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Proceedings of the Royal Society 
their effects. Still less should we, under such limitations, he 
justified in the corresponding conclusions with regard to a mixture 
of three or more systems, each of equal spheres, which form the 
subject of the corollary to Maxwell’s Prop. YI. 
We now pass to a different, but closely connected subject. 
9. Boltzmann’s generalisation of the corollary to Clerk-Maxwell’s 
Theorem, in which it is asserted that, after numerous collisions, the 
average energy is the same for each degree of freedom of the similar 
and equal complex particles of a colliding system, has proved a 
stumbling-block in the way of the Kinetic Theory, by being appa- 
rently irreconcilable with one or other of two experimental facts, 
(1) the value of the ratio of the specific heats of a gas, (2) the com- 
plexity of the spectrum of a self-luminous gas. 
It appears from the above that there is an immediate mode of 
escape from this difficulty, provided the complex particles be so 
constructed that there is not perfect access for collision between 
every degree of freedom of one particle and every degree of freedom 
of every other. We cannot further consider this here, but pass for 
a moment to another view of the subject. 
Eor, even if Boltzmann’s Theorem were true without this condi- 
tion, we must not at onee conclude that a gas cannot consist of such 
complex particles. Every experiment shows that some, at least, of 
the quicker vibrating parts of the particle must be constantly losing 
energy by uncompensated radiation; and when the whole is, in spite 
of this, kept at what we call constant temperature, the requisite 
supply of energy comes in a translational form by impacts on the 
walls of the vessel. We may form an approximation, to what would 
then happen, by the simple expedient of supposing the coefficient 
of restitution to be less than unity for some of the degrees of 
freedom. In such a case the equations of§ 5 become, respectively, 
-«*)- - (1 p+Q Q (» - - Q(»' - 0 
P(m' 2 - I P« 2 - Q» 2 + (*i 2 + « 2 ) \ 
(r + q)) ( a ' 
Q(*' 2 - *> 2 ) - 2 ( p^2 Q { w w - kr p (“ 2 + * 2 ) } • 
and 
