XXX LOGARITHMS. 



practice. On the other hand, the retention of the point renders the 

 table complete and strictly self-consistent ; that is, any mantissa in 

 the table is thru the completely expressed logarithm of the cor- 

 responding tabular number. This fact tends materially toward clear 

 comprehension on the part of the beginner or occasional computer. 

 The table is also then perfectly assimilated to the "Notation by 

 Powers of io," page xv, which affords not only the clearest basis of 

 explanation of mantissa and characteristic, but by far the easiest 

 method of obtaining and following the characteristic in computations. 

 The points do not add necessarily to the bulk of the tables and are 

 no hindrance to their use by computers accustomed to other rules 

 than those here given respecting the characteristic. They are 

 therefore retained in these tables. 



Antilogarithm = Number Corresponding. Given the logarithm to 

 find the " number corresponding," i.e. the number of which this is 

 the logarithm. This number is also called the " antilogarithin." 



From the Log Tables. 



Example. To find the antilog of 2.4857, inspect the body of the four-place 

 log table to find the mantissa .4857 (or the next smaller than this if the exact 

 value does not appear). It will be found to lie on line 3.0 and in column 6, and 

 is, hence, the log of 3.06. The characteristic 2 is the log of io 2 . 

 .'. antilog 2.4857 = 3.06- io 2 or 306. 



Example. To find the antilog of 2.4860. In the table this mantissa does 

 not appear exactly, but the next smaller is .4857, whose antilog is 3.06, and the 

 difference from this to the next larger is 14. 



.4860 - .4857 = 3, and f \ = .2, 



.*. antilog .4860 is ^ or 0.2 of the way from 3.06 to 3.07, 

 /. antilog .4860 = 3.062, 

 also antilog 2. = io 2 , 



.'. antilog 2.4860 = 3.062 -lo 2 or 306.2. 



The interpolation can be mentally made by the marginal interpolation tables. 

 The tabular difference is 14, and it is desired to know what decimal fraction the 

 difference 3 is of this. Looking down the column under 14 for the number 

 nearest to 3 it is found to be 3 and to stand opposite to 2. /. 3 is 0.2 of 14, and 

 antilog .4860 = 3.062. 



It will be noticed that in the four-place and five-place log tables 

 those mantissas have been printed in heavier type in which the first 

 figure changes from one digit to the next. This serves as a guide 

 to the eye in looking for any desired mantissa whose antilog is sought. 



From Tables of Antilogarithms. Some computers prefer to employ 

 a special table for antilogarithms instead of working backward in 

 the ordinary logarithm table as in the preceding example. Whether 



