Prof. Bartlett on Molecular Motions in Polarized Light. 365 
Next, take the wave in which the molecular motions are per- 
pendicular to the plane of incidence and therefore parallel to the 
axis y; these are parallel to the deviating surface. The motions 
in the incident, reflected and refracted waves are parallel to one 
another, and, by the principles of parallel forces, the sum of the 
motions in the reflected and refracted waves must be equal to 
that in the incident. The equation for the living force will be 
the same as before. Whence :— 
A.cosp. V.a2y,+A,.cosg’. V,.024,—A.cosp. V.a2y;=0; 
A.cosp. V.cy,+A,.cosg’. V,.cy;—A.cosy. V.eyi0. (12) 
{n which 4 and 4, are, as before, the densities of the medium of 
incidence and of intromittance, respectively; or, 
A, sing! cosg’ B 
Lait, Saleen ‘ _ bed 8 
wT A ‘sing cosp : ide 
A! sing’ cosg! 
rae jean pS ED i US 1B, 
Bi cop’ OM (18.) 
Transposing the terms containing «y, and ¢y; to the second mem- 
bers, and dividing the first by the second, we find:— 
ty, ages. se ey vs (BR) 
That is, the greatest displacement in the refracted is equal to the 
sum of the greatest displacements in the incident and reflected 
waves, 
a2 
Substituting the value of a as given by equation (7), in 
equation (18), we have Se 
tt cag t= is. coe sy 
Substituting in this, first the value of ¢,, and then of ays, de- 
duced from equation (14), we readily get:— 
tan(? =), Ho EAB) 
Cyr = — Ovi tan (@+e)’ i ale 
4cos 9’. sin g’ bong Ow 
yt Cyt og +snIe” . 
Multiplying the first of these by A, and the second by equa- 
hon (7), and making — 
AA .Gy=1; /A.e y="; Jb, Oy w' 5 
there will result, 
tan (7 — #) es (1B) 
v= el ee 
tan(p +) 
pa wee Cw 8) 
