92 Prof. W. Voigt on the Behaviour of Pleochroitic 

 terms of the real velocity co and the absorption-index k, 



v= z 



(?) 



and if G, F denote the real amplitudes, and R their relative 

 retardation, 



G _ |R 



'/~¥ e W 



The formulae (5) and (6) express the fact that in every 

 direction there are propagated two elliptically polarized waves 

 with, in general, different velocities and different rates of 

 damping. 



4. Of special interest are those crystals in which absorp- 

 tion is so weak that k? may be neglected in comparison with 

 unity, so that we may write 



v 2 = co' 2 {l + 2U) (9) 



Such crystals produce no appreciable absorption in a 

 thickness corresponding to a few wave-lengths, and are the 

 only ones exhibiting the remarkable phenomena whose ex- 

 planation forms the subject of the present paper. We have 

 in the first place to consider the effects obtained within a 

 small region in the neighbourhood of the optic axes defined 

 by equations (2) ; in this region the variation of co is, as 

 may be shown, very slight, and the quantity 2/ca> 2 = k has a 

 variation corresponding almost exactly to that of the analo- 

 gous function k/co characteristic for absorption. 



The two complex equations (5) and (6) thus define, within 

 the region now considered, the real and imaginary parts of 

 the two unknown quantities v and c/jf, as well as the real 

 velocity of propagation «, the parameter of absorption A\ the 

 ratio G/F of the real amplitudes, and the relative retard- 

 ation R. 



5. Regarding these four quantities it must here suffice to 

 state four propositions which, though only qualitative, are 

 easily understood and extremely helpful towards an explan- 

 ation of the effects considered. These propositions follow 

 from the equations (5) and (6). In order to arrive at them, 

 consider once more all the directions as passing through the 

 centre of a sphere, and defined by their intersections with 

 the spherical surface. The region surrounding an optic axis 

 A x may then be approximately represented by a plane, as 

 shown in fig. 2. We here have, besides the direction of the 

 optic axis, represented by the point A,, and that of the wave 

 normal, represented by the point Z, also the plane A 1 A 2 of 

 the optic axes ; A 2 being inclosed in brackets in order to 



