and their Magneto-optic Properties. 279 



(25) by writing, instead of p, (2p — 1), (3p — 2), and so on. 

 In particular, for H= H c =10,000, L e. for Z= ±k, we have, 

 neglecting (T/t) 4 , 



and similar expressions for J 2 , etc., with (2;j>— 1), etc., 

 instead of p. Returning to ('20), and remembering that 

 6i, 9 2 , etc., are small angles, we can put (25 a), etc., into the 

 more suggestive form 



T 1 sin 2 f, T ., sin 2 f 2 , /oc \ 



Jl=rl ~~7^' J 2 =1 ~ (2p-l)" ■ ( ) 



If the angles of rotation, £\, f 2 , etc., are small (as it would 

 follow from our above considerations) then J 1? J 2 , etc., would 

 differ but little from unity. That is to say, a field which 

 reduces the fundamental line to about -^ () of its intensity 

 would weaken but little the remaining lines of the spectrum, 

 while Wood and Ribaud's experiments seem to indicate that 

 the fluorescence is strongly reduced as a whole. Thus, our 

 theory seems to be just to the fundamental line, but not 

 so to the higher lines of the resonance-spectrum. The 

 reason of this outstanding difficulty seems obvious. In fact, 

 formulae (25), etc., for the first and higher lines have been 

 deduced from the equations (12) under the assumption that 

 the coefficients c u c 2 , etc., have the same values in the presence 

 of H as in the absence of any magnetic field *. Now, as 

 has already been mentioned, this is only approximately true, 

 and may well require a considerable correction when such 

 strong fields as H c = 10,000 gauss are in question. The 

 results, however, of my theoretical investigations concerning 

 this matter are better postponed until spectrophotometry 

 measurements of the magnetic reduction of the separate lines 

 of the series are available. 



Such measurements would also enable us to find the time t, 

 and since f gives tjt, we should be able to estimate 7) = q/mV, 

 which need not, thus far, be the electronic ratio. Mean- 

 while, it may be interesting to see what i is like if rj is of the 

 order of the electronic ratio. Now, returning to (23), and 

 taking again for J Wood and Ribaud's value ^q, for 

 H = 30,000 gauss, we have 10,000 [17 1 =& = 2/t, i. e. 



9 10 _4_ 7 



T =~ l-SC ==1'1. 10- 11 sec, . . . (27) 



* The reader -will notice that this concerns only ci, c 2 , etc., hut not c , 

 the coefficient for the fundamental line. 



