.MR. G. A. SCHOTT ON THE REFLECTION AND REFRACTION OF LIGHT. 827 
' ^ ~ ^ Vi^)rations perpendicular to plane of incidence. 
These are satisfied by 
/ . . 2 ;rMii COS ip . . COS i’o , 277^000 \ / ^ \ 
w = — Sin ^ 0 * ^ r Sin in. e ^ ^ -j- r a,.. e -v -M . e‘ v a ■'’0 
2 jr/ao C 08 i'o 
2TTiJ.Q cos {q 
V = ( COS ^o . t A 
IV = { e A 
2 rrjLio C 03 ?o 
+ r cos t’o . e ‘ a •* + it sin \. e 
2irtJ.o cos io \ / 27rv \ 
X _|_ X j ^ V A ' 
2 ir(Xfian \ / 2 : 71 / \ 
I. e‘ \—y-^n 
Here the first term represents an incident wave, the second the reflected, and the 
third a pressural wave, v/hich last travels along the boundary £c = 0, and rapidly 
diminishes away from that boundary. 
Iq is the angle of incidence ; «(, is a constant which is found to be + ^sin^iy — 
r, T are complex constants ; H, R' are the amplitudes, p, p the retarda¬ 
tions of phase, of the reflected and pressural waves. 
mi • -10 \ , /Hiil _ 0 • 
ihe pressure is proportional to “r =- r . e a + a a > 
thus r vanishes for the electromagnetic theory and for Lord Kelvin’s theory, for 
which Wq vanishes. 
Second Medium. 
This is of constant quality (/r^, m^) and extends from x = d to x = oo ; the 
equations (II.) are 
„ 3 (du dv\ 3 /du dv\ -tTr® ^ 1 
3^; \d.v + 02 /) + 02 / (3y “ dx) + ~ ^ I 
m 
3 A. / 
/3i4 
dv\ 
/ 3^ 
dx) 
,^'.= 0 j 
Vibrations jiarallel to plaue of 
incidence. 
d~w dho Ttt- ,, TV -vT-1 i.- Tlx 1 L‘ ■ ■ ^ 
^ . p.^-' .w=0 Vibrations perpendicular to plane ol incidence. 
They are satisfled by 
u = 
V = 
2iTp.iQ.osil 
{jO — d) 
fl- soL^. e 
Jira,aj 
—r~ ~ . e" V A 
iv = s.e^ A 
s sin . e A 
. 2i7>ti cos ii , ... 2717^1 \ /2771/ \ 
scos^J.e‘ A -f-t .5 sni i|.€‘ a 
_ / 
( 27 rjUiC 0 SZi 2 itv \ 
- \x-d)+^y-vl) 
5 N 2 
