1904] Mills — Molkcular Attraction. 169 



density: First, by the action of a pressure; second, by the 

 action of molecular attraction. Accordingly the theoretical 

 density of the gas at its critical temperature and under its 

 critical pressure was calculated. The gas would be reduced to 

 that condition if there -were no molecular attraction. The 

 remainder of the condensation, to the actual density, must be the 

 work of the attraction alone. 



The theoretical critical density can be calculated by the 

 equation, 



[19] D = 0.0 4 16014 ~^-. 



If the attraction obeys the law assumed we can use equation 

 . 2 to calculate the energy necessary to overcome the attraction 

 and expand the gas from its observed to its theoretical den- 

 sity. If to the energy so calculated we add the energy neces- 

 sary to overcome the external pressure during the change in 

 volume, we have the total energy, A -j- E t , required by the 

 change. The equation will become, 



c i [20] A + E, = /*' (f/~d — f/ D" ) + 0.0 4 31833 p( i- — -^)Cals. 



By Crompton's theory we can calculate the energy neces- 

 sary to change the gas from its observed to its theoretical 

 density as if the change were produced by pressure alone, the 

 equation being: 



[21] L = X+E, = ?^-Tlog4cals. 



In these equations T is the critical temperature, d denotes 

 the critical density, and D is the theoretical density of the 

 vapor at the critical point. 



The results of equation 20 are given in Table 24 

 under heading Mills. The results from equation 21 are given 

 under the heading Crompton. The difference is also given 

 The agreement is as perfect as could be desired. The dif- 

 ference is usually less than one calorie and amounts to a 

 divergence of more than four per cent, only in the case of 

 normal octane and the associated substances. (To these lat- 



