Theory of Surface Forces, 217 



The element of the potential is therefore 



2V( z -oe n(/)/ ff. 



In the integration the limits of/ are AP and BP. The former 

 is denoted by £, and the latter may be identified with go , 

 since z or B, is supposed to be a very large multiple of the 

 range of the forces. Accordingly for the potential at P 

 of the whole shell, we have 



dY= wi5=m±m ) . . . , (17) 



z 

 where, as usual, 



*(?)=J"n : c/w. .... (is) 



To find the whole potential at P, (17) must be integrated with 

 respect to f from -co to +co , p f being treated as a function 

 of f. As we need only consider P near the layer of transition, 

 z in (17) may be identified with P. 



If the transition is continuous, we may expand p' in the 

 series 



and then at the point P, 



+*{*£■**%*<*£*. : .}, . . ... (19 ) 



where (as in Maxwell's " Capillary Action ") 



M =irjr^^ rf? ' N=!jj" + > fm . . (20 ) 



Phil. Mag. S. 5. Vol. 33. No. 201. Feb. 1892. Q 



