SURFACES OF DISCONTINUITY 705 



treatment will be found in the paper by Otto Stern. In the 

 space available the writer can only hope to try to throw some 

 light for the beginner on the fundamental equations used. Re- 

 garding the surface of the mercury as the origin from which 

 the distances z of parallel planes in the solution are measured, 

 we represent the electric potential at a plane distant z from the 

 cathode surface by \p(z), or briefly xp* The quantity \p changes 

 continuously, from the value xpo at the cathode, to zero well out 

 in the solution, i.e., practically at s = oo. If we denote the 

 concentration of a positive ion at z by Ci(z), and of a negative 

 by C2(z), then the concentrations in the solution are Ci(oo) 

 and Ci(x,). These are equal if we adopt as a simple view 

 that there are only two kinds of equi-valent ions, so that we write 



Cl(oo) = C2(00) = C. 



Statistical theory then shows that 



C.(.)=Cexp[-^^} 

 Ciiz) = C exp + -^ J' 



where F is the numerical value of the charge on a gram-equiva- 

 lent of ions, and R is the universal gas constant, t being the 

 absolute temperature. Hence the electric charge density p at 

 the position z in the solution is given by 



p{z) = F[Ci{z) - C,{z)\ 



r r F^p{z)i vF^p{z)y 



= FC 



In addition to this there is a well-known theorem of Poisson 

 connecting the potential of a distribution of electric charge with 

 the density of this charge. It is 



aV av 9V 47r ^ . ^ 



* It has been referred to as V hitherto in conformity with Gibbs' 

 notation. The alteration is made to conform to Stern's symbol. 



