[ 69 ] 
had occafion for it, but in the particular circuni- 
ftance of this problem. 
Let, therefore, r z = X', hence z log . r = log . x ; 
therefore * log. r = (fluxion of the log. x = ) fL, 
ora* = - j confequently * = i_, and — = 
* «AT r* CiXX 
but the fluent of — is (— =) — ; and 
***■ ' ax * ar * 
therefore the fluent of — — will be +_d— » 
p r z p*r z 
The fum of the two fluents will be 5 ~i~ — L_ . 
p * pir* 3 
but, when z ~ o, the whole fluent fhould be — o ; 
let therefore the whole fluent be - 4- a — o. 
p J pir z 1 JL 
Now, when z — o, then * — o, and 
cLpr 1 
be’ 
comes (for r 7 = i,) confequently ~ + q 
and q — — : therefore the area of a curve, 
whofe ordinate is * — JL_ will be ( - - — — + — 
* pr z ' 
But y = — 1 — — = — ; therefore i - ~ 
r— I r — i Xr z r 1 
r— i x and the expreflion for the area becomes 
Z P 
—=? — — : And putting n inflead of z, that area, or 
nXt — i cm 
the value of the life, will be exprefled by £ - 
r— I «#, 
Thofe 
