394 Mr. A. J. Ellis. Improved Bimodular Method of [Feb. 3, 



Ex. 1. To Table I. — Find nat. log N" to sixteen places. Tlie letters 

 refer to the following explanations. Every figure required by the 

 most moderate calculator is inserted. 



a=N^10 n . 1 -92 699 928 576 a 



b-Ga. 11 ) -56 199 571 456 b 



c=b^-U. 1 -05 1)09 051 950 545 454 54 c 



e 210 209 051 950 545 454 54 )18 103 901 090 909 09 d 





16 



816 724 156 043 63 



(8 



f 



J 



•900*086 123 318 301 099 1 



287 176 934 865 46 





ft 



y 



•0 13 53 233 1 



261 254 311 703 27 



(6 





•049 742 091 894 814 074 



25 922 623 162 69 





k 



2 -397 895 272 798 370 544 



21 020 905 195 05 



(1 



I 



8'208 240 530 771 944 999 — 10 



4 901 717 967 14 





in 



25 -328 436 022 934 502 524 



4 204 181 039 01 



V 



ii 



25 '984 400 041 717 986 473 



697 536 928 13 









630 627 155 90 



(3 





d=2(c-l -051) x 10 19 = dividend. 



66 909 772 23 







e=2(c+l -051) xl0 19 = divisor. 



63 062 715 59 



(3 





/= d^e= quotient. 



3 847 056 64 







full correction, see below. 



2 102 090 64 



(2 





h=mt. logl 051. 



1 744 966 12 







7i=nat. log 11. 



1 681 672 41 



(8 





Z=arithm. comp. of nat. log 6. 



63 293 71 







m=ll nat. log 10. 



63 062 72 



(3 





ii= nat. log N, true to 18 places. 



230 99 









210 21 (01 



Calculation of g. Log/, taking six significant places, 20 78 







=±log -0 4 861 233= -935 1206 - 5 



18 92 (09 





31og/=2 -805 3618 -15 



1 86 







+ -920 8188 - 2 



1 89 



(9 



log 



g=\og •0 13 532 329= "726 1806 -14 







prepare, then, for seventeen places, by carrying the quotient c far 

 enough to allow of obtaining eighteen places, that is, fourteen signifi- 

 cant places of the quotient /. As at least 2 digits of the divisor 

 must remain for the last contracted divisor, we shall require only 

 fifteen places of the divisor, and the last five are rejected (shown 

 by drawing a line under them). The successive digits of the quotient 

 are written to the right after ( (following Briggs's use), and are 

 collected in/. The rest of the process is evident from the notes 



