This leads us to enter upon the question of whether it is possible to determine with any approach to accuracy the actual density or massiveness of the ether of space, compared with those forms of matter to which our senses have made us accustomed.

The arguments on which an estimate may be made of the density or massiveness of the ether as compared with that of matter depend on the following considerations, the validity of which again is dependent upon an electrical theory of matter. In this theory, or working hypothesis, an assumption has to be made: but it is one for which there is a large amount of justification, and the reasons for it are given in many books,—among others in my book on Electrons, and likewise at the end of the new edition of Modern Views of Electricity, also in my Romanes Lecture, published by the Clarendon Press in 1903. Put briefly, the assumption is that matter is composed, in some way or other, of electrons; which again must be considered to be essentially peculiarities, or singularities, or definite structures, in the ether itself. Indeed, a consideration of electrons alone is sufficient for the argument, provided it be admitted that they have the mass which experiment shows them to possess, and the size which electrical theory deduces for them: the basis of the idea—which, indeed, is now experimentally proved—being that their inertia is due to their self-induction,—i.e. to the magnetic field with which they must be surrounded as long as they are in motion.

The mass, or inertia, of an electron is comparable to the thousandth part of that of the atom of hydrogen. Its linear dimension, let us say its diameter, is comparable to the one-hundred-thousandth part of what is commonly known as molecular or atomic dimension; which itself is the ten-millionth part of a millimetre.

Hence, the mass and the bulk of an electron being known, its density is determined, provided we can assume that its mass is all dependent on what is contained within its periphery. But that last assumption is one that quite definitely cannot be made: its mass is for the most part outside itself, and has to be calculated by magnetic considerations. (See Appendix 2.)

These details are gone into in my paper in the Philosophical Magazine for April, 1907, and in Chapter XVII of Modern Views of Electricity. But without repeating arguments here, it will suffice to say that although the estimates may be made in various ways, differing entirely from each other, yet the resulting differences are only slight; the calculated densities come out all of the same order of magnitude, namely, something comparable to 10¹² C.G.S. units,—that is to say, a million million grammes per cubic centimetre, or, in other words, a thousand tons to the cubic millimetre.

But, throughout, we have seen reason to assert that the ether is incompressible; arguments for this are given in Modern Views of Electricity, Chapter I. And, indeed, the fundamental medium filling all space, if there be such, must, in my judgment, be ultimately incompressible; otherwise it would be composed of parts, and we should have to seek for something still more fundamental to fill the interstices.

The ether being incompressible, and an electron being supposed composed simply and solely of ether, it follows that it cannot be either a condensation or a rarefaction of that material, but must be some singularity of structure, or some portion otherwise differentiated. It might, for instance, be something analogous to a vortex ring, differentiated kinetically, i.e. by reason of its rotational motion, from the remainder of the ether; or it might be differentiated statically, and be something which would have to be called a strain-centre or a region of twist, or something which cannot be very clearly at present imagined with any security; though various suggestions have been made in that direction.

The simplest plan for us is to think of it somewhat as we think of a knot on a piece of string. The knot differs in no respect from the rest of the string, except in its tied-up structure; it is of the same density with the rest, and yet it is differentiated from the rest; and, in order to cease to be a knot, would have to be untied—a process which as yet we have not learned how to apply to an electron. If ever such a procedure becomes possible, then electrons will thereby be resolved into the general body of the undifferentiated ether of space,—that part which is independent of what we call "matter."

The important notion for present purposes is merely this: that the density of the undifferentiated or simple ether, and the density of the tied-up or be-knotted or otherwise modified ether constituting an electron, are one and the same. Hence the argument above given, at least when properly worked out, tends to establish the etherial density as of the order 10¹² times that of water.

There ought to be nothing surprising (though I admit that there is something very surprising) in such an estimate; inasmuch as many converging lines of argument tend to show that ordinary matter is a very porous or gossamer-like substance, with interspaces great as compared with the spaces actually occupied by the nuclei which constitute it. Our conception of matter, if it is to be composed of electrons, is necessarily rather like the conception of a solar system, or rather of a milky way; where there are innumerable dots here and there, with great interspaces between. So that the average density of the whole of the dots or material particles taken together,—that is to say, their aggregate mass compared with the space they occupy,—is excessively small.

In the vast extent of the Cosmos, as a whole, the small bulk of actual matter, compared with the volume of empty space, is striking—as we shall show directly; and now on the small scale, among the atoms of matter, we find the conditions to be similar. Even what we call the densest material is of extraordinarily insignificant massiveness as compared with the unmodified ether which occupies by far the greater proportion of its bulk.

When we speak of the density of matter, we are really though not consciously expressing the group-density of the modified ether which constitutes matter,—not estimated per unit, but per aggregate; just as we might estimate the group or average density of a cloud or mist. Reckoned per unit, a cloud has the density of water; reckoned per aggregate, it is an impalpable filmy structure of hardly any density at all. So it is with a cobweb, so perhaps it is with a comet's tail, so also with the Milky Way, with the cosmos,—and, as it now turns out, with ordinary matter itself.

For consider the average density of the material cosmos. It comes out almost incredibly small. In other words, the amount of matter in space, compared with the volume of space it occupies, is almost infinitesimal. Lord Kelvin argues that ultimately it must be really infinitesimal (Philosophical Magazine, Aug., 1901, and Jan., 1902), that is to say that the volume of space is infinitely greater than the total bulk of matter which it contains. Otherwise the combined force of gravity—or at least the aggregate gravitational potential—on which the velocity generated in material bodies ultimately depends, would be far greater than observation shows it to be.

The whole visible universe, within a parallax of ¹/₁₀₀₀ second of arc, is estimated by Lord Kelvin as the equivalent of a thousand million of our suns; and this amount of matter, distributed as it is, would have an average density of 1·6 × 10^-23 grammes per c.c. It is noteworthy how exceedingly small is this average or aggregate density of matter in the visible region of space. The estimated density of 10^-23 c.g.s. means that the visible cosmos is as much rarer than a "vacuum" of a hundred millionths of an atmosphere, as that vacuum is itself rarer than lead.

It is because we have reason to assert that any ordinary mass of matter consists, like the cosmos, of separated particles, with great intervening distances in proportion to their size, that we are able to maintain that the aggregate density of ordinary stuff, such as water or lead, is very small compared with the continuous medium in which they exist, and of which all particles are supposed to be really composed. So that lead is to the ether, as regards density, very much as the "vacuum" above spoken of is to lead. The fundamental medium itself must be of uniform density everywhere, whether materialised or free.