[GARVER] POLYMERIZATION OF LIQUID SUBSTANCES 103 
with the additional evidence that the attractive forces in a liquid film 
may be expressed in terms of the pressure which the substance would 
exert as a perfect gas seems to establish conclusively the validity of the 
proposed application. 
Illustrative Applications 
In accordance with the theory above presented as to the relation 
of the heat liberated to the molecular change which takes place when a 
substance passes from the vapour to the liquid phase, a few examples 
representing different sorts of chemical compounds will be calculated 
so as to indicate the method and determine the numerical results. 
Since, as stated above, the value of H being a pure energy relation, it 
remains to express it as a function of the change in the number of 
molecules. In order to do this satisfactorily, data are necessary which 
are available in only a comparatively few cases. As a first illustration 
we shall take the case of water at 0°C. Since in all the cases to be con- 
sidered the mass will be unity, we may substitute the reciprocal of the 
volume for the density, and vice versa, depending upon which value is 
most readily available. Also in order to avoid the use of double, nega- 
tive signs, the order of integration limits will be reversed, when necessary. 
The volume of 1 gm of saturated vapour of water at 0°C is 204000 
e.c. The liquid density will be taken as 1. The intrinsic pressure of 
liquid water at zero C or 273° A is 1235 atm, as calculated from À de 
m 
L the heat of vapourization expressed in ergs will be 606.5 X 4.2 X 107 
ergs — 2.543 X 10" ergs. The value of 

204000 
R 7 
car T ay 2 1-524 X 10” ergs = W (say) 
V 
1 
L 2-54: 
ences? —— OR A 1-67, and H = (2543-1524) 107 ergs. 

W 1-524 
The ratio 7 will be found the more convenient value to use as a check. 
In order to simplify the discussion H may be expressed in calories. 
Hence since H = L—W = 1019 X 107 ergs, 243 may be taken as the 
number of calories representing the excess heat given out over and 
above all the work due to forces, external and internal, done upon the 
substance. From the preceding theory, this excess must be attributed 
to a decrease in the number of molecules. To determine approximately 
the molecular change we may apply Maxwell’s law, writing E, and E, 
