of a homogeneous fluid mass that revolves upon an axis. 145 
consequently in equilibrio, begin to revolve about a diameter 
with a rotatory velocity causing a centrifugal force at the 
equator, very small in proportion to the gravitation ; the 
sphere will acquire a small degree of oblateness at the poles, 
and the new surface of equilibrium must come under the 
equation (A). Now, from these considerations alone, with- 
out any reference to the other condition of equilibrium, it has 
been proved by Legendre and Laplace , that the particles of 
the fluid will arrange themselves very nearly in an ellipsoid 
of revolution, the deviation being proportional to the square 
and higher powers of the oblateness. But, as the coincidence 
of the true figure of equilibrium with the ellipsoid is not 
exact, the result seems to be inconsistent with what M’Laurin 
has so ably and elegantly demonstrated to be true. This 
argument will acquire greater force, and will even become 
conclusive, against the theory which makes the equation (A) 
the only condition of the equilibrium, if we consider the ob- 
lateness as a finite quantity, and push the approximation so 
as to take in the square and higher powers :* for, by this 
procedure, we obtain a series of figures in which the ellipsoid 
is not included. 
There is a great analogy between the modern theory of 
spheroids little different from spheres, and the assumption of 
Newton, who tacitly supposed that the fluid sphere, in the 
nascent change of its form, will become, either exactly or 
very nearly, an elliptical spheroid, oblate at the poles. Both 
views of the subject leave us in ignorance of the exact form 
of the surface of equilibrium, although, in the supposed cir- 
cumstances, it is proved in the one, and assumed in the other y 
that it is nearly an ellipsoid. 
* Mec. Celeste, Vol. ii, p. 105, No. 37. 
u 
MDCCCXXIV. 
