1 199 1 199 1599 1599 1599 1598 1598 1999 1999 1999 1998 1998 2399 2399 2399 2398 2397 2799 2799 2799 2797 2797 3198 3198 3198 3197 3196 3598 3598 3598 3596 3596 6842 9751 6012660 5569 8478 4062 6459 8856 5671252 3648 30 29 28 27 26 400 400 399 399 399 799 799 799 799 798 1 199 1 199 1 198 1198 1 197 1598 1598 1597 1597 1596 1998 1998 1997 1997 1996 2397 2397 2396 2396 2395 2797 2797 2795 2795 2794 3196 3196 3194 3194 3193 3596 3596 3594 3594 3592 6021385 4294 7203 60301 1 2 3021 6043 8437 5680832 3225 5619 25 24 23 22 21 399 399 399 399 399 798 798 798 798 797 1 197 1197 1197 1197 1 196 1596 1596 1596 1596 1594 1996 1996 1995 199s 1993 2394 239s 2393 2394 2392 2794 2794 2793 2793 2790 3193 3193 3192 3192 3189 3592 3592 3591 3591 3587 5930 8839 6041748 4657 7566 801 1 5690403 2795 5187 7577 20 19 18 17 16 399 399 399 398 398 797 797 797 797 797 II 96 1 196 1 196 1195 1 195 1594 1594 1594 1593 1593 1993 1993 1993 1992 1992 2392 2392 2392 2390 2391 2790 2790 2790 2788 2788 3189 3189 3189 3186 3186 3587 3587 3587 3585 3585 6050474 3383 6292 9201 60621 10 45 46 47 48 49 9968 5702357 4747 7136 9524 15 14 13 12 II 398 398 398 398 398 797 797 796 796 796 1 195 1 195 1 194 1194 1 194 1593 1593 1592 1592 1592 1992 1992 1991 1990 1990 2389 2390 2389 2388 2388 2788 2788 2787 2786 2786 3186 3186 3185 3184 3184 3585 3585 3583 3582 3582 5019 7928 6070837 3746 6655 50 51 52 53 54 5711912 4299 6686 9073 5721459 10 9 8 7 6 398 398 398 398 398 796 796 796 795 795 1 193 1 193 1 193 1 193 1 193 1591 1591 1591 1590 1590 1989 1989 1989 1988 1988 2387 2387 2387 2386 2385 2785 2785 2785 2783 2783 3182 3182 3182 3181 3180 3580 3580 3580 3578 3578 9563 6082472 5381 8290 6091 199 55 56 57 58 59 60 3844 6229 8614 5730998 3381 5764 5 4 3 2 I 398 398 397 397 397 397 795 795 795 794 794 794 1 193 1 193 1 192 1191 1191 1191 1590 1590 1589 1588 1588 1588 1988 1988 1987 1986 1986 1986 2385 2385 2384 2383 2383 2383 2783 2783 2781 2780 2780 2780 3180 3180 3178 3177 3177 3177 3578 3578 3576 3574 3574 3574 4108 7017 9926 6102835 5744 8652 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 55 Degrees. 36] 35 Degrees. Difference for Seconds. M. 1 Sine. M. lo" 20" 30" 40" 50" 60" 1 70" 80" 90" Arc. o I 2 3 4 5735764 8147 5740529 . 2911 5292 60 59 58 57 56 397 397 397 397 397 794 794 794 794 793 1191 1191 1191 1190 1190 1588 1588 1588 1587 1587 1986 1985 1985 1984 1984 2383 2382 2382 2381 2380 2780 2779 2729 2778 2777 3177 3176 3175 3174 3574 3573 3573 3572 3570 6103653 6x1 1 562 4471 7380 6120289 5 6 7 8 9 7672 5750053 2432 4811 7190 55 54 53 52 51 397 397 397 397 396 793 793 793 793 793 1190 1190 1190 1190 1 189 1586 1586 1586 1586 1586 1983 1983 1983 1983 1982 2381 2379 2379 2379 2378 2776 2776 2776 2776 2775 3173 3172 3172 3172 3171 3569 3569 3569 3569 3568 3198 6107 9016 6131925 4834 lO II 12 13 14 9568 5761946 4323 6700 9076 50 49 48 47 46 396 396 396 396 396 793 793 792 792 792 1 189 1 189 1 189 1 189 1188 1586 1586 1585 1585 1584 1982 1982 1981 1981 1980 2378 2377 2377 2376 2376 2775 2775 2773 2773 2772 3171 3171 3170 3170 3169 3568 3568 3567 3566 3565 7742 614065 1 3560 6469 9378 15 i6 17 i8 20 21 22 23 24 5771452 3827 6202 8576 5780950 45 44 43 42 41 396 396 396 396 396 792 792 791 791 791 1188 1188 1187 1187 1 186 1584 1584 1583 1583 1582 1980 1980 1979 1979 1978 2375 2375 2374 2374 2373 2771 2771 2770 2770 2769 3167 3167 3166 3166 3164 3564 3563 3562 3561 3560 6152287 5196 8105 6161014 3923 3323 5696 8069 5790440 2812 40 39 38 37 36 396 396 395 395 395 791 791 791 791 790 1186 1 186 1 186 1 186 1 186 1582 1582 1582 1582 1581 1978 1978 1977 1977 1976 2373 2373 2371 2372 2371 2769 2769 2768 2767 2766 3164 3164 3163 3162 3162 3560 3560 3559 3558 3557 6831 9740 6172649 5558 8467 25 26 27 28 29 30 31 32 33 34 5183 7553 9923 5802292 4661 35 34 33 32 31 395 395 395 395 395 790 790 790 790 790 1185 1185 1185 1185 1185 1580 1580 1580 1580 1580 1975 1975 1975 1975 1975 2370 2370 2369 2369 2369 2765 2765 2764 2764 2764 3160 3160 3159 3159 3159 3555 3555 3554 3554 3554 6181376 4285 7194 6190103 3012 7030 9397 5811765 4132 6498 30 29 28 27 26 395 395 395 394 394 789 789 789 789 789 1184 1 184 1 184 1 183 1 183 1579 1579 1578 1578 1579 1974 1974 1973 1972 1972 2367 2368 2367 2366 2366 2763 2763 2762 2761 2761 3158 3158 3156 3155 3155 3552 3552 3551 3550 3550 5919 8828 6201737 4646 7555 37 38 39 8864 5821230 3595 5959 8323 25 24 23 22 21 394 394 394 394 394 789 788 788 788 788 1 183 1 183 1182 1 182 1 182 1579 1578 1576 1576 1576 1972 I971 1970 1970 1970 2366 2365 2364 2364 2364 2761 2759 2758 2758 2758 3155 3154 3152 3152 3152 3550 3548 3547 3546 3546 6210464 3373 6282 9191 6222100 40 41 42 43 44 5830687 3050 5412 7774 5840136 20 19 18 17 16 394 394 394 394 394 788 787 787 787 787 1182 1181 1181 1181 T181 1576 1575 1575 1575 1574 1970 1969 1969 1969 1968 2363 2362 2362 2362 2361 2757 2756 2756 2756 2755 3151 3150 3150 3150 3148 3545 3544 3543 3543 3542 5008 7917 6230826 3735 6644 45 46 47 48 49 2497 4857 7217 9577 5851936 15 14 13 12 II 393 393 393 393 393 787 787 787 786 786 1 180 1 180 1 180 1 180 1179 1574 1574 1574 1573 1572 1967 1967 1967 1966 1965 2360 2360 2360 2359 2358 2754 2754 2754 2752 2751 3147 3147 3147 3146 3144 3541 3541 3541 3539 3537 9553 6242462 5371 8280 625 II 89 50 51 52 53 54 4294 6652 9010 5861367 3724 10 9 8 7 6 393 393 393 393 393 786 786 786 786 785 1 179 1 179 1 179 1178 1178 1572 1572 1572 1571 1571 1965 1965 1965 1964 1964 2358 2358 2357 2357 2356 2751 2751 2750 2750 2749 3144 3144 3143 3142 3142 3537 3537 3536 3535 3534 4097 7006 9915 6262824 5733 55 56 57 58 60 6080 8435 5870790 3145 5499 7853 5 4 3 2 1 393 393 393 392 392 392 785 785 785 785 785 1178 1178 1178 1177 1 177 1177 1570 1570 1570 1570 1569 1569 1963 1963 1963 1962 1962 1962 2355 2355 2355 2354 2354 2353 2748 2748 2748 2747 2747 2746 3141 3140 3140 3139 3139 3138 3533 3533 3533 3532 3531 3531 8642 6271551 4460 7369 6280278 3186 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. Sec. ' Uifif. 10 485 20 970 30 1454 40 1939 50 2424 60 2909 70 3394 80 3878 90 4363 54 Degrees. 36 Degrees. DilTerence for Seconds. [3' M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 1 90" Arc. o I 2 3 4 5877853 5880206 2558 4910 7262 60 59 58 57 56 392 392 392 392 392 784 784 784 784 784 1 176 1 176 1176 1 176 1175 1568 1568 1568 1568 1567 196 1 i960 i960 i960 1959 1959 1958 1958 1958 1958 1957 1957 1956 1955 1955 2353 2352 2352 2352 2351 2745 2744 2744 2744 2743 3137 3136 3136 3136 3134 3529 3528 3528 3528 3526 3526 3524 3524 3524 3524 6283185 6094 9003 6291912 4821 Arc. Sec. Diff. 10 20 30 40 50 60 70 80 90 485 5 6 7 8 9 lO II 12 13 14 9613 5891964 4314 6663 9012 55 54 53 52 51 392 392 392 392 392 784 783 783 783 783 1175 1 175 1 17s 1175 1175 1567 1566 1566 1566 1566 2351 2350 2349 2349 2349 2348 2348 2347 2346 2346 2743 2741 2741 2741 2741 3134 3133 3132 3132 3132 3130 3130 3129 3128 3128 7730 6300639 3548 6457 9366 970 1454 1939 2424 2909 3394 3878 4363 5901361 3709 6057 8404 5910750 50 49 48 47 46 391 391 391 391 391 783 783 782 782 782 1 174 1 174 1173 1173 1 173 1565 1565 1564 1564 1564 2739 2739 2738 2737 2737 3521 3521 3520 3519 3519 6312274 5183 8092 6321001 3910 15 i6 17 i8 19 3096 5442 7787 5920132 2476 45 44 43 42 41 391 391 391 39 i 391 782 782 782 781 781 1173 1 172 1172 1172 1172 1564 1563 1563 1562 1562 1955 1954 1954 1953 1953 2346 2345 2345 2344 2343 2737 2736 2736 2734 2734 3128 3126 3126 3125 3125 3519 3517 3517 3515 3515 6819 9728 6332637 5546 8455 20 21 22 23 24 25 26 27 28 29 4819 7163 9505 5931847 4189 40 39 38 37 36 35 34 33 32 JL 30 29 28 27 26 391 390 390 390 390 781 781 781 781 780 1 172 1171 1171 1171 1 1 70 1562 1561 1561 1561 1560 1953 1952 1952 1952 195 1 2344 2342 2342 2342 2341 2734 2732 2732 2732 2731 3125 3122 3122 3122 3121 3515 3513 3513 3513 3511 6341363 4272 7181 6350090 2999 5908 8817 6361726 4635 7544 6530 8871 5941211 3550 5889 390 390 390 390 390 780 780 780 780 780 II 70 1 170 1169 1 169 1 169 1560 1560 1559 1559 1559 1951 1950 1949 1949 1949 2341 2340 2339 2339 2339 2731 2730 2729 2729 2729 3121 3120 3118 3118 3118 3511 3510 3508 3508 3508 30 31 32 33 34 8228 5950566 2904 5241 7577 390 390 390 389 389 779 779 779 779 779 1 169 1169 1 169 1 168 1 168 1558 1558 1558 1557 1557 1948 1948 1948 1947 1947 2338 2338 2337 2336 2336 2727 2727 2727 2725 2725 3117 3117 3116 3114 3114 3506 3506 3506 3504 3504 6370452 3361 6270 9179 6382088 - 35 36 37 38 39 9913 5962249 4584 6918 9252 25 24 23 22 21 389 389 389 389 389 779 778 778 778 778 1 168 1 167 1 167 1 167 1 167 1557 1556 1556 1556 1556 1947 1946 1945 1945 1945 2336 2335 2334 2334 2334 2725 2724 2723 2723 2723 3114 3113 3112 3112 3112 3504 3502 3502 3502 3502 4997 7906 6390815 3724 6633 40 41 42 43 44 5971586 3919 6251 8583 5980915 20 19 18 17 16 389 389 389 389 389 778 777 777 777 777 1 166 1 166 1 166 1 166 1 166 1555 1554 1554 1554 1554 1944 1943 1943 1943 1943 2333 2332 2332 2332 2331 2722 2720 2720 2720 2720 3110 3109 3109 3109 3108 3499 3497 3497 3497 3497 9540 6402449 5358 8267 641 1 1 76 45 46 47 48 49 50 51 52 53 54 3246 5577 7906 5990236 2565 15 14 13 12 11 389 388 388 388 388 777 777 777 776 776 1 166 1 165 1 165 1 164 1 164 1554 1553 1553 1552 1552 1943 1942 1942 1941 1941 2331 2330 2330 2329 2329 2720 2718 2718 2717 2717 3108 3106 3106 3105 3105 3497 3495 3495 3493 3493 4085 6994 9903 6422812 5721 8629 6431538 4447 7356 6440265 • 4893 7221 9549 6001876 4202 10 9 8 7 6 388 388 388 388 388 776 776 776 776 775 1 164 1 164 1 163 1 163 1163 1552 1552 1551 1551 1550 1940 1940 1939 1939 1938 2328 2328 2327 2326 2326 2716 2716 2715 2713 2713 3104 3104 3162 3101 3101 3492 3492 3490 3488 3488 55 56 57 58 59 60 6528 8854 6011179 3503 5827 8150 5 4 3 2 I 388 388 387 387 387 387 775 775 775 775 774 774 1 163 1 163 1 162 1162 1161 1161 1550 1550 1549 1549 1548 1548 19^8 1938 1937 1937 1936 1936 2326 2325 2324 2324 2323 2323 2713 2713 2711 27 1 1 2710 2710 3101 3100 3098 3098 3097 3097 3488 3488 3486 3486 3484 3484 3174 6083 8992 6451901 4810 7718 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 53 Degrees. 38] 37 Degrees . Difference for Seconds. M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o 1 6018150 6020473 60 59 387 387 774 774 1161 1161 1548 1548 1936 1935 2323 2322 2710 2709 3097 3484 6457718 6460627 Arc. 3096 1 3483 Diff. 2 3 2795 5117 58 57 387 387 774 774 1161 1161 1548 1548 1935 1935 2322 2322 2709 2709 3096 3096 3483 3483 3536 6445 48s 970 1454 4 7439 56 387 774 773 1160 1547 1934 2321 2708 3094 3481 9354 20 30 <; 9760 55 387 1160 1546 1933 2320 2706 3093 3479 6472263 6 6032080 54 387 773 1160 1546 1933 2320 2706 3093 3479 5172 40 1939 7 4400 53 387 773 1 160 1546 1933 2319 2706 3092 3479 8081 50 2424 8 6719 52 387 773 1160 1546 1933 2319 2706 3092 3479 6480990 60 2909 9 9038 51 50 386 773 1159 1545 1932 2318 2704 3090 3477 3899 70 80 3394 lO 6041356 386 773 1159 1545 1932 2318 2704 3090 3477 6807 3878 II 3674 49 386 772 1158 1544 193 1 2317 2703 3089 3475 9716 90 4363 12 5991 48 386 772 1158 1544 193 1 2317 2703 3089 3475 6492625 n 8308 47 386 772 1158 1544 1930 2316 2702 3088 3474 5534 14 6050624 46 386 772 1158 1544 1930 2316 2702 3088 3474 8443 I? 2940 45 386 772 1157 1543 1929 2315 2701 3086 3472 6501352 i6 5255 44 386 772 1157 1543 1929 2315 2701 3086 3472 4261 17 7570 43 386 771 1157 1542 1928 2314 2699 3085 3470 7170 i8 9884 42 386 771 1157 1542 1928 2314 2699 3085 3470 6510079 19 6062198 41 386 771 1157 1542 1928 2313 1 2699 3084 3470 2988 20 4511 40 386 771 1157 1542 1928 2313 2699 3084 3470 5896 21 6824 39 385 771 1156 1541 1927 2312 2697 3082 3468 8805 22 , 9136 38 .385 770 1155 1540 1926 2311 2696 3081 3466 6521714 23 6071447 37 385 770 1155 1540 1926 23 1 1 2696 3081 3466 4623 24 3758 36 385 770 1155 1540 1926 2311 2696 308 X 3466 7532 2S 6069 35 385 770 1155 1540 1925 2310 2695 3080 3465 6530441 26 8379 34 385 770 1155 1540 1925 2310 2695 3080 3465 3350 27 6080689 33 385 770 1154 1539 1924 2309 2694 3079 3463 6259 28 2998 32 385 769 1 154 1538 1923 2308 2692 3077 3461 9168 29 30 5306 31 385 769 1154 1538 1923 2308 2692 3077 3461 6542077 7614 30 385 769 1154 1538 1923 2308 2692 3077 3461 4984 31 9922 29 385 769 1154 1538 1923 2307 2692 3076 3461 7893 32 6092229 28 384 769 1153 1537 1922 2306 2690 3074 3459 6550802 33 4535 27 384 769 1153 1537 1922 2306 2690 3074 3459 3711 34 3S 6841 26 384 769 1153 1537 1922 2306 2690 3074 3459 6620 9147 25 384 768 1152 J 536 1921 2305 2689 3073 3457 9529 36 6101452 24 384 768 1152 1536 1920 2304 2688 3072 3456 6562438 37 3756 23 384 768 1152 1536 1920 2304 2688 3072 3456 5347 3« 6060 22 384 768 1151 1535 1919 2303 2687 3070 3454 8256 39 8363 21 384 768 1151 1535 1919 1919 2303 2687 3070 3454 6571165 • 40 61 10666 20 384 768 1151 1535 2303 2687 3070 3454 4073 41 2969 19 384 767 1151 1534 1918 2301 2685 3069 3452 6982 42 5270 18 384 767 1151 1534 1918 2302 2685 3069 3452 9891 43 7572 17 384 767 1151 1534 1918 2301 2685 3068 3452 6582800 44 9873 16 383 767 1 1 50 1533 1917 2300 2683 3066 3450 5709 4'; 6122173 15 383 766 1150 1533 1917 2300 2683 3066 3450 86x8 46 4473 14 383 -jee 1 149 1532 1916 2299 2682 3065 3448 659x527 47 6772 13 383 766 1149 1532 1916 2299 2682 3065 3448 4436 48 9071 12 383 766 1 149 1532 1915 2298 2681 3064 3447 7345 49 50 6131369 II 383 766 1149 1532 1915 2297 2681 1 3064 1 3447 6600254 3666 10 383 766 1 149 1532 1915 2298 2681 3064 3447 3162 51 5964 9 383 765 1 148 1530 1913 2296 2678 3061 3443 607X 52 8260 8 383 765 1 148 1530 1913 2296 2678 3061 3443 8980 S3 6140556 7 383 765 1 148 1530 1913 2296 2678 3061 3443 661x889 54 2852 6 383 765 1148 1530 1913 2295 2678 3060 3443 3443 4798 7707 55 5147 5 383 765 1 148 1530 1913 2295 2678 3060 56 7442 4 382 765 1147 1529 1912 2294 2676 3058 3441 6620616 57 9736 3 382 764 1 146 1528 1911 2293 2675 3057 3439 3525 5« 6152029 2 382 764 1146 1528 1911 2293 2675 3057 3439 6434 59 4322 I 382 764 1146 1528 1911 2293 2675 3057 3439 9343 60 6615 382 764 1146 1528 1910 2292 2674 3056 3438 663225 X M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 52 Degrees. 38 Degrees. Difference for Seconds. 51 Degrees. 40] 39 Degrees. Difference for Seconds. M. Sine. M. 10" 20" 30" 1 40" 50" 60" 70" 80" 90" Arc. o 6293204 60 377 753 1 130 1 1506 1883 2260 2636 3013 3389 6806784 Arc. ... >• I 2 5464 7724 59 58 377 377 753 753 1 130 1 130 1506 1506 1883 1883 2260 2259 2636 2636 3013 3012 3389 3389 9693 6812602 .Sec. DifT. 3 4 9983 6302242 57 56 377 376 753 753 1 130 1129 1506 1505 1883 1882 2259 2258 2636 2634 3012 3010 3389 3387 55" 8420 10 20 485 970 1454 1939 2424 2909 ■; 4500 55 376 753 1129 1505 1882 2258 2634 3010 3387 6821329 6 6758 54 376 752 1128 1504 1881 2257 2633 3009 3385 4238 ■^0 7 9015 53 376 752 1128 1504 1881 2257 2633 3009 3385 7147 40 8 6311272 52 376 752 1128 1504 1880 2256 2632 3008 3384 6830056 50 60 70 9 3528 51 376 752 1128 1504 1503 1880 ~^79 2256 2632 3008 3384 2965 lO 5784 50 376 752 1127 2255 2631 3006 3382 5873 3394 II 8039 49 376 751 1127 1502 1878 2254 2629 3005 3380 8782 80 3878 12 6320293 48 376 751 1127 1502 1878 2254 2629 3005 3380 684 I 69 I 90 4363 1.3 2547 47 376 751 1127 1502 1878 2253 2629 3004 3380 4600 14 4800 .4^ 45 376 376 751 1127 1502 1878 2253 2629 3004 3380 7509 IS 7053 751 1127 1502 1878 2253 2629 3004 3380 6850418 i6 9306 44 375 750 1126 1501 1876 2251 2627 3002 3378 3327 17 6331557 43 375 750 1 126 1 501 1876 2252 2627 3002 3378 6236 i8 3809 42 375 750 1125 1500 1875 2250 2626 3001 3376 9145 19 20 6059 8310 41 375 750 1125 1500 1875 2251 2626 3001 3376 6862054 40 375 750 1124 1499 1874 2249 2624 2998 3373 4962 21 6340559 39 375 750 1 124 1499 1874 2249 2624 2998 3373 7871 22 2808 38 375 750 1 124 1499 1874 2249 2624 2998 3373 6870780 23 5057 37 375 749 1 124 1498 1873 2248 2622 2997 3371 5689 24 7305 36 375 749 1 124 1498 1873 2248 2622 2997 3371 6598 2? 9553 35 375 749 1 124 1498 1873 2247 2622 2996 3371 9507 26 6351800 34 374 749 1 123 1497 1872 2246 2620 2994 3369 68S2416 27 4046 33 374 749 1 123 1497 1872 2246 2620 2994 3369 5325 2S 6292 32 374 748 1122 1496 1871 2245 2619 2993 3367 8234 29 8537 -3L 30 374 748 1122 1496 1871 2245 2619 2993 3367 6891 143 30 6360782 374 748 1122 1496 1870 2244 2618 2992 3366 4051 31 3026 29 374 748 1122 1496 1870 2244 2618 2992 3366 6960 32 5270 28 374 748 1121 H95 1869 2243 2617 2990 3364 9869 33 7513 27 374 748 1121 1495 1869 2243 2617 2990 3364 6902778 34 35 9756 6371998 26 25 374 747 1121 1494 1868 2242 2615 2989 3362 5687 8596 374 747 1121 1494 1868 2242 2615 2989 3362 36 4240 24 374 747 1121 1494 1868 2241 2615 2988 3362 691 1 505 37 6481 23 373 747 1 1 20 1493 1867 2240 2613 2986 3360 4414 3H 8721 22 373 747 1 1 20 1493 1867 2240 2613 2986 3360 7323 39 6380961 21 373 747 1 1 20 1493 1867 2240 2613 2986 3360 6920232 40 3201 20 373 746 1119 1492 1866 2239 2612 2985 3358 3139 41 5440 19 373 746 1119 1492 1865 2238 261 1 2984 3357 6048 42 7678 18 373 746 1119 1492 1865 2238 261 1 2984 3357 8957 43 9916 17 373 745 1118 1491 1864 2237 2610 2982 3355 6931866 44 4S 6392153 16 373 745 1118 1491 1864 2237 2610 2982 3355 4775 7684 4390 15 373 745 1118 1490 1863 2236 2608 2981 3353 46 6626 14 373 745 1118 1490 1863 2236 2608 2981 3353 6940593 47 8862 13 373 745 1118 1490 1863 2235 2608 2980 3353 3502 48 6401097 12 373 745 1118 1490 1863 2235 2608 2980 3353 641 1 49 3332 II 10 372 745 1117 1489 1862 2234 2606 2978 3351 3349 9320 50 5566 372 744 1116 1488 1861 2233 2605 2977 6952228 51 7799 9 372 744 1116 1488 1861 2233 2605 2977 3349 5137 S2 6410032 8 372 744 1116 1488 i860 2232 2604 2976 3348 8046 S3 2264 7 372 744 1116 1488 i860 2232 2604 2976 3348 6960955 54 55 4496 6 372 744 1116 1488 i860 2232 2604 2976 3348 3864 6728 5 372 743 1115 i486 1858 2230 2602 2974 3345 6773 56 8958 4 372 7^3 1115 i486 1858 2231 2602 2974 3345 9682 57 642 1 1 89 3 372 743 HIS i486 1858 2229 2601 2972 3344 6972591 5« 3418 2 372 743 1115 i486 1858 2229 2601 2972 3344 5500 59 5647 I 372 743 1115 i486 1858 2229 2601 2972 3344 8409 60 7876 M. 371 743 1114 1485 1857 2228 2599 2970 3342 6981317 M., Cosine. 10" 20" 30" 40" I 50" 60" 1 70" 80" 90" Arc. 50 Degrees. 40 Degrees, Difference for Seconds. r4^ M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o 6427876 6430104 2332 60 59 58 371 371 371 743 743 742 1 1 14 1 1 14 1113 i486 i486 1484 1857 1857 1856 2228 2228 2599 2599 2598 2970 3342 6981317 4226 7135 Arc. 2 2227 2970 2969 3342 3340 Sec. 1 Difif. 3 4559 57 371 742 1113 1484 1855 2226 2597 2968 3339 6990044 4 6785 56 371 742 1113 1484 1855 2226 2597 2968 3339 2953 10 20 485 5 901 1 55 371 742 1112 1483 1854 2225 2596 2966 3337 5862 970 6 6441236 54 371 742 1112 1483 1854 2225 2596 2966 3337 8771 3^ 1454 7 3461 53 371 741 1112 1482 1853 2224 2594 2965 3335 7001680 40 1939 8 5685 52 371 741 1112 1482 1853 2224 2594 2965 3335 4589 5^ 60 70 80 2424 9 7909 51 371 741 IIJ2 1482 1853 1853 2223 2223 2594 2594 2964 2964 3335 7498 2909 lO 6450132 50 371 741 III2 1482 3335 7010406 3394 3878 Alfs-i II 2355 49 370 741 IIII 1481 1852 2222 2592 2962 3333 331S QO 12 4577 48 370 740 I I 10 1480 1851 2221 2591 2961 3331 6224 13 6798 47 370 740 IIIO 1480 1851 2221 2591 2961 3331 9133 H 9019 40 370 740 1 1 10 1480 1851 2221 2591 2961 3331 7022042 15 6461240 45 370 740 IIIO 1480 1850 2220 2590 2960 3330 4951 16 3460 44 370 740 1 109 1479 1849 2219 2589 2959 3329 7860 17 5679 43 370 740 1 109 1479 1849 2219 2589 2959 3329 7030769 18 7898 42 370 739 1 109 1478 1848 2218 2587 2957 3326 3678 19 64701 16 41 370 739 II09 1478 1848 2218 2587 2957 3326 6587 20 2334 40 370 739 I 109 1478 1848 2217 2587 2956 3326 9495 21 4551 39 370 739 1 109 1478 1848 2216 2587 2956 3326' 7042404 22 6767 38 370 739 1 109 1478 1848 2217 2587 2956 3326 5313 23 8984 Zl 369 738 1 107 1476 1846 2215 2584 2953 3322 8222 24 648 1 1 99 36 369 738 1107 1476 1846 2215 2584 2953 3322 7051131 '25 3414 35 369 738 I 107 1476 1845 2214 2583 2952 3321 4040 26 5628 34 369 738 1 107 1476 1845 2214 2583 2952 3321 6949 27 7842 ■iZ 369 738 1 107 1476 1845 2214 2583 2952 3321 9858 28 6490056 32 369 in 1 106 1474 1843 2212 2580 2949 3317 7062767 29 2268 31 369 737 1 106 1474 1843 2212 2580 2949 3317 5676 30 4480 30 369 Til II06 1474 1843 2212 2580 2949 3317 8584 31 6692 29 369 lyj IIO6 1474 1843 221I 2580 2948 3317 7071493 32 8903 28 369 737 II06 1474 1843 2211 2580 2948 3317 4402 33 6501 1 14 27 368 737 1 105 1474 1842 2210 2578 2946 3315 731 1 34 3324 26 368 736 1 104 1472 1 841 2209 2577 2945 3313 7080220 35 5533 25 368 736 1 104 1472 1 841 2209 2577 2945 3313 3129 3(5 7742 24 368 Ti^ 1 104 1472 1 841 2209 2577 2945 3313 6038 37 9951 23 368 736 1 104 1472 1840 2207 2576 2944 3312 8947 3« 6512158 22 368 736 1 104 1472 1840 2208 2576 2944 3312 7091856 39 4366 21 368 735 1 103 1470 1838 2206 2573 2941 3308 4765 40 6572 20 368 735 1 103 1470 1838 2206 2573 2941 3308 7672 41 8778 19 368 735 1 103 1470 1838 2206 2573 2941 3308 7100581 42 6520984 18 368 735 IIO3 1470 1838 2205 2573 2940 3308 3490 43 3189 17 368 735 IIO3 1470 1838 2205 2573 2940 3308 6399 44 5394 16 367 735 1 102 1469 1837 2204 2571 2938 3306 9308 45 7598 15 367 734 IIOI 1468 1836 2203 2570 2937 3304 7112217 4b 9801 14 367 734 IIOI 1468 1836 2203 2570 2937 3304 5126 47 6532004 13 367 734 IIOI 1468 1835 2202 2569 2936 3303 8035 48 4206 12 367 734 IIOI 1468 1835 2202 2569 2936 3303 7120944 49 6408 II 367 734 1 100 1467 1834 2201 2568 2934 3301 3853 50 8609 10 367 734 1 100 1467 1834 2201 2568 2934 3301 6761 SI 6540810 9 367 733 1 100 1466 1833 2200 2566 2933 3299 9670 52 3010 8 367 733 1 100 1466 1833 2199 2566 2932 3299 7132579 53 5209 7 367 733 1 100 1466 1833 2199 2566 2932 3299 5488 54 7408 6 367 IZZ 1 100 1466 1465 1833 1832 2199 2197 2566 2932 3299 8397 55 9607 5 366 733 1099 2564 2930 3297 7141306 56 6551804 4 366 733 1099 1465 1832 2198 2564 2930 3297 4215 57 4002 3 366 732 1098 1464 1831 2196 2563 2929 3295 7124 5« 6198 2 366 732 1098 1464 1831 2197 2563 2929 3295 7150033 59 8395 I 366 732 1097 1463 1829 2195 2561 2926 3292 2942 60 6560590 366 732 1097 1463 1829 2195 2561 2926 3292 5850 M. Cosine. M. 10" 20" 30- 40" 50" 60" 70" 80" 90" Arc. <9 Degrees. 