Of GREATEST ATTRACTION. 223 
THE value of g, now found, is remarkable for being a near 
approximation to any arch of which ¢ is the tangent, provided 
that arch do not exceed 45°. The lefs-the arch is, the more 
near is the approximation ; but the expreflion can only be con- 
fidered as accurate when @ = o. 
Tuts will be made evident by comparing the fraétion 
t(9+22’) 
g+ 52 
with the feries, that gives the arch in terms of the 
tangent ¢, viz. @ =f 255 + = — ? +, &c. The fraction’ 
alg rigk 9 pune + SRO LSB Te pt &c. The two firft 
9+ 5 3 i Ei a 
terms of thefe feries agree; and in the third terms, the differ- 
ence is inconfiderable, while ¢ is lefs than unity ; but the agree- 
ment is never entire, unlefs ¢ = 0, when both feries vanith. 
THE attraction, therefore, or the gravitation at the pole of 
an oblate fpheroid, is not a maximum, until the eccentricity of 
the generating ellipfis vanifh, and the fpheroid pafs into a 
{phere. 
~, From the circumftance of the value of 9g aboye found, agree- 
ing nearly with an indefinite number of arches, we muft con- 
clude, that when a {phere paffes into an oblate {pheroid, its at- 
traction varies at firft exceeding flowly, and continues to-do fo 
till its oblatenefs, or the eccentricity of the generating ellipfis, 
become very great. This may be fhewn, by taking the value 
of F, and fubftituting in it that of g, in terms of tan ¢. 
Wr Haven me: and fince ¢ = tan g — 
cof @? 
——3 
tan g 
+ 3 
