Apkil 6, 1917] 



SCIENCE 



327 



h being Planck's constant and A^ and Aj 

 the energies in the two stationary states. 



This assumption gives no physical pic- 

 ture of the way in which the radiation takes 

 place. It merely specifies the energy rela- 

 tions which must he satisfied. The prin- 

 ciple of conservation of energy obviously 

 requires that the energy radiated be 

 A^ — Aj. Also this radiation must be as- 

 signed some frequency v and Bohr placed 

 it proportional to the energy because of the 

 Planck evidence that ether waves origi- 

 nating in an atom carry away from the 

 atom an energy which is proportional to v. 



C, the various possible circular orbits, 

 for the case of a single electron rotating 

 around a single positive nucleus, to be de- 

 termined by T^^rhn, in which t is a 

 whole number, n is the orbital frequency, 

 and T is the kinetic energy of rotation. 

 This condition was imposed by the experi- 

 mentally determined relationship of the 

 frequencies represented by the Balmer 

 series. 



It will be seen that if circular electronic 

 orbits exist at all, no one of these assump- 

 tions is in any way arbitrary. Each one of 

 them is merely the statement of the existing 

 experimental situation. The results de- 

 rived from them must be correct if the 

 original assumption of electronic orbits is 

 sound. Now it is not at all surprising that 

 A, B, and C predict the sequence of fre- 

 quencies found in the hydrogen series. 

 They have been made on purpose to do it, 

 except for the numerical values of the con- 

 stants involved. It was this sequence which 

 determined the form given to C. The evi- 

 dence for the soundness of the conception 

 of non-radiating orbits is to be looked for 

 then, first in the success of the consta7its 

 and second in the physical significance, if 

 any, which attaches to assumption C. If 

 the constants come out right within the lim- 

 its of experimental error, then the theory 

 of non-radiating electronic orbits has been 



given the most critical imaginable of tests, 

 especially if these constants are accurately 

 determinable. 



Wliat are the facts ? The constant of the 

 Balmer series in hydrogen is known with 

 the great precision attained in all wave- 

 length determinations and has the value 

 3.290 X 10^^ From A, B and C it is given 

 by the simplest algebra as 



^^=?^. (5) 



I have recently redetermined e^- with an es- 

 timated accixracy of one part in 1,000 and 

 obtained again the value 4,774 X 10"", 

 which I published in 1913. I have also de- 

 termined "h" photoelectricallyi^ with an 

 error in the case of sodium of no more than 

 I per cent., the value for sodium being 

 6.56 X 10-^^ The value found by Web- 

 ster^* by the method discovered by Duane 

 and Hunt is 6.53 X 10"". Taking the 

 mean of these two results, viz., 6,545 X 10"^'' 

 as the most probable value, we get with the 

 aid of Bucherer's value of e/m which is 

 probably correct to one tenth per cent. 

 N = 3,294 X 10^^, which agrees within a 

 tenth per cent, with the observed vahie. 

 This agreement constitutes most extraordi- 

 nary justification of the theory of non- 

 radiating electronic orbits. It demonstrates 

 that the behavior of the negative electron 

 in the hydrogen atom is at least correctly 

 described by the equation of a circular 

 orbit. If this equation can be obtained 

 from some other physical condition than 

 that of an actual orbit it is obviously in- 

 cumbent upon those who so hold to show 

 what that condition is. Until this is done 

 it is justifiable to suppose that the equation 

 of an orbit means an actual orbit. 



Again, the radii of the stable orbits for 

 hydrogen are given easily from Bohr's as- 

 sumptions as 



12 R. A. Millikan, Proc. Nat. Acad., April, 1917. 



13 R. A. MilUkan, Phys. Bev., VII., 362, 1916. 



14 Phys. Sev., Dec, 1916. 



