[ r.8 ] 



Briggs's fyftem, reprefented by^ in the feries ; by which if Na- 

 pier's loffarithms of ^, and —1— be multiplied we fhall get 

 ^ 4 125 



Briggs's logarithms of the fame numbers. If then we fubtrad 



Briggs's logarithm of -5, from his logarithm of 10, and divide the 

 4 



remainder by 3 ; or if we add Briggs's logarithm of —:— to his 



125 



logarithm of 1000, and divide the fum by 10 ; we fliall have 

 Briggs's logarithm of 2. — The logarithm of 2 being found, the 

 logarithms of all other numbers may have their computation faci- 

 litated by fome one or other of the preceding methods of increafing 

 the convergency of the feries. 



As a due application of the binomial theorem furnifhes us with 

 a feries for finding the logarithm of any natural number, (which 

 is the fame with the logarithm of the ratio of that number to 

 unity) fo likewife it may be fhewn from the fame principles that 

 the fum of the feries i + 1 + Z_ + - 1- + -^^ + ^^• 

 will be the natural number correfponding to Napier's logarithm 



/; and 



