424 The Theory of Aether and Electrons in the 



external field are so arranged as to neutralize each other's electric 

 fields outside the molecule. For simplicity we may suppose 

 that in each molecule only one corpuscle, of charge e, is capable 

 of being displaced from its position ; it follows from what has 

 been assumed that the other corpuscles in the molecule exert 

 the same electrostatic action as a charge - e situated at the 

 original position of this corpuscle. Thus if e is displaced to an 

 adjacent position, the entire molecule becomes equivalent to an 

 electric doublet, whose moment is measured by the- product of e 

 and the displacement of e. The molecules in unit volume, taken 

 together, will in this way give rise to a (vector) electric moment 

 per unit volume, P, which may be compared to the (vector) 

 intensity of magnetization in Poisson's theory of magnetism.* 

 As in that theory, we may replace the doublet -distribution P 

 of the scalar quantity p by a volume-distribution of p, determined 

 by the equationf 



p = - div P. 



This represents the part of jo due to the dielectric molecules. 



Moreover, the scalar quantity pw x has also a doublet-distri- 

 bution, to which the same theorem may be applied ; the average 

 value of the part of pw x , due to dielectric molecules, is therefore 

 determined by the equation 



pwx = - div (W.J.?) = - w x div P - (P . V) w x , 

 or 



/ow = - div P . w - (P . V) w. 



We have now to find that part of ju which is due to dielectric 

 molecules. For a single doublet of moment p we have, by 

 differentiation, 



f JJ pM dx dy dz = dp/dt, 



where the integration is taken throughout the molecule; so 

 that 



/// P M dxdydz = (d/dt) ( FP), 



where the integration is taken throughout a volume V, which 

 *Cf. p. 64. 



t We assume all transitions gradual, so as to avoid surface-distributions. 



