Logarithmotechnia Generalis : or, a Genei'al Method of Making Logarithms. 

 By Mr. John Craig. N° 328, p. IQl. Translated from the Latin. 



For perfecting this very useful part of arithmetic, the only thing wanting 

 seems to be, a general method of finding all logarithmic series. And such is 

 the following; being both easy and genuine, as derived from the very nature of 

 logarithms themselves. 



By the letter /, prefixed to any number, in what follows, is to be understood 

 the logarithm of that number, as usual. Now as the logarithm of any pro- 

 posed number may be found in two ways, we may therefore divide this business 

 into two parts : in the first of which we deduce the log. immediately from the 

 number itself; but in the latter we derive the log. of the proposed number 

 from the logarithms of some antecedent numbers. 



Part I. — Let a ■\- \ ho. any proposed number, and x its log. to be found. 

 Now, by the hypothesis, x = I. (a + 0? which equation may be called a gene- 

 ral canon. Then, 1st, assume an equation between terms any how composed 

 of a and y, and combined v.ith any other numbers, in any manner, by addition, 



VOL. V. 4 I 



