202 Albert P. Mathews 



studied by Guye and Mallet 1 of very high molecular weight 

 and complexity, such as durol, cymol, diphenyl and diphenyl 

 methane. So far as I can find, the evidence is that these sub- 

 stances associate but little; so the deviationc annot be attrib- 

 uted to that. It may be that Guye and Mallet's determina- 

 tions have some constant source of error which brings them 

 higher than determinations on similar substances by Altschul, 

 but I do not think this is the explanation of the facts. The 

 fact that the deviation is in the opposite direction in the sim- 

 plest from what it is in the most complex substances leads 

 me to believe, as stated on page 192, that the calculation of 

 "a" by this formula may be at fault. 



While there can be little doubt that this formula gives a 

 value for " a " approximately correct for all normal substances, 

 as van der Waals has recently reaffirmed, and accordingly 

 that the ratio 27/64 is at least approximately true for all 

 substances, yet it is not certain that this ratio is exactly con- 

 stant for all substances. It can only be strictly justified for 

 the simplest substances in which "6," the volume of the mole- 

 cule, is constant. I believe it to be far more likely that this 

 ratio changes a little with progressive increase in molecular 

 complexity, and a resulting greater compressibility of the 

 molecule, as indeed van der Waals has suggested, than that 

 the law, which I have here attempted to establish, of the de- 

 pendence of cohesion on molecular weight and valence holds 

 strictly only for substances of medium complexity.- This re- 

 lationship of cohesion to these two molecular properties seems 

 so probable and so fundamental that I believe we may, with 

 some confidence, anticipate that if it holds at all, it holds 

 everywhere. 



It seems not worth while to consider this question further 

 until it is decided whether "a" is in all instances determined 

 by the formula just mentioned; or whether the ratio 27/64 

 is true only for the simplest substances with constant molec- 

 ular volume, that is a constant " 6; " and that for more complex 



1 Guye and Mallet: Comptes rendus, 133, 1288 (1901); 134, 168 (1902). 



