of senses, the verifications of theory occur in that world. Laying the
theoretic conception at the root of matters, we determine by deduction
what are the phenomena which must of necessity grow out of this root.
If the phenomena thus deduced agree with those of the actual world, it
is a presumption in favour of the theory. If, as new classes of
phenomena arise, they also are found to harmonise with theoretic
deduction, the presumption becomes still stronger. If, finally, the
theory confers prophetic vision upon the investigator, enabling him to
predict the occurrence of phenomena which have never yet been seen,
and if those predictions be found on trial to be rigidly correct, the
persuasion of the truth of the theory becomes overpowering.
Thus working backwards from a limited number of phenomena, the human
mind, by its own expansive force, reaches a conception which covers
them all. There is no more wonderful performance of the intellect than
this; but we can render no account of it. Like the scriptural gift of
the Spirit, no man can tell whence it cometh. The passage from fact to
principle is sometimes slow, sometimes rapid, and at all times a
source of intellectual joy. When rapid, the pleasure is concentrated,
and becomes a kind of ecstasy or intoxication. To any one who has
experienced this pleasure, even in a moderate degree, the action of
Archimedes when he quitted the bath, and ran naked, crying 'Eureka!'
through the streets of Syracuse, becomes intelligible.
How, then, did it fare with the Emission Theory when the deductions
from it were brought face to face with natural phenomena? Tested by
experiment, it was found competent to explain many facts, and with
transcendent ingenuity its author sought to make it account for all.
He so far succeeded, that men so celebrated as Laplace and Malus, who
lived till 1812, and Biot and Brewster, who lived till our own time,
were found among his disciples.
§ 3. _The Undulatory Theory of Light_.
Still, even at an early period of the existence of the Emission
Theory, one or two great men were found espousing a different one.
They furnish another illustration of the law that, in forming
theories, the scientific imagination must draw its materials from the
world of fact and experience. It was known long ago that sound is
conveyed in waves or pulses through the air; and no sooner was this
truth well housed in the mind than it became the basis of a theoretic
conception. It was supposed that light, like sound, might also be the
product of wave-motion. But what, in this case, could be the material
forming the waves? For the waves of sound we have the air of our
atmosphere; but the stretch of imagination which filled all space with
a _luminiferous ether_ trembling with the waves of light was so bold
as to shock cautious minds. In one of my latest conversations with Sir
David Brewster, he said to me that his chief objection to the
undulatory theory of light was, that he could not think the Creator
capable of so clumsy a contrivance as the filling of space with ether
to produce light. This, I may say, is very dangerous ground, and the
quarrel of science with Sir David, on this point as with many
estimable persons on other points, is, that they profess to know too
much about the mind of the Creator.
This conception of an ether was advocated, and successfully applied to
various phenomena of optics, by the illustrious astronomer, Huyghens.
He deduced from it the laws of reflection and refraction, and applied
it to explain the double refraction of Iceland spar. The theory was
espoused and defended by the celebrated mathematician, Euler. They
were, however, opposed by Newton, whose authority at the time bore
them down. Or shall we say it was authority merely? Not quite so.
Newton's preponderance was in some degree due to the fact that, though
Huyghens and Euler were right in the main, they did not possess
sufficient data to _prove_ themselves right. No human authority,
however high, can maintain itself against the voice of Nature speaking
through experiment. But the voice of Nature may be an uncertain voice,
through the scantiness of data. This was the case at the period now
referred to, and at such a period, by the authority of Newton, all
antagonists were naturally overborne.
