(354) 



and by which therefore the multiple lines in the ZEEMAN-effect migh 

 perhaps be explained, I have been led to the assumption that in a 

 source of light there exist not only the primary vibrations we have 

 so far considered, but also secondary vibrations which are produced 

 in the way of von Helmholtz's combination tones. This assumption is 

 by no means a new one. Many years ago, Mr. V. A, Julius ^) has 

 remarked that the many equal differences existing between the fre- 

 quencies of different lines of a spectrum, seem to indicate the presence 

 of such secondary vibrations. Indeed, it seems difficult to conceive 

 another cause for the constancy of the difference of frequencies 

 which is found e.g. in the doublets of the alkali metals. It ought to 

 be remarked that secondary vibrations, the word being taken in its 

 widest sense, may arise in very different ways. The displacements 

 may be so largo that the elastic forces — and in our spheres also 

 the electric forces — are no longer propoi'tional to the elongations. 

 Or, perhaps, the vibrations will cause the superficial density of the 

 charged shell to vary lo such a degree, that the convection current 

 cannot be reckoned proportional to the velocity and the original 

 density. Moreover, two vil)rating particles may act upon each other 

 and each or one of them may tlius be made to vibrate as a whole. 

 This case would present itself e.g., if there were hvo concentric 

 spherical shells, each of them capable of vibrating in the way we 

 have examined. They might have different frequencies, or even one 

 of them might have the frequency 0; i.e., one sphere might be 

 charged to an invariable density proportional to some surface harmonic. 

 It is not necessary to make any special assumption concerning the 

 mechanism by which the secondary vibrations are produced. It will 

 suffice to assume that the system is perfectly symmetrical all around 

 the centre of a particle and that, if in one primary vibration we 

 have to do with expressions of the form : 



(j cos {)it -\- c), (15) 



and in a second one with similar expressions : 



q' cos {n't -{- c') , (16) 



the derived vibrations will depend on the product 



') V. A. Julius, De lineaire spectra der elementen. Verli. der Kon. Akad. 

 Weteusch., Deel 26. 



