366 Prof. Burtlett on Molecular Motions of Polarized Light. 
18. Divide Sone (10) by equation ), = equation (19) 
by equation (18), replace v, u, v' and w’ by their values, and sub- 
stitute for the ratio of the ot a roots of ne! lewnitieg its value 
andi ; 
as given in equation (7), w 
@z4-COSY! iy sin 2 q’ 
Gzr.COSP COS sin (p—q’)’ 
“Se sin 2 g! 
tyr  sin(p—g).cos(p+q/) °° °° om 
But @,;.cosg’ and @,,.cos@, are the com ed perils to the 
alicore surface of the displacements which a e plane of 
ence; @; and ¢,, are already parallel to the avtishing sur- 
pon whence, as long as >’, that is as long as the velocity 
of wave-motion in the medium of incidence exceeds that in the 
medium of intromittance, the molecular phases in the refracted 
and reflected waves will be opposite, an conversely. 
Denote the living force in the incident wave of common light 
by unity, that in each of its com ern waves will be denoted 
by half of unity; and the total Extig force in the reflected com- 
ponents will, eqs. (9) and (18), b 
pt bye in2(p— a tan 2(p — 9’) 1. 
te sint@tg) tt inte) © ! 
and in the refracted components, eqs. “ and (19), 
ae ee sin 22 n?29 
= t- sin sin 2(p-p9) + 2 nieiy. sin 2(p—g’) Gy 
If 9+9’=90°, then will:— 
sin y= msin g/ = m cos g, 
a tang=m; 
hic 
fhérefote be wholly poll and since eq. (21) will orn in 
co firs 
pevatheee of the reflected and wanconenrssnee components wi 
respectively, under this conditio 
$cos? 2@ and Th Saas ae 229. 
West Point, N. Y., 1860, 
a 
