432 Sir J. J. Thomson on the Origin of 



the positive oharge on an electron is given by the equation 



-p, Qx 2 d fsin 2 .r „ ) 



R = — =-z — j- 1 — -. — (- sm a? cos- a? > , 

 c dx ( x~ J 



where x = c/r, when x is small, i, e. when r is large, this 

 expression reduces to 



so that it gives the right value of the force at a great 

 distance from the atom. Again, when x is considerable, the 

 positions of equilibrium are given by 



IT 



cosa?=0, or x = (2p-\-l)^ , 



where p is an integer. 

 Since 



L* . fRrfa? 2Q (sin 2 a; . „ \ 



1R ,//•=— c\ — = _^> --_, . + sin a? cos 2 a? V 

 J J . r - c 1 /r J 



(2) 



At a position of equilibrium we see from equation (1), since 

 sin- a?=l, 



where /3 is a constant, if the magnetic induction vanishes at 

 the point of equilibrium where p=po, 



s== 4_ 



P {7T(2p +l)\>' 



Hence n, the frequency of the vibrations, is given by the 

 equation 



which may be written in the form 



2Qe 



7T 2 ck 



a series of the Rydberg type. 



If c Q = ±^ 



Q 7T 4 em ' 



the coefficient of the variable term is the same as in Bohr's 

 theory. 



The lines in the spectrum only give information about the 

 value of the magnetic force at a number of isolated points ;, 



f _i LI 



