to be feared and avoided rather than employed. They had observed its
action in weak vessels and were unduly impressed by its disasters.
But they might with equal justice point to exploded boilers as an
argument against the use of steam. Bounded and conditioned by
coöperant reason, imagination becomes the mightiest instrument of
the physical discoverer. Newton’s passage from a falling apple to a
falling moon was a leap of the imagination. When William Thomson
tries to place the ultimate particles of matter between his compass
points, and to apply to them a scale of millimeters, it is an
exercise of the imagination. And in much that has been recently said
about protoplasm and life, we have the outgoings of the imagination
guided and controlled by the known analogies of science. In fact,
without this power our knowledge of nature would be a mere
tabulation of coëxistences and sequences. We should still believe in
the succession of day and night, of summer and winter; but the soul
of force would be dislodged from our universe; casual relations
would disappear, and with them that science which is now binding the
parts of nature to an organic whole.
I should like to illustrate by a few simple instances the use that
scientific men have already made of this power of imagination, and
to indicate afterwards some of the further uses that they are likely
to make of it. Let us begin with the rudimentary experiences.
Observe the falling of heavy rain drops into a tranquil pond. Each
drop as it strikes the water becomes a center of disturbance, from
which a series of ring ripples expands outwards. Gravity and inertia
are the agents by which this wave motion is produced, and a rough
experiment will suffice to show that the rate of propagation does
not amount to a foot a second.
A series of slight mechanical shocks is experienced by a body
plunged in the water as the wavelets reach it in succession. But a
finer motion is at the same time set up and propagated. If the head
and ears be immersed in the water, as in an experiment of
Franklin’s, the shock of the drop is communicated to the auditory
nerve—the _tick_ of the drop is heard. Now this sonorous impulse is
propagated, not at the rate of a foot a second, but at the rate of
4,700 feet a second. In this case it is not the gravity but the
_elasticity_ of the water that is the urging force. Every liquid
particle pushed against its neighbor delivers up its motion with
extreme rapidity, and the pulse is propagated as a thrill. The
incompressibility of water, as illustrated by the famous Florentine
experiment, is a measure of its elasticity, and to the possession of
this property in so high a degree the rapid transmission of a
sound-pulse through water is to be ascribed.
But water, as you know, is not necessary to the conduction of sound;
air is its most common vehicle. And you know that when the air
possesses the particular density and elasticity corresponding to the
temperature of freezing water, the velocity of sound in it is 1,090
feet a second. It is almost exactly one-fourth of the velocity in
water; the reason being that though the greater weight of the water
tends to diminish the velocity, the enormous molecular elasticity of
the liquid far more than atones for the disadvantage due to weight.
By various contrivances we can compel the vibrations of the air to
declare themselves; we know the length and frequency of sonorous
waves, and we have also obtained great mastery over the various
methods by which the air is thrown into vibration. We know the
phenomena and laws of vibrating rods, of organ pipes, strings,
membranes, plates, and bells. We can abolish one sound by another.
We know the physical meaning of music and noise, of harmony and
discord. In short, as regards sound we have a very clear notion of
the external physical processes which correspond to our sensations.
In these phenomena of sound we travel a very little way from
downright sensible experience. Still the imagination is to some
extent exercised. The bodily eye, for example, cannot see the
condensations and rarefactions of the waves of sound. We construct
them in thought, and we believe as firmly in their existence as in
that of the air itself. But now our experience has to be carried
into a new region, where a new use is to be made of it.
Having mastered the cause and mechanism of sound, we desire to know
the cause and mechanism of light. We wish to extend our inquiries
from the auditory nerve to the optic nerve. Now there is in the
human intellect a power of expansion—I might almost call it a power
of creation—which is brought into play by the simple brooding upon
facts. The legend of the Spirit brooding over chaos may have
originated in a knowledge of this power. In the case now before us
it has manifested itself by transplanting into space, for the
purposes of light, an adequately modified form of the mechanism of
sound. We know intimately whereon the velocity of sound depends.
