276 Mr. Gr. H. Livens : Influence of Density on Position 



different for different electrons in the atom, we write for the 

 components of the force 



(a, y, z) being interpreted, as before stated, for each electron 

 as the components in three definite directions of its displace- 

 ment from the equilibrium position it occupied when the 

 atom was undisturbed by any electrical actions. 



(b) Resistance to the motion. — The second force is a re- 

 sistance to the motion of the electron. We shall introduce 

 some action of this kind because without it we could not 

 possibly account for absorption. Following the example set 

 by Helmholtz we shall put this as 



— Tub, —hy, — hz, 



where h is some positive constant. 



Lorentz, in his book, discusses the origin of this force 

 very fully but rather abortively. 



(c) The force acting on the electron due to the electro- 

 magnetic field. — We have now to consider the forces on the 

 electron due to the electromagnetic field in the aether. At 

 first sight it might be thought that this action is to be repre- 

 sented by <?E, where E (a vector) is the electric force in- 

 tensity, and this is what is taken by most authors. On 

 closer examination one finds, however, that a term must be 

 added on account of the polarization in the medium. The 

 force in a polarized body depends on having a cavity in the 

 body, and the result depends on the shape and not on the 

 size of the cavity when small. In the theory of polarized 

 media " the division of the forcive per unit volume into a 

 molecular and a molar part is made by means of the ideal 

 volume and surface densities of Poisson, which are the equi- 

 valent as regards outside points of the actual polarization of 

 the material. The method consists essentially in computing 

 the forcive by combining opposed poles of neighbouring 

 elements instead of taking the single polarized element as 

 the unit. It shows that these adjacent poles nearly com- 

 pensate each other, except as regards a simple volume density 

 whose attraction has no molecular part and a surface density 

 partly at the outer surface and partly at the surface of the 

 cavity which contains the point under consideration. The 

 effect of the latter surface density, depending as it does 

 wholly on the immediate surroundings, is the molecular or 



cohesive part of the average forcive The intensity 



of this local part of the regular force acting at an electron 

 has been assigned as JP very approximately for the case of 



