On the Origin of Spectra and Planck's Law. ! L9 



Combining (39) and (40), we deduce that 



which is the same as equation (4) of § 1. 



It will be noticed that in § 1 the equation (2) has been 

 used with more general types of function taking the place of 

 the polynomials F(p), A(p). It is natural to suppose that 

 the equation (2) still remains valid ; but formal proofs are 

 more troublesome, as might be expected *. 



XXXVI. On the Origin of Spectra and Planck' 's Law. 

 By Sir J. J. Thomson, O.M., P.R.Sj 



fl^HE results of investigations on the number of electrons 

 JL in the atoms of the various elements show that the 

 structure of these atoms, if expressed in terms of electrical 

 charges, is in some cases of a very simple character. The atom 

 of hydrogen, for example, is believed to contain only one 

 electron and one unit positive charge. The question arises 

 whether, if we regard the electrons and the positive charge 

 as centres of forces varying inversely as the square of the 

 distance, we have the potentiality of explaining by mecha- 

 nical principles the properties of the atom. The explanation 

 of some of these properties such as, for example, the specific 

 inductive capacity of the gas, the formation of molecules 

 by union with other atoms, whether of hydrogen or of 

 some other element, seems to be within the scope of this 

 verjr simple system ; there are, however, other properties 

 of which this cannot be said. Prominent among these is 

 the spectrum emitted by the gas. Hydrogen, as is well 

 known, can emit several spectra. We need, however, for our 

 purpose only refer to the best known ones : the second spec- 

 trum, which is a spectrum containing an exceeding^ large 

 number of lines and extending far into the ultra-violet, 

 and the so-called four-line spectrum, which contains, we 

 have reason to believe, an infinite number of lines, the 

 frequencies of which are connected by a simple numerical 

 relation discovered by Balmer. The vibrations which would 



* This problem has been considered with the aid of complex integrals 

 in my paper on "Normal Coordinates in Dynamical Systems" already 

 quoted (Proc. Lond. Math. Soc. vol. xv.) ; the sections §§ 4, 5, 8 have 

 special bearing on this question. Short summaries are also given in the 

 "*' Abstracts " of the Proceedings (vol. xiii. ser. 2, 1914, p. xxvii, and 

 vol. xviii. January 1919). 



f Communicated by the Author. 



2G2 



