792 



Mr. E, H. Fowler on the 



where 2j= 1/kT. Consider an infinite plane slab of thickness 

 df, which is small compared with a, and let us calculate the 

 average attraction dF of all the molecules in this slab on a 

 molecule distant z from the slab*. The calculation is a 

 generalization of the classical calculation of Laplace's theory 

 of surface tension f, generalized in such a way as to recognize 

 the real molecular structure of the fluid. 



Suppose first that the selected molecule is at P and that 

 z>a. Then the average number of molecules in the slab, 

 per unit area of the slab at a distance r from P. is 



vdfi 



2jn(r) 



where we have written, for convenience, 



il(r)= (f>(,v)dw. . . 



• (6) 



Eiflr. 1. 



The number in the annulus at distances between r and 

 r + dr from P is 



27T rsme.^.vdfe 2 ^ r \ 

 sin 6 



and their resultant attraction along PO is 



2irvzdf4>{r)e 2jU{r) dr. . . . . (7) 



To obtain the attraction of the whole slab, we must 

 integrate the expression for values of r from z to infinity. 



* For shortness a molecule is said to be in the slab or distant % from 

 the slab, when its centre is in or distant z from the slab. 



t See, e. g. Kayleigh, Scientific Papers, vol. iii. pp. 397, 513 (1890, 

 1892) ; < The Theory of Surface Forces.' 



