308 Scientific Proceedings, Royal Dublin Society. 
In most cases, where the only forces intervening are interac- 
tions between parts of the system, the energy can be expressed in 
the form required by the theorem. But this is not the case when 
certain external forces come into operation, as, for example, when 
the zther acts on molecules as well as the molecules or parts 
of a molecule on one another. 
Nevertheless, the theorem is of value in the interpretation 
of nature, because in many cases the ether intervenes some- 
what as perturbating forces do in the case of the planets, 
modifying but not annulling the dynamical condition which 
would prevail if the sun’s attraction alone exercised dominion 
over them. 
On the other hand, it must be remembered that such a vast 
number of molecular events are crowded together within a 
duration that appears very short to us, that small effects have 
superabundant opportunity of gradually accumulating and becom- 
ing conspicuous, within a small fraction (e.g. within the thousandth 
part) of one second of time. 
In estimating the average energy, the average may be struck 
either over a great succession of events happening to one molecule, 
or over what occurs simultaneously to a vast number of molecules. 
The importance and value of these results depend— 
1. On the small volume and the short time, as estimated by 
what are involved in human experiments, which suffice for the 
requisite averages—each cube of a micron (the thousandth part of 
a millimetre) in the volume of the gas containing about 1000 
millions of molecules if it be under the same pressure and tempera- 
ture as atmospheric air, and each of these molecules meeting with 
about seven million encounters within the thousandth part of one 
second. 
2. They also depend on the principle recited above, viz. :— 
that if the data of a dynamical theorem be slightly altered, the 
conclusions are only disturbed to a small extent. 
3. And they depend on the circumstance that the forces to be 
taken account of in applying the theorem, may be confined to 
such forces as are concerned in those events which either directly 
1 See Phil. Mag. for August, 1868, p. 141. 
