ETHER.
Ether proved by light—Light-waves—Elasticity of ether—Its
universal diffusion—Influences molecules and atoms—Is influenced
by them—Successive orders of the infinitely small—Illustrated
by the differential and integral calculus—Explanation of this
calculus—Theory of vortex rings.
Perhaps the best way to convey some idea of this order of magnitudes
to the ordinary reader is to quote Sir W. Thomson’s illustration, that
if we could suppose a cubic inch of water magnified to the size of the
earth—i.e. to a sphere 24,000 miles in circumference—the dimensions of
its ultimate particles, magnified on the same scale, or, as he expresses
it, its degree of coarse-grainedness, would be something between the size
of rifle-bullets and cricket-balls.
Extraordinary as these dimensions are, they are not more so than those
at the opposite extremity of the scale, where the distance of stars
and nebulæ has to be measured by the number of thousand years their
light, travelling at the rate of 192,000 miles per second, takes to
reach us. Infinitely small, however, as those dimensions appear to our
original conceptions derived from our natural senses, they are certain
and ascertained facts, if not as to the precise figures, yet beyond all
doubt as to the orders of magnitude. In dealing with them also we are to
a great extent on familiar ground. Molecules are nothing more nor less
than small pieces of ordinary matter; and atoms are also matter, for they
obey the law of gravity, have definite weights, and build up molecules as
surely as molecules build up ordinary matter, and as squared stones build
up pyramids.
But to understand the constitution of the material universe we must
go a step further, part from the familiar world of sense, and deal
with an all-pervading medium, which is at the same time matter and not
matter, which lies outside the laws of gravity, and yet obeys other laws
intelligible and calculable by us; of which it may be said we know it and
we know it not. We call it Ether.
Ether is a medium assumed as a necessary consequence from the phenomena
of light, heat, and electricity—primarily from those of light. Respecting
light two facts are known to us with absolute certainty.
1st. It traverses space at the rate of 192,000 miles per second.
2nd. It is propagated not by particles actually travelling at this rate,
but, like sound through air, by the transmission of waves.
The first fact is known from the difference of time at which eclipses of
Jupiter’s satellites are seen according as the earth is at the point of
its orbit nearest to or farthest from Jupiter—i.e. from the time light
takes to traverse the diameter of the earth’s orbit, which is about 180
millions of miles; and this velocity of light is confirmed by direct
experiments, as by noting the difference of time between seeing the
flash and hearing the sound of a gun, which gives the velocity of light
compared with the known velocity of sound.
The second fact is equally certain from the phenomena of what are called
interferences, when the crest of one wave just overtakes the hollow of
a preceding one, so that, if the two waves are of equal magnitude, the
oscillations exactly neutralise one another, and two lights produce
darkness. This is shown in a thousand different ways, and for all the
different colours depending on different waves into which white light
is analysed when passed through a prism. It is a certain result of
wave-motion, and of wave-motion only, and therefore we know without a
doubt that light is propagated by waves.
But waves imply a medium through which waveforms are transmitted, for
waves are nothing but the rhythmic motion of something which rises and
falls, or oscillates symmetrically about a mean position of rest, slowly
or quickly according to the less or greater elasticity of the medium.
The waves which run along a large and slack wire are large and slow,
those along a small and tightly stretched wire are small and quick; and
from the data we possess as to light, its velocity of transmission,
its refraction when its waves pass from one medium into another of
different density, and from the distance between the waves as shown by
interference, it is easy to calculate the lengths and vibratory periods
of the waves, and the elasticity of the medium through which such waves
are transmitted.
The figures at which we arrive are truly extraordinary. The dimensions
and rates of oscillations of the waves which produce the different
colours of visible light have been measured and calculated with the
greatest accuracy, and they are as follows:
DIMENSIONS OF LIGHT-WAVES.
