Read LECTURE II. of Six Lectures on Light Delivered In The United States In 1872-1873, free online book, by John Tyndall, on ReadCentral.com.

Se. Origin and Scope of Physical Theories.

We might vary and extend our experiments on Light indefinitely, and they certainly would prove us to possess a wonderful mastery over the phenomena. But the vesture of the agent only would thus be revealed, not the agent itself. The human mind, however, is so constituted that it can never rest satisfied with this outward view of natural things. Brightness and freshness take possession of the mind when it is crossed by the light of principles, showing the facts of Nature to be organically connected.

Let us, then, inquire what this thing is that we have been generating, reflecting, refracting and analyzing.

In doing this, we shall learn that the life of the experimental philosopher is twofold. He lives, in his vocation, a life of the senses, using his hands, eyes, and ears in his experiments: but such a question as that now before us carries him beyond the margin of the senses. He cannot consider, much less answer, the question, ’What is light?’ without transporting himself to a world which underlies the sensible one, and out of which all optical phenomena spring. To realise this subsensible world the mind must possess a certain pictorial power. It must be able to form definite images of the things which that world contains; and to say that, if such or such a state of things exist in the subsensible world, then the phenomena of the sensible one must, of necessity, grow out of this state of things. Physical theories are thus formed, the truth of which is inferred from their power to explain the known and to predict the unknown.

This conception of physical theory implies, as you perceive, the exercise of the imagination-a word which seems to render many respectable people, both in the ranks of science and out of them, uncomfortable. That men in the ranks of science should feel thus is, I think, a proof that they have suffered themselves to be misled by the popular definition of a great faculty, instead of observing its operation in their own minds. Without imagination we cannot take a step beyond the bourne of the mere animal world, perhaps not even to the edge of this one. But, in speaking thus of imagination, I do not mean a riotous power which deals capriciously with facts, but a well-ordered and disciplined power, whose sole function is to form such conceptions as the intellect imperatively demands. Imagination, thus exercised, never really severs itself from the world of fact. This is the storehouse from which its materials are derived; and the magic of its art consists, not in creating things anew, but in so changing the magnitude, position, grouping, and other relations of sensible things, as to render them fit for the requirements of the intellect in the subsensible world.

Descartes imagined space to be filled with something that transmitted light instantaneously. Firstly, because, in his experience, no measurable interval was known to exist between the appearance of a flash of light, however distant, and its effect upon consciousness; and secondly, because, as far as his experience went, no physical power is conveyed from place to place without a vehicle. But his imagination helped itself farther by illustrations drawn from the world of fact. ‘When,’ he says,’ one walks in darkness with staff in hand, the moment the distant end of the staff strikes an obstacle the hand feels it. This explains what might otherwise be thought strange, that the light reaches us instantaneously from the sun. I wish thee to believe that light in the bodies that we call luminous is nothing more than a very brisk and violent motion, which, by means of the air and other transparent media, is conveyed to the eye, exactly as the shock through the walking-stick reaches the hand of a blind man. This is instantaneous, and would be so even if the intervening distance were greater than that between earth and heaven. It is therefore no more necessary that anything material should reach the eye from the luminous object, than that something should be sent from the ground to the hand of the blind man when he is conscious of the shock of his staff.’ The celebrated Robert Hooke at first threw doubt upon this notion of Descartes, but he afterwards substantially espoused it. The belief in instantaneous transmission was destroyed by the discovery of Roemer referred to in our last lecture.

Se. The Emission Theory of Light.

The case of Newton still more forcibly illustrates the position, that in forming physical theories we draw for our materials upon the world of fact. Before he began to deal with light, he was intimately acquainted with the laws of elastic collision, which all of you have seen more or less perfectly illustrated on a billiard-table. As regards the collision of sensible elastic masses, Newton knew the angle of incidence to be equal to the angle of reflection, and he also knew that experiment, as shown in our last lecture (fi, had established the same law with regard to light. He thus found in his previous knowledge the material for theoretic images. He had only to change the magnitude of conceptions already in his mind to arrive at the Emission Theory of Light. Newton supposed light to consist of elastic particles of inconceivable minuteness, shot out with inconceivable rapidity by luminous bodies. Optical reflection certainly occurred as if light consisted of such particles, and this was Newton’s justification for introducing them.

