90 THE ROYAL SOCIETY OF CANADA 
T x Vm=RT=0Vm 
2€ 
where V'm is the volume of a gram. mol. of liquid and Vm is the volume 
of a gram. mol. of the same substance in the vapour phase, or, omitting 
the R T 
(¥/2 €) Vim = © Vm 
Although the theory from which the value of € is derived, has at 
first sight no immediate relation to the general gas equation, it is evident 
that the two equations (D) and (H) are closely related. They reduce 
to an identity when the value of € from one is substituted in the other. 
The equation (H) was obtained from (D) by substituting for its value, 
que T, from the general gas equation. However, they are not iden- 
m 
tical experimentally as may easily be seen as follows: The ratio, w/a 
for a vapour, may be obtained directly from experiment. The same 
is true for the ratio y/p for the liquid phase. If now we find the ratio 
of the two above experimentally determined ratios and call it 2 € then 
for the given pair of values we have identically 
D a aa 
a p 
of necessity, for that pair of values. Now if not functionally related, 
2 € as a ratio found from experimental values, may be a constant, a 
variable or merely an arbitrary ratio, having unrelated values for each 
pair of ratios. But in this case € is functionally related to the general 
gas equation from the fact that it is the ratio of two ratios one of which 
is manifestly a function of the general gas equation, since € is computed 
i y a 
from, and is equal to, —- X —. It has also been shown that 2e 
p wo 
: 7 9 . 
correctly represents the dynamical value of —— over a very wide 
po 
range of values. Therefore it must satisfy the general gas equation 
F : Ya 
just as exactly and to the same degree as its equal —— for the sub- 
pw 
stance, temperature and pressure being the same, ¥/2 € p corresponds 
: : 0) R 
with and is equal to, — = — T. 
a m 
For low temperatures where the vapour-density 4, and the vapour- 
pressure © cannot be measured accurately, the value of € from the gene- 
ral gas equation is the more reliable value of the two. Take the case of 
alcohol at 20° C. The different values of p and w as given by good and 
