﻿48 The Magnetic Field oj an Atom. 



Thus the core of the lithium atom would have to be equivalent 

 to about 2500 magnetons ! "We are forced to the conclusion 

 that the magnetic field can be responsible for only a small 

 part of the term in question. The assumptions that we have 

 been compelled to make as to the constitution of the atom, 

 namely, that the magnetic field may be regarded as equi- 

 valent to that set up by an elementary magnet and that the 

 electrostatic field may be treated as varying inversely as the 

 square of the distance from the centre, involve so much 

 simplification that we can hardly expect the result to do 

 more than point the way towards the correct form for the 

 expression D in the denominator of a sequence. If, for 

 example, we treat the core of the atom as a positive nucleus 

 surrounded by a continuous ring of negative electricity, 

 analysis shows that the electrostatic field gives rise to a term 

 in the expression D of the same form as S/a 2 . Thus in the 

 case of an element containing a large number of electrons, it 

 may be possible to obtain an approximate formula which 

 would agree with that proposed by Ritz (or perhaps that 

 proposed by Hicks), but in the case of elements like helium 

 and lithium, which contain only a few electrons, the diffi- 

 culties in the way of Bohr's theory put forward by Nichol- 

 son * still remain serious if not insuperable. 



The general conclusion that may be drawn from the 

 present work is that the magnetic forces set up by the atom,, 

 though they may play a part in controlling and perhaps 

 stabilising the motion of the electrons, are insufficient to 

 account for more than a small fraction of the effect that 

 would be necessary to give the observed distribution of lines 

 in spectral series. 



Summary. 



It is shown that a formula, similar to that of Ritz, repre- 

 senting the distribution of lines in spectral series can be 

 deduced from the assumptions following : — 



(1) The core of an atom gives rise not only to an electro- 

 static field varying inversely as the square of the distance 

 from the centre, but also to a magnetic field such as would 

 be set up by an elementary magnet. 



(2) The steady states of motion of an electron in the field 

 of the atom are determined by the ordinary laws of electro- 

 dynamics, combined with specified assumptions as to the 

 angular momentum and the energy of the electron. 



(3) The energy of the radiation, as in Bohr's theory, is 



* Nicholson, Phil. Mag. vol. xxviii. p. 90 (1914). 



