218 M. Lorenz on the Theory of Light. 



since these values either lead to identical expressions or back to 

 equation (20), it being always understood that d> e } f stand for 

 small quantities. 



If r denotes the space moved through within the crystal by 

 the plane wave, the components of the excursion for the case 

 p = 2, will be given by the equations 



£= +wAsin k It — ), 



9? = AcosA; It j, )■ 



f= + uk sin k ( t — J. 



(23) 



The ray divides itself accordingly into two circularly polarized 

 rays, which advance with somewhat unequal velocities. These 

 latter may be deduced from (20) ; thus 



Sl = b(\ + luc*d+±wa*f), 

 s 2 =b(l — iuc^d— \wa^f) , 



where s l corresponds to the upper sign in (23), and s 2 to the 

 lower sign. In the latter case the circular polarization is right- 



handed, because -j- and - then have contrary signs. 



When both rays have advanced by the distance r, the plane 

 of vibration has rotated through the angle 



!(H>-5 (Bc2W/) -- • • (24) 



The rotation is thus proportional to the distance traversed, and 



is towards the right when d and / are negative. Moreover, 

 2_ 



since k is equal to s-r-, the rotation is nearly proportional to 



A> 



-g, or to the inverse square of the wave-length. 



The transition is easy from the general case here treated to 

 the particular cases of optically uniaxal and isotropic bodies. 

 Circular polarization has been really demonstrated only in these 

 two cases ; but the hope of detecting it in biaxal crystals also 

 ought not to be given up, especially since this property escaped 

 observation till lately in several uniaxal crystals (as chlorate of 

 soda, sulphate of strychnine, cinnabar, &c). 



In nature, circular polarization appears as the exceptional case, 

 while in the mathematical treatment of the subject it appears as 

 the most general case. This results from the symmetry which 

 pervades all nature, whereby the constants A become nothing, 



