Faraday s "Magnetic Lines" as Quanta. 533 



After substituting on the right-hand side in terms of 

 n and n' , this yields the value 



(n+n') 



N=- v ' ~' . x 



u (n + n r ) 2 

 r=n + n' (16) 



11. Up to this point it has been assumed that the mass of 

 the nucleus is so great that it may be treated as at rest. In 

 § 9 of the paper in the Annalen der Physik, Sommerfeld 

 discusses the effect of the finite mass of the nucleus on the 

 relative motion and on the quantum conditions. It is shown 

 that if m is the mass of the electron, M the mass of the 

 nucleus, it is necessary to replace m in the equations by 

 the "resultant mass," /a, defined by 



77lM 



Further, the "phase integrals ;? expressing the quantum 

 relations for the electron and the nucleus are additive. 



It follows from these results that the total number of 

 quantum tubes that must be associated with the system is 

 still represented by the sum of the integers n and n'. 



12. Sommerfeld discusses in § 7 of his paper the orienta- 

 tion of the plane of the orbit in space, and shows that when 

 there is some direction fixed physically giving rise to a fixed 

 plane of reference, the angle u between the plane of the 

 orbit and this reference plane can assume only particular 

 values determined by 



ni 

 COS cc = 



n, + n< 



Here ?i 1? n 2 are new integers, determined by the quantum 

 relations 



p. • f 



J p^d^ = n l 1i, \ p 6 dO = n 2 Ji, 



the polar co-ordinates of the electron being ?•, 0, i/r. 



The sum of the new integers ?ii + n 2 corresponds to the 

 integer n in the earlier work. The energy of the motion 

 depends on the sum of the integers n x -f- n 2 + n f . Thus from 

 our present standpoint the total number of tubes linked with 

 the orbit is still 1^+ n 2 + n' , but if magnetic tubes arc 

 physical entities the reason why the angle a can take only 

 assigned values becomes apparent. 



