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MAGNETIC TUBES 
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If we regard the angular momentum of the revolving electron 
as the angular momentum of moving Faraday tubes, as we did 
in the case of a circular orbit, it is easy to show by just the 
same method we employed before, that the angular momentum 
may be written as 
is 
.¡M- 
(f) 871 
This summation extends over the whole space occupied by mag 
netic tubes at the particular instant which we are considering. 
Consequently 
2 vi aH 2 
10:14 
where p is the constant value of the angular momentum. We 
see, then, that the sum 
t«H 2 
■&7 = 
10 :15 
Now this sum represents the instantaneous value of the electro- 
kinetic energy. We can determine the average value of the 
electrokinetic energy in one revolution, or the average value of 
%P'(j), and we find 
pnv or \n<phv 10 : 16 
But another way of expressing the electrokinetic energy is in 
terms of the magnetic lines threading a current circuit. If we 
have a current, i, flowing round a circuit, and there are N lines 
threading through the circuit, the electrokinetic energy will be 
£NY. If we identify this expression |-N« with \n^hv, we find on 
putting i — ev 
N = 10 :17 
that is to say, the number of magnetic tubes threading the cir 
cuit and corresponding to the angular motion is an integral 
number of times (^j, the integer being the azimuthal quantum 
number n#. 
The radial quantum motion may be treated in the same way 
pp r dr = pmrdr = pmr^dt = nji . . 10 :18 
Here mr 2 is equal to twice the instantaneous value of that part 
of the kinetic energy which depends on the radial motion. But 
we have to integrate that instantaneous value with regard to the 
time, so the quantum equation expresses the fact that 
2 (Average value of kinetic energy) 
= »A