MR. G. A. SCHOTT OH THE REFLECTION AND REFRACTION OF LIGHT. 837 
Write 
A = "Y [ ^ ^ ^ f {d — x) dx, 
d J Q rf" J 0 J 0 
D = — I ju.%^ dx, E = Jr j jjdx {d — x) dx, E — ^ | [jd [d — xY dx. 
TT 
(x) 
1 fM“ — v" . X v" dx _ 1 dx 
'■'^ dx 
0 /^" 
1 dx 
d Jo 
1= — [ [jd [tt (d) — TT (x)] dx, K = “[ [x^ [tt [x)Y dx, 
d Jq d Jq 
L = — [ jx^TT (x) [77 (d) — 77 (x)] dx, M = — [ [jd {tt (c/) — 77 (x)]^ dx, 
cL i 0 ' J 0 
, 1 M dx 1 X dx 1 r 
d j n TV? ’ 
1 {d, — x) dx 
0 
Then there are the following relations between these constants— 
D + E=B, E + F=:C, D + 2E + F = B + C = A, D-F = B-C. 
TT{d) = \- v^(d=^a, K + L = (1 - 1^3 G) H, L + M =•• (1 - I, 
K + 2L A M = (1 - t^-G) (H + I) = (1 - i.2G)hA = a^A. 
H 
0 JQ 
(I rx 
/^x 
/i- / d- JqJq 
^. d^dx ; 
I = (l -i.2G)A 
Hence 
K - Mr 
so that for = 0, 
And lastly, 
d Cx 
H = C - I I '^..d^dx. 
d- J 0 J 0 d'x 
(1 -I.2G)(H-I) = (I-7^2G)(B- C-l^J), 
K - M = B ~ C. 
B' + C' = A\ 
Using this notation we have for VtbrcitiOTis PcTpcndtcidctT to Plcinc oj" dnc'id6Tic6 
t 
ddps = _ ^1 _ S».(F -iv^)] + to, {1 + 8ME - ktd)], 
\ Gt6 j — Q 
dip) =-,.„{i + SME-i.'’')S+«'.(i-SMD-i-OS.-. (V.) 
\CtX jx^O, 
