MAGNETISM AND LIGHT 339 



stronger fields and better resolving power showed that the effect of 

 establishment of the field was usually considerably more compli- 

 cated than in the simple case which we have treated, though for 

 some lines there is mere tripling, as described above.* For instance, 

 the sodium line D 1 shows a quadrupling in the equatorial direction, 

 the polarisation indicating that the central line is doubled. D 2 shows 

 six lines, and the polarisation indicates that the two side lines are also 

 doubled. Lorentz f showed that if there are n degrees of freedom 

 in the vibrating source, all coinciding before the establishment of 

 the field, and so giving one line in the spectrum, we may suppose 

 them to be made all slightly different when the field is established, 

 thus giving n lines. Thus in our simple case w = 3, and each of 

 the degrees has the same period if there is no field. When the 

 field is put on there are three periods and three lines in place 

 of one. 



Since Zeeman made his great discovery a very great deal of 

 work has been done by himself and by others in investigating the 

 details of the effect, but these details belong more to optics than 

 to magnetism. J 



We shall conclude with a very interesting calculation which 

 Zeeman made, in his first paper, of the value given for e/m by the 

 observed widening of the lines. From the values of N x and N 2 

 we get 



N X 2- N 2 2 = 



and 



where \ v X a are the wave lengths of the two side lines, and V is 

 the velocity of light, 



..gTryXg-Xj 1 



fir JT~ *x' 



-luce in the denominator X 15 A 2 may be put equal to A, the 

 original wave length. Now, as 2 ~ * was found to be ^QQQQ, for 

 X = 0-000059, when H was 10,000, and as V is 3 X 10 10 , e/m is about 



* S.-hu-ter's Tlicnn/ of (Jj>ti<-*, I.e. . . 



t The Theory of VUctrvH* (1909), i. 112 ; or Congrts International cle Physique 



(1'JOO), vol. iii. p. 1. 



J A bibliography is giveii iii Zeemaii's work (see p. 330). 



