of a homogeneous fluid mass that revolves upon an axis . 141 
( 1 + * a ) ( A — - B) 4 — 
4 ^ . 
C 1 + A 2 ) B — ■— 
\ 7T 
for the terms on the right-hand sides will be made to coin- 
cide by giving a proper value to the arbitrary quantity C„ 
Hence, 
— (1 + A 2 ) B — A, 
4 1C v 1 ' 
Now put, 
then, restoring the values of A and B, we shall obtain, 
Arc. Tan. a. 
)• 
From this formula it appears that q = o, both when x is equal 
to zero and when it is infinitely great. There is therefore 
no rotatory motion in either of the extreme cases, when the 
oblateness is nothing, and when it is infinite ; or when the 
fluid mass is a sphere, and when it is a circular sheet spread 
out in the plane of the equator. In order to discover whether 
q is evanescent in any other circumstances, put Tan. = x ; 
then 
2 1 / 1 2 \ ( 
q q 3 \Sin. 2 p 3 / 1 
1 p Cos. o\ 
or, in a series, 
— Sin . 2 ~ Sin . 4 
5 r 1 5-7 r 
2.4.6 
5.7.9. M 
i . 2 . 4. 6 . 8 
5.7.9. 11 
&C. 
Sin . 8 <p 
Sin. 10 , 
>3 
Now this series being evanescent both when Sin. = 0, and 
when Sin. q> ess 1 , it follows that, for every other value of 
Sin. <p, q will be positive ; and hence it will first increase from 
zero to a maximum, and then decrease to the first limit. If 