But this is not all. In another important particular, also, Newton’s conceptions regarding the nature of light were influenced by his previous knowledge. He had been pondering over the phenomena of gravitation, and had made himself at home amid the operations of this universal power. Perhaps his mind at this time was too freshly and too deeply imbued with these notions to permit of his forming an unfettered judgment regarding the nature of light. Be that as it may, Newton saw in Refraction the result of an attractive force exerted on the light-particles. He carried his conception out with the most severe consistency. Dropping vertically downwards towards the earth’s surface, the motion of a body is accelerated as it approaches the earth. Dropping downwards towards a horizontal surface-say from air on to glass or water-the velocity of the light-particles, when they came close to the surface, is, according to Newton, also accelerated. Approaching such a surface obliquely, he supposed the particles, when close to it, to be drawn down upon it, as a projectile is deflected by gravity to the surface of the earth. This deflection was, according to Newton, the refraction seen in our last lecture (fi. Finally, it was supposed that differences of colour might be due to differences in the ‘bigness’ of the particles. This was the physical theory of light enunciated and defended by Newton; and you will observe that it simply consists in the transference of conceptions, born in the world of the senses, to a subsensible world.

But, though the region of physical theory lies thus behind the world 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.

Se. 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.

Se. 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.

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. 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:-

’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.

Se. 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 raréfactions 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 raréfactions 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 raréfactions 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.

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.

Se. Interference of Light.

The principle of interference, as just stated, applies to the waves of light as it does to the waves of water and the waves of sound. And the conditions of interference are the same in all three. If two series of light-waves of the same length start at the same moment from a common origin (say A, fi, crest coincides with crest, sinus with sinus, and the two systems blend together to a single system (A m n) of double amplitude. If both series start at the same moment, one of them being, at starting, a whole wavelength in advance of the other, they also add themselves together, and we have an augmented luminous effect. The same occurs when the one system of waves is any even number of semi-undulations in advance of the other. But if the one system be half a wave-length (as at A’ a’, fi, or any odd number of half wavelengths, in advance, then the crests of the one fall upon the sinuses of the other; the one system, in fact, tends to lift the particles of ether at the precise places where the other tends to depress them; hence, through the joint action of these opposing forces (indicated by the arrows) the light-ether remains perfectly still. This stillness of the ether is what we call darkness, which corresponds with a dead level in the case of water.

It was said in our first lecture, with reference to the colours produced by absorption, that the function of natural bodies is selective, not creative; that they extinguish certain constituents of the white solar light, and appear in the colours of the unextinguished light. It must at once occur to you that, inasmuch as we have in interference an agency by which light may be self-extinguished, we may have in it the conditions for the production of colour. But this would imply that certain constituents are quenched by interference, while others are permitted to remain. This is the fact; and it is entirely due to the difference in the lengths of the waves of light.

Se. Colours of thin Films. Observations of Boyle and Hooke.

This subject may be illustrated by the phenomena which first suggested the undulatory theory to the mind of Hooke. These are the colours of thin transparent films of all kinds, known as the colours of thin plates. In this relation no object in the world possesses a deeper scientific interest than a common soap-bubble. And here let me say emerges one of the difficulties which the student of pure science encounters in the presence of ‘practical’ communities like those of America and England; it is not to be expected that such communities can entertain any profound sympathy with labours which seem so far removed from the domain of practice as are many of the labours of the man of science. Imagine Dr. Draper spending his days in blowing soap-bubbles and in studying their colours! Would you show him the necessary patience, or grant him the necessary support? And yet be it remembered it was thus that minds like those of Boyle, Newton and Hooke were occupied; and that on such experiments has been founded a theory, the issues of which are incalculable. I see no other way for you, laymen, than to trust the scientific man with the choice of his inquiries; he stands before the tribunal of his peers, and by their verdict on his labours you ought to abide.

Whence, then, are derived the colours of the soap-bubble? Imagine a beam of white light impinging on the bubble. When it reaches the first surface of the film, a known fraction of the light is reflected back. But a large portion of the beam enters the film, reaches its second surface, and is again in part reflected. The waves from the second surface thus turn back and hotly pursue the waves from the first surface. And, if the thickness of the film be such as to cause the necessary retardation, the two systems of waves interfere with each other, producing augmented or diminished light, as the case may be.

But, inasmuch as the waves of light are of different lengths, it is plain that, to produce extinction in the case of the longer waves, a greater thickness of film is necessary than in the case of the shorter ones. Different colours, therefore, must appear at different thicknesses of the film.

