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SCIENCE 



[N. S. Vol. XLV. No. 1162 



In other words, since t is a whole number, 

 the radii of these orbits bear the ratios 1, 

 4, 9, 16, 25. If normal hydrogen is as- 

 sumed to be that in which the electron is on 

 the inmost orbit, 2a the diameter of the nor- 

 mal hydrogen atom, comes out 1.1 X 10"*. 

 The best determination for the diameter of 

 the hydrogen molecule yields 2.2 X 10"^, in 

 extraordinarily close agreement with the 

 prediction from Bohr's theory. Further, 

 the fact that normal hydrogen does not ab- 

 sorb at all the Balmer series lines which it 

 emits is beautifully explained by the fore- 

 going theory, since according to it normal 

 hydrogen has no electrons in the orbits cor- 

 responding to the lines of the Balmer se- 

 ries. Again, the fact that hydrogen emits 

 its characteristic radiations only when it is 

 ionized favors the theory that the process 

 of emission is a process of settling down to 

 a normal condition through a series of pos- 

 sible intermediate states, and is therefore 

 in line with the view that a change in orbit 

 is necessary to the act of radiation. Simi- 

 larly, the fact that in the stars there are 33 

 lines in the Balmer series, while in the lab- 

 oratory we never get more than 12 is easily 

 explicable from the Bohr theory, but no 

 other theory has offered even a suggestion 

 of an explanation. But while these quali- 

 tative successes of the Bohr atom are sig- 

 nificant, it is the foregoing numerical agree- 

 ments which constitute the most compelling 

 evidence in favor of the single arbitrary 

 assumption contained in Bohr's theory, 

 viz., the assumption of non-radiating elec- 

 tronic orbits. 



Another triumph of the theory is that 

 the assumption G, devised to fit a purely 

 empirical situation, viz., the observed rela- 

 tions between the frequencies of the Balmer 

 series, is found to have a very simple and 

 illuminating physical meaning, viz., the 

 atomicity of angular momentum. Such re- 



lationships do not in general drop out of 

 empirical formulas. When they do we 

 usually see in them real interpretations of 

 the formulas — -not merely coincidences. 



Again the success of a theory is often 

 tested as much by its adaptability to the 

 explanation of deviations from the behavior 

 predicted by its most elementary form as 

 by the exactness of the fit between calcu- 

 lated and observed results. The theory of 

 electronic orbits has had remarkable suc- 

 cesses of this sort. Thus it predicts, as can 

 be seen from 4, 5 and 3, the relationship 

 which we assumed, viz., that for corre- 

 sponding lines (like values of n^ and n^ in 

 4) the orbital frequencies n are propor- 

 tional to the observed frequencies v and 

 similarly it predicts the Moseley law (2). 

 But this latter relation, which is the only 

 one of the two which can be directly tested, 

 was found inexact, and it should be inexact 

 when there is more than one electron in the 

 atom, as is the case save for H atoms and 

 for the He atoms which have lost one nega- 

 tive charge, and that because of the way in 

 which the electrons influence one another's 

 fields. It will probably be found to break 

 down completely for very light atoms like 

 that of lithium. The more powerful the 

 nucleus, however, and the closer to it the 

 inner orbit the smaller should this effect be. 

 Now precisely this result is observed. The 

 Moseley law (2) holds most accurately 

 when tested for hydrogen and the elements 

 of highest atomic number and much less 

 accurately when tested for hydrogen and 

 aluminum or magnesium. Similarly the 

 ratio between the frequencies of the a and 

 /3 lines of the K series approaches closer to 

 the theoretical value (that for hydrogen) 

 the higher the atomic number of the ele- 

 ment. 



Again, it is now well known that the 

 a, /?, y lines in the characteristic X-ray 

 spectrum are not single lines as required by 

 the simple theory. Accordingly Sommer- 



