_Optical Effect of Ether Drift through Dense Stationary Bodies._

The calculation of the lag in phase caused by Fresnel's etherial motion may proceed thus:--A dense slab of thickness _z_, which would naturally be traversed with the velocity V/, is traversed with the velocity (V/) cos e + (v/) cos ?; where _v_ is the relative velocity of the ether in its neighbourhood; whence the time of journey through it is

(z) / V(cos e + (a/) cos ?), instead of z/V,

So the equivalent air thickness, instead of being ( - 1)z, is

z / (cos e + (a/) cos ?) - z = ( ( cos e - a cos ?) / (1 - a/) - 1 )z,

or, to the first order of minutiae,

( - 1)z - az cos ?;

? being the angle between ray and ether drift inside the medium.

So the extra equivalent air layer _due to the motion_ is approximately a z cos ?, a quant.i.ty independent of .

Hence, no plan for detecting this first-order effect of motion is in any way a.s.sisted by the use of dense stationary substances; their extra ether, being stationary, does not affect the lag caused by motion, except indeed in the second order of small quant.i.ties, as shown above.

Direct experiments made by Hoek,[11] and by Mascart, on the effect of introducing tubes of water into the path of half-beams of light, are in entire accord with this negative conclusion.

Thus, then, we find that no general motion of the entire medium can be detected by changes in direction, or in frequency, or in phase; for on none of them has it any appreciable (i.e. first-order) effect, even when a.s.sisted by dense matter.

Another mode of stating the matter is to say that the behaviour of ether inside matter is such as to enable a potential-function,

? v cos? ds,

to exist throughout all transparent s.p.a.ce, so far as motion of ether alone is concerned. (See Appendix 3.)

The existence of this potential function readily accounts for the absence of all effect on direction due to the general drift of the medium, whether in the presence of dense matter (such as water-filled telescopes) or otherwise. Whatever may be the path of a ray by reason of reflexion or refraction in a stationary ether, it is precisely the same in a moving one if this condition is satisfied, although the wave-normals and wave-fronts are definitely shifted.

However matter affects or loads the ether inside it, it cannot on this theory be said either to hold it still, or to carry it with it. The general ether stream must remain unaffected, not only near, but inside matter, if rays are to retain precisely the same course as if it were relatively stationary.

But it must be understood that the etherial motion here contemplated is the _general drift of the entire medium_; or its correlative, the uniform motion of all the matter concerned. There is nothing to be said against aberration effects being producible or modifiable by motion of _parts_ of the medium, or by the artificial motion of transparent bodies and other part.i.tioned-off regions. _Artificial_ motion of matter may readily alter both the time of journey and the path of a ray, for it has no potential conditions to satisfy; it may easily describe a closed contour, and may take part in conveying light.

But I must repeat that this conveyance of light by moving matter is an effect due to the material load only; it represents no disturbance of the ether of s.p.a.ce. Fresnel's law, in fact, definitely means that moving transparent matter does _not_ appreciably disturb the ether of s.p.a.ce. Direct experiment, as recorded in Chapter V, shows that close to rapidly-moving opaque matter there is no disturbance either.

I regard the non-disturbance of the ether of s.p.a.ce by moving matter as established.

FOOTNOTES:

[10] _Philosophical Magazine_, Dec., 1887.

[11] _Archives Neerlandaises_ (1869), Vol. IV, p. 443, or _Nature_, Vol XXVI, p. 500. Also Chapter IV above.

SUMMARY.

The estimates of this book, and of _Modern Views of Electricity_, are that the ether of s.p.a.ce is a continuous, incompressible, stationary, fundamental substance or perfect fluid, with what is equivalent to an inertia-coefficient of 10 grammes per c.c.; that _matter_ is composed of modified and electrified specks, or minute structures of ether, which are amenable to mechanical as well as to electrical force and add to the optical or electric density of the medium; and that elastic-rigidity and all potential energy are due to excessively fine-grained etherial circulation, with an intrinsic kinetic energy of the order 10 ergs per cubic centimetre.

APPENDIX 1

ON GRAVITY AND ETHERIAL TENSION

In the arithmetical examples of Chapter IX we reckon merely the force between two bodies; but the Newtonian tension mentioned in Chapter VIII does not signify that force, but rather a certain condition or state of the medium, to variations in which, from place to place, the force is due. This Newtonian tension is a much greater quant.i.ty than the force to which it gives rise; and, moreover, it exists at every point of s.p.a.ce, instead of being integrated all through an attracted body.

It rises to a maximum value near the surface of any spherical ma.s.s; and if the radius be R and the gravitational intensity is _g_, the tension at the surface is T0 = gR. At any distance _r_, further away, the tension is T = gR/r.

This follows at once thus:--

Stating the law of gravitation as F = ?mm'/r, the meaning here adopted for etherial tension at the surface of the earth is

T = ?{R,8} ?E/r dr = ?E/R;

so that the ordinary intensity of gravity is

g = -dT/dR = ?E/R = 4/3p??R.

Accordingly, near the surface of a planet the tension is T0 = gR, or for different planets is proportional to ?R.

The velocity of free fall from infinity to such a planet is v(2T0); the velocity of free fall from circ.u.mference to centre, a.s.suming uniform distribution of density, is v(T0); and from infinity to centre it is v(3T0).

Expanding all this into words:--

The etherial tension near the earth's surface, required to explain gravity by its rate of variation, is of the order 6 10 c.g.s.

units. The tension near the sun is 2500 times as great (p. 103). With different spheres in general, it is proportional to the density and to the superficial area. Hence, near a bullet one inch in diameter, it is of the order 10?6; and near an atom or an electron about 10? c.g.s.

If ever the tension rose to equal the const.i.tutional elasticity or intrinsic kinetic energy of the ether,--which we have seen is 10 dynes per square centimetre (or ergs per c.c.) or 10 tons weight per square millimetre,--it seems likely that something would give way.

But no known ma.s.s of matter is able to cause anything like such a tension.

A smaller aggregate of matter would be able to generate the velocity of light in bodies falling towards it from a great distance; and it may be doubted whether any ma.s.s so great as to be able to do even that can exist in one lump.

In order to set up a tension equal to what is here suspected of being a critical, or presumably disruptive, stress in the ether [10 c.g.s.], a globe of the density of the earth would have to have a radius of eight light years. In order to generate a velocity of free fall under gravity equal to the velocity of light, a globe of the earth's density would have to be equal in radius to the distance of the earth from the sun, or say 26,000 times the earth's radius. If the density were less, the superficial area would have to be increased in proportion, so as to keep ? R constant.

The whole visible universe within a parallax of 1/1000 second of arc, estimated by Lord Kelvin as the equivalent of 10? suns, would be quite incompetent to raise etherial tension to the critical point 10 c.g.s. unless it were concentrated to an absurd degree; but it could generate the velocity of light with a density comparable to that of water, if _ma.s.s_ were constant.

If the average density of the above visible universe (which may be taken as 1.6 10? grammes per c.c.) continued without limit, a disruptive tension of the ether would be reached when the radius was comparable to 10 light years; and the velocity of light would be generated by it when the radius was 107 light years. But heterogeneity would enable these values to be reached _more_ easily.