1358 
course this difference will be exceedingly small at ordinary tempe- 
ratures and will only get a noticeable value at extremely low tempe- 
ratures, at which the molecules in the liquid phase which can be 
regarded as vibrators of a shorter period than those of the vapour, 
have less kinetic energy than they should have according to the 
equipartition-law. This will of course have influence on the density 
of the vapour phase, which will be found to be smaller than we 
should expect according to classical statistical mechanics. 
Corresponding considerations apply to the contact difference of 
potential at very low temperatures. 
Besides the distribution of particles in space there are other problems 
which may be treated with the aid of considerations of the same 
kind, e.g. the orientation of the axes of polar particles under the 
influence of directing forces. The probability that the axis of such 
a particle, with moment m, in a field of forces, whose intensity is 
§, forms an angle « with the direction of this force, is according to 
classical statistical mechanics equal to 
mS) cos « 
0 sina 5 
e — da seen sce Ly See ea ale a 
According to our considerations the probability that it has a con- 
siderable amount will at low temperatures be smaller than is indicated 
by this formula. Accordingly we find e.g. the Curm-point at a 
higher temperature than would be dedneed from this formula, at 
least for those substances, for which this point lies so low, that at 
the Curim-temperature the mean kinetic energy of the rotations of 
the molecules is smaller than it should be according to the equi- 
partition law. 
§ 8. It is obvious that the above considerations have an exceedingly 
provisional character. Many problems are referred to, but not for a 
single one have we found a sufficiently conclusive solution. I hope 
to be able to treat some problems more in detail on a later occasion, 
In the meantime I think that I have shown that the drawing 
up of a new system of mechanics as aimed at in my former com- 
munication upon this subject is of the highest importance for all 
thermodynamic questions. I have done this with a view to draw 
the attention of the mathematicians to the problem and more in 
particular to the integral equation (Sa) or a corresponding equation *), 
1) I say a corresponding equation because, as I have already remarked on 
p. 1180 I was not perfectly sure that | was right in leaving the “proper coordi- 
nates” of the electron in this equation out of consideration. It is possible that the 