+---------------+---------------+-----------------------+
| Colours |No. of waves in|No. of oscillations in |
| | one inch | one second |
+---------------+---------------+-----------------------+
|Red | 39,000 | 477,000,000,000,000 |
|Orange | 42,000 | 506,000,000,000,000 |
|Yellow | 44,000 | 535,000,000,000,000 |
|Green | 47,000 | 577,000,000,000,000 |
|Blue | 51,000 | 622,000,000,000,000 |
|Indigo | 54,000 | 658,000,000,000,000 |
|Violet | 57,000 | 699,000,000,000,000 |
+---------------+---------------+-----------------------+
The elasticity of this wonderful medium is even more extraordinary.
The rapidity with which wave-motion is transmitted depends, other things
being equal, on the elasticity of the medium, which is proportional to
the square of the velocity with which a wave travels through it. As the
velocity of the sound-wave in air is about 1,100 feet in a second, and
that of the light-wave about 192,000 miles in the same time, it follows
that the velocity of the latter is about a million times greater than
that of the former, and if the density of ether were the same as that of
air, its elasticity must be about a million million times greater. But
the elasticity is the same thing as the power of resisting compression,
which in the case of air we know to be about 15 pounds to the square
inch; so that the ether, if equally dense, would balance a pressure of
15 million million pounds to the square inch—that is, it would require
a pressure of about 750 millions of tons to the square inch to condense
ether to the density of air. On the other hand, its density, if any,
must be so infinitesimally small that the earth moving through it in its
orbit with a velocity of 1,100 miles a minute suffers no perceptible
retardation.
Consider what this means. Air blowing at the rate of 100 miles an hour
is a hurricane uprooting trees and levelling houses. If ether were as
dense as air the resistance to the earth in passing through it would
be 600 times that of going dead to windward in a tropical hurricane.
But in point of fact there is no sensible resistance, for the earth and
heavenly bodies move in their calculated paths according to the law of
gravity exactly as they would do if they were moving in a vacuum. Even
the comets, which consist of such excessively rare matter that when one
of them got entangled among the satellites of Jupiter it did not affect
their movements, are not retarded by the ether, or so slightly, that any
retardation in the case of one or two of them is suspected rather than
proved. But, if the ether has no weight, how can we call it material,
weight being, as we have seen, the invariable test and measure of all
matter down to the minutest atom? And yet how can we deny its existence
when it is demonstrably necessary to account for undoubted facts revealed
to us every day by the prism, the spectroscope, electricity, and chemical
action, and deductions from these facts based on the strict laws of
mathematical calculation? For the existence of the ether is not based
only on the phenomena of light: it is an equally necessary postulate to
explain those of heat, electricity, and chemical action. We must conceive
of our atoms and molecules as forming systems and performing their
movements, not in vacuo, but in an all-pervading medium of this ether, to
which they impart, and from which they receive, impulses.
These impulses are excessively minute, and when they occur in irregular
order they produce no appreciable effect; but when the vibrations of
the ether keep time with those of the atoms, the multitude of small
effects becomes summed up into one considerable enough to produce great
changes. Just so a rhythmic succession of tiny ripples may set a heavy
buoy oscillating, and the footfalls of a regiment of soldiers marching
over a suspension-bridge may make it swing until it breaks down, while
a confused mob could traverse it in safety. The latter affords a good
illustration of the way in which molecular structures may be broken down,
and their atoms set free to enter into other combinations, by the action
of heat, light, or chemical rays beyond the visible end of the spectrum.
Conversely the phenomena of the spectroscope all depend on the fact that
the vibrations of atoms and molecules can propagate waves through the
ether, as well as absorb ether-waves into their own motions, and thus
give spectra distinguished by bright or dark lines peculiar to each
substance, by which it can be identified. Whatever ether may be, this
much is certain about it: it pervades all space. That it extends to the
boundaries of the infinitely great we know from the fact that light
reaches us from the remotest stars and nebulæ, and that in this light
the spectroscope enables us to detect waves propagated and absorbed by
the very same vibrations of the same familiar atoms at these enormous
distances as at the earth’s surface. Glowing hydrogen, for instance, is a
principal ingredient of the sun’s atmosphere and of those distant suns we
call stars, and it affects the ether and is affected by it exactly in the
same manner as the hydrogen burning in an ordinary gas-lamp.
