294 
NATURE 
[JANUARY 28, 1904 
The effect is to compress H in one half and expand it in 
the other half of a period, with corresponding strengthen- 
ing and weakening of intensity, and also with a shifting 
of the nodes towards the compressed part. When w/v is 
made large, there is a great concentration at $,;=@)=47, 
im, 447, &c., with only a weak disturbance of opposite 
sign between them. That is, there is a tendency to turn 
the original simply periodic vibration into periodic pulses, 
which become very marked as wu increases towards v. The 
radiation of energy is very rapid. It involves (l.c.) the 
factor (1—u*/v*)-*. This becomes so great as seemingly 
to shut out the possibility of anything more than momentary 
persistence of revolution. But there might be a solitary 
partial revolution, or nearly complete, in cometary fashion, 
which would generate a single pulse, if there cannot be a 
sequence of several at speeds nearly equal to that of light. 
Three suggestions have been made about the X-rays. 
R6ntgen suggested a longitudinal ether disturbance. This 
has not found favour, because it requires a new theory of 
electricity. Schuster suggested very rapid vibrations. 
This is tenable, because in the inside of an atom rudimen- 
tary calculations show that vibrations much more frequent 
than light are easily possible with revolving electrons. 
Stokes suggested collisional pulses. This is tenable too, 
for the collisions must produce electromagnetic pulses. I 
think X-rays are mixed Stokes pulses and Schuster vibra- 
tions, the latter arising from the atoms of the body struck. 
Now a pulse is not the same as a continued vibration, 
though it may be analysed into the sum of various sorts of 
continued vibrations, just as the distorted simply periodic 
vibration in (5) above may be. There ought, then, to be a 
physical difference between the effects of collisional pulses 
and continued very rapid vibrations. Apart from the 
emission of electrons and matter, there might be six sorts 
of radiation at least, say, light vibrations, below light, 
above light, collisional pulses, cometary pulses, and possibly 
periodic pulses. The last may have to be excluded for 
the reason mentioned. The cometary pulses would re- 
semble the collisional pulses, though less dense. The above 
light vibrations need not require w/v to be more than a 
small fraction, though even then their maintenance is a 
difficulty. They require renewal again and again, perhaps 
in a collisional manner. There is a good deal to be found 
out yet in the relations of electricity to matter. There is 
also sometimes a good deal of misconception as to the re- 
lations of theory to fact. A purely dynamical theory of 
electricity, like Maxwell’s, can give no information about 
the connection between electricity and matter. For ex- 
ample, Zeeman’s experiment, as interpreted by Lorentz, 
brought out the striking fact that it was the negative 
electricity that revolved, not seemingly the positive, and 
the fact harmonises with J. J. Thomson’s negative 
corpuscles. Theory could never predict such a fact, because 
it is not in the theory. It could not be there, because it 
has no dependence upon the dynamics of electricity in the 
theory. The same may be said of various other new facts 
much discussed of late. Now, though the theory cannot 
predict such facts, it is useful, of course, as a guide in 
framing hypotheses to account for the new facts, for it is 
no use flying in the face of solid theory. Whether the 
solid theory itself (not meaning that the ether is solid) will 
need to be altered remains to be seen. There is no sign 
of it yet, though I cannot believe the ethereal theory is 
complete. ; 
To analyse the dopplerised vibrations expressed by (1), 
(2) into simply periodic vibrations seemed to involve very 
complicated work at first, save just for two or three terms. 
But there is a trick in it, which, when found, allows the 
complete expansions to be developed in a few lines. First 
show that (this is the trick) 
a? cos $= — Zp? cos), a (sin ¢, — 8)= — 2 sin $,- (6) 
0 
‘0 db 
Next, by the theorem known as Lagrange’s, sin ¢, can be 
at once put in the form of a series involving the derivatives 
of various powers of cos ¢,. Do not find the derivatives 
from them, but put cos”, in terms of the sum of first 
powers of cosines by the well known circular formula. The 
NO. 1787, VOL. 69] 
full ditferentiations, not forgetting those in (6), may then 
be done at sight in one operation. ‘The result is 
a3(sin ¢,—8)=sin ¢,—B. 2 cos 2) — 28'(9 sin 3,+Sin ,) 
403 Bs ier patents 
+ *63(4 cos 4p) + cos 29) + — —( 5" Sin 5p + 5-3" SIN 3p 
33 |4 2 
+10 sin 0) = fe (6 cos 6p) + 6.44 cos 4) + 15.24 cos 200 ) 
=. ~ (7) 
and so on to any extent. Then, to find the other one, 
differentiate the series in (7) with respect to , and divide 
the nth term by n. Thus 
a cos @;=Cos $) + 2B sin 2) — q(27 COS 3) + cos 0) -...(8) 
and soon. This analysis of the vibrations is useful in some 
special developments, but of course the original distorted 
simple vibration is the most significant. In fact, the result 
of the analysis exhibits the common failing of most series 
developments that the resultant meaning is not evident. 
Another way. Use Bessel’s series for the sine and cosine 
of ,, and then carry out (6). It is remarkable that the 
relation between the eccentric and mean anomaly in a 
planetary orbit should be imitated, for the dynamics is quite 
different. ; 
When I was a young child I conceived the idea of an 
infinite series of universes, the solar system being an atom 
in a larger universe on the one hand, and the mundane atom 
a universe to a smaller atom, and so on. I do not go so 
far as that now, but only observe that there is a tendency 
to make the electrons indivisible, and all exactly alike. But 
they must have size and shape, and be therefore divisible. 
Unless, indeed, they are infinitely rigid. Or they may vary 
in shape without dividing. There are infinite possibilities 
in the unknown. Kaufmann’s measurements go to show 
that the mass of an electron, if there is any, is only a small 
fraction of its effective electromagnetic mass, although that 
is not a definite quantity subject to the Newtonian second 
law. But it is too soon to say that the electron has no 
mass at all, that is, to be quite sure that negative electricity 
is absolutely separable from matter, though it seems likely. 
It would be well to have, if possible, similar measurements 
made on positive electricity. If permanently attached to 
matter, it should not exhibit the increased inertia with in- 
creased speed in a sensible manner. 
January 11. OLIVER HEAVISIDE. 
Atmospheric Electricity. 
Your correspondent Mr. George Simpson truly points out 
that the sun’s « rays would be stopped by the upper atmo- 
sphere, whereas his 6 rays would penetrate much further ; 
and perhaps he may have also noticed that an energetic 
separation of these oppositely charged rays would be effected 
by the earth’s magnetic field, the negative being conveyed 
toward the poles, and the positive remaining near the tropics 
along with the maximum sunshine. 
Consequently quadrantal earth-currents would be gener- 
ated, and likewise a Leyden jar action would be set up 
in the tropical region of the lower atmosphere, sufficient to 
account for prevalent tropical thunderstorms. Some mag- 
netic perturbations could also be accounted for. 
Otiver LopGcE. 
Nomenclature and Tables of Kinship, 
A circutar letter, arranged like the following, is about 
t» be issued for carrying out certain inquiries into heredity, 
and I am anxious, before taking a more definite step, to 
have it criticised and to receive suggestions. I send it to 
Nature not only for my own advantage, but because I 
think it will interest those readers who occupy themselves 
in analysing experiences in breeding animals of any kind, 
although this table has been specially designed to receive 
hereditary facts concerning man. : 
The processes that it is desired to facilitate are, in out- 
