254 Mr. William Sutherland on the 



case of the meniscus we can say that e is not less than a/2'2. 

 It will suffice to write e = a/2'2. 



Now according to the definition of a in our theoretical 

 expression for the internal virial, it is the radius of the sphe- 

 rical vacuum artificially used to represent the domain of a 

 molecule ; hut as it occurs in the expression log 2L/a, where 

 2L/a is a very large number and the value of L is indefinite, 

 we see that there is no inaccuracy in making it identical with 

 a the mean distance apart of the molecules. However, for 

 the sake of formal completeness, we can easily find the rela- 

 tion between the two quantities which we have denoted by 

 the one symbol a. Let us now denote by x the mean dis- 

 tance apart of the molecules, that is the edge of the cube in 

 a cubical distribution of the molecules ; then, from the defi- 

 nition of a, os and a are connected by the relation 



2,Am 2 y= £*4>!rAm'dr/a?r, 



J a 



the summation being extended to all the molecules in a sphere 

 of radius R. By actual summation up to R = 5^ we find 

 approximately a = '9x. 



With our previous estimate of e as a/2'2, which we must 

 now write x/2'2 on account of our change of symbol for mean 

 distance apart, we have the two equations, 



Z = A7r(41og2L/-<k<-16/3), 

 a=7rp 2 A^/2-2(2+N/2). 



We can replace p by p, the difference between them being 

 necessarily very slight. Then for ethyl oxide we have the 

 following data : a at the boiling-point according to Schiff is 

 1-57 grammes weight per metre, or 1-57/10 5 kilog. per cm. ; 

 I is 7500 kilog. cm. 4 , and v x — 1*44 cm. 3 Eliminating A from 

 the two equations, we have a relation between x and L ; 

 namely 



x=7'5v 1 2 ^(9'2log l0 2L/'9x-16/3). 



L being hypothetical is not known to us, but we can give it a 

 series^ of possible values, and calculate by trial from the last 

 equation the corresponding series of values for x, with the 

 following results : — 



L. x. 



1/10 5 cm. 4-6/10 7 cm. 

 V10* » 7-7 „ „ 



1/10 3 „ 11-0 „ „ 



