476 Mr. D. L. Chapman : A Contribution 



double-layer theory, given by the equation 



V,-V w +— log 7 -^ = 0*, 



in which e is the charge on a gram ion o£ the metal, and s 

 and m refer to points at some distance within the solution 

 and on the surface of the metal respectively. 



The above equation only holds if it is assumed that the 

 charge on the metal is much closer to the surface than the 

 charge in the solution — an assumption which can be shown 

 to be in complete accord with Schuster's estimate of the 

 concentration of the free negative electrons in conductors. 



Assuming provisionally that the charge on the metal 

 resides entirely on its surface, and that there is accordingly 

 no difference of potential between the surface of the metal 

 and its interior, we propose to investigate the distribution of 

 potential and electric density within the solution, and thence 

 to deduce the capacity of the condenser which the double 

 layer forms. 



Consider a plane surface of the metal, and let x be the 

 perpendicular distance of a point in the solution from the 

 surface of the metal. Let the potential at any point x be 

 represented by Y X) and the pressure of the metal ion at the 

 same point by p x > Then 



Y -Y =— 1o<lA (A) 



x °° e ° e p x v 7 



Indicating by the affix ' that the symbol for a dimensional 

 magnitude refers to the negative ion we obtain similarly for 

 the anion • 



R*, v 



^-V^-log^, (A') 



e 



From (A) and (A') 



P 



<_] 



pJ = ^- (i.) 



V* - 

 since p a0 =pj. 



If by p x we indicate the electric density of the positive 

 charge on the metal ion 



_ e P* 

 Px "W 9 



whilst , epj 



* We shall leave out of consideration the effect of potential energy 

 arising from non-electrical forces at the surface. 



