8 NATURE 
[MarcH 4, 1915 

x 
perature and u=| C,aT, where C, is the atomic heat. 
° 
The fact that emerges most clearly from all the 
work done on this subject is that the atomic heats 
of similar substances may all be represented by the 
same function f(vy of the atomic frequency v. There- 
fore, if A is the same for isotopes, and this would seem 
to be the definition of the word, their atomic frequen- 
cies must be identical. But as v is a function of the 
atomic weight and of the forces acting between the 
atoms, the latter must vary when the atomic weights 
are different. If the force of attraction between two 
atoms is ag(r) and the repulsive force by(r), r being 
the distance, then at a sufficiently low temperature 
the quasi-elastic force holding an atom in position is 
a= 2h(ap'(x)—bw'(7)). The constant k represents the 
action of the surrounding atoms and depends only 
upon the type of space-lattice formed by the atoms. 
. c I Tay . 
As the atomic frequency v=— Re “ is the same for all 
27 
M 
ap (r) = b'(7) 
MERE 
atomic weight M may be. © As Prof. Soddy has shown 
that the atomic volume and consequenily r is also con- 
stant, it follows that both a and b must be proportional 
to the atomic weight. 
This conclusion might, perhaps, be tested by a 
measurement of the vapour pressure of the different 
sorts of lead. The latent heat of sublimation \ is pro- 
oO ‘co 
isotopes, must be identical, whatever the 
proportional to af rar W(7)a7, that is to M, as vis 
r (3 
in both cases. 
the same The well-known equation 
slits as where p is the vapour pressure, leads to 
6 
AT — Ag 
eR 

if the 
be 
chemical constant is equal. This is of the order e! 
if M varies by 0-26 per cent, 7.e. about 20 per cent. at 
too? C.. The vapour pressure of radium D the atomic 
360 
weight of which is 210 should be about ¢7 times less 
than that of ordinary lead, that is, 2:6 times less at 
100° C. 
Another posible test would be to measure the melting 
[Tn As 
M7 
v cannot vary, and as Prof. Soddy has shown that r is 
constant, the melting point T,, should be propor- 
tional to M. Thus, for instance, the melting point 
of Prof. Soddy’s lead should be 1-54° higher than that 
of ordinary lead. In all probability the atomic weight 
of the final product of thorium is 2084, in which case 
the difference in the melting point should be as much 
as 3-75°. These consequences are not necessary but, 
admitting the absolute chemical identity, highly 
probable. They include the assumption that the 
radii of the atoms are equal as well as _ their 
In any case, 
as the ratio of the vapour pressures, 
point. In a great. many cases v=const. A/ 
mean distance apart in the solid state. 
a measurement would seem well worth while, as a 
negative result would be of almost as great interest 
as if a difference were observed. Unfortunately, the 
elastic constants which should vary by a corresponding 
amount can scarcely be measured with sufficient 
accuracy. 
The following conclusions about the structure of the 
atom would seem to result. The purely chemical 
properties are determined by the external electrons 
which probably also account for the apparent radius 
of the atom. The forces of attraction and repulsion 
between the atoms, the interaction of which results in 
NO. 2366, VOL. 95] 

the solid state, have their origin in the nucleus. In 
isotopes they are proportional to the atomic weight, 
i.e. probably to the number of positive particles. They 
cannot, however, be considered simply as the sum of 
the forces between the positive particles, as they are 
additive only in isotopes, that is, when the charge on 
the nucleus is equal. The simplest assumption, there- 
fore, would appear to be that the nuclei of isotopes 
differ in their linear dimensions, but not at all, or 
only very little, in the arrangement of the particles. 
: ; F. A. LINDEMANN. 
Sidholme, Sidmouth, February to. 
The Green Flash. 
Pror. Porrer’s explanation of the green flash 
(Nature, February 18) is unable to account for its 
appearance at sunrise, when it can be observed with 
great brilliance. When I was passing through the 
Indian Ocean on my way to observe the total eclipse 
of 1875 I happened to be on deck before sunrise one 
morning, and, watching for the first ray of the sun, 
was surprised to see the first flash of light appear as 
a vivid green. I had never heard of the phenomenon 
before, but atmospheric dispersion seemed to me 
sufficient to account for it, and I took it for 
granted that it was a well-known occurrence. I con- 
tinued to observe the same effect several mornings 
in succession. 
Since then I have undertaken many sea journeys, 
and though I do not recollect having ever again 
observed the flash or tried to observe it at sunrise, 
I have never lost an opportunity of watching for it 
at sunset. My experience does not support Prof. 
Porter’s explanation, because the redder the sun at 
sunset, the less likely is the green flash to appear. 
The atmospheric conditions must be such that there 
is as little absorption as~ possible of the more re= 
frangible part of the spectrum. 
Those who want to see the appearance at its best 
should keep one eye closed as long as possible, and 
when the sun is just about to disappear, shut the 
eye which has been watching the setting sun, and 
open the other, which is then unaffected by the trouble- 
some after-images which are otherwise seen. It is, 
of course, impossible to open the eye just at the 
critical moment, so that this alone is not sufficient 
to disprove Prof. Porter’s explanation. 
ARTHUR SCHUSTER. 
Yeldall, Twyford, Berks., February 21. ; 

Hormones and Heredity. 
Tue reviewer of Mr: H. Elliot’s 
Lamarck’s ‘* Philosophie Zoologique’’ in Nature of 
February 11 remarks: ‘*Unless we have misunder- 
stood, a similar suggestion was made by Mr. J. T. 
Cunningham in 1908.’ The word ‘“‘similar’’ refers 
to an alleged suggestion by Prof. MacBride that 
hormones may afford a clue to a possible modus 
operandi of the transmission of modifications. I 
should be glad to know when and where Prof. Mac- 
Bride’s suggestion was published, as | have not 
heard of it before. It would seem from the terms 
of this review that neither Mr. H. Elliot nor J. A. T. 
are fully acquainted with my paper on the heredity 
of secondary sexual characters in relation to hor- 
mones, published in the Archiv fiir Entwicklungs- 
mechanik in 1908. The hormone theory of heredity 
is elaborated in considerable detail in my paper. I 
do not think it is possible te misunderstand it, and 
it is much more than a “suggestion.” 
J- T. CunnNINGHAM. 
S.W. Polytechnic, Chelsea, February 15. . 
translation of 
Ir seemed to me that there was some historical 
interest in recalling Mr. Cunningham’s paper of 1908- 
