81 



is not constant, but if its intensity increases slowly and uniloinily from zero, it is 

 further simply shown that the electric induction forces, which will accompany the 

 change in the intensity of the magnetic force, will just effect that a rotation as 

 that described will be impressed on the original motion of the system.') Moreover, 

 as regards the effect of the magnetic field on the total energy of the system,-) it will 

 be observed that the superposed rotation under consideration will not affect the 

 mutual potential energy of the particles, while, with neglect of small quantities pro- 

 portional to H-, it will produce a change in the kinetic energy equal to 2-Poh, 



>) Compare P. Langevin, Ami. de Cliim. et de Pliys. V, p. 7U (1905), who has deduced this result in 

 connection with his well known theor3' of the magnetic properties of atomic systems based on the 

 classical theory of electrons. 



-') In an earlier paper (Phil. Mag. XXVII, p. 506 (1914)) the writer had assumed that the total 

 energy in the stationary states of the hydrogen atom' in the presence of a magnetic field would not be 

 different from the energy in the corresponding states without field, as far as small quantities propor- 

 tional to the intensity of the magnetic force are concerned; the effect on the kinetic energy of the electron 

 due to the superposed rotation being assumed to be compensated by some kind of "potential" energy of 

 the whole atom relative to the magnetic field. This assumption seemed not only suggested by the ab- 

 sence of paramagnetism in many elements, the atoms and molecules of which, according to the 

 theory to be discussed in Part IV, must be expected to possess a resultant angular momentum, but it 

 was especially thought to be supported by the fact, that the spectrum, emitted by hydrogen in the 

 presence of a magnetic field, apparently did not form a combination spectrum of the type which should 

 be expected, if the frequency' of the radiation, emitted during a transition between two stationary states 

 of the atom in the presence of the field, could be calculated directly from the values of the energv in 

 these states by means of relation (1). As remarked by Debye. (Phys. Zeitschr. XVII, p. oil (1916)). this 

 view, however, would not be reconcilable with Einstein's theoiy of temperature radiation (see Part I. 

 page 7) which implies the general validity of relation (1); and, moreover, as will be shown in the fol- 

 lowing, the Zeeman effect of the hydrogen lines maj' actually be considered, not as involving a devia- 

 tion from the combination principle, but rather as affording an instructive example of a S3-stematic dis- 

 appearance of certain possible combination lines, for which a simple explanation can be obtained from 

 a consideration based on the general formal relation between the quantum theory of line spectra and 

 the ordinary theory of radiation. Further, with reference to this relation — and remembering that on 

 ordinary electrod3namics the magnetic field will not directh* influence the exchange of energy- during 

 a process of radiation, since the forces due to this field, being alwaj's perpendicular to the direction 

 of the velocity, will not perform work on the moving electron — it seems also natural to assume that 

 it is possible, simplj' from the effect of the superposed rotation on the kinetic energj- of the electron, 

 to determine the effect of the magnetic field, as regards the differences between the values of the 

 energj' in the different stationarj' states of the atom. 'Scr.v, in a discussion of the spectrum to be ex- 

 pected on the quantum theory, we are concerned onh' with these differences and not with the 

 absolute values of the additional energy of the system due to the presence of the magnetic field. 

 It would therefore be possible to escape from the difficulty, mentioned above, as regards the absence 

 of paramagnetism, by assuming that only the energy in the soealled ''normal " state of an atomic 

 system (i. e. the stationary' state of the sj'stem which possesses the smallest value for the total energy: 

 see Part IV) is not altered in the presence of a magnetic field, as far as small quantities proportional 

 to the intensity of the magnetic force are concerned. On this view, the absence of paramagnetism would 

 thus be a special property of the normal state, connected with the impossibility of spontaneous transi- 

 tions from this state to other stationarj- states of the system. To this question we shall come back in 

 thç following parts of this paper; for the sake of simplicity, however, we shall not, in the considera- 

 tions of this section, enter more closeh' on the consequences of the mentioned hypothesis, which would 

 implj' small modifications in the form of the following considerations, but would not affect the results. 



