MAGNETIC TUBES 
145 
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4. Quantum Magnetic Tubes for any Number of Circuits 
By making appropriate assumptions the results which we 
have obtained for a single current circuit and for two current 
circuits may be extended to any number of current circuits. In 
the case of a heavy atom Bohr’s later theory postulates the exist 
ence of a large number of independent electron orbits. There 
is a certain amount of evidence from the work of Ellis and others 
that quantum relations hold even within the nucleus, which may 
be composed of positive electrons (protons) and negative elec 
trons (corpuscles) in orbital motion. On this view an atomic 
and also a molecular system is an extremely complex system of 
orbits, in which positively or negatively electrified particles are 
circulating at high speed, thus virtually constituting a system 
of current circuits. 
Let us consider a single Faraday tube of magnetic induction 
linked with any number of current circuits, i lt i 2 , i 3 . . . i n . 
wH 2 
The energy per unit volume in the magnetic field is iL—. If 
on 
A is the area of cross-section of the tube at any point and ds 
is an element of its length we get for the energy in an element 
of the tube, 
and the energy associated with the whole tube can be expressed 
as 
the integral extending for the whole length of the tube. Now 
we know that ¿itHA is constant along the tube, for the magnetic 
flux is the same throughout, we therefore write for the energy 
Since the tube is linked with several current circuits we have 
where proper attention must be paid to the signs of these quan 
tities. Consequently the energy is 
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* * • l l 
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ite quantum tube: 
eflned byJ/i. 1 
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4 
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T — l^uHA^' 1 + ¿2 + H + • • • + k) 
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