of Stationary States of Motion. 259 



by most physicists ; wherever emission in quanta occurs, it 

 is attributed to some cause arising from the constitution of 

 the atom rather than that of the radiant energy itself, a 

 position taken up by Barkla * in his recent lecture on X-ray 

 phenomena. We have sufficient reason for supposing that 

 the emission of spectrum series is a process of a very special 

 kind, to which the quantum hypothesis may perhaps be 

 peculiarly applicable, whilst it may not hold for the ordinary 

 emission of energy radiation which we have found to 

 accompany all motions of electric charges involving acce- 

 leration. 



20. It should be noticed that in our restatement of hypo- 

 thesis A the constancy of the electromagnetic energy of the 

 electron is expressly postulated, in spite of the fact that I 

 have myself mentioned elsewhere two possible internal 

 electromagnetic sources of energy from which the radiant 

 energy might conceivably be derived. It is, however, easily 

 shown that neither of these sources is available when we 

 adopt Bohr's theory. 



The first source of this kind is the acceleration energy, as 

 I have called it elsewhere f, which is equal to 



-2e 2 ftftfdc(l-ft 2 y. 



But in a stationary motion, such as is postulated in Bohr's 

 theory, secular changes of ft, ft are clearly excluded, so that 

 the acceleration energy cannot undergo any such change and 

 therefore cannot supply the energy radiated. 



The second source is the electrostatic energy of the elec- 

 tron, which can be tapped when the electron surfers a secular 

 expansion, as I have shown elsewhere. But in this case the 

 motion is only quasistationary and is subject to a secular 

 variation, which however is much too fast to be recon- 

 cilable with the remaining hypotheses of Bohr's theory, in 

 particular with Nicholson's hypothesis of constant angular 

 momentum. In order to prove this we shall make use of 

 the equations of motion of: the electron {, adapted to the case 

 of a fixed equal positive charge, but shall neglect the assumed 

 small secular changes of the speed ft and the radius of curva- 

 ture of the path p wherever they occur in the small radiation 



* Barkla, Proc. Roy. Soc. vol. xcii. A. p. 504 (1916). 



t Schott, Phil. Mag. ser. 6, vol. xxix. p. 49 (1915) ; ' Electromagnetic 

 Radiation,' p. 177, 



X Schott, 'Electromagnetic Radiation,' pp. 188- L92 ; loc. cit. p. 179, 

 eq. (219). 



S2 



