SOME CONlE.XfPOR.-IRY .tPr.lXCCS IX niYSICS- I'll 307 



If thf ciKTRV may assume only those dofiiiitf v.iliics, the electron 

 may tlescril>c only rertain defmite orbits. But there is no obvious 

 reason why the electron should not describe any of an infinity of 

 other orbits, circular or elliptical. To consider only the circular 

 «)rbits: if the atom may have no other \alues of energy than —liR, 

 and —liR 4, and —liR it, and the rest of the series, then it may not 

 revolve in any other circular orbits than those of whi»-h the radii are 

 f' 2hR. and e- '2(liR 4), and e-, 2(liR !»), and so forth; but why just 

 these? What prevents it from revolving in a circular orbit of radius 

 f- '2(hR 2). or any other value not in the series.-* And for that matter 

 how can it revolve in a closed orbit at all, since accoriling to the 

 fundamental notions of the electromagnetic theor\' it must be radiating 

 its energy- as it revolves, and so must sink into the nucleus in a gradu- 

 ally narrowing spiral? 



Bohr did not resol\-e these difficulties, and no one has e\-er resolved 

 them except by ignoring them. The customary procedure is to 

 select some common feature of these permitted orbits, and declare 

 that it is this feature which makes these orbits permissible, and 

 forl)ids the electron to follow any other. For example, there is the 

 fact that the angular momentum of the electron in any one of the 

 permitted circular orbits is an integer multiple of the constant quan- 

 tity h 2?r, /) being the same constant as we have met hitherto, which 

 is hardly an accidental coincidence. If one could only think of some 

 plausible reas<5n why an electron should want to revolve only in an 

 orbit where it can have some integer multiple of // 2w for its angular 

 momentum, and should radiate no energy at all while so revolving, 

 and should refuse to revolve in an orbit where it must have a frac- 

 tional multiple of /; 2r, the model would certainly be much for- 

 tified. Failing this it is necessary to put this assertion about the 

 angular momentum as a downright a.ssumption, in the hope that its 

 value will be so great and its range of usefulness so widespread that 

 it will commend itself as an ultimate basic principle such as no one 

 thinks of questioning. So far this hope has not been thoroughly 

 realized. On the one hand, Sommerfeld and VV. Wilson did succeed 

 in generalizing it into a somewhat wider form, and using it in this 

 wider form they explained the fine structure of the lines of hydrogen 

 and ionized helium, and Epstein explained the effect of an electric 

 field upon these lines. These are truly astonishing successes, and 

 no one. I think, can wf)rk through the details of these applications 

 to the final triumphant comparisons of theory with experiment, and 

 not experience an impression amounting almost or quite to con- 

 viction. Vet on the other hand this generalization does not account 



