324 Mr. B. Hargreaves on Radiation 



In a general formula it may be convenient to measure n' 

 in the same direction as n ; with this arrangement, which. 

 may be marked by the use of suffixes, the group of relations 

 for reflexion is 



l 1 :l 2 = m 1 :w 2 = Y — ion 1 :Y—wn 2 \ 



= -(Yn l -w):(Yn 2 -w)=Y-TJ 1 :Y--V 2 , | 



and we may deduce I 



lj 2 + m i m 2— nin 2 = l — (n 1 + n 2 )w/Y, J 



which will be o£ service later. 



ThuS 1/77, N n l n 2 , 1 n 2N 



- {l l l 2 -\-m l m 2 — n l n 2 ) = =— +-t-(1 — n 2 ) 



1 /??! ?? 2 \ 1 nm 2 fl 1\ 



= Tr n ih+T 2 )=T 2 -^\k + l 2 > 



using Z 2 ( V n i — w ) + k (Vw 2 — w ) = 0, 



= 7 £i-y(»i+w»)|> 

 using 1A w« 2 \ 1/-, ^'A 



When V//it is written for Y and wjjj? for iv, the results are 

 applicable to the reflexion of a wave, moving with modified 

 velocity in a dielectric, at a surface sharing the motion of 

 the dielectric. In refraction when u and v exist, $ always 

 intervenes in the determination of n" from n, viz., from 



follows 



1-wn/Y l-wn"/nY 



Y U" 

 l:l"=m:m"=Y-TJ:--^ 



=7Jl = (* ~ —*) ( u cos + 7j sin 0)/V. 



v'1-rc 2 /* Vl 



The first-order relation between ray-cosines may be noticed.' 

 We have 7/(1 -U/V) =fd"(l~U"jfj,Y) exactly, and there- 

 fore to the first order 



(/-«/V)/(i-u/Y).= /t (r^y)/(i-u''/ /1 v) ; 



but to this order — 



V,„ u\t/Y U"< 



^=(VZ- U )/(V-U) and ■ t" = gl»- y|(l- £) 



and 50 l r =/J.l r ", w r —fJim r ' 1 . 



§ 8. It was noted above, in regard to the formulae for' 

 -sr and V, that the change to a moving standpoint was the 



