EXPLANATION" OF TABLES. 47 



Example.Fiud 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 1.369726 



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. 



Tabular diff. =236 .-. 5th fig. = 2 



6th fig. = 3 

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



The number derived from a six-place logarithm is not 

 reliable beyond the sixth figure. 



At the end of table XXIV. is a small table of logarithms of 

 numbers from 1 to 100, with the characteristic prefixed, for 

 easy reference when the given number does not exceed two 

 digits, But the same mantissas may be tound in the larger 

 table. 



APPENDIX X. The logarithmic sine, tangent, 

 etc. of an arc is the logarithm of the natural sine, tangent, 

 etc. of the same arc, but with 10 added to tne characteristic to 

 avoid negatives. This table gives log sines, tangents, cosines, 

 and cotangents for every minute of the quadrant. With the 

 number of degrees at the lef t side of the page are to be read 

 the minutes in the left-hand column ; with the degrees on 



