the Radiation from Electron Orbits. 651 



11. An alternative is found by assuming that some physical 

 agencies are at work which prevent Maxwell's law from 

 becoming established. An approximation to such a state of 

 things, which will be seen a posteriori to be sufficiently good 

 for our present purpose, will be obtained by supposing all 

 the electrons to have exactly the same value of Gr, this 

 being now given by G = 3RT/m. The number of orbits of 

 given type described per unit time will now be proportional 

 simply to HcJH, or (§ 9) to yu,cot/3coseo'-'#, so that when p 

 is large the whole radiation F p wall be of the limiting form 



and this will clearly vanish in the same way as the 

 exponential 



12. The limiting form just obtained will agree with 

 Planck's law if 



3 



ll = -H-/**W, 



where h is Planck's constant of which the value is 6*5 x 10 " 27 . 

 Since the value of m is 8 x 10~ 28 , it follows that /jl must be 

 3*8 in c.G.s. units. The force exerted on an electron at 

 distance r is mfju/r J or 3 x 10 ~ 27 /r 3 . Thus if the force m/j,/r d 

 is accompanied by an ordinary electrostatic force + e 2 /r 2 , 

 then the latter force will predominate over the former at all 

 distances greater than 1*5 x 10" 8 cm. 



The distance of closest approach of an electron to the 

 centre of force m///? j3 is given by 



A* p 3RT 



r' m 



so that r 2 = 7 x 10" 12 /T. At 700° abs. the closest approach 

 is 10~~ 7 cm. 



This distance is greater than molecular distances and so is 

 much too large to reconcile with the hypothesis that the orbit 

 is described entirely under the law r fir~ 3 from a single centre 

 of force. Since this is known to be the only type of open 

 orbit which can give radiation similar to that observed, it 

 appears that the hypothesis that the radiation proceeds from 

 electrons describing open orbits is one which must be 

 abandoned. The consideration of closed orbits may be 

 reserved for a separate paper. 



Cambridge, 

 July 23, 1910. 



