133 
1921-22.] On the Quantum Mechanism in the Atom. 
and denoting by A the sum of the values 
become respectively 
and 
Aij>- 
mx + 
~}slea^x 
Mea^ij/ 
of 
a, 
equations (1) and (2) 
. . . . (3) 
. . . . 0) 
The magnetic structure now consists essentially of a number of 
magnetic poles revolving in a circle of radius a, their corresponding poles 
of contrary sign being at rest at the centre of the circle. We can speak 
of this arrangement as a magnetic current, since it is in some sense a 
magnetic analogue of an ordinary electric current formed by the motion of 
electrons along a circular wire : and the equations (3) and (4) express the 
dynamical interaction between a circular magnetic current and an electron 
moving along its axis. 
We shall take this magnetic structure to be a model of the mechanism 
within the atom which enables an approaching electron to induce a 
magnetic current in the atom. 
We now proceed to integrate the differential equations (3) and (4) 
Equation (3) may be integrated as it stands, giving 
AiA — / o = constant. 
We shall suppose that the electron is initially projected from — oo with 
velocity u, the magnetic structure being initially at rest : so the last 
equation is 
Axj/- 
Mea; 
= Me 
Moreover, if we multiply equations (3) and (4) by \j/ and x respectively, add, 
and integrate, we obtain 
+ ^mx^ = constant, 
which is the equation of conservation of energy of the system : since 
initially i}/ is zero and x is u, the equation is 
+ ..... ( 6 ) 
From equations (5) and (6) we see that when the electron, moving with 
its initial velocity u from x = —oo , comes into the presence of the magnetic 
structure, its velocity begins to diminish : its kinetic energy is, in fact, being 
expended in setting the magnetic structure into rotation. It may happen 
that the electron’s initial kinetic energy is entirely used up in this way, in 
which case the electron gets only as far as a point x determined by the 
equation 
elslx 
= eM — \/Am . u ; 
(7) 
