[ I 7 6 ] 
expreffion for fuch area confining of an infinite number of factors mul- 
tiplied together j to render the fame ufeful in practice, fome theorems 
are requifite for afcertaining the limits of fuch products. The theorems 
which I have hitherto been able to inveftigate fuitable tohat purpofe, I 
(hall give in the next two articles. 
III. 
N 
The limit of i — m~ x 2 1 — m~ X 3* — n? (2) X — r- -' is = — X fin$ 
% * + 1 m 
of m S ; N being the number whofe hyp. log, is 1, and S the femi- 
periphery of the circle, whofe radius is 1. 
Whence, by taking m equal o > we find the limit of T. 2*. 3* 
N 
2 x 
( 2 )x— +r = 2S > 
IV. 
The limit 0 fdz-\-aydz-\-a dydz 4- a 4* 2 d x 
N 
* 
2 55 2 X 
2 d z 
1S=2 
« 1 
7* » 
■ ■ — . % 
Hence, being - 1.3,5 W^ 2 > it appears. 
that the lfmit of 1.3 • 5 (*) X 
N' 
* X 
2 Z 
is 2 *. 
I fhall now give fome examples, to fhew the ufe of the above 
articles. 
Writing 
