392 
NATURE 
[ FEBRUARY 25, I904 
LETTERS, TO DHE EDITOR: 
(The Editor does not hold himself responsible for opinions 
expressed by his correspondents. Neither can he undertake 
to return, or to correspond with the writers of, rejected 
manuscripts intended for this or any other part of NaTuRE. 
No notice is taken of anonymous communications.] 
Cancer and Parthenogenesis. 
May I be allowed to refer to the interesting and stimu- 
jating discoveries of Messrs. Farmer, Moore and Walker, 
and Drs. Bashford and Murray? The former have demon- 
strated that nuclear changes occur in cancerous tissues, by 
which cells of malignant growths may be justly considered 
homologous to active sexual elements (‘‘ gametoid ’’). 
Giant cells are suggested to be “‘ fusion-figures ’? which 
recall normal fertilisation (sic) in cancer. : 
I write to ask if botanists or zoologists are of the opinion 
that *‘ post-heterotypic ’’ cells (homotypic) are ‘‘ inclined ”’ 
at all to develop without fertilisation by the spermatozoon 
(t.e. by parthenogenesis from ? chemical stimulus). 
Does parthenogenesis occur in the embryosac of flower- 
ing plants or in the prothallium of the higher cryptogams 
under any and what conditions? 
On what known states does parthenogenesis in the eggs 
of the honey bee, in ascaris, in artemisia, &c., depend ? 
This sexual character of the cells of cancer explains partly 
its parasitic and invading nature; the wonderful power of 
mimicry of the tissues from which they originate suggests 
that metastases commence as cells self-fertilised and 
maturating. A knowledge of the (? chemical) causes 
underlying both these changes might afford a clue to pre- 
vention. F. BUSHNELL. 
5S. Devon Hospital and Public Dispensary, Plymouth. 
In reply to the queries contained in the letter of Dr. 
Bushnell, it may at once be said that parthenogenesis is 
known to follow the application of certain stimuli in the 
ease of a few animals and plants, Loeb’s experiments on 
sea-urchins and Nathansohn’s observations on Marsilea 
furnishing instances to the point. 
Parthenogenesis occurs in the embryosac of species of 
Alchemilla, perhaps also in some species of figs, but the 
underlying conditions are not yet understood. 
In other examples of parthenogenesis, as noted in animals, 
it arises in consequence of the lack of separation of the 
second polar body from the egg, or follows on the re-fusion 
of it with the egg. This represents, perhaps, a modified 
kind of fertilisation. Apogamy as occurring in ferns is 
a more remote event, but is apparently possessed of a similar 
significance. 
I quite agree with Dr. Bushnell as to the importance of 
reaching an understanding of the chemical and _ other 
agencies that produce the change in cells previously normal, 
and the concluding paragraph of the article to which he 
refers emphasises this side of the subject. 
J. B. Farmer. 
Magdalen College, Oxford, February 13. 
On a Dynamical System illustrating the Spectrum 
Lines and the Phenomena of Radio-activity. 
By the study of a system of particles, which is similar 
to a Saturnian system, I was led to the discussion of dis- 
turbances which propagate in the system, having close 
analogy with the band and line spectra’ while illustrating 
the phenomena of radio-activity. . The system consists of 
a large number of particles of equal mass arranged in a 
circle at equal angular intervals, and repelling each other 
with forces inversely proportional to the square of distance 
between the particles; at the centre of the circle is placed 
a large particle attracting the other particles forming the 
ring according to the same law of force. If the repelling 
particles. be revolving about the attracting centre, the 
system will, generally remain stable for small oscillations, 
which. consist of the transversal vibration perpendicular to 
the plane of the orbit, together with the radial and angular 
disturbances representing the rarefaction and condensation 
in the distribution of the particles. Small oscillations of 
this kind have already been treated by Maxwell in his essay 
NO. 1791, VOL. 69] 
on the stability of Saturn’s rings; the system will be the 
same if the repelling particles of the present system be sub- 
stituted by the attracting satellites. Evidently the system 
here considered will be approximately realised if we place 
negative electrons in the ring and a positive charge at the 
centre. Such an ideal atom will not be contradictory to 
the results of recent experiments on kathode rays, radio- 
activity, and other allied phenomena. 
The frequency of the transversal vibration is given by 
n=w—am?>+bm*+ 
where w is the principal term and m the whole number. 
Plotting the lines of frequency, we find the crowding of 
lines when the value of m is small and when it is large. 
Generally the coefficient a>o, so that with increasing m 
the frequency decreases, and the interval between the lines 
becomes wider. The distribution of lines resembles that of 
a band spectrum proceeding from violet towards the red. 
Taking the converging point of the lines for large values 
of m as the beginning, it is convenient to count the lines 
from the point, which I suppose to correspond to m=m,. 
Then putting 
St GOs 
' 
m=m,—m 
we obtain, remembering that 6n=o0 for m=m,, 
n=w'+a'm'?+blme+ 
| m increases with m’, and the distribution resembles the band 
spectrum of carbon type, the interval between the lines 
gradually widening from red towards the violet. In fact, 
the above equation is an extension of Deslandres’s formula. 
If we suppose that the particles are negative electrons, we 
can easily prove that the transversal vibration will not be 
sensibly affected by the external magnetic field. This is 
another characteristic of the band spectrum. 
The radial and angular waves propagating round the 
ring have frequencies given by 
C = 
V1 Am? +Bmi+... 
The distribution of lines is such that they crowd together 
for tolerably large values of m towards a region of high 
frequency, and is in its general aspect similar to a band 
spectrum, with the difference that the interval between the 
successive lines is about nine times wider than in the band 
spectrum above described. This we may identify with the 
line spectrum, although m is not the same as in the formula 
of Kayser and Runge, or of Rydberg. ‘The supposition that 
the particles are electrons leads to the conclusion that a 
single line is separated into doublets, circularly polarised 
in Opposite senses. 
The ring here considered is quasi-stable. It may be set 
to disturbances the radial and angular components of which 
are nearly proportional to 
n= 
pvt 
Cams 
where k is a constant, vy the number of particles in a ring, 
and t the time. If the disturbance continues for a 
sufficiently long time, the ring will be torn asunder and the 
system will fly off with great velocity. If the particles are 
electrons, those in the ring will give rise to B rays, and the 
central positive charges will form the a rays. 
The ideal atom here considered will have 
weight when v is large; consequently the 
easier to produce when the atom is massive. Where there 
are several series of regular spectra we shall have to con- 
sider different rings of particles giving rise to these different 
sets. The complexity of spectrum is by no means a 
guarantee for the heaviness of atom; on the contrary, if 
high atomic weight is accompanied with comparatively 
simple spectral structure, we may consider that the system 
of rings is less complex, and » may be quite a large 
quantity. This probably accounts for the remarkable’ radio- 
active property of radium, which, in spite of its high atomic 
weight, presents only a certain number of characteristic 
spectrum: lines. 
The kinetics of the system here considered may be ex- 
tended to investigations which have analogies with the 
flutings of spectrum lines. Considered as electrons, the 
phenomena of actino-electricity, the ionisation of flames, the 
change of resistance of semi-insulators by exposure to light, 
the problem of coherer, the phenomena of fluorescence and 
high atomic 
instability is 
