when i speak of the infinitely minute, i use the word infinitely not in its absolute sense, but relatively. actual infinity of minuteness is as utterly beyond our conceptions as actual infinity of vastness. but we may speak of what is very much less than the least object of which our senses can make us directly conscious as for us infinitely minute. among the greatest wonders science has to deal with are those relating to bodies and movements thus beyond the direct ken of our senses. there is a universe within the universe which our senses reveal to us,—a universe whose structure is so fine that the minutest particle which the microscope can reveal to us is, by comparison, like one of the suns which people our universe compared with the unseen particles constituting matter.
it is a strange thought that the objects constituting our universe, so long regarded by man as the only universe, are in a sense pervaded by the materials of an utterly different universe,—which yet is as essential to our very existence as what we commonly call matter. we cannot live without light and heat, for instance, and again, light and heat affect matter as we know it; but they thus exist and affect such matter by means only of a form of matter unlike any which we can conceive. it is certain that if absolute vacancy separated our earth from the sun, even by the narrowest imaginable gap, his heat and light could never reach us. they could no more pass that vacant space than the wave-motion of water can cross a space where water itself is wanting. it is because of relations such as these that it has been said, and justly, that matter is the less important half of the material constituting the physical universe.
our knowledge of this universe within our universe has been obtained within comparatively recent years. men were unwilling or at least they spoke and thought as if they were unwilling, to believe that the universe of matter which they had so long recognised was dependent on another universe for its chief if not all its properties. they regarded heat as some sort of substance, which might, with more delicate means than they possessed, admit of being dealt with as chemists had dealt with the gases. the sun was full of this fluid, this phlogiston, as it was called. light, in so far as it could be distinguished from heat, was another fluid; electricity was another. these were the imponderables, or unweighable substances of last century's science,—not as with us, the effects of modes of motion taking place in a universe which, though material, is yet not made of matter such as we know, or even such as we can at present conceive.
this is the greatest of all human scientific marvels,—the greatest because it includes all others. we know of a universe which is as infinite in extent, and doubtless in duration, as our own universe; which pervades all forms of matter: and yet we know of this universe only indirectly; by the effects of movements taking place within it, not by any perception of these movements themselves. waves are ever beating upon the shores of our material universe, and constantly changing the form and condition of the coast line, but the waves themselves are unseen. we only know of their existence through the changes wrought by them.
we speak of the ether of space, and of waves traversing it, as though the ether were simply some fluid very much more attenuated than the rarest gas, even in a so-called vacuum. but in reality, so soon as we attempt to apply to the movements taking place in such an ether the mechanical considerations which suffice for the motions of all ordinary forms of matter, we perceive that it must of necessity be utterly unlike any kind of substance known to us. for instance, we find that though it is like a gas in being elastic, its elasticity is infinite compared with that of any material gas. again, it is like a solid in retaining each of its particles always very near to a fixed position; but again, no solid we know of can be compared with it for a moment as respects this kind of rigidity. it is at once infinitely elastic and infinitely rigid. we cannot, for example, explain the phenomena of light unless we suppose the elasticity of the ether at least 800,000,000,000 times greater than the elasticity of air at the sea-level; and yet, as sir j. herschel long since pointed out, every phenomenon of light points strongly to the conclusion that none of the particles of the ether can be "supposed capable of interchanging places, or of bodily transfer to any measurable distance from their own special and assigned localities in the universe. again, how are we to explain the continuance of the ether in its present condition, when we recognise the fact that a gas of similar elastic power would expand in all directions with irresistible force, diminishing correspondingly in density; yet the ether of space remains always, so far as we can judge, absolutely unchanged in position. its characteristics certainly remained unchanged. light travels at the same rate now as it did last year, last century, a million years ago. the ether, then, that bears it has presumably remained unchanged. if it were gaseous, and bounded on all sides by vacuum, it would expand with inconceivable velocity. to suppose it infinite in extent is to get rid of the difficulty perfectly; but only by introducing a difficulty far greater."[2]
a wonderful feature of the infinitely tenuous ether is, that while its ultimate particles must be inconceivably more minute than the ultimate atoms of ordinary matter, the movements taking place in it are transmitted with enormous velocities. the structure of our universe is on a grander scale; its least atom may comprise millions of millions of the largest component portions of that infinitely tenuous ether. but amid that ether motions are transmitted with velocities transcending all but infinitely those which take place among the particles of matter composing the universe in which we "live and move and have our being." the planets, immense aggregates of matter such as we know it, sweep onwards upon their immense orbits, traversing many thousands of miles in an hour; but light and heat sweep along the ether of space, and by virtue of motions taking place within that ether at the rate of many tens of thousands of miles per second. the suns which people space rush onwards with mightier momentum, but less swiftly than the planets in their orbits. comets attain the greatest velocities of all the bodies that science deals with, rushing sometimes, in their periastral swoop, with a velocity of hundreds of miles per second,—though yet in mid-space the comets of widest orbital range lag slowly enough, insomuch that some of those which, when nearest our sun, travel at the rate of two or three hundred miles per second, move more slowly when very far from him than many of our rivers. taking even the swiftest rush of a comet within the solar domain, we find that light speeds along five hundred times more quickly,—so that if we represent the velocity of light by that of an express train (reducing light's velocity in scale to about one-10,000,000th part of its real value), the velocity of the most swiftly-moving comet would be represented by that of a walk at the rate of one-eighth of a mile per hour,—a very slow walk indeed.
