MakcH 10, 1904] 
NATURE 437 
3 
by the late Sir George Stokes and Prof. J. J. Thomson, it is to 
be expected that Réntgen rays would be set up at the sudden 
starting as well as at the sudden stopping of the electron 
or B particle. As a result of the sudden expulsion of the 6 
particle from radium, it is to be expected that a narrow 
electromagnetic pulse, i.e. a ‘‘ hard ’’ or penetrating type of 
R6ntgen rays, would be generated. In addition, on account 
of the great speed of the B particle, it is able to penetrate 
through a considerable thickness of matter before it is 
stopped. A broad pulse or “‘ soft’’ Rontgen rays should 
thus arise at the point of incidence of the f rays. 
E. RUTHERFORD. 
McGill University, Montreal, February 18. 
Learned Societies. 
My attention has recently been directed to the letters of 
Messrs. Buchanan and Heaviside, and I quite agree that 
the existing system of referring papers by learned societies 
is capable of great improvement. But what I wish to point 
out is that every author who feels aggrieved has a remedy 
in his own hands, which consists in abstaining for the 
future from sending papers for publication to the society 
against which he has cause of complaint. 
A sufficient supply of papers for publication in their Trans- 
actions or Proceedings constitutes the life-blood of the 
societies to which I refer, and if the supply were cut off 
these societies would soon die of inanition. At the present 
day there are a large number of mathematico-physical peri- 
odicals, most of which supply authors with a reasonable 
number of gratuitous copies of their paper for private dis- 
tribution, so that authors gain the same advantages which 
learned societies offer them, without being subjected to the 
disadvantage of having their papers referred to a secret 
inquisition composed of persons whom I can testify, from 
personal experience as a former councillor of a learned 
society, frequently know far less about the subject-matter 
of the paper than the author does, and whose reports, to my 
own personal knowledge, have frequently contained errors 
from not understanding the papers. 
There is absolutely no reason why authors should employ 
learned societies as the medium for the publication of their 
papers, and if they have a legitimate cause of complaint 
against any particular society, the practical and common 
sense course to pursue is to boycott it. If this were done, it 
would soon be possible to start a *‘ British Journal of Mathe- 
matics and Physics ’’ on the same lines as the American and 
various other foreign journals, the absence of which consti- 
tutes a very serious blot upon British scientific enterprise. 
A. B. Basset. 
Grand Hotel, Alassio, Italy, March 3. 
A Dynamical System illustrating the Spectrum Lines 
and the Phenomena of Radio-activity. 
In Nature of February 25 there appeared a letter by 
Prof. Nagaoka, of Tokyo, relative to the stability and 
vibrations of a ring of negative electric charges revolving 
about a central positive charge. Prof. Nagaoka states that 
such a-system is generally stable, but as the result of an 
investigation by the method used by Maxwell for Saturn’s 
ring, I came to the conclusion some five years ago that 
the system is unstable if the law of electric force be that 
of the inverse square and the magnetic force be neglected. 
Consequently I thought the result not worth publication, 
but in view of Prof. Nagaoka’s letter it may now be of 
interest to your readers. 
Maxwell (‘‘ Collected Papers,’’ vol. i. p. 315) finds the 
frequency equation for displacements perpendicular to the 
plane of a ring of revolving satellites to be 
n?=S+(R/u)J, 
where S is the mass of Saturn, R/u that of each satellite, 
and the radius of the ring is unity. The displacements are 
of the type ¢=C cos (mé+n't+-y), where C, y are arbitrary 
constants, @ is the arc from a point of the ring to the 
satellite, and m is an integer. 
If p be the number of satellites and r an integer, we 
have 
J== sin? m6/2 sin® @ 
NO. 1793, VOL. 69] 
with 6=rz/p; the summation is taken for all values of r 
from 1 to p—1/2 if y be odd, and from r to p/2 if p be even, 
with the coefficient 4 for the last term in place of 3. The 
disturbance which is most likely to cause instability is that 
for which m=p—1/2, or p/2, as the case may be. 
In the electrical problem R/z is to be replaced by 
—e*/Ma*, if e be the charge and M the mass of each 
electron of the ring of radius a; the minus sign is due to 
the fact that the electrons repel each other. S is to be re- 
placed by + qe*/Ma’*, if the central positive charge be qe. 
The frequency equation now is 
n!* —(e*/Ma*) (q—J). 
In the same way the angular velocity w is given by the 
equation 
w?=(e*/Ma*) (q—K), 
where 
Kees e/2esinn os 
Steady motion is possible so long as q>K; this motion is 
stable (for these disturbances) if q>J. 
All the terms of K and J are positive, and the lower terms, 
due to charges near the one considered, increase very rapidly 
as p increases. Ultimately K is of order p log p, and J of 
order p* log p. The first few values are as follows :— 
SN 2 NS NEA Ns pe oN Bef] ol 
Foes llors 3) fis16) |-249 Ns on G4 rasa) itso ence 
I find that K>% when > 472 about ; obviously |> when p> 7. 
For an electrically neutral system it follows that p <8. 
Prof. Nagaoka considers the motion to be quasi- 
stable ; let us therefore consider the value of n/ when p=8. 
In this case K=2-80. Thus w’*=(e?/ma‘)x5-2, and 
nw? = — w X3-2/5:2, n’ = J—1w X078. The time in which 
the disturbance is multiplied «*” times, that is, 535 times, 
is thus 1-27 x the period of revolution; this implies a high 
degree of instability for p=8, and a fortiori for p>8. 
Let us now consider the radial and tangential disturb- 
ances; let their frequency be xw. The frequency equation 
is of the form 
(x? —a)’=b—cx, 
where a is a positive constant, and b>a’; c is smaller than 
either, and, in fact, vanishes when m=p/2. In the Saturn 
problem b can be made less than a* by making the number 
of satellites small enough, but in the electrical problem this 
cannot be done. 
Since b=o for m=p/2, all arrangements of an even 
number of electrons in a ring are unstable; this excludes 
p=2, 4 and 6. 
When m=(p—1)/2, I find for 
23) a=0'44, b=1°23, 6=0°24'; 
5: O55; 380, 0°47 3 
Fie 0°85, 10 80, 0°66. 
The parabolas 
y=x*—a and y=b—cx 
in these cases intersect in only two points; thus two fre- 
quencies are imaginary, and the system is unstable. 
Of course, the whole investigation assumes symmetrical 
arrangement of the electrons. When there are three rings 
the frequency equations involve toroidal functions and are 
difficult to deal with. The effect of magnetic force has not 
been taken into account, but I do not see any reason why 
it should seriously affect the conclusions. 
G. A. Scnorr. 
University College of Wales, Aberystwyth, February 29. 
P.S.—I am at present examining the case of three or more 
rings; the axial motion for three rings can be made stable 
by taking the radii nearly equal and the electrons of the 
middle ring of opposite sign to those of the other two; as 
to the radial and tangential motions, I am not yet able 
to express an opinion. Two rings are obviously unstable. 
March 7. 
The -Rays. 
In trying to repeat Blondlot’s experiments I have met 
with the usual lack of success, but one experiment I have 
made seems worthy of record. A small quantity of radium 
salt was accidentally spilled upon a barium platinocyanide 
screen, which consequently became faintly luminous in the 
dark. The light was very faint, and in order to see it more 
