864 Prof. Bartlett on Molecular Motions in Polarised fagit, 
directions of the motions in the latter waves are inclined to one 
another, is 180°—(p+¢’). Whence:— 
V nave — #') 
« Vityese A. Ts ip ph dt 6 
A.cos@ LT cos ay; sin ( n} 
sin 29 
A .cosg’. V,.¢,,—=A.cosp. V.a,;.— algae 
A,. COs prt aie (PJ 3 
ar, gp Sa Agi. 
Aa 
=4,;.—. —.—_.—_—_—_.. . Me ii 
Halegded A, cosg’ sing’ sin (g + 9’) (6) 
Substituting these in equation (4.), we readily find:— 
A __ 400s? g'.sin? g _ cos? g’.sin? gy . 
4, sin?2p ~~ cos?g.sin?g ’ 
whence, 
5 Oe — cosp.sing 
A, =ava/A. Ppt Site’ Tey 
Vad. eee sin g’ yee cos 9’ .sin g () 
Substituting the above ratio of the densities in the equation just 
preceding, we get:— 
2 cos gy’. sin 7’. i (8.) 
sing@ty)? 7” 
multiplying this by equation (7), member by rine ar and the 
equation giving the value of @,,, by A, and taking 
VA. Oi3=1; pS py a 
Ort &zj. 
we find :— 
paul sin (p — 9’) ‘ ey 
_— sin (9 + gy’) . . *. * ? 
ais sin 29 be Gna gee ee 
sin (9 + ¢’) 
‘To which may be added the relations, 
in2 
sing = SEP, cosa’ =| 1-}*. 
Transposing the term of which @,, is a factor “rn ve second mem- 
ber in equation (4), ocean equation (5) from a; = @si, a 
viding the first result by the second, and snnltiplying the quo- 
tient by equation (5), we readily 4 find :— 
Og; tee Ort oT legend (11.) 
coe. 
ae ny the projection in the (eee of ig pi i th 
the "deviating surface, of the greates ment in ike 
incident, increased by that in the rstected. — is ante 
Projection of the greatest displacement in the refracted wa 
