Radiation and the Structure oj the Atom. 399 



to explain many characteristic properties of the atoms. In 

 my previous papers an attempt was made in certain cases to 

 overcome this difficulty by assuming, that if a very small 

 alteration of the forces would make circular orbits possible 

 on ordinary mechanics, the configuration and energy of the 

 actual system would only differ very little from that calcu- 

 lated for the altered system. It will be seen that this 

 assumption is most intimately connected with the hypo- 

 thesis F on the stability of the configurations. Such 

 considerations were used to explain the general appearance 

 of the Rydberg constant in the spectra of the elements, and 

 were also applied in discussing possible configurations of the 

 electrons in the atoms suggested by the observed chemical 

 properties. These calculations have been criticised by 

 Nicholson *, who has attempted to show that the configura- 

 tions chosen for the electrons in the atoms are inconsistent 

 with the main principles of the theory, and has also attempted 

 to prove the impossibility of accounting for other spectra by 

 help of assumptions similar to those used in the interpreta- 

 tion of the hydrogen spectrum. 



Although I am quite ready to admit that these points 

 involve great and unsolved difficulties, I am unable to agree 

 with Nicholson's conclusions. In the first place, his calcu- 

 lations rest upon a particular application to non-circular 

 orbits of the principle of constancy of angular momentum 

 for each electron, which it does not seem possible to justify 

 either on the Quantum theory or on the ordinary mechanics, 

 and which has no direct connexion with the assumptions used 

 in my papers. It has not been proved that the configura- 

 tions proposed are inconsistent with the assumption C. But 

 even if it were possible to prove that the unrestricted use of 

 ordinary mechanics to the stationary states is inconsistent 

 with the configurations of the electrons, apparently necessary 

 to explain the observed properties of the elements, this 

 would not constitute a serious objection to the deductions 

 in my papers. It must be remarked that all the applica- 

 tions of ordinary mechanics are essentially connected 

 with the assumption of periodic orbits. As far as the 

 applications are concerned, the first part of the assumption 

 might just as well have been given the following more 

 cautious form : — 



" The relation between the frequency and energy of the 

 particles in the stationary states can be determined by means 

 of the ordinary laws of mechanics if these laws lead to 

 periodic orbits." 



* Nicholson, Phil. Mag. xxvii. p. 541 and xxviii. p. 90 (1914). 



