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LIX. The Theory of Spectral Series. By Prof. H. A. 

 Wilson, F.R.S., F.B.S.C., McGill University, .Montreal*. 



AN important question with regard to the spectra o£ the 

 elements is whether the different frequencies are due 

 to the different modes of vibration of one kind of system or 

 to the vibrations of systems of different kinds. In recent 

 years the second alternative has come to appear the more 

 probable. 



Thus Ritz t hi his earlier papers regarded the different 

 lines as due to the different modes of vibration of a kind of 

 two-dimensional system, but later he abandoned this theory 

 and supposed the" different lines due to different systems, 

 each system having only one possible period. 



Ritz obtained his different systems by supposing an 

 electron to vibrate in the field on the axis of a bar-magnet 

 which was built up of a varying number of elementary 

 magnets. This theory, though undoubtedly useful and 

 important, seems to the writer to be extremely artificial 

 and improbable. Also it seems impossible to reconcile it 

 with other theories of atomic structure such as Sir J. J. 

 Thomson's well-known theory which, as far as can be seen 

 at present, must contain a considerable element of truth. 



On Sir J. J. Thomson's theory an atom consists of a 

 sphere of positive electricity of uniform density containing 

 negative electrons which can move about freely inside the 

 sphere. 



It is easy to show that such an atom has only one period 

 of vibration which can produce appreciable radiation. For 

 it is well known t that the radiation from a number of 

 electrons occupying a volume of dimensions small compared 

 with the wave-length of light is very approximately the 

 same as that emitted by one electron moving with an 

 acceleration equal to the resultant of the accelerations of all 

 the electrons. 



Take the centre of the positive sphere as origin and let 



x i lh Z i X 2i y-2-> Z -2-> • • • x m Uni z n 



be the coordinates of the n electrons which it contains. The 

 components of the resultant of the accelerations of all the 

 electrons are 



x 1 + Hi 2 + ... = % &' , %y and X z . 



* Communicated by the Author. 



f Gesammelte Werke, Paris, 391 1. 



| H. A. Lorentz, ' Theory of Electrons/ p. 120. 