The march of mind is rhythmic, not uniform, and this great Emission
Theory, which held its ground so long, resembled one of those circles
which, according to your countryman Emerson, the intermittent force of
genius periodically draws round the operations of the intellect, but
which are eventually broken through by pressure from behind. In the
year 1773 was born, at Milverton, in Somersetshire, a circle-breaker
of this kind. He was educated for the profession of a physician, but
was too strong to be tied down to professional routine. He devoted
himself to the study of natural philosophy, and became in all its
departments a master. He was also a master of letters. Languages,
ancient and modern, were housed within his brain, and, to use the
words of his epitaph, 'he first penetrated the obscurity which had
veiled for ages the hieroglyphics of Egypt.' It fell to the lot of
this man to discover facts in optics which Newton's theory was
incompetent to explain, and his mind roamed in search of a sufficient
theory. He had made himself acquainted with all the phenomena of
wave-motion; with all the phenomena of sound; working successfully in
this domain as an original discoverer. Thus informed and disciplined,
he was prepared to detect any resemblance which might reveal itself
between the phenomena of light and those of wave-motion. Such
resemblances he did detect; and, spurred on by the discovery, he
pursued his speculations and experiments, until he finally succeeded
in placing on an immovable basis the Undulatory Theory of Light.
The founder of this great theory was Thomas Young, a name, perhaps,
unfamiliar to many of you, but which ought to be familiar to you all.
Permit me, therefore, by a kind of geometrical construction which I
once ventured to employ in London, to give you a notion of the
magnitude of this man. Let Newton stand erect in his age, and Young in
his. Draw a straight line from Newton to Young, tangent to the heads
of both. This line would slope downwards from Newton to Young,
because Newton was certainly the taller man of the two. But the slope
would not be steep, for the difference of stature was not excessive.
The line would form what engineers call a gentle gradient from Newton
to Young. Place underneath this line the biggest man born in the
interval between both. It may be doubted whether he would reach the
line; for if he did he would be taller intellectually than Young, and
there was probably none taller. But I do not want you to rest on
English estimates of Young; the German, Helmholtz, a kindred genius,
thus speaks of him: "His was one of the most profound minds that the
world has ever seen; but he had the misfortune to be too much in
advance of his age. He excited the wonder of his contemporaries, who,
however, were unable to follow him to the heights at which his daring
intellect was accustomed to soar. His most important ideas lay,
therefore, buried and forgotten in the folios of the Royal Society,
until a new generation gradually and painfully made the same
discoveries, and proved the exactness of his assertions and the truth
of his demonstrations."
It is quite true, as Helmholtz says, that Young was in advance of his
age; but something is to be added which illustrates the responsibility
of our public writers. For twenty years this man of genius was
quenched--hidden from the appreciative intellect of his
country-men--deemed in fact a dreamer, through the vigorous sarcasm of
a writer who had then possession of the public ear, and who in the
_Edinburgh Review_ poured ridicule upon Young and his speculations. To
the celebrated Frenchmen Fresnel and Arago he was first indebted for
the restitution of his rights; for they, especially Fresnel,
independently remade and vastly extended his discoveries. To the
students of his works Young has long since appeared in his true light,
but these twenty blank years pushed him from the public mind, which
became in time filled with the fame of Young's colleague at the Royal
Institution, Davy, and afterwards with the fame of Faraday. Carlyle
refers to a remark of Novalis, that a man's self-trust is enormously
increased the moment he finds that others believe in him. If the
opposite remark be true--if it be a fact that public disbelief weakens
a man's force--there is no calculating the amount of damage these
twenty years of neglect may have done to Young's productiveness as an
investigator. It remains to be stated that his assailant was Mr. Henry
Brougham, afterwards Lord Chancellor of England.
§ 4. _Wave-Motion, Interference of Waves, 'Whirlpool Rapids' of
Niagara_.
Our hardest work is now before us. But the capacity for hard work
depends in a great measure on the antecedent winding up of the will; I
would call upon you, therefore, to gird up your loins for coming
labours.
In the earliest writings of the ancients we find the notion that sound
is conveyed by the air. Aristotle gives expression to this notion, and
the great architect Vitruvius compares the waves of sound to waves of
water. But the real mechanism of wave-motion was hidden from the
ancients, and indeed was not made clear until the time of Newton. The
central difficulty of the subject was, to distinguish between the
motion of the wave itself, and the motion of the particles which at
any moment constitute the wave.