4.2] 41 Degrees. Difference for Seconds. M. Sine. xM. 10" 20" 30" 40" 50" 60" 70" 80" 90" Aire. o I 6560590 2785 60 59 366 366 732 732 1097 1097 1463 1463 1829 1829 2195 2195 2561 2561 2926 2926 3292 3292 7155850 8759 Arc. Sec Diff 2 4980 7174 58 57 366 366 731 731 1097 1097 1462 1462 1828 1828 2194 2193 2559 2559 2925 2924 3290 3290 7161668 4577 485 970 1454 4 1 9367 56 366 731 1097 1462 1828 2193 2559 2924 3290 7486 20 30 6571560 55 365 731 1096 1461 1827 2192 2557 2922 3288 7170395 6 3752 54 365 730 1096 1461 1827 2192 2557 2922 1 3288 3304 40 1939 7 5944 53 365 730 1095 1460 1826 2191 2556 2921 3286 6213 50 2424 8 8135 52 365 730 1095 1460 1826 2191 2556 2921 3286 9122 60 2909 9 lO 6580326 51 365 730 1095 1460 1825 2190 2555 2920 3285 7 1 8203 1 70 80 3394 2516 50 365 730 1095 1460 1825 2190 2555 2920 3285 4939 3878 II 4706 49 365 730 1094 1459 1824 2189 2554 2918 3283 7848 90 4363 12 6895 48 365 729 1094 1458 1823 2188 2552 2917 3281 7190757 n 9083 47 365 729 1094 1458 1823 2x88 2552 2917 3281 3666 , 14 15 6591271 46 365 729 1094 1458 1823 2187 2552 2916 2916 3281 6575 3458 45 365 729 1094 1458 1823 2187 2552 3281 9484 16 5645 44 364 729 1093 1457 1822 2186 2550 2914 3279 7202393 17 7831 43 364 729 1093 1457 1822 2186 2550 2914 3279 5302 18 6600017 42 364 729 1093 1457 1822 2185 2550 2914 3279 8211 19 2202 41 364 728 1092 1456 1820 2184 2548 2912 3276 7211120 20 4386 40 364 728 1092 1456 1820 2184 2548 2912 3276 4028 21 6570 39 364 728 1092 1456 1820 2184 2548 2912 3276 6937 22 8754 38 364 728 1091 1455 1819 2182 2547 2910 3275 9846 23 6610936 37 364 728 1091 1455 1819 2183 2547 2910 3274 7222755 24 3119 36 35 364 727 1091 1454 1818 2181 2545 2909 3272 5664 2S 5300 364 727 1091 1454 1818 2182 2545 2909 3272 8573 26 7482 34 363 727 1090 1453 1817 2180 2543 2906 3270 7231482 27 9662 33 363 727 1090 1453 1817 2180 2543 2906 3270 4391 28 6621842 32 363 727 1090 1453 1817 2180 2543 2906 3270 7300 29 30 4022 31 363 726 1089 1452 1816 2178 2542 2905 3268 7240208 6200 30 363 726 1089 1452 1816 2179 2542 2905 3268 3116 31 8379 29 363 726 1089 1452 1815 2178 2541 2904 3267 6025 32 6630557 28 363 726 1088 145 1 1814 2177 2540 2902 3265 8934 33 2734 27 363 726 1088 145 1 1814 2176 2540 2902 3265 7251843 34 4910 26 363 726 1088 1451 1814 2177 2540 2902 3265 4752 31 7087 25 363 725 1088 J 450 1813 2175 2538 2900 3263 7661 36 9262 24 363 725 1088 1450 1813 2175 2538 2900 3263 7260570 37 6641437 23 363 725 1088 1450 1813 2175 2538 2900 3263 3479 38 3612 22 362 725 1087 1449 1812 2173 2536 2898 3261 6387 39 5785 21 362 725 1087 1449 1812 2174 2536 2898 3261 9296 40 .. 7959 20 362 724 1086 1448 1811 2172 2535 2897 3259 7272205 41 665013 1 19 362 724 1086 1448 1811 2173 2535 2897 3259 5114 42 2304 18 362 724 1085 1447 1809 2171 2533 2894 3256 8023 43 4475 17 362 724 1085 1447 1809 2171 2533 2894 3256 7280932 44 6646 16 362 724 1085 1447 1809 2171 2533 2894 3256 3841 4'! 8817 15 362 723 1085 1446 1808 2170 2531 2893 3254 6750 46 6660987 14 362 723 1085 1446 1808 2169 2531 2892 3254 9659 47 3156 13 362 723 1085 1446 1808 2169 2531 2892 3254 7292568 48 5325 12 361 723 1084 1445 1807 2168 2529 2890 3252 5477 49 7493 II 361 723 1084 1445 1807 2168 2529 2890 3252 8385 50 9661 10 361 72a 1083 1444 1806 2167 2528 2889 3250 7301294 51 6671828 9 361 722 1083 1444 1806 2166 2527 2888 3249 4203 52 3994 8 361 722 1083 1444 1805 2166 2527 2888 3249 7112 53 6160 7 361 722 1083 1444 1805 2166 2527 2888 3249 7310021 54 55 8326 6 361 722 1082 1443 1804 2164 2526 2886 3247 2930 6680490 5 361 722 1082 1443 1804 2165 2526 2886 3247 5839 56 2655 4 361 721 1082 1442 1803 2163 2524 2884 3245 8748 57 4818 3 361 721 1082 1442 1803 2163 2524 2884 3245 7321657 58 6981 2 361 721 1082 1442 1803 2163 2524 2884 3245 4566 59 9144 I 360 721 1081 1441 1802 2162 2522 2882 3243 7475 60 6691306 360 721 1081 1441 1802 2162 2522 2882 3243 7330383 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 48 Decrees. 42 Degrees. Difference for Seconds. [43 M. 1 Sine. M. 10" 20" 30" 40" „ 50' 60" 70" 80" 90" Arc. o I 2 3 4 6691306 3468 5628 7789 9948 60 59 58 57 56 360 360 360 360 360 721 720 720 720 720 1081 1080 1080 1080 1080 1441 1440 1440 1440 1440 1802 1801 1 801 1800 1800 2162 2160 2l6l 2159 2160 2522 2521 2521 2520 2520 2882 2881 2881 2880 2880 3243 3241 3241 3238 3240 7330383 3292 6201 9110 7342019 Arc. Sec. Difif. 10 20 30 40 50 60 70 80 90 485 5 6 7 8 9 6702108 4266 6424 8582 6710739 55 54 53 52 51 360 360 360 359 359 719 719 719 719 719 1079 1079 1079 1079 1078 1438 1438 1438 1438 1437 1798 1798 1798 1798 1797 2158 2158 2158 2157 2156 2517 2517 2517 2517 251S 2877 2877 2877 2876 2874 3236 3236 3236 3236 3234 4928 7837 7350746 3655 6564 970 1454 1939 2424 2909 3394 3878 4363 lO II 12 13 14 2895 5051 7206 9361 6721515 50 49 48 47 46 359 359 359 359 359 719 718 718 718 718 1078 1077 J077 1077 1076 1437 1436 1436 1436 1435 1797 1796 1796 1795 1794 2156 2155 2155 2154 2153 2515 2514 2514 2513 2512 2874 2873 2873 2872 2870 3234 3232 3232 3231 3229 9472 7362381 5290 8199 7371 108 15 i6 17 i8 19 20 21 22 23 24 25 26 27 28 J9 30 31 32 33 34 35 36 37 38 39 3668 5821 7973 673012s 2276 45 44 43 42 41 359 359 359 359 359 718 717 717 717 ■717 1076 1076 1076 1076 1076 1435 1434 1434 1434 1434 1794 1793 1793 1793 1793 2153 2152 2152 2151 2151 2512 2510 2510 2510 2510 2870 2869 2869 2868 2868 3229 3227 3227 3227 3227 4017 6926 9835 7382744 5653 4427 6577 8727 6740876 3024 40 39 38 36 358- 358 358 358 717 717 716 716 716 1075 1075 1074 1074 1074 1433 1433 1432 1432 1432 1792 1792 1 791 1790 1790 2150 2150 2149 2148 2148 2508 2508 2507 2506 2506 2866 2866 2865 2864 2864 3225 3225 3223 3222 3222 8561 7391470 4379 7288 7400197 5172 7319 9466 6751612 3757 35 34 33 32 31 358 358 358 358 716 716 715 715 715 1073 1073 1073 1073 1073 1431 143 1 1430 1430 1430 1789 1789 1788 1788 1788 2147 2147 2146 2145 2145 2505 2505 2503 2503 2503 2862 2862 2861 2860 2860 3220 3220 3218 3218 3218 3106 6015 8924 741 1833 4742 5902 8046 6760190 2333 4476 30 29 28 27 26 25 24 23 22 21 357 357 357 357 357 715 715 714 714 714 1072 1072 1071 1071 1071 1429 1429 1428 1428 1428 1787 1787 1786 1786 1785 2144 2144 2143 2143 2142 2501 2501 2500 2500 2499 2858 2858 2857 2857 2856 3216 3216 3214 3214 3213 7650 7420559 3468 6377 9286 6618 8760 6770901 3041 5181 357 357 357 357 357 714 7H 713 713 713 1071 1070 1070 1070 1070 1428 1427 1426 1426 1426 1785 1784 1783 1783 1783 2142 2141 2140 2140 2139 2499 2498 2496 2496 2496 2856 2854 2853 2853 2852 3213 3211 3209 3209 3209 7432195 5104 8013 7440922 3831 40 41 42 43 44 7320 9459 6781597 3734 5871 20 19 18 17 16 357 356 356 356 356 713 713 712 712 712 1070 1069 1068 1068 1068 1426 1425 1424 1424 1424 1783 1782 1781 1781 1780 2139 2138 2137 2137 2136 2496 2494 2493 2493 2492 2852 2850 2849 2849 2848 3209 3207 3205 3205 3204 6738 9647 7452556 5465 8374 45 46 47 48 49 50 51 52 53 54 8007 6790143 2278 4413 6547 15 14 13 12 II 356 356 356 356 712 712 712 711 711 1068 1067 1067 1067 1067 1424 1423 1423 1422 1422 1780 1779 1779 1778 1778 2136 2135 2135 2134 2134 2492 2491 2491 2489 2489 2848 2846 2846 2845 2845 3204 3202 3202 3200 3200 7461283 4192 7101 7470010 2919 8681 6800813 2946 5078 7209 10 9 8 7 6 356 356 355 355 ^5' 711 711 711 710 710 1067 1067 1066 1065 1065 1422 1422 1421 1420 1420 1778 1778 1777 1776 1775 2132 2133 2132 2131 2130 2489 2489 2488 2486 2485 2844 2844 2843 2841 2840 *3200 3200 3199 3196 3195 5827 8736 748164s 4554 7463 55 56 57 58 .59 60 9339 68 1 1 469 3599 5728 7856 9984 5 4 3 2 I M. 355 355 355 355 355 355 710 710 710 709 709 709 20" 1065 1065 1064 1064 1064 1064 1420 1420 1419 141S 1418 1418 1775 1775 1774 1773 1773 1773 2130 2130 2129 2128 2128 2127 2485 2485 2484 2482 2482 2482 2840 2840 2838 2837 2837 2836 31 31 31 31 31 31 95 95 93 91 91 91 7490372 3281 6190 9099 7502008 4916 M. ( o~,ine. 10" 30'' 40" 50'' 1 60" 70" 80" 90" Arc. 47 Degrees. 44 43 Degrees. Diflfeience for Seconds. M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. ' ire. o I 6819984 68221 1 1 60 59 355 354 709 709 1064 1063 1418 1417 1773 1772 2127 2126 2482 2480 2836 2834 3191 3189 7504916 7825 J^ Sec. Diff. 2 3 4237 6363 58 57 354 354 709 708 1063 1063 1417 1417 1772 1772 2126 2126 2480 2480 2834 2834 3189 3189 7510734 3643 48s 970 1454 1939 2424 2909 3394 4 8489 56 354 708 1062 1416 1771 2124 2479 2833 3187 6552 20 30 ? 6830613 55 354 708 1062 1416 1771 2125 2479 2833 3187 9461 6 2738 54 354 708 1061 1415 1769 2123 2477 2830 3184 7522370 40 7 4861 53 354 ! 708 1061 1415 1769 2123 2477 2830 3184 5279 50 8 6984 52 354 1 708 1061 1415 1769 2123 2477 2830 3184 8188 60 9 9107 51 354 707 1061 1414 1768 2122 2475 2829 3182 7531097 70 lO 6841229 50 354 707 1061 1414 1768 2121 2475 2828 3182 4005 80 3878 II 3350 49 354 707 1061 1414 1768 2121 2475 2828 3182 6914 90 4363 12 5471 48 353 707 1060 1413 1767 2120 2473 2826 3180 9823 1,3 7591 47 353 707 1 060 1413 1767 2120 2473 2826 3180 7542732 H 9711 46 353 706 1059 1412 1766 2119 2472 2825 3178 5641 15 6851830 45 353 706 1059 1412 1765 21 18 2471 2824 3177 8550 i6 3948 44 353 706 1059 1412 1765 2118 2471 2824 3177 7551459 17 6066 43 353 706 1059 1412 1765 2118 2471 2824 3177 4368 i8 8184 42 353 705 1058 1410 1763 21 16 2468 2821 3173 7277 19 6860300 41 353 705 1058 1410 1763 21 16 2468 2821 3173 7560186 20 2416 40 353 705 1058 1410 1763 2116 2468 2821 3173 3094 21 4532 39 353 705 1058 1410 1763 2115 2468 2820 3173 6003 22 6647 38 352 705 1057 1409 1762 2114 2466 2818 3171 8912 23 8761 37 352 705 1057 1409 1762 2114 2466 2818 3171 7571821 24 6870875 36 352 704 1056 1408 1761 2113 2465 2817 3169 4730 25 2988 35 352 704 1056 1408 1761 2113 2465 2817 3169 7639 26 5101 34 352 704 1056 1408 1760 2112 2464 2816 3168 7580548 27 7213 33 352 704 1056 1408 1760 2112 2464 2816 3168 3457 28 .„ 9325 32 352 704 1055 1407 1759 2110 2463 2814 3166 6366 29 6881435 31 352 704 1055 1407 1759 2111 2463 2814 3166 9275 30 3546 30 352 703 1055 1406 1758 2109 2461 2813 3164 7592183 31 5655 29 352 703 1055 1406 1758 2110 2461 2813 3164 5092 32 7765 28 351 703 1054 1405 1757 2108 2459 2810 3162 8001 33 .0 9^73 27 351 703 1054 1405 1757 2108 2459 2810 3162 7600910 34 689 I 98 I 2b 351 703 1054 1405 1757 2108 2459 2810 3162 3819 35 4089 25 351 702 IOS3 1404 1756 2106 2458 2809 3160 6728 36 6195 24 351 702 1053 1404 1756 2107 2458 2809 3160 9637 37 8302 23 351 702 1052 1403 1754 2105 2456 2807 3158 7612546 3« 6900407 22 351 702 1052 1403 1754 2105 2456 2807 3158 5455 39 2512 21 351 702 1052 1403 1754 2105 2456 2807 3158 8364 40 4617 20 351 701 1052 1402 1753 2104 2454 2805 3155 762 1 27 1 41 6721 19 351 701 1052 1402 1753 2103 2454 2804 3155 4180 42 8824 18 351 701 1052 1402 1753 2103 2454 2804 3155 7089 43 6910927 17 350 701 105 1 1401 1752 2102 2452 2802 3153 9998 44 3029 lb 350 701 105 1 1401 1752 2102 2452 2802 3153 7632907 45 5131 15 350 700 1050 1400 1751 2101 2451 2801 3151 5816 46 7232 14 350 700 1050 1400 1750 2100 2450 2800 3150 8725 47 9332 13 350 700 1050 1400 1750 2100 2450 2800 3150 7641634 48 6921432 12 350 700 1050 1399 1749 2099 2449 2798 3148 4543 49 50 3531 II 350 700 1049 1399 1749 2099 2449 2798 3148 7452 5630 10 305 ^99 1049 1398 1748 2098 2447 2797 3146 7650360 SI 7728 9 350 799 1049 1398 1748 2097 2447 2796 3146 3269 52 9825 8 350 799 1049 1398 1748 2097 2447 2796 3146 6178 53 6931922 7 349 799 1048 1397 1747 2096 2445 2794 3144 9087 54 4018 b 349 799 1048 1397 1747 2096 2445 2794 3144 7661996 55 61 14 5 349 698 1047 1396 1746 2095 2444 2793 3142 4905 i>^ 8209 4 349 698 1047 1396 1746 2095 2444 2793 3142 7814 57 6940304 3 349 698 1047 1396 1745 2094 2443 2792 3141 7670723 55 2398 2 349 698 1046 1395 1744 2093 2442 2790 3139 3632 59 4491 I 349 698 1046 1395 1744 2093 2442 2790 3139 6541 60 6584 349 697 1046 1394 1743 2092 2440 2789 3137 9449 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 46 Degrees. 44 Degrees. Difference for Seconds. t4f M. Sine. M. 10" 20" 30" 40 50" 60" 70" 80" 90" Arc. o I 2 3 4 6946584 8676 6950767 2858 4949 60 59 58 56 349 349 349 349 348 697 697 697 697 697 1046 1046 1046 1046 1045 1394 1394 1394 1394 1393 1743 1743 1743 1743 1742 2092 2091 2091 2091 2090 2440 2440 2440 2440 2438 2789 2788 2788 2788 2786 3137 3137 3137 3137 3135 7679449 7682358 5267 8176 7691085 Arc. Sec. Diff. 10 20 30 40 50 60 70 80 90 485 5 6 7 8 9 7039 9128 6961217 3305 5392 55 54 53 52 51 348 348 348 348 348 696 696 696 696 696 1044 1044 1044 1043 1043 1392 1392 1392 1391 1391 1 741 1 741 1740 1739 1739 2089 2089 2088 2087 2087 2437 2437 2436 2435 2435 2785 2785 2784 2782 2782 3133 3133 3132 3130 3130 3994 6903 9812 7702721 5630 970 1454 1939 2424 2909 lO II 12 13 H 7479 697 I 65 I 3736 5821 50 49 48 47 46 348 348 348 348 347 695 695 695 695 695 1043 1043 1043 1043 1042 1390 1390 1390 1390 1389 1738 1738 1738 1738 1737 2086 2086 2085 2085 2084 2433 2433 2433 2433 2431 2781 2781 2780 2780 2778 3128 3128 3128 3128 3126 8538 771 1447 4356 7265 7720174 3394 3878 4363 17 i8 19 7905 9988 6982071 4153 6234 45 44 43 42 41 347 347 347 347 347 694 694 694 694 694 1041 1041 1041 1040 1040 1388 1388 1388 1387 1387 1736 1736 1735 1734 1734 2083 2083 2082 2081 2081 2430 2430 2429 2428 2428 2777 2777 2776 2774 2774 3124 3124 3123 3121 3121 3083 5992 8901 7731810 4719 20 21 22 23 24 8315 6990396 2476 6633 40 39 38 37 36 347 347 347 346 346 694 693 693 693 693 693 692 692 692 692 1040 1040 1040 1039 1039 1387 1386 1386 1385 1385 1734 1733 1733 1732 1732 2081 2080 2079 2078 2078 2428 2426 2426 2424 2424 2774 2773 2772 2770 2770 3121 3119 3119 3117 3117 7627 7740536 3445 6354 9263 25 26 27 28 29 8711 7000789 2666 4942 7018 35 34 33 32 31 346 346 346 346 346 1039 1038 1038 1038 1037 1385 1384 1384 1384 1383 1732 1731 1730 1730 1729 2078 2077 2076 2076 2075 2424 2423 2422 2422 2421 2770 2769 2768 2768 2766 3117 31 15 3114 3114 3112 7752172 5081 7990 7760899 3808 30 31 32 33 34 9093 701 1 167 3241 5314 7387 30 29 28 27 26 346 346 346 346 345 691 691 691 691 691 1037 1037 1037 1037 1036 1382 1382 1382 1382 1381 1728 1728 1728 1728 1727 2074 2074 2073 2073 2072 2419 2419 2419 2419 2417 2765 2765 2764 2764 2762 3110 3110 3110 3110 3108 6716 9625 7772534 5443 8352 35 36 37 38 39 9459 702 1 53 1 3601 5672 7741 25 24 23 22 21 345 345 345 345 345 691 690 690 690 690 1036 1035 1035 1035 1035 1381 1380 1380 1380 1380 1727 1726 1726 1725 1725 2072 2070 2071 2069 2070 2417 2415 2415 2415 2415 2762 2760 2760 2760 2760 3107 3105 3105 3105 3105 7781261 4170 7079 9988 7792897 40 41 42 43 44 9811 7031879 3947 6014 8081 20 19 18 17 16 345 345 345 345 344 689 689 689 689 689 1034 1034 1034 1034 1033 1378 1378 1378 1378 1377 1723 1723 1723 1723 1722 2068 2068 2067 2067 2066 2412 2412 2412 2412 2410 2757 2757 2756 2756 2754 3101 3101 3101 3101 3099 5804 8713 7801622 4531 7440 45 46 47 48 49 7040147 2213 4278 6342 8406 15 14 13 12 II 344 344 344 344 344 689 688 688 688 688 1033 1032 1032 1032 103 1 1377 1376 1376 1376 1375 1722 1721 1720 1720 1719 2066 2065 2064 2064 2063 2410 2409 2408 2408 2407 2754 2753 2752 2752 2750 3099 3097 3096 3096 3094 7810349 3258 6167 9076 7821985 50 51 52 53 54 7050469 2532 4594 6655 8716 10 9 8 7 6 344 344 344 344 343 688 687 687 687 687 1031 103 1 1031 1031 1030 1375 1374 1374 1374 1373 1719 1718 1718 1718 1717 2063 2062 2061 2061 2060 2407 2405 2405 2405 2403 2750 2749 2748 2748 2746 3094 3092 3092 3092 3090 4893 7802 78307 1 1 3620 6529 55 56 57 58 59 60 7060776 2835 4894 6953 901 1 7071068 5 4 3 343 343 343 343 343 343 687 686 686 686 686 686 1030 1029 1029 1029 1028 1028 1373 1372 1372 1372 1371 1371 1717 1716 1716 1715 1714 1714 2059 2059 2059 2058 2057 2056 2403 2402 2402 2401 2400 2400 2746 2745 2745 2744 2742 2742 3090 3088 3088 3087 3085 3085 9438 7842347 5256 8165 7851074 3982 M. Cosine, j M. 10" 1 20" 30" 40" 50" 60" 70" 80" 90" Arc. 45 Degrees. 46] 45 Degrees. Difference for Seconds. M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o 7071068 60 343 685 685 1028 1028 1370 1713 2056 2056 2398 2398 2741 3083 7853982 Arc. I 3124 59 343 1370 1713 2741 3083 6891 * 2 5180 58 343 685 685 1028 1028 1370 1713 2056 2398 2398 2741 3083 9800 Sec. um. ^ 7236 57 343 1370 1713 2055 2740 3083 7862709 4 9291 56 342 685 1027 1369 1712 2054 2396 2738 3081 5618 10 20 30 40 50 60 485 ■; 7081345 55 342 684 1026 1368 1711 2053 2395 2737 3079 8527 970 1454 1939 6 3398 54 342 684 1026 1368 1711 2053 2395 2737 3079 7871436 7 5451 53 342 684 1026 1368 1711 2053 2395 2737 3079 4345 8 7504 52 342 684 1026 1368 1710 2052 2394 2736 3078 7254 2424 2909 3394 3878 9 9556 51 342 684 1025 1367 1709 2051 2393 2734 3076 7880163 70 80 lO 7091607 50 342 683 1025 1366 1708 2050 2391 2733 3074 3072 II 3657 49 342 683 1025 1366 1708 2050 2391 2733 3074 5981 90 4.-^6i 12 5707 48 342 683 1025 1366 1708 2050 2391 2733 3074 8890 13 7757 47 342 683 1025 1366 1708 2049 2391 2732 3074 7891799 14 9806 46 341 683 1024 1365 1707 2048 2389 2730 3072 4708 !■; 7101854 45 341 682 1023 1364 1706 2047 2388 2729 3070 7617 i6 3901 44 341 682 1023 1364 1706 2047 2388 2729 3070 7900526 17 5948 43 341 682 1023 1364 1706 2047 2388 2729 3070 3435 i8 7995 42 341 682 1023 1364 1705 2046 2387 2728 3069 6344 19 7110041 41 341 682 1022 1363 1704 2045 2386 2726 3067 9253 20 2086 40 341 681 1022 1362 1703 2044 2384 2725 3065 7912160 21 4130 39 341 681 1022 1362 1703 2044 2384 2725 3065 5069 22 6174 38 341 681 1022 1362 1703 2044 2384 2725 3065 7978 23 8218 37 341 681 1022 1362 1703 2042 2384 2724 3065 7920887 24 7120260 3b 341 681 1022 1362 1703 2043 2384 2724 3065 3796 2S 2303 35 340 680 1020 1360 1701 2041 2381 2721 3061 6705 26 4344 34 340 680 1020 1360 1701 2041 2381 2721 3061 9614 27 6385 33 340 680 1020 1360 1 701 2041 2381 2721 3061 7932523 28 8426 32 340 680 1019 1359 1699 2039 2379 2718 3058 5432 29 30 7130465 31 340 680 1019 1359 1699 2039 2379 2718 3058 8341 2504 30 340 680 1019 1359 1699 2039 2379 2718 3058 7941249 31 4543 29 340 679 1019 1358 1698 2038 2377 2717 3056 4158 •32 6581 28 340 679 1019 1358 1698 2037 2377 2716 3056 7067 33 8618 27 340 679 1019 1358 1698 2037 2377 2716 3056 9976 34 35 7140655 26 339 679 1018 1357 1697 2036 2375 2714 3054 7952885 2691 25 339 679 1018 1357 1697 2036 2375 2714 3054 5794 36 4727 24 339 678 1017 1356 1696 2035 2374 2713 3052 8703 37 6762 23 339 678 1017 1356 1695 2034 2373 2712 3051 7961612 3« 8796 22 339 678 1017 1355 1695 2034 2373 2712 3051 4521 39 40 7150830 21 339 678 1016 1355 1694 2033 2372 2710 3049 7430 2863 20 339 677 1016 1354 1693 2032 2370 2709 3047 7970338 41 4895 19 339 677 1016 1354 1693 2032 2370 2709 3047 3247 42 6927 18 339 677 1016 1354 1693 2032 2370 2709 3047 6156 43 8959 17 338 677 1015 1353 1692 2030 2368 2706 3045 9065 44 7160989 16 338 677 1015 1353 1692 2030 2368 2706 3045 7981974 45 3019 15 338 677 1015 1353 1692 2030 2368 2706 3045 4883 46 5049 14 338 676 1014 1352 1691 2029 2^,67 2705 3043 7792 47 7078 13 338 676 1014 1352 1690 2028 2366 2704 3042 7990701 48 9106 12 338 676 1014 1352 1690 2028 2366 2704 3042 3610 49 50 7171134 II 338 676 1013 1351 1689 2027 2365 2702 3040 6519 3161 10 338 675 1013 1350 1688 2026 2363 2701 3038 9427 51 5187 9 338 675 1013 1350 1688 2026 2363 2701 3038 8002336 52 7213 8 338 675 1013 1350 1688 2025 2363 2700 3038 5245 53 9238 7 338 675 • 1013 1350 1688 2025 2363 2700 3038 8154 54 7181263 6 337 675 1012 1349 1687 2024 2361 2698 3036 8011063 55 3287 5 337 674 lOII 1348 1686 2023 2360 2697 3034 3972 50 5310 4 337 674 ion 1348 1686 2023 2360 2697 3034 6881 57 7333 3 337 674 ion 1348 1685 2022 2359 2696 3033 9790 5« 9355 2 337 674 lOII 1348 1685 2022 2359 2696 3033 8022699 59 7191377 I 337 674 lOIO 1347 1684 2021 2358 2694 3031 5608 60 3398 337 673 lOIO 1346 1683 2020 2356 2693 3029 8515 M. Cosine. M. 10" 20" 30" 40'' 50" 6a" 70" 80" 90" Arc. 44 Degrees. 46 Degrees. Difference for Seconds. [4*7 M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o 7193398 60 337 673 lOIO 1346 1683 2020 2356 2693 3029 8028515 Arc. I 2 5418 7438 59 58 337 337 673 673 lOIO lOIO 1346 1346 1683 1683 2020 2019 2356 2356 2693 2692 3029 3029 8031424 4333 Co/- 1 T"\:«" 3 4 9457 7201476 57 56 337 336 673 673 lOIO 1009 1346 1345 1683 1682 2019 2018 2356 2354 2692 2690 3029 3027 7242 80401 5 1 10 20 485 970 ■; 3494 55 336 672 1008 1344 1681 2017 2353 2689 3025 3060 6 5511 54 336 672 1008 1344 1681 2017 2353 2689 3025 5969 •^0 1454 1939 2424 7 7528 53 336 672 1008 1344 1680 2016 2352 2688 3024 8878 40 8 9544 52 336 672 1007 1343 1679 2015 2351 2686 3022 8051787 50 9 7211559 51 336 672 1007 1343 1679 2015 2351 2686 3022 4696 60 70 2909 lO 3574 50 336 671 1007 1343 1679 2015 2351 2686 3022 7604 3394 II 5589 49 336 671 1007 1342 1678 2013 2349 2684 3020 8060513 80 3878 12 7602 48 336 671 1007 1342 1678 2013 2349 2684 3020 3422 90 4363 n 9615 47 336 671 1007 1342 1678 2013 2349 2684 3020 6331 14 7221628 46 335 671 1006 1341 1677 2012 2347 2682 3018 9240 IS 3640 45 335 670 1005 1340 1676 201 1 2346 2681 3016 8072149 i6 5651 44 335 670 1005 1340 1675 2010 2345 2680 3015 5058 17 7661 43 335 670 1005 1340 1675 2010 2345 2680 3015 7967 i8 9671 42 335 670 1005 1340 1675 2010 2345 2680 3015 8080876 19 7231681 41 335 670 1004 1339 1674 2009 2344 2678 3013 3785 20 3690 40 335 669 1004 1338 1673 2008 2342 2677 301 1 6693 21 5698 39 335 669 1004 1338 1673 2007 2342 2677 301 1 9602 22 7705 38 335 669 1004 1338 1673 2007 2342 2677 301 1 80925 1 1 23 9712 37 335 669 1004 1338 1673 2007 2342 2677 3011 5420 24 7241719 36 334 668 1002 1336 1671 2005 2339 2673 3007 8329 2S 3724 35 334 668 1002 1336 1671 2005 2339 2673 3007 8101238 26 5729 34 334 668 1002 1336 1671 2005 2339 2673 3007 4147 27 7734 33 334 668 1002 1336 1670 2004 2338 2672 3006 7056 28 9738 32 334 668 lOOI 1335 1669 2003 2337 2670 3004 9965 29 7251741 31 334 668 lOOI 1335 1669 2003 2337 2670 3004 81 12874 30 3744 30 334 667 lOOI 1334 1668 2002 2335 2669 3002 5782 31 5746 29 334 667 lOOI 1334 1668 2001 2335 2668 3002 8691 32 7747 28 334 667 lOOI 1334 1668 2001 2335 2668 3002 8121600 33 9748 27 333 667 1000 1333 1667 2000 2333 2666 3000 4509 34 7261748 26 333 667 1000 1333 1667 2000 2333 2666 3000 7418 8130327 3"; 3748 25 333 666 999 1332 1666 1999 2332 2665 2998 36 5747 24 333 666 999 1332 1665 1998 2331 2664 2997 3236 37 7745 23 333 666 999 1332 1665 1998 2331 2664 2997 6145 38 9743 22 333 666 998 1331 1664 1997 2330 2662 2995 9054 39 7271740 21 333 665 998 1330 1663 1996 2328 2661 2993 8141963 40 3736 20 333 665 998 1330 1663 1996 2328 2661 2993 4871 41 5732 19 333 665 998 1330 1663 1996 2328 2661 2993 7780 42 7728 18 332 665 997 1329 1662 1994 2326 2658 2991 8150689 43 9722 17 332 665 997 1329 1662 1994 2326 2658 2991 3598 44 7281716 16 332 665 996 1329 1662 1994 2326 2658 2991 6507 4? 