[ 322 ] 
r .... I I I I 
of this ratio is x 2 n z - z — -7 
p q t> p 3 
<7 3 X 
2 n i z- 
1 , 1 2 if 2, 5 
r* + ? x 
&c 
3 p * p ' r 1 *' s ' 
This ratio by Art. 18. is greatefl at the point of con- 
trary flexure, or when z — Subflitute this 
for z in the feries, and it will become - 
p q 
2 \/' 
P 9 
I I 1,1 
~ y~ P~ T ,x 
2 p 
l Xq I 
P* p i 3 x« — 1 11 
&fc. which, therefore, exprefles the logarithm of the 
ratio when greatefl, and will eaflly difcover it in 
every cale. ’Tis apparent that the value of this 
feries is greatefl when p is leafl in refpeft of q. Sup- 
pofe then p — 2, and q infinite. In this cafe, the 
value of the feries will be 1.072, and the num- 
ber anfwering to this logarithm is not greater than 
2.92. The fluxion, therefore, of C f when greatefl, 
cannot be three times the contemporary fluxion of 
F t ; from whence it follows that the fluxion of 
2^— * muft be Greater than the fluxion of — - . 
4 4 
It is eafy to fee how thefe demonftrations are to be 
varied when q is lefs than p , and how in this cafe fimilar 
conclufions may be drawn. Or, the fame conclu- 
lions will in this cafe immediately appear, by changing 
p into q and q into p , which will not make any differ- 
ence in the demonftrations. 
In the manner fpecified in this Article we may al- 
ways find within certain limits how near the value of 
Qj comes to the arithmetical mean between F t and 
C f which limits grow narrower and narrower, as 
4 p and 