Stand upon the seashore and observe the advancing rollers before they
are distorted by the friction of the bottom. Every wave has a back and
a front, and, if you clearly seize the image of the moving wave, you
will see that every particle of water along the front of the wave is
in the act of rising, while every particle along its back is in the
act of sinking. The particles in front reach in succession the crest
of the wave, and as soon as the crest is past they begin to fall. They
then reach the furrow or _sinus_ of the wave, and can sink no farther.
Immediately afterwards they become the front of the succeeding wave,
rise again until they reach the crest, and then sink as before. Thus,
while the waves pass onwards horizontally, the individual particles
are simply lifted up and down vertically. Observe a sea-fowl, or, if
you are a swimmer, abandon yourself to the action of the waves; you
are not carried forward, but simply rocked up and down. The
propagation of a wave is the propagation of a _form_, and not the
transference of the substance which constitutes the wave.
The _length_ of the wave is the distance from crest to crest, while
the distance through which the individual particles oscillate is
called the _amplitude_ of the oscillation. You will notice that in
this description the particles of water are made to vibrate _across_
the line of propagation.[10]
And now we have to take a step forwards, and it is the most important
step of all. You can picture two series of waves proceeding from
different origins through the same water. When, for example, you throw
two stones into still water, the ring-waves proceeding from the two
centres of disturbance intersect each other. Now, no matter how
numerous these waves may be, the law holds good that the motion of
every particle of the water is the algebraic sum of all the motions
imparted to it. If crest coincide with crest and furrow with furrow,
the wave is lifted to a double height above its sinus; if furrow
coincide with crest, the motions are in opposition and their sum is
zero. We have then _still_ water. This action of wave upon wave is
technically called _interference_, a term, to be remembered.
To the eye of a person conversant with these principles, nothing can
be more interesting than the crossing of water ripples. Through their
interference the water-surface is sometimes shivered into the most
beautiful mosaic, trembling rhythmically as if with a kind of visible
music. When waves are skilfully generated in a dish of mercury, a
strong light thrown upon the shining surface, and reflected on to a
screen, reveals the motions of the liquid metal. The shape of the
vessel determines the forms of the figures produced. In a circular
dish, for example, a disturbance at the centre propagates itself as a
series of circular waves, which, after reflection, again meet at the
centre. If the point of disturbance be a little way removed from the
centre, the interference of the direct and reflected waves produces
the magnificent chasing shown in the annexed figure.[11] The light
reflected from such a surface yields a pattern of extraordinary
beauty. When the mercury is slightly struck by a needle-point in a
direction concentric with the surface of the vessel, the lines of
light run round in mazy coils, interlacing and unravelling themselves
in a wonderful manner. When the vessel is square, a splendid
chequer-work is produced by the crossing of the direct and reflected
waves. Thus, in the case of wave-motion, the most ordinary causes give
rise to most exquisite effects. The words of Emerson are perfectly
applicable here:--
[Illustration: Fig. 10.]
'Thou can'st not wave thy staff in the air,
Or dip thy paddle in the lake,
But it carves the brow of beauty there.
And the ripples in rhymes the oars forsake.'
The most impressive illustration of the action of waves on waves that
I have ever seen occurs near Niagara. For a distance of two miles, or
thereabouts, below the Falls, the river Niagara flows unruffled
through its excavated gorge. The bed subsequently narrows, and the
water quickens its motion. At the place called the 'Whirlpool Rapids,'
I estimated the width of the river at 300 feet, an estimate confirmed
by the dwellers on the spot. When it is remembered that the drainage
of nearly half a continent is compressed into this space, the
impetuosity of the river's escape through this gorge may be imagined.
