QUADRATURE of the CONIC SECTIONS, &c. 325 



which n (x — 1) approaches, when n is conceived to be inde- 

 finitely increafed, will be variable, as it depends upon the par- 

 ticular value of the number x. 



T 



Let us therefore denote the limit of m (b — 1), or that of 

 1 

 m (b' n — 1) 

 , (for they are evidently the fame), by B, and then 



in the fyflem whofe bafis is b, the logarithm of x will be the li- 

 mit of either of thefe two expreffions 



1 



1 n (x — 1) n (x — 1) 



n 

 X 



B B 



when n is conceived to increafe indefinitely, or to fpeak brief- 



1 



n ( x - T 1 



ly> logx = — - — ?j -> when n is indefinitely great. 



B 



The conftant multiplier - is what writers on the fubjecl of 



logarithms have denominated the modulus of the fyilem. As in 

 Napier's fyftem it is unity, we have, n being indefinitely great, 



1 

 Nap. log x — n (x* — 1), and fince in any fyftem whatever 



1 i_ 



B zz m (b™ — 1), or B = n {b n —*■ 1), for we may pat m or » 



S s 2 indifcriminately : 



