130 Dielectrics and Inductive Capacity [OH. v 



tion we should be able to deduce all the results of the theory, by first 

 deducing equation (73) from Mossotti's hypothesis, and then the required 

 results from equation (73) in the way in which they have been deduced in 

 the present chapter. 



Thus the influence of the conducting molecules produces physically the 

 same result as if the properties of the medium were altered in the way 

 suggested by Faraday, and mathematically the properties of the medium are 

 in either case represented by the presence of the factor K in equation (73). 



Relation between Inductive Capacity and Structure of Medium. 



148. The electrostatic unit of force was defined in such a way that the 

 inductive capacity of air was taken as unity. It is now obvious that it would 

 have been more scientific to have taken ether as standard medium, so that 

 the inductive capacity of every medium would have been greater than unity. 

 Unfortunately, the practice of referring all inductive capacities to air as 

 standard, has become too firmly established for this to be possible. The 

 difference between the two standards is very slight, the inductive capacity 

 of normal air in terms of ether being 1 '00059. Thus the inductive capacity 

 of a vacuum may be taken to be '99941 referred to air. 



So long as the molecules are at distances apart which are great compared 

 with their linear dimensions, we may neglect the interaction of the charges 

 induced on the different molecules, and treat their effects as additive. It 

 follows that in a gas K K , where K is the inductive capacity of free ether, 

 ought to be proportional to the density of the gas. This law is found to be 

 in exact agreement with experiment*. 



149. It is, however, possible to go further and calculate the actual value 

 of the ratio of K K to the density. We have seen that this will be 

 a constant for a given substance, so that we shall determine its value in the 

 simplest case: we shall consider a thin slab of the dielectric placed in a 

 parallel plate condenser, as described in 139. Let this slab be of thickness e, 

 and let it coincide with the plane of yz. Let the dielectric contain n mole- 

 cules per unit volume. 



The element dydz will contain nedydz molecules. If each of these is 

 a doublet of strength p, the element dydz will have a field which will be 

 equivalent at all distant points to that of a single doublet of strength 

 npedydz. This is exactly the field which would be produced if the two 

 faces of the slab were charged with electricity of surface density n/j,. 



We can accordingly at once find the field produced by these doublets it 

 is the same as that of a parallel plate condenser, in which the plates are at 



* Boltzmann, Wiener Sitzungsber. 69, p. 812. 



