Faraday's "Magnetic Lines " as Quanta. 531 



equivalent to a current o£ strength ev. Identifying the two 

 expressions for the momentum we find 



N>>ev 



=mv 2 . 



Therefore 



1 m(ee 2 /p) 2 



N 9 = 



ev ev 



Substituting for e, p, and v the values given previously, we 

 obtain 



N 



_ h r (n + n')(in + n r ) jli 



(?) ^ 



me' 



If we deal in the same way with the momentum mvi = 

 perpendicular to the radius vector, we find ^ 



Hence 



2 

 Si 



= 7711 



= mv.. 



mvi 



ev ev 



(n+n'Y/h 



Ni =S^b>- (10) 



Since the direction in which the tubes Ni pass through 

 the orbit is opposite to that in which the tubes N 2 pass, the 

 total number of magnetic tubes actually linked with the 

 elliptic orbit is 



N = N 1 -N 2 



=^[(«w)w (2re w)]@ 

 =(«+«')(*) (ii) 



Thus the value of N, the total number of tubes associated 

 with the orbit, is an integral number of. times the unit 

 quantum tube defined by Ji/e. 



It is instructive to consider the actual number of these 

 quantum tubes in a few particular cases corresponding to 

 the simpler orbits. 



