\i:i TH.MS. 



XXVll 



tables in o. i per cent work. Thn is a not infrequent practice, most common 



- in chemical computation, ami, <>f course, arisim: from tin- ex* 

 conven .iinini: four-place logarithms. It will be shown at 



: surtVient fnro.i percent direct computations, 

 and tin- error if four-; .thins an- used is sensibly the same. The com- 



0.2 or o. 3 per cent with four-place tables even 



To Find the Logarithms of a Number. 



lit I.K. Regard the number Q as separated into two factors 

 g x 10 '", where q begins in the units' place (see "Notation by 

 Powers of 10," page xv). Find in the tables the logarithm of g. 

 This will be the mantissa of the desired logarithm. Prefix to this 

 the characteristic or index n. 



A t \\ Camples will sufficiently elucidate the process. 



Example. Desired the logarithm to four decimal places of the number 306. 



Write the number, <>r, better, merely consider it as if factored in the form 

 3.06-10-. In the four-place table, on the line 3.0 and in the column headed 

 6 will be found .4857. which is 101:3.06. obviously, loir 10- 2. Therefore 

 log 306. = log 3.06 + log lo 2 = .4857 -f 2, which is usually written 24857. 



Further Examples. Interpolation. Desired to four decimal places the 

 logarithm of 3< 



I will lie between tin- lo-s of 306 and 307 (and approximately 0.2 of tin- 

 way), ami 1 out further we must interpolate. 



7 w- tind 

 > we tind 

 >lation,o,2 



4860 

 log 306.2 = log 3.062 -f log lo 2 = 24860 



14= 2.8 = 

 log 3.062= 



.4871 

 .4857 



Difference = .0014, usually written 



14. 



desiivd mantissa will be 0.2 of 

 the way t'l-Min .4857 to 4871. 1! 

 we must add to the former number 

 0.214. =3. 



Tin- interpolation may always be made by subtracting and multi- 

 plying as in this rxamplr. but to save tin* labor, logarithm tallies 



, provided with marginal interpolation tables, by ti. 

 of whieh interpolations may easily be made int'iit ally. 



1 log 3. 06 = .4857. By inspect 

 ence - 14. In ih.- in- 2, stands | 



log 3.062 .4860. 

 illy. 

 tbles are arranged so tin 



onwpond 

 gives them a cm. i Dually to avoid 



:'l tllC lljll. 



t at the IK .ei of die nearest difference table. 

 i 

 large or too small la negli. 



