100 Prof. J. W. Nicholson on Atomic Structure 



If n is not 2, X contains the (n — 2)th power of some constant 

 length, and it is very difficult to imagine what the length 

 could represent physically. For it is of the same order ;is 

 the diameter of the atom. This alone is perhaps sufficient 

 to remove the possibility of any law except the inverse 

 square. Nevertheless, we may give a brief account of some 

 other laws. For the inverse cube, n = 3, and 



t 2 A 2 9 2 X 

 4<? 4 



W 



X + T 2 h 2 



4.TT 2 , 



Spectrum lines on Bohr's theory would then show series of 

 the type 



B 



hv=A 



a 2 + /3V 



conclusions follow from the inverse fourth power. In fact, 

 for any inverse power beyond the second, the radius is a 

 function of t 2 , not r itself, and so is the variable part of any 

 ensuing series formula. This is quite at variance with fact. 

 Any composite inverse law, such as a mixed square and cube, 

 produces the same result. A glance at the accurate Hicks' 

 formula already quoted for helium, which is quite typical, 

 will show the impossibility of a theory which only introduces 

 the variable integer of series spectra in the forms of even 

 powers. When n = l, the potential energy is 



4<? 2 



and cannot be admitted as a possible value, on account of the 

 behaviour of the logarithm. . \ . • 



Thus on no possible law of electronic repulsion can we 

 derive any series for helium similar to the usual forms. The 

 inverse square, as shown in the i Mouthly Notices,' usually 

 leads (o series like Balmer's which do not correspond with 

 tact. We cannot indeed derive the forms 



N N 

 — — gr- (Hicks) or =— (Ritz), 



(*+■+?) (*+•+§} 



or anything analogous to-them for the variable part of series 

 spectra under the combined hypotheses that the angular 