Take with you a little bottle of spirit of turpentine, and pour it into one of your country ponds. You will then see the glowing of those colours over the surface of the water. On a small scale we produce them thus: A common tea-tray is filled with water, beneath the surface of which dips the end of a pipette. A beam of light falls upon the water, and is reflected by it to the screen. Spirit of turpentine is poured into the pipette; it descends, issues from the end in minute drops, which rise in succession to the surface. On reaching it, each drop spreads suddenly out as a film, and glowing colours immediately flash forth upon the screen. The colours change as the thickness of the film changes by evaporation. They are also arranged in zones, in consequence of the gradual diminution of thickness from the centre outwards.

Any film whatever will produce these colours. The film of air between two plates of glass squeezed together, exhibits, as shown by Hooke, rich fringes of colour. A particularly fine example of these fringes is now before you. Nor is even air necessary; the rupture of optical continuity suffices. Smite with an axe the black, transparent ice-black, because it is pure and of great depth-under the moraine of a glacier; you readily produce in the interior flaws which no air can reach, and from these flaws the colours of thin plates sometimes break like fire. But the source of most historic interest is, as already stated, the soap-bubble. With one of the mixtures employed by the eminent blind philosopher, Plateau, in his researches on the cohesion figures of thin films, we obtain in still air a bubble ten or twelve inches in diameter. You may look at the bubble itself, or you may look at its projection upon the screen; rich colours arranged in zones are, in both cases, exhibited. Rendering the beam parallel, and permitting it to impinge upon the sides, bottom, and top of the bubble, gorgeous fans of colour, reflected from the bubble, overspread the screen, rotating as the beam is carried round. By this experiment the internal motions of the film are also strikingly displayed.

Not in a moment are great theories elaborated: the facts which demand them become first prominent; then, to the period of observation succeeds a period of pondering and of tentative explanation. By such efforts the human mind is gradually prepared for the final theoretic illumination. The colours of thin plates, for example, occupied the attention of Robert Boyle. In his ‘Experimental History of Colours’ he contends against the schools which affirmed that colour was ’a penetrative quality that reaches to the innermost parts of the object,’ adducing opposing facts. ‘To give you a first instance,’ he says, ’I shall need but to remind you of what I told you a little after the beginning of this essay, touching the blue and red and yellow that may be produced upon a piece of tempered steel; for these colours, though they be very vivid, yet if you break the steel they adorn, they will appear to be but superficial.’ He then describes, in phraseology which shows the delight he took in his work, the following beautiful experiment:-

’We took a quantity of clean lead, and melted it with a strong fire, and then immediately pouring it out into a clean vessel of convenient shape and matter (we used one of iron, that the great and sudden heat might not injure it), and then carefully and nimbly taking off the scum that floated on the top, we perceived, as we expected, the smooth and glossy surface of the melted matter to be adorned with a very glorious colour, which, being as transitory as delightful, did almost immediately give place to another vivid colour, and that was as quickly succeeded by a third, and this, as it were, chased away by a fourth; and so these wonderfully vivid colours successively appeared and vanished till the metal ceasing to be hot enough to hold any longer this pleasing spectacle, the colours that chanced to adorn the surface when the lead thus began to cool remained upon it, but were so superficial that how little soever we scraped off the surface of the lead, we did, in such places, scrape off all the colour.’ ’These things,’ he adds, ’suggested to me some thoughts or ravings which I have not now time to acquaint you with.’

He extends his observations to essential oils and spirits of wine, ’which being shaken till they have good store of bubbles, those bubbles will (if attentively considered) appear adorned with various and lovely colours, which all immediately vanish upon the retrogressing of the liquid which affords these bubbles their skins into the rest of the oil.’ He also refers to the colour of glass films. ’I have seen one that was skilled in fashioning glasses by the help of a lamp blowing some of them so strongly as to burst them; whereupon it was found that the tenacity of the metal was such that before it broke it suffered itself to be reduced into films so extremely thin that they constantly showed upon their surface the varying colours of the rainbow.’

