604 Albert P. Mathews 



at the critical temperature; and in some cases they are not 

 more than half those calculated recently by Lewis 1 from the 

 latent heats of expansion of liquids. 



Walden, 2 also, has recently calculated the value of "a" and 

 the internal pressure from the surface tension. His calculation 

 is, however, almost wholly empirical. 



It is based, first, on Stefan's conclusion 3 that it takes one- 

 half the work to move a particle into the surface which is 

 required to carry it all the way to the vapor; and, second, 

 upon an empirical relationship found by Walden between the 

 surface tension and the molecular latent heat at the boiling 

 point. It is, however, by no means certain that Stefan's 

 conclusions are correct and his reasoning does not carry con- 

 viction. There is, also, probably an error in the assumption 

 that the molecules do not change in size on passing from the 

 liquid to the vapor and that the latent heat of vaporization 

 represents only the work done in overcoming molecular co- 

 hesion. Finally Walden's values for "a" resemble Traube's. 

 "a" is always much less than when computed by van der 

 Waals' method from the critical data and much less than the 

 values of Lewis. The values which Walden has obtained are 

 about two-thirds the values given in this paper. 



Values still smaller have been computed by Davies 4 from 

 the latent heat of vaporization. The values he obtains are 

 only about one- third those of Lewis. Winther 5 has still other 

 results. 



Many modifications of van der Waals' equation have been 

 proposed in which "a" was considered variable with the tem- 

 perature and "6" more, or less, constant. These attempts 

 have not been fruitful. It is far more probable that "6," 

 the volume correction, varies with temperature and volume 

 and that "a," which is the ''mass" factor of the cohesion, is 



1 Lewis: Phil. Mag., [6] 25, 61 (1912). 



2 Walden: Zeit. phys. Chem., 66, 385 (1909). 



3 Stefan: Wied. Ann., 29, 655 (1886). 



4 Davies: Phil. Mag., [6] 24, 422 (1912). 



5 Winther: Zeit. phys. Chem., 60, 603 (1907). 