Two kinds of motion are here obviously active, a motion of translation
and a motion of undulation--the race of the river through its gorge,
and the great waves generated by its collision with the obstacles in
its way. In the middle of the stream, the rush and tossing are most
violent; at all events, the impetuous force of the individual waves is
here most strikingly displayed. Vast pyramidal heaps leap incessantly
from the river, some of them with such energy as to jerk their summits
into the air, where they hang suspended as bundles of liquid pearls,
which, when shone upon by the sun, are of indescribable beauty.
The first impression, and, indeed, the current explanation of these
Rapids is, that the central bed of the river is cumbered with large
boulders, and that the jostling, tossing, and wild leaping of the
waters there are due to its impact against these obstacles. A very
different explanation occurred to me upon the spot. Boulders derived
from the adjacent cliffs visibly cumber the _sides_ of the river.
Against these the water rises and sinks rhythmically but violently,
large waves being thus produced. On the generation of each wave there
is an immediate compounding of the wave-motion with the river-motion.
The ridges, which in still water would proceed in circular curves
round the centre of disturbance, cross the river obliquely, and the
result is, that at the centre waves commingle which have really been
generated at the sides. This crossing of waves may be seen on a small
scale in any gutter after rain; it may also be seen on simply pouring
water from a wide-lipped jug. Where crest and furrow cross each other,
the wave is annulled; where furrow and furrow cross, the river is
ploughed to a greater depth; and where crest and crest aid each other,
we have that astonishing leap of the water which breaks the cohesion
of the crests, and tosses them shattered into the air. The phenomena
observed at the Whirlpool Rapids constitute, in fact, one of the
grandest illustrations of the principle of interference.
§ 5. _Analogies of Sound and Light._
Thomas Young's fundamental discovery in optics was that the principle
of Interference was applicable to light. Long prior to his time an
Italian philosopher, Grimaldi, had stated that under certain
circumstances two thin beams of light, each of which, acting singly,
produced a luminous spot upon a white wall, when caused to act
together, partially quenched each other and darkened the spot. This
was a statement of fundamental significance, but it required the
discoveries and the genius of Young to give it meaning. How he did so
will gradually become clear to you. You know that air is compressible:
that by pressure it can be rendered more dense, and that by
dilatation it can be rendered more rare. Properly agitated, a
tuning-fork now sounds in a manner audible to you all, and most of you
know that the air through which the sound is passing is parcelled out
into spaces in which the air is condensed, followed by other spaces in
which the air is rarefied. These condensations and rarefactions
constitute what we call _waves_ of sound. You can imagine the air of a
room traversed by a series of such waves, and you can imagine a second
series sent through the same air, and so related to the first that
condensation coincides with condensation and rarefaction with
rarefaction. The consequence of this coincidence would be a louder
sound than that produced by either system of waves taken singly. But
you can also imagine a state of things where the condensations of the
one system fall upon the rarefactions of the other system. In this
case (other things being equal) the two systems would completely
neutralize each other. Each of them taken singly produces sound; both
of them taken together produce no sound. Thus by adding sound to sound
we produce silence, as Grimaldi, in his experiment, produced darkness
by adding light to light.
Through his investigations on sound, which were fruitful and profound,
Young approached the study of light. He put meaning into the
observation of Grimaldi, and immensely extended it. With splendid
success he applied the undulatory theory to the explanation of the
colours of thin plates, and to those of striated surfaces. He
discovered and explained classes of colour which had been previously
unnoticed or unknown. On the assumption that light was wave-motion,
all his experiments on interference were accounted for; on the
assumption that light was flying particles, nothing was explained. In
the time of Huyghens and Euler a medium had been assumed for the
transmission of the waves of light; but Newton raised the objection
that, if light consisted of the waves of such a medium, shadows could
not exist. The waves, he contended, would bend round opaque bodies and
produce the motion of light behind them, as sound turns a corner, or
as waves of water wash round a rock. It was proved that the bending
round referred to by Newton actually occurs, but that the inflected
waves abolish each other by their mutual interference. Young also
discerned a fundamental difference between the waves of light and
those of sound. Could you see the air through which sound-waves are
passing, you would observe every individual particle of air
oscillating to and fro, _in the direction of propagation_. Could you
see the luminiferous ether, you would also find every individual
particle making a small excursion to and fro; but here the motion,
like that assigned to the water-particles above referred to, would be
_across_ the line of propagation. The vibrations of the air are
_longitudinal_, those of the ether _transversal_.
