Electric and Magnetic Fields on Spectral Lines. 513 



on the lines of: a spectrum may be due to two different 

 causes: — 



(1) The field may influence the stationary states of the 

 emitting system, and thereby the energy possessed by the 

 system in these states. 



(2) It may influence the mechanism of transition between 

 the stationary states, and thereby the relation between 

 the frequency of the radiation and the amount of energy 

 emitted. 



Considering an external electric field we shall not expect 

 an effect of the second kind. Having assumed the atoms to 

 be systems of particles governed by electrostatic forces, we 

 may consider the presence of the field simply as a compli- 

 cation of the original system ; but on the interpretation 

 given in the former section of the general principle of Ritz 

 of combination of spectral lines, we may expect that the 

 relation (1) will hold for every system of electrified 

 particles. 



It appears that a necessary condition for the correctness 

 of this view is that the frequencies of the components of 

 spectral lines produced by the electric field can be expressed 

 by a formula of the type (2). As we shall see, this seems to 

 be consistent with Stark's experiments. 



Let us first consider the effect of an electric field on the 

 hydrogen spectrum. In order to find the effect of the field 

 on the energy of the atom in the different stationary states, 

 we shall seek for its influence on the relation between the 

 energy and the frequency of the system. In this calculation 

 we shall make use of the ordinary mechanics, from analogy 

 with the considerations of the former section. 



For simplicity, let us suppose that the mass of the nucleus 

 is infinitely great in comparison with that of the electron. 

 Consider an electron originally moving in a circular orbit 

 round the nucleus. Through the effect of an external 

 electric field the orbit will be deformed. If the force is 

 not accurately perpendicular to the plane of the orbit, this 

 deformation will in course of time be considerable, even if 

 the external electric force is very small compared with the 

 attraction between the particles. In this case, the orbit 

 may at every moment be considered as an ellipse with the 

 nucleus in the focus, and the effect of the field will consist 

 in a gradual variation of the direction of the major-axis as 

 well as of the eccentricity. During this variation, the length 

 of the major-axis will approximately remain constant and 

 equal to the diameter of the original circular orbit. A de- 

 tailed investigation of the motion of the electron may be 



