Double-Layer of Solid and Liquid Bodies. 301 



We see that the distribution of electricity in the double- 

 layer is anti-symmetrical with respect to the surface. 



For the total value of the charge inside or outside the 

 surface we easily find from (1) 



e= +^ner per sq. cm (2) 



We assume that the mean value of the electric intensity E x 

 in a plane at a distance x from the surface may be derived 

 from the equation 



dE x 





(3) 



with the condition that E x = for %=■ 



—r. This gives 





E,= _^ (,._!*:)', 



i*&. • • • 



(4) 



where \a\ is the absolute value of as. E x is always negative, 

 i. e. directed outwards, and reaches its largest value 

 E ='7rner = 4z'jT€ on the surface, with respect to which it is 

 distributed anti-symmetrically. To find the distribution of 

 potential Y x in the double-layer, we integrate the equation 



dV x 



■~Y? = — E x with the condition that V x =0 for x= —r. We 



easily get from (4) 



V,= ™F±[<- 3 -(r + .0 3 ]}, • • • '(5) 



where the upper signs refer to the case .t->0 and the lower 

 to the case x<0. At w=r, V x reaches its maximum value 

 which it preserves throughout the interior of the metal, 

 forming what has been called the intrinsic potential V r , 



V r =§ra?r>, (6) 



of the latter. 



§ 3. The deduction of (4) and (5) was based upon the 



dE 

 approximate equation (3) -^ =4:irp x , the strict one being 



CLX 

 Wr BE, BE, , - 



d# ^y d~ r ' 



where E y and E z denote the two components of E perpen- 

 dicular to the axis #, E being the real value of the electric 

 intensity at a given point of the plane x. The lines above 

 the differential coefficients indicate that their mean values 

 over the whole plane should be taken. We have thus tacitly 