it is not only amid the depths of space that these wonderfully swift motions take place in the ethereal universe. as i have said, that universe pervades ours throughout its entire extent. the densest of our solids is as freely traversed by the ether as a forest by the summer breeze. as the foliage of a thick forest may prevent the passage of fierce winds, so may a solid body prevent the passage of light-waves—though all solid bodies, as we know, do not prevent, and some scarcely even modify, the passage of light. but substances which prevent the passage of light are yet found capable of transmitting ethereal motions of similar velocity. according to wheatstone's experiments electricity travels at the rate of more than 200,000 miles per second along stout copper wire. fizeau's experiments gave a lower speed; but they did not negative wheatstone's, the conditions not being the same. can anything be more wonderful than the thought of the transmission of electricity with this enormous velocity? what really happens we do not know. perhaps if we were told what really takes place between and among the particles of the wire, we should find ourselves utterly unable to conceive it—for, as we have seen, the properties of the ether, and, therefore, the processes taking place in the ethereal universe, are probably unlike any within our experience. but this we know—a certain condition of the molecules of the wire is transmitted, by virtue of the ethereal medium pervading the wire, at a rate so enormous that, if the wire itself could move at that rate, the force required to bring its mass to rest would suffice to generate enough heat to turn many times as much metal into the vaporous state.
nay, even as regards the energy of their action on the matter of our universe, these movements in the ethereal universe enormously exceed the forces we are accustomed to regard as most powerful. the effects produced by gravity, for instance, are almost evanescent compared with those produced by heat. the sun's rays poured on a piece of metal for a few minutes produce motions in every one of the ultimate particles of the metal. each particle vibrates with inconceivable rapidity (referring to the rate at which the vibrations succeed each other), and with great actual velocity of motion. summing up the energy thus pervading the piece of metal, we find that it incalculably exceeds the energy represented by the velocity which the sun's attraction would communicate in the same interval to that piece of metal, supposed to be entirely under its influence at the earth's distance from the sun.
or take another instance. "think for a moment," say the authors of the "unseen universe," "of the fundamental experiments in electricity and magnetism, known to men for far more than 2000 years,—the lifting of light bodies in general by rubbed amber and of iron filings by a loadstone. to produce the same effect by gravitation-attraction,—at least, if the attracting body had the moderate dimensions of a hand-specimen of amber or loadstone,—we should require it to be of so dense a material as to weigh, at the very least, 1,000,000,000 pounds, instead of (as usual) a mere fraction of a pound. hence it is at once obvious that the imposing nature of the force of gravity, as usually compared with other attractive forces, is due, not to its superior qualitative magnitude, but to the enormous masses of the bodies which exercise it."
we may put this illustration in another form. when we place a powerful magnet near a piece of iron, say at a distance of one inch, and the magnet lifts that piece of iron by virtue of its attractive power, a contest has been waged, if one may so speak, between the attractive powers of the small magnet and of the mighty earth, and the magnet has conquered the earth. now the magnet has been much nearer than the earth to the piece of iron, for we know that the earth's attractive influence has been the same as though the entire mass of the earth were gathered at its centre, say 4000 miles from the piece of iron. a distance of 4000 miles contains 4000 times 1760 times thirty-six inches, or, roughly, 250 millions of inches. (this is in truth very near the true number of inches in the earth's radius, insomuch that many suppose the inch to have been originally taken as the 500,000,000th part of the earth's diameter. a british inch is about one-500,000,000th part of the polar diameter of the earth.) since attraction diminishes as the square of the distances increases, and vice versa, it follows that if the earth's entire mass could act on the piece of iron, at a distance of one inch, the attraction would exceed that actually exerted by the earth 250 million times 250 million times, or 62,500 millions of millions of times. in this degree, then, the earth is at a disadvantage compared with the magnet as respects distance. and one-62,500,000,000,000,000th part of the earth's mass would be capable of attracting the piece of iron as strongly as the earth actually attracts it, if that fraction of the earth's mass could exert its pull from a distance of only one inch. but a 62,500,000,000,000,000th part of the earth would be an enormous mass. it would weigh about 97,500 tons, or some 218 millions of pounds. thus a magnet which a child can lift exerts a greater attraction on the piece of iron at the same distance than a mass at least 1000 million times its weight could exert by its gravity only.
in fact we see from this illustration that gravity, though it produces effects so tremendous, though it sways the moon round the earth, the earth and all the other planets around the sun, and urges the sun and his fellow-suns through space, is, after all, but a puny force in itself. a child can lift his own weight against the attraction of the mighty earth; and by combined strength as many children as would have a weight equal to the earth's would easily bear a weight exceeding the earth's, if the force could be wholly and directly applied to such work.[3]
the attraction of gravity must, however, be regarded as only one manifestation of the energies of the infinitely minute. it is in this sense well worthy of careful study. i propose to present in a future paper some of the strange thoughts which are suggested by the action of this wonderful force, the range of whose activity is seemingly co-extensive with the material universe.
