of a homogeneous fluid mass that revolves upon an atois* 143 
neous fluid cannot be in equilibrio unless it have that figure. 
In this case, therefore, the fluid would first extend itself, and 
flatten to a certain degree with a decreasing velocity of rota- 
tion, and then oscillate back with an increasing rotatory mo- 
tion. But the tenacity of the particles would gradually dimi- 
nish, and finally destroy, the oscillations of the fluid ; which 
would therefore ultimately settle in one of the figures of equi- 
librium; that is, in an elliptical spheroid of revolution having 
the equatorial diameter more than 2-7179 times the axis of 
revolution. 
When the oblate figures are little different from spheres, 
as in the case of the planets, x, which is equal to the excen- 
tricity of the meridian divided by half the polar axis, is so 
small that we may consider x 2 as equal to Sin. 2 <p, and may 
reject all the powers of these two quantities. The series for 
q will thus be reduced to its first term, viz. 
<7 = — Sin. 2 (p = — x 2 . 
5 5 _____ 
But the polar axis is to the equatorial diameter as 1 to V 1 -{- x s , 
or as 1 to 1 + 2 : wherefore the same proportion is equal 
to that of 1 to 1 -f- -T q. 
Again, we have 
q = 
now, ~ tt being the mass of a sphere of which the density and 
the radius are each equal to unit, it will represent the gravi- 
tation at the surface ; and, if we suppose the same sphere to 
revolve with the given rotatory velocity, u will be the cen- 
trifugal force at the equator* Wherefore q is the proportion 
of the centrifugal force at the equator to the gravity ; a pro- 
portion which remains the same in all spheres that have the 
