302 Dr. Beer on tJie Motion of Light. 



In the place of this ellipsoid of polarization let us substitute 

 another, concentric, similar, and similarly situated to the former, 



but whose dimensions are to those of the first in the ratio of 2" : !• 



We thus obtain at once, in the reciprocal values of its semiaxes, 

 the velocities of the conjugate plane waves. The equation of the 

 second ellipsoid differs from that of the first only in the circum- 

 stance, that in the second the place of — is taken by the unit. 

 For the equation thus modified let us set, for the sake of shortness, 



+ 2dvwyz + 2euwxz + 2fuvxy = 1 . 



On experimental grounds it is to be assumed, that, of the three 

 species of oscillations, which, according to the above, belong to 

 a plane of undulation, there are two always parallel to the said 

 plane, these two being within the limits of observation ; while 

 the third, which corresponds to an imperceptible motion of the 

 sether, coincides with the normal to the wave. According to the 

 theory, this is exactly the case in isotropic media ; also in homo- 

 geneous media generally, when the wave falls in a principal sec- 

 tion ; and for vibrations parallel to an axis, when the plane of 

 the waves is parallel to the said axis. From this we conclude, 

 that we incur an imperceptible eiTOr, if, instead of the axes 

 of the ellipsoid of polarization, which are nearly parallel with the 

 plane of the waves, and which alone correspond to the motion 

 which produces light, we make use of the axis of the diametral 

 section D, which is parallel with the plane of the waves P. From 

 the equation of the plane of this section, that is, from 



icic-\-vy + wz = 0, 



and from the equation of the ellipsoid, we obtain for the projec- 

 tion of the section upon the plane of yz the equation 



y^{{X-\-B-2f)u%^-^av'^i-bu^} + z^{A-{-C-2e)uhv^-\-aw'^-^cu^} 



2yz{{A-^d'-e—f)u^+a}vw=^l. 



The plane of the diametral section D intersects an ellipsoid E', 

 whose equation is 



a/^a + y% 4- z^c^ 1, 



in an ellipse D', for the projection of which on the plane yz we 



