2G0 Prof. W. Pe Idie on the 



tli^re is uniformly distributed a charge A/r n of positive 

 electricity, while an equal negative charge is distribute;! 

 over the shell of radius r n u , where r n '<r n <r n ", there will be 

 no resultant force at r n ; and, in the region between r n ' and 

 r n ", the force will be towards r n . The frequency of radial 

 vibration of an electron at r n is v n where 



fke 1 

 V m rj 



Outside r n " the field is A/?* 3 as before ; and the process of 

 construction may be repeated for a whole series of values of 

 n corresponding to any given spectrum series. 



To obtain, for example, Balmer's hydrogen series we must 

 determine the r's by the condition 



/Ae 1 /l 1\ 

 V — .— 2=27rC( — § ), 



where C = 3'29(10) 15 . pi = 2, p n =n which is any integer 

 from 3 onwards. 



In the region between r n and r n " an electron can circulate 

 with a frequency v n ' given by 



fke 1 



\7TVn =\/ • — 2 



r.' 



where f lies between and r n " — i' n . If v„ represents a 

 frequency in the visible spectrum, v n ' must correspond to a 

 frequency far outside the visible spectrum at the red end if 

 r n " —rj is very small in comparison with r n , and extending 

 to infinity as the energy of revolution is radiated away. If, 

 further, r n " — rn' is very small in comparison with r n+ ^ — r n 

 or r n — r n -\, a very small proportion of the electrons which 

 are projected into the atom from the outside can be 

 retained. The great majority are scattered, some at low, 

 some at high, angles. Only those which strike the atom 

 almost centrally can be retained, and of them, indeed, only a 

 small proportion. 



Because of the smallness of r n " — rn, the energy of an 

 electron approaching the atom radially must be practically 

 equal to it V Aem.v n if it is to reach the region r n . Identi- 

 fying this with hv n , as Sir J. J. Thomson does (loc. cit.), we 

 get A = 10~ 17 . Thus the quantum hv n of energy disappears,, 

 taking the form of potential energy, before the radiation of 

 frequency v n can be excited. 



