398 
MR. J. H. JEANS ON THE DISTRIBUTION OF MOLECULAR ENERGY. 
admit an interaction, no matter how small, between the molecules and the sur¬ 
rounding ether. That such an interaction must exist is shown hy the fact that a 
gas is capable of radiating energy. In fact, Boltzmann’s Theorem rests on the 
assumption that the molecules of a gas form a conservative dynamical system, and 
it will appear that the introduction of a small dissipation function may entirely 
invalidate the conclusions of the theorem.* Thus we may regard the Boltzmann 
distribution as unstable, in the sense that a slight deviation from perfect conserva¬ 
tion of energy may result in a complete redistribution of the total energy, and it 
will appear that this new distribution of energy will lead to values for the ratios of 
the two specific heats which are not open to the objections mentioned above. 
§ 2. A second difficulty, of a mathematical rather than physical nature, may be 
mentioned here, as it will occur incidentally in the course of the analysis. It is 
well illustrated by the consideration of an imaginary type of molecule which has 
been suggested by Boltzmann.! A loaded sphere, that is to say, a sphere of which 
the centre of gravity is at a small distance r from the geometrical centre, will, for 
the present purpose, possess five degrees of freedom, and this is true, however, small 
r may be. The ratio of the specific heats of an ideal gas whose molecules are of 
this type ought accordingly to be If. If, however, r actually vanishes, the molecules 
must be regarded as completely symmetrical, and possessing only three degrees of 
freedom, so that the ratio ought now to be l-f. There is thus seen to be a discontinuity 
when r has a zero value, and this requires investigation. 
It must be borne in mind that a degree of freedom, for purposes of Boltzmann’s 
Theorem, is not idendical with the usual dynamical degree of freedom. In the strict 
dynamical sense every sphere possesses six degrees of freedom, the principal momenta 
being the momenta of the centre of gravity in three rectangular directions and the 
three rotatory momenta about the principal axes of inertia. But if the sphere is 
perfectly smooth, rigid, and symmetrical, it is impossible to change the three latter 
momenta by the application of any forces which are at our disposal in the kinetic theory 
of gases, and for this reason the corresponding degrees of freedom must be left out 
of account, when apjfiying Boltzmann’s Theorem. Similar remarks apply, in the 
case of the loaded sphere, to the degree of freedom which arises from rotation about 
the axis of symmetry, so that the loaded sphere must be supposed to possess five 
degrees of freedom, and not six. 
* The matter may he looked at from a slightly different point of view as follows: If an interaction 
between matter and ether exists, no matter how small this interaction may be, the complete dynamical 
system will consist of the molecnles of the gas, together with the ether, and must therefore be regarded as 
a system 2 )ossessing an infinite nundjer of degrees of freedom. Apj^lying Boltzjiaxn’s Theorem to this 
system we arc merely led to the conclusion that no steady state is possible until all the energy of the gas 
has been dissi|)ated by radiation into the ether. This apjdication of the theorem may or may not be 
legitimace, out it is, I think, certain that no other ap})lication is legitimate. 
t ‘ Vorlesungen iiber Gastheorie,’ Part 11., p. 129. 
