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XXIT. On Bohrs Hypothesis of Stationary States of Motion 

 and the Radiation from an accelerated Electron. By G. A. 

 Schott, B.A., JD.Sc, Professor of Applied Mathematics, 

 University College of Wales, Aberystwyth*. 



1. T30HR/S theory of the Balmer Series is based upon 

 JD several novel hypotheses in greater or less contra- 

 diction with ordinary mechanics and electrodynamics, and 

 amongst them the hypothesis of stationary states of motion 

 occupies a prominent position. In his latest paper | on the 

 subject Bohr states it in the following form : — 



"A. An atomic system possesses a number of states in 

 which no emission of energy radiation takes place, even if 

 the particles are in motion, and such an emission is to be 

 expected on ordinary electrodynamics. The states are de- 

 noted as the states of stationary motion of the system under 

 consideration.' 1 



Although Nicholson's J criticism of the theory indicates 

 that it cannot be applied in its present form to elements 

 other than hydrogen, and perhaps helium, yet the repre- 

 sentation afforded by it of the line spectrum of hydrogen is 

 so extraordinarily exact that a considerable substratum of 

 truth can hardly be denied to it. Therefore it is a matter 

 of great theoretical importance to examine how far really it 

 is inconsistent with ordinary electrodynamics, and in what 

 way it can be modified so as to remove the contradiction. 

 The object of the present investigation is to consider Bohr's 

 hypothesis A from this point of view. 



2. In 1897 Lienard § published his well-known expression 

 for the irreversible radiation from an accelerated electron. 

 It is essentially positive and only vanishes when the accele- 

 ration vanishes, a possibility which is obviously excluded in 

 the case of an electron moving in any way inside the atom. 

 Thus it contradicts Bohr's hypothesis A unavoidably, and we 

 must inquire how far Lienard's expression is a necessary 

 consequence of ordinary electrodynamics. 



An examination of Lienard's proof shows that it merely 

 presupposes the usual expressions for the retarded scalar 

 and vector potentials together with Poynting's expression 



* Communicated by the Author. 



t Bohr, Phil. Mag. ser. 6, vol. xxx. p. 394 (1915). 



% Nicholson, Phil. Mas - , ser. 6, vol. xxvii. p. 541, and vol. xxviii. 

 p. 90 (1917). 



§ Lienard, U Eclairage Electrique, July 1898. Also Schott, ' Electro- 

 magnetic Kadiation,' p. 251, $ 231. 



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