402 Dr. N. Bohr on the Quantum Theory of 



emitting the spectrum, in contrast to those emitting the 

 hydrogen spectrum, are supposed to carry an excess posi- 

 tive charge, and therefore must be expected to acquire great 

 velocities in the electric field in the discharge-tube. 



In paper IV. an attempt was made on the basis of the 

 present theory to explain the characteristic effect of an 

 electric field on the hydrogen spectrum recently discovered 

 by Stark. This author observed that if luminous hydrogen 

 is placed in an intense electric field, each of the lines of the 

 Balmer series is split up into a number of homogeneous 

 components. These components are situated symmetrically 

 with regard to the original lines, and their distance apart is 

 proportional to the intensity of the external electric field. 

 By spectroscopic observation in a direction perpendicular to 

 the field, the components are linearly polarized, some parallel 

 and some perpendicular to the field. Further experiments 

 have shown that the phenomenon is even more complex than 

 was at first expected. By applying greater dispersion, the 

 number of components observed has been greatly increased, 

 and the numbers as well as the intensities of the components 

 are found to vary in a complex manner from line to line*. 

 Although the present development of the theory does not 

 allow us to account in detail for the observations, it seems that 

 the considerations in paper IV. offer a simple interpretation 

 of several characteristic features of the phenomenon. 



The calculation can be made considerably simpler than in 

 the former paper by an application of Hamilton's principle- 

 Consider a particle moving in a closed orbit in a stationary 

 field. Let a> be the frequency of revolution, T the mean 

 value of the kinetic energy during the revolution, and "W the 

 mean value of the sum of the kinetic energy and the potential 

 energy of the particle relative to the stationary field. We 

 have then for a small arbitrary variation of the orbit 



SW=-2o,sg) (7) 



This equation was used in paper IV. to prove the equivalence 

 of the formulae (2) and (6) for any system governed by 

 ordinary mechanics. The equation (7) further shows that if 

 the relations (2) und (6) hold for a system of orbits, they will 

 hold also for any small variation of these orbits for which the 

 value of W is unaltered. If a hydrogen atom in one of its 

 stationary states is placed in an external electric field and the 

 electron rotates in a closed orbit, we shall therefore expect 

 that W is not altered by the introduction of the atom in. 

 * Stark, Elektrische SpeMralanalyse che.mischer Atome, Leipzig, 1914. 



