160 Mr Glazebrook, On some equations connected with [Nov. 28, 



We know moreover that the velocity of propagation is inversely 

 proportional to the radius vector of the ellipsoid 



(a, b, c being here the principal velocities, not the components of 

 magnetic induction, with which we are not at present concerned,) 

 which is parallel to \ fi, v. 



Let p be the perpendicular on the tangent plane to this ellipsoid 

 at X, /a, v; r the length of the radius vector. Then 



I=(aV + &y+cV)r>. 



p 2 x 



Let x De the angle between the perpendicular on the tangent and 

 the radius vector p — r cos %, 



therefore aV + &V + cV = -, — = V 2 sec 2 v. 



^ r cos % /v 



Again, we know that 



I m n 



X(a?- V 2 ) " /x(6 2 - V 2 ) v(?-V*) 

 1 



V[XV+ ^+ z/V- 2V 2 (aV+ by + cV) + F 4 } P*tan % ' 



7 _X(a 2 -7 2 ) 

 therefore l - p tan % , etc -> 



therefore a = nF ( c2 ~ h ^ cot %• 5 ( 15 )' 



Ao-ain, if X', /a', v are the direction cosines of a, /3, 7, we have 

 X' = mi> — nfi 



p V \ff -V 2 - (c 2 - V 2 )} _ fi v (b 2 - c 2 ) 

 V 2 tan % ' F 2 tan % ' 



therefore a = 47rFX'>S , l 



Similarly, /3 = 4arVfi' S ^ (16). 



7 = 47rI 7 V$ J 



Thus the value of the magnetic force corresponding to an elec- 

 tric displacement S is 4ir . V . S, 



and its direction lies in the wave front and is perpendicular to the 

 electric displacement. 



We knew previously that this was the case for a plane wave in 

 an isotropic medium. Thus the crystal produces the same effect 



