676 BELL SVSTEM TECHNICAL JOURNAL 



{W22-Wn)h=Ra\\& = \.m-U). The wave-length difference, which 

 is the quantity' directly measured by spectroscopists, varies from one 

 doublet to another; for the first doublet of the Balmer series, known 

 as //a, the mean wavelength of which is 6.563' 10~' cm., it should 

 be equal to 1.58'I0~^ cm. 



Many independent measurements of these wavelength differences 

 have been made, most of them upon the first doublet of the series, 

 a few upon other doublets as far along as the fifth. Some were made 

 long before, others after Sommerfeld published the foregoing theory. 

 The various values found for the various wavelength-differences 

 have all been within 20% of the value required by equation (66); 

 within this range they have fluctuated, one or two spectroscopists 

 of repute have maintained that the actual values are unmistakably 

 different from the computed value; but the balancing of eN'idence now 

 seems to point more and more closely to the desired \alue as the 

 right one ". 



This prediction of the wa\eleiigtii-(iifferences between the com- 

 ponents of the doublets which make up the Balmer series may be 

 taken tentatively as the third of the numerical agreements which 

 fortify Bohr's atom-model. So taking it, let us generalize the theory 

 to the full extent already suggested. Returning for a moment (merely 

 for ease of explanation) to the over-simplified case of an atom con- 

 sisting of a nucleus and a revolving electron of which the mass does 

 not vary with its speed: we saw that the energy-value —Rh/n- is 

 entailed by each and every one of the n elliptical orbits for which 

 the integral of the angular momentiiin and the integral of the radial 

 momentum are given by assigning the ii \alues ^ = 1, 2, 3 . . . « to 

 the symbol k in the following equations: 



J p^'l4> = kli.\ pr(lr = {n-k)li. (67) 



This I will express in another wa>' by saying that the energy-\alue 

 — Rh/n- is entailed by each of the Ji orbits having the azimutlial 



" This is one of those embarrassing questions as to which the experimental doctors 

 still disagree, malcing it folly indeed for anyone else to pretend to decide. The 

 three latest measurements, which are those of Shrum, Oklcnberg, and Geddes, 

 agree passably with the value resulting from the theory I have presented. Vet 

 Gehrcke and Lau defend their measurements, made in 1920 and 1922, which give 

 values about 20' J too low; an<l (iehrcke at least is an authority to whom lack of 

 experience in this field certainh cannot be imputed. I evade this issue In- referring 

 the reader to the articles by Shrum {Proc. Roy. Soc. A105, pp. 259-270; 1923) for 

 the bibliography of earlier work and the account of the latest; of Kuark (/. c. supra) 

 for the contention that the data sustain the theory; of Lau {Pliys. ZS. 25, pp. 

 00-6S; 1924) for the contrary contention. 



The issue is further complicated by the predictions quoted in the next paragraph 

 alravc, although not seriously enough to disqualify the foregoing remarks. 



