144 
THE QUANTUM 
[x.3 
* H. S. Allen, Phil. Mag., vol. 48, p. 429, 1924. 
Since p x — constant and the x cycle is from o to i, we get 
p x = etc io : 30 
If we substitute this expression in the value for W, the latter 
takes the form 
pr x 2 — 2/t 1 t 2 -f 0T 2 2 
ab — j 2 
W = \h 2 - 
10:31 
Now let us seek to use this method for the two current cir 
cuits. The expression for the electrokinetic energy for two 
current circuits is 
W = + \~L 2 i 2 2 . . 10 : 32 
This expression is of the form used in equation 10 : 24, but we 
notice that when we take pdi for a complete period the result 
corresponds to an electric charge, and must be capable of ex 
pression as an integral multiple of the fundamental electron 
charge, i.e. pdi — Ke where k is an integer. When we apply 
the quantum conditions, we find that 
-j- M 12 i 2 ) — t -\}i 
K 2,6 (M! 1 2^ 1 H - L 2^ 2) == T ‘¡P 
10:33 
Employing the results on page 142, we find the total number 
of quantum tubes linked with a circuit given by 
10:34 
and so 
As in our previous work, the simplest interpretation of these 
results is to assume the existence of discrete quantum tubes of 
magnetic induction, the unit tube being defined by h/e. That 
is to say, the integer k x may be supposed to divide exactly into 
the integer r lf and /c 2 divide exactly into r 2 . 
The suggested existence of half-quanta may represent a case 
where these integers will not divide exactly. 
In concluding the discussion of the case of two current cir 
cuits, attention may be directed to a mechanical model * repre 
senting the behaviour of two such circuits, constructed on the 
lines of a model due to Clerk Maxwell (1876). It has been found 
possible to make a model showing very close analogy to the 
electrical system and suggestive in dealing with the present 
problem.