and Electromagnetic Theory, 339 



Since n— r = v(l — m), and dv/(l~r 2 )=dn/(l — rn) 2 , 

 (n-r)(l-rn)dn = vdv(l-rnyi(l-r 2 ) = vdv(l-±rv) 

 to the order required. Thus 



P A \ l A 9 vdvil-4rv)=*p'*]A*{l+4rv)vdv, j 



cO Jo f 



and . (51) 



jt; 4 ( ^Wvfl-lrv) =*r i \ 1 B*vdv. 

 Jo Jo 



Since A 2 + B 2 =l, only two independent integrals are 

 wanted for each type of polarization, viz. J Wvdv and 

 \ Wv 2 dv, say B x and B 2 . Then 



Ai+ B x = J and A 2 + B 2 = l. 

 In terms of these 



p'=p{l-2rA 2 /A l ) and tj=/?(l-rB 3 /B 1 ) ; 

 and the pressure is 



X _|v^(l + A 2 )= x (i + A 2 )=x(|-B 2 ). 



Also each of these integrals is a mean of that for the polari- 

 zations (i.) and (ii.) above, say 2B 1 = B/ + B | // . We may 

 now replace v v" in these formulae by the statical nn" . 



(i.) With B 9 = 4/wm"/ (w + ixn"f, ^n" = ^/ M « + ^-l, 



and 1 _ ^/ii'-h/js — l—n 

 n+fAti fjb 1 — 1 

 (»2«1)2 r»i 



4-^-3/= | ^inx/^ + ^-Uy^ + ^-l-n) 8 



«, 



= \ dn {/i 2 (2^-+-yu, 2 -l)v / n 2 + ^ 2 -l-2n 3 (ri 2 + ^ 2 -l) 

 c 



_/i 3 -l /* 2 -l. 



6-1 1 







(V 2 — 1) 2 B / ^1 



-—4 J =J ^n{n 3 (27i 2 + y a 2 -l) v /n2 + ^_i_2^( n 2 + At2 _ 1) l 



_2 M 7 ^ ^ 3 2 2 2 / 2 



Z2 