When we lessen the density of a medium and preserve its elasticity
constant, we augment the velocity. When we highten the elasticity
and keep the density constant, we also augment the velocity. A small
density, therefore, and a great elasticity are the two things
necessary to rapid propagation.
Now light is known to move with the astounding velocity of 185,000
miles a second. How is such a velocity to be obtained? By boldly
diffusing in space a medium of the requisite tenuity and elasticity.
Let us make such a medium our starting point, endowing it with one
or two other necessary qualities; let us handle it in accordance
with strict mechanical laws; give to every step of your deduction
the surety of the syllogism; carry it thus forth from the world of
imagination to the world of sense, and see whether the final outcrop
of the deduction be not the very phenomena of light which ordinary
knowledge and skilled experiment reveal. If in all the multiplied
varieties of these phenomena, including those of the most remote and
entangled description, this fundamental conception always brings us
face to face with the truth; if no contradiction to our deductions
from it be found in external nature; if, moreover, it has actually
forced upon our attention phenomena which no eye had previously
seen, and which no mind had previously imagined; if by it we are
gifted with a power of prescience which has never failed when
brought to an experimental test; such a conception, which never
disappoints us, but always lands us on the solid shores of fact,
must, we think, be something more than a mere figment of the
scientific fancy. In forming it that composite and creative unity in
which reason and imagination are together blent, has, we believe,
led us into a world not less real than that of the senses, and of
which the world of sense itself is the suggestion and justification.
Far be it from me, however, to wish to fix you immovably in this or
in any other theoretic conception. With all our belief of it, it
will be well to keep the theory plastic and capable of change. You
may, moreover, urge that although the phenomena occur _as if_ the
medium existed, the absolute demonstration of its existence is still
wanting. Far be it from me to deny to this reasoning such validity
as it may fairly claim. Let us endeavor by means of analogy to form
a fair estimate of its force.
You believe that in society you are surrounded by reasonable beings
like yourself. You are, perhaps, as firmly convinced of this as of
anything. What is your warrant for this conviction? Simply and
solely this, your fellow-creatures behave as if they were
reasonable; the hypothesis, for it is nothing more, accounts for the
facts. To take an eminent example, you believe that our president is
a reasonable being. Why? There is no known method of superposition
by which any one of us can apply himself intellectually to another
so as to demonstrate coincidence as regards the possession of
reason. If, therefore, you hold our president to be reasonable, it
is because he behaves _as if_ he were reasonable. As in the case of
the ether, beyond the “_as if_” you cannot go. Nay, I should not
wonder if a close comparison of the data on which both inferences
rest caused many respectable persons to conclude that the ether had
the best of it.
This universal medium, this light-ether as it is called, is a
vehicle, not an origin of wave motion. It receives and transmits,
but it does not create. Whence does it derive the motions it
conveys? For the most part from luminous bodies. By this motion of a
luminous body I do not mean its sensible motion, such as the flicker
of a candle, or the shooting out of red prominences from the limb of
the sun. I mean an intestine motion of the atoms or molecules of the
luminous body. But here a certain reserve is necessary. Many
chemists of the present day refuse to speak of atoms and molecules
as real things. Their caution leads them to stop short of the clear,
sharp, mechanically intelligible atomic theory enunciated by Dalton,
or any form of that theory, and to make the doctrine of multiple
proportions their intellectual bourne. I respect the caution, though
I think it is here misplaced. The chemists who recoil from these
notions of atoms and molecules accept without hesitation the
undulatory theory of light. Like you and me they one and all believe
in an ether and its light-producing waves. Let us consider what this
belief involves.
