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_ June 9, 1923] 
NATURE 
771 

e Letters to the Editor. 
[The Editor does not hold himself responsible for 
opinions expressed by his correspondents. Neither 
can he undertake to return, nor to correspond with 
the writers of, rejected manuscripts intended for 
this or any other part of NATURE. No notice is 
taken of anonymous communications.) 
. The Isotopes of Germanium. 
Usinc the improved method of accelerated anode 
trays I have been successful in obtaining the mass- 
oo of germanium. The anode contained a 
fluorine compound made by the action of HF on a 
ure specimen of germanium oxide for which I am 
indebted to Prof. Dennis of Cornell University. 
The effects are somewhat feeble, but satisfactory 
evidence of three isotopes has been obtained. Their 
mass-lines are at 70, 72, 74, and appear to be whole 
numbers though the accuracy of measurement is not 
so high as usual. The intensities are roughly in the 
proportion 2: 4:5, which agrees reasonably well with 
the value 72°5 for the chemical atomic weight at 
present in use. 
These values conform to the general rule connecting 
even atomic number with even atomic weight. It 
will be noticed that Ge” is isobaric with the weakest 
and heaviest component of zinc discovered by 
‘Dempster, and Ge* isobaric with the lightest and 
weakest isotopes of selenium announced in NATURE 
of November 18, 1922, p. 664. F. W. Aston. 
Cavendish Laboratory, 
Cambridge, May 23. 

The Wave Theory and the Quantum Theory. 
In a letter published in NAtrurRE on December 23, 
1922, I put forward a theory of dispersion which 
attempted to begin the reconciliation of the quantum 
theory with the wave theory. I have received several 
letters criticising my hypothesis, and it seemed to me 
that it would be well to acknowledge the justice of 
the criticism. By a small change it is possible to 
meet the objection, but this change carries certain 
important implications. In my former letter, in 
order to be concise, I had to get as quickly as possible 
to the positive results, but here I wish to set out the 
train of thought from which the hypothesis started, 
and to indicate some of its consequences. It is 
perhaps well at once to say that in its present shape 
the hypothesis is in rather severe difficulties over one 
phenomenon, but nevertheless the argument leads to 
a good many criticisms of existing theories which 
may be of interest. 
It must be taken as absolutely certain that both 
the electromagnetic theory and the quantum theory 
‘are valid in their respective fields, and equally certain 
that the two descriptions are incompatible. We can 
only conclude that they are parts of an overriding 
system, which would give rise to mathematical 
formulz identical with those of the present theories. 
It is true that from the present theories predictions 
can be made which are verified ; this does not con- 
firm the physical pictures associated with those 
theories, but only shows that the limits of their 
validity have not been reached. Now although the 
developments of the quantum theory in the past ten 
years have been enormous, and though there is no 
sign of their ceasing, yet these developments have not 
’ tended in the very smallest degree towards closing 
the gap which separates it from the wave theory. 
For this reason it seemed to me that the only hope 
of finding a reconciliation must lie in some other 
NO 2797, VOL. IIT] 
direction, and that it would be best deliberately to 
give up thinking of details and to go back to funda- 
mentals. 
In starting to modify existing theories it is obviously 
best to change as little as possible, and therefore we 
have at once to choose whether it shall be the wave 
theory or the quantum theory which shall serve as 
basis. On this question there will be a great diversity 
of opinion, but to me it seems that the wave theory 
is undoubtedly to be preferred. The chief reason for 
this is that, so far as we know, the classical theory 
gives correctly the observed results in the interference 
of light, no matter how high the frequency or how 
feeble the intensity ; so that even if we could find 
a new language in which to describe interference, it 
would be possible exactly to transform the mathe- 
matics which expressed it into the present language 
of waves. In other words, the wave equations imply 
an infinite number of degrees of freedom and it can 
make no difference by what name these degrees are 
called. The main objection to the electromagnetic 
theory is that it claims to present a complete system 
of mechanics, and it is this completeness that is its 
fault; but the wave theory is only a part of the 
electromagnetic theory, and we can get a large 
latitude for modification by retaining only this part 
and altering the part which describes the interaction 
of waves with matter. 
In the quantum theory it must be conceded that, 
for such things as resonance potentials or the hydro- 
gen spectrum, it is extraordinarily difficult to conceive 
of any alternative explanation; but, even allowing 
for the danger of being over-critical of an avowedly 
incomplete theory, it is not too much to say that 
from first to last the associated physical picture is in 
great difficulties. In the first place frequency, which 
plays such a leading part in the theory, is not at all 
the same thing as it is in mechanics, and is, not 
susceptible of any clear definition. Then there is the 
difficulty that the quantum conditions determining 
the permissible Bohr orbits can only be explained 
physically by attributing to the electrons a know- 
ledge of the future. Again there is the extreme 
formalism of the Correspondence Principle, a most 
owerful method of advance, but one which even by 
itself would force one to believe in the inadequacy of 
the quantum picture. A great part of the success of 
the theory of spectra has lain in the demonstration 
that the properties of the atom can be described in 
terms of whole numbers, but the dynamical concepts 
associated with these numbers are chiefly derived 
from analogy with the case of hydrogen, and could be 
reinterpreted in conformity with any new interpreta- 
tion that was found for hydrogen. For all these 
reasons it is natural to suppose that the complete 
picture will resemble the classical theory much more 
closely than it will the quantum theory. 
In my former letter I brought up the point that 
there is no reason to believe in an exact conservation 
of energy, but only in a statistical balance. The 
point is not at all new, but from much discussion of 
the subject I think there is no doubt that many 
physicists consider a breach of the law of conserva- 
tion as a serious objection to any theory. If we are 
to believe at all in the wave theory it is much more 
reasonable to maintain the exact opposite. The 
photoelectric effect is an impossibility in conjunction 
with the wave theory if energy is exactly conserved, 
but if only a statistical balance is required, then it 
becomes nothing more than one unexplained problem 
among others. Again there exist rigorous proofs 
that no system of differential equations can give the 
observed law for the partition of energy among a 
large number of degrees of freedom; but these 
