IN CRYSTALLIZED MEDIA. 307 



are in a plane parallel to the wave's front, and of which the 



equation is 



Q = ax + by + cz ..................... (12); 



the same therefore will be true for the ellipsoid whose equation 

 is (11), as this is only a particular case of the former. But the 

 section of the last ellipsoid by the plane (12) is evidently given by 



'" ( ' l) ' 



By what precedes, the two axes of this elliptical section will 

 give the two directions of disturbance which will cause a wave 

 to be propagated without subdivision, and the velocity of pro- 

 pagation of each wave will be inversely as the corresponding 

 semi-axes of the section: which agrees with Fresnel's con- 

 struction, supposing, as he has done, the actual direction of the 

 disturbance of the particles of the ether is perpendicular to the 

 plane of polarization. 



Let us again consider the system as quite free from extra- 

 neous pressure, and take the most general value of < 2 containing 

 twenty-one coefficients. Then, if to abridge, we make 



du _ du _ du _ ., 



dx~^ dy~^ ds~*' 



dv dw _ du dw _ Q du dv _ 

 Tz + ~fy =< *' dz + dx~~P' d^ + dx~ % 



we shall have 



- <k = (f ) r + w T? + > r + 2 bo tf+ 2 <K) fr+ 2 (^ ft 



+ (a 2 ) a + (f?) fP + (V) y + 2 03 7 ) /3y + 2 (ay) ay + 2 (aft) a/9 



+ 2 (aij) out + 2 (/&?) ^ + 2 (y,) yi, 



where (f 2 ), (a 2 ), &c. are the twenty-one coefficients which enter 

 into (f> y Suppose now the equation to the front of a wave is 



= ax + by -f 02. 



202 



