LETTERS: LO THES EDITOR: 
[The Editor does not hold himselj responsible for 
opinions expressed by his correspondents. Neither 
can he undertake to return, or to correspond with 
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The Constitution of Atoms and Molecules. 
DR. VAN DEN BROEK’s letter (NATURE, May 7, p. 241) 
contains one or two misapprehensions of the views 
put forward in my paper (Phil. Mag., April, 1914), 
and I shall accordingly endeavour to make my mean- 
ing clearer. The paper does not purport to show that 
Dr. van den Broek’s hypothesis is incorrect—in fact, 
in my own belief, it is fundamentally correct, though 
not necessarily in complete detail—but only to show 
that it is incompatible with the present form of Bohr’s 
theory. Any atomic theory has two main things to 
explain in connection with optics—the X-ray spectra 
investigated by Moseley and the ordinary light spectra 
of atoms. The fact that coplanar rings are mathe- 
matically impossible is conclusive against them, 
whether on Bohr’s theory or the present dynamical 
one. This must be admitted, in the face of any other 
evidence which appears to support them. There can 
be rings of electrons in an atom provided that they 
are not coplanar, but they must be of the same order of 
radius. There is only one case in which coplanar 
rings are possible—the case in which bound electrons 
do not repel each other, which is considered in detail 
in a paper to be published shortly, but such a supposi- 
tion is in complete contrast to the present form of 
Bohr’s theory. 
As my letter to NATuRE pointed out, we do not 
require an inner ring in order to explain X-rays having 
lengths of the order 10-*. They can come from an 
ordinary ring of atomic size if the nucleus is of 
strength 10 or more, and the Balmer lines can be con- 
sidered as an X-ray spectrum of hydrogen. X-rays 
can even come from the confines of a_ structural 
nucleus. Many physicists have not yet realised that 
the size of the wave-length given by a ring bears no 
fundamental relation to its radius alone. The angular 
velocity of the ring is the important deciding factor. 
If we suppose that the frequency of a line is the 
frequency of the vibration of the ring about its steady 
rotation, dynamics shows that it is of the same order 
as the frequency of rotation, w. If C is the velocity 
of light, the wave-length is of order C/w, and a ring 
of any radius can give any wave-length if it rotates 
with the proper angular velocity. So also can any 
portion of a structural nucleus, and, coplanar rings 
being impossible, the X-rays can come from the 
nucleus. The wave-lengths on Bohr’s theory are also 
determined by the order C/w, and not in any funda- 
mental way by the radius, as may be seen by an 
examination of Bohr’s mathematics. : 
Although it is the only published attempt, Bohr’s 
theory does not constitute the only one which can be 
suggested to deal with Moseley’s results. The writer 
has obtained, for example, a simpler explanation of 
them by more ordinary dynamics, which will shortly 
be published, by attaching a definite structure to the 
nucleus—a structure which can explain a great deal 
more in connection with such phenomena as the 
velocity of emitted a particles. In this method, the 
meaning of N is essentially the same as in Dr. van den 
Broek’s hypothesis. The difference is in detail only. 
Tt is not possible to dispute Moseley’s contention that 
there is a fundamental number which changes by 
steps of I in passing from one element to another 
in the table, nor that it is an ‘“‘atomic number” 
NO.. 2324, VOL. 93] 
NATURE 
—— 
[May 14, 1914 
related to the charge on the nucleus. But there is an 
assumption—perhaps correct—made in identifying it 
with the exact place occupied by an element in the 
table as we now know it, and Bohr’s theory is in- 
compatible with this assumption. For the paper 
showed that if the atomic number of lithium, for 
example, is 3, it must (1) have no valency on Bohr’s 
theory, and (2) it must have all its electrons in one 
ring, or moving in a manner prohibiting any two of 
them from forming a ring. ‘The radii of the orbits 
of the two inner electrons cannot be more nearly 
equal than in the ratio 12 to I. 
Again, as in another paper (Monthly Notices of R.A.S., 
April, 1914), no approach to the ordinary helium spec- 
trum can be obtained from Bohr’s theory if the atomic 
number of helium is 2. These are only illustrations 
of much more decisive results. Thev have related, in 
the work published already, to the supposition that the 
laws of force between bound electrons are those used 
by Bohr. But they are equally valid for other laws of ~ 
force. The one case in which the coplanar rings can 
exist—when bound electrons experience no force from 
each other—is the only avenue towards the extension 
of the theory. But it has difficulties, and, in par- 
ticular, it gives no place to Moseley’s constant b, 
which is then zero in all atoms. The K radiation then 
leads to the conclusion that the atomic number usually 
differs by 1 from the place of the element in the table. 
Dr. van den Broek lays stress on the fact that N—b 
changes from one element to another, and not N. But 
we must repeat, quite definitely, that b is zero in the 
only modification of Bohr’s theory which can have 
more than one coplanar ring. By this statement, 
however, we do not imply that b has no existence in 
fact. Its different values for K and L radiation 
demonstrate that it is real. The theory would demand 
an identity of these radiations even if they came from 
different rings, when such rings can exist. A recon- 
ciliation with experiment can only be obtained by 
putting the electrons as a constituent part of the 
nucleus itself, or by supposing that X-radiation comes 
from the confines of the atom—the K type from a 
neutral atom, and the L type perhaps from an atom 
which has lost an electron. But this latter alterna- — 
tive is quite at variance with Dr. van den Broek’s 
hypothesis, when calculations are performed, and the 
first has no relation to Bohr’s theory. 
The strongest argument in favour of Dr. van den 
Broek is the recent generalisation of the periodic table 
put forward by Soddy and Fajans, against which 
mathematical considerations cannot be raised; in fact, 
they tend to support it. This generalisation, however, 
in no case demands a strict identity between the 
nucleus charge, and the place in the table. The other 
phenomena depending on the atomic number could 
depend equally well, within the order of accuracy, on 
a number which differed from it by 1 or 2. In con- 
clusion, so far as the table is concerned, Dr. van den 
Broek may be completely correct, but, if so, Bohr’s 
theory cannot be modified to take account of X-ray 
spectra. The periodic table, however, is not a suffi- 
cient test. Astrophysical spectra demand, as proved 
in many papers in the Monthly Notices, the existence 
of simple ‘‘elements” the spectra of which can be 
calculated, which not only agree with actual 
spectra, but also have actually led to the discovery 
of several lines which the formule predicted. The 
atomic weight of one of these, with 6 electrons, is 
2-94, as calculated theoretically. By an application of 
their interference method to a line in nebula, MM. 
Bourget, Buisson, and Fabry (Comptes rendus, April 
6, 1914) have verified this value for the mass of the 
atom which emits the line. They have also made 
preliminary experiments on another element, and 
found results which support the theoretical value of 
