MR. J. H. JEANS ON THE DISTRIBUTION OF MOLECULAR ENERGY. 
40o 
of an actual molecule, vet at any rate, of a dynamical system which contains all the 
features we believe to be essential to a molecule. 
Ileferring back to equations (x.), (xi.) and (xiv.), it is now clear that, for a non- 
luminous gas, the equations determining H and K will be 
dKjdt =: - PpK^-.(xvi.), 
and 
eH = .(xvii.). 
Equation (xvii.) is the relation between H and K which must now replace the 
etpiation of Maxwell and Boltzmaxx, viz. : 
H |K. 
It therefore a})pears tliat, in the present case, the total radiation Avill be propor¬ 
tional to K® ", and in the more general case discussed in Part II., the radiation will be 
seen to increase still more rapidly with the temperature. Thus it is easy to see 
how it is possible for the total radiation to increase very rapidly near the temperature 
of incandescence, whereas if we supposed the energy divided in any invariable ratio 
between the diherent degrees of freedom, it is dihicult to see how the radiation could 
be anything but directly proportional to tlie temperature. 
Extension of the fo)rgoinrj Theory. 
§ 10. It is possible, under certain conditions, to apply the above methods to a 
more general type of molecule. 
Let the energy of the molecide consist partly of translational energy, and partly 
of various kinds of internal energy, potential as well as kinetic. The only case 
considered will be that in Avhich the internal energy is small ; the potential energy 
will therefore arise from small oscillations about a position of equillljiium, and these 
oscillations will be of definite period, and such as may be supposed to result in the 
emission of liglit possessing a line-spectrum. Thus the total energy corres])onding 
to any such principal mode of vibration, will, when averaged over a large number of 
molecules, be half potential and half kinetic. 
It is necessary for tlie success of the present method that the })robability of a 
collision between tw^o molecules shovdd depend solely on their relative velocity, and 
not on their internal co-ordinates. Now a rotation is to Ije regarded as Internal 
energy, and a rapid rotation will be equivalent to an increase of volume, and will 
therefore increase the probability of a collision unless the molecules are spheres of 
invariable radius, and of which the centres move in straight lines. Thus the 
molecules must either be spheres of which the centre of gruvity and the geometrical 
centre coincide, or else as in the former case, they must ditter by so little from this, 
that the divergence has no effect on the final result {of. § 5). 
