380 TRANSACTIONS OF SECTION A. 
well known Balmer’s series, the Paschen infra-red series, the Pickering (¢ Puppis) 
series, and the series recently discovered by Fowler. There is remarkably close 
numerical agreement between the calculated value of the constant R, (Rydberg’s 
constant) and its observed value. 
The series of results obtained in this way are, I think, far too striking to be 
dismissed merely as accidental. At the same time, it would be futile to deny 
that there are difficulties, still unsurmounted, which appear to be enormous. 
I would mention in particular the difficulties of explaining the Zeeman effect 
and interference. 
The consideration of this last difficulty introduces us to a wider problem— 
namely, the difficulty of reconciling the hypothesis of the quantum theory with 
the established facts of the undulatory theory of light. It is hardly too much 
to say that the two theories appear to be in active antagonism wherever they 
come in contact. Everywhere the undulatory theories demand that radiation 
should be capable of spreading and dividing indefinitely; while the quantum 
theory demands the reverse, at least when there is interaction between matter 
and ether. The conflict is, perhaps, shown at its keenest in the case of X-rays. 
These can be reflected and diffracted as though they were subject to the spread- 
ing and division required by the undulatory theory, while the same rays have the 
capacity of ionisation at a distance of, perhaps, 100 yards, exactly as though 
their energy were atomic and concentrated in the way demanded by the quantum 
theory. The conflict of the two sets of views appears so definitely and so acutely 
in this case that it may, perhaps, be hoped that the resolution of the difficulty 
here may go a long way towards solving the wider general problem. 
Another problem of a more abstract nature which exhibits the conflict of the 
two theories is the following : Consider a very few electrons shut up in a radia- 
tion-free and perfectly reflecting enclosure, left to move freely. According to 
the classical laws (or any system of continuous laws) the electrons will set up an 
electro-magnetic field, and the energy of this field must ultimately be dis- 
tributed according to the law of equi-partition 8m RT A-‘da. Would this 
really happen? If not, at what exact point do the classical laws break down? 
If it does happen, is the resulting energy in the ether identical with ordinary 
light, or is it something quite different? If it is the same, how does it happen 
that radiation in thermodynamical equilibrium at temperature T can obey the 
law 8% RT a-4 dA, and can also obey Planck’s law? 
The boldest and simplest attempt at reconciliation between the conflicting 
theories lies in abandoning the ether altogether, and relying on some purely 
descriptive principle, such as that of relativity. There is probably no adequate 
reason why the ultimate interpretation of the universe should be expected to be 
dynamical rather than kinetic and descriptive. On the other hand, it is doubtful 
whether this very drastic remedy does more than merely shift the difficulty from 
one point to another; if there were no ether Debye’s interpretation of heat- 
energy would demand quanta of material energy, each one indivisible, and yet 
spread over a finite region of space. 
Any attempt at a dynamical interpretation demands a consideration of the 
meaning of h. The following vague suggestion is put forward very tentatively. 
The value of hf is given by 
h | (4me)? 
a fe . 
2a V 
where ¢ is a numerical constant, of which the value is very nearly, or perhaps 
exactly, equal to unity. Is, then, the new unit A anything more than a reappear- 
ance of the old unit (4me)? Is the apparent atomicity of action or energy or 
angular momentum anything more than the atomicity of electricity? For con- 
sider what is meant by the fact that e is constant throughout the universe. We 
are probably no longer content to regard the electrons as ‘ manufactured articles,’ 
all originally made similar. It is more rational to suppose the electrons to be 
formed out of some pervading medium, and to be all similar because the pro- 
perties of this medium require that they should be all similar. If we definitely 
suppose this medium to be the ether, then the Maxwell equations cannot be the 
full and complete equations of the ether, for they do not imply the constancy 
of e. We must imagine the full equations to involve ¢ (or fh) as well as the 
