( 306 ) 
of these substances appears to follow the laws of the perfect gases 
the more accurately as the temperature at which it is investigated 
is lower. So the density of saturated vapour of water at 100°, 
appears to be 2'/, pCt. higher than would follow from the applica- 
tion of the laws for perfect gases; whereas the saturated vapour of 
water at ordinary temperature presents a density which does not 
deviate noticeably from that, which follows from the laws of Borre 
and Gay-Lussac. If for molecular transformation the type of acetic 
acid were the only one which could occur in nature, then the 
supposition that water is also subjected to this transformation would 
involve that the deviation would be found to increase when the 
temperature is lowered. It is highly probable that the deviation 
of 2%/, pCt. of saturated vapour of water at 100°, which cannot 
be accounted for by the ordinary deviation from the laws of 
Borre and Gay-Lussac which also normal substances present, must 
be ascribed to the presence of more complex molecules; but at the 
same time we must then assume, that the heat of transformation 
lies below the limit which we have indicated above. 
The equation which we have used here, is taken from Cont. H, 
p. 29 and there it had been obtained by the direct application of 
the principle of equilibrium, according to which a given quantity of 
matter at a given temperature in a given volume will arrange itself 
in such a way that the free energy is a minimum. It is therefore 
that we had to take a fixed quantiy of the substance, e.g. a unit 
of weight, which might be divided into 1—# grams simple, and 
z grams double molecules. When « varies, the total quantity of the 
substance remains constant. 
We may, however, also consider a mixture, consisting of a number 
of 1—2 simple and « multiple molecules and then we may apply 
the thesis that, when equilibrium is established the thermodynamic 
potential for a molecular quantity of the multiple molecules must be 
n times greater than that for the simple molecules. The linear function 
of z, however, which in other cases may be omitted, must in this 
case of course be preserved. If we then put: 
$= MRT {u + (1-2) 1 (1-a) + ele) 4+ Tia (1-2) + Bal + y (1-2) 4+ de 
then we have: 
0 
Sr 5 = MRT ju—ayp', + 1(1—a)} 4+ aT + 7, 
EDT 
0 
and §-+ (l—z) 5 : — MRT {u + (1—a) wle + BT + 0. 
pT 
ds 5 
From § + (1—z2) =n Se we deduce: 
Oa »T der 
