[ 508 ] 



LXII. Attempt at a Theory of the (Anomalous) Dispersion of 

 Light in Sinai// and Doubly Refracting Media. By Professor 

 E. Ketteler. 



[Continued from p. 422.] 

 12. FN the present investigation we now come to perhaps 

 J- the most essential difficulty which has hitherto stood 

 in the way of the extension of Fresnel's theory of reflection to 

 anisotropic media. 



In the universal aether as first medium let a wave-plane po- 

 larized under any azimuth be supposed to fall upon a plane 

 face of a crystal with any orientation whatever ; there will in 

 general arise, besides the reflected wave, two refracted ones. 

 In order to determine them according to amplitude and azi- 

 muth, we require, as with the transmission of light into an 

 isotropic medium, four different limit-equations. But while 

 (on account of the divisibility of the fundamental theorem of 

 the vires vivos) two principles there suffice for their derivation, 

 three are necessary here. We designate them briefly as the 

 principle of so-called continuity, the principle of equality of 

 work, and the principle of vires vivce. The first and third we 

 owe to Fresnel and Neumann, while the second is, as far as I 

 know, new. 



I. The principle of the equivalence of the quantities of motion 

 or continuity parallel to the dividing surface. — Let the whole 

 of the vibrations be referred to a system of coordinates whose 

 Z-axis falls in the vertical direction, its Y-axis is perpendicular 

 to the plane of incidence, and its X-axis is consequently the 

 intersection of the planes of incidence and division. Further, 

 let the vibrations p of the aether particles of the boundary 

 layer be analyzed parallel to the axes into the components £, 

 rj, f. The fundamental principle of continuity then requires 

 that for the two former parallel to the dividing plane, there- 

 fore parallel as well as perpendicular to the plane of incidence, 

 the sum of the components of the velocities of vibration in the 

 incident and reflected wave be equal to the sum of these com- 

 ponents in the two refracted waves. We have consequently : — 



dt dt 



dt dt 



= 0. . . (27) 



I particularly remark that this fundamental theorem is to 

 be referred only to the complete excursions — that is, to those 

 which have hitherto been denoted by p w and their amplitude, 



