and their Magneto-optic Properties. 275 



5. Magnetic Rotation and Kilipticity of the First 

 and the Higher Lines. 



For any line of the resonance series, and for any field H, 

 p and 6 are determined by the general formula (15), which 

 gives at once 



_ {[(N^-n 2 ) 2 + (P~Z> 2 ] 2 + 4Z 2 n 2 ffl 2 -n 2 ) 2 p 

 P ~ ' (N*-n*)» + (Jfe + Z)Y ' { } 



, ,_ 2Zn(N 8 -n 2 ) ' . 



tan U - ~ (N 2 -n 2 ) 2 + (F-Z> 8 ' * * * Uy> 



Here we have to insert n — l&p for the first, ?i = N(2p — 1) 

 for the second line of the spectrum, and so on. Introducing 

 (18) and (19) into (16), we obtain the corresponding rotations 

 f and the ratios ~b\a of the axes of the ellipses described by 

 the end-point of the fluorescent vector r, for any line and for 

 any field H. 



It will be enough to develop the final formulas for £,. 



-, for the special intensity H = H C of the magnetic field, 



when the above formulas are considerably simplified. la 

 fact, if the resonator carries, say, a negative charge *, then,, 

 by (17;, Z + &=0, and (18), (19) become 



, a Jmk 1 



tan V= ^ o, p — w . 



£S 2 —n 2 r jcos<9| 



Substituting these values in (16) we have, finally, with a 

 magnetic field H c (which would produce a rotation of the- 

 fundamental line through f = 45°) for any of the higher 

 lines of the spectrum : 



l-;cos0| b 



wnere 



tan £ ■■ 



b l+|COS#| 



tantf = 2nk 



tan g 



(20) 



N 2 



Thus, all the lines, beginning with the first, will be 

 elliptically polarized, and their a-axes will make with E the 

 angles f u f 2 , etc., expressed by (20) with n = l$p, N(2/> — 1),. 

 etc., respectively. All of these angles will differ more or 

 less from f = 45°. 



If either f or h\a could be measured on any one of these 

 lines, in the field H c , then 6, and therefore by the third of 



* If it is positively charged, Z = k, and we obtain the same final 

 formulas if the roles of #, y are exchanged, as will be seen at once from 

 (15). Thus, the amount of rotation and the shape of the ellipse will be 

 the same, but with reversed sense. 





