510 Prof. E. Ketteler on the Dispersion of Light 



following : — 



sin a E sin oc R sin a 7 D sin a" D 



A E cos U E + A R cos U R = (A' D cos U' D + A% cos U%) , f < 29 ) 

 A E cos Y E + A R cos V R = (A' D cos Y' d + A" D cos V" D ) . 

 The first leads, with respect to the angles a, to the values 

 * E = e, u R = 360 o -e, a D = 180° + ^ 



where e and r are absolute quantities. In the last two, again, 

 on account of the presupposed state of rest of the medium, the 

 velocity-amplitudes are proportional to the excursion-ampli- 

 tudes. 



II. The principle of the work perpendicular to the dividing 

 surface. — If the preceding fundamental principle corresponded 

 to the law of equivalence of pushing force or apparently also 

 to Cauchy's assumption of the continuous reciprocal thrust of 

 each two corresponding curves represented by the resultant 

 oscillation-velocities of the aether particles in the first and 

 second media as functions of their position (#, y } z), on the 

 other hand the principle now in question represents an evi- 

 dently mechanical requisite. There remains, namely, always 

 to bear in mind that the originally interfering spontaneous 

 force which causes the vibratory motion has a certain mecha- 

 nical work to accomplish, which consists, when the force ope- 

 rates in pure aether, in overcoming its force of elasticity — and 

 when in the interior of a ponderable medium, in overcoming 

 not merely the elasticity of the aether, but also the resistance 

 of the corporeal particles. In each case this work will he 

 comparable to the pulling-open of an elastic spring or the 

 raising of a weight. The mechanical work once applied, 

 maintains itself then, by means of the deformation-force of the 

 aether, in the totality of the vibrating particles as their energy. 

 If therein we fix our attention upon a single particle of aether, 

 on its part it accomplishes now negative work, when it freely 

 follows the pull of the elastic force and transforms its tension 

 into vis viva, and now positive work, when the acquired vis 

 viva expends itself and, through the increasing resistance which 

 it encounters, is retransformed into tension. 



As regards particularly those aether particles which are im- 

 mediately adjacent to the dividing surface, they are compelled 

 by the Z component of the incident and the reflected wave 

 now to approach, now to recede from this limit-plane ; and a 

 particle which in the position of equilibrium lies in that plane 

 itself is impelled alternately into the upper and the under me- 



