EQUATION AND THE NATURE OF COHESION. 27 



calculated by tbem arc, as will be seen, in very good agreement, 

 however, except in a few instances with calculation of a from 

 the surface tension and in other ways, and they give at least an 

 approximation, as close as we can get at present,. to the real value 

 of a. This calculation is also quite independent of the value of 

 the other constant b. The values of a calculated by these two 

 formulas are given in columns 4 and 5 of Table 2. It will be seen 

 that on the whole they agree well with the values calculated in 

 other ways except in the case of octane and the heavier esters, 

 where the values thus calculated from the internal latent heat are 

 higher than expectation. On the basis of the relation that dPJ'dT 

 at the critical temperature is equal to 2M/V Mills has computed 

 another value for his constant //; and the values of a calculated 

 from the formula using this value of [jJ are more nearly those 

 computed from the gravitation, but this relationship of dl J jdT = 

 2RjV c can only be justified when # c =F~/2. It may be that sonic 

 decomposition close to the critical temperature makes the latent heat 

 of vaporization somewhat high in those substances of a high critical 

 temperature like octane. On the other hand there may of course 

 be some other explanation. 



d. Calculation of a from the surface tension. 



This method I have discussed more at length elsewhere 1 ). We 

 may compute a from the surface tension by means of Thomas 

 Young's formula, making the calculation at absolute zero; or we 

 can determine it from EötvöY constant. The law of Young is in 

 reality only the law of Eötvös at absolute zero, the temperature 

 at which the cohesion of the vapor can be completely neglected. 

 I found that C, the constant in Eötvös' law had the value: 

 C = adJS MDP 1 * T c . Eötvös' law is: sF 2 ' 3 = C{T—T). Cis deter- 

 mined by experiment ; s is the surface tension in dynes per cm ; Af is 

 the molecular weight ; d is the density at absolute zero ; 2\. the critical 

 temperature ; and F J/:J , the two thirds power of the volume of a 

 gram mol of the liquid. The density at absolute zero may be cal- 

 culated from the relation: {d—D)/d = {(T c — r J , )/T c ) il3 . In computing 

 a from the surface tension it must be remembered that many 

 of the determinations of surface tension are made by the capillary 

 rise method and that the errors in this method all tend to make 

 s low. Also the determination of the surface tension by this 



r ) Mathews: Journ. phyg. cliem. , 20, 567 (1916). 



