274 Mr. Gr. H. Livens : Influence oj Density on Position 



an average polarization in the arrangement of the groups of 

 electrons in the particles, .... With anything else than the 

 mean aggregates of the various tjpes that can be thus 

 separated out, each extended over the effective element of 

 volume, mechanical science, which has for its object matter 

 in bulk as it presents itself to our observation and experiment, 

 is not directly concerned." 



We have thus got to express ourselves in terms of 

 statistical or averaged sums over all the electrons in the 

 element of volume. Statistically the effect of an electric 

 force on a body is to polarize the molecules, that is, to twist 

 them round or alter them in some way so that they have 

 a definite polarity. We can express this polarity as an 

 averaged sum over all the electrons per unit volume. 



The ^-component of the moment of a simple bipolar 

 element is 



ex' —ex, 



(%' y' z') being the coordinates of the positive pole, and 

 (x, y, z) those of the negative pole of the doublet referred 

 to fixed rectangular axes. 



If the element of volume is small enough we have simply 

 to add up vectorially the moments of the simple doublets 

 contained in it to get the resultant moment of the element, 

 i. e. its polarization. 



The ^-component of the intensity of polarization is thus 



where 2 is taken per unit volume over all doublets. [The 

 meaning of " per unit volume " is that we calculate the sum 

 for the small element dr and then divide the result by dr.] 



This is seen to be 2 ex, taken for all electrons per unit 

 volume, due regard being paid to sign. Thus 



P*=2 



ex 



is the ^'-component of the intensity of polarization. 



It may be here noticed that we have spoken of doublets 

 formed of a negative electron and an equal and similar 

 positive charge ; whereas our assumptions on the " model " 

 atom come to the fact that the positive electrification is 

 distributed as a volume density throughout the atom. 

 However, we are not concerned with the actual distribution 

 of this positive charge in any particular form, and we may 

 safely assume that it is distributed in such a way that we 

 can conceive definite doublets in the above form. The only 



