230 ANNUAL KEPORT SMITHSONIAN INSTITUTION, 193 5 



This assumption, of course, was orthodox in 1905, but it is of 

 interest to note that as a matter of logic the electrical theory of 

 matter can claim no supporting evidence from the special theory of 

 relativity. 



On the basis of this result of Einstein, Sommerfeld ^^ introduced 

 a modification into Bohr's theory of the atom. On Bohr's theory 

 the hydrogen atom was regarded as consisting of a negative electron 

 revolving in a Keplerian ellipse around a positively charged nucleus, 

 the attraction between the two charges being balanced by the cen- 

 trifugal force of the revolving electron. Sommerfeld (p. 45) makes 

 the orthodox assumption that the electrical charges remain constant, 

 but that the mass of the revolving electron varies with its speed 

 according to Einstein's formula. In consequence the mass of the 

 electron fluctuates as it describes its orbit, being greatest at perihelion 

 and least at aphelion, and its centrifugal force will vary slightly 

 from that in a nonrelativistic Keplerian ellipse. Because of this the 

 orbit becomes an ellipse with a moving perihelion, like that of the 

 planet Mercury, The effect of this will be to split up the spectral 

 lines, producing what Sommerfeld called the relativistic fine structure. 



This predicted effect has actually been found in the spectra of 

 hydrogen and helium, the number of the component lines and their 

 relative separation being in accordance with theory. 



As to the value of this result as a confirmation of the electrical 

 theory of matter, it is to be observed that Sommerfeld would have 

 obtained exactly the same modification of the Keplerian ellipse if 

 he had assumed the charge to decrease and the mass to remain con- 

 stant, thereby disturbing the balance by reducing the centripetal 

 attraction instead of increasing the centrifugal force. 



The logic of the whole situation is that the electrical theory of 

 matter can claim no independent support from Millikan, Einstein, or 

 Sommerfeld. It rests for the present on J. J. Thomson's theory, 

 and even this theory assumes tacitly that the charge is unaltered by 

 the motion. It is remarkable that everyone we have mentioned, from 

 J. J. Thomson onward, when confronted with the necessity of mak- 

 ing a choice, prefers to keep the charge constant and let the mass 

 take the consequences, and this without comment or apology. 



Of course, there must be a reason for this; and although it is 

 explicitly stated by no writer that I have seen, the reason is doubt- 

 less to be found in a fundamental law of electricity, that of the con- 

 servation of electrical charge, with its corollary, the exact equivalent 

 of positive and negative electricity. This law states that no one 

 has ever produced the slightest trace of a positive charge without 

 the simultaneous production of an equal and opposite negative charge 

 somewhere in the neighborhood. 



"8 Sommerfeld, Ann. Phys., vol. 51, p. 1, 1916. 



