MR. G. A. SCHOTT ON THE REFLECTION AND REFRACTION OF LIGHT. 831 
Hence 
fdvi 
j _ 
IVq. 
+ 
IV-^. 
/ dio ' 
\df, 
j _ 
IV^. 
+ 
u\. 
1 — —v)^ d-q I 
1 + S'. 17^(1 — r])d-q —j 
(V.). 
Vibrations parallel to plane of incidence {Electromagnetic and Contractile Ether 
Theories). 
The equations to be solved are (HI.), p. 829, with m, IT zero, viz., 
IV '4 - 8 _ z,2) u = 0, - 1 8v + h\ixH = 0, 
whence eliminating u 
df- d^ 
— ( —+ S^fxh = 0 
(^2 _ j,-3 -TO [XV 
with the conditions that when ^ = 0, v = Vq, and when ^ v = 
Put V =-v^ 8V + • • . where 
[li? - p- <l( I ' d^Xiif-v’- ( 1(1 !>■«,■■■ 
and when ^ = Q, v^ = Vq, v =■ . . = 0, when ^ = 1, -n® = v' = . . = 0. 
Write 
Jo M J 
f dr] 
~2 
J 0 /2-“ ■ J 0 
SO that TT {^) increases as long as < [x^ and maximum of tt < 1. We have at once 
„ 7 r(l)— 7 r(f) 
= Va - ... ■ + Vi 
V 
° 7 r(l) ' ''^ 7 r(l) 
> 
'= — — 7r{p)}.v^dp + [x^ ( 77 ( 1 ) — 7r{p)] V^dp, . . . 
whence 
_ ^1 - ^0 . dv _ __ p 3 0 , r 3 ^( 1 ) - TT (^). 0 , 
[X^-V^ d^ 7 r(l) d^ ~ -v .dp + V.ap,... 
with the same notation as before 
rf 
V 
0 ) 
— [ jitV {p ). v^^- ^idp, 0 < ^ < 1, 
Jo 
