( 4A4 ) 



-f- rt representing the force of tlie field of the electron itself. — 7^ 

 is the external Held required foi- the motion. So we see that the 

 sign of the external force — A., agrees with that of j). and that 

 therefore acceleration requires increase, retardation decrease of the 

 external force. 



We conclude that the behaviour of an electron moving with 5>, 

 though in many respects it ditfers cousideralMy from that of an 

 ordinary body, does not show at all that paradoxal character, to which 

 we should conclude from the expression negative mass. Nothing 

 prevents us from assuming that electrons really can behave in such 

 a way. Accordingly I do not see any reason for assuming with 

 WiFA ^) that a moving electron must suifer a deformation in order 

 that the possibility of a motion with 35, as it requires an inliiiite amount 

 of energy, will be i)recluded. 



Finally a remark concerning the series of the emission spec- 

 tra of elements. The e(piations of motion of the electron are 

 integral or functional equations, and may l)e developed into ditfe- 

 rential equations of an infinitely high ordei'. An intinite number of 

 constants occur accordingly in the solution. If the equations are 

 linear, these constants represent the amplitudes and phases of har- 

 monic vibrations; the system may therefore vibrate with an infinite 

 number of periods ^). We are inclined to thiid^ that the periods of 

 the lines of a spectral series are the solutions of such an equation. 

 We have then the great advantage that \\q need not ascribe to the 

 electron a degree of freedom for each line in the spectrum. A degree 

 of freedom in the atom is then not required foi- each line, but only 

 for each series of lines. 



SoM.MERFKT.D tries to account for the spectral series by means of 

 the vibrations an electron performs when it is not subjected to 

 external forces. The periods which he finds, do not agree 'with those 

 of light. It seems to me that we might have expected this a pi-iori. 

 For the vibrations of light are not emitted l)v isolated electrons but 

 they are characteristic for atoms or positive ions, and areinfiuenced 

 by the forces by ^vhich the electron is connected to the other parts 

 of the atoms or ions. But also with the aid of these forces we cannot 

 account for the spectral series without a nnich better insight into 



1) W. WiEN. Über Elektronen. Vortrag gehalten auf der 77. Versammlung Deut- 

 scher Naturforscher und Arzte in Meran p. 20. 



~) Gomp, also these Proceedings Marcli 1900 p. 534. Then however, I tliouglit 

 erroneously that the solution obtained in this way was ditTerent from that, which 

 1 had first developed with the aid of integrals of Fourier. 



