_OF THE INFINITELY MINUTE._
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 versâ_, 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.