_Gravitation_ is thus supposed to be the result of a mechanical tension inherently, and perhaps instantaneously, set up throughout s.p.a.ce whenever the etherial structure called an electric charge comes into existence; the tension being directly proportional to the square of the charge and inversely as its linear dimensions. _Cohesion_ is quite different, and is due to a residual electrical attraction between groups of neutral molecules across molecular distances: a variant or modification of chemical affinity.
APPENDIX 2
CALCULATIONS IN CONNEXION WITH ETHER DENSITY
Just as the rigidity of the ether is of a purely electric character, and is not felt mechanically--since mechanically it is perfectly fluid,--so its density is likewise of an electromagnetic character, and again is not felt mechanically, because it cannot be moved by mechanical means. It is by far the most stationary body in existence; though it is endowed with high intrinsic energy of local movement, a.n.a.logous to turbulence, conferring on it gyrostatic properties.
Optically, its rigidity and density are both felt, since optical disturbances are essentially electromotive. Matter loads the ether optically, in accordance with the recognised fraction (-1) / ; and this loading, being part and parcel of the _matter_, of course travels with it. It is the only part amenable to mechanical force.
The mechanical density of matter is a very small portion of the etherial density; whereas the optical or electrical density of matter--being really that of ether affected by the intrinsic or const.i.tutional electricity of matter--is not so small. The relative optical virtual density of the ether inside matter is measured by ; but it may be really a defect of elasticity, at least in non-magnetic materials.
Electrical and optical effects depend upon _e_. Mechanical or inertia effects depend upon e. Electric charges can load the ether optically, quite appreciably; but as regards mechanical loading, the densest matter known is trivial and gossamer-like compared with the unmodified ether in the same s.p.a.ce.
_Ma.s.siveness of the Ether deduced from Electrical Principles._
Each electron, moving like a sphere through a fluid, has a certain ma.s.s a.s.sociated with it; dependent on its size, and, at very high speeds, on its velocity also.
If we treat the electron merely as a sphere moving through a perfect liquid, its behaviour is exactly as if its ma.s.s were increased by half that of the fluid displaced and the surrounding fluid were annihilated.
Ether being incompressible, the density of fluid inside and outside an electron must be the same. So, dealing with 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 the effective ma.s.s is 2p?a, where ? is the uniform density. If an electron is of some other shape than a sphere, then the numerical part is modified, but remains of the same order of magnitude, so long as there are no sharp edges.
If, however, we consider the moving electron as generating circular lines of magnetic induction, by reason of some rotational property of the ether, and if we attribute all the magnetic inertia to the magnetic whirl thus caused round its path,--provisionally treating this whirl as an actual circulation of fluid excited by the locomotion,--then we shall proceed thus:--
Let a spherical electron _e_ of radius _a_ be flying at moderate speed _u_, so that the magnetic field at any point, _r?_, outside, is
H = eu sin? / r,
and the energy per unit volume everywhere is H/8p.
But a magnetic field has been thought of by many mathematicians as a circulation of fluid along the lines of magnetic induction--which are always closed curves--at some unknown velocity _w_.
So consider the energy per unit volume anywhere: it can be represented by the equivalent expressions
?w = H/8p = /8p eusin? / r;
wherefore
w/u = v(/4p?) e sin? / r.
The velocity of the hypothetical circulation must be a maximum at the equator of the sphere, where r=a and ?=90; so, calling this _w0_,
w0/u = v(/4p?) e / a,
and
w/w0 = a sin? / r;
wherefore 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
? ?{0,p} ?{a,8} w 2p r sin ? rd? dr,
whence, subst.i.tuting the above value of _w_, the energy comes out equal to 4/3 p?a w0.
Comparing this with a ma.s.s moving with speed _u_,
m = 8/3 p?a(w0/u).
This agrees with the simple hydrodynamic estimate of effective inertia if w0 = v3u; that is to say, if the whirl in contact with the equator of the sphere is of the same order of magnitude as the velocity of the sphere.
Now for the real relation between _w0_ and _u_ we must make a hypothesis. If the two are considered equal, the effectively disturbed ma.s.s comes out as twice that of the bulk of the electron. If _w0_ is smaller than _u_, then the ma.s.s of the effectively disturbed fluid is less even than the bulk of an electron; and in that case the estimate of the fluid-density ? must be _exaggerated_ in order to supply the required energy. It is difficult to suppose the equatorial circulation _w0_ _greater_ than _u_, since it is generated by it; and it is most reasonable to treat them both as of the same order of magnitude. So, taking them as equal,
e = a v(4p?/)
and m = twice the spherical ma.s.s.
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 ma.s.s of ether equal to the electron in bulk. But the linear dimension of an electron is 10? centimetre diameter, and its ma.s.s is of the order 10?7 gram. Consequently the density of its material must be of the order 10 grams per cubic centimetre.
This, truly, is enormous, but any reduction in the estimate 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 cannot be accused of under-estimating the probable velocity of magnetic spin by treating it as of the same order of magnitude, at the bounding surface of the electron, as its own speed: a relation suggested, though not enforced, by gyrostatic a.n.a.logies.
_Some Consequences of this Great Density._
The amplitude of a wave of light, in a place where it is most intense, namely near the sun where its energy amounts to 2 ergs per c.c., comes out only about 10?7 of the wave-length. The maximum tangential stress called out by such strain is of the order 10 atmospheres.
The hypothetical luminous circulation-velocity, conferring momentum on a wave-front, in accordance with Poynting"s investigation, comes out 10? cm. per sec. These calculations are given in the concluding chapter of the new edition of _Modern Views of Electricity_.
The supposed magnetic etherial drift, along the axis of a solenoid or other magnetic field, if it exist, is comparable to 003 centim. per sec., or 4 inches an hour, for a field of intensity 12,000 c.g.s.
But it is not to be supposed that this hypothetical velocity is slow everywhere. Close to an electron the speed of magnetic drift is comparable to the locomotion-velocity of the electron itself, and may therefore rise to something near the speed of light; say 1/30th of that speed: but in spite of that, at a distance of only 1 millimetre away, it is reduced to practical stagnation, being less than a millimicron per century.
In any solenoid, the ampere-turns per linear inch furnish a measure of the speed of the supposed magnetic circulation along the axis--no matter what the material of the core may be--in millimicrons per sec.
[1 micron = 10?6 metre; 1 millimicron is 10?? metre = 10?7 centimetre, or a millionth of a millimetre.]
To get up an etherial speed of 1 centimetre per second--such as might be detected experimentally by refined optical appliances, through its effect in accelerating or r.e.t.a.r.ding the speed of light sent along the lines of magnetic force,--would need a solenoid of great length, round every centimetre of which 1000 amperes circulated 3000 times. That is to say, a long field of four million c.g.s. units of intensity.
In other words, any streaming along magnetic lines of force, such as could account for the energy of a magnetic field, must be comparable, in centimetres per second, to one four-millionth of the number of c.g.s. units of intensity in the magnetic field.