COS Dr. T. H. Havelock on Surfaces of 



there may be the production o£ a discontinuity of the second 

 order. 



Supposing these discontinuities to be produced in some 

 such manner, we proceed to discuss the method of their 

 propagation. 



§ 7. Discontinuity of the Second Order. 

 In this case we have on S 



©]-©'• -[P] -(!)"- 



Hence, supplying these value? in the second-order equations 

 given in (9), we have 



Thus the discontinuity is propagated in the medium as a 

 wave-front moving with a constant normal velocity c. 

 Using the notation 



a >i -p fit B/ 3A w 



R.N = scalar product, 

 and ExN = vector product, 



we have from (10) and (8) 



R.N = 



[u, v, ty] = ^RxN 



(12) 



Hence the vector denning the discontinuity lies every- 

 where in the wave-front. And the discontinuities in the 

 electric and magnetic currents are also tangential to the wave- 

 front and at right angles to each other, while the electric and 

 magnetic forces are supposed continuous. 



§ 8. Discontinuity of the First Order. 

 In this case we have 



Ld*J V-' U.J- X 3 V ' LsJ- x ^; • ( 13 ) 



LsFJ- X dr • 



and similar relations in (rj, p) and (f, v). 



(14) 



