1168 
‘Tn what follows we shall now determine the entropy constant a 
through the direct calculation of the vapour tension according to 
classical statistieal mechanics, hence for higher temperatures, while 
we shall of course have to know again the thermodynamic behaviour 
of the condensed phase for very low temperatures; the latter is, 
however, the case at present for solid substances on certain simpli- 
fying suppositions. In this way we shall not only get a direct 
confirmation of the formulae given before (with z=2z,=z,—1), 
but shall also be able to establish the general *) definition of probability 
(of course for higher temperatures) for gases and liquids, which 
must be applied for the entropy determination. 
As a further elucidation of the results found for multi-atomic 
molecules we shall also insert a few hypothetical considerations on 
the forces acting in the chemical binding between the atoms. 
The main point in our considerations is the discussion of the 
exchangeability of similar atoms and molecules and of the influence 
of this on the thermodynamic probability and the entropy. 
§ 2. Suppositions on the properties of the solid substance. 
As we shall have to know the entropy of the solid substance, 
and as we can only give this at present theoretically when the 
motions of the molecules and atoms consist of sine vibrations, 
hence when the potential energy is a quadratic function of their 
eoordinates, we shall have to suppose this of our solid substance. 
We may do this when the amplitude of the molecular motion is 
slight on the whole, when the molecules therefore depart little from 
their position of equilibrium. This. however, does not exclude that 
some rare molecules possessing an exceptionally great energy pass 
over larger distances, for which the general assumption does not 
hold, that they even now and then slip through between the 
surrounding molecules, or can detach themselves from the molecule 
complex, and pass into the vapour state, provided their number be 
so small at the considered temperature that it may be neglected for 
the calculation of averages. 
Our assumption implies that the volume of the solid substance is 
independent of pressure*) and temperature. The specific heat at 
“constant pressure then becomes equal to that at constant volume, 
whereas in reality it is as much as from + to 12°/, greater at the 
temperatures that are to be considered. Though our theoretical 
1) Cf. however, the conclusion of § 3. 
®) Large pressures do not occur in our problem. 
