82 Mr. Ivory on the Method of computing , &c. 
= — ~ (arc. tan. x — ) : in this case then we shall 
have 
V== 
3M 
2k 
arc. tan. x 
3M.a a 
zk i 
arc. tan. x 
} 
3M 
2^ 3 
• + {arc.tan.x - ^ 
If this value of V be substituted in the equation of the sur- 
face of a homogeneous fluid mass which is in equilibrium by 
the joint effect of the attractions of its molecules and a rota- 
tory motion ;* it will be proved that the oblate spheroid satis- 
fies the conditions of equilibrium, and the relation between 
the velocity of rotation and the eccentricity of the spheroid 
will likewise be determined. 
* Mec. Cel. Liv. 3c, No. 23 et 24. 
