in Singly and Doubly Refracting Media. 511 



diurn. The oscillations of these particles, however, pass regu- 

 larly only when they have equal mechanical work to accom- 

 plish in a vertical direction on both sides of the plane 2 = 0. 



Now, if a weight p to be raised corresponds to the resistance 

 in the first medium, and likewise p' D p" D denote the relative 

 resistances of the refracted wave in the second medium, then 

 the principle of equality of work requires 



or, if, so far as these weights come out proportional to one 

 another, we pass by integration from the time dt to t, 



x? E +? E )=p' D r D +/' D ?'w=o. . . (30) 



Here £ self-evidently refers to the actual excursions p, A in 

 contrast to the, under circumstances, possible p Q) A . As 

 regards now the ratio of these resistances, in the first medium 

 the vertical raising of the weight p to the height 1 produces 

 for the aether-mass m, which is thereby at the same time dis- 

 placed in its obliquely situated path-line, an effective vis viva 

 me 2 . Likewise, in consequence of an equal change of level of 

 the weight p D , an equal aether-mass in in the second medium 

 receives the same vis viva me 2 ; but simultaneously the neigh- 

 bouring corporeal mass Urnf receives the energy %m f c f2 , — both 

 taken in their respective path-lines. Evidently we have then 



p :p> D = mc 2 : (7nc 2 + 2mV 2 ). 



But it has already been shown that, when in any refracting 

 medium a given quantity of work is distributed to corporeal 

 and aethereal particles, the ratio of the distribution becomes 

 identical with the so-called refracting force. Corresponding 

 to this, becomes 



p:p D = l:n 2 (3) 



And thus, if we designate the angle between the direction of 

 vibration and the vertical by TO and put, analogously as above, 



. 2?r f , , 2 cos « + x sin a ^. 1 

 p = Acos-^r^ t+ - W >, 



the principle of the equality of the work perpendicular to the 

 dividing surface receives the final form 



A E cos Wi E + A R cosOT R = A^cosOT'j/ 2 + A" D co&m" D n" 2 , (32) 



where self-evidently n', n!' denote here the corresponding sine- 

 ratios. 



It will be observed that this fundamental principle, although 

 Fresnel entirely disregarded it, and Cauchy by bringing in 

 longitudinal waves more circumscribed it externally, is an ex- 



