154 



Mr. A. B. Basset on an 



Let us now suppose that the relation between electromotive 

 force and electric displacement is given by (1) ; then if we 

 substitute in (5) and put 



^K 1= A- 2 , /*K 2 =B- 2 , /*K 3 =C- 2 , 

 dx ay dz 



d d 



da=& 

 and recollect that 



a^s-^i+^s 



dx dy dz ' 



(6) 

 (?) 



(8) 

 (9) 



(5) will become 

 d 2 f 



dt 2 



(Pg 

 dt 2 



dVi 



dt 2 



vy dx r dco\dz dy) 

 t* dy dco \dx dz / 

 dco \dy dx 



(10) 



.^(^-^ J 



Equations (10) are the equations of electric displacement 

 in a' doubly refracting medium which exhibits rotatory polari- 

 zation. The first two terms on the right-hand side produce 

 double refraction, and the last terms produce rotatory polari- 

 zation. These last terms are quantities in the nature of 

 angular velocities, and are analogous to the components of 

 molecular rotation in Hydrodynamics ; one of the results of 

 our hypothesis therefore is, that something in the nature of 

 vortex motion takes place in a medium which exhibits rota- 

 tory polarization. 



3. In order to obtain the equations of magnetic induction, 

 differentiate (3) with respect to t, and we shall obtain 



d?a _dQ__dn 

 dt 2 ~~ dz dy 



_p 2 d /da db\ ^ d 

 dy \dy dx, 



by (1). The last term is equal to 



1 _d_(dh_dc y 

 47TfM da \dz dy, 



dc 



1 dz \dx 



_da\ 



TzJ 



df 



da 



