Some Orbits of an Electron. 209 



electron, it is not strictly comparable with the formula for the 

 mass, but it suffices for a rough estimate. The particular 

 character of the orbits gives rise to a great simplification in the 

 integrand of Abraham's expression, but the final integration 

 is laborious. If W is the whole energy radiated and e is the 



whole energy of the electron fe=mc 2 ^ — -7= — 2 — 1 > K 



then we find that W/e, for a given value of the velocity V, 

 increases very rapidly with decreasing p. It is about 2 or 



3 per cent, when p = ±p 0T it. for velocities *9c and *lc. For 

 both the high and low velocities *99c and *01c it is about 



4 per cent, when ^ = 9p C rit. In all these cases quite a small 

 decrease in p will very much increase W/e. Thus if radiation 

 is emitted according to the ordinary electromagnetic equations, 

 we may suppose that the critical^ is about three or four times 

 as large as it would be if there were no radiation. 



6. The experiments of Geiger and Marsden * show that 

 the nucleus can be regarded as a point charge down to 

 distances of about 10 ~ 12 cm. Beyond this we cannot go, as 

 no a particle can explore any closer. But this distance is 

 quite sufficient to allow for a considerable part of our orbits, 

 and to bring out their spiral character. That an actual 

 coalescence between two point charges should take place 

 seems very improbable; the charge of the nucleus is charac- 

 teristic of the substance and a coalescence would change its 

 value and cause a transmutation of elements. There must 

 therefore be some way by which the electron can escape 

 from the extreme neighbourhood of the nucleus. This is 

 contrary to the ordinary electromagnetic theory, which 

 therefore requires some modification ; and this modification 

 extends to parts of the theory not simply concerned with the 

 emission of radiation. Hitherto the emission and absorption 

 of radiation have been almost the only points of definite 

 disagreement between theory and experiment. 



7. We may suppose that the earlier parts of the orbits are 

 of the form calculated, and that the later processes, though 

 quite different, do not give back its velocity to a particle. 

 Thus the function of the nucleus is simply that in certain 

 cases it destroys the velocity of a /3 particle. In this way, 

 using the numbers found above, values for the absorp- 

 tion coefficient can be deduced which are surprisingly close 

 to those observed. We proceed neglecting all scattering 

 and merely counting those /£ particles whose velocity is 



* Loc. cit. 



