85r. MR. G. A. SCHOTT ON THE REFLECTION AND REFRACTION OF LIGHT. 
--^. This result is in agreement with Green and in opposition to Haughton, 
A''! “t A^ii 
^2 ^ „ 
who proposes to make M = ' 2 1 > where n < — , ascribing it to a difierence between 
n i- /Xq 
the refractive index for the pressural-wave and that for light ; but it has been shown 
above that no such difference could diminish n and therefore M. 
The formulae VITL, IX., and X. can be put into a more suitable form for calculation ; 
the quantities experimentally determined are usually and pX — pl l. In doing 
so we neglect powers of S above the second and make use of Snell’s law 
2 _ 0 
p,i 3 sin Iq = sin and the equations sin (^o — fj) sin (fg + ?j) = 
sin ?,j sin z,, 
2 2 
and cos (tg — h) cos (tg -h q) = 1 — — - - sin ^g sin 
With the same notation for the constants of the variable layer as before, viz., 
d = thickness, 8 = , p = refractive index, and A = p^ dx= mean value of p“, 
B - c = Af' (2x - d) dx, G = AfA _ J = 1 4^,1^ 
rt" J 0 (Ho P“ (C J 0 -’ 0 \P|" Px ”' 
since these enter into the expressions in different combinations, we shall introduce 
a different set of constants, involving A, B — C, G, J, and d together with pg, pj, and 
di'tined by tlie following equations— 
A = 
4 {A (pp+p,,^)- 2p„v,2} (A - p, 2 - p/ + GpoVd”) + {(B - C) (PC + p.r) - JpoVrKpr - po") 
/ 2 2 \ 2 
(/^i — ) 
B - 4pgPj 
(A 
Pll — PC + Gpypp)- 
(PC — PC) 
C = 64 
P„V,^ . {(A - p,;) (A - pd) + (pd - P-) (B - O] I2^d\ 
(PC A p,,^) 
2\4 
X 
D ^ 
Ao 
PC-A 
Pi^ - Pu^ 
2'7t(1 
X ’ 
A 2 2 I rt ^ 
Pll Pi ~t Gpy~py 
2 O 
Pi Po” 
'Zird 
X 
R I 
Then the expressions for X- ^ and pX — p II become— 
