Double- Layer of Solid and Liquid Bodies, 303 



Now every real atom maybe considered, from the electro- 

 static point of view, as a superposition of an adequate 

 number of such hydrogen-like atoms with a common centre 

 containing the nuclei and with different radii corresponding 

 to the different electronic rings. If there are k v electrons in 

 the ring of radius r, they will form on the surface a double- 

 layer of thickness 2r and with a charge e r = + -j-enr. 



The corresponding portion of the intrinsic potential would 

 be V r =§7r<?/e r .n . r 2 , if these electrons were efficient in 

 producing it. It can be easily shown that on account of the 

 rapid decrease of the radius of successive rings, the portion 

 of the intrinsic potential due to the central electrons — even 

 in the case of such a heavy element as Hg — would be of the 

 same order of magnitude as that due to the external (valency) 

 electrons only. As a matter of fact, however, these central 

 electrons — or rather the portions of the atoms corresponding 

 to them in the above sense — are inefficient in the creation of 

 intrinsic potential, their radii being small compared with 

 the interatomic distances. These central portions of the 

 atoms behave like the molecules of a gas, hardly interacting 

 with each other and exerting no sensible influence on the 

 free electrons (if any). We may, therefore, replace the 

 atoms by simplified models, consisting of the external " valency " 

 electrons only and a corresponding positive charge at the centre. 

 In connexion with this it may be mentioned that such 

 simplified models of chemical atoms have been very success- 

 fully applied by Kossel * to the explanation of the laws of 

 chemical action, upon which the central electrons appear 

 thus to have no effect save that of reducing the charge of 

 the nucleus. We are now prepared to deduce on the same 

 principles the laws of phenomena depending upon the 

 surface electric double-layer. 



Let the radius of the external ring be r, the number of 

 electrons in it k (k is in general equal to the valency of the 

 element). Then, to get the charge on either side of the 

 metallic surface and the intrinsic potential Y, we need but 

 multiply (2) and (6) by k. Thus 



e—±-^enr (7) 



V=+! 7r/W n- 2 (8) 



* Kossel, Ann. cl. Phj/s. Heft iii. (1916). 



