CAPILLARY ACTION. 



Let us now suppose that by some change in the form of the boundary 

 of UM film iU area is changed from S to S+dS. If its tension is T the 

 work required to eflect this increase of surface will be TdS, and the energy 

 of the film will be increased by this amount. Hence 



(13). 

 But since J/ is constant, 



Q ............................ (14). 



Eliminating dS from equations (13) and (14), and dividing by S, we find 



In this expression a- denotes the mass of unit of area of the film, and 

 the energy of unit of area. 



If we take the axis of z normal to either surface of the film, the radius 

 of curvature of which we suppose to be very great compared with its thick- 

 ness c, and if p is the density, and \ * ne ener gj f un ^ f mass a ^ depth z, 



=t' pdz 



j 



(16), 

 and 



(17). 



Both p and \ aie functions of z, the values of which remain the same 

 when z c is substituted for z. If the thickness of the film is greater than 

 2, there will be a stratum of thickness c 2e in the middle of the film, 

 within which the values of p and \ w ^ ^ P an( ^ X' ^ n ^ e ^ wo strata 

 on either side of this the law, according to which p and x depend on the 

 depth, will be the same as in a liquid mass of large dimensions. Hence in 

 this case 



(7= 1C 



(18), 



