EXPLANATION OF TABLES. 109 



the same line, but for a given case the difference needs to be 

 verified by actual subtraction, at least so far as the last figure 

 is concerned. The lower part of the page contains a complete 

 list of differences, with their multiples divided by 10. 



To find the logarithm of a number having six 

 figures : Take out the mantissa for the four superior places 

 directly from the table, and find the difference between this 

 mantissa and the next greater in the table. Add to the man- 

 tissa taken out the quantity found in the table of proportional 

 parts, opposite the difference, and in the column headed by the 

 fifth figure of the number; also add T *o the quantity in the col- 

 umn headed by the sixth figure. The sum is the mantissa 

 required, to which must be prefixed a decimal point and the 

 proper characteristic. 



Example. Find the log of 23.4275. 



For 2342 mantissa is 369587 



" diff. 185 col. 7 129.5 



" " " " 5 9.2 



Ans. For 23.4275 log is L369726 



The decimals of the corrections are added together to deter- 

 mine the nearest value of the sixth figure of the mantissa. 



To find the number corresponding to a given 

 logarithm. If the given mantissa is not in the table find the 

 one next less, and take out the four figures corresponding to it; 

 divide the difference between the two mantissas by the tabu- 

 lar difference in that part of the table, and annex the figures of 

 the quotient to the four figures already taken out. Finally, 

 place the decimal point according to the rule for characteristics, 

 prefixing or annexing ciphers if necessary. The division re- 

 quired is facilitated by the table of proportional parts, which 

 furnishes by inspection the figures of the quotient. 



Example. Find the number of which the logarithm is 

 8.263927 8.263927 



First 4 figures 1836 from 263873 



Diff. 54J) 

 Tabular diff. =236 , . 5th fig. =2 47. 2 





6.80 



6th fig. = 3 7.08 



Ans. No. = .0183623 or 183,623,000. 



