M. Lorenz on the Theory of Light. 



209 



For ci p — we have 



« 1 ; 2 =— ?,(^Jalh p y « 1)3 =— %(jf) a v c q> 



02,3 



Since these quantities are independent of /, m, n, the direction of 

 the axes of coordinates may be chosen so that we have 



0i,2 = O; a h3 = ; a 2 , 3 = (8) 



If we further denote the velocity of light in the body by s, the 

 wave-length by \, and the cosines of the angles which the per- 

 pendicular to the plane of the wave makes with the axes by 

 u, v } w, we have 



o 



C = cos (kt — Ix — my —nz) = cos — (st—ux~vy — wz) ; 



accordingly 



. 2tt 2tt 



— ,. ■ ; /:= — u: ?w = — v 



2tt 

 n = — — w. 

 A. 



Lastly, by putting 



_ o 2 a 2 o 2 



01,1 = ~JV> 02,2— Tq'> a 3,3-~<.~&) 



02,2 — 7 2 > 



we have, by the equations (B), 



s 2 _ _ _ 



^^Zo—uiuSo + vVo + wZo), 



S 2 _ _ _ 



S*T. 



5)=?o- w; ( w ?o+^o+ w; ?o)- 



w 



Hence it follows that the velocity s of the light is determined by 

 the following equation : 



+ 



fl 2__ s 2 ■ #*_ 



^ + 



?/r 



0, 



(10) 



The body under consideration behaves therefore like a biaxal 

 crystal, and doubly refracts light according to the known laws of 

 double refraction. 



The reader will bear in mind that the components f , tj, f are 

 not identical with the components f, rj, £, inasmuch as we put 



^~ CdP^* ^~~ CO? V > *~* CO? ?''« 



Pfo7. 3%. S. 4. Vol. 26. No. 174. £grf. 1863. P 



