678 KP.I.L SYSTEM TECHSICAL JOIRXAL 



the data" to which I there allude, are agreements of the same ciiar- 

 acter as the agreement between the spacing of the component lines 

 of the Balmer series doublets, and the numerical value of the ex- 

 pression in equation (73). That is to say: the pattern of the fine 

 structure, into which by a good spectroscope the lines of ionized 

 helium are resolved, agrees more or less with the pattern to be ex- 

 pected from the theory, not only in appearance but in scale. Com- 

 bining these agreements with the other one, we are probably justified 

 in counting the latter as the third of the conspicuous numerical 

 agreements which make Bohr's atom-model plausible '-. 



Now let us examine the situation again. (Considering the abstruse- 

 ness of these matters, I hope that few readers will resent these fre- 

 quent repetitions of past remarks.) Accepting for the atom of hydrogen 

 (and of ionized helium) an atom-model consisting of a nucleus and 

 an electron, we have traced orbits for the electron such as entail 

 energy-values for the atom equal to those of the known stationary 

 states. At first we ignored both the experimental fact that the lines 

 of hydrogen and those of ionized helium have a fine structure, and 

 the tlieoretical likelihood that the mass of the electron varies w^th 

 its speed; and we found that the orbits are ellipses. Later on, we 

 took cognizance of both these things; and we found that the orbits 

 are rosettes. Vet merely to trace the orbits which yield the required 

 energy-values, the so-called "permissible" orbits, amounts to little. 

 It is essential to find distinctive features which set the permissible 

 orbits apart from all the others — on success in achieving this, the 

 whole value of the theory depends. 



Now at the \'ery beginning it was shown that, if we ignore the 

 \ariation of the mass of the electron with its speed, and if we consider 

 circular orbits only — then the permissible circular orbits which yield 

 the reciuired energy-values —Rh/ti- of the stationary states (fine- 

 slructtire being ii^nored!) are those for which 



)'p,pd<t> = nli (69) 



ill wliicli e(iuali()ii p^ stands for liie angular iiKmR'iuum of the nintioii, 

 and n for any posili\e integer; and the integral is taken around a com- 

 plete cycle of <t>. 



"Tor the txperiniental results and the comparison of data with predictions sec 

 Paschen's great paper {Ann. d. Phys. SO, pp. 901-941); 1915) which however is any- 

 thing l)ul easy to read, so that Soninierfeld's presentation will probably be pre- 

 ferre<l; likewise Birge's article (Phys. Rev. 17, pp. 5S9 fl:, 1921) to which the same 

 words apply. The agreements are impressive. On the other hand I note thai I.au 

 (/. f. supra) concludes from the same data that there is a disagreement between 

 flala and predictions, in the same sense and of about the same magnitude as the 

 disagreement which he claims to occur in the hydrogen spectrum. 



