838 MR. G. A, SCHOTT OH THE REFLECTION AND REFRACTION OF LIGHT. 
Electromagnetic Theory. Vibrations Parallel to Plane of Incidence. 
d 
d 
dv \ 
(h\ 
dx 
a 
COS^ 
a 
M 
a 
COS'’ ^Q 
r/l + 8—) 
a '\ «/ 
i + 8^L) + 
cos- 1 -^ 
a 
K 
,vi-8 ^~ ... (vr.) 
Elastic Solid Theory—Vibrations Parallel to the Plane of Incidence. 
d 
ih^ 
dx I.C = 
-,V,.{l-8^(F-i.=)} 
+ *.,.{ 1+ 8'^ (E - i t>=)} - i 1^0;, . 8“ 
- nn 
^ LvS + '?’q) + 11/8 {i\ ~ Vq) B' — SiTqA' 
U<; = d 
= ITo + ivv,. -^P)[ 
y ■ (Vir.). 
A r / dv 
/ dv 
rjT l\dxj:i;^d U/+.i-=o 
— LPi\ . {1 + ^ 8^ . (D — } + Sicq . (A — v~) 
~8v,.{C - v^B') - 8i’i.(B - Z/3+ 
+ Lv 8X10 . (I — A') + tj/ 8^. iifj . (C — -g- v~) 
where 
Uq = — siij z'o (1 — r) + a./, i’y = cos (1 + r) + t sin f . r\ = y/, 
iCq = 1 + r, = cos ii . 6' + t sin . s', Wi —■ s. 
We found also that the series (V') converge at least as rapidly as the geometrical 
/d -\3 /rJ 
progression 1 + ( — X 4-53 ^ X yj + . . . 
The series (VB.) converge at least as fast as 
1 + (y X 6-28 Xj^y-V(y'l X 6-28 X y^^ -\- . . . 
and the series (VII'.) at least as fast as 
1 + X 7 ’66 X y^ 7’6GX y^ + . . . 
where y denotes the greatest value y has in the variable layer. 
The greatest refractive index for transparent substances (excluding metals) occurs 
in Greenockite, and has the value 2'66. Taking this value for y the three ratios are 
