( 106 ) 
xisting liquid and vapour phases would thus remain unaltered, while 
their common pressure would be simply proportional to 7. Although 
with helium the maximum vapour pressure diminishes less rapidly 
with the temperature than is the case with ordinary normal substan- > 
ces, the diminution is still very much greater in reality than would 
be the case under the conditions above assumed, 
A substance that fulfilled these conditions would, moreover, exhibit 
some other very unusual properties. The energy change at constant 
temperature would be zero, the latent heat of vaporization would 
alone be necessary for external work, and so the internal latent 
heat of vaporization would be zero. 
To realise the importance of the moditications which the ther- 
modynamical properties of a substance undergo when the molecular 
attraction decreases with the temperature, let us assume that it 
decreases more rapidly than in simple ratio; in that case one is 
brought to the deduction of still stranger properties. We may here 
mention the case in which a =c7"™ for temperatures below 7, < 7. 
With such a substance at a temperature beneath 7’, lowering of the 
temperature would diminish the difference between the liquid and 
vapour densities, and this difference would disappear at a temperature 
2 
dp dp 
Ty; determined from the conditions P=Oand = — 0 by the equa- 
av ane 
tion Ti Ty = 7T,°. Hence, an inferior critical point occurs from 
which to the absolute zero the substance onee more behaves as a 
perfect gas. For this case the change of energy with volume is 
negative, and so too is, therefore, the internal latent heat. 
We have still to examine if in other domains there are assumptions 
which are consistent with a decrease in the molecular attraction 
as the absolute zero is approached. 
The nearest comes in this respect KrerviN’s and J. J. Taomson’s idea 
of the structure of atoms. Assume, for example, that an atom consists 
of a sphere of uniformly distributed positive electricity inside which 
is an electron; then two such atoms would, at the absolute zero 
where the electron comes to rest, exert no electrical attraction upon 
each other. As soon, however, as the electrons begin to oscillate 
about their positions of equilibrium, and begin to describe orbits 
about their centres, attraction begins to be felt. An investigation 
similar to those made by van per Waats Jr. based upon the prin- 
ciples of statistical mechanics would be necessary before one could 
say how the molecular attraction of a system of such atoms would 
depend upon the effects of collisions and of temperature radiation 
(they are, in fact, vibrators such as those assumed by PLANCK and | 