Subsequent to Boyle the colours of thin plates occupied the attention of Robert Hooke, in whose writings we find a dawning of the undulatory theory of light. He describes with great distinctness the colours obtained with thin flakes of ‘Muscovy glass’ (talc), also those surrounding flaws in crystals where optical continuity is destroyed. He shows very clearly the dependence of the colour upon the thickness of the film, and proves by microscopic observation that plates of a uniform thickness yield uniform colours. ‘If,’ he says, ’you take any small piece of the Muscovy glass, and with a needle, or some other convenient instrument, cleave it oftentimes into thinner and thinner laminae, you shall find that until you come to a determinate thinness of them they shall appear transparent and colourless; but if you continue to split and divide them further, you shall find at last that each plate shall appear most lovely tinged or imbued with a determinate colour. If, further, by any means you so flaw a pretty thick piece that one part begins to cleave a little from the other, and between these two there be gotten some pellucid medium, those laminated or pellucid bodies that fill that space shall exhibit several rainbows or coloured lines, the colours of which will be disposed and ranged according to the various thicknesses of the several parts of the plate.’ He then describes fully and clearly the experiment with pressed glasses already referred to:-

’Take two small pieces of ground and polished looking-glass plate, each about the bigness of a shilling: take these two dry, and with your forefingers and thumbs press them very hard and close together, and you shall find that when they approach each other very near there will appear several irises or coloured lines, in the same manner almost as in the Muscovy glass; and you may very easily change any of the colours of any part of the interposed body by pressing the plates closer and harder together, or leaving them more lax-that is, a part which appeared coloured with a red, may presently be tinged with a yellow, blue, green, purple, or the like. ‘Any substance,’ he says, ‘provided it be thin and transparent, will show these colours.’ Like Boyle, he obtained them with glass films; he also procured them with bubbles of pitch, rosin, colophony, turpentine, solutions of several gums, as gum arabic in water, any glutinous liquor, as wort, wine, spirit of wine, oyl of turpentine, glare of snails, &c.

Hooke’s writings show that even in his day the idea that both light and heat are modes of motion had taken possession of many minds. ‘First,’ he says, ’that all kind of fiery burning bodies have their parts in motion I think will be easily granted me. That the spark struck from a flint and steel is in rapid agitation I have elsewhere made probable;... that heat argues a motion of the internal parts is (as I said before) generally granted;... and that in all extremely hot shining bodies there is a very quick motion that causes light, as well as a more robust that causes heat, may be argued from the celerity wherewith the bodies are dissolved. Next, it must be a vibrative motion.’ His reference to the quick motion of light and the more robust motion of heat is a remarkable stroke of sagacity; but Hooke’s direct insight is better than his reasoning; for the proofs he adduces that light is ‘a vibrating motion’ have no particular bearing upon the question.

Still the Undulatory Theory had undoubtedly dawned upon the mind of this remarkable man. In endeavouring to account for the colours of thin plates, he again refers to the relation of colour to thickness: he dwells upon the fact that the film which shows these colours must be transparent, proving this by showing that however thin an opaque body was rendered no colours were produced. ‘This,’ he says, ’I have often tried by pressing a small globule of mercury between two smooth plates of glass, whereby I have reduced that body to a much greater thinness than was requisite to exhibit the colours with a transparent body.’ Then follows the sagacious remark that to produce the colours ’there must be a considerable reflecting body adjacent to the under or further side of the lamina or plate: for this I always found, that the greater that reflection was the more vivid were the appearing colours. From which observation,’ he continues, ’it is most evident, that the reflection from the further or under side of the body is the principal cause of the production of these colours.

He draws a diagram, correctly representing the reflection at the two surfaces of the film; but here his clearness ends. He ascribes the colours to a coalescence or confusion of the two reflecting pulses; the principal of interference being unknown to him, he could not go further in the way of explanation.

Se. Newton’s Rings. Relation of Colour to Thickness of Film.

