286 Mr. G. H. Livens : Influence of Density on Position 



the element if a certain condition holds, which condition is 

 equivalent in our case to 



(tew, %ey 9 2«s) = 0, 



always. The sum 2 being in each case taken over all the 

 negative electrons in the element dr. It should be noted 

 that this is not precisely the way Larmor states the condition. 

 The coordinates (a, y, z) are not the absolute coordinates of 

 the electron, but coordinates relative to the moving molecule. 

 However, as both the positive charges and negative electrons 

 partake of the motion of the molecules in emission, and as 

 they are paired in equal quantities in the neighbourhood of 

 certain fixed points in the molecule, we see that the contri- 

 bution to the sum 2 in Larmor's case, due to the motion of 

 the molecules, would vanish, and we should be left with the 

 result as stated. 



But 2 (ex, ey, ez) — (P^, P y , F s ) dr, 



where P is a vector expressing what we may still describe 

 as a polarization in the element dr. It is exactly analogous 

 to the polarization in our previous theory. 



The statement is therefore equivalent to saying that there 

 is no radiation from the element if 



(P*, F y ,Pz)dr=0 

 continuously. 



Thus we conclude that if we are to obtain any radiation 

 from the element dr at all, it must be polarized electrically. 

 The vapour, of course, on the whole exhibits no signs of 

 polarization, except those arising from the phenomena of its 

 radiation. The polarization in the various elements of the 

 vapour will be different in both direction and magnitude, and 

 also continuously changing, the statistical result for the whole 

 body being that it is not polarized. We have thus got a 

 state of affairs analogous to that which was pictured and 

 used to explain the older theories of dielectric polarization. 

 The substance was supposed to contain innumerable polarized 

 elements which, in the absence of any directive force, were 

 scattered indiscriminately and turned in all sorts of directions, 

 thereby neutralizing one another's effects, and leaving the 

 body as a whole unpolarized. 



Now if the element dr is polarized to an intensity P, there 

 is a force aeV acting on any electron in the element. The 

 force aeF in the equations of motion of the electron, as pre- 

 viously given, was seen to arise from the local polarized 

 distribution of molecules and electrons about the one under 