The most familiar illustration of the interference of sound-waves is
furnished by the _beats_ produced by two musical sounds slightly out
of unison. When two tuning-forks in perfect unison are agitated
together the two sounds flow without roughness, as if they were but
one. But, by attaching with wax to one of the forks a little weight,
we cause it to vibrate more slowly than its neighbour. Suppose that
one of them performs 101 vibrations in the time required by the other
to perform 100, and suppose that at starting the condensations and
rarefactions of both forks coincide. At the 101st vibration of the
quicker fork they will again coincide, that fork at this point having
gained one whole vibration, or one whole wavelength, upon the other.
But a little reflection will make it clear that, at the 50th
vibration, the two forks condensation where the other tends to produce
a rarefaction; by the united action of the two forks, therefore, the
sound is quenched, and we have a pause of silence. This occurs where
one fork has gained _half a wavelength_ upon the other. At the 101st
vibration, as already stated, we have coincidence, and, therefore,
augmented sound; at the 150th vibration we have again a quenching of
the sound. Here the one fork is _three half-waves_ in advance of the
other. In general terms, the waves conspire when the one series is an
_even_ number of half-wave lengths, and they destroy each other when
the one series is an _odd_ number of half-wave lengths in advance of
the other. With two forks so circumstanced, we obtain those
intermittent shocks of sound separated by pauses of silence, to which
we give the name of beats. By a suitable arrangement, moreover, it is
possible to make one sound wholly extinguish another. Along four
distinct lines, for example, the vibrations of the two prongs of a
tuning-fork completely blot each other out.[12]
The _pitch_ of sound is wholly determined by the rapidity of the
vibration, as the _intensity_ is by the amplitude. What pitch is to
the ear in acoustics, colour is to the eye in the undulatory theory of
light. Though never seen, the lengths of the waves of light have been
determined. Their existence is proved _by their effects_, and from
their effects also their lengths may be accurately deduced. This may,
moreover, be done in many ways, and, when the different determinations
are compared, the strictest harmony is found to exist between them.
This consensus of evidence is one of the strongest points of the
undulatory theory. The shortest waves of the visible spectrum are
those of the extreme violet; the longest, those of the extreme red;
while the other colours are of intermediate pitch or wavelength. The
length of a wave of the extreme red is such, that it would require
39,000 such waves, placed end to end, to cover one inch, while 64,631
of the extreme violet waves would be required to span the same
distance.
Now, the velocity of light, in round numbers, is 186,000 miles per
second. Reducing this to inches, and multiplying the number thus found
by 39,000, we find the number of waves of the extreme red, in 186,000
miles, to be four hundred and sixty millions of millions. _All these
waves enter the eye, and strike the retina at the back of the eye in
one second_. In a similar manner, it may be found that the number of
shocks corresponding to the impression of violet is six hundred and
seventy-eight millions of millions.
All space is filled with matter oscillating at such rates. From every
star waves of these dimensions move, with the velocity of light, like
spherical shells in all directions. And in ether, just as in water,
the motion of every particle is the algebraic sum of all the separate
motions imparted to it. One motion does not blot out the other; or, if
extinction occur at one point, it is strictly atoned for, by augmented
motion, at some other point. Every star declares by its light its
undamaged individuality, as if it alone had sent its thrills through
space.
§ 6. _Interference of Light_.
[Illustration: Fig. 11.]