EQUATION AND THE NATURE OF COHESION. 11 



of van der Waals' equation. Obviously nothing can with any cer- 

 tainty be said concerning the additivity of a, or its relation to 

 such properties of molecules as their gravitational mass and number 

 of valences, until we have a method of determining, approximately 

 at any rate, the real value of a. This is a difficulty all have 

 felt who have worked with the van der Waals' equation, or who 

 have studied a. There are five or six methods I have used to 

 determine this constant and the results are given in detail in the 

 following pages. The first two methods depend on van der Waals' 

 equation, but the others are independent of it. The first method 

 is to start out with an assumption as to the condition of things 

 at the critical temperature. Obviously from the law of corresponding- 

 states, there is something which all substances must have in common 

 at the critical temperature. The only difficulty is to know what 

 that common condition is. As we know that in many substances b c 

 is very nearly V c /2 the first assumption which suggests itself is 

 that in all substances at the critical temperature b ( . is always VJ% 

 or very nearly that. That is, the molecules always accupv the same 

 proportion of the total space. This assumption, I may say at once, 

 is not true, but it is very nearly true for many different substances, 

 in fact it is approximately true for all except the Simplest gases, 

 such as nitrogen and hydrogen. It is interesting to see, also, how 

 closely the value of a computed on this basis agrees with the 

 real value. The first method, then, of computing a is by the 

 assumption that b, = F" c /2.03. This was the value computed by 

 van der Waals for C0 2 assuming a constant but b variable with 

 the volume. 



The second method is the correct method and rests on the 

 probability that at the critical temperature ajV is always 6.5 PV. 

 Here we make an .assumption, which I hope to be able presently 

 to substantiate, that it is not a fixed relation of the volumes of 

 the molecules to the total volume at the critical temperature which 

 is common to all substances, but in reality it is the partition of 

 energy. Always in all normal substances the same fraction of the 

 kinetic energy is used in overcoming internal pressure and the 

 same fraction for exerting the external pressure at the critical tem- 

 perature. This assumption I believe to be true, and it is the second 

 method for computing a-. a\V* = 6.5 P c . 



The third and fourth methods are from the internal heat of 

 vaporization. I have found two equations from which the calculation 

 can be made, namely those of Mills and Dieterici. 



The fifth method is to compute a from the total heat of 



