536 Dr. H. Stanley Allen on 



electron as that of moving Faraday tubes, it is easy to show 

 by the methods employed in earlier papers that it has the 



2 uH 2 

 value - X— — , where the summation extends over the whole 



space occupied by magnetic tubes at the instant considered. 

 Hence 2 v /xH 2 



or the instantaneous value o£ the electrokinetic energy 

 V ^ 1 • 



Consequently the average value of the electrokinetic 

 energy in one revolution is the average value o£ ^p(p, which 

 is pirv or \nliv. 



It we identify this with the expression ^Ni we find 

 ^i = nltv, or putting i = ev 



N 



-© ^ 



Thns the angular motion corresponds to an integral 

 number n of quantum tubes. 



As regards the radial motion the quantum relation is 



^p r dr== §mrdr= Jmr 2 dt = n'h. . . (S. 9) 



Here mr 2 is twice the instantaneous value of that part of 

 the kinetic energy which corresponds to radial motion. But 

 the instantaneous value is integrated with regard to the time 

 over the complete period of the orbit. Hence the equation 

 expresses the fact that 



2 (Average value of kinetic energy) _ ,, 

 v 



or the average value of the kinetic energy =^?i'hv. 



If N' be the magnetic flux corresponding to the equivalent 

 current and arising from the radial motion, the electro- 

 kinetic energy is ^N'ev. If, then, we identify the average 

 kinetic energy with the electrokinetic energy, 



^s'ev — ^nltv 



'=»'(') ^ 



15. It will be observed that in each application of the 

 quantum relation in which a result of the form 



or 



X 



X 



--© 