In this way, then, by the active operation of different minds, facts are observed, examined, and the precise conditions of their appearance determined. All such work in science is the prelude to other work; and the efforts of Boyle and Hooke cleared the way for the optical career of Newton. He conquered the difficulty which Hooke had found insuperable, and determined by accurate measurements the relation of the thickness of the film to the colour it displays. In doing this his first care was to obtain a film of variable and calculable depth. On a plano-convex glass lens (D B E, fi of very feeble curvature he laid a plate of glass (A C) with a plane surface, thus obtaining a film of air of gradually increasing depth from the point of contact (B) outwards. On looking at the film in monochromatic light he saw, with the delight attendant on fulfilled prevision, surrounding the place of contact, a series of bright rings separated from each other by dark ones, and becoming more closely packed together as the distance from the point of contact augmented (as in fi. When he employed red light, his rings had certain diameters; when he employed blue light, the diameters were less. In general terms, the more refrangible the light the smaller were the rings. Causing his glasses to pass through the spectrum from red to blue, the rings gradually contracted; when the passage was from blue to red, the rings expanded. This is a beautiful experiment, and appears to have given Newton the most lively satisfaction. When white light fell upon, the glasses, inasmuch as the colours were not superposed, a series of iris-coloured circles was obtained. A magnified image of Newton’s rings is now before you, and, by employing in succession red, blue, and white light, we obtain all the effects observed by Newton. You notice that in monochromatic light the rings run closer and closer together as they recede from the centre. This is due to the fact that at a distance the film of air thickens more rapidly than near the centre. When white light is employed, this closing up of the rings causes the various colours to be superposed, so that after a certain thickness they are blended together to white light, the rings then ceasing altogether. It needs but a moment’s reflection to understand that the colours of thin plates, produced by white light, are never unmixed or monochromatic.

Newton compared the tints obtained in this way with the tints of his soap-bubble, and he calculated the corresponding thickness. How he did this may be thus made plain to you: Suppose the water of the ocean to be absolutely smooth; it would then accurately represent the earth’s curved surface. Let a perfectly horizontal plane touch the surface at any point. Knowing the earth’s diameter, any engineer or mathematician in this room could tell you how far the sea’s surface will lie below this plane, at the distance of a yard, ten yards, a hundred yards, or a thousand yards from the point of contact of the plane and the sea. It is common, indeed, in levelling operations, to allow for the curvature of the earth. Newton’s calculation was precisely similar. His plane glass was a tangent to his curved one. From its refractive index and focal distance he determined the diameter of the sphere of which his curved glass formed a segment, he measured the distances of his rings from the place of contact, and he calculated the depth between the tangent plane and the curved surface, exactly as the engineer would calculate the distance between his tangent plane and the surface of the sea. The wonder is, that, where such infinitesimal distances are involved, Newton, with the means at his disposal, could have worked with such marvellous exactitude.

To account for these rings was the greatest optical difficulty that Newton, ever encountered. He quite appreciated the difficulty. Over his eagle eye there was no film-no vagueness in his conceptions. At the very outset his theory was confronted by the question, Why, when a beam of light is incident on a transparent body, are some of the light-particles reflected and some transmitted? Is it that there are two kinds of particles, the one specially fitted for transmission and the other for reflection? This cannot be the reason; for, if we allow a beam of light which has been reflected from one piece of glass to fall upon another, it, as a general rule, is also divided into a reflected and a transmitted portion. The particles once reflected are not always reflected, nor are the particles once transmitted always transmitted. Newton saw all this; he knew he had to explain why it is that the self-same particle is at one moment reflected and at the next moment transmitted. It could only he through some change in the condition of the particle itself. The self-same particle, he affirmed, was affected by ‘fits’ of easy transmission and reflection.

Se. Theory of ‘Fits’ applied to Newton’s Rings.

If you are willing to follow me in an attempt to reveal the speculative groundwork of this theory of fits, the intellectual discipline will, I think, repay you for the necessary effort of attention. Newton was chary of stating what he considered to be the cause of the fits, but there can hardly be a doubt that his mind rested on a physical cause. Nor can there be a doubt that here, as in all attempts at theorising, he was compelled to fall back upon experience for the materials of his theory. Let us attempt to restore his course of thought and observation. A magnet would furnish him with the notion of attracted and repelled poles; and he who habitually saw in the visible an image of the invisible would naturally endow his light-particles with such poles. Turning their attracted poles towards a transparent substance, the particles would be sucked in and transmitted; turning their repelled poles, they would be driven away or reflected. Thus, by the ascription of poles, the transmission and reflection of the self-same particle at different times might be accounted for.

