1881.] the Electromagnetic Theory of Light. 161 



as an isotropic medium whose specific inductive capacity is equal 

 to that of the crystal in the direction of the electric displacement. 



An important distinction between the magnetic and electric 

 displacements must be noted. The velocity of propagation of both 

 is given by the same construction, that is to say, it is inversely 

 proportional to one of the axes of the section of a certain ellipsoid 

 by the wave front. The electric displacement is parallel to that 

 axis which determines the velocity while the magnetic is perpen- 

 dicular to it. 



The electromotive force in the crystal we know is not in the 

 direction of the electric displacement. 



If we construct an ellipsoid whose axes are jK lf JK 2 , JKs 

 and if r be the radius vector of the ellipsoid in the direction 

 of displacement, and p the perpendicular on the tangent plane, 

 then it is easy to shew that the E. M. F. is in the direction of 

 this perpendicular and is equal to 4nrS'/rp, 8' being the electric 

 displacement. 



Again, if % be the angle between this perpendicular and 

 the direction of displacement, and we resolve this force along S, 

 and at right angles to it in a plane passing through r and p, we 

 have for the components 



4tt£' , 4ttS' . 



- cos v, and sin v, 



rp * rp * 



but p = r cos %. 



Thus the E. M. F. along and perpendicular to S' respectively, is 



4tt£' , 4tt£\ 



r *~> and -^tan % . 



And if K' be the specific inductive capacity of the medium in 

 the direction of displacement r* = K' and the components are 



4ttS' . 4ttS\ 



„. , and — ~ , tan v. 

 A K ^ 



If a wave of transverse displacement be traversing the crystal 

 since the direction of displacement is an axis of the section of the 

 wave surface by the plane of the wave it is clear that the direction 

 of this last component is the wave normal. And the angle % is, 

 if the medium be magnetically isotropic, the angle between the 

 ray and the wave normal. Thus the E. M. F. produced by a 

 displacement S' in a direction in which A"' is the specific in- 

 ductive capacity is 



