﻿Atomic Model ivith a Magnetic Core. 721 



only is emitted in passing from one state to another. This 

 is required both for ordinary spectra and for X-ray spectra. 

 In the second place, it appears necessary to assume that 

 there is no force between bound electrons, so that any one 

 of these electrons is independent of the others. This 

 supposition may be related to Sir J. J. Thomson's con- 

 ception of tubes of force. A bound electron may have the 

 tube (or tubes) of force originating from it attached to the 

 nucleus, and if all the electrons in question are connected 

 to the nucleus in this way, they cannot exert force on one 

 another. 



Perhaps it may be necessary to suppose that a bound 

 electron has both the ends of the double tube of force 

 belonging to it attached to a definite part of the core in such 

 a way that the attraction on the electron is proportional to e 2 

 instead of to (N<?) 2 . 



A further difficulty in applying the theory of Bohr to actual 

 series lies in the fact that the denominator of a sequence 

 contains terms which are not simple integers. Thus in 

 Rydberg's formula we have m + /j, where m is an integer, 

 jj, a fraction, in the formula of Moggendorf and Hicks we 

 have m + jju+a-lm, in the formula of Ritz m + jjl + (3 / 'm 2 '. 

 Nicholson * has shown that the theory in its original form is 

 insufficient to account for such additional terms when electro- 

 static forces only are considered. The development which 

 I have given f, supposing the electron to be under the action 

 of magnetic forces, yields a formula containing a term of the 

 form B/m 2 , where B is proportional to the magnetic moment 

 of the core, but does not account for the fractional part //,. 

 In attempting to apply this formula to actual elements, it is 

 found that in general the value of /3 obtained by Ritz is 

 much too large to be due to a small number of magnetons. 

 Further, in the case of hydrogen, if we suppose the fractional 

 part due to a term of the form B/m 2 , it is necessary to assume 

 different values for B in the two sequences, impjying the 

 existence of two types of state in the core. This suggested 

 that the core itself might be intimately concerned in the 

 emission of radiation, and that the term in jll, and perhaps 

 also terms such as otjm and /3//>r, might depend upon the 

 angular momentum of the core. 



This line of thought, associating the constants in the 

 formula with the core of the atom, may be supported by 



* Loc. cit. 



f Phil. Mag-, vol. xxix. pp. 40-49, 140-143 (1915). 



Phil. Mag. S. 6. Vol. 29. No. 173. May 1915. 3 A 



