ME. J. H. JEANS ON THE DISTEIBUTION OF MOLECULAR ENERGY. 
403 
In Boltzmann’s steady state, = 0, and H = |K, since the energy is equally 
divided between the five degrees of freedom. This leads to the relation 
« = — 3/^, 
and equation (vii.) may be written 
'll = (H - |K).(viii.). 
The rate of variation of 11 on account of collisions is therefore given by 
'f = - (H - |K).(ix.). 
Int7'oduct{on of Dissipation. 
5 7. If the changes in the values of H and K arise solelv from collisions, the 
equations just found will enable us to trace these changes, starting from any initial 
values. Let us, ho-wever, suppose that there is a secenid cause of change in H 
and K ; suppose that the angular velocity ax is retarded by a frictional reaction 
betA^'een the molecules and the surrounding medium, the amount of this retardation 
being ecir. It is not suggested that a reaction of this type exists in nature, but this 
reaction may be taken as being the simplest reaction possible, just as a loaded sphere 
has been taken as the simplest dynamical system which will serve our purpose. Due 
to a frictional reaction of this kind, the mean rotational energy H will suffer a 
decrease of amount 2eII 2 >er unit time. 
The equations expressing tlie rates of change of II and K will therefore be 
(IK 
(It 
cm 
(It 
= (ipx/K (II _ |K) . . . . 
= - 2eII - (II - ^K). 
(x.), 
(xi.). 
§ 8. A steady state is now impossible, on account of the dissipation of energy 
which takes place. If, however, we supjjose the translational energy to be in some 
way increased at such a rate as exactly to counterlxdance the loss of energy, the gas 
will rapidly assume a steady state given by c/U/c/^ = 0, or, l)y equation (xi.), 
2eH + fp^/K (H - |K) = 0.(xii.). 
The value of IT corresponding to a given value of K is therefore 
(xiii.). 
Hence if e, /8, K have values such that e is very great in comparison with /Sy/K, 
then H will be very small in comparison with K. The rate at which the external 
agency introduces energy is 2eH, and this may be made very small by supposing e to 
be very small, although great in com})arison with /S^/K. If this agency is removed 
3 F 2 
