139 
1921-22.] On the Quantum Mechanism in the Atom. 
From (17) and (18) we have now 
and combining this with (16) we have 
hv = \], (19) 
which is ]Drecisely PlancJcs equation connecting the frequency of the 
emitted radiation with the amount of kinetic energy absorbed from the 
bombarding electron. This completes the concordance between the 
behaviour of our model and the behaviour of the actual atom as found 
experimentally. 
{Added May 11, 1922.) 
§ 5. An Alternative Model for the Transformation of 
THE Energy into Radiation. 
In the discussion on the above paper, when it was read to the Royal 
Society of Edinburgh on May 8, 1922, more than one speaker found 
difficulty in the change of the model from the rotating magnetic structure 
described in § 3 to the discharging condenser described in § 4. The 
following alternative form of the radiating apparatus is offered to meet 
this difficulty. 
Suppose that to the magnetic structure described in § 3 * we merely 
add a circuit of wire, which is linked once with the structure. We shall 
suppose the wire perfectly-conducting, in order to avoid transformation 
of energy into Joulian heat. Then when the magnetic structure rotates, 
the increment of electric potential in going round a closed path linked 
once with it is 47t X the magnetic current, and is therefore 2Mi/^. This 
acts as an electromotive force in the wire circuit ; so if the coefficient of 
self-induction in the wire circuit is A, and the electric current in it is g 
at time t, we have 
Xg=-2Uf (20) 
The principle of conservation of energy yields the equation 
J Ai|^2 -(- \\g- = constant ; 
differentiating this with respect to the time, and using (20), we obtain 
Aif-2M^ = 0 ...... (21) 
* As the poles which are at rest at the centre of the structure play no part in the 
functioning of the model, it is simpler to regard them as non-existent and to assume frankly 
that magnetic currents can exist in an atom, without laying stress on their realisation by 
means of bar-magnets. 