Bring your imaginations once more into play and figure a series of
sound waves passing through air. Follow them up to their origin, and
what do you there find? A definite, tangible, vibrating body. It may
be the vocal chords of a human being, it may be an organ pipe, or it
may be a stretched string. Follow in the same manner a train of
ether waves to their source, remembering at the same time that your
ether is matter, dense, elastic, and capable of motions subject to
and determined by mechanical laws. What then do you expect to find
as the source of a series of ether waves? Ask your imagination if it
will accept a vibrating multiple proportion—a numerical ratio in a
state of oscillation? I do not think it will. You cannot crown the
edifice by this abstraction. The scientific imagination, which is
here authoritative, demands as the origin and cause of a series of
ether waves a particle of vibrating matter quite as definite, though
it may be excessively minute, as that which gives origin to a
musical sound. Such a particle we name an atom or a molecule. I
think the imagination when focused so as to give definition without
penumbral haze is sure to realize this image at last.
To preserve thought continuous throughout this discourse, to prevent
either lack of knowledge or failure of memory from producing any
rent in our picture, I here propose to run rapidly over a bit of
ground which is probably familiar to most of you, but which I am
anxious to make familiar to you all.
The waves generated in the ether by the swinging atoms of luminous
bodies are of different lengths and amplitudes. The amplitude is the
width of swing of the individual particles of the wave. In water
waves it is the hight of the crest above the trough, while the
length of the wave is the distance between two consecutive crests.
The aggregate of waves emitted by the sun may be broadly divided
into two classes, the one class competent, the other incompetent, to
excite vision.
But the light-producing waves differ markedly among themselves in
size, form, and force. The length of the largest of these waves is
about twice that of the smallest, but the amplitude of the largest
is probably a hundred times that of the smallest. Now the force or
energy of the wave, which, expressed with reference to sensation,
means the intensity of the light, is proportional to the square of
the amplitude. Hence the amplitude being one hundred-fold, the
energy of the largest light-giving waves would be ten thousand-fold
that of the smallest. This is not improbable. I use these figures,
not with a view to numerical accuracy, but to give you definite
ideas of the differences that probably exist among the light-giving
waves. And if we take the whole range of solar radiation into
account—its non-visual as well as its visual waves—I think it
probable that the force or energy of the largest wave is a million
times that of the smallest.
Turned into their equivalents of sensation, the different light
waves produce different colors. Red, for example, is produced by the
largest waves, violet by the smallest, while green is produced by a
wave of intermediate length and amplitude. On entering from air into
more highly refracting substances, such as glass or water or the
sulphide of carbon, all the waves are retarded, but the smallest
ones most. This furnishes a means of separating the different
classes of waves from each other—in other words, of analyzing the
light. Sent through a refracting prism, the waves of the sun are
turned aside in different degrees from their direct course, the red
least, the violet most. They are virtually pulled asunder, and they
paint upon a white screen placed to receive them “the solar
spectrum.”
Strictly speaking, the spectrum embraces an infinity of colors, but
the limits of language and of our powers of distinction cause it to
be divided into seven segments: Red, orange, yellow, green, blue,
indigo, violet. These are the seven primary or prismatic colors.
Separately, or mixed in various proportions, the solar waves yield
all the colors observed in nature and employed in art. Collectively
they give us the impression of whiteness. Pure unsifted solar light
is white; and if all the wave constituents of such light be reduced
in the same proportion, the light, though diminished in intensity,
will still be white. The whiteness of Alpine snow with the sun
shining upon it is barely tolerable to the eye. The same snow under
an overcast firmament is still white. Such a firmament enfeebles the
light by reflection, and when we lift ourselves above a
cloud-field—to an Alpine summit, for instance, or to the top of
Snowdon—and see, in the proper direction, the sun shining on the
clouds, they appear dazzlingly white. Ordinary clouds, in fact,
divide the solar light impinging on them into two parts—a reflected
part and a transmitted part, in each of which the proportions of
wave motion which produce the impression of whiteness are sensibly
preserved.
It will be understood that the conditions of whiteness would fail if
all the waves were diminished _equally_, or by the same absolute
quantity. They must be reduced _proportionately_ instead of equally.
