102 Prof. J. W. Nicholson on Atomic Structure 



constant cannot be retained for any other helium atom with 

 a different charge, — when the law of force between the 

 electrons is the inverse square. Now the Pickering spectrum 

 is at least due to hydrogen or helium. Bohr's theory cannot 

 deduce it for hydrogen, and can only do so for helium by a 

 process which destroys the possibility of even preserving 

 Rydberg's constant, or a constant approximately equal to it, for 

 the rest of the helium spectrum. Thus with any modification 

 which we may make of the law of angular momentum, the 

 inverse square law between electrons cannot be retained. 



But the inverse n\h power of the distance between the 

 electrons is equally of no service, and is subject to all the 

 difficulties mentioned before, which are decisive against it. 

 There is no necessity to give the analytical treatment, which 

 can easily be supplied by the reader. Bohr's theory cannot 

 therefore explain the helium spectrum, or indeed any other 

 series spectrum, by any modification which will retain the 

 simpler theory of hydrogen and the Pickering series, when 

 there is force between bound electrons. If, on the other 

 hand, no such force exists, we obtain as the variable part of 

 a series spectrum from an atom of nucleus N*?, 



2ttW N 2 



v (f(T)T 



where r is an integer. Every electron is independent of 

 every other, but yet the angular momentum may depend on 

 the number of electrons, if the nucleus has the property 

 of compelling the existence of a definite angular momentum, 

 or set of angular momenta, about it. In order to preserve 

 the universal constant of series, N must divide into f(r) ; but 

 this involves either that it shall do so in helium with one 

 electron, also thus excluding the Pickering series, or else 

 that half integers may be used for t in the ordinary helium 

 series, which is quite at variance with the known spectrum of 

 helium. We are supposing, of course, as is necessary for any 

 theory of actual spectra, that 



/(T)=A(r+« + f(r)), 



where A and a are constants and yjr(r) is a small quantity. 

 Into A the division of N is to take place. Preservation of 

 the universal constant involves that A = l before or after 

 division, and the alternatives are therefore A = l, A = N, 

 which lead to the conclusions above. 



All other possible stationary states of a helium atom under 

 any laws of force are subject to the same analysis, and 