3710 15 332 664 996 1328 1661 1993 2325 2657 2989 9416 46 5703 14 332 664 996 1328 1660 1992 2324 2656 2988 8162325 47 7695 13 332 664 995 1327 1659 1991 2323 2654 2986 5234 48 9686 12 332 664 995 1327 1659 1991 2323 2654 2986 8143 49 7291677 II 332 664 995 1327 1659 1991 2323 2654 2986 8171052 50 3668 10 332 663 995 1326 1658 1989 2321 2652 2984 3960 51 5657 9 332 663 995 1326 1658 1989 2321 2652 2984 6869 52 7646 8 332 663 995 1326 1658 1989 2321 2652 2984 9778 53 9635 7 331 663 994 1325 1657 1988 2319 2650 2982 8182687 54 55 7301623 6 331 662 993 1324 1656 1987 2318 2649 2979 5596 3610 5 331 662 993 1324 1656 1987 2318 2649 2979 8505 56 5597 4 331 662 993 1324 1655 1986 2317 2648 2979 8191414 57 7583 3 331 662 992 1323 1654 1985 2316 2646 2977 4323 5« 9568 2 331 662 992 1323 1654 1985 2316 2646 2977 7232 59 7311553 I 331 661 992 1322 1653 1984 2314 2645 2975 8200141 60 3537 331 661 992 1322 1653 1984 2314 2645 2975 3048 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 43 Degrees. 48] 47 Degrees l< Difference for Seconds. M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o I 7313537 5521 60 59 331 330 661 661 .992 991 1322 1321 1653 1652 1984 1982 2314 2313 2645 2643 2975 2974 8203047 5956 Arc. 2 7503 58 330 661 991 1321 1652 1983 2313 2643 2974 8865 Sec. urn. 3 9486 57 330 661 991 1321 1652 1981 2312 2642 2973 82 1 1 774 4 7321467 56 330 661 991 1321 1652 1982 2312 2642 2973 4683 10 20 485 5 3449 55 330 660 990 1320 1650 1980 2310 2640 2970 7592 970 6 5429 54 330 660 990 1320 1650 1980 2310 2640 2970 8220501 30 1454 7 7409 53 330 660 989 1319 1649 1979 2309 2638 2968 3410 40 1939 8 9388 52 330 660 989 1319 1649 1979 2309 2638 2968 6319 50 60 70 80 2424 9 lO mn^i 51 330 659 989 1318 1648 1978 2307 2667 2966 9228 2909 3394 3878 4363 3345 50 330 659 989 1318 1648 1977 2307 2636 2966 8232136 II 5322 49 330 659 989 1318 1648 1977 2307 2636 2966 5045 90 12 7299 48 329 659 988 1317 1647 1976 , 2305 2634 2964 7954 13 9275 47 329 658 987 1316 1646 1975 2304 2633 2962 8240863 15 7341250 46 329 658 987 1316 1646 1975 2304 2633 2962 3772 3225 45 329 658 987 1316 1645 1974 2303 2632 2961 6681 16 5 199 44 329 658 987 1316 1645 1974 2303 2632 2961 9590 17 7173 43 329 658 986 1315 1644 1973 2302 2630 2959 8252499 i8 9146 42 329 657 986 1314 1643 1972 2300 2629 2957 5408 19 735 1 1 18 41 329 657 986 1314 1643 1972 2300 2629 2957 8317 20 3090 40 329 657 986 1314 1643 1971 2300 2628 2957 8261225 21 5061 39 329 657 986 1314 1643 1971 2300 2628 2957 4134 22 7032 38 328 657 985 1313 1642 1970 2298 2626 2955 7043 23 9002 yi 328 656 984 1312 1641 1969 2297 2625 2953 9952 24 7360971 36 328 656 984 1312 1641 1969 2297 2625 2953 8272861 25 . 2940 35 328 656 984 1312 1640 1968 2296 2624 2952 5770 26 4908 34 328 656 983 1311 1639 1967 2295 2622 2950 8679 27 6875 33 328 656 983 1311 1639 1967 2295 2622 2950 8281588 28 ^ 8842 32 328 655 983 1310 1638 1966 2293 2621 2948 4497 29 7370808 31 328 655 983 1310 1638 1965 2293 2620 2948 7406 30 2773 30 328 655 983 1310 1638 1965 2293 2620 2948 8290314 31 4738 29 328 655 983 1310 1638 1965 2293 2620 2948 3223 32 6703 28 327 654 981 1308 1636 1963 2290 2617 2944 6132 33 8666 27 327 654 981 1308 1636 1963 2290 2617 2944 9041 34 7380629 26 327 654 981 1308 1636 1963 2290 2617 2944 8301949 35 2592 25 327 654 981 1308 163s 1961 2289 2616 2943 4858 36 4553 24 327 654 981 1308 1635 1962 2289 2616 2943 7767 37 6515 23 327 653 980 1306 1633 i960 2286 2613 2939 8310676 3« 8475 22 327 653 980 1306 1633 i960 2286 2613 2939 3585 39 7390435 21 327 653 980 1306 1633 1633 1959 2286 2612 2939 6494 40 2394 20 327 653 980 1306 1959 2286 2612 2939 9403 41 4353 19 326 653 979 1305 1632 1958 2284 2610 2937 8322312 42 63 II 18 326 652 978 1304 163 1 1957 2283 2609 2935 5221 43 8268 17 326 6S2 978 1304 1631 1957 2283 2609 2935 8130 44 7400225 16 326 652 978 1304 1630 1956 2282 2608 2934 8331039 45 2181 15 326 652 978 1304 1630 1956 2282 2608 2934 3948 46 4137 14 326 6^2 977 1303 1629 1955 2281 2606 2932 6857 47 6092 13 326 651 977 1302 1628 1954 2279 2605 2930 9766 48 8046 12 326 651 977 1302 1628 1954 2279 2605 2930 8342675 49 7410000 II 326 651 977 1302 1628 1953 2279 2604 2930 5584 SO 1953 10 325 651 976 1301 1627 1952 2277 2602 2928 8492 51 3905 9 325 651 976 1301 1627 1952 2277 2602 2928 8351401 52 5857 8 325 650 975 1300 1626 1951 2276 2601 2926 4310 53 7808 7 325 650 975 1300 1625 1950 2275 2600 2925 7219 54 55 9758 6 325 650 975 1300 1625 1625 1950 2275 2600 2925 8360128 7421708 5 325 650 975 1300 1950 2275 2600 2925 3037 5^ 3658 4 325 649 974 1298 1623 1948 2272 2597 2921 5946 57 5606 3 325 649 974 1298 1623 1948 2272 2597 2921 8855 5« 7554 2 325 649 974 1298 1623 1948 2272 2597 2921 8371764 59 9502 I 324 649 973 1297 1622 1946 2270 2594 2919 4673 60 M. 7431448 324 649 973 1297 1622 1946 2270 2594 2919 7580 Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 42 De. Difference for Seconds. M. Sine. iM. 10" 20" 30" 40" so" 60" 70" 80" 90" Arc. 959931 1 9602220 o I 8191520 3189 60 59 278 278 556 556 834 833 II12 mi 1391 1389 1669 1667 1947 1945 2225 2222 2503 2500 Arc. Sec. ^ 2 3 4856 6523 58 57 278 278 556 555 833 833 nil mo 1389 1388 1667 1666 1945 1943 2222 2221 2500 2498 5129 8038 Diff. 485 ' 4 8189 56 278 555 833 mo 1388 1665 1943 2220 2498 9610947 10 20 30 40 50 60 5 6 7 8 9854 8201519 3183 4846 55 54 53 52 278 277 277 277 555 555 554 554 833 832 831 831 mo 1109 1 108 1 108 1388 1387 1386 1386 1665 1664 1663 1663 1943 1 941 1940 1940 2220 2218 2217 2217 2498 2496 2494 2494 3856 6765 9674 9622583 970 1454 1939 2424 2909 3394 3878 9 6509 51 277 554 830 1107 1384 1661 1939 2216 2493 5492 70 80 lO 8170 50 277 554 830 1 107 1384 1662 1939 2216 2493 9628400 II 9832 49 277 553 830 1 106 1383 1660 1936 2213 2489 9631309 90 4363 12 821 1492 48 277 553 830 1 106 1383 1660 1936 2213 2489 4218 n 3152 47 277 553 830 1 106 1383 1659 1936 2212 2489 7127 14 481 1 46 276 553 829 1 105 1382 1658 1934 2210 2487 9640036 I? 6469 45 276 553 829 1 105 1382 1658 1934 2210 2487 2945 i6 8127 44 276 552 828 1 104 1381 1657 1933 2209 2485 5854 17 9784 43 276 552 828 1 104 1380 1656 1932 2208 2484 8763 i8 8221440 42 276 552 828 1 104 1380 1656 1932 2208 2484 9651672 19 20 3096 41 276 552 827 1 103 1379 1655 1 93 1 2206 2482 4581 4751 40 276 551 827 no2 1378 1654 1929 2205 2480 9657489 21 6405 39 276 551 827 1 102 1378 1654 1929 2205 2480 9660398 22 8059 38 276 551 827 1 102 1378 1653 1929 2204 2480 3307 23 9712 Zl 27s 551 826 1 102 1377 1652 1927 2202 2478 6216 24 8231364 36 275 550 825 IIOO 1376 1651 1926 2201 2476 9125 2? 3015 35 275 550 82s IIOO 1376 165 1 1926 2201 2476 9672034 26 4666 34 275 550 825 IIOO 1375 1650 1925 2200 2475 4943 27 6316 33 275 550 825 1099 1374 1649 1924 2198 2473 7852 28 7965 32 275 550 824 1099 1374 1649 1924 2198 2473 9680761 29 9614 31 275 549 824 1098 1373 1648 1 1922 2197 2471 3670 ,30 8241262 30 275 549 824 1098 1373 1647 1922 2196 2471 9686578 31 2909 29 275 549 824 1098 1373 1647 1922 2196 2471 9487 32 4556 28 274 549 823 1097 1372 1646 1920 2194 2469 9692396 33 6202 27 274 548 822 1096 1371 1645 1919 2193 2467 5305 34 3S 7847 26 •274 548 822 1096 1370 1644 1918 2192 2466 8214 9491 25 274 548 822 1096 1370 1644 1918 2192 2466 9701 123 36 8251 135 24 274 548 821 1095 1369 1643 1917 2190 2464 4032 37 2778 23 274 547 821 1094 1368 1642 1915 2189 2462 6941 3» 4420 22 274 547 821 1094 1368 1642 1915 2189 2462 9850 39 40 6062 21 274 547 821 1094 1368 1641 1915 2188 2462 9712759 7703 20 273 547 820 1093 1367 1640 1913 2x86 2460 5667 41 9343 19 273 547 820 1093 1367 1640 1913 2186 2460 8576 42 8260983 18 273 546 819 1092 1366 1639 1912 2185 2458 9721485 43 2622 17 273 546 819 1092 1365 1638 1911 2184 2457 4394 44 4260 16 273 546 818 1091 1364 1637 1910 2182 2455 7303 4=; 5897 15 273 546 818 1091 1364 1637 1910 2182 2455 9730212 46 7534 14 273 545 818 1091 1364 1636 1908 2181 2453 3121 47 9170 13 273 545 818 1090 1363 1 636 1908 2181 2453 6030 48 8270806 12 272 545 817 1089 1362 1634 1906 2178 2451 8939 49 2440 II 272 545 817 1089 1362 1634 1906 2178 2451 9741848 4074 10 272 545 817 1089 1362 1634 1906 2178 2451 4755 SI 5708 9 272 544 816 1088 1360 1632 1904 2176 2448 7664 52 7340 8 272 544 816 1088 1360 1632 1904 2176 2448 9750573 53 8972 7 272 544 815 1087 1359 163 1 1903 2174 2446 3482 54 55 8280603 6 272 544 815 1087 1359 163 1 1903 2174 2446 6391 2234 5 272 543 815 1086 1358 1630 1901 2173 1 2444 9300 56 3864 4 272 543 815 1086 1358 1629 1901 2172 2444 9762209 57 5493 3 271 543 814 1085 1357 1628 1899 2170 2442 5118 5« 7121 2 271 543 814 1085 1357 1628 1899 2170 24-42 8027 59 8749 I 271 542 813 1084 1356 1627 1898 2169 2440 9770936 60 M. 8290376 271 542 813 1084 1355 1626 1897 2168 2439 3844 Cosine. M. 10" 20" 30" 40". 50" 60" 70" 1 80" 90" Arc. 34 Degrees. 56 Degrees. Difference for Seconds. [5- M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o I 8290376 2002 60 S9 271 271 542 542 813 813 1084 1084 1355 1355 1626 1626 1897 1897 2168 2168 2439 2439 9773844 6753 Arc. "> 2 3 3628 5252 58 57 271 271 541 541 812 812 1082 1082 1353 1353 1624 1625 1894 1894 2165 2165 2435 2435 9662 8782571 Sec. Ultt. 4 6877 56 271 541 812 1082 1353 1623 1894 2164 2435 5480 10 20 30 40 50 60 485 5 8500 55 271 541 812 1082 1353 1623 1894 2164 2435 8389 970 1454 1939 2424 2909 3394 3878 6 8300123 54 270 541 811 1081 1352 1622 1892 2162 2433 8791298 7 1745 53 270 540 810 1080 1351 1621 1891 2161 2431 4207 8 3366 52 270 540 810 1080 1351 1621 1891 2161 2431 7116 9 4987 51 270 540 810 1080 1350 1620 1890 2160 2430 9800025 70 80 lO 6607 50 270 540 809 1079 1349 1619 1889 2158 2428 9802933 II 8226 49 270 540 809 1079 1349 1619 1889 2158 2428 5842 90 4.'^6^ 12 9845 48 270 539 809 1078 1348 1618 1887 2157 2426 8751 13 83 II 463 47 270 539 809 1078 1348 1617 1887 2156 2426 98 II 660 14 3080 46 269 539 808 1077 1347 1616 1885 2154 2424 4569 I? 4696 45 269 539 808 1077 1347 1616 1885 2154 2424 7478 i6 6312 44 269 538 807 1076 1346 1615 1884 2153 2422 9820387 17 7927 43 269 538 807 1076 1345 1614 1883 2152 2421 3296 i8 9541 42 269 538 807 1076 1345 1614 1883 2152 2421 6205 19 8321155 41 269 538 806 1075 1344 1613 1882 2150 2419 9114 20 2768 40 269 537 806 1074 1343 1612 1880 2149 2417 9832022 21 4380 39 269 537 806 1074 1343 1611 1880 2148 2417 4931 22 5991 38 269 537 806 1074 1343 1611 1880 2148 2417 7840 23 7602 37 268 537 805 1073 1342 1610 1878 2146 2415 9840749 24 9212 36 268 537 805 1073 1342 1610 1878 2146 2415 3658 2S 8330822 35 268 536 804 1072 1340 1608 1876 2144 2412 6567 26 2430 34 268 536 804 1072 1340 1608 1876 2144 2412 9476 27 4038 33 268 536 804 1072 1340 1608 1876 2144 2412 9852385 28 5646 32 268 535 803 1070 1338 1606 1873 2141 2408 5294 29 30 7252 31 268 535 803 1070 1338 1606 1873 2141 2408 8203 8858 30 268 535 803 1070 1338 1605 1873 2140 2408 9861 1 1 1 31 8340463 29 268 535 803 1070 1338 1605 1873 2140 2408 4020 32 2068 28 . 267 535 802 1069 1337 1604 1871 2138 2406 6929 33 3672 27 267 534 801 1068 1336 1603 1870 2137 2404 9838 34 3'; 5275 26 267 534 801 1068 1335 1602 1869 2136 2403 9872747 6877 25 267 534 801 1068 1335 1602 1869 2136 2403 5656 36 8479 24 267 534 800 1067 1334 1601 1868 2134 2401 8565 37 8350080 23 267 533 800 1066 1333 1600 1866 2133 2399 9881474 38 1680 22 267 533 800 1066 1333 1599 1866 2132 2399 4383 39 3279 21 267 533 800 1066 1333 1599 1866 2132 2399 7292 40 4878 20 266 533 799 1065 1332 1598 1864 2130 2397 9890200 41 6476 19 266 533 799 1065 1332 1598 I 1864 2130 2397 3109 42 8074 18 266 532 798 1064 1330 1596 1862 2128 2394 6018 43 9.670 17 266 532 798 1064 1330 1596 1862 2128 2394 8927 44 8361266 16 266 532 798 1064 1330 1596 1862 2128 2394 9901836 4'; 2862 15 266 531 797 1062 1328 1594 1859 2125 2390 4745 46 4456 14 266 531 797 1062 1328 1594 1859 2125 2390 7654 47 6050 13 266 531 797 1062 1328 1593 1859 2124 2390 9910563 48 7643 12 266 531 797 1062 1328 1593 1859 2124 2390 3472 49 9236 II 265 530 795 1060 1326 1591 1856 2121 2386 6381 SO 8370827 10 26^ 530 795 1060 1326 1 591 1856 2121 2386 9919288 SI 2418 9 26.; 530 795 1060 1326 1591 1856 2121 2386 9922197 S2 4009 8 265 530 794 1059 1324 1589 1854 2118 2383 5106 S3 5598 7 265 530 794 1059 1324 1589 1854 2118 2383 8015 54 7187 6 265 529 794 1058 1323 1588 1852 2117 2381 9930924 ss 8775 S 265 529 794 1058 1323 1588 1852 2117 2381 3833 S6 8380363 4 26? 529 794 1058 1323 1587 1852 2116 2381 6742 S7 1950 3 264 529 793 1057 1322 1586 1850 2114 2379 9651 S8 3536 2 264 S28 792 1056 1321 1585 1849 2113 2377 9942560 S9 5121 I 264 S28 792 1056 1321 1585 1849 2113 2377 5469 60 6706 264 528 792 1056 1320 1584 1848 2112 2376 8377 M. Cosine. M. 10" 20" 30" 40" so" 60" 70" 80" 90" Arc. 33 Degrees. 58] 57 Degrees. Difference for Seconds. M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o 8386706 60 264 528 792 1056 1320 1584 1848 2112 2376 9948377 Arc. A I 2 8290 9873 59 S8 264 264 528 527 791 791 1055 1054 1319 1318 1583 1582 1847 1845 2110 2109 2374 2372 9951286 4195 Cpp i^;ec 3 4 8391455 3037 57 56 264 263 527 527 791 791 1054 1054 1318 1318 1582 1581 1581 1845 1845 2109 2108 2372 2372 7104 9960013 10 20 485 970 1454 1939 24.24. S 4618 55 263 527 791 1054 1318 1845 2108 2372 2922 6 6199 54 263 526 789 1052 1316 1579 1842 2105 2368 5831 30 40 7 7778 53 263 526 789 1052 1316 1579 1842 2105 2368 8740 8 9357 52 263 526 789 1052 1316 1579 1842 2105 2368 9971649 l^O 9 8400936 51 263 526 788 1051 1314 1577 1840 2102 2365 4558 60 70 290Q 339^ lO 2513 50 263 526 788 105 1 1314 1577 1840 2102 2365 9977466 II 4090 49 263 525 788 1050 1313 1576 1838 2101 2363 9980375 80 3878 12 5666 48 263 525 788 1050 1313 1575 1838 2100 2363 3284 90 4363 n 7241 47 263 525 788 1050 1313 1575 1838 2100 2363 6193 14 8816 46 262 525 787 1049 1312 1574 1836 2098 2361 9102 M 8410390 45 262 524 786 1048 1311 1573 1835 2097 2359 999201 1 i6 1963 44 262 524 786 1048 1311 1573 1835 2097 2359 4920 17 3536 43 262 524 786 1048 1310 1572 1834 2096 2358 7829 i8 5108 42 262 524 785 1047 1309 1571 1833 2094 2356 1-0000738 19 6679 41 262 523 785 1046 1308 1570 1831 2093 2354 3647 20 8249 40 262 523 785 1046 1308 1570 1831 2093 2354 6555 21 9819 39 262 523 785 1046 1308 1569 1831 2092 2354 9464 22 8421388 38 261 523 784 1045 1307 1568 1829 2090 2352 1-0012373 2-X, 2956 37 261 523 784 1045 1307 1568 1829 2090 2352 5282 24 2? 4524 36 261 522 783 1044 1306 1567 1828 2089 235^ 8191 6091 35 261 522 783 1044 1305 1566 1827 2088 2349 I -0021 100 26 7657 34. 261 522 782 1043 1304 1565 1826 2086 2347 4009 27 9222 33 261 522 782 1043 1304 1565 1826 2086 2347 6918 28 8430787 32 261 521 782 1042 1303 1564 1824 2085 2345 9827 29 2351 31 261 521 782 1042 1303 1563 1824 2084 2345 1-0032736 30 3914 30 261 521 782 1042 1303 1563 1824 2084 2345 5644 31 5477 29 260 521 781 104 1 1302 1562 1822 2082 2343 8553 32 7039 28 260 520 780 1040 1 301 1561 1821 2081 2341 1-0041462 33 8600 -27; 260 520 780 1040 1 301 1 561 1821 2081 2341 4371 34 8440161 26 260 520 779 1039 1299 1559 1819 2078 2338 7280 3S 1720 25 260 520 779 1039 1299 1559 1819 2078 2338 I -0050189 ' 36 3279 24 260 520 779 1039 1299 1559 1819 2078 2338 3098 37 4838 23 260 519 779 1038 1298 1557 1817 2076 2336 6007 38 639s 22 260 519 779 1038 1298 1557 1817 2076 2336 8916 39 40 7952 21 259 519 778 1038 1297 1556 1815 2074 2334 1-0061825 9508 20 259 519 778 1038 1297 1556 1815 2074 3334 4732 41 8451064 19 259 518 in 1036 1295 1554 1813 2072 2331 7641, 42 2618 l8. 259 518 in 1036 1295 1554 1813 2072 2331 1-0070550 43 4172 17 259 518 777 1036 1295 1554 1813 2072 2331 3459 44 5726 16 259 517 77b 1034 1293 1552 1810 2069 2327 6368 \S 7278 15 259 517 776 1034 1293 1552 1810 2069 2327 9277 46 8830 14 259 517 776 1034 1293 1551 1810 2068 2327 I -0082 1 86 47 8460381 J 3 259 517 77b 1034 1293 1551 1810 2068 2327 509s 48 1932 12 2<;8 516 77\ 1032 1291 1549 1807 2065 2323 8004 49 3481 II 258 •516 77A 1032 1291 1549 1807 2065 2323 2323 I -0090913 3821 50 5030 10 2^8 516 77\ 1032 1291 1549 1807 2065 51 6579 9 2S8 516 773 103 1 1289 1547 1805 2062 2320 6730 52 8126 8 2S8 516 772, 103 1 1289 1547 1805 2062 2320 9639 S3 - 9673 7 258 515 773 1030 1288 1546 1803 2061 2318 1-0102548 54 847 1 2 19 6 258 515 773 1030 1288 1546 1803 2061 2318 5457 55 2765 5 257 515 772 1029 1287 1544 1801 2058 2316 8366 56 4309 4 257 515 772 1029 1287 1544 1801 2058 2316 1-0111275 57 5853 3 257 51s 772 1029 1287 1544 1801 2058 2316 4184 58 7397 2 257 514 771 1028 1285 1542 1799 2056 2313 7093 59 • 8939 I 257 514 771 1028 1285 1542 1799 2056 2313 ro 1 20002 60 8480481 257 514 770 1027 1284 1541 1798 1 2054 23 II 2910 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 32 Degrees. 58 Degrees. Difference for Seconds. \5i M. Sine. M. 10" 20" 30' 40" [ 50" j 60" 70" 80" 90" Arc. o I 2 3 4 8480481 2022 3562 5102 6641 60 59' 58 57 56 257 257 257 257 256 514 513 513 513 513 770 770 770 770 769 1027 1026 1026 1026 1025 X284 1283 1283 1283 1282 1 541 1540 1540 1539 1538 1798 1796 1796 1796 1794 2054 2053 2053 2052 2050 231 1 2309 2309 2309 2307 1-0122910 5819 8728 1-0131637 4546 Arc. A Sec. Diff. 10 20 30 40 50 60 70 80 90 485 I 7 8 __9. |o II 12 13 8179 9717 8491254 2790 4325 55 54 53 52 51 256 256 256 256 256 513 512 512 512 512 769 768 768 767 767 1025 1024 1024 1023 1023 1282 1281 1280 1279 1279 1538 1537 1536 1535 1535 1794 1793 1792 1 791 I79I 2050 2049 2048 2046 2046 2307 2305 2304 2302 2302 2300 2300 2298 2298 2296 7455 1-0140364 3273 6182 9091 970 1454 1939* 2424- 2909 5860 7394 8927 8500459 1991 50 49 48 47 46 256 256 255 255 255 511 5" 511 511 510 767 767 766 766 765 1022 1022 I02I I02I 1020 1278 1278 1277 1277 1276 1534 1533 1532 1532 1531 1789 1789 1787 1787 1786 2045 2044 2042 2042 2041 1-0151999 4908 7817. I -0160726 3635 3394 3878 436s IS i6 17 i8 19 3522 5053 6582 8111 9639 45 44 43 42 41 255 255 255 255 255 510 510 510 509 509 765 764 764 764 764 1020 IOI9 IOI9 IOI8 IOI8 1276 1274 1274 1273 1273 1531 1529 1529 1528 1528 1786 1784 1784 1782 1782 2041 2038 2038 2037 2037 2296 2293 2293 2291 2291 6544 9453 1-0172362 5271 8180 20 21 22 23 24 8511167 2693 4219 5745 7269 40 39 38 37 36 254 254 254 254 254 509 509 .509 508 508 763 763 763 762 762 IOI7 IOI7 IOI7 IO16 IOI6 1272 1272 1272 1270 1270 1526 1526 1526 1524 1524 1780 1780 1780 1778 1778 2034 2034 2034 2032 2032 2289 2289 2289 2286 2286 I -018 1 088 3997 6906 9815 I -0192724 26 27 28 29 8793 8520316 1839 3360 4881 35 34 33 32 31 254 254 254 254 254 508 508 507 507 507 761 761 761 761 761 IOI5 IOI5 IOI4 IOI4 IOI4 1269 1269 1268 1268 1268 1523 1523 1521 1521 1521 1777 1777 1775 1775 .1775 2030 2030 2028 2028 2028 2284 2284 2282 2282 2282 5633 8542 1-0201451 4360 7269 30 31 32 33 34 6402 7921 9440 8530958 2475 30 29 28 27 26 253 253 253 253 253 506 506 506 506 506 759 759 759 758 758 IOI2 IOI2 IOI2 ion lOII 1266 1266 1265 1264 1264 1519 1519 1518 1517 1517 1772 1772 I77I 1770 1770 2025 2025 2024 2022 2022 2278 2278 2277 2275 2275 I -02 10 1 77 3086 5995 8904 ro22i8i3 35 36 37 38 39 3992 5508 7023 8538 854005 1 25 24 23 22 21 253 253 253 252 252 505 505 505 504 504 758 758 756 756 lOIO lOIO lOIO 1008 1008 1263 1263 1263 1261 1261 1516 1515 1515 1513 1513 1768 1768 1768 1765 1765 2021 2020 2020 2017 2017 2273 2273 2273 2269 2269 4722 7631 1-0230540 3449 6358 40 41 42 43 44 1564 3077 4588 6099 7609 20 19 18 17 16 252 252 252 252 252 504 504 504 503 503 756 755 755 755 755 1008 1007 1007 1006 1006 1261 1259 1259 1258 1258 1513 1511 1511 1510 1510 1765 1763 1763 1 761 I76I 2017 2014 2014 2013 2013 2269 2266 2266 2264 2264 9265 1-0242174 5083 7992 I -02 5090 1 46 47 48 49 9119 8550627 2135 3643 5149 15 14 13 12 II 251 251 251 251 251 503 503 503 502 502 754 754 754 753 753 1005 1005 1005 1004 1004 1257 1257 1257 1255 1255 1508 1508 1508 1506 1506 1759 1759 1759 1757 1757 2010 2010 2010 2008 2008 2262 2262 2262 2259 2259 3810 6719 9628 1-0262537 5446 50 SI 52 53 54 ^^|5 8160 9664 8561168 2671 10 9 8 7 6 251 251 251 251 250 502 501 501 501 501 752 752 752 752 751 1003 1002 1002 1002 lOOI 1254 1253 1253 1253 1252 1505 1504 1504 1503 1502 1756 1754 1754 1754 1752 I75I I75I 1750 1749 1749 1747 2006 2005 2005 2004 2002 2001 2001 2000 1998 1998 1997 2257 2255 2255 2255 2253 8354 1-0271263 4172 . 7081 9990 55 56 57 58 59 60 4173 5674 717s 8675 8570174 1673 5 4 3 2 I 250 250 250 250 250 250 500 500 500 500 500 499 750 750 750 749 749 749 1000 1000 1000 999' 999 998 . 1251 1251 1250 1249 1249 1248 1501 1501 1500 1499 1499 1498 2251 2251 2250 2248 2246 2246 1-0282899 5808 8717 1-0291626 4535 7443 M. Cosine, j M. 10" 20" 1 30" 40" 50" 60 70" j 80" 1 90" Arc. 31 Degrees. 60] 59 Degrees • Difference for Seconds. M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" j 90" Arc. o I 8571673 3171 60 59 250 250 499 499 749 749 998 998 1248 1248 1498 1497 1747 1747 1997 1996 2246 2246 1-0297443 1-0300352 Arc. A Sec. Diff. 2 3 4668 6164 58 57 249 249 499 499 748 748 997 997 1247 1247 1496 1496 1745 1745 1994 1994 2244 2244 3261 6170 485 970 1454 4 7660 56 249 498 747 996 1246 1495 1744 1993 2242 9079 20 30 5 9155 55 249 498 747 996 1245 1494 1743 1992 2241 1-0311988 6 8580649 54 249 498 747 996 1245 1494 1743 1992 2241 4897 40 IQ39 7 2143 53 249 497 746 994 1243 1492 1740 1989 2237 7806 50 2424 8 3635 52 249 497 746 994 1243 1492 1740 1989 2237 I -03 207 1 5 60 290Q 9 5127 51 249 497 746 994 1243 1492 1740 1989 2237 3624 70 80 3394 lO 6619 50 248 497 745 993 1242 1490 1738 1986 2235 6532 3878 II 8109 49 248 497 745 993 1242 1490 1738 1986 2235 9441 90 4363 12 9599 48 248 496 744 992 1241 1489 1737 1985 2233 1-0332350 n 8591088 47 248 496 744 992 1240 1488 1736 1984 2232 5259 14 2576 46 248 496 744 992 1240 1488 1736 1984 2232 8168 I"? 