On the Dispersion of Light in Refracting Media. 509 



in contradistinction to A, by A . In reference to this distinc- 

 tion, however, the mere geometrical continuity is, as we see, 

 not sufficient. We have much rather to consider the vis viva 

 of the individual aether particles adjacent to the dividing sur- 

 face as a pushing force in -j- ; and now not merely will the 



quantity of the motion parallel to the plane z = in the first 

 medium be equal to that in the second, but it is evident 

 that in an outward direction it can be represented only by the 

 amplitude A of the refracted waves and not by A. If the 

 continuity alone indeed gave the measure, we could for media 



in motion, as for those at rest, exchange p and -=- for one an- 

 other at pleasure, which is demonstrably wrong. Correspond- 

 ing to this requirement, in the foregoing equations the f , rj 

 of the refracted waves also are externally indicated. 



Since these equations preserve their validity moreover for 

 all points (z = Q) of the continuously successive wave-planes 

 which fall into the dividing surface itself, it seems appropriate 

 here to refer the excursions not, as above, to the direction of 

 the ray, but to the normal, and therefore to put generally 



Po 



. 2-7T / z cos a + x sin a ~. A 

 = A cos -^ lt+ -®'j, 



where a denotes successively the angles of incidence, reflection, 

 and refraction, and by X=&>T is to be understood the wave- 

 length along the normal. 



I moreover take leave, differing from Cauchy, who treats all 

 velocities of propagation alike, to characterize them according 

 to their direction, by opposite signs. I thus write them more 



naturally ( @ = — ) : — 



Pr = A r cos2^ - (e+ *<™'» + *™«' ) }, ,(88) 



f t /~ % cos a D + x sin a D \ ) 

 rt = A° D cos2,r| T -(e+- -JL- ^)|- 



If, lastly, U, V, W are the angles made with the axes of 

 coordinates by the directions p perpendicular to the ray, and 

 if we insert these values in the limit-equations, they subdivide, 

 so far as they remain valid for all values of t and x, into the 



