520 
NATURE 
[Marcu 28, 1907 
Massiveness of the Ether. 
Each electron, moving like a sphere th ough a fluid, 
has a certain mass associated with it; dependent on its 
size, and, at very high speeds, on its velocity also. 
Now how shall that mass be treated? 
Shall we deal with it on the analogy of « sphere moving 
through a perfect irrotational liquid, without examining 
into details any further? 
Or shall we consider it as generatin,; circular lines 
of magnetic induction by its movement, by reason of the 
rotational properties of the ether, and attribute all its 
inertia to the magnetic whirl thus caused round its path: 
treating the whirl as an actual circulation of fluid excited 
by the locomotion? 
Both methods may be adopted, to see whether they will 
agree. 
Now treating it by the first method, and considering the 
electron merely as a sphere moving through a perfect 
liquid, its behaviour is exactly as if its mass were in- 
creased by half that of the fluid displaced and the surround- 
ing fluid were annihilated. It has been argued in the 
book, from the result of the Cavendish surface-charge 
experiment, and from the phenomena of gravitation, that 
the ether is incompressible, to a high degree of exactness ; 
and accordingly the density of fluid inside and outside an 
electron must be the same. So that, treating it in this 
simplest fashion, the resultant inertia is half as great again 
as that of the volume of fluid corresponding to the electron : 
that is to say, is 2mpa*, where p is the uniform density. If 
it is of some other shape than a sphere, then the numerical 
pate is modified, but remains of the same order of magni- 
tude. 
Now treat it by the other, or magnetic whirl, method. 
Let a spherical electron e of radius a be flying at speed 
u, so that the magnetic field at any point 16, outside, is 
Ha sin 6, 
2 
7 
and the energy per unit volume everywhere is #H*/8z. 
It has been shown by Lord Kelvin, Mr. Heaviside, 
G. F. FitzGerald, and Prof. Larmor, that a magnetic 
field may be thought of, hypothetically, as a circulation 
of fluid along the lines of magnetic induction—which are 
always closed curves—at some unknown velocity w. 
Consider the energy per unit volume anywhere, it can 
be represented by the equivalent expressions 
Apes HH? ge ex? sin? 8 
i 8x 8x /) 
wherefore 
On the cog-wheel analogy the highest velocity will be 
that in contact with the moving charge, and there is some 
reason to suppose that the maximum velocity w at the 
equator of the moving sphere may be equal to the speed u. 
Elsewhere it will decrease with the inverse square of the 
distance just as H decreases. 
But without any hypothesis, if there be a circulation at 
all, its velocity must be a maximum at the equator of the 
sphere, where r=o0 and @=90; so, calling this w,, 
and 
and therefore the major part of the circulation is limited 
to a region not far removed from the surface of the 
electron. 
The energy of this motion is 
us 
5 2 
ie| x . 2m7 sin 6 
Ua 
or substituting the above value of w the energy comes out 
equal to $zpa* w,”. 
WOP1Q52, VOT...75| 
7ae . ar, 
Comparing this with a mass moving with speed u, 
This agrees with the simple hydrodynamic estimate of 
efiective inertia, if w,—3/3u; that is to say, if the whirl 
in contact with the equator of the sphere is of the same 
order of magnitude as the longitudinal rack-motion or 
cog-wheel spin at the same place. 
Now for the real relation between w, and « we must 
make a hypothesis. If the two are considered equal, the 
effectively disturbed mass comes out as twice that of the 
bulk of the electron. If w, is much smaller than w, then 
the mass of the effectively disturbed fluid is much less 
even than the bulk of an electron; and in that case the 
estimate of the fluid-density p must be exaggerated 
enormously, in order to supply the required energy. It is 
difficult to suppose the equatorial circulation w, greater 
than u, since it is generated by it; and it is not unreason- 
able to treat them both as of the same order of magnitude. 
So, taking them as equal, 
e=a’ 4™p 
Mw 
and m=twice the spherical mass. 
Hence all the estimates of the effective inertia of an 
electron are of the same order of magnitude, being all 
comparable with that of a mass of ether equal to the 
electron in bulk. : 
This would also be the conclusion drawn, if, instead of 
integrating the magnetic energy from a to infinity, we 
integrated from a to a larger radius b, or say na; the 
inertia would then come out 
my yf 2(2—1) pe” 
Bae ( =) e 3 ce 
and be still of the same order of magnitude for all reason- 
able values of n; the reason being that all the effective 
disturbance is concentrated in the neighbourhood of the 
charge. 
Now the linear dimension of an electron is 10—** centi- 
metre diameter, and its mass is of the order 10—-* gram, 
being about the 1/7ooth part of the atom of hydrogen. 
Consequently, if its mass were due to its contents, the 
density of its material must be of the order 
10-27+10-°°=10" grams per cubic centimetre. 
1s 
This, truly, is enormous, but any reduction in the esti- 
mate of the circulation speed, below that of an electron, 
would only go to increase it; and since electrons move 
sometimes at a speed not far below that of light we can- 
not be accused of underestimating the probable velocity 
of magnetic spin by treating it as of the same order of 
magnitude, at the bounding surface of the electron: a 
relation suggested, though not enforced, by the cog-wheel 
and gyrostat analogy. 
Incidentally, we may notice how enormous is the 
magnetic field surrounding the equator of an electron 
moving along an axis with, say, one-thirtieth the speed of 
light: it amounts to 10’° C.G.S. lines per sq. centimetre. 
And the magnetic energy there is correspondingly 
enormous, being 4X107° ergs per c.c. At the velocity of 
light it would equal the constitutional energy of the ether 
itself. 
Value of the Ethereal Constants. 
It has been argued throughout the book that the 
ethereal density is what we know in magnetism as 47; 
wherefore an approximate estimate of the absolute value 
of the magnetic constant » for free space, on this view, 
is 10'* grams per c.c. 
Using the value 4ru=p, we get for the charge of an 
electron 
e=47a’, 
or comparable to its superficies. 
The speed with which waves travel through the medium 
is the square root of 107? C.G.S. ; consequently. the elas- 
ticity of the ether must be of the order 1o** dynes per 
square centimetre, which is what in static electricity we 
denote by 47/«. Wherefore an approximate estimate of 
