1881.] computing Natural and Tabular Logarithms, &>c. 395 



made. The result happens to be correct to eighteen places, in place 

 of the guaranteed seventeen ; but this is quite accidental, as the last 

 or eighteenth place of all the logarithms used is always in excess or 

 defect. 



Ex. 2. To Table II. — Find tab. log N to twelve places by the short 

 corrections. 



a=N^10 n . 





1 '92 699 928 576 



b = ha. 





9) '63 499 642 880 



c=b + 9. 





1 -07 0)55 515 875 556 



d=5x bimodulus x 10 10 . 



43 429 448 190 



5x 



xlO 9 . 



4 342 944 819 



5x 



XlO 8 . 



434 294 482 



6 = 1 X „ 



XlO?. 



08 685 890 



5x 



xlO 6 . 



4 342 945 



8x 



x 10 5 . 



694 871 



7x 



xlO 4 . 



60 801 



5x 



xlO 3 . 



4 343 



5x 



xlO 2 . 



434 



5x 



xlO. 



43 



6x 





5 



g 214 055 515 875 556)48 220 476 823 



/ 



42 



811 103 175 



("2 



h -000 225 270 891 2 5 



409 373 648 





h -0 n 5 4 



281 110 318 



(2 



m -029 383 777 685 2 1 



128 263 330 





n '954 242 509 439 3 1 



070 277 579 



(5 



p -301 029 995 664 0-1 



57 985 751 





q 11 -0 



42 811 103 



(2 



r 11 -284 881 553 684 7 



15 174 648 







14 983 886 



(7 



/=(c-l -070) x 10 14 X bimodulus = dividend. 



190 762 





g=(c+l -070) x 10 14 =divisor. 



171 244 



(08 



h=f-Z- g — quotient. 



19 518 





Jc = short correction for quotient *000 225. 



19 265 



(9 



m— tab. log 1 "070. 



253 





tab. log 9. 



214 



(1 



p = arithm. comp. of tab. log 5. 39 



2 = 11 tab. log 10. 40 (2 



r=tab. logN, correct to 13 places. 



