[ 495 ] 
ther thefe two expreffions, viz. 
-P 
— + — and 
-i 2 n 
— - — are equal, or nearly fo. 
r — i a.n 
It is well known, that the hyperbolic logarithm 
of any number, r, is equal to the infinite feries. 
2 r 
- x - 
I r-f-i 
I , 2 r — i 
- - 4 — x 
3 r+ 1 
, 2 r — i 
4- -X 
5 r + 1 
&c. and, in this 
cafe (fince the intereft of money has not, for many 
years, exceeded f /. per cent, and is continually de- 
creafing), r will be always expounded by fome of the 
following numbers, 1,05. 1,04.. 1,03. &c. or others 
intermediate to them ; in the greatefi: of which [viz. 
1,05) r — 1 will he expounded by (,05 or) 4 _, anc j 
T , the firft 
2 . 
r -j- 1 by ( 2, Of or) ; whence, - x 
I r- f- 1 
2 2 r — 1 
term of the feries will be ■ — , and - x 
41 3 1 
2 1 
, x ~ = 
3 41 
n 
206763’ 
will be 
a fraction too final 1 to affedt 
r- 
a calculation of this kind: and therefore, - x — 
1 r-j- 1 
the firfi term of the feries, will be nearly equal to a, 
and may he wrote for it. 
Now by writing — x ■ for cc, the value of the 
expreffion, — — . ^ 
will become 
a n 
r — j 
■ r + * 
