LOGARITHMS. XXV 



ative. Hence, taking first a specific example, the logarithm of 306.2, 



of course the same as the logarithm of its equal, is tin- 

 as the logarithm of 3.06 2- io 2 (see "Notation by 1'owers of io," page 

 xv), which is, log 3.062 -h log io 2 = .4860 -f- 2., which is usually 

 written 2.4860. The .4860 is found from tables, as shown later. 



- :ilarly, log 0.00306 2 = log 3.062 i o~ 3 = log 3.062 + log ic" 3 = 

 .4860 3., whi.-h is usually written either 3.4860 or 7.4860 io, as 

 will b' further explained. 



The logarithm then consists of, or may be separated into, two 



viz. lirst, the decimal part called the mantissa, which is the 



hiu of the tirst factor in the above separation; second, the 



il part, or whole number, preceding the decimal point, and 



called the characteristic or index, which is the logarithm of the 



second factor io n , and which, therefore, is u. 



Tables of logarithms contain the logarithms of the numbers from 



io., by steps larger or smaller, and to as many decimal pla 

 may be requisite for the accuracy sought in the work in which they 

 are to be employed. ]>ut all numbers whatever, from o to <x>, ar 

 of these numbers i. to io. multiplied by some power of ten, i.e. by 

 io in . For example, 



4 628 326 = 4.62 832 6'io 8 , and 0.03 986 = 3.986-10 -. 



. the tables enable one, by merely prefixing to the tabular 

 the prop.-r "ch;; fcn, to obtain the logarithm of 



imber\\: :roiu zero to infinity. The quantity i 



given in tin- table is ohvi<u>l\ the mantissa of the desired logarithm. 



II therefore always a decimal fraction. 

 Since any table gives the mantissa to only a specified number of 



. it can represent only a correspondingly rest: 



number of places of siguitir inal number. It is 



inhered that a change of one unit in the last decimal place 

 of the mantissa em-responds at all points throughout a table to a 

 consta ntage change ( I>etinition : >lanations ") in the 



nuiiil" i ...mnt of this change is such that it 



proper custom to use logarithm tables giving the m.i 

 imber of places equal to the number of signiti 

 tained in the original <\ , f the numbers enterii 



the compM- re properly retained to four places of sign 



figures, a four-place logarithm table should be used in oonnectioi 

 ; if to five si t figures. ; ice table; and so on. 



