Spectra of the Elements, and Structure of the Atom. 563 



characterizing the principal vibration of the atom, thus 

 obtainiuo-, if y denotes 2ir 2 me 4: /h 3 , 



= !"o(n-Js„) 3 , 



and everything in his paper which appears to support the 

 origin of the X-ray spectra from Bohr's theory depends on 

 the factor f . The doubtful character of an argument based 

 on the coincidence of the experimental constant with j has 

 been emphasized by Dr. Lindemann * in a recent discussion, 

 for there is a large choice of values possible to r x and t 2 . 

 But as we see, on Bohr's theory, that constant should not 

 be f-, but 3, if the ring contains four electrons. For Bohr's 

 theory definitely stipulates that in passage from one stationary 

 state to another, only one quantum of energy is radiated from 

 the atom f . If four quanta, or one quantum for each electron 

 in the ring, were evolved, the constant j would be obtained, 

 but only with this modification of Bohr's hypothesis. 



We shall examine the two alternatives separately. In the 

 first place, let us adhere to Bohr's view, that one quantum 

 only is concerned. Then 



-^(N-^S„) 2 (l,-l 2 ) 



or, as expressed in wave-lengths, as tenth metres, 



3647 14 . t yV . 1_ 



X ~ 4 t?^t? n(N-l$ n ) 2 ' 



With t 1= =1, t.=2, 



. 1-21571 in _ 5 



should be the principal X-ray from a ring of n electrons 

 surrounding a nucleus ~Ne. The principal X-ray of calcium 

 has a wave-length 



X=3-368.10- S cm., 



so that, for the ring producing it, 



n(N-J-SJ 2 = (1215-71)/(3'368)=360'U6, 



or almost precisely 361. This is satisfied very accurately by 

 N=19, n=l, but N = 20, the supposed atomic number of 

 calcium, gives no good approximation at all, for any value of 

 ??, and the same applies to any number close to it except 19, 



* 'Nature/ Feb. 5, 1914. 



t Phil. Mag-. July 1913, p. 13. 



