Radius of the Sphere of Action of a Molecule. 841 



It will be necessary first "to obtain an expression for tbe 

 surface tension of a liquid by means of a method due to 

 Laplace. The surface tension will be expressed in terms of 

 the work done in separating beyond the range of molecular 

 forces the two parts A and B of a slab of liquid into which 

 it is cut by a given plane. Suppose the part B divided 

 by planes parallel to the interface into thin layers whose 

 thickness is dz. Let the attraction on unit area of a layer by 

 the slab A be denoted by <£(#) . dz, where x is the perpen- 

 dicular distance of the layer from the surface of A. The 

 work done in moving unit area of the layer outside the 

 attraction of A is therefore 



if 



dz 1 <f>(x) • dx = w . dz, 



J z 



w = 1 <f>(x)dx, 



where c x is the diameter of the sphere of action of a molecule. 

 Hence the work required to move the whole of the liquid 

 standing on unit area of the surface of the slab A outside the 

 attraction of the slab is 



1 w . dz, 



x- 



Integrating by parts we have 



The term within the brackets vanishes at both limits, and 



hence the work done in producing; two new units of area of 

 surrace is 



Therefore 



y*K*).dt 



2\ 



. In 



where \ is the surface tension. Differentiating this equation 

 with respect to c l we obtain 



a^-oi+OO (i) 



Phil. Mac,. S. 6. Vol. 19. No. 114. June 1910. 3 I 



