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SCIENCE 



[N. S. Vol. LIII. No. 1369 



by the nuclear mass correction. This correc- 

 tion is taken care of in the present theory 

 with the same accuracy if we assume a slight 

 modification to our law of quantum repulsion, 

 viz. replace equation (2) by 



--e 



nhy 



(9) 



where M is the mass of the nucleus. This 

 seems to indicate that the quantum force is 

 due to an interaction between the electron 

 and the nucleus in which both masses play 

 a similar role. For example, it may be 

 imagined that both are set into rotation in 

 opposite directions about the axis connecting 

 them. 



Sommerfield has accounted for the fine-line 

 structure of spectral lines by considering a 

 relativity correction due to the rapid motion 

 of the electron. This would seem to be ex- 

 cellent proof that the electrons do move. 

 However, it is possible that the motion resides 

 within the electron and nucleus. It is prob- 

 ably significant that the relativity correction 

 can be taken into account in the present 

 theory if we substitute in e<iuation 2 in place 

 of n^ the expression 



in. + n.y-.^Z'-(!^^+l). 



(10) 



where a is a constant calculated by Sommer- 

 feld. A consideration of this equation may 

 lead to more definite conceptions of the 

 structure of the electron and nucleus. The 

 quantities n^ and «,. refer to what Sommerfeld 

 calls angular and radial quanta. It is not 

 yet clear just what interpretation is to be 

 placed upon these in the present theory but 

 they are evidently only of secondary impor- 

 tance in determining the forces between the 

 electrons and the nucleus. 



When we consider other atoms such as 

 helium it seems as if the new theoi-y may lead 

 us much further than the usual theory, for 

 the determination of equilibrium positions 

 under static forces is extremely simple com- 

 pared to the corresponding dynamical prob- 

 lem. Furthermore we are not troubled by 



mysterious quantum conditions which are 

 theoretically applicable only to periodic orbits 

 while the calculated orbits in atoms are not 

 periodic. 



At present T am studying the spectra of 

 helium and lithium from this viewpoint. The 

 following tentative conclusions may be stated. 



The quantum force between quantized 

 electrons is not as simple as between electrons 

 and nuclei. The quantum force between elec- 

 trons on opposite sides of a nucleus is one of 

 repulsion whose magnitude is approximately 

 given by equation (2) if the quanta are all 

 of the " angular " type, but is considerably 

 less when the quanta are of the " radial " type. 

 But if the electrons are on the same side of 

 the nucleus, the quantum force between elec- 

 trons is one of attraction, also given approxi- 

 mately by equation (2). Thus if one of the 

 electrons in the helium is uniquantic, and the 

 other one is diquantic, the latter can take 

 equilibrium positions eitlier on the opposite 

 side of the nucleus from the uniquantic elec- 

 tron or on the same side. This perhaps ex- 

 plains the fact that helium (as well as other 

 elements with two outer electrons such as cal- 

 cium, etc.) has two separate complete sets of 

 spectra (helium and parhelium). It is also 

 in accord with the remarkable facts in regard 

 to the helium specti'um which were recently 

 pointed out by Franck and Reiche. 



These properties of the electron are in full 

 accord with those which are needed to ac- 

 count for chemical relationships. The new 

 theory fulfills the predictions of G. N. Lewis 

 who in 1916 wrote^ in reference to Bohi-'s 

 theory : 



Now this is not only inconsistent with the ac- 

 cepted laws of electromagnetics but, I may add, is 

 logically objectionable, for that state of motion 

 which produces no physical effect whatsoever may 

 ■better be called a state of rest. 



It is also in accord with the conclusion 

 which I gave in a paper entitled " The proper- 

 ties of the electron as derived from the chem- 

 ical properties of the elements,"^ viz. : 



ijour. Amer. Cliem. Soc, 38, 773 (1916). 

 2Phys. Bev., 8, 300 (1919). 



