326 NEW SERIES for the 
indifcriminately ; therefore B= Nap. log 4, and confequently 
Nap. log x 
og « (to bafis 2) Naples 
as is commonly known. 
58. Stnck, therefore, the logarithms of any propofed fyftem 
may be deduced from thofe of Naprer’s fyftem, I {hall 
throughout the reft of this Paper attend only to the formula 
Nap. log x =2 (x" —1), being indefinitely great. 
Ler us then, agreeably to the mode of proceeding employ- 
ed in the former part of this paper, affume the identical equa- 
tion 
X+1_ X+1 1X—I 
X'—1- 2(X—1) 2X+1° 
aN LF a Wr : 
In this expreffion let x2, x*, «®, x**, &c. be fubftituted fuc- 
P 
ceflively for X, and let the refults be multiplied by the corre- 
{ponding terms of the feries, I, =, ? &c. Thus hete-will be 
formed a feries of equations, which, putting » for their num- 
ber, and m for 2", may ftand as follows: 
x+tr 
“x—TI 
