1920-21.] x^Ether and the Quantum Theory. 
37 
2 H 2 
may be written 4^^^- ] = - X . Hence the total angular momentum 
Such an electrical system might correspond to an atom in one of its steady 
states. The equivalent mass per unit volume of a tube is 4tt/xD 2 sin 2 0 , 
where D is the electric polarisation or displacement, and 0 is the angle 
between the direction of the tube and its velocity. Hence the angular 
momentum for unit volume of the tube is ^tt/ulD 2 sin 2 Or 2 co. The moving 
Faraday tubes are accompanied by a magnetic field, at right angles to their 
length and to their direction of motion, given by H = 47rD sin Oreo. Hence 
D sin dr = H/47ro), and the angular momentum for unit volume of the tube 
of the system takes the form — , the summation extending over the 
whole space occupied by the magnetic tubes. 
If the frequency of rotation be sufficiently high, the movement of the 
charges e v e 2 , . . . may be regarded as equivalent to currents i v i 2 , . . . 
1 • 6-i ft) . Soft) 
where h = ^, . . . 
H 2 
The sum , which represents the electrokinetic energy, may be 
expressed in the form JL 1 i 1 2 + . . +M 12 vi 2 + . . . , where L x is the self- 
inductance for the circuit i v M 12 the mutual inductance for the circuits 
i,, i 2 , etc. 
Hence the total angular momentum 
2Mi2^2 
0) 
where N x = L x i x + M 12 i 2 + . . , and denotes the total number of magnetic 
tubes passing through the circuit i r 
In this case the application of the quantum theory to the steady state 
t Zv 
pd<p = nh (n an integer), since the integration is to be 
extended over the full period, which is common to all the rotating charges. 
Hence 
27 rp — nh. 
Identifying p with the above expression for the angular momentum we 
find 
2 e i N i =nh - 
