143-147] Molecular Theory 129 



is infinite when r = and when r = oo . Thus the important contributions 

 come from very small and very large values of r. 



Hence, as regards the contributions from shells for which r is small, we 

 see that the field produced at any point by all the doublets in these 

 shells may be regarded as arising entirely from the doublets in the immediate 

 neighbourhood of the point. The force will obviously vary as we move in 

 and out amongst the molecules, depending largely on the nearness and 

 position of the nearest molecules. If, however, we average this force through- 

 out a small volume, we shall obtain an average intensity of the field produced 

 by the doublets, and this will depend only on the strength and number of 

 the doublets in and near to this element of volume. Obviously this average 

 intensity near any point will be exactly proportional to the average strength 

 of the doublets near the point, and this again will be exactly proportional to 

 the strength of the inducing field by which the doublets are produced, so 

 that at any point we may say that the average field of the doublets stands 

 to the total field in a ratio which depends only on the structure of the 

 medium at the point. 



146. Now suppose that our measurements are not sufficiently refined to 

 enable us to take account of the rapid changes of intensity of the electric 

 field which must occur within small distances of molecular order of magnitude. 

 Let us suppose, as we legitimately may, that the forces which we measure 

 are forces averaged through a distance which contains a great number of 

 molecules. Then the force which we measure will consist of the sum of the 

 average force produced by the doublets, and of the force produced by the 

 external field. The field which we observe may accordingly be regarded as 

 the superposition of two fields, or what amounts to the same thing, the 

 observed intensity R may be regarded as the resultant of two intensities 

 R lt R 2 , where 



R! is the average intensity arising from the neighbouring doublets, 



jR 2 is the intensity due to the charges outside the dielectric, and to 



the distant doublets in the dielectric. 



These forces, as we have seen, must be proportional to one another, so 

 that each must be proportional to the polarisation P. It follows that P is 

 proportional to R, the ratio depending only on the structure of the medium 

 at the point. If we take the relation to be 



then K is the inductive capacity at the point, and the relation between R 

 and P is exactly the relation upon which our whole theory has been based. 



147. The theory could accordingly be based on Mossotti's theory, instead 

 of on Faraday's assumption, and from the hypothesis of molecular polarisa- 

 j. 9 