In the direction also of the infinitely small, ether permeates the
apparently solid structure of crystals, whose molecules perform their
limited and rigidly definite movements in an atmosphere of it, as is
shown by the fact that in so many cases light and heat penetrate through
them. A whole series of remarkable phenomena arise from the manner in
which the vibrations of ether which cause light are affected by the
structure of the molecules of crystals through which they pass. In
certain cases they are what is called polarised, or so affected that
while they pass freely if the crystal is held in one direction, they
are stopped if it is turned round through an angle of 90° to its former
position, so that one and the same crystal may be alternately transparent
and non-transparent. It would seem as if its structure were like that
of wood, grained, and more easy to penetrate if cut with the grain
than against it, so that when a ray of light attempted to penetrate,
its vibrations were resolved into two, one with the grain which got
through, the other against it which was suppressed; so that the emerging
ray, which entered with a circular vibration, got out with only one
rectilinear vibration parallel to the diameter which coincided with the
grain.
Other crystals of more complicated structure affect transmitted light in
a more complex way, developing a double polarity very similar to that
induced in the iron filings when brought under the influence of the
two poles of the magnet. With this polarised light the most beautiful
coloured rings can be produced from the waves of the different colours
into which the white light has been analysed in passing through the
crystal, which alternately flash out and disappear as the crystal is
turned round its axis, and which present a remarkable analogy to the
curves into which the iron filings form themselves under the single or
double poles of the magnet.
The importance of this will appear afterwards, but for the present it
is sufficient to show that the waves of ether which cause light really
penetrate through the molecules of crystals, but in doing so may be
affected by them.
[Illustration: RINGS OF POLARISED LIGHT, UNIAXIAL CRYSTALS. RINGS OF
POLARISED LIGHT, BIAXIAL CRYSTALS.]
In dealing with these excessively small magnitudes it may assist the
reader who has some acquaintance with mathematics in forming some
conception of them, to refer to that refinement of calculation, the
differential and integral calculus. And even the non-mathematical reader
may find it worth while to give a little attention in order to gain
some idea of this celebrated calculus which was the key by which Newton
and his successors unlocked the mysteries of the heavens. The first
rough idea of it is gained by considering what would happen if, in a
calculation involving hundreds of miles, we neglected inches. Suppose we
had a block of land to measure, 300 miles long and 200 wide; as there
are, say, 5,000 feet in a mile, and the error from omitting inches could
not exceed a foot, the utmost error in the measurement of length could
not exceed 1/1500000th, and in width 1/1000000th part of the correct
amount. In the area of 300 × 200 = 60,000 square miles, the limit of
error would, by adding or omitting the rectangle formed by multiplying
together these two small errors, not exceed 1/1500000 × 1/1000000 =
1/1500000000000th part. It is evident that the first error is an
excessively small part of the true figure, and the second error a still
more excessively small part of the first error. But, as we are dealing
with abstract numbers, we can just as readily conceive our initial error
to be the 1/100th or 1/1000th of an inch, as one inch; and, in fact,
diminish it until it becomes an infinitesimally small or evanescent
quantity. In doing so, however, it is evident that we shall make the
second error such a still more infinitesimally small fraction of the
first that it may be considered as altogether disappearing.
The first error is called a differential of the first order and denoted
by _d_, the second a differential of the second order denoted by d₂.
