128 Dielectrics and Inductive Capacity [OH. v 



having a number of insulated uncharged conducting molecules in the space 

 between the plates. Imagine a tube of strength e meeting a molecule. At 

 the point where this occurs, the tube terminates by meeting a conductor, so 

 that there must be a charge 6 on the surface of the molecule. Since the 

 total charge on the molecule is nil there must be a corresponding charge on 

 the opposite surface, and this charge may be regarded as a point of restart- 

 ing of the tube. The tube then may be supposed to be continually stopped 

 and restarted by molecules as it crosses from one plate of the condenser to 

 the other. At each encounter with a molecule there are induced charges 

 e, 4- e on the surface of the molecule. Any such pair of charges, being 

 at only a small distance apart, may be regarded as forming a small doublet, 

 of the kind of which the field of force was investigated in 64. 



144. We have now replaced the dielectric by a series of conductors, the 

 medium between which may be supposed to be air or ether. In the space 

 between these conductors the law of force will be that of the inverse square. 

 In calculating the intensity at any point from this law we have to reckon 

 the forces from the doublets as well as the forces from the original charges 

 on the condenser-plates. A glance at fig. 46 will shew that the forces from 

 the doublets act in opposition to the original forces. Thus for given charges 

 on the condenser-plates the intensity at any point between the plates is 

 lessened by the presence of conducting molecules. 



This general result can be seen at once from the theorem of 121. The 

 introduction of new conductors (the molecules) lessens the energy cor- 

 responding to given charges on the plates, i.e. increases the capacity of the 

 condenser, and so lessens the intensity between the plates. 



145. In calculating that part of the intensity which arises from the 

 doublets, it will be convenient to divide the dielectric into concentric spherical 

 shells having as centre the point at which the intensity is required. The 

 volume of the shell of radii r and r + dr is 4<7rr 2 dr, so that the number of 

 doublets contained by it will contain r*dr as a factor. The potential produced 



by any doublet at a point distant r from it is , so that the intensity 



will contain a factor . Thus the intensity arising from all the doublets in 



the shell of radii r, r + dr will depend on r through the factor . r~dr 



dr 



or . 

 r 



The importance of the different shells is accordingly the same, as regards 

 comparative orders of magnitude, as that of the corresponding contributions 



fdr 



to the integral I . The value of this integral is log?* -fa constant, and this 



