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II. On the Electron Theory of Matter and the Explanation 



of Fine Spectrum Lines and of Gravitation. By Gr. A. 



Schott, B.A., B.Sc, University College of Wales, 



Aberystwyth* . 

 § 1. T ORD RAYLEIGrTf and Mr. Jeans J have recently 

 1 J discussed, in the pages of the Philosophical 

 Magazine, the question o£ the explanation of the fineness of 

 the spectrum lines. Jeans finds it necessary to postulate 

 forces of unknown origin between electrons in addition to the 

 electric and magnetic forces required by Maxwell's theory of 

 the electromagnetic field, and makes the periods of vibration 

 of systems of electrons depend on the action of these two 

 types of forces ; on this view spectrum lines are of dynamical 

 origin. Lord Rayleigh, on the other hand, maintains that 

 the relations between the spectrum lines studied by Balmer, 

 Rydberg, and Kayser and Runge, point to a kinematical 

 origin, but finds difficulty in explaining the existence of fine 

 lines at all. The explanation developed in the present paper 

 overcomes this difficulty, and at the same time leaves us free 

 to adopt a kinematical or dynamical origin for the spectrum 

 series. Moreover it offers some prospect of explaining 

 gravitation on the lines of the hydrodynamic theories of 

 Bjerknes and Pearson. 



§ 2. We shall consider the case of n equidistant electrons 

 moving in a circle with uniform velocity. Let the radius of 



the circle be p, the velocity r, the velocity of light C, - =/?, 

 the mass of an electron /??, its charge e. 



Further let T, P be. the components, along the tangent and 

 towards the centre, of the mechanical force on one of the 

 electrons. The equations of motion are 

 d(mv) 2e*-& 



dt + a^(i-W 



p = — 

 p ' 



The second term in the first equation represents the reaction 

 of the aether on the electron due to radiation. 



The first term vanishes in steady motion ; it is retained here 

 for the sake of generality, so as to include the possibility of 

 m varying while v is constant. This is essential for what 

 follows. 



The general equations of motion of an electron, of which 

 those just written constitute a special case, can be obtained 



* Communicated by the Author. 



+ Phil. Mag. ser. 5, xliv. p. 356 ; ser. 6, xi. p. 123. 



X Phil. Mag. ser. 6, ii. p. 421 ; xi. p. 601, 



WloSZ 



