630 
of the cylinder and its contents. An infinitesimal pro- 
portion of the radiation will be condensed, and the 
pressure will fall to the equilibrium value, p—dp, 
corresponding to the temperature T—dT. There is 
no cnuange of frequency since the volume is not altered. 
Complete the cycle by condensing the volume v at 
T—dT, and heating the cylinder to its original tem- 
perature. The cycle is reversible, and the infinitesimal 
CdT may be made as small as we please in com- 
parison with E+pv. The external work done in the 
cycle is v(dp/dT)dT, and is equal to the fraction 
dT/T of the heat absorbed, E+pv. Whence 
E/v=T(dp/dT)—p. 
I cannot see any escape from this conclusion so long 
as Carnot’s principle is accepted for the definition of 
the absolute scale of temperature. Still less is there 
any escape from the conclusion, depending only on 
the first law, that the quantity measured experiment- 
ally is E/v+p, and not E/v, as generally assumed. 
Both conclusions are inconsistent with much of Wien’s 
reasoning, but I have shown that they are not incon- 
sistent with his displacement law. My formula satis- 
fies all three conditions, makes the entropy of the 
distribution a maximum, and the thermodynamic 
potential the same for each frequency. 
H. L. CaLLenpar. 
Imperial College of Science, S.W. 
Atomic Models and X-Ray Spectra. 
I aM unable to agree with Sir Oliver Lodge (NaturgE, 
January 29, p. 609) that the impossibility of 
the existence of two coplanar rings of  elec- 
trons with the same angular velocity is_ self- 
evident, though it is proved very simply. For 
the mutual repulsions of the electrons in different 
rings are complicated, and their effect on any ring 
varies very much with the number of electrons. I 
think the amount of proof given in my letter is neces- 
sary, especially since, in discussions of two rings, 
inequality of angular velocity has not often been men- 
tioned. 
Although my illustrative case concerns rings with 
the same angular velocity, the greater part of the 
letter relates to rings with different angular velocities, 
as, of course, in Bohr’s theory, the angular momenta 
of the electrons are equal, thus precluding identity 
of angular velocity in any two coplanar rings. It must 
be borne in mind that the portion of Bohr’s theory 
which deals with coplanar rings is admittedly more 
tentative than that relating to spectra. The point of 
my letter was that this part of the theory needs modi- 
fication; and, of course, it is not essential to the other. 
The variations from circular orbits may be shown to 
be cumulative, when the orbits are coplanar, and, in 
fact, it is possible to prove the non-existence of approxi- 
mately circular orbits from considerations of angular 
momentum alone, and as this investigation will be 
published in detail shortly, there is no necessity to 
enter further upon it now. But, in particular, the 
nearest possible approximation to a circular orbit 
for the two inner electrons of Bohr’s lithium atom 
makes their distances from the nucleus in the ratio 
12 to 1 for certain positions. 
In fact, the only possible arrangement of three 
electrons with equal angular momenta, in which the 
orbits are circular, requires all to be in the same 
circle, and such an atom can be shown by Bohr’s 
method to be as inert as helium. Lithium therefore 
cannot have a nucleus of strength 3e, and we cannot 
retain both Bohr’s theory and van den Broek’s hypo- 
thesis. One at least must be abandoned, and the 
latter must certainly, for lithium, beryllium, and 
boron, all of which can be treated very simply on 
theoretical grounds, 
NO. 2310, VOL: 92] 
NATURE 
[FEBRUARY 5, 1914 
An important argument can be derived from astro- 
physics. These three elements are, so far as can be 
judged, practically unknown in celestial spectra, where 
hydrogen and helium are sa This seems to imply 
no great similarity in constitUtion. 
J. W. NicHOoLson. 
University of London, King’s College. 
In the recent discussion in NaTureE on the constitu- 
tion of the atom, attention has been directed mainly 
to the electrostatic forces exerted by the positively 
charged portion of the atom. Prof. Nicholson has 
been successful in calculating the frequencies of the 
lines in the nebular and coronal spectra on this basis 
by employing Rutherford’s model atom consistin 
of a central nucleus surrounded by a ring (or rings 
of electrons. Bohr’s theory, though not dependent on 
the usual dynamical laws, involves the calculation by 
ordinary mechanics of the steady motion of the elec- 
tron in the electrostatic field of the positive nucleus. 
In the case of a simple nucleus this procedure leads 
to results as to the frequencies that agree with ob- 
servation. It may, however, be necessary to suppose, 
at least in the case of the heavier atoms, that the 
nucleus produces not only an electrostatic but also a 
magnetic field. Such a view has recently been de- 
veloped by Prof. Conway using the atomic model of 
Sir J. J. Thomson. If we adopt Rutherford’s model 
the expulsion of a and # particles from radio-active 
substances with large velocities may indicate that the 
particles possess these velocities within the nucleus. 
If they are in orbital motion a magnetic field would 
exist outside the nucleus.! This hypothesis may be 
associated with the theory of the Zeeman effect put 
forward by Ritz, and also with the theories of mag- 
netic action developed by Langevin and by Weiss. 
According to the latter, there exists an elementary 
magnet, the magneton, which is common to the atom 
of a large number of different substances. 
Prof. Nicholson regards Planck’s universal con- 
stant h as an angular momentum. According to 
Bohr’s thecry the angular momentum of an electron 
is constant and is h/2mz. Prof. Conway, using a 
different model, obtains the value h/z. Prof. McLaren 
identifies the natural unit of angular momentum with 
the angular momentum of the magneton. It has been 
pointed out (Phys. Zeitsch., vol. xii., p. 952, 1911) that 
Planck’s constant may be connected with the magnetic 
moment of the magneton. Suppose that an electron 
aed e, mass m) is moving in a circular orbit 
radius a) with angular velocity w. Then its angular 
momentum is ma*w, and the magnetic moment of the 
equivalent simple magnet is dea*w. 
netic moment is equal to some constant multiplied by 
he/m. ‘Taking (for illustration only) Bohr’s value for 
the angular momentum, we obtain as the magnetic 
moment 92x 10-°* E.M.U. The magnetic moment 
of the magneton, as given by Weiss, is a quantity of 
about the same order of magnitude, viz. 15-94 x 10-27. 
My chief object is to direct attention to the work 
of Prof. Carl Stormer, of Christiania, on the path of 
an electron in the magnetic field of an elementary 
magnet. It would be of great interest if it should 
prove that his results, originally obtained in connec- 
tion with cosmical problems, are applicable within the 
atom. In addition to computing the trajectories corre- 
sponding to different circumstances of projection in 
the field of an elementary magnet, he has investigated 
the corresponding problem when the electron is also 
under the action of a central force varying inversely 
as the square of the distance from the centre of the 
magnet (Videnskabs-Selskabets Skrifter, 1907, Chris- 
1 This view necessitates a larger estimate for the diameter of a complex 
nucleus than that at present accepted. 
Thus the mag- _ 
