MULTIPLICATION BY LOGARITHMS- ^^c; 



Then, as 127 : 100 : : 81 : 64 nearly, the numeral 

 difference. 



Therefore 34*09264 is the number sought, two integers 

 being marked off, because the index of the given logarithm 

 is I. Had the index been negative, thus, -1—1*^326606, 

 its corresponding number would have been '3409264, 

 wholly decimal. . • 



Or, the proportional numeral difference may be found, 

 in the best tables, by inspection of the small tables of pro- 

 portional parts, placed in the margin. 



MuLriPLICATlON RT LOGARITHMS. 



R U L E. 



Take out the logarithms of the factors from the table, 

 then add them together, and their sum will be the logar- 

 ithm of the product required. Then, by means of the ta- 

 ble, take out the natural number answering to the sum, for 

 the product sought. 



Note i. In every operation, what is carried from the 

 decimal part of a logarithm to its index is aiFirmative ; and 

 is therefore to be added to the index, when it is affirma- 

 tive ; but subtracted, when it is negative. 



Note 2. When the . indices have- like signs, that Is, 

 both -j- or both — ^, they are to be added, and the sum 

 has the common sign ; but when they have unlike signs, 

 that is, one -{- and the other — , their difference, with 

 the sign of the greater, is to be taken for the index of the 

 $um. 



EXAMPLES, 