Consider these rings of Newton as seen in pure red light: they are alternately bright and dark. The film of air corresponding to the outermost of them is not thicker than an ordinary soap-bubble, and it becomes thinner on approaching the centre; still Newton, as I have said, measured the thickness corresponding to every ring, and showed the difference of thickness between ring and ring. Now, mark the result. For the sake of convenience, let us call the thickness of the film of air corresponding to the first dark ring d; then Newton found the distance corresponding to the second dark ring 2 d; the thickness corresponding to the third dark ring 3 d; the thickness corresponding to the tenth dark ring 10 d, and so on. Surely there must be some hidden meaning in this little distance, d, which turns up so constantly? One can imagine the intense interest with which Newton pondered its meaning. Observe the probable outcome of his thought. He had endowed his light-particles with poles, but now he is forced to introduce the notion of periodic recurrence. Here his power of transfer from the sensible to the subsensible would render it easy for him to suppose the light-particles animated, not only with a motion of translation, but also with a motion of rotation. Newton’s astronomical knowledge rendered all such conceptions familiar to him. The earth has such a double motion. In the time occupied in passing over a million and a half of miles of its orbit-that is, in twenty-four hours-our planet performs a complete rotation; and in the time required to pass over the distance d, Newton’s light-particle might be supposed to perform a complete rotation. True, the light-particle is smaller than the planet, and the distance d, instead of being a million and a half of miles, is a little over the ninety thousandth of an inch. But the two conceptions are, in point of intellectual quality, identical.

Imagine, then, a particle entering the film of air where it possesses this precise thickness. To enter the film, its attracted end must be presented. Within the film it is able to turn once completely round; at the other side of the film its attracted pole will be again presented; it will, therefore, enter the glass at the opposite side of the film and be lost to the eye. All round the place of contact, wherever the film possesses this precise thickness, the light will equally disappear-we shall therefore have a ring of darkness.

And now observe how well this conception falls in with the law of proportionality discovered by Newton. When the thickness of the film is 2 d, the particle has time to perform, two complete rotations within the film; when the thickness is 3 d, three complete rotations; when 10 d, ten complete rotations are performed. It is manifest that in each of these cases, on arriving at the second surface of the film, the attracted pole of the particle will be presented. It will, therefore, be transmitted; and, because no light is sent to the eye, we shall have a ring of darkness at each of these places.

The bright rings follow immediately from the same conception. They occur between the dark rings, the thicknesses to which they correspond being also intermediate between those of the dark ones. Take the case of the first bright ring. The thickness of the film is 1/2_d_; in this interval the rotating particle can perform only half a rotation. When, therefore, it reaches the second surface of the film, its repelled pole is presented; it is, therefore, driven back and reaches the eye. At all distances round the centre corresponding to this thickness the same effect is produced, and the consequence is a ring of brightness. The other bright rings are similarly accounted for. At the second one, where the thickness is 11/2_d_, a rotation and a half is performed; at the third, two rotations and a half; and at each of these places the particles present their repelled poles to the lower surface of the film. They are therefore sent back to the eye, and produce there the impression of brightness. This analysis, though involving difficulties when closely scrutinised, enables us to see how the theory of fits may have grown into consistency in the mind of Newton.

It has been already stated that the Emission Theory assigned a greater velocity to light in glass and water than in air or stellar space; and that on this point it was at direct issue with the theory of undulation, which makes the velocity in air or stellar space greater than in glass or water. By an experiment proposed by Arago, and executed with consummate skill by Foucault and Fizeau, this question was brought to a crucial test, and decided in favour of the theory of undulation.

In the present instance also the two theories are at variance. Newton assumed that the action which produces the alternate bright and dark rings took place at a single surface; that is, the second surface of the film. The undulatory theory affirms that the rings are caused by the interference of waves reflected from both surfaces. This also has been demonstrated by experiment. By a proper arrangement, as we shall afterwards learn, we may abolish reflection from one of the surfaces of the film, and when this is done the rings vanish altogether.

Rings of feeble intensity are also formed by transmitted light. These are referred by the undulatory theory to the interference of waves which have passed directly through the film, with others which have suffered two reflections within the film, and are thus completely accounted for.

Se. The Diffraction of Light.

Newton’s espousal of the Emission Theory is said to have retarded scientific discovery. It might, however, be questioned whether, in the long run, the errors of great men have not really their effect in rendering intellectual progress rhythmical, instead of permitting it to remain uniform, the ‘retardation’ in each case being the prelude to a more impetuous advance. It is confusion and stagnation, rather than error, that we ought to avoid. Thus, though the undulatory theory was held back for a time, it gathered strength in the interval, and its development within the last half century has been so rapid and triumphant as to leave no rival in the field. We have now to turn to the investigation of new classes of phenomena, of which it alone can render a satisfactory account.

