426 
MR. J. H. JEANS ON THE DISTRIBUTION OF MOLECULAR ENERGAL 
This merely shows that, neglecting small quantities of the order of the coefficients 
in G, the energy of any of the s modes of vibration must he equally divided 
between kinetic and potential energy. 
It is now clear, that at high temperatures the last term in equation (xxi.) is small 
in comparison with the others, so that the law of distribution will be very little 
altered by the presence of a dissipation function, w^hereas at .sufficiently low teinj^era- 
tures, the term arising from the dissij^ation function becomes as important as any 
other term in the equation, and, therefore, the presence of a dissipation function, 
however small, will l3e sufficient to entirely alter the law of distribution. 
And without investigating the solution of the system of equations which determine 
the coefficients in y, it is clear that since they are all linear, every coefficient must 
be a single-valued function of h only. Hence, as before, there is only one approxi¬ 
mately steady state for a given temperature, but it is no longer true that the various 
lines of the spectrum increase in brightness in the same ratio when the temperature 
is increased. Since the u, q modes of energy sufter very little loss of energy, and 
since energy passes freely between these modes, it follows that the energies of these 
modes will very approximately be distributed according to Boltzmaxx’s Law. 
Hence all that w^as said about the ratio of the two specific heats with reference to 
the former type of molecule considered, will apply also to molecules of the tyjje wdiich 
we have just been discussing. 
PART HI. 
Physical consequences of the Foregoing Theory. 
§28. We have thus been led to the same results in both parts of this paper. It 
seems natural to suppose that I'esults which are qualitatively the same will be found 
to be valid for any gas, and, assuming this to be the case, to examine some of the 
consequences of these results. 
Radiation at a given Temperature. 
§ 29. In the first dynamical illustration, the radiation from each degree of freedom 
at temperature T was found to be 2 )roportional to T^ ", In the second illustration, the 
expression for the radiation would have been too complicated for the calculation of it 
to have been profitable. 
A modification of the system discussed in Part 11., leads to an interesting 
expression for the radiation. In tliis modified system the molecules are to be 
spheres with modes of internal vibration to and from which energy only passes with 
difficulty. Each sphere is surrounded by a field of force, such that when two molecules 
