158 THE QUANTUM [ XI 5 
point of the general electromagnetic field can be made to coincide 
in direction. This direction determines an electromagnetic line 
continuous through hyperspace. The procedure in constructing 
such a line, characterized by the collinearity along it of the 
transformed electric and magnetic forces, is precisely analogous 
to the method of constructing a line of force in an ordinary electro 
static field. From a set of electromagnetic lines an electro 
magnetic tube can be constructed. Four such tubes, mutually 
perpendicular, can be constructed containing any point, and each 
is characterized by the constancy of the flux of a specified 
quantity over its cross section. In a later paper Milner * shows 
that there is exact equivalence between the stress system of a 
four-dimensional electro-magnetic field and that of an electro 
static field in three dimensions. 
5. Calamoids as Quanta 
In the four-dimensional world action is of more importance 
than energy, and as the quantum theory points to an atomicity 
of action, it is of interest to see whether the representation of the 
field by means of four-dimensional tubes of force can be pressed 
into service to illustrate, or to elucidate, the character of the 
quantum. 
Let dS represent an element of area of an electropotential 
surface at a point, and let dT represent an element of area of a 
magnetopotential surface at the same point. Then since dS 
and dT are “ absolutely perpendicular ” to each other, we see 
that dSdT is an element of hypervolume, and is equal to 
dxdydzdt. With the previous notation, in which D denotes the 
electric force and H the magnetic force, 
V(D 2 — H 2 ) . dS — strength of the tube of force standing on d S, 
and 
V(D 2 — H 2 ) . dT — strength of the tube of force standing on dT. 
Therefore the products of the strengths of the two tubes 
= (D 2 - H 2 )^S . dT 
= (D 2 — H 2 ) dxdydzdt 
— an element of the action. 
According to the accepted principles of the quantum theory, the 
integral of the action during any stationary state of the system 
is nh, where n is an integer, and h is Planck’s constant. So we 
see that for a stationary state the products of the strengths of 
the two tubes, integrated over the region corresponding to the 
period, is an integral number of times Planck’s constant. 
* S. R. Milner, Phil. Mag., vol. 46, p. 125, 1923.