to the Theory of Electrocapillarity. 477 



Whence 



px + px'=jj- t (px-p X ') 



= m(^- P t) (from(i0) 



We shall now show that, with the assistance of Poisson's 

 equation, 



V v K , 



the electric state o£ any point in the field can be found, and 

 the charge on the double layer condenser expressed as a 

 function of the difference of potential between the solution 

 and the metal. 



In the special case under investigation Poisson's equation 

 becomes 



d 2 V 

 On substituting the value of -7-^, which can be obtained 



from (A) , this reduces to 



The above differential equation admits of solution in a 

 simple form. Multiplying both sides of the equation by 

 d loge^z, and integrating between x = x and #=00 , we obtain 



UH 2 K VI d , \i /d, \ 2 1 . ft pj 



(i l0 - ^) 2 " (£ l0 ^^) 2 ] = "^ + ^P- " 



e 2 SirL\dx 



but since -r^gep^ is zero, this reduces to 



pa 



€ 



v£i lo ^ =± ( v ^ _ %} 



(Jit is obvious that the negative sign must be taken on the 

 right-hand side of the equation ; so that we obtain finally as 

 the first integral of the differential equation 



7V8,i lw=: v;"^' • • (C) 



