554 
NATURE 
[January 15, «tga 
between r, Nne?, m, and h; and if we introduce this 
relation in Dr. Lindemann’s expressions for v, all the 
different expressions become identical. 
By a consideration of dimensions only, we cannot 
calculate the numerical factors which determine the 
exact values for the frequencies of the spectrum of an 
element; in order to do this, we must introduce more 
detailed assumptions as to the constitution of the atom 
and the mechanism of emission of radiation. A dis- 
cussion of the special assumptions used in my calcula- 
tions will be found in a paper on the influence of 
electric and magnetic fields on spectral lines, which 
will appear shortly in the Philosophical Magazine. 
N. Boner, 
The University, Copenhagen, January 5. 
Dr. F.. A. Linpemann (Nature, January 1) dis- 
agrees with the theoretical interpretation of my recent 
work on X-ray spectra (Phil. Mag., December, 1913). 
He objects to my statement that the results so far 
obtained strongly support the views of Bohr, and con- 
siders that they yield no information about the structure 
of the atom beyond confirming the views of Rutherford 
and van den Broek. My work was undertaken for 
the express purpose of testing Broek’s hypothesis, 
which Bohr has incorporated as a fundamental part 
of his theory of atomic structure, and the result of the 
test certainly confirms the hypothesis. In my opinion, 
however, further definite conclusions can be drawn 
from the results, and these conclusions strongly sup- 
port other features of Bohr’s theory. Moreover, I 
cannot accept the alternatives which Dr. Lindemann 
offers to my formula representing the values of the 
princinal frequencies observed. 
Dr. Lindemann’s arguments are based on the prin- 
ciple of dimensions. This method of treatment is of 
historical interest, as we owe to it the introduction 
of Planck’s quantum h into the discussion of atomic 
structure. So long as the only factors, common to all 
atoms, on which this structure was known to depend, 
were e, m, the charge and mass of an electron and 
Ne the charge of the nucleus, it was impossible to 
obtain a quantity of the dimensions, of a frequency. 
In an electromagnetic system the introduction of c, 
the velocity of light, might get over this difficulty, 
but it has proved more profitable to treat the problem 
as electrostatic and make definite calculation possible 
by using h. 
We will call the assumption that h is a funda- 
mental factor in the atom the h hypothesis. It then 
follows from the principle of dimensions that the 
am : : 
frequency of an atom, v=/ ja? Where f is a numerical 
constant which depends on N, and also on the arrange- 
ment of the electrons in the atom. 
The reason why Dr. Lindemann arrives by the 
same argument at an indefinite result is that he takes 
y, the distance of the electron from the nucleus, or 
else yN to be an independent factor in the calculation. 
No independent natural unit of length, which would 
apply to an electrostatic problem, is known, and the 
separate introduction of r or rN appears to me to be 
unwarranted. Bohr has pointed out that the funda- 
mental frequency .y, of ordinary series spectra is 
obtained by putting f=27* in the formula given above, 
while my work shows that the frequency of the prin- 
cipal line in the X-ray spectrum of elements from 
Ca, N=20 to Zn, N=30 corresponds with 
’ f=2n?.3(N—1)?. 
The simplicity of the expression f in these two cases 
is itself an argument in favour of the h hypothesis. 
It is, however, more strongly supported by the fact 
that the frequencies in the X-ray spectrum are pro- 
NO, 2307, VOL. 92] 
portional to (N—1)?. Two alternative explanations 
can be given for the occu (N—1) and not N. 
It is just possible that two of the elements which 
precede calcium have the same atomic number. A 
mistake would then have been made each time in 
reckoning N, and » would really be oo N?. It is much 
more likely that the repulsion of the other electrons 
cannot be neglected compared with the attraction of 
the nucleus, and then N must be replaced by (N— a,). 
In either case we conclude that as we pass from atom 
to atom yv o(Fr?)?, where F is the resultant electro- 
static force on the vibrating electron. In other words, 
a quantity of dimensions T(ML*T-?)? remains con- 
stant, and since the mass is always the mass of an 
electron MPL?T-! remains constant. By putting p=1 
a quantity is obtained of the same dimensions as h. 
For these reasons I conclude that the experiments 
support the h hypothesis, which has been put forward 
in three distinct forms, first by Nicholson, then by 
Bohr, and recently by J. J. Thomson. 
I have not succeeded in obtaining agreement be- 
tween my results and the vibrations considered by 
Nicholson. Bohr’s theory, on the other hand, explains 
why there is a general spectroscopic constant,  ), 
given by f=2z?, and at the same time demands that 
the principal X-ray frequency should be given by 
f=2n?.3(N— )?. This agrees with the experi- 
mental result if the vibrating system is a ring 
of four electrons, all vibrating together; since 
a,=0-96. Two things, however, suggest that either 
Bohr’s theory or my interpretation of it requires modi- 
fication. In the first place, it fails to account for the 
second weaker line found in each spectrum. In the 
second place it is difficult to see how a ring of four 
electrons can store up enough energy to vibrate as a 
whole. Perhaps the examination of the spectra of 
other groups of elements will suggest a solution of 
these difficulties. H. Mose ey. 
Oxford, January 5. 
** Atmospherics ’’ in Wireless Telegraphy. 
WirtH reference to Prof. Perry’s letter on “atmo- 
spherics”’ in Nature of January 8, a description of 
some experiments made by us in the summer of 1912, 
and continued last summer, may be of interest. A 
receiving station was erected near Rothbury, in 
Northumberland, with an antenna consisting of two 
horizontal wires stretched about 3 ft. from the ground. 
The receiving apparatus consisted of a galena-tellu- 
rium detector and telephone circuit coupled to two 
inductances connected to the antenna wires and 
having a variable condenser in circuit between them. 
The length of the antenna was varied during the 
experiments, but for most of the time was about 500 
yards each way, ‘the direction of the wires being 
approximately north-west and south-east. No earth 
connection was used. ] 
The antenna was laid on a slight slope, the receiv- 
ing hut being situated in a field, but in each direction 
the antenna wires passed through extensive woods, 
the whole district in the vicinity being thickly wooded. 
During the observations of 1912 the ground was 
nearly always very wet owing to the excessive rain- 
fall. 
According to the views put forward by Prof. Perry, 
it would naturally be expected that atmospherics would 
be either absent or greatly diminished in intensity 
with an antenna such as we used. So far from this 
being the case they were both numerous and loud, 
so much so that we adopted this form of antenna as 
being suitable for investigating the direction from 
which atmospherics emanate. For this purpose we 
used crossed horizontal wires connected to a form of 
radio-goniometer, the well-known directive effect of 