If by the act of reflection the waves of red light are split into
exact halves, then, to preserve the light white, the waves of
yellow, orange, green, and blue must also be split into exact
halves. In short, the reduction must take place, not by absolutely
equal quantities, but by equal fractional parts. In white light the
preponderance as regards energy of the larger over the smaller waves
must always be immense. Were the case otherwise, the physiological
correlative, _blue_, of the smaller waves would have the upper hand
in our sensations.
My wish to render our mental images complete, causes me to dwell
briefly upon these known points, and the same wish will cause me to
linger a little longer among others. But here I am disturbed by my
reflections. When I consider the effect of dinner upon the nervous
system, and the relation of that system to the intellectual powers I
am now invoking; when I remember that the universal experience of
mankind has fixed upon certain definite elements of perfection in an
after-dinner speech, and when I think how conspicuous by their
absence these elements are on the present occasion, the thought is
not comforting to a man who wishes to stand well with his
fellow-creatures in general, and with the members of the British
Association in particular. My condition might well resemble that of
the ether, which is scientifically defined as an assemblage of
vibrations. And the worst of it is that, unless you reverse the
general verdict regarding the effect of dinner, and prove in your
own persons that a uniform experience need not continue
uniform—which will be a great point gained for some people—these
tremors of mine are likely to become more and more painful. But I
call to mind the comforting words of an inspired, though uncanonical
writer, who admonishes us in the Apocrypha that fear is a bad
counsellor. Let me then cast him out, and let me trustfully assume
that you will one and all postpone that balmy sleep, of which dinner
might, under the circumstances, be regarded as the indissoluble
antecedent, and that you will manfully and womanfully prolong your
investigations of the ether and its waves into regions which have
been hitherto crossed by the pioneers of science alone.
Not only are the waves of ether reflected by clouds, by solids, and
by liquids, but when they pass from light air to dense, or from
dense air to light, a portion of the wave motion is always
reflected. Now our atmosphere changes continually in density from
top to bottom. It will help our conceptions if we regard it as made
up of a series of thin concentric layers or shells of air, each
shell being of the same density throughout, and a small and sudden
change of density occurring in passing from shell to shell. Light
would be reflected at the limiting surfaces of all these shells, and
their action would be practically the same as that of the real
atmosphere.
And now I would ask your imagination to picture this act of
reflection. What must become of the reflected light? The atmospheric
layers turn their convex surfaces towards the sun; they are so many
convex mirrors of feeble power, and you will immediately perceive
that the light regularly reflected from these surfaces cannot reach
the earth at all, but is dispersed in space.
But though the sun’s light is not reflected in this fashion from the
ærial layers to the earth, there is indubitable evidence to show
that the light of our firmament is reflected light. Proofs of the
most cogent description could be here adduced; but we need only
consider that we receive light at the same time from all parts of
the hemisphere of heaven. The light of the firmament comes to us
across the direction of the solar rays, and even against the
direction of the solar rays; and this lateral and opposing rush of
wave motion can only be due to the rebound of the waves from the air
itself, or from something suspended in the air. It is also evident
that, unlike the action of clouds, the solar light is not reflected
by the sky in the proportions which produce white. The sky is blue,
which indicates a deficiency on the part of the larger waves. In
accounting for the color of the sky, the first question suggested by
analogy would undoubtedly be, is not the air blue? The blueness of
the air has, in fact, been given as a solution of the blueness of
the sky. But reason basing itself on observation asks in reply, How,
if the air be blue, can the light of sunrise and sunset, which
travels through vast distances of air, be yellow, orange, or even
red? The passage of the white solar light through a blue medium
could by no possibility redden the light. The hypothesis of a blue
air is therefore untenable. In fact, the agent, whatever it is,
which sends us the light of the sky, exercises in so doing a
dichroitic action. The light reflected is blue, the light
transmitted is orange or red. A marked distinction is thus exhibited
between the matter of the sky and that of an ordinary cloud, which
latter exercises no such dichroitic action.
