552 



Mr. A. Schuster. 



in different ways. The same holds as regards the action between 

 electrified and non-electrified particles. If the theory of electrolytic 

 convection in gases is true, some hypothesis of this nature is 

 necessary to explain the asymmetry of the discharge. Positive ions, 

 according to the theory, will be delivered at the kathode, either by 

 direct decomposition or by diffusion ; negative ions will, in the same 

 way, appear at "the anode. If, as we must assume by analogy from 

 liquids, a certain normal force is required to effect the interchange of 

 electricities at the electrode, this will become covered, in the first 

 instance, with the ions until the necessary normal force is obtained 

 But we are face to face with the questions previously raised relating 

 to the distribution of ions against the surface of the kathode. If 

 the conditions are such that positive gaseous ions behave partly, at 

 any rate, as a gas ; if, instead of clinging to the electrode, they form 

 an atmosphere round it, the fall of potential at the kathode is 

 explained. The law according to which their density diminishes as 

 the distance from the electrode increases depends on an experi- 

 mental term, as has been stated, and I have not yet arrived afc a 

 satisfactory theoretical foundation for the law ; but various supposi- 

 tions may be made, and if we may imagine the layer of positive ions 

 to behave like a thin liquid film having a definite vapour pressure, 

 we may easily imagine that the falling off will take place very much 

 as it actually does. The large fall of potential at the kathode, 

 according to this view, is not so much due to the amount of work 

 which has to be done to effect the interchange of electricity, but 

 chiefly to the fact that for the same surface density at the kathode 

 the thickness of the polarising layer is greater, which must 

 necessarily increase the fall of potential. Thus, if a is the surface 

 density, and D the molecular distance, the fall of potential would be 

 4ttl i2 Do-, if the ions covered the kathode as in an electrolyte ; but, 

 according to the observed law, the potential in the neighbourhood of 

 the kathode is given by 



V = Y (l - e"-), 



which gives for the surface density 



kYq/^v 2 , SO that V = 4i7TV 2 <tIk; 



but 1/k is of the order of magnitude of a millimeter, and this shows 

 how much the fall of potential is increased by the increased thick- 

 ness of the layer. Comparing the two expressions, we may say that 

 the fall of potential at the kathode would be the same as in an 

 electrolyte if in the latter case the mean distance of the polarising 

 layer from the kathode was 1/k instead of the molecular distances. 

 The numerical vah.es for 1/k are, on the average, about six or seven 

 times as great as the mean free path. 



