Electric and Magnetic Fields on Spectral Lines. 519 



of structure in the undisplaced lines. Theoretical expla- 

 nations of these results have been proposed by Voigt * and 

 Sommerfeld |. 



Since in the presence of a magnetic field the spectrum of 

 an element cannot be expressed by a formula of the type (2), 

 it follows that the effect of the field cannot be explained 

 by considerations analogous to those employed in section 2 

 in considering the effect of an electric field. If we retain the 

 principal assumption of stationary states, we must assume 

 that a magnetic field exerts an influence on the mechanism 

 of transition between the stationary states, and thereby on 

 the relation between the frequency of the radiation and the 

 amount of energy emitted (cf. p. 513). In order to investigate 

 this problem we shall seek a connexion with ordinary 

 mechanics in the region of slow vibrations, from analogy 

 with the procedure of the former sections. 



Consider an electron rotating round a positive nucleus of 

 infinite mass. In the stationary states of the system the 

 motion of the electron without any field will be an ellipse 

 with the nucleus in the focus. Similarly, suppose that in the 

 presence of a magnetic field the motion of the electron in 

 the stationary states can be calculated in the ordinary way; 

 then, according to a general theorem of Larmor J, the orbit 

 of the electron in the field will be a superposition of an 

 elliptical orbit and a uniform rotation round an axis through 

 the nucleus parallel to the magnetic force. This implies a 

 neglect of terms proportional to the square of the magnetic 

 force. The frequency of rotation is equal to t in (23). 

 According to ordinary electrodynamics the radiation emitted 

 by the rotating system will correspond to a Zeeman triplet, 

 the central component of which has the same frequency as the 

 frequency of revolution in the elliptical orbit. In addition, 

 Langevin § has shown that the total energy of the system 

 is not altered by the rotation, since a possible gain in the 

 kinetic energy of the electrons may be considered as balanced 



* Ann. d. Phys. xl. p. 368, xli. p. 403, xlii. p. 210 (1913). 



t Ann. d. Phys. xl. p. 748 (1913). 



X '^Ether and Matter,' Cambridge, 1900, p. 341. 



§ Ann. de Chim. et de Phys. v. p. 70 (1905). In this connexion it may- 

 be remarked that on the present theory the rotation will give rise to 

 diamagnetism only, since the kinetic energy of the electrons in the 

 stationary states cannot be transferred into heat motion such as is sup- 

 posed by Langevin in his theory of magnetism. This conclusion seems 

 consistent with experiments which show that the monatomic gases 

 helium and argon are diamagnetic (see P. Tanzler, Ann. d. Phys. xxiv. 

 p. 931 (1907)), although the structure of these atoms, proposed in my 

 former paper, was of a type which on Langevins theory should show 

 paramagnetism. 