Thus if we call the base of our rectangle _x_ and its height _y_, the
area will be _xy_. Let us suppose _x_ to receive the addition of a very
small increment _dx_, and _y_ the corresponding increment _dy_, what
will be the corresponding increment of the area, or _d.xy_? Clearly
the difference between the old area _xy_ and the new area (_x_ + _dx_)
multiplied by (_y_ + _dy_). This multiplication gives
_x_ + _dx_
_y_ + _dy_
------------
_xy_ + _ydx_
_xdy_ + dx.dy
------------------------------
_xy_ + _xdy_ + _ydx_ + _dx.dy_
The difference between this and _xy_ is _xdy_ + _ydx_ + _dx.dy_. But
_dx.dy_ is, as we have seen, a differential of the second order and may
be neglected. Therefore _dxy_ = _xdy_ + _ydx_. In like manner _dx_² =
(_x_ + _dx_)²-_x_² = 2_xdx_ + _dx_², which last term may be neglected,
and _dx_² = 2_xdx_. In this way the differentials of all manner of
functions and equations of symbols representing dimensions and motions
may be found. Conversely the wholes may be considered as made up of an
infinite number of these infinitely small parts, and found from them by
summing up or integrating the differentials. Thus if we had the equation
_xdy_ + _ydx_ = 2_zdz_
we know that the left-hand side is the differential of _xy_, and
therefore that by integrating it we shall get _xy_; while the right side
is the differential of _z_² which we shall get by integrating it. The
relation expressed therefore is that _xy_ = _z_², or, in other words,
that a rectangle whose sides are _x_ and _y_ exactly equals a square
whose side is _z_.
[Illustration: FIG. 1. FIG. 2. FIG. 3.]
The use of this device in assisting calculation will be apparent if we
take the case of an area bounded by a curved line. We cannot directly
calculate this area, but we can easily tell that of a rectangle. Now it
is evident that if we inscribe rectangles in this area ABC, the more
rectangles we inscribe the less will be the error in taking their sum
as equal to the curved area. This is apparent if we compare fig. 2 with
fig. 3. Suppose we take a point P on the curve, call BN = _x_ and PN =
_y_, and suppose N_n_ to be _dx_, the differentially small increment of
_x_, and _pq_ = _dy_ the corresponding small increment of _y_. The area
of the rectangle P_qn_N = PN × N_n_ = _ydx_, and differs from the true
curvilinear area P_pn_N by less than the little rectangle of P_q_ × _pq_
or of _dx_._dy_. But, as we have seen, if we push our division to the
first infinitesimal order, or make N_n_ and _pq_ differentials of _x_ and
_y_, _dx_._dy_ may be neglected—i.e. multiply the number of rectangles
indefinitely, and the sum of their areas will differ from the true area
inclosed by the curve by an error which is evanescent.
If then _x_ and _y_ are connected by some fixed law, as must be the case
if the extremity of _y_ traces out some regular curve, the relation
between them may be expressed by an equation, which will remain one
however often it may be differentiated or again integrated, and whatever
modifications or transformations it may receive by mathematical processes
which do not alter the essential equality of the two sides connected by
the symbol of equality =. Thus by differentiating and casting off as
evanescent all differentials of a lower order than that which we are
working with, we may arrive at forms of which we know the integrals, and
by integrating get back to the results in ordinary numbers, which we were
in search of but could not attain directly.
The same thing will apply if our symbols are more numerous, and if
they express relations of motion as well as of space, or, in fact, any
relations which are governed by fixed laws expressible by equations. If
I have succeeded in conveying to the readers any idea of this celebrated
calculus, they will perceive what an analogy it presents to the idea
of modern physical and chemical science, that of molecules, atoms, and
ether, forming differentials of successive orders of the infinitely
small. It is certainly most remarkable that while the former was a
purely intellectual idea based on mathematical abstractions, and which
was invented and worked as an instrument for solving the most intricate
astronomical problems for nearly two centuries, without a suspicion
that it represented any objective reality: the latter idea, based on
actual experiment, seems to show that differentials and integrals have
their real counterpart in nature and represent fundamental facts in the
constitution of the universe.
Those who are of a mystic or metaphysical turn of mind may discern in
this, arguments for matter and laws of matter being after all only
manifestations of one universal, all-pervading mind; but in following
such speculations we should be deserting the solid earth for cloudland,
and passing the limit of positive knowledge into the region where
reflections of our own hopes, fears, religious feelings, and poetical
sentiments form and dissolve themselves against the background of the
great unknown. For the present, therefore, I confine myself to pointing
out how these undoubted truths of mathematical science, which have
verified themselves in the practical form of enabling us to predict
eclipses and construct nautical almanacs, correspond with and throw light
upon the equally certain facts of this succession of infinitely small
quantities of successive orders in the constitution of matter.
