420 Prof. E. Ketteler on the Dispersion of Light 



or 



cos S cos'-' a cos 2 b 



r,(l + «) + r (l+/3) + r (l +7 )' 



cos 2 a cos 2 b 



(21) 



r 2 rj(l + «) a i(l+/3) 2 ^(l + 7) 2 



If the penultimate of these be introduced into equation (18), 

 and at the same time we put for shortness 



r (l + «) VA' r (l + /8) \W,— ' 



the equation takes the following definitive form : — 

 m! 



^_i = S _^|0) cos 2 «+(^) cos 2 6+0) cos 2 c}.(22) 



L 2 " 1 



If, finally, we epitomize the three sums as A, B, C, it is 

 written more briefly, 



n" = (1 + A) cos 2 a + (1 + B) cos 2 b '+ (1 + 0) cos 2 c, j 



cos 2 5 . cos 2 c b > (23) 



+ =- + 



and in this form it may have henceforth to replace the 

 "second" or Pliicker's ellipsoid ((?), the expression of which 



has hitherto been = -• 



r a 



With the ellipsoid represented by equation (23) a second is 

 then associated, represented by 



1 _ cos 2 a cos 2 b cos 2 c ~\ 



n 2 ~T+A + T+B" + T+TJ ; I . . (24) 



a) 2 = ft>2 cos 2 a + (o\ cos 2 b + co 2 3 cos 2 c . 



This may take the place of what has hitherto been named the 

 first or reciprocal ellipsoid (E), for which it has up to the pre- 

 sent been assumed that r cos B = co. 



With the two planes mentioned the further theory of double 

 refraction is, as is known, completely traced. 



10. Up to this point we have held fast to the special case 

 for compound media, that the angle between the ray and the 

 wave-normal has the same value for all the individual optico- 

 chemical elements ; we can now drop this supposition. Even 

 with the most common composition of the medium, the oscil- 

 latory motion about a point of it will, after the lapse of the 

 time-unit, have advanced as far as to a perfectly determined 

 closed plane. To a determinate radius vector of the same cor- 