4064 45 248 496 743 991 1239 1487 1735 1982 2230 I -0341077 i6 5551 44 248 495 743 990 1238 i486 1733 1981 2228 3986 17 7037 43 248 495 7f^3 990 1238 i486 1733 1981 2228 6895 i8 8523 42 247 495 742 989 1237 1484 1731 1978 2226 9804 19 8600007 41 247 495 742 989 1237 1484 1731 1978 2226 1-03527x3 20 1491 40 247 495 742 989 1237 1484 1731 1978 2226 5621 21 2975 39 247 494 741 9^ 1235 1482 1739 1976 2223 8530 22 4457 38 247 494 741 988 1235 1482 1729 1976 2223 1-0361439 23 5939 37 247 494 740 987 1234 1481 1728 1974 2221 4348 24 7420 36 247 494 740 987 1234 148 1 1728 1974 2221 7257 2? 8901 35 247 493 740 986 1233 1479 1726 1972 2219 1-0370166 26 8610380 34 247 493 740 986 1233 1479 1726 1972 2219 3075 27 1859 33 246 493 739 985 1232 1478 1724 1970 2217 5984 28 3337 32 246 493 739 985 1232 1478 1724 1970 2217 8893 29 4815 31 246 492 738 984 1231 1477 1723 1969 2215 1-0381802 30 6292 30 246 492 738 984 1230 1476 1722 1968 2214 4709 31 7768 29 246 492 737 983 1229 1475 1 721 1966 2212 7618 32 9243 28 246 491 737 982 1228 1474 1719 1965 2210 1-0390527 33 86207 1 7 27 246 491 737 982 1228 1474 1719 1965 2210 3436 34 2191 26 246 491 737 982 1228 1473 1719 1964 2210 6345 35 3664 25 246 491 737 982 1228 1473 1719 1964 2210 9254 36 5137 24 245 490 735 980 1226 147 1 1716 1961 2206 I -0402 1 63 37 6608 23 245 490 735 980 1226 1471 1716 1961 2206 5072 3« 8079 22 245 490 735 980 1225 1470 1715 i960 2205 7981 39 9549 21 245 490 735 980 1225 1470 1715 i960 2205 I -0410890 40 863 10 I 9 20 245 490 734 979 1224 1469 1714 1958 2203 3798 41 2488 19 245 489 734 978 1223 1468 1712 1957 2201 6707 42 3956 18 245 489 734 978 1223 1467 1712 1956 2201 9616 43 5423 17 244 489 733 977 1222 1466 1710 1954 2199 1-0422525 44 6889 16 244 489 733 977 1222 1466 1465 1710 1954 2199 5434 45 8355 15 244 488 732 976 1221 1709 1953 2197 8343 46 9820 14 244 488 732 976 1220 1464 1708 1952 2196 1-0431252 47 8641284 13 244 488 732 976 1220 1464 1708 1952 2196 4161 48 2748 12 244 488 731 975 1219 1463 1707 1950 2194 7070 49 421 1 II 244 487 731 974 1218 1462 1 70s 1949 2192 9979 50 5673 10 244 487 731 974 1218 1461 1705 1948 2192 I -0442887 51 7134 9 244 487 731 974 1218 1461 1705 1948 2192 5796 52 0. ^595 8 243 487 730 973 1217 1460 1703 1946 2190 8705 53 8650055 7 243 486 729 972 1216 1459 1702 1945 2188 1-0451614 54 1514 6 243 486 729 972 1216 1459 1702 1945 2188 4523 55 2973 5 243 486 728 971 1214 1457 1700 1942 2185 7432 56 4430 4 243 486 728 971 1214 1457 1700 1942 2185 I -046034 1 57 5887 3 243 486 728 971 1214 1457 1700 1942 2185 3250 58 7344 2 243 485 728 970 1213 1455 1698 1940 2183 6159 59 8799 I 243 485 728 970 1213 1455 1698 1940 2183 9068 60 M. 8660254 242 485 727 969 1212 1454 1696 1938 2181 - 90" 1-0471976 Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" Arc. 30 Degrees. 60 Degrees. Difference for Seconds. [6 M. Sine. M. 10" 20" ! 30" 40" 50" 60" 70" 80" 90" Arc. o 8660254 60 242 485 484 727 726 969 1212 1454 1696 1938 2181 1-0471976 Arc. I 1708 59 242 968 1211 1453 1695 1937 2179 4885 N 2 3161 58 242 484 484 726 726 968 1211 1453 1695 1937 2179 7794 Sec. Ultt. i 4614 5/ 242 968 1210 1452 1694 1936 2178 1*0480703 4 6066 56 242 484 725 967 1209 1451 1693 1934 2176 3612 10 20 30 40 50 60 485 5 7517 55 242 483 725 966 1208 1450 1691 1933 2174 6521 970 6 8967 54 242 483 725 966 1208 1450 1691 1933 2174 9430 1454 1939 7 8670417 53 242 483 725 966 1208 1449 1691 1932 2174 1-0492339 8 1866 52 241 483 724 965 1207 1448 1689 1930 2172 5248 2424 2909 3394 3878 9 lO 3314 51 241 483 724 723 965 1207 1448 1689 1930 2172 8157 70 80 4762 50 241 482 964 1206 1447 1688 1929 2170 I -0501065 II 6209 49 241 482 723 964 1205 1446 1687 1928 2169 3974 90 /I'Kd-K 12 7655 48 241 482 722 963 1204 1445 1686 1926 2167 6883 13 9100 47 241 481 722 962 1203 1444 1684 1925 2165 9792 14 8680544 46 241 481 722 962 1203 1444 1684 1925 2165 I -05 1 270 1 IS 1988 45 241 481 722 962 1203 1443 1684 1924 2165 5610 i6 3431 44 241 481 722 962 1203 1443 1684 1924 ■2165 8519 17 4874 43 240 480 720 960 1 201 'I441 1681 192 1 2161 1-0521428 i8 6315 42 240 480 720 960 1201 1441 1681 1921 2161 4337 19 7756 41 240 480 720 960 1200 1440 1680 1920 2160 7246 20 0. 9196 40 240 480 720 960 1200 1440 1680 1920 2160 1-0530154 21 8690636 39 240 479 719 958 1 198 1438 1677 1917 2156 3063 22 2074 3« 240 479 719 958 1 198 1438 1677 1917 2156 5972 23 3512 37 240 479 719 958 1 198 1437 1677 1916 2156 8881 24 3S 4949 36 240 479 719 958 1 198 1437 1435 1677 1916 2156 1-0541790 6386 35 239 478 717 956 1 196 1674 1913 2152 4699 26 7821 34 239 478 717 956 1 196 1435 1674 1913 2152 7608 27 9256 33 239 478 717 956 1 196 H35 1674 1913 2152 1-0550517 28 8700691 32 239 478 716 955 1 194 1433 1672 1910 2149 3426 J9_ 30 2124 31 239 478 716 955 1 194 1433 1672 1910 2149 6335 3557 30 239 477 716 954 "93 1432 1670 1909 2147 9243 31 4989 29 239 477 716 954 1 193 1431 1670 1908 2147 1-0562152 32 6420 28 239 477 716 954 1 193 1431 1670 1908 2147 5061 33 7851 27 238 477 715 953 1 192 1430 1668 1906 2145 7970 34 35 9281 26 238 476 714 952 1191 1429 1667 1905 2143 1-0570879 8710710 25 238 476 714 952 1190 1428 1666 1904 2142 3788 36 2138 24 238 476 714 952 1190 1428 1666 1904 2142 6697 37 3566 23 238 476 713 951 1189 1427 1665 1902 2140 9606 38 4993 22 238 475 713 950 1188 1426 1663 1901 2138 1-0582515 _39_ 40 6419 21 238 475 713 950 1 188 1425 1663 1900 2138 5424 7844 20 238 475 713 950 1 188 1425 1663 1900 2138 8331 41 9269 19 237 47 s 712 949 1 187 1424 1661 1898 2136 1-0591240 42 8720693 18 237 474 711 948 1 186 1423 1660 1897 2134 4149 43 2116 17 237 474 711 948 1 185 1422 1659 1896 2133 7058 44 3538 16 237 474 711 948 1185 1422 1659 1896 2133 9967 45 4960 15 237 474 ' 710 947 1 184 142 1 1658 1894 2131 1-0602876 46 6381 14 237 473 710 946 1 183 1420 1656 1893 2129 5785 47 7801 13 237 473 710 946 1 183 1420 1656 1893 2129 8694 48 9221 12 237 473 710 946 1183 1419 1656 1892 2129 I -06 1 1603 49 50 8730640 II 236 473 709 945 1 182 1418 1654 1890 2127 4512 2058 10 236 472 708 944 1181 1417 1653 1889 2125 7420 51 3475 9 236 472 708 944 1 180 1416 1652 1888 2124 1*0620329 52 4891 8 236 472 708 944 1 180 1416 1652 1888 2124 3238 53 6307 7 236 472 707 943 1 179 1415 1651 1886 2122 6147 54 7722 6 236 472 ion 943 1 179 1415 165 1 1886 2122 9056 55 9137 5 236 471 707 942 1178 1413 1649 1884 2120 I -063 1 965 56 8740550 4 236 471 707 942 1178 1413 1649 1884 2120 4874 57 1963 3 235 471 706 941 1177 1412 1647 1882 2117 7783 58 3375 2 235 470 705 940 1 1 76 1411 -1646 1881 2116 I -0640692 59 4786 I 235 470 705 940 1176 141 1 1646 1881 2116 3601 60 6197 M. 235 470 70s 940 1 175 1410 1645 1880 2115 6508 M. Cosine. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 29 Degrees. 62] 61 Degrees. Difference for Seconds. M. j Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o 8746197 60 235 470 705 940 1 175 1410 1645 1880 2115 I '0646508 Arc. I 2 7607 9016 59 58 235 235 470 470 704 704 939 939 1 174 1 174 1409 1409 1644 1644 1878 1878 2113 2113 9417 1-0652326 Sec.j Diff. 3 4 8750425 1832 57 56 235 235 469 469 704 704 938 938 1173 1 173 1407 .1407 1642 1642 1876 1876 2111 2111 5235 8144 10 485 20 1 970 30 . 1454 40 1939 50 s 2424 60 2909 70 I 3394 S 3239 55 234 469 703 937 1172 1406 1640 1874 2109 1*0661053 6 4645 54 234 469 703 937 1172 1406 1640 1874 2109 3962 7 6051 53 234 468 702 936 II 70 1404 1638 1872 2106 6871 8 9 7455 8859 52 51 234 234 468 468 702 702 936 936 1 1 70 II 70 1 168 1404 1404 1638 1638 1872 1872 2106 2106 9780 1-0672689 5597 lO 8760263 50 234 467 701 934 1402 1635 1869 2102 II 1665 49 234 467 701 934 1 168 1402 1635 1869 2102 8506 80 3878 12 3067 48 234 467 701 934 1168 1401 1635 1868 2102 1-0681415 90 4363 n 4468 47 233 467 700 933 1167 1400 1633 1866 2100 4324 14 5868 46 233 467 700 933 1 167 1 1400 1633 1866 2100 7233 15 7268 45 233 466 699 932 1 165 1398 163 1 1864 2097 1-0690142 i6 8666 44 233 466 699 932 1165 1398 1631 1864 2097 3051 17 8770064 43 233 466 699 932 1 165 1398 1631 1864 2097 5960 i8 1462 42 233 465 698 930 1 163 1396 1628 1861 2093 8869 19 2858 41 233 465 698 930 1 163 1396 1628 1861 2093 1-0701778 4686 20 4254 40 233 465 698 930 1 163 1395 1628 i860 2093 21 5649 39 232 465 697 929 1 162 1394 1626 1858 2091 7595 22 7043 38 232 465 697 929 1 162 1394 1626 1858 2091 I -0710504 2.3 8437 37 232 464 696 928 1161 1393 1625 1857 2089 3413 24 9830 36 232 464 696 928 1160 1392 1624 1856 2088 6322 25 8781222 35 232 464 695 927 1159 1391 1623 1814 2086 9231 26 2613 34 232 464 695 927 1159 1391 1623 i8-;4 2086 I -0722 140 27 4004 33 232 463 695 926 1158 1390 1621 1853 2084 5049 28 5394 32 232 463 695 926 1158 1389 1621 i8c;2 2084 7958 29 6783 31 231 462 694 925 1157 1388 1619 1850 2082 1-0730867 30 8171 30 231 462 694 925 1157 1388 1619 1850 2082 3774 31 9559 29 231 462 693 924 1156 1387 16 1 8 1849 2080 6683 32 8790946 28 231 462 693 924 1155 1386 1617 1848 2079 9592 33 2332 27 231 462 692 923 1 154 1385 1616 1846 2077 1-0742501 34 3717 26 231 462 692 923 1154 1385 1616 1846 2077 5410 35 5102 25 231 461 692 922 1153 1384 1614 1845 2075 8319 36 6486 24 231 461 692 922 1153 1383 1614 1844 2075 1-0751228 37 7869 23 230 461 691 921 1152 1382 1612 1842 2073 4137 38 9251 22 230 461 691 921 1152 1382 1612 1842 2073 7046 39 8800633 21 230 460 690 920 1151 1381 1611 1 841 2071 9955 40 2014 20 230 i 460 690 920 1 150 1380 1610 1840 2070 1-0762863 41 3394 19 230 460 690 920 1150 1380 1610 1840 2070 5772 42 4774 18 230 459 689 918 1 148 1378 1607 1837 2066 8681 43 6152 17 230 459 689 918 1 148 1378 1607 1837 2066 1-0771590 44 7530 16 230 459 689 918 1 148 1377 1607 1836 2066 4499 45 8907 15 230 459 689 918 1 148 1377 1607 1836 2066 7408 46 8810284 14 229 459 688 917 1 147 1376 1605 1834 2064 1-0780317 47 1660 13 229 458 687 916 1 146 1375 1604 1833 2062 3226 48 3035 12 229 458 687 916 1 145 1374 1603 1832 2061 6135 49 4409 II 229 458 686 915 1 144 1373 1602 1830 2059 9044 50 5782 10 229 458 686 915 1 144 1373 1602 1830 2059 1-0791952 51 7155 9 229 457 686 914 1 143 1372 1600 1829 2057 4861 52 8527 8 229 457 686 914 1 143 1371 1600 1828 2057 7770 53 9898 7 228 456 684 912 1141 1371 1600 1828 2057 I -0800679 54 8821269 6 228 456 684 912 1141 1369 1597 1825 2053 3588 55 2638 5 228 456 684 912 1141 1369 1597 1825 2053 6497 56 4007 4 228 456 684 912 1 141 1369 1597 1825 2053 9406 57 5376 3 228 456 683 911 1 139 1367 1595 1822 2050 1-0812315 5« 6743 2 228 456 683 911 1139 1367 1595 1822 2050 5224 59 8110 I 228 455 683 910 1 138 1366 1593 1821 2048 8133 60 9476 228 455 683 910 1138 1365 1593 1820 2048 1-0821041 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70' 80" 90" Arc. 28 Degrees. 62 Degrees. Difference for Second s. [61 M. o I 2 3 4 5 6 7 8 9 Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90"- Arc. 8829476 8830841 2206 3569 4933 60 59 58 57 56 228 228 227 227 227 455 455 454 454 454 683 683 681 681 681 910 910 908 908 908 1138. 1 138 1 136 1 136 1135 1365 1365 1363 1364 1362 1593 1593 1591 1591 1589 1820 1820 1818 1818 1816 2048 2048 2046 2046 2043 ro82io4i 3950 6859 9768 1-0832677 Arc. Sec. Diff. 10 20 30 40 50 60 -JO 80 90 485 6295 7656 9017 8840377 1736 55 54 53 52 51 227 227 227 227 227 454 454 453 453 453 680 680 680 680 680 907 907 906 906 906 1 134 1 134 1133 1 133 1 133 I36I I36I 1360 1359 1359 1358 1357 1356 1356 1354 1588 1588 1586 1586 1586 1584 1583 1582 1582 1579 1814 1814 1813 1812 1812 '2041 2041 2039 2039 2039 5586 8495 1*0841404 4313 7222 I "0850130 3039 5948 8857 1-0861766 970 1454 1939 2424 2909 lO II 12 13 H 3095 4453 5810 7166 8522 50 49 48 47 46 226 226 226 226 226 453 452 452 452 451 679 678 678 678 677 905 904 904 904 902 1132 1131 1130 1 130 1128 1810 1809 1808 1808 1805 2037 2035 2034 2034 2030 3394 3878 4363 15 i6 17 i8 19 9876 8851230 2584 3936 5288 45 44 43 42 41 226 226 225 225 225 451 451 451 451 450 677 677 676 676 675 902 902 901 901 900 1128 1128 1127 1127 1 126 1354 1354 1352 1352 I35I 1579 1579 1577 1577 1576 1805 1805 1802 1802 1 801 2030 2030 2028 2028 2026 4675 7584 I "0870493 3402 6311 20 21 22 23 24 6639 7989 9339 8860688 2036 40 39 38 36 225 225 225 225 225 450 450 450 449 449 675 675 674 674 674 900 900 899 898 898 1125 1125 1124 1123 1123 1350 1350 1349 1348 1347 1575 1575 1574 1572 1572 1800 1800 1798 1797 1796 2025 2025 2023 2021 2021 9219 1-0882128 5037 7946 1-0890855 25 26 27 28 29 3383 4730 6075 7420 8765 35 34 33 32 31 225 224 224 224 224 449 448 448 448 448 674 672 672 672 671 898 896 896 896 895 1 123 1121 1121 1121 1119 1347 1345 1345 1345 1343 1572 1569 1569 1569 1567 1796 1793 1793 1793 1790 2021 2017 2017 2017 2014 3764 6673 9582 1-0902491 5400 30 31 32 33 34 8870108 145 1 2793 4134 5475 30 29 28 27 26 224 224 224 224 223 448 447 447 447 447 671 671 671 671 670 895 894 894 894 893 1119 1118 1118 1118 1117 1343 1342 I34I I34I 1340 1567 1565 156s 1565 1563 1790 1789 1788 1788 1786 2014 2012 2012 2012 2010 8308 I -09 1 1 217 4126 7035 9944 35 36 37 38 39 6815 8154 9492 8880830 2166 25 24 23 22 21 223 223 223 223 223 446 446 446 446 446 669 669 669 668 668 892 892 892 890 891 1116 HIS ins 1113 1 1 14 1339 1338 1338 1336 1337 1562 1561 iS6i 1560 iS6o 1785 1784 1784 1782 1782 2008 2007 2007 2005 2005 1-0922853 5762 8671 I -093 1 5 80 4489 40 41 42 43 44 45 46 47 48 49 3503 4838 6172 7506 8839 20 19 18 17 16 223 222 222 222 222 445 445 445 444 444 668 667 667 666 666 890 889 889 888 888 1113 1 112 1112 nil 1 1 10 1335 1334 1334 1333 1332 ISS8 1556 1556 1555 1554 1780 1778 1778 1777 1776 2003 2001 2001 1999 1998 739/ 1-0940305 3214 6123 9032 88901 7 1 1503 2834 4164 5493 15 14 13 12 II 222 222 222 222 222 444 444 443 443 443 666 665 665 665 665 888 887 886 886 886 1 1 10 1 109 1 108 1108 1 108 1332 I33I 1330 1329 1329 1554 1553 1551 1551 1551 1776 1774 1773 1772 1772 1998 1996 1994 1994 1994 1-0951941 4850 7759 I -0960668 3577 50 51 52 53 54 55 56 57 58 59 60 6822 8149 9476 8900803 2128 10 9 8 7 6 221 221 221 221 221 442 442 442 442 442 663 663 663 662 662 884 884 884 883 883 1 106 1 106 1 106 1 104 1104 1327 1327 1327 1325 1325 1548 1548 1548 1546 1546 1769 1769 1769 1766 1766 1990 1990 1990 1987 1987 648^ 9394- 1-097230-^ 5212 8i2r 3453 4777 6100 7423 8744 89100J5 5 4 3 2 I 221 221 221 220 220 220 441 441 441 440 440 440 662 662 662 660 660 660 882 882 882 880 880 880 1103 1 103 1 103 IIOI IIOI HOC 1324 1323 1323 I32I I32I 1320 1544 1544 1544 1541 1541 1540 1765 1764 1764 1761 1761 1760 1985 1985 198s 1981 198 1 1980 I -0981030 3939 6848 9757 I -0992666 5574 M. ' Cosine, j M, 10" 1 20" 1 30" 40" 50" 60" 70" 80" 90" Arc. 27 Degrees. 64] 63 Degrees Difference : or Seconds. M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o I 2 3 4 8910065 1385 2705 4024 5342 60 59 58 11 220 220 220 220 220 440 440 440 439 439 660 660 659 659 659 880 880 879 878 878 HOG IIOO 1099 1098 1098 1320 1320 1319 1318 1317 1540 1540 1539 1537 1537 1760 1760 1758 1757 1756 1980 1980 1978 1976 1976 I '0995574 8483 1*1001392 4301 7210 Arc. A Sec. Diff. 10 20 30 40 50 60 70 80 90 485 970 1454 1939 2424 2909 3394 5 6 7 8 9 6659 7975 9291 8920606 1920 55 54 53 52 51 50 49 48 47 46 219 219 219 219 219 439 439 438 438 438 658 658 657 657 657 877 877 876 876 876 1097 1097 1096 1095 1095 1316 1316 1315 1314 1314 1535 1535 1534 1533 1533 1754 1754 1753 1752 1752 1974 1974 1972 1971 1971 1*1010119 3028 5937 8846 1*1021755 lO II 12 13 3234 4546 5858 7169 8480 219 219 219 219 218 437 437 437 437 436 656 656 656 656 654 874 874 874 874 872 1093 1093 1093 1093 IO9I 1312 1312 1311 1311 1309 1530 1530 1530 1530 1527 1749 1749 1748 1748 1745 1967 1967 1967 1967 1963 4663 7572 1*1030481 3390 6299 3878 4363 15 16 17 18 19 9789 8931098 2406 3714 5021 45 44 43 42 41 218 218 218 218 218 436 436 436 436 435 654 654 654 653 653 872 872 872 871 870 IO9I 1090 1090 1089 1088 1309 1308 1308 1307 1305 1527 1526 1526 1525 1523 1745 1744 1744 1742 1740 1963 1962 1962 i960 1958 9208 1-1042117 5026 7935 1*1050844 20 21 22 23 24 6326 7632 8936 8940240 1542 40 39 38 37 36 218 217 217 217 217 435 435 435 434 434 653 652 651 651 870 879 869 868 868 1088 1087 1087 1085 1085 1306 1304 1304 1302 1302 1523 1521 1521 1519 1519 1 741 1738 1738 1736 1736 1958 1956 1956 1953 1953 3752 6661 9570 1*1062479 5388 25 26 27 28 29 2844 4146 5446 6746 8045 35 34 33 32 31 217 217 217 217 217 434 433 433 433 433 651 650 650 650 650 868 866 866 866 866 1085 1083 1083 1083 1083 1302 1300 1300 1299 1299 1519 1516 1516 1516 1516 1736 1733 1733 1732 1732 1953 1949 1949 1949 1949 8297 1*1071206 4115 7024 9933 30 31 32 33 3+ 9344 8950641 1938 3234 4529 30 29 28 27 26 216 216 216 216 216 433 432 432 432 432 650 648 648 647 647 866 864 864 863 863 862 862 861 860 860 108 1 I081 1080 1079 1079 1078 1078 1077 1076 1075 1297 1297 1296 1295 1295 1294 1293 1292 1291 1291 1513 1513 1512 1511 1511 1729 1729 1728 1726 1726 1945 1945 1944 1942 1942 1*1082841 5750 8659 1*1091568 4477 35 36 37 38 39 5824 7118 8411 .9703 8960994 25 24 23 22 21 216 216 215 215 215 431 431 431 430 430 647 647 646 645 645 1509 1509 1507 1506 1505 1725 1724 1722 1721 1720 1940 1940 1938 1936 1935 7386 1*1100295 3204 6113 9022 40 41 42 43 44 2285 3575 4864 6153 7440 20 19 18 17 16 215 215 215 215 215 430 430 430 429 429 645 644 644 644 644 860 869 859 858 858 1075 1074 1074 1073 1073 1290 1289 1289 1287 1287 1287 1285 1285 1284 1283 1505 1504 1504 1502 1502 1720 1718 1718 1716 1716 1935 1933 1933 193 1 193 1 11111929 4838 7747 1-1120656 3565 45 46 47 48 49 50 51 52 53 54 8727 8970014 1299 2584 3868 15 14 13 12 II 215 214 214 214 214 429 428 428 428 428 644 642 642 642 641 858 856 856 856 855 1073 107 1 IO7I 1070 1069 1502 1499 1499 1498 1497 1716 1713 1713 1712 1710 193 1 1927 1927 1926 1924 6474 9383 1*1132292 5201 8110 5151 6433 7715 8996 89'^o276 10 9 8 7 6 214 214 214 213 213 427 427 427 427 426 641 641 641 640 639 854 854 854 853 852 1068 1068 1068 1067 1066 1282 1282 1281 1280 1279 1495 1495 1495 1493 1492 1709 1709 1708 1706 1705 1922 1922 1922 1920 1918 1-1141018 3927 6836 9745 1*1152654 11 57 58 59 60 1555 2834 4112 5389 6665 7940 5 4 3 2 I 213 213 213 213 213 213 426 426 426 425 425 425 639 639 638 638 638 638 852 852 851 850 850 850 1066 1065 1064 1063 1063 1063 1279 1278 1277 1276 1275 1275 1492 1491 1490 1488 1488 1488 1705 1704 1702 1 701 1700 1700 1918 1917 1915 1913 1913 1913 5563 8472 1*1161381 4290 7199 1*1170107 M. Cosine M. 10" 20" 33" 40" 50" 60" 70" 80" 90" Arc. 26 Decrees. 64 Detfrees. Difference for Seconds, [6 M. Sine. M. 10" 20" 30" 40" so" 60" 70" 80" 90" Arc. o I 2 3 4 8987940 9215 8990489 1763 3035 60 59 58 57 56 55 54 53 52 51 213 2X2 212 212 212 425 425 425 424 424 638 637 637 636 636 "635 635 635 634 850 849 849 848 848 1063 1062 1062 1060 1060 1275 1274 1274 1272 1272 1488 i486 i486 1484 1484 1700 1698 1698 1696 1696 1913 1911 1911 1908 1908 i"ii7oio7 3016 5925 8834 rii8i743 Arc. Sec. Difif. 10 20 30 40 50 60 70 80 90 48s 5 6 7 8 9 4307 5578 •6848 8117 9386 212 212 212 212 211 424 423 423 423 423 847 846 846 846 845 1059 1058 1058 1058 1057 1271 1270 1269 1269 1268 1483 1481 148 1 1481 1479 1694 1693 1692 1692 1690 1906 1904 1904 1904 1902 4652 7561 1-1190470 3379 6288 970 1454 1939 2424 2909 3394 3878 4363 lO II 12 13 H 9000654 192 1 3188 4453 5718 50 49 48 47 46 211 211 211 211 211 422 422 422 422 421 633 633 632 632 632 844 844 843 843 842 1056 1056 1054 1054 1053 1267 1267 1265 1265 1264 1478 1478 1476 1476 1474 1689 1689 1686 1686 1685 1900 1900 1897 1897 1895 1895 1893 1893 1 891 1891 9196 1-1202105 5014 7923 1*1210832 15 16 17 18 19 6982 8246 9508 9010770 2031 45 44 43 42 41 211 210 2IO 210 210 421 421 421 420 420 632 631 631 630 630 842 841 841 840 840 1053 1052 1052 1051 1051 1264 1262 1262 1261 1261 1474 1472 1472 1471 147 1 1685 1682 1682 1681 1681 3741 6650 9559 1-1222468 5377 20 21 22 23 24 3292 4551 5810 7068 8325 40 39 38 37 36 210 210 210 210 210 420 420 419 419 419 629 629 629 629 629 839 839 838 838 838 1049 1049 1048 1048 1048 1259 1259 1258 1257 1257 1469 1469 1467 1467 1467 1678 1678 1677 1676 1676 1888 1888 1886 1886 1886 8285 1-1231194 4103 7012 9921 25 26 27 28 29 9582 9020838 2092 3347 4600 35 34 33 32 31 209 209 209 209 209 419 418 418 418 418 628 627 627 626 626 837 836 836 835 835 1047 1045 1045 1044 1044 1256 1254 1255 1253 1253 1465 1464 1464 1462 1462 1674 1673 1673 1671 1671 1884 1882 1882 1880 1880 1-1242830 5739 8648 1-1251557 4466 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 5853 7105 8356 9606 9030856 30 29 28 27 26 25 24 23 22 21 209 209 208 208 208 208 208 208 208 208 417 417 417 417 416 626 626 62s 625 624 834 834 833 833 832 1043 1043 1042 1042 1041 1252 1251 1250 1250 1249 1461 1460 1458 1458 1457 1670 1668 1666 1666 1665 1878 1877 1875 1875 1873 7374 1-1260283 3192 6101 9010 2105 3353 4600 5847 7093 416 416 416 415 415 624 623 623 623 623 832 831 831 830 830 1040 1039 1039 1038 1038 1248 1247 1247 1246 1245 1456 U55 1455 1453 1453 1664 1662 1662 1661 1660 1872 1870 1870 1868 1868 1-1271919 4828 7737 I -1 280646 3555 8338 9582 9040825 2068 3310 20 19 18 17 16 15 H 13 12 II 207 207 207 207 207 4IS 414 414 414 414 622 621 621 621 620 829 828 828 828 827 1037 1036 1036 1035 1034 1244 1243 1243 1242 1241 145 1 1450 1450 1449 1448 1658 1658 1658 1656 1654 1866 1865 1865 1863 1861 6462 9371 1-1292280 5189 8098 46 47 48 49 50 51 52 S3 54 55 56 57 58 59 60 4551 5792 7032 8271 9509 207 207 207 206 206 414 413 413 413 412 620 620 620 619 618 827 826 826 825 824 1034 1033 1033 1032 103 1 1 241 1240 1239 1238 1237 1448 1446 1446 1444 1443 1654 1653 1652 1650 1649 1861 1859 1859 1857 1855 1-1301007 3916 6825 9737 1-1312643 9050746 1983 3219 4454 5688 10 9 8 7 6 206 206 206 206 206 412 412 412 411 411 618 618 617 617 617 824 824 823 822 822 103 1 1030 1029 1028 1028 1237 1236 1235 1234 1234 1443 1442 1441 1439 1439 1649 1648 1646 1645 1645 1855 1854 1852 1850 1850 5551 8460 ri32i369 4278 7187 6922 8154 9386 9060618 1848 3078 5 4 3 2 I M 205 205 205 205 205 205 411 411 411 410 410 410 616 616 616 615 615 614 821 821 821 820 820 819 1027 1027 1027 1025 1025 1024 1232 1232 1232 1230 1230 1229 1437 1437 1437 1435 1435 1434 1642 1642 1642 1640 1640 1638 1848 1848 1848 1845 1845 1843 i-i 330096 3005 5914 8823 1-1341732 4640 M. 1 Cosine. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 25 Degrees. 