Polarization in perfectly transparent Media. 469 
tion give equation (16), which therefore will 4 need to be 
considere in addition to the = three equatior 
lines p, and ps, of which a, y 7, and a, Ao, 7. are eee 
the components, will now be the semi-axes of the displace- 
ment-ellipse, and therefore at right angles. (See $9.) The 
case of circular polarization will not constitute any exception. 
Hence, 
a,+f,8,+y,y,=9. (21) 
and by § 9, 
O=L(f6,y,—y,8,) +M(y,a, fla +N(a, P— B, a)=p, Pry (22) 
where we are to read + or — in the last member according as 
the system of displacements haa the character of a right-handed 
or a left-hande 
15. Equation (19) | is now reduced to the form 
24, A, + 208, Bot 2eMi Vet e(Piy¥o+ Vi fs) 
+P (Vit 2) +9 (a4 f.+ Bya)=0, (28) 
which has a very simple geometrical signification. If we con- 
sider the ellipsoid 
ax® + by* + ez’ + eye + fex+ gay, (24) 
2: Mara its central section by a plane parallel to the 
of the wave-system which we are donseritig: it will 
cel appear that the equation 
2H; Hy + 2by,y> + 202,2,+ €(Yre +2,Ye) 
+ f (Zits + 212s) +9 (Yo + Yikes) =0 
will hold of any two points 2, y,, z and a, Ys, 2, which belon 
to conjugate diameters of this central section. Therefore — 
Ne ¢ are ne at right iia to ae 
ne it follows that ¢ tbey are parallel to the axes of the cen-— 
ral section of the ellipsoid (24) ve a Lenhae That is:— 
* ay reader will perceive that an earlier a of the position of the 
a supposition of this nature, involving a limitation of the values - ae rs 
V1; @a, rk Ye, would have been embarrassing in t the operations of the last para- 
graph. 