An attempt has recently been made, based on abstruse mathematical
calculations, to carry our knowledge of the constitution of matter one
step further back, and identify atoms with ether. This is attempted by
the vortex theory of Helmholz, Sir W. Thomson, and Professor Tait. It is
singular how some of the ultimate facts discovered by the refinements
of science correspond with some of the most trivial amusements. Thus
the blowing of soap-bubbles gives the best clue to the movement of waves
of light, and through them to the dimensions of molecules and atoms;
and the collision of billiard-balls, knocked about at random, to the
movements of those minute bodies, and the kinetic theory of gases. In the
case of the vortex theory the idea is given by the rings of smoke which
certain adroit smokers amuse themselves by puffing into the air. These
rings float for a considerable time, retaining their circular form, and
showing their elasticity by oscillating about it and returning to it if
their form is altered, and by rebounding and vibrating energetically,
just as two solid elastic bodies would do, if two rings come into
collision. If we try to cut them in two, they recede before the knife, or
bend round it, returning, when the external force is removed, to their
original form without the loss of a single particle, and preserving
their own individuality through every change of form and of velocity.
This persistence of form they owe to the fact that their particles are
revolving in small circles at right angles to the axis or circumference
of the larger circle which forms the ring; motion thus giving them
stability, very much as in the familiar instance of the bicycle. They
burst at last because they are formed and rotate in the air, which is a
resisting medium; but mathematical calculation shows that in a perfect
fluid free from all friction these vortex rings would be indivisible and
indestructible: in other words, they would be atoms.
The vortex theory assumes, therefore, that the universe consists of one
uniform primary substance, a fluid which fills all space, and that what
we call matter consists of portions of this fluid which have become
animated with vortex motion. The innumerable atoms which form molecules,
and through molecules all the diversified forms of matter of the material
universe, are therefore simply so many vortex rings, each perfectly
limited, distinct, and indestructible, both as to its form, mass, and
mode of motion. They cannot change or disappear, nor can they be formed
spontaneously. Those of the same kind are constituted after the same
fashion, and therefore are endowed with the same properties.
The theory is a plausible one, and the reputation of its authors must
command for it respectful consideration; but it is as yet a long way
from being an established theory which can be accepted as a true
representation of facts. In the first place it is based solely on
mathematical theory, and not, as in the case of atoms and light-waves,
upon actual facts of weight and measurement tested by experiment, and to
which mathematical reasoning affords only an aid and supplement. No one
has proved the existence of such a medium or of such vortex rings, much
less weighed or measured them.
Moreover the theory is open to some very obvious objections. How can
aggregations of imponderable matter acquire weight, and become subject
to the law of gravity, which, as we have seen, is one of the essential
and permanent qualities of atoms? If a cubic millionth of a millimetre of
ether formed into a big vortex ring of, say, an atom of mercury, has a
weight equal to 200 times that of an atom of hydrogen, which itself has
a definite weight, why has it no weight in its original form? And if it
had weight, however small, how could the enormous mass of ether filling
all space produce no perceptible effect on bodies, even of attenuated
cometic vapour, revolving through it with immense velocities? Again,
how could these innumerable vortex rings be formed out of the ether
without disturbing the uniformity and continuity of the medium, which
are essential for the propagation of the light-waves through it? And how
could the motions requisite to form the vortex rings be impressed on them
_de novo_ consistently with the principle of the conservation of energy?
Energy can no more be created out of nothing than matter, by any process
known in nature or conceivable by the human intellect; and to assume it
is simply a more refined manner of falling back on the supernatural,
which is itself only a more refined manner of saying that we know nothing.
For the present, therefore, we must be content with atoms and ether as
the ultimate terms of our knowledge of the material or quasi-material
components of the universe.