66] 65 Degrees. Difference for Seconds. M. Sine. M. 10" 20' 30" 40" 50" 60" 70" 80" 90" Arc. o 9063078 60 205 410 614 819 1024 1229 1434 1638 1843 1-1344640 Arc I 2 4307 5535 59 58 205 205 409 409 614 614 819 818 1023 1023 1228 1227 1432 1432 1637 1636 1841 1 841 7549 1-1350458 A Diff 3 4 6762 7989 57 56 205 204 409 409 614 613 818 817 1023 1022 1227 1226 1432 1430 1636 1634 1 841 1839 3367 6276 10 20 485 970 <; 9215 55 204 408 612 8x6 1021 1225 1429 1633 1837 9185 6 9070440 54 204 408 612 816 1021 1225 1429 1633 1837 1-1362094 30 «.I454 7 1665 53 204 408 611 815 1019 1223 1427 1630 1834 5003 40 1939 8 2888 52 204 408 612 816 1020 1223 1427 1630 1834 7912 50 2424 9 4111 51 204 407 611 814 1018 1222 1425 1629 1832 1-1370821 60 70 2909 lO 5333 50 204 407 611 814 1018 1221 1425 1628 1832 3729 3394 n 6554 49 204 407 611 814 1018 1221 1425 1628 1832 6638 80 3878 12 7775 48 203 407 610 813 1017 1220 1423 1626 1830 9547 90 43(33 n 8995 47 203 406 609 812 1016 1219 1422 1625 1828 1-1382456 14 9080214 46 203 406 609 812 1015 1218 1421 1624 1827 5365 IS 1432 45 203 406 608 811 1014 1217 1420 1622 1825 8274 i6 2649 44 203 406 608 811 1014 1217 1420 1622 1825 1-1391183 17 3866 43 203 405 608 810 1013 1216 1418 1621 1823 4092 i8 5082 42 203 405 608 810 1013 1215 1418 1620 1823 7001 19 6297 41 202 405 607 809 1012 1214 1416 1618 1821 9910 20 7511 40 202 405 607 809 1012 1214 1416 1618 1821 1-1402818 21 .. 8725 39 202 404 606 808 lOII 1213 1415 1617 1819 5727 22 9938 38 202 404 606 808 lOIO 1212 1414 1616 1818 8636 2^ 9091150 37 202 404 605 807 1009 1211 1413 1614 1816 1-1411545 24 2"; 2361 36 202 404 605 807 1009 1211 1413 1614 1816 4454 3572 35 202 403 605 806 1008 1209 1411 1612 1814 7363 26 4781 34 202 403 60s 806 1008 i 1209 1411 1612 1814 1-1420272 27 5990 33 202 403 605 806 1008 1209 141 1 1612 1814 3181 28 7199 32 201 402 603 804 1006 1207 1408 1609 1810 6090 29 8406 31 201 402 603 804 1006 1207 1408 1609 1810 , 8999 30 9613 30 201 402 603 804 1005 1206 1407 1608 1809 1-1431907 ^I 9100819 29 201 402 602 803 1004 1205 1406 1607 1807 4816 32 2024 28 201 401 602 802 1003 1204 1404 1605 1805 7725 ^^ 3228 27 201 401 602 802 1003 1204 1404 1605 1805 I -1440634 34 4432 26 25 201 200 401 602 802 1003 1203 1404 1604 1805 3543 ^i; 5635 401 601 801 1002 1202 1402 1602 1803 6452 36 6837 24 200 400 600 800 lOOI 1 201 1401 1601 1 801 9361 37 8038 23 200 400 600 800 1000 1200 1400 1600 1800 1-1452270 3B 9238 22 200 400 600 800 1000 1200 1400 1600 1800 5179 _39 40 91 10438 21 200 400 599 799 999 1 199 1399 1598 1798 8087 1637 20 200 399 599 798 998 1 198 1397 1597 1796 I -1460996 41 2835 19 200 399 599 798 998 1 198 1397 1597 1796 3905 42 4033 18 199 399 598 797 997 1 196 1395 1594 1794 6814 43 5229 17 199 399 598 797 997 1 196 1395 1594 1794 9723 44 6425 16 199 398 597 796 996 1 195 1394 1593 1792 I -1472632 45 7620 15 199 398 597 796 996 1 195 1394 1593 1792 5541 46 8815 14 199 398 596 795 994 1 193 1392 1590 1789 8450 47 9120008 13 199 398 596 795 994 1 193 1392 1590 1789 1-1481358 48 i2or 12 199 397 596 794 993 1 192 1390 1589 1787 4267 49 2393 II 10 199 199 397 397 596 794 993 1191 1390 1588 1588 1787 1787 7176 50 3584 596 794 993 1191 1390 1-1490084 51 4775 9 198 397 595 793 992 1190 1388 1586 1785 2993 52 5965 8 198 396 594 792 991 1 189 1387 1585 1783 5902 53 7154 7 198 396 594 792 990 1188 1386 1584 1782 881 1 54 55 8342 6 198 396 593 791 989 1187 1385 1582 1780 1-1501720 9529 5 198 396 593 791 989 1187 1385 1582 1780 4628 56 9130716 4 198 395 593 790 988 1186 1383 1581 1778 7537 57 1902 3 198 395 593 790 988 1185 1383 1580 1778 1-1510446 5« 3087 2 197 395 592 789 987 1 184 1381 1578 1776 3355 59 4271 I 197 395 592 789 987 1 184 1381 1578 1776 6264 bo 5455 197 394 591 788 985 1182 1379 1576 1773 9'73 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 24 Degrees. 66 Degrees. Difference for Seconds. [67 M. Sine. 1 M. 10" 20" 30" 40" 50" j 60" 70" j 80" 90" Arc, o I 2 3 4 9135455 6637 7819 9001 9140181 60 59 58 57 56 197 197 197 197 197 197 196 196 196 196 394 394 394 393 393 591 591 591 590 590 788 788 788 786 786 985 985 985 983 983 1182 1 182 1182 1 180 1 180 1379 1379 1379 1376 1376 1376 1374 1373 1373 1371 1576 1576 1576 1573 1573 1773 i773 1773 1769 1769 1-1519173 1-1522082 4991 7900 1-1530809 Arc. Sec. Diff. 10 20 30 40 60 70 80 90 485 5 6 7 8 9 1361 2540 • 3718 4895 6072 55 54 53 52 51 393 393 392 392 392 590 589 588 588 587 786 784 784 783 783 783 782 782 781 983 982 981 981 979 1 179 1178 1177 1177 1175 1572 1570 1569 1569 1566 1769 1767 1765 1765 1762 1762 1762 1760 1760 1758 3718 6627 9536 1-1542445 5354 970 1454 1939 2424 2909 lO II 12 13 H 7247 8422 9597 9150770 1943 50 49 48 47 46 196 196 196 196 195 392 392 391 391 391 587 587 587 587 586 979 979 978 978 977 1175 1175 1 173 1 173 1172 1371 1371 1369 1369 1367 1566 1566 1564 1564 1562 8262 1-1551171 4080 6989 9898 3394 3878 4363 15 i6 17 i8 19 3115 4286 5456 6626 7795 45 44 43 42 41 195 195 195 195 195 390 390 390 390 389 585 58s 585 584 584 780 780 780 779 778 976 975 975 974 973 1171 1 170 1 170 1 169 1 168 1366 1365 1365 1364 1362 1561 1560 1560 1558 1557 1756 1755 1755 1753 1751 1-1562807 5716 8625 1-1571534 4443 20 21 22 23 24 8963 9160130 1297 2462 3627 40 39 38 37 36 195 19s 194 194 194 389 389 388 388 388 584 584 582 582 582 778 778 776 776 776 973 973 971 971 970 1 167 1 167 1 165 1 165 1 164 1362 1362 1359 1359 1358 1556 1556 1553 1553 1552 1751 1751 1747 1747 1746 7351 1-1580260 3169 6078 8987 25 26 27 28 29 4791 595 5 7118 8279 9440 35 34 33 32 31 194 194 194 194 194 388 388 387 387 387 582 581 581 581 581 776 775 774 774 774 970 969 968 968 968 1 164 "63 1161 1161 1161 1358 1357 1355 1355 1355 1552 1550 1548 1548 1548 1746 1744 1742 1742 1742 I -1 591896 4805 7714 I -1600623 3532 30 31 32 33 34 9170601 1760 2919 4077 5234 30 29 28 27 26 193 193 193 193 193 386 386 386 386 386 579 579 579 578 578 772 772 772 771 771 966 966 965 964 964 1159 1 159 1158 1157 1157 1352 1352 1351 1350 1350 1545 1545 1544 1542 1542 1738 1738 1737 1735 1735 6440 9349 1-1612258 5167 8076 .35 ■36 37 38 39 40 41 42 43 44 6391 7546 8701 9855 9181009 25 24 23 22 21 193 193 192 192 192 385 385 3?5 384 578 578 577 577 576 770 770 769 769 768 963 963 962 962 960 1155 1154 1154 1152 1348 1348 1346 1346 1344 1540 1540 1538 1538 1536 1733 1733 1731 1731 1728 I -1620985 3894 6803 9712 1-1632621 2161 3313 4464 5614 6763 20 19 18 17 16 192 192 192 192 192 384 384 383 383 576 575 575 575 575 768 767 766 766 766 960 959 958 958 958 1152 1151 1150 1 149 1 149 1344 1343 1341 1341 1341 1536 1534 1533 1532 1532 1728 1726 1724 1724 1724 5528 8437 1-1641346 4255 7164 45 46 47 48 49 7912 9060 9190207 1353 2499 15 14 13 12 II 191 191 191 191 19I 383 382 382 382 382 574 573 573 573 572 765 764 764 764 763 957 956 955 955 954 1 148 1 147 1 146 1 146 1 145 1339 1338 1337 1337 1336 1530 1529 1528 1528 1526 1722 1720 1719 1719 1717 1-1650073 2982 5891 8800 1-1661709 SO SI 52 53 54 3644 4788 5931 7073 8215 10 9 8 7 6 191 191 190 190 190 381 381 381 381 380 572 572 571 571 570 762 762 761 761 760 953 953 952 952 951 1 144 1 143 1 142 1 142 1 141 1334 1334 1332 1332 1331 1525 1524 1522 1522 1521 1715 1715 1713 1713 1711 4617 7526 1-1670435 3344 6253 55 56 57 58 59 60 9356 9200496 1635 2774 3912 5049 S 4 3 2 I 190 190 190 190 190 189 380 380 380 379 379 379 570 569 569 569 569 568 760 759 759 758 758 757 950 949 949 948 948 947 1 140 II39 1 139 1 138 "37 1136 1330 1329 1329 1327 1327 1325 1520 1518 1518 1517 1516 1514 1710 1708 1708 1706 1706 1704 9162 I -168207 1 4980 7889 1-1690798 3706 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90' Arc. 23 Degrees. 68] 67 Degrees. Difference ) or Seconds. M. Sine. M. 10" 20" 30" 40" so" 60" 70" 80" 90" Arc. o I 2 3 9205049 6185 7320 8455 60 59 58 57 189 189 189 189 379 378 378 378 568 567 567 567 757 756 756 756 947 946 946 945 1 136 1 135 1135 1 134 1325 1324 1324 1323 I5I4 I5I3 I5I3 I5I2 1704 1702 1702 1701 1-1693706 6615 9524 1-1702433 Arc, Sec. Diff. 10 20 30 485 970 1454 4 . 9589 56 189 378 566 755 944 1133 1322 I5I0 1699 5342 1 9210722 55 189 m 566 754 943 I132 1320 1509 1697 8251 6 1854 54 189 377 566 754 943 I132 1320 1509 1697 1-1711160 40 1939 2424 7 2986 53 188 377 5(^5 753 942 1 130 I3I8 1506 1695 4069 50 8 4116 52 188 m 5(^5 753 942 1 130 I3I8 1506 1695 6978 60 2909 3394 9 5246 51 188 376 564 752 941 1 1 29 I3I7 1505 1693 9887 70 80 lO 6375 50 188 376 564 752 941 1 1 29 I3I7 1505 1693 1-1722795 3878 II 7504 49 188 376 564 752 940 1 128 I3I6 1504 1692 5704 90 4363 12 8632 48 188 375 563 750 938 1 126 I3I3 1 501 1688 8613 n 9758 47 188 375 563 750 938 1 126 I3I3 I50I 1688 1-1731522 9220884 46 188 375 563 750 938 I126 I3I3 1 501 1688 4431 2010 45 187 375 t;62 749 937 1 124 I3II 1498 1686 7340 i6 3134 44 187 375 562 749 937 1 124 I3II 1498 1686 1-1740249 17 4258 43 187 374 561 748 936 1 123 I3I0 1497 1684 3158 i8 5381 42 187 374 561 748 935 II22 1309 1496 1683 6067 19 6503 41 187 374 560 747 934 II2I 1308 1494 1681 8976 20 7624 40 187 374 560 747 934 II2I 1308 1494 1681 1-1751884 21 8745 39 187 373 560 746 933 1 1 20 1306 1493 1679 4793 22 9865 38 187 373 560 746 933 III9 1306 1492 1679 7702 2.3 9230984 Zl 186 373 559 745 932 III8 1304 1490 1677 11760611 24 2102 36 186 373 559 745 932 II18 1304 1490 1677 3520 2S 3220 35 186 372 558 744 930 III6 1302 I4g'8 1674 6429 26 4336 34 186 372 558 744 930 III6 1302 1488 1674 9338 27 ■ 5452 33 186 372 557 743 929 III5 1 301 i486 1672 1-1772247 28 6567 32 186 372 557 743 929 III5 1 301 i486 1672 5156 29 7682 31 186 371 557 742 928 III3 1299 1484 1670 8065 30 8795 30 186 371 557 742 928 III3 1299 1484 1670 1-1780973 31 9908 29 185 371 556 741 927 III2 1297 1482 1668 3882 32 9241020 28 185 370 555 740 926 nil 1296 1481 1666 6791 33 2131 27 185 370 555 740 926 nil 1296 1481 1666 9700 34 3242 26 185 369 554 739 924 1 109 1294 1478 1662 1-1792609 3"; 4351 25 185 369 554 739 924 1 109 1294 1478 1662 5518 36 5460 24 185 369 554 738 923 1 108 1292 1477 1661 8427 37 6568 23 185 369 554 738 923 1 108 1292 -i-Ml 1661 1-1801336 3« 7676 22 184 369 553 737 922 1106 1290 1474 1659 4245 39 8782 21 184 369 553 737 922 921 1 106 1290 1474 1659 7154 40 9888 20 184 368 552 736 1 105 1289 1473 1657 i-l8ioo6i 41 9250993 19 184 368 552 736 920 1 104 1288 1472 1656 2970 42 2097 18 184 368 552 736 920 1 104 1288 1472 1656 , 5879 43 3201 17 184 367 551 734 918 1 102 1285 1469 1652 87S8 44 4303 16 15 184 367 551 734 918 1102 IIOI 1285 1285 1469 1652 1-1821697 45 5405 184 367 551 734 918 1468 1652 4606 46 6506 14 183 367 550 733 917 1 100 1283 1466 1650 7515 47 7606 13 183 367 550 733 917 IIOO 1283 1466 1650 I -1 830424 48 8706 12 183 366 549 732 916 1099 1282 1465 1648 3333 49 9805 II 183 366 548 731 914 1097 1280 1462 1645 6242 50 9260902 10 183 366 548 731 914 1098 1280 1462 1645 9150 51 2000 9 183 365 548 730 913 1096 1278 1461 1643 1-1842059 52 3096 8 183 365 548 730 913 1096 1278 1461 1643 4968 53 4192 7 182 365 547 729 912 1094 1276 1458 1641 7877 54 55 5286 6 182 365 547 729 912 1094 1276 1458 1641 1-1850786 6380 5 182 365 547 729 912 1094 1276 1458 1 641 3695 5<3 7474 4 182 364 546 728 910 1092 1274 1456 1638 6604 57 8566 3 182 364 546 728 910 1092 1274 1456 1638 9513 5« 9658 2 182 363 545 726 908 1090 I27I 1453 1634 i-i 862422 59 9270748 I 182 363 545 726 908 I09I I27I 1453 1634 5330 bo 1839 182 363 545 726 908 1089 I27I 1452 1634 8239 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 22 De^irees. 68 Degrees. Difference for Seconds. [( M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o 9271839 2928 60 182 181 363 363 545 726 908 1089 1271 1452 1734 1-1868239 Arc. 59 544 725 907 1088 1269 1450 1632 1-1871148 ■> 2 4016 58 181 363 544 725 907 1088 1269 1450 1632 4057 Sec. Ultt. 3 5104 57 181 362 543 724 906 1087 1268 1449 1630 6966 4 6191 5b 181 362 543 724 905 1086 1267 1448 1629 9875 10 20 30 40 50 6n 485 5 7277 55 181 362 543 724 905 1086 1267 1448 1629 1-1882784 970 6 8363 54 181 361 542 722 903 1084 1264 1445 1625 5693 1454 1939 7 9447 53 181 361 542 722 903 1084 1264 1445 1625 8602 8 9280531 52 181 361 542 722 903 1083 1264 1444 1625 1-189151 1 2424 9 1614 51 180 361 541 721 902 1082 1262 1442 1623 4420 70 80 2909 3394 3878 lO 2696 50 180 361 541 721 902 1082 1262 1442 1623 7328 II 3778 49 180 360 540 720 900 1080 1260 1440 1620 1-1900237 90 A^6l 12 4858 48 180 360 540 720 900 1080 1260 1440 1620 3146 13 5938 47 180 360 539 719 899 1079 1259 1438 1618 6055 14 7017 46 180 360 539 719 899 1079 1259 1438 1618 8964 15 8096 45 1 80 359 539 718 898 1077 1257 1436 1616 1-1911873 i6 9173 44 180 359 539 718 898 1077 1257 1436 1616 4782 17 9290250 43 179 359 538 717 897 1076 1255 1434 1614 7691 i8 1326 42 179 358 537 716 896 1075 1254 1433 1612 1-1920600 19 2401 41 179 358 537 716 895 1074 1253 1432 1611 3509 20 3475 40 179 358 537 716 895 1074 1253 1432 1611 6417 21 4549 39 179 358 536 715 894 1073 1252 143 1 1610 9326 22 5622 38 179 357 53t 714 893 1072 1250 1429 1607 1-1932235 23 6694 37 179 357 53b 714 893 107 1 1250 1428 1607 5J44 24 25 7765 30 178 357 535 713 892 1070 1248 1426 1605 8053 8835 35 178 357 535 713 892 1070 1248 1426 1605 1-1940962 26 9905 34 178 35(^ 534 712 891 1069 1247 1425 1603 3871 27 9300974 33 178 35(^ 534 712 890 1068 1246 1424 1602 6780 28 2042 32 178 3S^ 533 711 889 1067 1245 1422 1600 9689 29 3109 31 178 356 533 711 889 1067 1245 1422 1600 1-1952598 30 4176 30 178 355 533 710 888 1065 1243 1420 1598 5506 31 5241 29 178 355 533 710 888 1065 1243 1420 1598 8415 32 6306 28 177 355 532 709 887 1064 1241 1418 1596 1-1961324 33 7370 27 177 355 532 709 887 1064 1241 1418 1596 4233 34 35 8434 26 177 354 531 708 885 1062 1239 1416 1593 7142 9496 25 177 354 531 708 885 1062 1239 1416 1593 1-1970051 36 9310558 24 177 354 530 707 884 106 1 1238 1414 1591 2960 37 1619 23 177 353 530 706 883 1060 1236 1413 1589. 5869 3« .2679 22 177 353 530 706 883 1060 1236 1413 I58<^ 8778 39 40 3739 21 176 353 529 705 882 1058 1234 1410 1587- 1-1981687 4797 20 176 353 529 705 882 1058 1234 1410 1587 4594 41 5855 19 176 352 5'^ 704 881 1057 1233 1409 1585 7503 42 6912 18 176 352 528 704 881 1057 1233 1409 1585 1-1990412 43 7969 17 176 352 528 704 880 1055 1231 1406 1581 3321 44 9024 16 176 352 528 704 880 1055 1231 1406 1581 6230 45 9320079 15 176 351 527 702 878 1054 1229 1405 1580 9139 46 1133 14 17b 351 527 702 878 1053 1229 1404 1580 1-2002048 47 2186 13 175 351 526 701 877 1052 1227 1402 1578 4957 48 3238 12 175 351 526 701 877 1052 1227 1402 1578 7866 49 50 4290 II 175 175 350 525 700 875 1050 1225 1400 1575 1*2010775 5340 10 350 525 700 875 1050 1225 1400 1575 3683 51 6390 9 175 350 524 699 874 1049 1224 1398 1573 6592 52 7439 8 175 350 524 699 874 1049 1224 1398 1573 9501 53 8488 7 175 349 524 698 873 1047 1222 1396 1571 I -2092410 54 55 9535 6 175 349 524 698 873 1047 1222 1396 1571 5319 9330582 5 174 349 523 697 872 1046 1220 1394 1569 8228 56 1628 4 174 348 522 696 871 1045 1219 1393 1567 1-2031137 57 2673 3 174 348 522 696 871 1045 1219 1393 1567 4046 5« 3718 2 174 348 521 695 869 1043 1217 1390 1563 6955 59 4761 I 174 348 521 695 869 1043 1217 1390 1563 9864 60 5804 174 347 521 694 868 1042 1215 1389 1562 1-2042772 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. [69 21 Degrees. 70] 69 Degrees. Difference for Seconds. M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o I 2 3 4 9335804 6846 7888 8928 9968 60 59 58 57 56 174 174 173 i73 173 347 347 347 '347 346 521 521 520 520 519 694 694 693 693 692 868 868 867 867 866 1042 1042 1040 1040 1039 1215 1215 1213 1213 1212 1389 1389 1386 1386 1385 1562 1562 1560 1560 1558 1*2042772 5681 8590 1-2051499 4408 Arc. Sec; Uiff. 10 ' •'8'* 5 6 7 8 9 9341007 2045 • 3082 . 4119 5154 55 54 53 52 51 173 173 173 173 173 346 346 346 345 345 519 518 518 518 518 692 691 691 690 690 865 864 864 863 863 1038 1037 1037 1035 1035 1211 1210 1210 1208 1208 1384 1382 1382 1380 1380 1557 1555 1555 1553 1553 7317 1*2060226 3135 6044 8953 20 30 40 50 60 70 80 90 t"3 970 1454 1939 2424 2909 lO II 12 13 14 6189 7223 8257 9289 9350321 50 49 48 47 46 172 172 172 172 172 345 345 344 344 344 517 516 516 515 689 689 688 688 687 862 862 860 860 859 1034 1034 1032 1032 103 1 1206 1206 1204 1204 1203 1378 1378 1376 1376 1374 1551 1551 1548 1548 1546 1*2071861 4770 7679 1*2080588 3497 3394 3878 4363 17 i8 19 1352 2382 3412 4440 5468 45 44 43 42 41 172 172 171 171 171 343 343 343 343 342 515 515 514 514 513 686 686 685 685 684 858 858 857 857 856 1030 1030 1028 1028 1027 1 201 1 201 1 199 1199 1 198 1373 1373 1370 1370 1369 1544 1544 1542 1542 1540 6406 9315 1*2092224 5133 8042 20 21 22 23 24 6495 7521 8547 9571 9360595 40 39 38 37 36 171 171 171 171 171 342 342 341 341 341 513 513 512 512 512 684 684 682 682 682 855 855 853 853 853 1026 1026 1024 1024 1023 1197 1 197 1 194 1 194 1 194 1368 1368 1365 1365 1365 1539 1539 1535 1535 1535 1*2100950 3859 6768 9677 1*2112586 25 26 27 28 29 1618 2641 3662 4683 5703 35 34 33 32 31 30 29 28 27 26 171 170 170 170 170 341 340 340 340 339 512 510 510 510 509 682 680 680 680 679 853 851 851 850 849 1023 1021 1021 1020 1019 1 194 1191 1 191 1190 1189 1365 1361 1361 1360 1358 1535 1531 1531 1530 1528 5495 8404 1*2121313 4222 7131 30 31 32 33 34 11 37 38 39 6722 7740 8758 9774 9370790 170 170 169 169 169 339 339 339 339 339 509 509 508 508 508 678 678 677 677 677 848 848 847 847 847 1018 1018 1016 1016 1016 1187 1 187 1 185 1185 1 185 1357 1357 1354 1354 1354 1526 1526 1523 1523 1523 1*2130039 2948 5857 8766 1*2141675 1806 2820 3833 4846 5858 25 24 23 22 21 169 169 169 169 169 338 338 338 337 337 506 506 506 506 676 675 674 674 845 844 844 843 843 1014 1013 1013 1012 lOII 1183 1 182 1182 1180 1180 1352 1350 1350 1349 1348 1521 1519 1519 1517 1517 4584 7493 1*2150402 3311 6220 . 40 41 42 43 44 6869 7880 8889 9898 9380906 20 19 18 17 16 169 168 168 168 168 337 336 336 336 336 506 504 504 504 503 674 672 672 672 671 843 841 841 840 839 ion 1009 1009 1008 1007 1 180 1177 1177 1 176 1175 1348 1345 1345 1344 1342 1517 1513 1513 1512 1510 9128 1*2162037 4946 7855 1*2170764 45 46 47 48 49 1913 2920 3925 4930 5934 15 14 13 12 II 168 168 168 167 167 336 335 335 335 335 503 503 503 502 502 671 670 670 669 669 839 838 838 837 837 1007 1005 1005 1004 1004 1175 1173 1173 1171 1171 1342 1340 1340 1338 1338 1510 1508 1508 1506 1506 3673 6582 9491 1*2182400 5309 50 51 52 53 54 11 57 58 59 60 6938 7940 8942 9942 9390943 10 9 8 7 6 167 167 167 167 167 334 334 333 334 333 501 501 500 500 500 668 668 666 667 666 835 835 833 834 833 1002 1002 1000 lOOI 999 1169 1169 1 166 1168 1 166 1336 1336 1333 1334 1332 1503 1503 1499 1 501 1499 8216 1*2191125 4034 6943 9852 1942 2940 3938 4935 5931 6926 5 4 3 2 I 166 166 166 166 166 166 .333 333 332 332 332 332 499 499 498 498 497 497 665 665 664 664 663 663 832 832 831 830 829 829 998 998 997 996 995 995 1 164 1 164 1 163 1 162 1161 1161 1330 1330 1329 1328 1326 1326 1497 1497 1495 1494 1491 1491 1*2202761 5670 8579 1*2211488 4397 7305 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 20 Degrees. 73 Degrees. Difference for Seconds. [7 M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o I 2 3 4 9396926 7921 8914 9907 9400899 60 59 58 11 166 166 166 165 165 332 331 331 331 331 497 497 497 496 496 663 662 662 661 661 829 828 828 827 827 995 993 993 992 992 1161 1159 1159 1157 1157 1326 1324 1324 1322 1322 1492 1490 1490 1488 1488 1*2217305 1-2220214 3123 6032 8941 Arc. Sec. Difif. 10 20 30 40 60 70 80 90 485 5 6 7 8 9 1891 2881 3871 4860 5848 55 54 53 52 51 165 165 165 165 165 330 330 330 329 329 495 495 494 494 494 660 660 659 658 658 825 825 824 823 823 990 990 989 988 987 1155 1155 1154 1152 1152 1320 1320 1318 1317 1316 1485 1485 1483 1481 1481 1*2231850 4759 7668 1-2240577 3486 970 1454 1939 2424 2909 lO II 12 13 14 6835 7822 8808 9793 9410777 50 49 48 47 46 165 164 164 164 164 329 329 328 328 328 494 493 492 492 491 658 657 656 656 655 823 822 821 820 819 987 986 985 984 983 1152 1150 1149 1148 1147 1316 1314 1313 1312 1310 1481 1479 1477 1476 1474 6394 9303 1-2252212 5121 8030 3394 3878 4363 15 i6 17 i8 19 1760 2743 3724 4705 5686 45 44 43 42 41 164 164 164 164 163 328 327 327 327 326 491 491 491 491 489 655 654 654 654 652 819 818 818 818 816 983 981 981 981 979 1 147 1 145 1 145 1145 1142 1310 1308 1308 1308 1305 1474 1472 1472 1472 1468 1-2260939 3848 6757 9666 1-2272575 20 21 22 23 24 25 26 27 28 29 6665 7644 8621 9598 9420575 40 39 38 37 36 163 163 163 163 163 326 326 326 326 325 489 488 488 488 488 652 651 651 651 650 816 814 814 814 813 979 977 977 977 975 1142 1 140 1 140 1140 1 138 1 305 1302 1302 1302 1300 1468 1465 1465 1465 1463 5483 8392 1-2281301 4210 7119 1550 2525 3498 4471 5444 35 34 33 32 _3L 30 29 28 27 26 163 162 162 162 162 325 324 324 324 324 488 486 486 486 485 650 648 648 648 647 813 811 811 811 809 975 973 973 973 971 1 138 1135 1135 1135 1133 1300 1297 1297 1297 1294 1463 1459 1459 1459 1456 1-2290028 2937 5846 8755 I -2301 664 30 31 32 33 34 6415 7386 8355 9324 9430293 162 162 162 162 161 324 323 323 323 322 485 485 485 485 483 647 646 646 646 644 809 808 808 808 806 971 969 969 969 967 1133 1131 1131 1131 1128 1294 1292 1292 1292 1289 1456 1454 1454 H54 1450 4572 7481 I -23 10390 3299 6208 35 36 37 38 39 1260 2227 3192 4157 5122 25 24 23 22 21 161 161 161 161 161 322 322 322 322 321 483 482 482 482 482 644 643 643 643 642 806 804 804 804 803 967 965 965 965 963 1128 1 126 1 126 1126 1 124 1289 1286 1286 1286 1284 1450 1447 1447 1447 "445 9116 1-2322025 4934 7843 1-2330752 40 41 42 43 44 6085 7048 8010 8971 9931 20 19 18 17 16 161 160 160 160 160 321 321 320 320 320 482 481 480 480 479 642 641 640 640 639 803 802 801 800 799 963 962 961 960 959 1 124 1122 1121 1 1 20 II 19 1284 1282 1281 1280 1278 1445 1443 1441 1440 1437 3661 6570 9479 1-2342388 5296 45 46 47 48 49 9440890 1849 2807 3764 4720 15 14 13 12 11 160 160 160 159 159 320 319 319 319 318 479 479 479 478 477 639 638 638 637 636 799 798 798 797 796 959 958 957 956 955 1119 1117 1117 1115 1114 1278 1277 1276 1274 1273 1437 1436 1436 1434 1432 8205 1-2351114 4023 6932 9841 50 51 52 S3 54 55 56 57 58 59 60 5675 6630 7584 8537 9489 10 9 8 7 6 159 159 159 159 159 318 318 318 317 317 477 477 476 476 476 636 636 635 634 634 796 795 794 793 793 955 954 953 952 952 1114 1113 1112 IIIO mo 1273 1272 1270 1269 1269 1432 143 1 1429 1427 1427 1-2362749 5658 8567 1-2371476 4385 9450441 1391 2341 3290 4238 5186 5 4 3 2 I 158 158 158 158 158 158 317 317 316 316 316 315 475 475 474 474 474 473 633 633 632 632 632 631 792 792 791 790 790 789 950 950 949 948 948 946 1 108 1 108 1 107 1 106 1 106 1 103 1266 1266 1265 1264 1264 1261 1425 1425 1423 1422 1422 1418 7294 1-2380203 3112 6021 8930 I -2391 838 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 19 Degrees. 