L . ) 2 R 2 n, 



612 Surfaces of Discontinuity in Rotationally Elastic Medium. 



Hence in this medium a persistent wave-front, consisting 

 o£ a first-order discontinuity separating two states which are 

 compatible up to the second order, is propagated in the 

 medium with constant normal velocity c. 



Moreover we have 



[X,Y,Z]=c[Curl(f, ,,,?)] ==^ExN 1 



[*,frv]=\^ t &V,S)]=^f t * !►• • (22) 



E.N = 



Thus the two vectors representing the discontinuities in 

 the electric and magetic forces are at right angles to each 

 other and lie in the wave-front. 



Also if E denote the Poynting radiation vector, we have 



[E] = [X, Y, Z] x [«, /3, 7 ] = - c |f E x (E x N) 



^t x&tj 



where n is unit vector in the direction of the normal to the 

 wave-front. 



Thus the discontinuity in the radiation vector is in a 

 direction normal to the wave-front and is of magnitude equal 

 to the square of the discontinuity in the magnetic force. 



§ 9. Stationary and Absolute Discontinuities. 



Up to the present we have assumed that the equation of 

 the surface of discontinuity contains the time, and we have 

 found that such a surface forms a wave-front expanding out- 

 wards with constant normal velocity. Consider the possibility 

 of a stationary discontinuity of the first order. Then from 

 (22) we see that the discontinuity of the magnetic force 

 vanishes; also since (21) becomes 



it follows that the vector E must also be zero. Hence there 

 cannot be a stationary surface o£ discontinuity at which the 

 tangential electric and magnetic forces do not vanish. 



In equations (7) and (8), the vector (f, t) i f) is regarded as 

 linear displacement from a natural state of the medium, in 

 which the electric force (X, Y, Z) is everywhere a circuital 

 vector. In order to have electric charges we must suppose 

 the natural state of the medium to include centres of intrinsic 



