and their Magneto-optic Properties. 273 



The meaning of this equation is obvious. Let the vector 



E denote — x incident electric force, apart from the factor 

 m 



e , and let r be the fluorescent light vector {oc, y, z) *. 



Then, in absence of the magnetic field, we have yjx=l, 



i. e. = and p = l, which means rectilinear polarization 



and r parallel to E. Owing to the magnetic field these 



rectilinear fluorescent oscillations become, in general, elliptic, 



and the major principal axes of the ellipses are turned away 



from E through certain angles f, in the plane x, y. These 



angles f are easily expressed by p alone, and the ratio of 



axes, say b : a, by 6 alone. In fact, if f be the angle 



contained between E and the a-axis, we have 



tan f = 



i+p' 



tanfl (16) 



And since, by (15), both p and 6 are functions of n 

 (n = n Q , n h n 2 , etc., for the fundamental, first, second, etc., 

 lines), the ellipticity and the rotation f will be different for the 

 different lines of the resonance-spectrum, having n = N for 

 its fundamental. The sense of the rotation round the 



magnetic field is easily ascertained. Since Z = — ttH, it is 



one way or the other according as the resonator, which need 

 not necessarily be an electron, is positively or negatively 

 electrified. Details concerning f and b/a, at least for the 

 zeroth and the first line of the series, will be given 

 presently. 



Such then should, according to our theory, be the behaviour 

 of the resonance lines in a magnetic field. As far as I know, 

 nothing of the kind has yet been observed, but I have reasons 

 to expect that the predicted rotations f will be detected even 

 with moderate fields H. 



The reader may be tempted to simplify (15) by neglecting k, 

 — at least, for the first and the higher lines. I must warn 

 him, however, not to do so, unless he is willing to neglect Z 

 as well. In fact, we shall see further on that, say, for 

 H= 10,000 gauss, |Z| and k are not only of the same order 

 but very nearly equal to one another. 



* In our present case z — 0. 



