166 PROCEEDINGS OF THE AMERICAN ACADEMY. 



molecules * of the gas were appreciable, then the progressive energy of 

 the molecules would be the same as if it were a perfect gas, but the pres- 

 sure would be greater than the pressure of a perfect gas. According to 

 our new theory the pressure in this case would be necessarily the same 

 as that of a perfect gas, and therefore the kinetic energy of the molecules 

 must be less than that of the molecules of a perfect gas. In general, 

 then, we should expect the internal kinetic energy to diminish with the 

 volume. 



This is an important consequence of the new theory, and it is evident 

 that the volume of the molecules must be as important in our theory as 

 in that of van der Waals ; but in the former the quantity " h " concerns 

 energy relations, while in the latter it concerns pressure relations. We 

 are thus led to a consideration of the total change in internal energy in 

 an isothermal change of volume of a liquid or a gas, and in the change 

 from a liquid to a vapor. 



It has frequently been assumed that the energy change in such a process 

 is a measure of the attractive forces which oppose or assist the process. 

 In an earlier paper t I have shown that this is the case only when the 

 specific heat at constant volume remains the same ; and, in fact, it is 

 obvious that the change in potential energy which is a measure of attrac- 

 tion is in general only one factor of the total change in energy which 

 includes also any change in the internal energy of the molecules as well 

 as the change in progressive energy of the molecules, which is assumed 

 in our present theory. 



These three factors will be designated as follows : The change in 

 potential energy, or Free Energy, which is the measure of intermolecular 

 attraction, will be represented hj dX; change in the progressive motion 

 of the molecules hy dE; change in the internal energy of the molecules 

 by dl. li d U is the total change in internal energy, 



dU=dX+dE+dL (17) 



In the paper % already referred to I have developed the general ther- 

 modynamic equation of condition, 



P = ^^_^Wr-^+rril^.r, (18) 



V dv J T^^ dv 



* This phrase is used in conformity to usage. The quantity "b" of van der 

 "Waals may be defined more generally and less hypothetically as a quantity depend- 

 ing on the difference between the time in which two molecules approach, collide, 

 and separate, and the time which two mathematical particles would require for 

 the same process. 



t Lewis, 1. c. t Iliid- 