72] 71 Degrees. Diflference for Seconds. M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o I 9455186 6132 60 59 158 158 315 315 473 473 630 630 788 788 946 946 1 103 1 103 1 261 I26I I418 I418 1-2391838 4747 Arc. 2 3 7078 8023 58 57 158 158 315 315 473 473 630 630 788 788 945 945 1 103 1 103 1260 1260 I418 I418 7656 1-2400565 bee. um. 485 4 8968 56 157 314 471 628 786 943 IIOO 1257 I414 3474 20 30 40 50 60 5 9911 55 157 314 471 628 786 943 IIOO 1257 1414 6383 970 1454 1939 2424 2909 3394 6 9460854 54 157 3H 470 627 784 941 1098 1254 141 1 9292 7 1795 53 157 314 470 627 784 941 1098 1254 I41I 1-2412201 8 2736 52 157 314 470 627 784 941 1098 1254 141 1 5110 9 3677 51 157 313 470 626 783 939 1096 1252 1409 8019 70 80 lO 4616 50 157 313 470 626 783 939 1096 1252 1409 1-2420927 3878 II 5555 49 156 313 469 625 782 938 1094 1250 1407 3836 90 4363 12 6493 48 156 312 468 624 781 937 1093 1249 1405 6745 13 7430 47 156 312 468 624 780 936 1090 1248 1404 9654 14 8366 46 156 312 467 623 779 935 I09I 1246 1402 1-2432563 15 9301 45 iS6 312 467 623 779 935 I09I 1246 1402 5472 i6 9470236 44 156 3H 467 622 778 934 1089 1245 1400 8381 17 1 170 43 156 311 467 622 778 933 1089 1244 1400 I -2441 290 i8 2103 42 155 3" 466 621 m 932 1087 1242 1398 4199 19 20 ■ 3035 41 155 310 465 620 77b 931 1086 I24I 1396 7108 3966 40 155 310 465 620 776 931 1086 1 241 1396 I -24500 1 5 21 4897 39 ^55 310 465 620 775 930 1085 1240 1395 2924 22 5827 38 155 310 464 619 774 929 1084 1238 1393 5833 23 6756 37 155 309 464 618 773 928 1082 1237 I39I 8742 24 7684 36 155 309 464 618 773 928 1082 1237 I39I I -246 1 65 1 25 8612 35 154 309 463 617 772 926 1080 1234 1389 4560 26 9538 34 154 309 463 617 772 926 1080 1234 1389 7469 27 9480464 33 154 308 462 616 771 925 1079 1233 1387 1-2470378 28 1389 32 154 308 462 616 770 924 1078 1232 1386 3287 29 2313 31 154 308 462 616 770 924 1078 1232 1386 6196 3° 3237 30 154 307 461 614 768 922 1075 1229 1382 9104 31 4159 29 154 307 461 614 768 922 1075 1229 1382 1*2482013 32 5081 28 154 307 461 614 768 921 1075 1228 1382 4922 33 6002 27 153 307 460 613 767 920 1073 1226 1380 7831 34 6922 26 153 307 460 613 767 920 1073 1226 1380 1-2490740 35 7842 25 153 306 459 612 765 918 I07I 1224 1377 3649 36 8760 24 153 306 459 612 765 918 I07I 1224 1377 6558 n 9678 23 153 306 458 611 764 917 1070 1222 1375 9467 3« 9490595 22 153 305 458 610 763 916 1068 I22I 1373 1-2502376 39 1511 21 153 305 458 610 763 915 915 1068 1220 1373 5285 40 2426 20 153 305 458 610 763 1068 1220 1373 8193 41 - 3341 19 152 305 457 609 762 914 1066 I218 I37I 1-2511102 42 4255 18 152 304 456 608 761 913 1065 I217 1369 4011 43 5168 17 152 304 456 608 760 912 1664 I216 1368 6920 44 6080 16 15 152 304 455 607 759 911 1063 1063 I214 1366 9829 45 6991 152 304 455 607 759 911 I214 1366 1-2522738 46 , 7902 14 152 303 455 606 758 910 I06I I213 1364 5647 47 ■> 8812 13 152 303 455 606 758 909 I06I I2I2 1364 8556 48 9721 12 151 303 454 605 757 908 I06I I2I2 1364 1-2531465 49 50 9500629 II 151 302 453 604 756 907 1058 1209 1360 4374 1536 10 151 302 453 604 756 907 1058 1209 1360 7282 51 ." 2443 9 151 302 452 603 754 905 1056 1206 1356 1-2540191 52 3348 8 151 302 452 603 754 905 1056 1206 1356 3100 S3 ■4253 7 151 301 452 602 753 904 1054 1205 1355 6009 54 55 S157 6 151 301 452 602 753 904 1054 1205 1355 8918 6061 5 150 301 451 601 752 902 1052 1202 1353 1-2551827 5<5 '. 6963 4 150 301 451 601 752 902 1052 1202 1353 4736 57 7865 3 150 300 450 600 751 901 105 1 1 201 I351 7645 5« 8766 2 150 300 450 600 750 900 1050 1200 1350 1-2560554 59 9666 I 150 300 449 599 749 899 1049 1 198 1347 3463 60 M. 9510565 150 300 449 599 749 899 1049 1 198 1347 6371 Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 18 Decrees. 72 I )egrees. Difference for Seconds. R M. o I Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 9510565 1464 60 59 150 150 300 299 449 449 599 598 749 748 899 897 1049 1047 1 198 1196 1348 1346 I "256637 1 9280 Arc Spr 1 TM(F 2 3 4 2361 3258 4154 58 57 56 150 149 149 299 299 299 449 448 448 598 597 597 748 747 747 897 896 896 1047 1 04s 1045 1 196 1 194 1 194 1346 1344 1344 1-2572189 5098 8007 oec. 10 20 30 48s 970 1454 5 5050 55 149 298 447 596 745 894 1043 1 192 1341 1-2580916 6 5944 54 149 298 447 596 745 894 1043 1 192 1341 3825 40 1939 7 6838 53 149 298 446 595 744 893 1042 1190 1339 6734 50 2424 8 7731 52 149 297 446 594 743 892 1040 1189 1337 9643 60 2909 9 8623 51 149 297 446 594 593 743 891 1040 1188 1337 1-2592552 70 80 3394 lO 9514 50 148 297 445 742 890 1038 1 186 1335 5460 3878 II 9520404 49 148 297 445 593 742 890 1038 1186 1335 8369 90 4363 12 1294 48 148 296 444 592 741 889 1037 1185 1333 1-2601278 1.3 2183 47 148 296 444 592 740 888 1036 1 184 1332 4187 H 3071 46 148 296 443 591 739 887 1035 1182 1330, 7096 15 3958 45 148 295 443 590 738 886 1033 1181 1328 I -26 1 0005 i6 4844 44 148 295 443 590 738 886 1033 1181 1328 2914 17 5730 43 148 295 443 590 738 885 1033 1 180 1328 5823 i8 6615 42 147 295 442 589 737 884 103 1 1178 1326 8732 19 7499 41 147 294 441 588 73i> 883 1030 1 177 1324 I -262 1 64 1 20' 8382 40 147 294 441 588 735 882 1029 1 176 1323 4549 21 9264 39 147 294 441 588 735 882 1029 1 176 1323 7458 22 9530146 38 147 294 440 587 734 881 1028 1 174 1321 1-2630367 23 1027 37 147 293 440 586 733 880 1026 1173 1319 3276 24 1907 3(3 35 147 293 440 586 733 879 1026 1172 1319 6185 2S 2786 146 293 439 585 732 878 1025 1171 1318 9094 26 3664 34 146 293 439 585 732 878 1025 1171 1318 1-2642003 27 4542 33 146 292 438 584 730 876 1022 1 168 1314 4912 28 5418 32 146 292 438 584 730 876 1022 1 168 1314 7821 29 6294 3' 146 292 438 584 730 876 1022 1 168 1314 1-2650730 30 7170 30 146 291 437 S82 728 874 1019 1 165 1310 3638 31 8044 29 146 291 437 582 728 873 1019 1 164 1310 6547 32 8917 28 146 291 437 582 728 873 1019 1 164 1310 9456 33 9790 27 145 291 436 581 727 872 1017 1 162 1308 1-2662365 34 3? 9540662 26 145 290 435 580 726 871 1016 1161 1306 5274 1533 25 145 290 435 580 725 870 1015 1160 1305 8183 36 2403 24 145 290 435 580 725 870 1015 1160 1305 I -267 1092 37 3273 23 145 289 434 578 723 868 1012 1157 1301 4001 38 4141 22 145 289 434 578 723 868 1012 1157 1301 6910 39 40 5009 21 145 289 434 578 723 867 1012 1 1 56 1301 9819 5876 20 145 289 434 578 723 867 1012 1 1 56 1301 1-2682727 41 6743 19 144 288 432 576 721 865 1009 1153 1297 5636 42 7608 18 144 288 432 576 721 865 1009 1153 1297 8545 43 8473 17 144 288 431 575 719 863 1007 1150 1294 1-2691454 44 9336 16 144 288 431 575 719 863 1007 1 1 50 1294 4363 4'? 9550199 15 144 288 431 575 719 863 1007 1150 1294 7272 46 1062 14 144 287 431 574 718 861 1005 1 148 1292 1-2700181 47 1923 13 144 287 431 574 718 861 1005 1 148 1292 3090 48 2784 12 143 286 429 572 716 859 1002 "45 1288 5999 49 3643 II 10 143 286 429 572 716 859 1002 1 145 1288 8908 4502 143 286 429 572 716 859 1002 1 145 1288 1-2711815 SI 5361 9 143 286 428 571 714 857 1000 1142 1285 4724 '52 6218 8 143 285 428 570 713 856 998 1 141 1283 7633 ';3 7074 7 143 285 428 570 713 856 998 1 141 1283 1-2720542 54 7930 6 143 285 428 570 713 855 998 1 140 1283 3451 S"? 8785 5 142 285 427 569 712 854 996 1 138 1281 6360 S6 9639 4 142 284 426 568 711 853 995 1137 1279 9269 S7 9560492 3 142 284 426 568 711 853 995 "37 1279 1-2732178 ^8 1345 2 142 284 426 568 710 852 994 1 136 1278 5087 59 2197 I 142 284 425 567 709 851 993 "34 1276 7996 60 M. 3048 Cosine. M. 142 283 425 566 708 850 991 "33 1274 1-2740904 10" 20" 30" 40" so" 60" 70" 80" 90" Arc. 17 Degrees. 74] 73 Degrees. Difference for Seconds. M. Sine. M. 10" 20" 30" 40" 50" 708 60" 70" 80" 1 133 90" Arc. o 9563048 60 142 283 425 566 850 991 1274 1*2740904 Arc I 2 3898 4747 59 58 142 141 283 283 425 424 566 565 708 707 849 848 991 989 1132 1130 1274 1272 3813 6722 Sec 1 TiiflT 3 4 5595 6443 57 56 141 141 283 282 424 423 565 564 707 706 848 847 989 988 1 130 1129 1272 1270 9631 1-2752540 5449 ^ 10 20 485 970 S 7290 55 141 282 423 564 705 846 987 1128 1269 6 8136 54 141 282 422 563 704 845 986 1126 1267 8358 30 1454 7 8981 53 141 281 422 562 703 844 984 1125 1265 1-2761267 40 1939 8 9825 52 141 281 422 562 703 844 984 1125 1265 4176 50 2424 9 lO 9570669 51 141 281 422 562 703 843 984 1124 1265 7085 60 70 2909 1512 50 140 281 421 561 702 842 982 1122 1263 9993 3394 II • 2354 49 140 280 420 560 701 841 981 1121 I26I 1-2772902 80 3878 12 3195 48 140 280 400 560 700 840 980 1 1 20 1260 5811 90 4363 n 4035 47 140 280 400 560 700 840 980 1 120 1260 8720 14 4875 46 140 280 419 559 699 839 979 1118 1258 1-2781629 M 5714 45 140 279 419 558 698 838 977 1117 1256 4538 i6 6552 44 140 279 419 558 698 837 977 1116 1256 7447 17 7389 43 139 279 418 557 697 836 975 1114 1254 1-2790356 i8 8225 42 139 278 417 556 696 835 974 1113 1252 3265 19 9060 41 139 278 417 556 696 835 974 1113 1252 6174 20 9895 40 139 278 417 556 695 834 973 1112 I25I 9082 21 9580729 39 139 278 416 555 694 833 972 IIIO 1249 I -2801990 22 1562 38 139 277 416 554 693 832 972 1109 1247 4899 23 2394 7>1 139 277 416 554 693 832 970 1 109 1247 7808 24 3226 36 138 277 415 553 692 830 968 1 106 1245 1-2810717 2'; 4056 35 138 277 415 553 692 830 968 1 106 1245 3626 26 4886 34 138 276 414 552 691 829 967 1 105 1243 6535 27 5715 33 138 276 414 552 690 828 966 1 104 1242 9444 28 6543 32 138 276 414 552 690 828 966 1 104 1242 1-2822353 29 30 7371 31 138 275 413 550 688 826 963 IIOI 1238 5262 8197 30 138 275 413 550 688 826 963 IIOI 1238 8171 31 9023 29 138 275 413 550 688 825 963 IIOO 1238 1-2831080 32 9848 28 137 275 412 549 687 824 961 1098 1236 3989 33 9590672 27 137 275 412 549 687 824 961 1098 1236 6898 34 1496 26 137 274 411 548 685 822 959 1096 1233 9807 35 2318 25 137 274 411 548 685 822 959 1096 1233 I -28427 16 36 3140 24 137 274 410 547 684 821 958 1094 I23I 5625 37 3961 23 137 273 410 546 683 820 956 1093 1229 8534 3« ■ 4781 22 137 273 410 546 683 819 956 1092 1229 I -285 1443 39 5600 21 136 273 409 545 682 818 954 1090 1227 4352 40 6418 20 136 273 409 545 682 818 954 1090 1227 7260 41 7236 19 136 272 408 544 681 817 953 1089 1225 1-2860169 42 8053 18 136 272 408 544 680 816 952 1088 1224 3078 43 8869 17 136 272 407 543 679 815 951 1086 1222 5987 44 9684 16 136 272 407 543 679 815 951 1086 1222 8896 45 9600499 15 136 271 407 542 678 813 949 1084 1220 1-2871805 46 ; I3I2 14 136 271 407 542 678 813 949 1084 1220 4714 47 2125 13 135 271 406 541 677 812 947 1082 I218 7623 48 2937 12 135 270 405 540 676 811 946 I08I I216 1-2880532 49 3748 II 135 270 405 540 675 810 945 1080 I215 3441 50 4558 10 135 270 405 540 675 810 945 1080 I215 6348 51 5368 9 135 270 404 539 674 809 944 1078 I2I3 9257 52 6177 8 135 269 404 538 673 807 942 1076 I2II 1-2892166 53 6984 7 135 269 404 538 673 808 942 1077 12II 5075 54 55 7792 6 134 269 403 537 672 806 940 1074 1209 7984 8598 5 134 268 402 536 671 805 939 1073 1207 1-2900893 56 9403 4 134 268 402 536 671 805 939 1073 1207 3802 57 9610208 3 134 268 402 536 670 804 938 1072 1206 671 1 5« IOI2 2 134 268 401 535 669 803 937 1070 1204 9620 59 1815 I 134 267 401 534 668 802 935 1069 1202 1-2912528 60 2617 134 267 401 534 668 801 935 1068 1202 5436 M. Cosine. M. 1 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 16 Degrees. 74 Degrees. Difference for Seconds. C7i M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o 961 26 I 7 60 134 267 401 534 668 801 935 1068 1202 1-2915436 Arc. I 3418 59 134 267 401 534 668 801 935 1068 1202 8345 K 2 4219 58 133 267 400 533 667 800 933 1066 1200 1*2921254 Sec. Diff. 3 5019 57 133 266 399 532 666 799 932 1065 1 198 4163 4 5818 56 55 133 266 399 532 665 798 931 1064 1062 II97 1 195 7072 10 20 485 ? 6616 133 266 398 531 664 797 930 9981 970 6 7413 54 133 266 398 531 664 797 930 1062 IJ95 1-2932890 3u 1454 7 8210 53 133 265 398 530 663 795 928 1060 1 193 5799 40 1939 8 9005 52 133 265 398 530 663 795 928 1060 1 193 8708 5^ 60 70 80 1 2424 9 9800 51 132 265 397 529 662 794 926 1058 1191 1-2941617 2909 lo 9620594 50 132 264 396 528 661 793 925 1057 1 1 89 4525 3394 08-78 II 1387 49 132 264 396 528 661 793 925 1057 1 189 7434 90 1 4363 12 2180 48 132 264 396 528 660 792 924 1056 1188 1-2950343 1.3 2972 47 132 263 395 526 658 790 921 1053 1 184 3252 H 3762 46 132 263 395 526 658 790 921 1053 1 184 6161 15 4552 45 132 263 395 526 658 790 921 1053 1 184 9070 i6 5342 44 131 263 394 525 657 788 919 1050 1182 I -296 1 979 17 6130 43 131 262 393 524 656 787 918 1049 1180 4888 i8 6917 42 131 262 393 524 656 787 918 1049 1180 7797 19 7704 41 131 262 393 524 655 786 917 1048 1 179 I -2970706 20 8490 40 131 262 392 523 654 785 916 1046 1177 3614 21 9275 39 131 262 392 523 654 785 916 1046 1177 6523 22 9630060 38 131 261 392 522 653 783 914 1044 1175 9432 23 0843 n 131 261 392 522 653 783 914 1044 1175 1-2982341' 24 1626 36 130 261 391 521 652 782 912 1042 1173 5250 2? 2408 35 130 260 390 520 651 781 911 1041 1171 8159 26 3189 34 130 260 390 520 650 780 910 1040 1 170 I -299 1 068 27 3969 33 130 260 389 519 649 779 909 1038 1 168 3977 28 4748 32 130 260 389 S19 649 779 909 1038 1 168 6886 29 5527 30 130 259 389 518 648 778 907 1037 1166 9795 30 6305 129 259 388 517 647 776 905 1034 1164 1-3002703 31 708 r 29 129 259 388 517 647 m 905 1034 1 164 5612 32 7858 28 129 258 387 516 646 775 904 1033 1 162 8521 33 8633 27 129 258 387 516 645 774 903 1032 1161 1-3011430 34 9407 26 129 258 387 516 645 774 903 1032 1161 4339 35 96401 8 I 25 129 258 386 515 644 773 902 1030 1159 7248 36 0954 24 129 257 386 514 643 772 900 1029 1157 I -3020 1 57 37 1726 23 129 257 386 514 643 771 900 1028 1157 3066 3« 2497 22 129 257 386 5H 643 771 900 1028 1157 5975 39 3268 21 128 256 384 512 641 769 897 1025 1153 8884 40 4037 20 128 256 384 512 641 769 897 1025 1153 1-3031792 41 4806 19 128 2S6 384 512 640 768 896 1024 1152 4701 42 5574 18 128 2S6 383 5" 639 767 895 1022 1150 7610 43 6341 17 128 256 383 511 639 767 895 1022 1150 1-3040519 44 7108 16 128 255 383 510 638 765 893 1020 1 148 3428 45 7873 15 128 255 383 510 638 765 893 1020 1 148 6337 46 8638 14 127 255 382 509 637 764 891 1018 1 146 9246 47 9402 13 127 254 381 508 635 763 890 1017 1 144 1-3052155 48 9650165 12 127 254 381 508 635 762 889 1016 1 143 5064 49 0927 II 127 254 381 508 635 762 889 1016 1 143 7973 SO 1689 10 127 253 380 506 633 760 886 1013 1 139 1-3060881 51 2449 9 127 253 380 506 633 760 886 1013 1 139 3790 52 3209 8 127 253 380 506 633 759 886 1012 1 139 6699 53 3968 7 126 253 379 505 632 758 884 lOIO 1137 9608 54 4726 6 126 253 379 505 632 758 884 lOIO 1137 1-3072517 55 5484 5 126 252 378 504 630 756 882 1008 1 134 5426 56 6240 4 126 252 378 504 630 756 882 1008 1134 8335 57 6996 3 126 252 377 503 629 755 881 1006 1132 I -308 1 244 5B 7751 2 126 251 377 502 628 754 879 1005 1 130 4153 59 8505 I 126 251 377 502 628 753 879 1004 1 130 7062 60 9258 126 251 377 502 628 753 879 1004 1 130 90" 9969 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" Arc. 15 Degrees. 76] 75 Degrees Difference for Seconds. M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o I 9659258 966001 1 60 59 126 125 251 250 377 375 502 500 628 626 753 751 879 876 1004 lOOI 1 130 1126 1-3089969 1-3092878 Arc. A Sec Diff. 2 3 0762 1513 58 57 125 125 250 250 375 375 500 500 626 625 751 750 876 875 lOOI 1000 1 1 26 1 125 5787 8696 485 970 1454 1939 2424 2909 ^iQ4 4 2263 56 125 250 374 499 624 749 874 998 1 123 1-3101605 20 30 40 S 3012 55 125 250 374 499 624 749 874 998 1123 4514 6 3761 54 125 249 - 374 498 623 747 872 996 1121 7423 7 4508 53 125 249 374 498 623 747 872 996 1121 I -3 1 10332 50 60 8 525 s 52 124 249 373 498 622 746 870 994 1119 3241 9 6001 51 .124 248 372 496 621 745 869 993 1117 6150 70 80 lO 6746 50 124 248 372 496 620 744 868 992 1116 9058 3878 II 7490 49 124 248 372 496 620 744 868 992 1116 1-3121967 90 4363 12 8234 48 124 248 371 495 619 743 867 990 1 1 14 4876 13 8977 47 124 247 371 494 618 741 865 988 1112 7785 14 9718 46 124 247 371 494 618 741 865 988 1112 1-3130694 I? 9670459 45 124 247 371 494 618 741 865 988 1112 3603 i6 1200 44 123 246 369 492 616 739 862 985 1 108 6512 17 1939 43 123 246 369 492 616 739 862 985 1 108 9421 i8 2678 42 123 246 368 491 614 737 860 982 1 105 1-3142330 19 3415 41 123 246 368 491 614 737 860 982 1 105 5239 20 4152 40 123 245 368 490 613 736 858 981 1 103 8147 21 4888 39 123 245 368 490 613 736 858 981 1 103 1-3151056 22 5624 38 122 245 367 489 612 734 856 978 IIOI 3965 23 6358 yi 122 245 367 489 612 734 856 978 IIOI 6874 24 7092 36 122 244 366 488 611 733 855 977 1099 9783 2? 7825 35 122 244 366 488 610 732 854 976 1098 I -3 1 62692 26 8557 34 122 244 365 487 609 731 853 974 1096 5601 27 9288 33 122 243 365 486 608 730 852 974 1095 8510 28 9680018 32 122 243 3^5 486 608 730 852 974 1095 1-3171419 29 0748 31 121 243 364 485 607 728 849 970 1092 4328 30 1476 30 121 243 364 485 607 728 849 970 1092 7236 31 2204 29 121 242 363 484 606 727 848 969 1090 1-3180145 32 2931 28 121 242 363 484 606 727 848 969 1090 3054 33 3658 27 121 242 362 483 604 725 846 966 1087 5963 34 4383 26 121 242 362 483 604 725 846 844 966 1087 8872 35 5108 25 121 241 362 482 603 724 965 1085 1-3191781 36 5832 24 121 241 362 482 603 723 844 964 1085 4690 37 6555 23 120 241 361 481 602 722 842 962 1083 7598 3« 7277 22 120 240 360 480 601 721 841 961 108 1 1-3200507 39 7998 21 120 240 360 480 601 721 841 961 108 1 3416 40 8719 20 120 240 359 479 599 719 839 958 1078 6324 41 9438 19 120 240 359 479 599 719 839 958 1078 9233 42 9690157 18 120 239 359 478 598 718 837 957 1076 1-3212142 43 0875 17 120 239 359 478 598 718 837 957 1076 5051 44 1593 16 119 239 358 477 597 716 835 954 1074 7960 45 2309 15 119 239 3^8 477 597 716 835 954 1074 1-3220869 46 3025 14 119 238 357 476 596 715 834 953 1072 3778 47 3740 13 119 238 356 475 594 713 834 952 107 1 6687 48 4453 12 119 238 35(> 475 594 714 833 952 107 1 9596 49 5167 II 119 237 356 474 593 712 830 949 1067 1-3232505 50 5879 10 118 237 30 474 593 712 830 949 1067 5413 51 6591 9 118 237 355 473 592 710 828 946 1065 8322 52 7301 8 118 237 355 473 592 710 828 946 1065 I -3241 23 1 53 801 1 7 118 236 354 472 591 709 827 945 1063 4140 54 8720 6 118 236 354 472 472 590 590 708 826 944 1062 7049 55 9428 5 118 236 354 708 826 944 1062 9958 56 9700136 4 118 235 353 470 588 706 82^ 941 1058 1-3252867 57 0842 3 118 235 353 470 588 j 706 823 941 1058 5776 5« 1548 2 118 235 353 470 588 705 823 940 1058 8685 59 2253 I 117 235 352 469 587 704 821 938 1056 1-3261594 60 2957 117 235 352 469 587 ! 704 821 938 1056 4502 M. Cosine. M. 10" 20" 30" 40" 1 50" i 60" 70" 80" 90" Arc. 14 Degrees. 76 Degrees. Difference for Seconds. [77 M. o I Sine. M. 10' 20'' 30" 40" 50" 60" 70" 80" 90" Arc. 9702957 3661 60 59 117 117 235 234 352 351 469 468 587 585 704 702 821 819 938 936 1056 1053 1-3264502 7411 Arc. Sec.| Diff. 2 3 4363 5065 58 57 117 117 234 233 351 350 468 467 585 584 702 701 819 818 936 934 1053 1051 1-3270320 3229 485 970 I4'i4 .4 5 5766 56 117 233 350 466 583 700 816 933 1049 6138 20 30 6466 55 117 233 350 466 583 699 816 932 1049 9047 6 7165 54 116 233 349 466 582 698 814 930 1047 1-3281956 40 1939 2424 7 7863 53 116 233 349 466 582 698 814 930 1047 4865 50 8 8561 52 116 232 348 464 581 697 813 929 1045 7774 60 2QOQ 9 9258 51 116 232 347 463 579 695 811 926 1042 1-3290683 70 80 3394 lO 9953 50 116 232 347 463 579 696 811 926 1042 3591 3878 II 9710649 49 116 231 347 462 578 694 809 925 1040 6500 90 4363 12 1343 48 116 231 347 462 578 693 809 924 1040 9409 13 2036 47 116 231 347 462 578 693 809 924 1040 1-3302318 14 2729 46 115 115 231 346 461 577 692 807 922 1038 5227 ^5 3421 45 230 345 460 576 691 806 921 1036 8136 16 4112 44 115 230 345 460 575 690 805 920 1035 I -331 1045 I? 4802 43 115 230 344 459 574 689 804 918 1033 3954 i8 5491 42 115 230 344 459 574 689 804 918 1033 6863 19. 20 6180 41 40 115 229 344 458 573 687 802 916 103 1 9772 6867 "5 229 344 458 573 687 802 916 103 1 1-3322680 21 7554 39 114 229 343 457 572 686 800 914 1029 5589 22 8240 38 114 229 343 457 572 686 800 914 1029 8498 23 8926 37 114 228 342 456 570 684 798 912 1026 I -333 1407 24 25 9610 9720294 36 114 228 342 456 570 684 798 912 1026 4316 35 114 227 341 454 568 682 795 909 1022 7225 26 0976 34 114 227 341 454 568 682 795 909 1022 1-3340134 27 1658 33 114 227 341 454 568 681 795 908 1022 3043 28 2339 32 114 227 341 454 568 681 795 908 1022 5952 29 30 3020 31 113 226 339 452 566 679 792 905 1018 8861 3699 30 113 226 339 452 566 679 792 905 1018 I -335 1 769 31 4378 29 113 226 339 452 565 678 791 904 1017 4678 32 5056 28 113 226 338 451 564 677 790 902 1015 7588 33 5733 27 113 22 s 338 450 563 676 788 901 1013 1-3360497 34 35 6409 7084 26 113 225 338 450 563 675 788 900 1013 3406 25 113 225 338 450 563 675 788 900 1013 6315 36 7759 24 112 224 336 448 561 673 785 897 1009 9224 37 8432 23 112 224 336 448 561 673 785 897 1009 1-3372132 38 9105 22 112 224 336 448 560 672 784 896 1008 5042 39 40 9777 21 112 224 336 448 560 672 784 896 1008 7950 9730449 20 112 223 335 446 558 670 781 893 1004 1-3380858 41 1119 19 112 223 335 446 558 670 781 893 1004 3767 42 1789 18 112 223 335 446 558 669 781 892 1004 6676 43 2458 17 III 222 333 444 556 667 778 889 1000 9585 44 3125 16 III 222 333 444 556 668 666 779 777 890 888 1000 1-3392494 45 3793 15 III 222 333 444 555 999 5403 46 4459 14 III 222 332 443 554 665 776 886 997 8312 47 5124 13 III 222 332 443 554 655 776 886 997 1-3401221 48 5789 12 III 222 332 442 553 664 774 885 995 4130 49 6453 II III 221 332 442 553 552 663 774 772 884 882 995 7039 50 7116 10 no 221 331 441 662 993 9946 51 7778 9 1 10 220 330 440 551 661 771 881 991 1-3412855 52 8439 8 no 220 330 440 551 661 771 881 991 5764 53 9100 7 no 220 330 440 550 660 770 880 990 8673 54 9760 6 no 220 329 439 438 549 548 659 769 767 878 877 988 1-3421582 55 9740419 5 no 219 329 658 986 4491 56 1077 4 110 219 329 438 548 657 767 876 986 7400 57 1734 3 109 219 328 437 547 656 766 875 985 1-3430309 58 2390 2 109 219 328 437 547 656 766 875 985 3218 59 3046 I 109 218 327 436 546 655 764 873 982 6127 60 3701 109 218 327 436 545 654 763 873 982 1-3439035 M. Cosine. M. 10" 20" 30" 40" so" 60" 70" 80" 90" Arc. 13 Degrees. 