Radiation and the Structure of the Atom. 103 



the field, and that the only variation of the total energy of 

 the system will be due to the variation of the mean value 

 of the potential energy relative to the external field. 



In the former paper it was pointed out that the orbit of the- 

 electron will be deformed by the external field. This defor- 

 mation will in course of time be considerable even if the 

 external electric force is very small compared with the force 

 of attraction between the particles. The orbit of the electron 

 may at any moment be considered as an ellipse with the 

 nucleus in the focus, and the length of the major axis will 

 approximately remain constant, but the effect of the field 

 will consist in a gradual variation of the direction of the 

 major axis as well as the excentricity of the orbit. A detailed 

 investigation of the very complicated motion of the electron 

 was not attempted, but it was simply pointed out that the pro- 

 blem allows of two stationary orbits of the olectron, and that 

 these may be taken as representing two possible stationary 

 states. In these orbits the excentricity is equal to 1, and the 

 major axis parallel to the external force ; the orbits simply 

 consisting of a straight line through the nucleus parallel to 

 the axis of the field, one on each side of it. It c;m very simply 

 be shown that the mean value of tlie potential energy relative 

 to the field for these rectilinear orbits is equal to +3/2«^E, 

 where E is the external electric force and 2a the major axis of 

 the orbit, and the two signs correspond to orbits in which the 

 direction of the major axis from the nucleus is the same or 

 opposite to that of the electric force respectively. Using the 

 formulae (I) and (5) and neglecting the mass of the electron 

 compared with that of the nucleus, we get, therefore, for the 

 energy of the system in the two states 



A, = _ F ^^Bjf-rf . . . (8) 



h 2 ir biT-^Sem v ' 



respectively. This expression is the same as that deduced in 

 paper IV. by an application of (G) to the expressions for the 

 energy and frequency of the system. Applying the relation 

 (1) and using the same arguments as in paper IV. p. 515, we 

 are therefore led to expect that the hydrogen spectrum in an 

 electric field will contain two components polarized parallel 

 to the field and of a frequency given by 



I/a a \ ato- 77 " 2 ^ 4 '^/ 1 l\--n 3/t , „ ox ,_. 



The table below contains Stark's recent measurements of 

 the frequency difference between the two strong outer com- 

 ponents polarized parallel to the field for the five first lines 



2 D 2 