By the force of imagination and reason combined we may penetrate
this mystery also. The cloud takes no note of size on the part of
the waves of ether, but reflects them all alike. It exercises no
selective action. Now the cause of this may be that the cloud
particles are so large in comparison with the size of the waves of
ether as to reflect them all indifferently. A broad cliff reflects
an Atlantic roller as easily as a ripple produced by a sea bird’s
wing; and in the presence of large reflecting surfaces the existing
differences of magnitude among the waves of ether may disappear. But
supposing the reflecting particles, instead of being very large, to
be very small, in comparison with the size of the waves. In this
case, instead of the whole wave being fronted and in great part
thrown back, a small portion only is shivered off. The great mass of
the wave passes over such a particle without reflection. Scatter
then, a handful of such minute foreign particles in our atmosphere,
and set imagination to watch their action upon the solar waves.
Waves of all sizes impinge upon the particles, and you see at every
collision a portion of the impinging wave struck off by reflection.
All the waves of the spectrum, from the extreme red to the extreme
violet, are thus acted upon. But in what proportions will the waves
be scattered? A clear picture will enable us to anticipate the
experimental answer. Remembering that the red waves are to the blue
much in the relation of billows to ripples, let us consider whether
those extremely small particles are competent to scatter all the
waves in the same proportion. If they be not—and a little reflection
will make it clear to you that they are not—the production of color
must be an incident of the scattering. Largeness is a thing of
relation; and the smaller the wave the greater is the relative size
of any particle on which the wave impinges, and the greater also the
ratio of the reflected portion to the total wave.
A pebble placed in the way of the ring-ripples produced by our heavy
rain-drops on a tranquil pond will throw back a large fraction of
the ripple incident upon it, while the fractional part of a larger
wave thrown back by the same pebble might be infinitesimal. Now we
have already made it clear to our minds that to preserve the solar
light white, its constituent proportions must not be altered; but in
the act of division performed by these very small particles we see
that the proportions _are_ altered; an undue fraction of the smaller
waves is scattered by the particles, and, as a consequence, in the
scattered light blue will be the predominant color. The other colors
of the spectrum must, to some extent, be associated with the blue.
They are not absent, but deficient. We ought, in fact, to have them
all, but in diminishing proportions, from the violet to the red.
We have here presented a case to the imagination, and assuming the
undulatory theory to be a reality, we have, I think, fairly reasoned
our way to the conclusion that, were particles, small in comparison
to the size of the ether waves, sown in our atmosphere, the light
scattered by those particles would be exactly such as we observe in
our azure skies. When this light is analyzed all the colors of the
spectrum are found; but they are found in the proportions indicated
by our conclusion.
Let us now turn our attention to the light which passes unscattered
among the particles. How must it be finally affected? By its
successive collisions with the particles, the white light is more
and more robbed of its shorter waves; it therefore loses more and
more of its due proportion of blue. The result may be anticipated.
The transmitted light, where short distances are involved, will
appear yellowish. But as the sun sinks towards the horizon, the
atmospheric distances increase, and consequently the number of the
scattering particles. They abstract, in succession, the violet, the
indigo, the blue, and even disturb the proportions of green. The
transmitted light under such circumstances must pass from yellow
through orange to red. This also is exactly what we find in nature.
Thus, while the reflected light gives us at noon the deep azure of
the Alpine skies, the transmitted light gives us at sunset the warm
crimson of the Alpine snows. The phenomena certainly occur _as if_
our atmosphere were a medium rendered slightly turbid by the
mechanical suspension of exceedingly small foreign particles.
Here, as before, we encounter our skeptical “as if.” It is one of
the parasites of science, ever at hand, and ready to plant itself
and sprout, if it can, on the weak points of our philosophy. But a
strong constitution defies the parasite, and in our case, as we
question the phenomena, probability grows like growing health, until
in the end the malady of doubt is completely extirpated.