and Electromagnetic Theory. 335 



aberrational effect is to be got from a terrestrial source of 

 light without an entry into and passage through a medium 

 in motion relative to the earth. 



§ 13. We proceed to the solution of the problem of 

 reflexion and refraction, which will be written for an 

 originating wave in free aether ; and for the dielectric M is 

 taken =1, K=/,6 2 , so that the connecting equations (25) 

 and (27) become 



a =/z(??iZ — ?iY), fili = n/3 — rwy (25 b) 



"- a ( 1 -^)%T 2 "«' x '= x ( 1 "iv) + ^ 2 » x • ( 27 > 



The solution is simplest when u = v = 0, so that U = nw, and 

 this case is taken first. For axis of x the line of intersection 

 of wave-front and reflecting surface is taken, and the cases 

 for which the magnetic and electric inductions are alone 

 this axis are taken separately. 



(i.) Magnetic induction along x, i.e. /3=y = and X = 0. 

 The scheme is, with r for w/V, 



OL =H, yLtY=— ?lH, JuZ=??lH, 



M (i-=>^x^r--5(^0|.(«) 



Writing these for the three waves with H, H' and H", and 

 equating a'Y' at the surface, 



[(l-rn)+H / (l+mO=H // (l-— \ 

 [(Vn- W )-H'(Vn'+<=H^(^-j); I (U ) 



Vn-w)(l-rn)W-(yn'+w)(l+rn')W 2 =(^ 



is the equation for transit of energy, the product HIT 

 vanishing by (21). These equations may be altered in form 

 by introducing the ratios 



\ : V : \"=y-vm : V+ wn' : - - ?£, 



and by using the kinematical cosines 



n — r _ _ n' + r „ _ n " — r//n 



1-rn " V ~ l + m n ~ I-771"//*' 



