506 Appendix. 
Equilibrium of a fluid mass in the form of an ellipsoid rotating 
about its shorter axis; by R. J. ADcocK. 
A FLUID mass, in the form of an ellipsoid, rotating about its 
shortest axis, under the action of the attraction of its own par- 
ticles and their centrifugal forces, is in equilibrium; and this 
is the only form of equilibrium. 
In my work on Gravitation, and in a paper* presented at 
the Dubuque meeting of the American Association for the 
Advancement of Science, it is shown that the ellipsoid is a form 
of equilibrium, and the expression found, for the force at any 
oint of its surface. It remains, then, only to demonstrate the 
ast part of the proposition, that the ellipsoidal form is the only 
one of equilibrium, under the given conditions. 
roof of this depends upon two propositions. 
First. The attractions of two similar bodies for any two ex- 
terior points similarly situated, are as their similar dimensions, 
and consequently as the distances, of the attracted points from 
n in er. 
This follows from formula (1) of Gravitation, and the propos! 
tion that these shells are the only ones which have the distances 
the attractions of its own particles and their centrifugal forces, 
attraction of the enveloping shell has no effect on the li i 
mass, a property just shown to belong only to the eUP 
dal shell whose outer inner surfaces are concent, © 
nd similarly placed. Hence, the ellipsoidal form 1s the 
one, under the given conditions, of equilibrium. — 
‘This paper and the one presented at the Dubuque meeting of th Ame 
te to be inserted in my work on Gravitation, ners w the earth on 