78] 77 Degrees. Difference for Seconds. M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o 9743701 60 109 218 327 436 545 654 763 872 981 I "3439035 Arc. I 2 4355 5008 59 58 109 109 218 217 326 326 435 434 544 543 ^53 652 762 760 870 869 979 977 1-3441944 4853 3 4 5660 631 1 57 56 109 109 217 217 326 326 434 434 543 543 651 651 760 760 868 868 977 977 975 7762 1-3450671 10 20 485 970 1454 1939 ") 6962 55 108 217 325 433 542 650 758 866 3580 6 7612 54 108 216 324 432 541 649 757 865 973 6489 30 40 7 8261 53 108 216 324 432 540 648 756 864 972 9398 8 8909 52 108 216 323 431 539 647 755 862 970 1-3462307 "JO 9 9556 51 108 216 323 431 539 647 755 862 970 5216 60 2QOQ lO 9750203 50 108 215 323 430 538 646 753 861 968 8124 70 3394 II 0849 49 108 215 323 430 538 645 753 860 968 I '347 1033 80 3878 12 1494 48 107 215 322 429 537 644 751 858 966 3942 90 4363 13 2138 47 107 214 321 428 536 643 750 857 964 6851 14 2781 46 107 214 321 428 535 642 749 856 963 9760 H 3423 45 107 214 321 428 535 642 749 856 963 I -3482669 i6 4065 44 107 214 320 427 534 641 748 854 961 5578 17 4706 43 107 213 320 426 533 639 746 852 959 84^7 i8 5345 42 107 213 320 426 533 640 746 853 959 1-349139$ 19 5985 41 106 213 319 425 532 638 744 850 957 4305 20 6623 40 106 212 318 424 531 637 743 849 955 7213 21 7260 39 106 212 318 424 531 637 743 849 955 1-3500122 22 7897 38 106 212 318 424 530 636 742 848 954 3031 23 8533 37 106 212 317 423 529 635 741 846 952 5940 24 9168 36 106 211 317 422 528 634 739 845 950 8849 2S 9808 35 106 211 317 422 528 633 739 844 950 1-3511758 26 9760435 34 106 211 317 422 528 633 739 844 950 4667 27 1068 33 105 210 315 420 526 631 736 841 946 7576 28 1699 32 105 210 315 420 526 631 736 841 946 1-3520485 29 2330 31 105 210 315 420 52s 630 735 840 945 3394 30 2960 30 105 210 314 419 524 629 734 838 942 6302 31 3589 29 105 210 314 419 524 629 734 838 942 921 1 32 4218 28 104 209 314 418 523 627 732 836 941 1-3532120 33 4845 27 104 209 314 418 523 627 732 836 941 5029 34 3S 5472 26 104 209 313 417 522 626 730 834 939 7938 6098 25 104 208 312 416 521 625 729 833 937 1-3540847 36 6723 24 104 208 312 416 520 624 728 832 936 3756 37 7347 23 104 208 3" 415 519 623 727 830 934 6665 3« 7970 22 104 208 311 415 519 623 727 830 934 9574 39 8593 21 104 207 311 414 518 622 725 829 932 1-3552483 40 9215 20 104 207 311 414 518 621 725 828 932 5391 41 9836 19 103 207 310 413 517 620 723 826 930 8300 42 9770456 18 103 206 309 412 516 619 722 825 928 1-3561209 43 1075 17 103 206 309 412 515 618 721 824 927 4118 44 1693 16 103 206 309 412 515 618 721 824 927 7027 45 231 1 15 103 206 308 411 514 617 720 822 925 9936 46 2928 14 103 205 308 410 513 616 718 821 923 1-3572845 47 3544 13 103 205 308 410 513 615 718 820 923 5754 48 4159 12 102 205 307 409 512 614 716 818 921 8663 49 4773 II 102 205 307 409 512 614 716 818 921 1-3581572 50 5387 10 102 204 306 408 510 612 714 816 918 4479 51 5999 9 102 204 306 408 510 612 714 816 918 7388 52 6611 8 102 204 305 407 509 611 713 814 916 1-3590297 53 7222 7 102 203 305 406 508 610 711 813 914 3206 54 55 7832 6 5 102 203 305 406 508 610 711 813 914 6115 8442 lOI 203 304 405 507 608 709 810 912 9024 56 9050 4 lOI 203 304 405 507 608 709 810 912 1-3601933 57 9658 3 lOI 202 303 404 506 607 708 809 910 4842 5« 9780265 2 lOI 202 303 404 505 606 707 808 909 775 1\ 59 0871 I lOI 202 302 403 504 605 706 806 906 I -36 1 0660 60 1476 lOI 201 302 402 503 604 704 805 905 3568 M. Cosine. M. 10" 20" 30" 40' 50" 60" 70" 80" 90" Arc. 12 Degrees. 78 Degrees. Diffe ence for Seconds. [71 M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o 9781476 60 lOI 201 302 402 503 604 704 805 905 1-3613568 Arc. I 2080 59 lOI 201 302 402 503 604 704 805 905 6477 ^ ^ ^ 2 2684 3287 58 57 lOI 201 302 402 401 503 502 603 602 704 702 804 802 905 9386 1-3622295 Sec. Diff. 3 301 903 4 3889 56 100 200 300 400 501 601 701 801 901 5204 10 20 485 5 4490 55 100 200 300 400 500 600 700 800 900 8113 970 6 5090 54 100 200 299 399 499 599 699 798 898 I -363 1 022 3^ 1454 7 5689 53 100 200 299 399 499 599 699 798 898 3931 40 1939 8 6288 52 100 199 299 398 498 598 697 797 896 6840 5^ 2424 9 6886 51 100 199 299 398 397 _498_ 497 597 596 697 695 796 896 9749 60 2909 lO 7483 50 99 199 298 794 894 1-3642657 70 3394 80 3878 90 4363 II 8079 49 99 198 297 396 496 595 694 793 892 5566 12 8674 48 99 198 297 396 495 594 693 792 891 8475 13 9268 47 99 198 297 396 495 594 693 792 891 1*3651384 14 9862 46 99 198 296 395 494 593 692 790 889 4293 1,5 979045s 45 99 197 296 394 493 592 690 789 887 7202 i6 1047 44 99 197 296 394 493 591 690 788 887 1-3660111 17 1638 43 98 197 29s 393 492 590 688 786 885 3020 i8 2228 42 98 197 295 393 492 590 688 786 885 5929 19 2818 41 98 196 294 392 490 588 686 784 882 8838 20 3406 40 98 196 294 392 490 588 686 784 882 1-3671746 21 3994 39 98 196 293 391 489 587 685 782 880 4655 22 4581 38 98 195 293 391 488 586 683 781 878 7564 23 5167 37 98 195 293 390 488 585 683 780 878 1-3680473 24 5752 36 98 ..19s 293 390 488 585 683 780 878 876" 3382 25 6337 35 97 195 292 389 487 584 681 778 6291 26 6921 34 97 194 291 388- 486 583 680 777 874 9200 27 7504 33 97 194 291 388 485 582 679 776 873 I -3692 1 09 28 8086 32 97 194 290 387 484 581 678 774 871 5018 29 8667 31 97 193 290 386 483 580 676 773 869 7927 30 9247 30 97 193 290 386 483 580 676 773 869 1-3700835 31 9827 29 96 193 289 385 482 578 674 770 867 3744 32 9800405 28 96 193 289 385 482 578 674 770 867 6653 33 0983 27 96 192 288 384 481 577 671 769 865 9562 34 1560 26 96 192 2S8 384 480 576 672 768 864 1-3712471 35 2136 25 96 192 288 384 480 576 672 768 864 5380 36 2712 24 96 191 287 382 478 574 669 765 860 8289 37 3286 23 96 191 287 382 478 574 669 765 860 1-3721198 3« 3860 22 96 191 287 382 478 573 669 764 860 4107 39 4433 21 95 191 286 381 477 572 667 762 858 7016 40 5005 20 95 190 285 380 476 571 666 761 856 9924 41 5576 19 95 190 285 380 476 571 666 761 856 1-3732833 42 6147 18 95 190 284 379 474 569 664 758 853 5742 43 6716 17 95 190 284 379 474 569 664 758 853 8651 44 7285 16 95 189 284 378 473 568 662 757 851 I -374 1 560 45 7853 15 95 189 284 378 473 567 662 756 851 4469 4b 8420 14 94 189 283 377 472 566 660 754 849 7378 47 8986 13 94 189 283 377 472 566 660 754 849 1-3750287 48 9552 12 94 188 282 376 470 564 658 752 846 3196 49 9810116 II 94 188 282 376 470 564 658 752 846 6105 50 0680 10 94 188 281 375 469 563 657 750 844 9013 SI 1243 9 94 187 281 374 468 562 655 749 842 1-3761922 52 '^°A 8 94 187 281 374 468 561 655 748 842 4831 53 2366 7 94 187 281 374 468 561 655 748 842 7740 54 2927 6 93 186 279 372 466 559 652 745 838 1-3770649 55 3486 5 93 186 279 372 466 559 652 745 838 3558 5b 4045 4 93 186 279 372 465 558 6^1 744 837 6467 57 4603 3 93 186 278 371 464 557 650 742 835 9376 5« 5160 2 93 185 278 370 463 556 648 741 833 1-3782285 59 5716 I 93 i8s 278 370 463 556 648 741 833 5194 (X) 6272 92 i8s 277 369 462 554 646 738 831 8102 M. Cosine. M. 10" 20" 30" 40" so" 60" 70" 80" 90" Arc. 11 Degrees. 801 79 Degrees DifTerence for Seconds. M. Sine. M. 10" 20" 30" 40'; 50" 60" 70" 80" 90" Arc. o I 9816272 6826 60 59 92 92 185 185 277 277 369 369 462 462 554 554 646 646 738 738 831 831 X-3788IOI I-379IOIO Arc. Qo/» 1 T\:rr. 2 3 7380 7933 58 57 92 92 184 184 276 276 368 368 461 460 553 552 645 644 737 736 829 828 3919 6828 x-'m. 485 970 1454 1939 2424 2909 3394 4 8485 9037 56 55 92 184 276 368 460 552 644 736 828 9737 20 30 40 92 183 275 366 458 550 642 734 825 1-3802646 6 9587 54 92 183 275 366 458 550 642 734 825 5555 7 9820137 53 92 183 275 366 458 549 641 732 824 8464 50 60 8 0686 52 91 183 274 365 457 548 639 730 821 ^■38^1373 9 1234 51 91 182 273 364 456 547 638 729 820 4282 70 80 lO 1781 50 91 182 273 364 455 546 637 728 819 7x90 3878 II 2327 49 91 182 273 364 455 546 637 728 819 X '3820099 90 4363 12 2873 48 91 181 272 362 453 544 634 725 815 3008 n 3417 47 91 181 272 362 453 544 634 725 815 5917 14 3961 46 91 181 272 362 453 543 634 724 815 8826 I"; 4504 45 90 181 271 361 452 542 632 722 813 i'383i735 i6 5046 44 90 180 270 360 451 541 631 721 811 4644 17 5587 43 90 180 270 360 451 541 631 721 8x1 7553 i8 6128 42 90 180 270 360 450 540 630 720 8x0 I -3840462 19 6668 41 90 179 269 358 448 538 627 717 806 3371 20 7206 40 90 179 269 358 448 538 627 717 806 6279 21 7744 39 90 179 269 358 448 538 627 717 806 9188 22 8282 38 89 179 268 357 447 536 62s 714 804 1-3852097 23 J 8818 37 89 178 267 356 446 535 624 713 802 5006 24 9353 36 89 178 267 356 356 446 535 624 713 802 7915 2i; 9888 35 89 178 267 445 534 623 712 801 1-3860824 26 9830422 34 89 178 266 355 444 53-3 622 711 800 3733 27 0955 33 89 177 266 354 443 532 620 709 797 6642 28 1487 32 89 177 266 354 443 532 620 709 797 9551 29 2019 31 88 177 265 353 442 530 618 706 795 1-3872460 30 2549 33 88 177 265 353 442 530 618 706 795 5368 31 3079 29 88 176 264 352 441 529 617 705 793 8277 32 3608 28 88 176 264 352 440 528 6x6 704 792 1-3881x86 33 4136 27 88 176 263 351 439 527 615 702 790 4095 34 31 4663 26 88 175 263 350 438 526 613 701 788 7004 S189 25 88 175 263 350 438 S26 613 701 788 9913 36 571S 24 87 175 262 349 437 524 611 698 786 X -3892822 37 6239 23 87 175 262 349 437 524 611 698 786 5731 38 6763 22 87 174 261 348 436 523 610 697 784 8640 39 7286 21 87 174 261 348 435 522 609 696 783 1-3901549 40 7808 20 87 174 261 348 435 522 609 696 783 4457 41 8330 19 87 173 260 346 433 520 606 693 779 7366 42 8850 18 87 173 260 346 433 520 606 693 779 I -3910275 43 9370 17 87 173 260 346 433 519 606 692 779 3184 44 9889 16 86 173 259 258 345 432 518 604 690 777 6093 4S 9840407 15 86 172 344 431 517 603 689 775 9002 46 0924 14 86 172 258 344 431 517 603 689 775 I-392I9XX 47 1441 13 86 172 257 343 429 515 601 686 772 4820 48 1956 12 86 172 257 343 429 515 601 686 772 7729 49 2471 II S6 171 257 342 428 514 599 685 770 1-3930638 •JO 2985 10 86 171 257 342 428 513 599 684 770 3545 "Ji 3498 9 85 171 256 341 427 512 597 682 768 6454 t'i^ 4010 8 85 170 255 340 426 511 596 681 766 9363 ^3 4521 7 85 170 255 340 426 511 596 681 766 X -3942272 :54 55 5032 6 «5 170 255 340 425 510 508 595 592 680 765 5x81 5542 5 85 169 254 338 423 677 761 8090 56 6050 4 85 169 254 338 423 508 592 677 761 1-3950999 57 6558 3 85 169 254 338 423 508 592 677 761 3908 58 7066 2 84 169 253 337 422 506 590 674 759 6817 59 7572 I 84 169 253 337 422 506 590 674 759 9726 60 8078 84 168 252 336 420 504 588 672 756 1-3962634 .¥• Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 10 Degrees. 80 Degrees. Difference for Seconds. [i M. o I 2 3 Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 9848078 8582 9086 9589 60 59 58 57 84 84 84 84 168 168 168 167 252 252 251 251 336 335 334 420 420 419 418 504 504 503 502 588 588 587 585 672 672 671 669 756 756 755 752 1-3962634 5543 8452 1-3971361 Ave. Sec. Diff. 485 970 1454 1939 4 9850091 56 84 167 251 334 418 502 585 583 669 752 4270 20 30 5 0593 55 83 167 250 333 417 500 666 750 7179 6 1093 54 83 167 250 333 417 500 583 666 750 1-3980088 40 7 1593 53 83 166 249 332 416 499 582 665 748 2997 50 2424 8 2092 52 83 166 249 332 415 498 581 664 747 5906 60 2909 9 2590 51 83 166 248 331 414 497 580 "578^ 662 745 8815 70 80 3394 lO 3087 50 83 165 248 330 413 496 661 743 I -3991 723 3878 II 3583 49 83 165 248 330 413 496 578 661 743 4632 90 4363 12 4079 48 83 165 248 330 413 495 578 660 743 7541 13 4574 47 82 165 247 329 412 494 576 658 741 I -4000450 14 5068 46 82 82 164 164 246 328 410 493 575 657 739 3359 15 5561 45 246 328 492 574 656 738 6268 16 6053 44 82 164 245 327 409 491 573 654 736 9177 17 6544 43 82 164 245 327 409 491 573 654 736 1-4012086 38 7035 42 82 163 245 326 408 489 571 652 734 4995 19 7524 41 82 163 245 326 408 489 571 652 734 7904 20 8013 40 81 163 244 325 407 488 569 650 732 1-4020812 21 8501 39 81 162 243 324 406 487 568 649 730 3721 22 8988 38 81 162 243 324 406 487 568 649 730 6630 23 9475 37 81 162 242 323 404 485 566 646 730 9539 24 9960 36 81 162 242 323 404 485 566 646 730 1-4032448 2S 9860445 35 81 161 242 322 403 484 564 645 725 5357 26 0929 34 8i i6i 242 322 403 483 564 644 72s 8266 27 1412 33 80 161 241 321 402 482 562 642 723 1-4041 175 28 1894 32 80 160 240 320 401 481 561 641 721 4084 29 30 2375 31 80 160 240 320 401 481 561 641 721 6993 2856 30 80 160 240 320 400 480 560 640 720 9900 31 3336 29 80 160 239 319 399 479 559 638 718 1-4052809 32 3815 28 80 159 239 318 398 478 557 637 716 5718 33 4293 27 80 159 239 318 398 477 557 636 716 8627 34 35 4770 26 79 J 59 238 317 397 476 555 634 714 1-4061536 5246 25 79 159 238 317 397 476 555 634 714 4445 36 5722 24 79 158 237 316 395 474 553 632 711 7354 37 6196 23 79 158 237 316 395 474 553 632 711 1-4070263 3« 6670 22 79 158 236 3'5 394 473 552 630 709 3172 39 7143 21 79 157 236 314 393 472 550 629 707 6081 40 7615 20 79 157 236 314 393 472 550 629 707 8989 41 8087 19 78 157 235 313 392 470 548 626 705 I -408 1 898 42 8557 18 78 157 235 313 392 470 548 626 705 4807 43 9027 17 78 156 234 312 391 469 547 625 703 7716 44 9496 16 78 156 234 312 391 468 546 624 702 1-4090625 45 9964 15 78 156 233 311 389 467 545 622 700 3534 46 9870431 14 78 155 233 310 388 466 543 621 698 6443 47 0897 13 78 155 233 310 388 466 543 621 698 9352 48 1363 12 77 155 232 309 387 464 541 618 696 1-4102261 49 50 1827 II 77 155 232 309 387 386 464 541 618 696 5170 2291 10 77 154 231 308 463 540 617 694 8078 51 2754 9 77 '54 231 308 385 462 539 616 693 1-4110987 52 3216 8 77 154 231 308 385 462 539 616 693 3896 53 3678 7 77 153 230 306 383 460 536 613 689 6805 54 4138 6 77 153 230 306 383 460 536 613 689 9714 55 4598 5 77 153 230 306 383 459 536 612 689 1-4122623 56 5057 4 76 153 229 305 382 458 534 610 687 5532 57 5514 3 76 152 228 304 381 457 533 609 685 8441 58 5972 2 76 152 228 304 380 456 532 608 684 1-4131350 59 6428 I 76 152 227 303 379 455 531 606 682 4259 60 M. 6883 76 152 227 303 379 455 531 606 682 7167 Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 9 Degrees. m 621 81 Degrees, Difference for Seconds. M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o I 2 3 4 9876883 7338 7792 8245 8697 60 59 58 57 56 76 76 76 75 75 75 75 75 75 75 152 151 151 151 150 228 227 227 226 225 304 302 302 301 300 380 378 378 377 376 455 454 453 452 451 531 529 529 527 526 606 605 604 602 601 682 680 680 678 676 1-4137167 1*4 1 40076 2985 5894 8803 Sec. Arc. DiffT 10 20 30 40 50 60 70 80 90 485 970 1454 1939 2424 2909 5 6 7 8 9 lO II 12 13 14 9148 9599 9880048 0497 0945 55 54 53 52 51 150 150 150 149 149 225 224 224 224 224 300 299 299 298 298 376 374 374 373 373 451 449 449 448 447 526 524 524 522 522 601 598 598 597 596 676 673 673 671 671 1-4151712 4621 7530 I -4 1 60439 3348 1392 1838 2284 2728 3172 50 49 48 47 46 74 74 74 74 74 149 149 148 148 148 223 223 222 222 221 297 297 296 296 295 372 372 370 370 369 446 446 444 444 443 520 520 518 517 594 594 592 592 590 669 669 666 666 664 6256 9165 1-4172074 4983 7892 3394 3878 4363 15 i6 17 i8 19 3615 4057 4498 4939 5378 45 44 43 42 41 74 74 74 73 73 147 147 147 146 146 221 221 221 219 219 294 294 294 292 292 368 368 368 366 366 442 441 441 439 439 515 515 515 512 512 589 588 588 585 585 662 662 662 658 658 1-4180801 3710 6619 9528 1-4192437 20 21 22 23 24 25 26 27 28 29 5817 6255 6692 7128 7564 40 39 38 37 36 73 73 73 73 72 146 146 H5 145 145 219 218 218 218 217 292 291 290 290 289 365 364 363 363 362 438 437 436 436 434 511 508 508 506 584 583 581 578 657 656 653 651 5345 8254 I -4201 163 4072 6981 7998 8432 8865 9297 9728 35 34 33 32 31 72 72 72 72 72 145 144 144 143 143 217 216 216 215 215 289 288 288 287 287 362 361 360 359 359 434 433 432 431 431 506 505 504 503 503 578 576 574 574 651 649 648 646 646 9890 I -42 1 2799 5708 8617 I -422 1 526 30 31 32 33 34 9890159 0588 1017 1445 1872 30 29 28 27 26 72 72 71 71 71 143 143 H3 142 142 215 215 214 213 213 286 286 28s 284 284 35^ 358 357 356 355 429 429 428 427 426 SOI 501 499 498 497 572 572 570 569 568 644 644 642 640 639 4434 7343 14-230252 3161 6070 35 36 37 38 39 2298 2723 3148 3572 3994 25 24 23 22 21 71 71 71 70 70 142 142 141 141 141 212 212 212 211 211 283 283 282 281 281 354 354 353 352 352 425 425 424 422 422 496 496 494 492 492 566 566 565 562 ^37 637 635 633 633 8978 I -4241 887 4796 7705 1-4250614 40 41 42 43 44 4416 4838 5258 5677 6096 20 19 18 17 16 70 70 70 70 70 141 140 140 140 139 211 210 209 209 209 281 280 279 279 278 352 350 349 349 348 422 420 419 419 418 492 490 489 489 487 562 560 558 557. 633 630 628 628 626 3523 6432 9341 1-4262250 5159 45 46 47 48 49 6514 6931 7347 7762 8177 15 14 13 12 II 70 69 69 69 69 139 139 138 138 138 209 208 207 207 206 278 277 276 276 275 348 347 346 346 344 417 416 415 415 413 487 485 484 484 482 556 554 553 553 550 626 624 622 622 619 8068 1-4270977 3886 6795 9703 50 51 52 53 54 11 11 1? 8590 9003 9415 9826 9900237 10 9 8 7 6 5 4 3 2 I 69 69 69 69 68 138 137 137 137 136 206 206 206 206 204 275 274 274 274 272 344 343 343 343 341 413 412 411 411 409 482 480 480 480 477 550 549 548 548 545 619 617 617 617 613 I -428261 1 5520 8429 1-4291338 4247 0646 1055 1462 1869 2275 2681 68 68 68 68 68 67 136 136 136 135 135 135 204 203 203 203 203 202 272 271 271 270 270 269 341 339 339 338 338 337 409 407 407 406 406 404 477 475 475 473 473 471 545 542 542 541 538 613 610 610 608 608 606 7156 1-4300065 2974 5883 8792 1-4311700 M. 1 Cosine. | M. 10" 20" 30" 40" 50" 60' 70" 80" 90" 1 Arc. 8 Degrees. 82 Be^ prees. Difference for Seconds. [81 M; Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o I 2 3 4 5 6 7 8 9 9902681 3085 3489 3891 4293 60 59 58 57 56 67 67 67 67 67 67 67 67 66 66 135 135 134 134 134 202 202 • 201 201 200 269 269 268 268 267 337 337 335 335 334 404 404 402 402 401 471 471 469 469 468 538 538 536 536 534 606 606 603 603 601 1-4311700 4609 7518 1-4320427 3336 Arc. A Sec. 10 20 30 40 60 70 80 90 i Diff. 485 4694 5095 5494 5893 6290 55 54 53 52 51 134 133 132 132 200 200 200 198 198 267 266 266 264 264 334 333 333 331 331 401 399 399 397 397 468 466 466 463 463 462 461 461 459 459 534 532 532 529 529 526 526 524 524 601 599 599 595 595 594 592 592 590 590 6245 9154 1-4332063 4972 7881 1-4340789^ 3698 6607 9516 1-4352425 970 1454 1939 2424 2909 lO II 12 13 6687 7083 7478 7873 8266 50 49 48 47 46 66 66 66 66 66 132 132 132 131 131 198 197 197 197 197 264 263 263 262 262 330 329 329 328 328 396 395 395 393 393 392 391 390 389 389 3394 3878 4363 15 i6 17 i8 19 8659 9051 9442 9832 9910221 45 44 43 42 41 65 65 65 65 65 131 130 130 130 130 129 129 129 128 128 196 195 195 194 194 261 260 260 259 259 327 326 325 324 324 457 456 455 454 454 522 521 520 518 588 586 585 582 582 5334 8243 1-4361152 4061 6970 20 21 22 23 24 0610 0997 1384 1770 2155 40 39 38 37 36 65 65 64 64 64 194 194 193 192 192 258 258 257 256 256 323 323 322 321 321 387 387 386 38s 385 452 452 450 449 449 516 516 514 513 513 581 581 579 577 577 9878 1-4372787 5696 8605 1-438x514 25 26 27 28 29 2540 2923 3306 3688 4069 35 It 32 31 64 64 64 64 63 128 128 127 127 127 191 191 191 191 190 255 255 254 254 253 319 319 318 317 383 383 382 381 380 447 447 445 445 443 510 510 509 508 506 574 574 572 572 570 4423 7332 1-4390241 3150 6059 30 31 32 33 34 4449 4828 5206 5584 5961 30 29 28 27 26 63 63 63 63 63 126 126 126 126 I2S 189 189 189 188 188 252 252 252 251 250 316 315 315 314 313 379 378 378 377 376 442 441 441 440 438 505 504 504 502 501 568 567 567 565 563 8967 I -4401 876 4785 7694 1-4410603 36 37 38 39 6337 6712 7086 7459 7832 25 24 23 22 21 63 62 62 62 62 125 125 124 124 124 188 187 186 186 186 250 249 248 248 248 313 312 311 ,3" 310 375 374 373 373 372 438 436 435 435 434 500 498 497 497 496 563 561 559 559 558 3512 6421 9350 1-4422239 5148 40 41 42 43 44 8204 8574 8944 9314 9682 20 19 18 17 16 62 62 62 61 61 123 123 123 123 122 185 185 185 184 183 246 246 246 245 244 308 308 308 307 306 370 370 370 368 367 431 431 431 429 428 493 493 493 490 489 554 554 554 552 550 8055 1-4430964 3873 6782 9691 45 46 47 48 49 9920049 0416 0782 1 147 1511 15 14 13 12 II 61 61 61 61 61 122 122 122 121 121 183 183 182 182 182 244 244 243 242 242 306 305 304 303 303 367 366 365 364 363 428 427 426 424 424 489 488 486 485 484 550 549 547 545 545 1-4442600 5509 8418 1-4451327 4236 50 SI 52 53 54 1874 2257 2599 2959 3319 10 9 8 7 6 61 60 60 60 60 121 121 120 120 120 182 181 180 180 180 242 241 240 240 240 303 302 300 300 300 363 362 360 360 360 424 422 420 420 420 484 482 480 480 480 545 543 540 540 540 7144 1-4460053 2962 5871 8780 S7 58 3679 4037 4394 4751 5107 5462 5 4 3 2 I 60 60 60 59 59 59 119 119 119 119 118 118 179 179 179 178 177 177 238 238 238 236 236 298 298 298 297 296 295 358 357 357 356 355 354 417 417 417 415 414 413 477 476 476 474 473 472 536 536 536 534 532 531 1-4471689 4598 7507 I -44804 1 6 3325 6233 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. ti 7 De'trees. 84] 83 Degrees Difference for Seconds. M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o J 9925462 5816 60 52 59 59 118 118 177 176 236 235 295 294 354 353 413 412 472 470 531 529 1-4486233 9142 Arc. Sec- Diff. 2 3 6169 6521 58 57 59 59 117 117 176 176 234 234 293 293 352 352 410 410 469 469 527 527 1-4492051 4960 485 . 