ATA SECTIONAL COMMUNICATIONS, 
hypothesis which should ultimately fit in with the final reconciliation of the two 
mechanics. 
The complete justification of the necessity for a quantum theory is a fairly difficult 
matter. Attempts are sometimes made to devise mechanical models which would 
account for phenomena without it.. These ad hoc models are invariably complicated, 
and if they existed would entail other consequences contrary to the facts. 
Possible chances of deveiopment might lie in the direction of discovering a method 
of quantising non-periodic processes, or of deciding the real meaning of frequency 
in the quantum relations. Another point of great interest is in the Zeeman effect. 
Here, the result of quantum theory is identical with that from classical mechanics, 
and an inspection of the quantum equation shows that the quantum occurs on both 
sides and so divides out. This suggests that many phenomena which at present are 
thought to be satisfactorily explained by dynamics are really quantum phenomena, 
but that the quantum has divided out from the equations. 
Another interesting point connects the quantum with Weyl’s extension of rela- 
tivity theory. In relativity the property of rigidity plays a certain part, and in the 
most recent developments of the theory this rigidity is typified in the expression 
‘radius of the electron.’ The quantum theory of spectra suggests that there is a 
much truer measure of this characteristic, and that is the radius of the permissible 
orbit which an electron describes about the nucleus. 
Sir Oriver Lopes, F.R.S.—I£ a projected electron enters a Bohr atomic system 
and is retained, the energy gained by the system, which must be re-radiated 
before a return to equilibrium, is 4 mu”, where uw is the velocity from infinity. 
Converted into an orbital velocity, v=u/ 4/2, this becomes mv” and is associated with 
an angular momentum mvr. Writing this as h/2m, and v as 2mrv, where v is the 
frequency belonging to the orbit in question, the energy gained and requiring 
emission ishy. You can therefore have multiples of it but no fractions. 
Now by Kepler’s third law applied to the case rv? = Ne?/m, where N is Moseley’s 
atomic number for the bombarded atom and Ne the charge of its kernel; so that 
this quantity rv” is constant for all the rings of any given atom, and changes by 
unit steps for atoms higher or lower in the series. 
But the bombarded atom has stepped down one in the series, by accretion of an 
extra electron in its kernel, so that whereas the first equilibrium condition of its 
sheath was 
rv? = Ne?/m, 
its second equilibrium condition is 
12022 = (N — 1)e?/m; 
and the energy that must have been radiated to attain this second condition is 
3 m (vy — t”), 
or, what is the same thing, 
1 2 | uli me ") Tit 
te [n(Z i air fs 
This therefore is what can be equated to hv. 
_ Moreover, since rv” is constant, and mrv is some multiple of h, say nh/2™ where n — 
is a whole number, it follows that the different orbital radii in a single atom proceed — 
as the squares of the number 7; so that, properly replacing 7, by 7»? and 7% by 
(n-+-1)? in the above expression, we get from it the Balmer and other series,— — 
Rydberg’s constant and all—except for a small correction which becomes less 
significant as N is large. 
The process of conversion from one stable circular orbit to another one, by reason — 
of the smaller attraction of the nucleus suddenly weakened by the incoming electron, 
can be traced dynamically through an ellipse—to the varying speed in which the 
radiation must be supposed due. The speed of every sheath electron is suddenly 
too big for the weakened nucleus to hold in a circular orbit; hence the ellipse, and 
the readjustment. (See Journ. Roy. Inst., Appendix I. to report of lecture on 
‘Ether and Matter,’ Feb. 28, 1919.) 
If it be objected that the gain of an electron has on this view precipitated an atom 
a step down the series, so that it would subsequently emit a different spectrum, the 
reply is that the percentage of converted atoms is excessively small and that the 
proportion of converted material may be inaccessible to observation. 
