6S2 BELL SYSTEM TECHXICAL JOURNAL 



It is important to note that if we had made allowance for the \-aria- 

 tion of the mass of the electron with its speed — if in other words we 

 had used the equations of relativistic mechanics, which are prohahh' 

 the right ones to use — separation of variables could not ha\e lu-en 

 effected either in this paraboloidal coordinate-system, or in an\' 

 other. Vet the stationary states are found by experiment to he 

 shari)ly defined, and to ha\e approcimately the energA-\alues deter- 

 mined by (72). This can mean only that the desired General Prin- 

 ciple for determining the permissible orbits is not completeh' expressed 

 by such sets of equations as (71) or (72). Those equations are valid 

 onl\- for systems of a certain kind (those for which separation of 

 variables is possible). The General Principle must be valid for 

 s\slems of this kind and the other kind as well. For systems of this 

 kind, it must become equivalent with the conditions formulated in 

 (71) and (72) — the General Quantum Conditions for Separable 

 Systems. Or at least, the results to which it leads must be indis- 

 tinguishable from the results to which these lead. The General 

 Principle for systems of ever>' kind has not been discovered; perhaps 

 it does not exist. Bohr is striving to infer it by generalizing from 

 the third of the properties of the permissible circular orbits, which 

 I mentioned in Section H and expressed by equation (23). He has 

 attained some notable successes, which I hope that it will be possible 

 to expoiiiiil ill tile I'iiird Part of the article. 



L. M.\(.m;ti( Proi'icktihs oi-" the Atom Modi^l 



After this rather arduous pilgrimage through a succession of abstract 

 reasonings, the reader may welcome an account in simpler fashion of 

 the manner in which Bohr's atom-model is adapted to explain the 

 l)eha\ior of the atom in a magnetic field. This is an alternati\-e 

 method of arri\ing at liie same results as are attained by means of 

 ec|ualions (71). 



It was stated in section K9 of the First Part of the article, that the 

 spectrum of a radiating substance in a magnetic field indicates that 

 the field acts by replacing each of the stationary states, which the 

 substance possesses when there is no magnetic field prevailing, by 

 two or more new stationary states. The energy of each of the new 

 stationary slates difTers from that of the stationary state which it 

 replaces, by the amount 



M' = seIIh Airmc {!'?,) 



in which // stands for the magnetic field strength and .f for an integer. 



