434 On the Molecular Theory of Galvanic Polarization. 

 further side by the circular arc r=r Q ; the repulsion now is 

 -R = 2p\og {(r\ + tf)i + (r\-?)n-p\og (A 2 + f) 



-HW- 



As we have seen, this expression increases indefinitely as r 

 increases. But if now, instead of a single electrical sheet, we 

 had a double electrical layer with an intervening vacuum 

 dielectric of thickness t, the repulsion exerted by it on the unit 

 charge in the plane of the positive face will be equal to 



.dR 

 t dh' 



But on differentiating the expression for It, it is obvious that 

 the first and last terms give parts which become zero when r 

 is infinite ; so that the repulsion of the infinite double layer 

 on the unit charge is finite, and is equal to 



2tph 



The repulsion exerted on a strip of unit breadth of density 

 p and extending from £=0 to £=oo therefore 



2tph 



< 



M 



h 2 + ? 



which is independent of h. 



The repulsion exerted on a strip of the same double sheet is 

 therefore 



2irp% 



t, e. it is the electrical energy of the distribution per unit 

 area. And this quantity that we have thus calculated is 

 clearly the surface-tension required. 



It is clear also that the stress across any line drawn on the 

 sheet is wholly tangential, and has no component normal to 

 the sheet ; so that this surface-tension is its complete speci- 

 fication. 



The calculation just made has been only for the case of an 

 infinite plane double sheet. For a single sheet the distant 

 parts exert a finite effect ; and we have seen that the stress 

 increases indefinitely when the size of the sheet increases. 

 But for a double sheet the parts very distant relatively to the 

 thickness no longer contribute sensibly to the result, and the 

 integrals converge. Thus, if the double sheet be of sensible 

 but finite curvature, we may calculate the integrals either 



