Maxwell's Electro-magnetic Theory of Light. 377 



Substituting for and A? this expression becomes 

 2K l P 2 sin 2 <9 + 2 K 2 P 8 cos 2 0. 



Also, if dv the volume of the element of the dielectric, and if there 

 are n molecules per unit volume, the number of molecules whose axes 

 are inclined at angles between 9 and 9 + d9 will be 



ndv . 



sin o . d9. 



Hence the resultant moment of the element dv of the strained 

 medium will be 



r f ' r 77 i 



ndvPq* < Ki sin 3 dO + K 2 cos 2 sin 9 de \ 



^ Jn * 



(1), 

 if M = W2 2 (|K 1 4-1K 2 ) (2). 



The electro-motive intensity, parallel to the direction of the fall 

 of potential, due to this element of the strained medium, at a point 

 distant r from it in a direction making an angle 9 with the direction 

 of the resultant moment, will be 



, (1-8008*0) 



PM.dv 



v 



Taking the point at which we wish to determine the electromotive 

 intensity as origin, and the axis of x parallel to the direction of fall 

 of potential, we shall have for the electromotive intensity due to a 

 slab of the strained dielectric, perpendicular to x and at a distance x 

 from the origin (if dx = the thickness of the slab, and h = r sin 9) 



The only slab of the dielectric which contributes anything to the 

 electro-motive intensity at the origin is that lying between the 

 planes at \dx and +^dx. The electro-motive intensity due to this 

 will be 



7 ^w = " 4srpM - 



2 / / 



Hence if D be the displacement other than that produced by the 

 polarization of the medium 



P = 47rD 47rMP 

 .*. P(l + 47rM) = 4?rD (3). 



