Surf ace-Tension with Temperature. 43 



Hence it is evident that 



K = 6, or K0 C = 1, 



again in fair agreement with "Walden's equation K0 C = O*94. 

 Hence, very roughly, the relation between the coefficients 

 a and K is 



a = nK=l'2lK. 



The values of 1*21 K have been calculated and placed in 

 the fourth column of Table IV., and it will be seen that the 

 agreement is as close as one could expect. The reason, 

 therefore, for the variability of Walden's results seems to 

 lie in the fact that the coefficient a is a function of the 

 temperature, while the assumption of proportionality between 

 a and the reciprocal of the critical temperature demands 

 that a shall be independent of the temperature. In fact a 

 is not rigorously equal to nb but is given by 



, ?i(n — 1) , 9ZJ 

 <x = nb ^ — ^-'b 2 + ..., 



and the remaining terms of the expansion are quite appre- 

 ciable even at moderate temperatures. 



It may then be considered that for unassociated liquids 

 equation (iii.) holds with very considerable accuracy, and may 

 safely be used to estimate critic.nl temperatures, even if the 

 observations of surface-tension have only been made over a 

 limited range of temperature. But it must be remembered 

 that in all the cases considered the surface-tension measured 

 is that of the liquid in contact with its own vapour, and it 

 remains to be seen whether the formula holds for liquids in 

 contact with air. In most cases the surface-tension of a 

 liquid in contact with air differs very slightly from that of a 

 liquid in contact with its own vapour, and this difference 

 would hardly be expected to be sufficient to invalidate the 

 formula. Unfortunately the data at my disposal for capil- 

 lary-rise in presence of air are somewhat scanty and scattered, 

 and I have therefore restricted myself to a discussion of the 

 numbers furnished by the careful experiments of Mr. J. L. 

 E. Morgan* on the drop-weights of various liquids. As- 

 suming proportionality between drop-weights and surface- 

 tension for drops falling from the same tip, we have 



w = ic (l-bd) n (xi.) 



* See, in particular, Morgan & Hig-gins, Journ. Araer. Chem. Soc. 

 xxx. p. 1055 (1908), and Morgan & Schwartz, xxxiii. p. 104J (1911) in 

 the same journal. 



