FREED FROM THE ACTION OF GRAVITY. 33 
the motion of rotation of the disc, and consequently hinders the 
central portions of the mass from participating gradually in the 
slackening of the equatorial portions. But that which is pro- 
duced by these two foreign forces would be equally produced by 
a greater initial velocity of rotation if we could annul them. 
18, When, by the aid of a moderate velocity of the disc, we 
limit ourselves to producing the flattening of the mass, the two 
foreign forces of which we have just spoken necessarily hin 
the latter from attaining an angular velocity equal in all its 
points, even though we keep turning the disc. The result is, 
that the mass cannot take exactly the figure which would corre- 
spond to that equality of angular velocity. ‘lhat which it adopts 
is a figure of revolution ; but on placing the eye at the height 
of the centre of the mass, it is easily recoznised that it is not an 
ellipsoid ; the curvature at the equator is too small, and this is 
the more evident in proportion as the flattening is more consi- 
derable. 
Now, is this difference between the figure thus produced and 
that which would correspond to the case of universal gravitation 
solely the result of the action of the two foreign forces in ques- 
tion, or is it in part caused by the difference of the laws which 
the two kinds of attraction follow? In other words, if we could 
eliminate or render insensible the differences of angular velocity 
of the several parts of the mass of oil, would the figure produced 
be an ellipsoid or not? Now, we should render these differences 
of angular velocity insensible if we could impress a movement 
of rotation on a mass of oil suspended in an isolated manner, 
without interior system, in the alcoholic liquid, and then leave 
it to itself. In this case the resistance of the ambient liquid 
would be exercised indeed on the exterior of the mass ; but no- 
thing maintaining the constancy of velocity of the central parts, 
these, by virtue of the strong self-adherence of the oil, would 
participate eventually in the slackening of the exterior portions, 
and we might consider the mass as having each instant an an- 
gular velocity equal throughout. 
; Now, it is very easy to realize the above, by availing our- 
selves of the fact that, when the ring of oil is formed, it returns, 
after some time, upon itself (§ 11). At the instant when the 
ring is well developed, and when we have just stopt the disc, 
we lift the latter cautiously by means of the metallic stopper 
which bears its axis. Then the mass of oil, which is again 
VOL. IV. PART XIII. D 
