of Edinburgh, Session 1885-86. 
371 
geneous after the first instant. But I find it' does continue homo- 
geneous, however the containing vessel he moved, provided the shape 
be ellipsoidal; that is to say (for the present limited case), an 
ellipsoid of revolution whether prolate or oblate. The possible 
incident of the containing vessel being brought again to rest in any 
position after any motion round any succession of diameters per- 
pendicular * to the figure of revolution is of course included. 
(2) Given a rigid solid, with a hollow space of any shape not a 
figure of revolution, within it, full of liquid : solid and liquid 
all rotating homogeneously. Let the given rotation of the solid he 
impulsively brought to rest or to any other rotation, whether 
rotation with changed angular velocity round the same axis, or 
rotation round another axis. The instantaneous motion of the 
liquid, at the instant of the completion of the impulse, will he 
the resultant of the given homogeneous rotation, with an irrota- 
tional motion superimposed upon it; this irrotational motion of 
the liquid being the same as the motion which would be generated 
from rest by giving to the solid (whether impulsively or gradually) 
an angular velocity the same as that which, compounded with 
the first given angular velocity, produced the second angular 
velocity to which we supposed the first angular velocity of the 
solid to be suddenly changed. 
In this second example, as in the first, the molecular rotation 
does not generally continue to be homogeneous in the altered 
condition in which the solid and liquid do not rotate as if all solid ; 
but it does continue to be homogeneous, if the shape of the hollow is 
ellipsoidal. 
(3) Given a spherical shell full of homogeneously rotating liquid, 
or a hollow of any shape in a rotating solid full of liquid, rotating 
homogeneously with the solid. By impulsive pressure at the 
boundary of the liquid, supposed now to be perfectly yielding, 
generate any prescribed normal components of velocity in all parts 
of the boundary. The effect will be to generate throughout the 
liquid an irrotational motion, the same as would have been gene- 
rated had the fluid been given at rest. The resultant motion 
throughout will be the resultant of this irrotational motion, com- 
* Rotation of the containing vessel round the axis of figure has no effect on 
the liquid, and need not be included to complicate our considerations. 
