360 Scientific Proceedings, Royal Dublin Society. 
but for the purposes of the theorem it may’ be reduced to— 
(2) T= 3 [|M (w+ 0° +") + B(w,’ + w;") |, 
since rotation round the axis of symmetry can neither be set gomg 
by the kinetic energy with which the molecules collide, nor if 
maintained in any other way can it in the least influence the 
values of w, v, and w. 
The model when dealt with in this way is instructive, because 
it illustrates, as Mr. Bryan has pointed out (Proceedings of Cam- 
bridge Phil. Soc. of Nov. 26, 1894) how a motion may exist in a 
molecule which does not come under the theorem, and which there- 
fore may be going on with any amount of energy. 
To describe the situation in other and very convenient language, 
the motions of translation of the ellipsoids of revolution between 
their encounters are A events, and the energy of these events, 
Viz. :— 
Average value of 3% 3 U/ (uw? +0 + uw”) 
is 2 of the whole of that energy of the mechanical model which 
comes under the notice of the theorem. The rotations w, and w; 
are Ba events, and their energy, viz. :— 
Average value of = 3 B (w," + w;7) 
is 2 of the energy dealt with by the theorem. ‘The rotation w, is 
a Be event, which can be kept outside the theorem. In it, 
accordingly, any amount of energy may reside. 
Another instructive mechanical illustration is constructed by 
considering each molecule as a rigid ellipsoid of one uniform 
density surrounded by a rigid envelope of another uniform density, 
extending from the surface of the ellipsoid to the smooth surface 
1Jt is very necessary to bear in’mind that, so far as the theorem is concerned, it is 
optional with us whether we make this reduction from 6 to 5 terms or not. But if we 
retain the term 3 dw,”, we must remember that the theorem only deals with motion 
subsequent to an initial condition in which an equal partition of energy had been made 
among the terms. It states that if this condition existed initially, it will continue 
subsequently ; and this is evident so far as the rotation round the axis of symmetry is 
concerned, since, if this rotation were once set up, it would continue unchanged. For 
some purposes we must retain the six terms, ¢.g. in order to see how the transition 
from the case of a solid of revolution to the case of a solid which differs but little from 
a solid of revolution, takes place without an abrupt change in the effect predicted by 
the theorem, so as to comply with the general principle of continuity in dynamics. 
