Law of Molecular Attraction. 497 



none the less real because it is not given in the above equation) 

 I do not see that the above supposition is legitimate. The 

 difference between the ordinates named, as I see it, might 

 not denote the latent heat of the liquid corresponding to the 

 temperatures named. I think that there are further ob- 

 jections to the proof given, but it seems to me that the one 

 named is sufficient. 



I do not see any reason to suppose, nor any way to prove, 

 that an infinite number of true and yet different relations 

 exist between L and p as a matter of reality, and if relations 

 are found mathematically which do not exist in reality the 

 fault is with the mathematics. 



7. The actual facts, it seems to me, are precisely the 

 reverse of the condition for which Kleeman is arguing. If 

 in nature there are two phenomena so dependent upon each 

 other that one can be expressed as a function of the other, 

 we have an equation. If, now, these same phenomena can 

 be connected by a different equation, and one which could 

 not be reduced to the first equation, it simply means that 

 the phenomena are related in another way. And the discovery 

 of the second relationship in no wise diminishes the signi- 

 ficance of the first relationship. Thus Dieterici has shown 

 that the internal heat of vaporization, X, is equal very 



approximately to CRT In =r. This fact in no wise diminishes 



the importance of the relation 



pointed out by the author. The one equation arises probably 

 from the motion of the molecules, the other from the 

 attractive forces that operate between them ; and since these 

 forces under certain conditions are in equilibrium, it becomes 

 possible to have two different expressions for the same 

 quantity. If Kleeman can show a third true equation for \, 

 which does not introduce constants or relations having no 

 natural significance, it simply means that there is some third 

 relation existing between the quantities and some " cause " 

 for this relation, and he will have discovered a fact of 

 consequence. The point I wish to stress is that when the 

 equations are really different and really true, they represent 

 different facts. 



8. Several years ago * I investigated certain equations 

 obtained on the supposition that the molecular attraction 

 varied as the inverse third, fourth, fifth, and sixth power of 



* Jour. Phyri. Cheni. xi. p. 156 (1907). 



