( 349 ) 



plied by quantities iiiflepeudeot uf the time. Tiien, iieglectiug 

 quantities of the order uf //', we may satisfy (8) and (9), by as- 

 suming either 



P% = + ipu « — "1 + "'i 



or 



Pi = — i-Pi > >' — >h — «'i • 

 In these fuiniuhie 



- _ ^1 _ ^^^ 



ur, writing e fur tlie tutal charge 4 /kï^o-j and m fur the tutal 

 mass 4 na-f/j 



, ^e 



4 m 



la the two modes of motion, which correspond to pa— +*Pi) ^^^ 

 P2 = — ipi , and the expressions for which are got in the ordinary 

 way by taking only the real parts of the complex quantities, the 

 coexisting Vx- and rj-vibrations will show a difference of phase of 

 V4 period. This difference will have opposite signs for the two modes. 



The vibrations corresponding to surface harmonics of the first 

 order may be roughly described as oscillations of the entire charge 

 in the direction of one of the axes of coordinates, or, to speak more 

 correctly, in these vibrations there exists at every instant an „electric 

 moment" parallel tu one of the axes. Thus it appears that the mode 

 of motion we have now examined closely resembles the one tliat is 

 assumed in the elementary theory of the ZEEMAN-effect and it is but 

 natural that we should again be led to the triplets and doublets of 

 this theory. Only, for equal values of e and m the change ?j'i of 

 the frequency is half of what it would be in the elementary cx{)lanatiun. 



§ 9. In investigating the vibrations of the second order we shall 

 introduce two new axes OX' and 01'', which are got by rotating 

 OX and OY in their plane and the first of which bisects the angle 

 XOV. \Vc shall take fur the fundamental harmonics : 



r,i=r.,„ y..^- ¥,-,/, Yos = y,,, r-2i=Yy,, y^^^y,,. 



We ni;iy really du so, because any harmonic of the second order 



