( 414 ) 



from a more rigorous theorv ^). If, how ever we want to apply it to 



points at a greater distance from an absorption band, as is the case 



with the magnetic rotation of transparent substances, we must turn 

 to Yoigt's more general formula ^) 



« = 1 -j- 2j 



If we may assume that only one term occurs under the summa- 

 tion in the second meml)er, and also that c/Ji and d-h^ are small 

 compared with 0-, a simple reduction shows that the new dispersion 

 curve may be derived from the original oiu* by uioving each point 



over a distance ^LchR — r, which de})en(ls on »> and hence also 



on the wave-length. In this case Hallo's relation will hold, if d is 



not supposed constant, but proportional to /'. 



Though it is uncertain whether for a given transparent substance 



we are entitled to accept the fornuUa for n with only one term 



under the summation, we may investigate to what results this would 



lead. From the elementary theory of the Zkeman effect it follows that 



e HT^ 

 T' — T= - 



m A:3t 



whence for the displacement of the dispersion curve 



e HT^V e HX" 

 in 4:t m 4.T v 



This value has been derived for the absorption band. From the 

 abo^e considerations it follows, however, that \ve may apply it for 

 each wave-length, and hence we find 



2jr e X^ dn e 7. dn 



co zr: Z — H ^:^ Z H ;. — . 



;. m ^ctV d). 7n2Vd). 



a> 



Whence follows for the rotation constant ^ = — — : 



Zll 



e. X dn 

 ^ ~ m 2V' IX ' 

 which formula corresponds with one, given by Voigt"), if we replace 

 the h occurring there by: 



m 2 



1) VoiGT. Wied. Ann. 67 p. 351. 



2) VoiGT. Wied. Ann. 67 p. 349. 

 s) VoiGT. Wied. Ann. 67 p. 351. 



