EQUATION AND THE NATURE OV COHESION. 71 



gen in a grain mol of water and yet hydrogen alone at absolute 

 zero would occupy the space of 21.3 c.c. One half a gram mol 

 of 2 at absolute zero occupies the spaee of 10.12 e.c. So the 

 total volume of a gram mol of water if the atoms occupied the same 

 space as they do in the elements at absolute zero should be 31.4 c.c. 

 It is actually only a little more than half this amount. One can 

 imagine the enormous cohesional pressure which must exist within 

 the molecule to condense the atoms in this fashion. It is no wonder 

 that the formation of water from the elements liberates such an 

 amount of heat, for this heat assuredly expresses the amount of 

 this compression or reduction of volume. 



V. THE CONSTANCY OF a. 



It has been a matter of dispute whether the constant a was con- 

 stant, or whether it was a function of the temperature. Van der 

 Waals has strongly supported the idea that it is constant and 

 independent of temperature, except in so far as temperature may 

 influence association, or what he terms, "quasi-association". On the 

 other hand Clausius and others have considered a to be a function 

 of temperature and have modified the characteristic equation on this 

 basis. Van Laar has recently expressed the opinion that a is not 

 constant but varies with the temperature. 11 is computations of the 

 additivity of a are based on a c that is a at the critical tempera- 

 ture. The foregoing pages contain, I believe, the indubitable proof 

 of the correctness of van der Waals' view that a is constant. 

 This proof is furnished by the fact that as long as association and 

 dissociation do not occur C in Eotvös' surface tension law is a 

 constant. I have found the true value of this constant,, namely, 

 a d u j 3 J/iY 1/j T c in which d is the density at absolute zero. This 

 is, besides, the law of Thomas Young. This law of Young's states 

 that the surface tension energy is one third the total cohesive energy 

 of a layer of particles as deep as the range of molecular cohesive 

 attraction It holds only at absolute zero at a point where the 

 cohesion in the vapor can be entirely neglected. The complete law 

 for all temperatures is that of Eotvös. Thomas Young's law has to 

 be multiplied by the fraction (7'. — T)jT c to make it a complete 

 expression holding at all temperatures. This converts it to the law 

 of Eötvös. The fact that we can compute a from the surface tension 

 in non-associating substances at all temperatures and that we find 

 it to be the same value, {troves that a is constant in non-associa- 

 ting substances. We get the same value of a in each of these sub- 