4 6873 56 59 117 176 234 293 351 410 468 527 7869 20 30 40 50 60 70 80 5 7224 55 58 116 174 232 291 349 407 465 523 1-4500778 970 1454 1939 2424 2909 339; 38-3 6 7 7573 7922 54 53 58 58 116 116 174 174 232 232 291 291 349 349 407 407 465 465 523 523 3687 6596 8 9 8271 8618 52 51 58 58 116 116 173 173 231 231 289 289 347 317 405 405 462 462 520 520 9505 1-4512414 lO 8965 50 58 115 173 230 288 345 403 460 518 5322 II 9310 49 58 "5 ^73 230 288 345 403 460 518 8231 90 436^ 12 9655 48 57 115 172 229 287 344 401 458 516 r452n4o 13 9999 47 57 114 171 228 286 343 400 457 514 4049 9930342 46 57 114 171 228 286 343 400 457 514 511 6958 0685 45 57 114 170 227 284 341 398 454 9867 i6 1026 44 57 114 170 227 284 341 398 454 5" I '4532776 17 1367 43 57 113 170 226 283 339 396 452 509 5685 i8 1706 42 57 113 170 226 283 339 396 452 509 8594 19 2P 204; 41 57 113 170 226 283 339 396 452 509 I -4541 503 2384 40 56 112 168 224 281 337 393 449 505 4411 21 2721 39 56 112 168 224 280 330 392 448 504 7320 ,.22 3057 38 56 112 168 224 280 336 392 448 504 1-4550229 23 3393 37 56 112 167 223 279 335 391 446 502 3138 24 3728 36 56 III 167 222 278 334 333 389 445 500 6047 25 4062 35 56 III 167 222 278 389 444 500 8956 26 4395 34 55 III 166 221 277 332 387 442 498 1-4561865 27 4727 33 55 no 165 220 276 331 386 441 496 4774 28 5058 32 55 no 165 220 276 331 386 441 496 7683 29 5389 31 30 55 no 165 220 275 330 385 440 495 1-4570592 30 5719 55 109 164 218 273 328 382 437 491 3500 31 6047 29 55 109 164 218 273 328 382 437 491 6409 32 6375 28 55 109 164 218 273 328 382 437 491 9317 33 6703 27 54 109 163 217 272 326 380 434 489 1-4582226 34 7029 2b 54 109 163 162 217 272 326 380 378 434 432 489 5135 35 7355 25 54 108 216 270 324 486 8044 36 7679 24 54 108 162 216 270 324 .378 432 486 I "4590953 37 8003 23 54 108 161 215 269 323 377 430 484 3862 3« 8326 22 54 107 161 214 268 322 375 429 482 6771 39 40 8648 21 54 107 161 214 268 321 375 428 482 9680 8969 20 54 107 161 214 268 321 375 428 482 1-4602588 41 9-90 19 53 107 160 213 267 320 373 426 480 5497 42 9610 18 53 106 159 212 265 318 371 424 477 8406 43 9-8 17 S3 106 159 212 265 318 371 424 477 1-4611315 44 9940246 lb 53 106 106 158 158 2X1 264 31T 370 422 475 4224 45 0563 15 53 211 264 3'7 370 422 475 7133 46 0880 14 53 105 158 210 263 315 368 420 473 I 4620042 47 1195 13 53 105 158 210 263 315 368 420 473 2951 48 1510 12 52 104 156 208 261 313 ,365 417 469 5860 41 50" 1823 II 52 104 156 ,208 r6i 313 365 417 469 8769 2136 10 52 104 156 208 260 312 364 416 468 1-4631677 SI 2448 9 52 104 156 208 260 312 364 416 468 4586 52 2760 8 52 103 155 206 258 310 361 413 464 7495 53 3070 7 52 103 155 206 2 -,8 309 361 412 464 1-4640404 54 55 3379 6 52 103 155 206 258 309 361 412 464 3313 3688 5 51 103 154 205 257 308 359 410 462 6222 5t) 3996 4 51 102 153 204 256 307 358 409 460 , 9131 57 4303 3 51 102 153 204 255 306 357 408 459 1*4652040 S^ 4609 2 51 102 152 203 254 305 356 406 457 4949 59 4914 I 51 102 152 203 254 305 356 406 457 7858 bo 5219 51 lOI 152 202 253 304 354 405 455 I -4660766 M. Cosine. M. 10" 20" 30" 40 50" 60" 70" 80" 90" Arc. 6 Decrees. 84 Degrees. Difference for Seconds. - [fi M. o I Sine. M. 10" 20" 30" 40" SO" 60" 70" 80" 90" Arc. 9945219 5523 60 59 51 so lOI lOI 152 151 202 201 253 252 304 302 354 352 405 402 455 453 I -4660766 3675 Arc. Qor 1 n.'ff 2 3 5825 6127 58 57 SO 50 lOI TOO 151 150 201 200 252 251 302 301 352 351 402 401 453 451 6584 9493 • 485 970 I4s4 4 6428 5b 50 100 150 200 251 301 351 401 451 I -4672402 20 30 5 6729 55 SO ZOO 149 199 249 299 349 398 448 S3II b 7028 54 50 100 149 199 249 299 349 398 448 8220 40 1939 2424 7 7327 53 SO 99 149 198 248 298 347 397 446 I -468 II 29 50 8 7625 52 49 99 148 197 247 296 345 394 444 4038 60 2909 3394 9 lO 7921 51 49 99 148 197 247 296 345 394 444 6947 70 80 8217 50 49 99 148 197 247 296 345 394 444 9855 3878 II 8513 49 49 98 147 196 245 294 343 392 441 1-4692764 90 4363 12 8807 48 49 98 147 196 245 294 343 392 441 5673 13 9101 47 49 97 146 194 243 292 340 389 437 8582 IS 9393 9685 46 45 49 97 146 194 243 292 340 389 388 437 1-4701491 49 97 146 194 243 291 340 437 4400 16 9976 44 48 97 145 193 242 290 338 386 435 7309 17 9950266 43 48 97 145 193 242 290 338 386 435 1-4710218 i8 0556 42 48 96 144 192 240 288 336 384 432 3127 19 20 0844 41 48 96 144 192 240 288 336' 384 432 6036 1132 40 48 96 H3 191 239 287 335 382 430 8944 21 1419 39 48 95 143 190 238 286 333 381 428 1-4721853 22 1705 38 48 95 143 190 238 285 333 380 428 ,4762 23 1990 37 47 95 142 189 237 284 331 378 426 7671 24 2274 36 47 94 141 188 236 283 330 377 424 1-4730580 2S 2557 35 47 94 141 188 236 283 330 377 424 3489 26 2840 34 47 94 141 188 235 282 329 376 423 6398 27 3122 33 47 94 140 187 234 281 328 374 421 9307 28 3403 32 47 93 140 186 233 280 326 373 419 1-4742216 29 30 3683 31 47 93 140 186 233 279 326 372 419 5125 3962 30 46 93 139 ^^5 232 278 324 370 417 8033 31 4240 29 46 93 139 185 232 278 324 370 417 1-4750942 32 4518 28 46 92 138 184 231 277 323 369 415 3851 33 4795 27 46 92 137 183 229 275 321 366 412 6760 34 35 5070 26 46 92 ^37 183 229 275 321 366 412 9669 5345 25 46 92 137 183 229 275 321 366 412 1-4762578 36 5620 24 46 91 137 182 228 273 319 364 410 5487 37 5893 23 45 91 136 181 227 272 317 362 408 8396 38 6165 22 45 91 136 i8i 227 272 317 362 408 1-4771305 39 6437 21 45 90 135 180 226 271 316 361 406 4213 40 670S 20 45 90 135 180 226 270 31S 360 405 7121 41 6978 19 45 90 134 179 224 269 314 358 403 1-4780030 42 7247 18 45 89 134 178 223 268 312 357 401 2939 43 7515 17 45 89 134 178 223 268 312 357 401 5848 44 45 7783 16 44 89 133 177 222 266 310 354 399 8757 8049 15 44 89 133 177 222 266 310 354 399 1-4791666 46 8315 14 44 88 132 176 221 265 309 353 397 4575 47 8580 13 44 88 132 176 220 264 308 352 396 7484 48 8844 12. 44 88 131 175 219 263 307 350 394 1-4800393 49 SO 9107 II 44 88 131 175 219 263 307 350 394 3302 9370 10 44 87 131 174 218 261 305 348 392 6210 51 9631 9 44 87 131 174 218 261 305 348 392 9119 52 9892 8 43 87 130 173 217 260 303 346 390 I -48 1 2028 53 9960152 7 43 86 129 172 216 259 302 345 388 4937 .54 55 0411 6 43 86 129 172 215 258 301 344 387 7846 0669 5 43 86 128 171 214 257 300 342 38s 1-4820755 56 0926 4 43 86 128 171 214 257 300 342 385 3664 57 1183 3 43 85 128 170 213 255 298 340 383 6573 58 1438 2 43 85 128 170 213 255 298 340 383 9482 59 1693 I 42 85 127 169 212 ; 254 296 338 381 1-4832391 60 M. 1947 42 84 126 168 211 253 295 337 379 5299 Cosine. M. 10" 20" 30" 40" so" 60" 70" 80" 90" Arc. 5 Degrees. 86] 85 Degrees. Difference for Seconds. M. Sine. M. 10" 20" 3o'' 40" 50" 60" 70" 80" 90" Arc. 1 Arc. A o 9961947 60 42 84 126 168 211 253 295 337 379 1-4835299 I 2 2200 2452 59 58 42 42 84 84 126 126 168 168 210 210 252 252 294 294 336 336 378 378 8208 1-4841117 Sec.| DiflF. 3 4 2704 2954 57 56 42 42 42 83 83 125 125 166 166 208 208 250 250 291 291 333 333 374 374 4026 6935 10 20 485 Q70 S 3204 55 83 125 166 208 249 291 332 374 9844 6 3453 54 41 83 124 165 207 248 289 330 372 1-4852753 30 H54 1939 2424 2909 3394 7 3701 53 41 82 123 164 206 247 288 329 370 5662 40 8 3948 52 41 82 123 164 206 247 288 329 370 8571 50 60 70 9 4195 51 41 82 122 163 204 245 286 326 367 I -486 1 480 lO 4440 50 41 82 122 163 204 245 286 326 367 4388 II 4685 49 41 81 122 162 203 244 284 325 365 7297 80 3878 12 4929 48 41 81 122 162 203 243 284 324 365 r48702o6 90 4363 n 5172 47 40 81 121 161 202 242 282 322 363 3115 14 5414 46 40 80 120 160 201 241 281 321 361 6024 I"? 5655 45 40 80 120 160 200 240 280 320 360 8933 i6 5895 44 40 80 120 160 200 240 280 320 360 1-4881842 17 6135 43 40 80 119 159 199 239 279 318 358 4751 i8 6374 42 40 79 119 158 198 238 277 317 356 7660 19 6612 41 40 79 119 158 198 237 277 316 356 I -4890569 20 6849 40 39 79 118 157 197 236 275 314 354 3477 21 7085 39 39 79 118 157 197 236 275 314 354 6386 22 7321 38 39 78 117 156 195 234 273 312 351 9295 23 7555 2,7 39 78 117 156 195 234 273 312 351 1-4902204 24 7789 36 39 78 116 155 194 233 272 310 349 "jin 2"; 8022 35 39 77 116 154 193 232 271 310 348 8022 26 8254 34 39 77 116 154 193 231 270 308 347 I -491093 r 27 8485 33 38 77 "5 153 192 230 268 306 345 38-40 28 8715 32 38 77 115 153 192 230 268 306 345 6749 29 8945 31 38 76 114 152 190 228 266 304 342 9658 30 9173 30 38 76 114 152 190 228 266 304 342 1-4922566 31 9401 29 38 7t 113 151 189 227 265 302 340 5475 32 9628 28 38 75 "3 150 188 226 263 301 338 8384 33 9854 27 38 75 "3 150 188 226 263 301 338 I -493 1 293 34 35 9970080 26 37 75 112 149 187 224 261 298 336 4202 0304 25 37 75 112 149 187 224 261 298 336 7111 36 0528 24 37 74 III 148 185 222 259 296 333 I -4940020 37 0750 23 37 74 III 148 185 222 259 296 333 2929 3S 0972 22 37 74 no 147 184 221 258 294 331 5838 39 1193 21 37 73 no 146 183 220 256 293 329 8747 40 1413 20 37 73 no 146 183 220 256 293 329 1-4951655 41 1633 19 36 73 109 145 182 218 254 290 327 4564 42 1851 18 36 73 109 145 182 218 254 290 327 7473 43 2069 17 36 72 108 144 181 217 253 289 325 1-4960382 44 2286 16 36 72 108 144 180 216 252 288 324 3291 45 2502 15 36 72 107 143 179 215 251 286 322 6200 46 2717 14 36 71 107 142 178 214 249 285 320 9108 47 2931 13 36 71 107 142 178 214 249 28s 320 I -49720 1 7 48 3U5 12 35 71 106 141 177 212 247 282 318 4926 49 3357 II 35 71 106 141 177 212 247 282 318 7835 50 3569 10 35 70 105 140 176 211 246 281 316 1-4980743 51 3780 9 35 70 105 140 175 210 245 280 315 f'f 52 3990 8 35 70 104 139 174 209 244 278 313 6561 53 4199 7 35 70 104 139 174 209 244 278 313 9470 54 4408 6 35 69 104 138 173 207 242 276 311 1-4992379 55 4615 5 35 69 104 138 173 207 242 276 311 5288 56 4822 4 34 69 103 137 172 206 240 274 309 8197 57 5028 3 34 68 102 136 171 205 239 273 307 1-5001106 5« 5233 2 34 68 102 136 170 204 238 272 306 4015 59 5437 I 34 68 102 136 170 204 238 272 306 6924 60 5641 34 67 lOI 134 168 202 235 269 302 9832 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70'- 80" 90" Arc. 4 Degrees. 86, Degrees, Difference for Seconds. fS! M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o 1 9975641 5843 6045 60 59 58 34 34 33 67 67 67 lOI lOI 134 134 133 168 168 202 235 235 2.T3 269 269 266 302 1-5009832 r5oi274i 5650 Arc. 2 100 167 200 302 300 Sec. Diff. 3 6245 57 33 67 100 133 167 200 233 266 300 8559 ■ 4 6445 56 33 67 100 133 167 200 233 266 300 1-5021468 10 20 485 5 6645 55 33 66 99 132 165 198 231 264 297 4377 970 6 6843 54 33 66 98 131 164 197 230 262 295 7286 30 1454 7 7040 S3 33 66 98 131 164 197 230 262 295 I -5030195 40 1939 8 7237 52 33 65 98 130 163 196 228 261 293 3104 SO 2424 9 7433 51 32 65 97 129 162 194 226 258 258 291 6013 60 2909 lO 7627 50 32 65 97 129 162 194 226 291 8921 70 1 3394 80 1 3878 90 ' 4363 II 7821 49 32 65 97 129 162 194 226 258 291 1*5041830 12 8015 48 32 64 96 128 160 192 224 256 288 4739 13 8207 47 32 64 96 128 160 192 224 256 288 7648 H 8399 46 32 63 95 126 158 190 221 253 284 1-5050557 IS 8589 45 32 63 95 126 158 190 221 253 284 3466 i6 8779 44 32 63 95 126 158 189 221 252 284 6375 17 8968 43 31 63 94 125 157 188 219 250 282 9284 i8 9156 42 31 62 93 124 156 187 218 249 280 I -5062 1 93 19 9343 41 31 62 93 124 156 187 218 249 280 5102 20 9530 40 31 62 93 124 1 55 186 217 248 279 8010 21 9716 39 31 61 92 122 153 184 214 245 27s I -5070919 22 9900 38 31 6i 92 122 153 184 214 245 275 3828 2.3 9980084 37 31 61 92 122 153 183 214 244 275 6737 24 0267 36 31 61 92 122 153 183 214 244 275 9646 25 0450 35 30 60 90 120 151 181 211 241 271 15082555 26 0631 34 30 60 90 120 150 180 210 240 270 5464 27 081 1 33 30 60 90 120 150 180 210 240 270 8373 28 0991 32 30 60 89 119 149 179 209 238 268 1-5091282 29 1 170 31 30 59 89 118 148 178 207 237 266 4191 30 1348 30 30 59 89 118 148 177 207 236 266 7098 31 1525 29 29 S9 88 117 147 176 205 234 264 I -5 100007 32 1 701 28 29 S9 88 117 147 176 205 234 264 2916 33 1877 27 29 58 87 116 146 175 204 233 262 5825 34 2052 26 29 58 86 115 144 173 202 231 260 8734 35 2225 25 29 58 86 115 144 173 202 231 260 1-5111643 3b 2398 24 29 57 86 114 143 172 200 229 257 4552 37 2570 23 29 57 86 114 143 172 200 229 257 7461 3« 2742 22 28 57 85 113 142 170 198 226 255 I -5 1 20370 39 2912 21 28 57 85 113 142 170 198 226 255 3278 40 3082 20 28 56 84 112 140 168 196 224 252 6187 41 3250 19 28 56 84 112 140 168 196 224 252 9096 42 3418 18 28 56 83 III 139 167 19s 222 250 I -5 1 32005 43 3585 17 28 55 83 no 138 166 193 221 248 4914 44 3751 16 28 55 83 no 138 166 193 221 248 7823 45 3917 15 27 55 82 109 137 164 191 218 246 1-5140732 4b 4081 14 27 55 82 109 137 164 191 218 246 3641 47 4245 13 27 54 81 108 136 163 190 217 244 6550 48 4408 12 27 54 81 108 135 162 189 216 243 9459 49 4570 II 27 54 80 107 134 161 188 214 241 I -5 1 52368 SO 4731 10 27 53 80 106 133 160 186 213 239 5276 51 4891 9 27 53 80 106 133 159 186 212 239 8185 52 5050 8 27 S3 80 106 133 159 186 212 239 1-5161094 53 5209 7 26 S3 79 105 132 158 184 210 237 4003 54 5367 6 26 52 78 104 131 157 183 209 23s 6912 55 5524 5 26 52 78 104 130 156 182 208 234 9821 56 5680 4 26 52 n 103 129 155 181 206 232 1-5172730 57 5835 3 26 SI 77 102 128 154 180 205 230 f^% S« 5989 2 26 SI 77 102 128 154 180 205 230 8548 59 6143 I 25 51 76 lOI 127 152 177 202 228 1-5181457 60 6295 25 SI 76 lOI 127 152 177 202 228 4364 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 3 Degrees. 88] 87 Degrees. Difference for Seconds. M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o I 998629s 6447 60 59 25 25 SI 50 76 75 lOI 100 127 126 152 151 177 176 202 201 228 226 1-5184364 7273 Arc. Sec Diff 2 6598 58 25 50 Ti 100 125 150 175 200 225 1-5190182 3 6748 57 25 50 75 100 125 150 175 200 225 3091 48s 970 1454 4 6898 56 25 49 74 98 123 148 172 197 221 6000 20 30 5 7046 55 25 49 74 98 123 148 172 197 221 8909 6 7194 54 24 49 11 1 97 122 146 170 194 219 1-5201818 40 1939 2424 2909 3394 7 7340 53 24 49 7i 97 122 146 170 194 219 4727 50 8 7486 52 24 48 72 i 96 121 145 169. 193 217 7636 60 9 7631 51 24 48 72 1 96 120 144 168 192 216 1-5210545 70 80 lO 7775 50 24 48 72 I 96 120 144 168 192 2X6 13453 3878 M 7919 49 24 47 71 94 118 142 166 190 213 6362 90 4363 12 8061 48 24 47 71 94 118 142 166 190 213 9271 M 8203 47 24 47 70 94 118 141 165 188 212 1-5222180 14 11 8344 46 23 47 46 70 1 93 117 140 163 186 210 5089 8484 45 23 69 92 116 139 162 185 208 7998 i6 8623 44 23 46 69 92 115 138 161 184 207 1-5230907 17 8761 43 23 46 69 92 "5 138 161 184 207 3816 i8 8899 42 23 45 68 90 "3 136 158 181 203 6725 19 9035 41 23 45 68 90 113 136 158 181 203 9634 20 9171 40 23 45 68 90 113 135 158 180 203 1-5242542 21 9306 39 22 45 67 89 112 134 156 178 201 5451 22 9440 38 22 44 66 88 III 133 155 177 199 8360 2,3 9573 yi 22 44 66 88 III 133 155 177 199 1-5251269 24 9706 36 22 44 65 87 109 131 153 174 196 4178 2"; 9837 35 22 43 65 87 109 131 153 174 196 7087 26 9968 34 22 43 65 86 108 130 151 173 194 9996 27 999(X)98 33 22 43 65 86 108 129 151 172 194 1-5262905 28 0227 32 21 43 64 85 107 128 149 170 192 5814 29 0355 31 21 42 63 84 106 127 148 169 190 8723 30 0482 30 21 42 63 84 106 127 148 169 190 1-5271631 31 0609 29 21 42 62 83 104 125 146 166 187 4540 32 0734 28 21 42 62 83 104 125 146 166 187 7449 33 0859 27 21 41 62 82 103 124 144 i6s 185 1-5280358 34 0983 26 21 41 62 82 103 123 144 164 185 3267 3? 1106 25 . 20 41 61 81 102 122 142 162 183 6176 36 1228 24 20 41 61 81 102 122 142 162 183 9085 37 1350 23 20 40 60 80 ICX) 120 140 160 180 1-5291994 3« 1470 22 20 40 60 80 100 120 140 160 180 4903 39 1590 21 20 40 39 59 79 99 119 139 158 178 7812 40 1709 20 20 59 78 98 118 137 157 176 1-5300720 41 1827 19 20 39 59 78 98 117 137 156 176 3629 42 1944 18 19 39 58 77 97 116 135 154 174 6538 43 2060 17 19 39 58 77 97 116 135 154 174 9+47 44 2176 16 19 38 57 76 95 114 133 152 171 1-53x2356 45 2290 15 19 38 57 76 95 114 152 171 5265 46 2404 14 19 38 56 75 94 113 132 150 169 8x74 47 2517 13 19 37 56 74 93 112 130 149 167 X-5321083 48 2629 12 19 37 56 74 93 III 130 148 167 3992 49 2740 n 19 37 56 74 93 III 130 148 167 690 X SO 2851 10 18 36 54 72 91 109 127 145 163 9808 SI 2960 9 18 3b 54 72 91 109 127 145 163 1-5332717 S2 3069 8 18 36 54 72 90 108 126 144 162 5626 S3 3177 7 18 36 53 71 89 107 125 142 160 8535 54 3284 6 18 35 53 70 88 106 123 141 158 X-5341444 55 3390 5 18 35 S3 70 88 105 123 140 IS8 4353 S<» 3495 4 18 35 53 70 88 105 123 140 158 7262 57 36cx> 3 17 35 52 69 87 104 121 138 156 1-5350171 S« 3704 2 17 34 51 68 85 102 119 136 153 3080 59 3806 I 17 34 51 68 85 102 119 136 153 5989 60 3908 17 34 50 67 84 lOI 118 134 151 8897 M. Cosine. • M. 10" 20" 30" 40" SO" 60" 70" 80 90" Arc. 2 Degrees. 88 Degrees. Difference for Seconds. [8 M. o I 2 3 Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc; 9993908 4009 4110 4209 60 59 58 57 17 17 17 17 34 34 33 33 51 SO 50 SO 68 67 66 66 ^5 84 83 83 lOI lOI 99 99 118 118 116 116 135 134 132 132 152 151 149 149 1-5358897 1-5361806 47 IS 7624 Arc. Sec. Diff. 485 4 4308 50 16 32 49 i>S 81 97 "3 130 146 1-5370533 20 30 40 50 60 70 80 5 6 4405 4502 55 54 16 16 32 32 48 48 64 64 81 80 97 96 "3 112 129 128 145 144 3442 6351 970 1454 1939 2424 2909 3394 3878 7 4598 53 16 32 48 64 80 95 III 127 143 9260 8 9 4693 4788 52 51 16 16 32 31 47 47 62 79 78 95 93 III 109 126 124 142 140 1-5382169 5078 lO 4881 50 16 31 47 62 78 93 109 124 140 7986 II 4974 49 15 31 4b 62 77 92 108 123 139 1-5390895 90 4363 12 5066 48 15 30 4b 61 7b 91 106 122 137 3804 13 5157 47 IS 30 45 60 7b 90 105 120 135 6713 H 5247 45 15 30 45 60 75 89 104 118 133 9622 IS 5336 45 15 29 44 58 73 88 102 117 132 I -540253 1 lb 5424 44 15 29 44 58 73 88 102 117 131 5440 17 5512 43 15 29 44 58 73 87 102 117 131 8349 l8 5599 42 15 29 44 58 73 85 102 116 131 1-5411258 19 20 5684 41 14 29 43 58 72 86 lOI 115 130 4167 5770 40 H 28 42 56 70 84 98 112 126 7075 21 5854 39 14 28 42 56 70 83 97 no 125 9984 22 5937 38 14 28 41 55 ^2 83 97 III 124 1-5422893 23 6020 37 14 27 41 54 68 81 95 109 122 5803 24 25 6101 3b 14 27 41 54 68 81 95 109 122 871I 6182 35 13 27 40 54 67 80 94 107 121 1-5431620 26 6262 34 13 26 40 S3 66 79 92 106 119 4529 27 6341 33 13 26 39 52 i>5 78 91 104 117 7438 28 6419 32 13 26 39 52 bS 78 91 104 117 1-5440347 29 6497 31 13 25 38 51 64 7b 89 102 114 3256 30 6573 30 13 25 38 51 64 76 89 102 114 6163 31 6649 29 13 25 38 50 b3 75 88 zoo 113 9072 32 6724 28 12 25 37 50 62 74 87 99 112 I -545 1 98 1 33 6798 27 12 24 37 49 61 73 85 98 no 4800 34 35 6871 25 25 12 24 36 48 60 72 84 96 108 7799 6943 12 24 36 48 60 72 84 96 108 1-5460708 30 7015 24 12 24 3b 48 60 71 83 95 107 3617 37 7086 23 12 23 35 47 59 70 82 94 105 6526 3« 7156 22 II 23 34 46 57 68 81 92 104 9435 39 7224 21 II 23 34 46 57 68 80 93 103 1-5472344 40 7292 20 II 23 34 46 57 68 80 91 103 5252 41 7360 19 II 22 33 44 55 66 77 88 99 8161 42 7426 18 II 22 33 44 55 66 77 88 99 1-5481070 43 7492 17 II 21 32 43 54 64 75 86 9b 3979 44 7556 16 II 21 32 43 54 64 75 86 96 6888 45 7620 15 II 21 32 42 S3 63 74 84 95 9797 46 7683 14 10 21 31 42 52 62 73 83 94 1-5492706 47 7745 13 10 21 31 42 52 62 73 83 94 5615 48 7807 12 10 20 30 40 50 60 70 80 90 8524 49 7867 II 10 20 30 40 50 60 70 80 90 1-5501433 50 7927 10 10 20 30 40 50 59 69 79 89 4341 51 7986 9 10 19 29 39 49 58 68 78 88 7250 52 8044 8 10 19 29 38 48 57 67 76 86 1-5510159 53 ' 8101 ; 7 9 19 28 38 47 56 66 75 85 3068 54 8157 6 9 19 28 38 47 5b 66 75 85 5977 55 ^^^3 5 9 18 27 36 45 54 63 72 81 8886 56 8267 4 9 18 27 36 45 54 63 72 8i 1-5521795 57 8321 3 9 18 27 3b 45 53 62 71 80 4704 5« 8374 2 9 17 26 35 44 52 61 70 78 7613 59 8426 I 9 17 26 34 43 51 60 68 77 1-5530522 60 8477 8 17 25 34 42 50 59 67 7b 3430 M. Cosine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. 1 Degrees. 90] 89 Degrees. Difference for Seconds. ■ M. Sine. M. 10" 20" 30" 40" 50" 60" 70" 80" 90" Arc. o 9998477 60 8 17 25 34 42 so S9 67 76 1*5533430 Arc. I 2 8527 8577 59 58 8 8 17 16 25 24 33 32 42 40 SO 48 S8 56 66 64 75 72 6339 9248 3 4 8625 8673 57 56 8 8 16 16 24 23 32 31 40 39 48 47 56 S5 • 64 62 72 70 1-5542175 5066 Sec' '^ "" uin. 10 20 30 40 50 60 70 485 970 1454 1939 2424 2909 3394 5 6 8720 8766 55 54 8 8 . IS 15 23 23 31 30 39 38 46 46 S4 S3 62 61 69 68 7975 1-5550884 7 8812 53 7 IS 22 30 37 44 S2 S9 67 3793 8 8856 52 7 IS 22 29 37 44 SI S8 66 6702 9 lO 8900 51 7 14 21 28 35 42 49 56 63 9611 8942 50 7 14 21 28 35 42 49 56 63 1-5562519 II 8984 49 7 14 21 28 35 41 48 SS 62 5428 80 3878 12 9025 48 7 13 20 27 34 40 47 54 60 8337 90 4363 n 9065 47 7 13 20 26 33 40 46 S3 59 1-5571246 14 9105 46 6 13 19 26 32 38 45 51 58 4155 1.5 9143 45 6 13 19 25 32 38 44 SO 57 7064 i6 918: 44 6 12 19 2S 31 37 43 SO 56 9973 17 9218 43 6 12 18 24 30 36 42 48 54 1-5582882 i8 9254 42 6 12 17 23 29 35 41 46 S2 5791 19 9289 41 6 11 17 23 29 34 40 46 SI 8700 20 9323 40 6 II 17 22 28 34 39 45 50 1-5591608 21 9357 39 5 II 16 22 27 32 38 43 49 4517 22 9389 38 5 II 16 21 27 32 37 42 48 7426 23 9421 37 5 10 16 21 26 31 36 42 47 1-5600335 24 9452 3b 5 10 IS 20 25 30 35 40 45 3244 2? 9482 35 5 10 14 19 24 29 34 38 43 6153 26 9511 34 5 9 14 18 23 28 32 37 41 9062 27 9539 33 5 9 14 18 23 28 32 37 41 1-5611971 28 9567 32 4 9 13 18 22 26 31 35 40 4880 29 9593 31 4 9 13 17 22 26 30 34 39 7789 30 9619 30 4 8 13 17 21 25 29 34 38 1-5620696 31 9644 29 4 8 12 16 20 24 28 32 36 3505 32 9668 28 4 8 12 16 20 24 28 32 36 6514 33 9692 27 4 7 II IS 19 22 26 30 33 9423 34 35 9714 26 4 7 II 14 18 22 25 29 32 1-5632332 9736 25 3 7 10 14 17 20 24 27 31 5241 36 9756 24 3 7 10 13 17 20 23 26 30 8150 37 9776 23 3 6 10 13 16 19 22 26 29 1-5641059 38 9795 22 3 6 9 12 15 18 21 24 27 3968 39 40 9813 21 3 6 9 12 15 18 21 24 27 6877 9831 20 3 5 8 II 14 16 19 22 24 9785 41 9847 19 3 S 8 10 13 16 18 21 23 1-5652694 42 9863 18 3 S 8 10 13 15 18 20 23 5603 43 9878 17 2 5 7 10 12 14 17 19 22 8512 44 9892 16 2 4 7 9 II 13 1 15 18 20 1-5661421 45 9905 15 2 4 6 8 10 12 14 16 18 4330 46 9917 14 2 4 6 8 10 II 13 15 17 7239 47 9928 13 2 4 5 7 9 II 13 14 16 I -5670148 48 9939 12 2 3 S 6 8 10 12 14 IS 3057 49 9949 II 2 3 S 6 8 9 II 13 14 5966 50 9958 10 3 4 6 7 8 10 II 13 8874 51 9966 9 2 4 5 6 7 8 10 II 1-5681783 52 9973 8 2 3 4 S 6 7 8 9 4692 53 9979 7 2 3 4 s 6 7 8 9 7601 54 9985 6 5 2 2 3 4 4 5 6 6 1-5690510 55 9989 I 2 2 3 4 4 5 5 3419 56 9993 4 I 2 2 3 3 4 4 S 6328 57 9996 3 I I 2 2 2 3 3 4 9237 53 9998 2 I I 1 2 2 2 2 3 1-5702146 59 I OOOCX)0 I 5055 60 0000 7963 M. Cosine. M. lo" 20" 30" 40" 50" 60" 70" 80" 90" Arc. Degrees. ^i. * THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW AN INITIAL PINE OF 25 CENTS WILL BE ASSESSED FOR FAILURE TO RETURN. THIS BOOK ON THE DATE DUE. THE PE^l^ WILL INCREASE TO SO CENTS ON THE FOUR^ sCerdue. '° ''"^ ^'^ ^"^ sev^ent'S":::; D£C__G_jg43 ___E£Bi01bo/ LD21-100r«-7,'39(402s) YE 02307 911^33 THE UNIVERSITY OF CALIFORNIA LIBRARY '^H.^';'^:^