1881.] computing Natural and Tabular Logarithms, fyc. 39 L 

 Bimodular Table II. — Tabular Logarithms — continued. 



2. For Preparation. 



No. 



Tabular Logarithm. 



1 -1 







041 



392 



685 



158 



225 



041 



1-2 







079 



181 



246 



047 



624 



828 



1-3 







113 



943 



352 



306 



836 



769 



1-4 







146 



128 



035 



678 



238 



026 



1-5 







176 



091 



259 



055 



681 



242 



1 6 







204 



119 



982 



655 



924 



781 



1-7 







230 



448 



921 



378 



273 



929 



1-8 







255 



272 



505 



103 



306 



070 









278 



753 



600 



952 



828 



962 



2-0 







301 



029 



995 



663 



981 



195 



3-0 







477 



121 



254 



719 



662 



437 



4-0 







•602 



059 



991 



327 



962 



390 



5-0 







698 



970 



004 



336 



018 



805 



6-0 







•778 



151 



250 



383 



643 



633 



7-0 







845 



098 



040 



014 



256 



831 



8-0 



0-903 



089 



986 



991 



943 



586 



9-0 



0-954 



242 



509 



439 



324 



875 



10 



1 



•000 



000 



000 



000 



000 



ooo 



11 -o 



1 



•041 



392 



685 



158 



225 



041 



12 -0 



1 



•079 



181 



246 



047 



624 



827 



3. Multiples of the Bimodulus. 



No. of 

 mult. 



Value of Multiple. 



1 







868 



588 



963 



806 



503 



655 



2 



1 



•737 



177 



927 



613 



007 



311 



3 



2 



•605 



766 



891 



419 



510 



966 



4 



3 



•474 



355 



855 



226 



014 



621 



5 



4 



342 



944 



819 



032 



518 



277 



6 



5 



211 



533 



782 



839 



021 



932 



7 



6 



080 



122 



746 



645 



525 



587 



8 



6 



948 



711 



710 



452 



029 



242 



9 



7 



817 



300 



674 



258 



532 



898 



4. For no Corrections. 



Differ- 

 ence. 



Quotnt. 



Trust Places 



■0.J00 



•0,431 



9 



And one more 



•O3653 



■0 3 282 



10 



place in each case 



•0 3 3C3 



•0,131 



11 



with a probable 



•0,141 



•0,609 



12 



error in it of one 



•0 4 653 



•0,282 



13 



unit in defect. 



•0 4 303 



•0 4 131 



14 





•0 4 141 



•0,609 



15 





•0 S 653 



•0 5 282 



16 





For intermediate Differences and Quo- 

 tients trust the number of places opposite 

 the next greater. 



5. For Full Corrections, Additive. 



Take six significant figures of the quotient and 

 use six significant figures of the correction from this 

 formula — 



tab. log cor. =3 tab. log quotient-1- '645 2501-1. 



Differ- 

 ence. 



Quotnt. 



Trust places 



•0 2 100 



•0,434 



14 



And one more place in each 



•0 3 893 



•0 3 388 



15 



case with a probable error in 



•0,284 



•0,123 



16 



it of one unit in defect. 



•0,231 



•0 3 100 



17 





•0 4 893 



•0^388 



18 





For intermediate Differences and Quotients trust 

 the number of places opposite the next greater. 



6. For Short Corrections, Additive, giving twelvi 

 places, with a possible error of one unit in tht 

 twelfth place on completion. 



Quotient. 



•0 3 000 

 104 

 150 

 178 

 199 



•0,217 



232 

 245 

 257 

 268 



•0 3 278 

 288 

 296 

 305 

 313 



•0 3 320 

 327 

 334 

 341 

 348 



Correction. Quotient. 



•o 1(J oo 



01 

 02 

 03 

 04 



•0 lo 05 

 06 

 07 

 08 

 09 



•o 10 io 

 11 



12 

 13 

 14 



•O 10 15 

 16 

 17 

 18 

 19 



•0,353 

 359 

 365 

 371 

 376 



•0 3 381 

 386 

 391 

 396 

 401 



•0 3 406 

 410 

 415 

 419 

 423 



•0,427 

 432 



Correction. 



•0 lo 20 

 21 



23 

 24 



•O 10 25 



•0 lo 30 

 31 



For intermediate quotients take the correction 

 opposite tne next less. 



Note. — The natural logarithms to eighteen places 

 in Table I are either taken direcr or calculated (by 

 subtracting nat. logs of 1,000 and 10) from "Wolf- 

 ramii Tabula L^garithmorum Naturalium" to forty- 

 eight places, appended to Vega's "Thesaurus Loga- 

 rirhmorum Completus," 1794. 



The tabular logarithms to eighteen places in 

 Table II are taken direct from Mr. Peter Gray's 

 "Tables for the formation of Logarithms and Anti- 

 Logarithms to twenty-four places," 1876. 



In both tables the arrangement and corrections are 

 original. 



YOL. XXXI. 



2 E 



