THE QUANTUM THEORY, 473 
DISCUSSION ON THE QUANTUM THEORY. 
Mr. C. G. DArwi1n.—In several branches of physics, the deductions from the 
principles of classical dynamics lead to results which are not borne out by experi- 
ment, and sometimes to results which would be quite impossible. In these cases the 
quantum theory supplies a working rule which has an extraordinary power of giving 
the right results. As atheory it has no complete logical foundation at present. 
The facts explained by it fall into two groups. On the one hand there are the 
photoelectric effect and the theory of spectra, and on the other radiation and 
specific heats, which involve considerations of the meaning of temperature. 
The essential feature of the theory is the existence of a universal constant, the 
quantum h=6:55 x 10-7 erg sec., which in some way, not yet explained, controls 
exchanges of energy. The simplest form of the rule is that if energy is exchanged 
with a system of frequency v vibrations per second, then it will be exchanged in 
amount hv. Its application is at present only known for periodic systems. The 
photoelectric effect is the simplest case. Here light falls on a metal surface and in the 
act electrons are emitted with a high velocity. Their energy is connected with the 
frequency of the light by the quantum relation. The same effect enormously enhanced 
is found with the X-rays, and here the converse effect is also found—that electrons 
of given energy can only excite X-rays of frequency below a certain amount. 
It was in the radiation theory that Planck discovered the quantum. It works in 
exactly the same way, though here complicated by the conception of temperature. 
It was in this connection that Poincaré proved that anything even remotely resembling 
the facts of radiation could only be explained by precisely Planck’s ideas. The 
theory of the specific heats of solids is more complicated than that of radiation, but 
follows the same lines. For the specific heats of gases it is rather different, as here it 
is necessary to ‘quantise’ rotations instead of vibrations.- In connection with radiation, 
Planck attempted partially to reconcile the new mechanics with the old by his Second 
Hypothesis, in which the absorption is continuous but the emission still discontinuous. 
This hypothesis raises a good deal of theoretical difficulty, and will not work in 
spectrum theory, but gives good results in other directions. Closely connected with 
it is the question of residual energy at the absolute zero of temperature, a matter 
that it should be possible soon to decide by experiment. 
The spectrum theory is far the most interesting branch of the quantum theory, as 
it has Jed and is stil] leading to extensions of quantum mechanics. ‘The first idea in 
it is a natural extension of the photoelectric effect. Bohr argued that if an atom 
emits radiation of frequency v, it must be because it has lost energy hy, and this 
explains the Combination Law, which is that the frequencies of the lines of a spectrum 
are given by the differences between pairs of terms of a sequence. Thus, it is possible 
to replace the study of the line by a study of the energy of the atom before and after 
theemission. But afurther use of the quantum is required, since on classical principles 
the nuclear atom lacks definiteness. This is done by ‘ quantising the orbits ’"—that is, 
limiting the number of orbits possible dynamically, by imposing non-dynamical 
conditions. The dynamical solution of the motion of a system of x degrees of freedom 
involves 2n arbitrary constants, and the quantisation consists in fixing half of these 
by a certain rule in terms of the quantum, and these are the only permissible orbits. 
For example, the hydrogen spectrum is due to a single electron describing a planetary 
orbit about a nucleus. The permissible orbits are such as have their major axis 
1,4,9... times 0-53 x 107" cm. in length, and eccentricities of certain definite values. 
In connection with permissible orbits an interesting point arises. In some cases (of 
which the above is one) the quantisation can be done in several ways and each leads to 
a different set of permissible orbits, but the energy of each has the same set of values 
and so they give the same spectrum. These are known as degenerate cases and are 
one of the most important points of difficulty in the theory. So far the Bohr theory 
has been successfully applied to the ordinary hydrogen spectrum, including its fine 
structure, the influence of electric and magnetic fields and partly the banded spectrum, 
too ; also to the enhanced helium spectrum and to the X-ray spectra, and a beginning 
has been made on the alkali spectra. 
Bohr has recently succeeded in extending the theory by his Principle of Analogy to 
the question of the intensity and polarisation of the lines. This reduces the character 
of a spectrum by means of a formal analogy with the (fallacious) predictions of the 
electro magnetic theory. Its physical meaning is hard to see, but it seems the sort of 
1921 K K 
