or 
OG 
Ou? ll OT par 
IE ge a 
BL vo hie 
or 
laa mp On r de ze dn Ov 
— Ty+rT| — -@+ T7-pr+a| — —-«T| — +pel — 
da Dz JT Ox Jo,T 0a), 7 Òz J.T = 
Zn RT? a ari 
in which it is jast the terms with 7 that are cancelled. Now it 
appears, however, that also this expression is still too simple, for 
now « is found in the result, in which also an indefinite constant 
occurs in consequence of the potential energy. So instead (6) we 
must have an expression of the form: 
= eo 0 
KT 
in which /(7’) is either a constant, or a function of 7’ which is 
still further to be determined. But let us now still put the condition 
that MN becomes equal to zero for very great volumes, and always 
remains positive in other cases. Then we see that (7) cannot satisfy 
this, because for very great volume the entropy becomes infinite and 
so the thermodynamic potential becomes negative infinite. This con- 
sideration requires a dependence of the form: 
came Et 
Nee BENS oe tl eee 
in which it does not make any difference whether we take C as 
a constant, or as a function of 7’, as long as (7) remains quite 
arbitrary. 
4. Further than equation (8) thermodynamic theory cannot go. 
So we must now try if we cannot confirm the up to now only 
plausible result in a kinetic way, and get a further insight into the 
nature of f(7’). By the way indicated by van per WAALS Sm. in his 
communication on the kinetic meaning of the thermodynamic poten- 
tial*} this is easily obtained. We need only modify the train of 
reasoning in so far, that we do not direct our attention to the 
equality of the number of molecules that passes from the liquid into 
1) Verslagen Kon. Akademie Ill, 205—219. 