Newton, who was familiar with the idea of an ether, and who introduced it in some of his speculations, objected, as already stated, that if light consisted of waves shadows could not exist; for that the waves would bend round the edges of opaque bodies and agitate the ether behind them. He was right in affirming that this bending ought to occur, but wrong in supposing that it does not occur. The bending is real, though in all ordinary cases it is masked by the action of interference. This inflection of the light receives the name of Diffraction.

To study the phenomena of diffraction it is necessary that our source of light should be a physical point, or a fine line; for when a luminous surface is employed, the waves issuing from different points of the surface obscure and neutralize each other. A point of light of high intensity is obtained by admitting the parallel rays of the sun through an aperture in a window-shutter, and concentrating the beam by a lens of short focus. The small solar image at the focus constitutes a suitable point of light. The image of the sun formed on the convex surface of a glass bead, or of a watch-glass blackened within, though less intense, will also answer. An intense line of light is obtained by admitting the sunlight through a slit and sending it through a strong cylindrical lens. The slice of light is contracted to a physical line at the focus of the lens. A glass tube blackened within and placed in the light, reflects from its surface a luminous line which, though less intense, also answers the purpose.

In the experiment now to be described a vertical slit of variable width is placed in front of the electric lamp, and this slit is looked at from a distance through another vertical slit, also of variable aperture, and held in the hand.

The light of the lamp being, in the first place, rendered monochromatic by placing a pure red glass in front of the slit, when the eye is placed in the straight line drawn through both slits an extraordinary appearance (shown in fi is observed. Firstly, the slit in front of the lamp is seen as a vivid rectangle of light; but right and left of it is a long series of rectangles, decreasing in vividness, and separated from each other by intervals of absolute darkness.

The breadth of these bands is seen to vary with the width of the slit held before the eye. When the slit is widened the bands become narrower, and crowd more losely together; when the slit is narrowed, the individual bands widen and also retreat from each other, leaving between them wider spaces of darkness than before.

Leaving everything else unchanged, let a blue glass or a solution of ammonia-sulphate of copper, which gives a very pure blue, be placed in the path of the light. A series of blue bands is thus obtained, exactly like the former in all respects save one; the blue rectangles are narrower, and they are closer together than the red ones.

If we employ colours of intermediate refrangibilities, which we may do by causing the different colours of a spectrum to shine through the slit, we obtain bands of colour intermediate in width, and occupying intermediate positions, between those of the red and blue. The aspect of the bands in red, green, and violet light is represented in fi. When white light, therefore, passes through the slit the various colours are not superposed, and instead of a series of monochromatic bands, separated from each other by intervals of darkness, we have a series of coloured spectra placed side by side. When the distant slit is illuminated by a candle flame, instead of the more intense electric light, or when a distant platinum wire raised to a white heat by an electric current is employed, substantially the same effects are observed.

Se. Application of the Wave-theory to the Phenomena of
Diffraction
.

Of these and of a multitude of similar effects the Emission Theory is incompetent to offer any satisfactory explanation. Let us see how they are accounted for by the Theory of Undulation.

And here, with the view of reaching absolute clearness, I must make an appeal to that faculty the importance of which I have dwelt upon so earnestly here and elsewhere-the faculty of imagination. Figure yourself upon the sea-shore, with a well-formed wave advancing. Take a line of particles along the front of the wave, all at the same distance below the crest; they are all rising in the same manner and at the same rate. Take a similar line of particles on the back of the wave, they are all falling in the same manner and at the same rate. Take a line of particles along the crest, they are all in the same condition as regards the motion of the wave. The same is true for a line of particles along the furrow of the wave.

The particles referred to in each of these cases respectively, being in the same condition as regards the motion of the wave, are said to be in the same phase of vibration. But if you compare a particle on the front of the wave with one at the back; or, more generally, if you compare together any two particles not occupying the same position in the wave, their conditions of motion not being the same, they are said to be in different phases of vibration. If one of the particles lie upon the crest, and the other on the furrow of the wave, then, as one is about to rise and the other about to fall, they are said to be in opposite phases of vibration.

There is still another point to be cleared up-and it is one of the utmost importance as regards our present subject. Let O (fi be a spot in still water which, when disturbed, produces a series of circular waves: the disturbance necessary to produce these waves is simply an oscillation up and down of the water at O. Let m n be the position of the ridge of one of the waves at any moment, and m’ n’ its position a second or two afterwards. Now every particle of water, as the wave passes it, oscillates, as we have learned, up and down. If, then, this oscillation be a sufficient origin of wave-motion, each distinct particle of the wave m n ought to give birth, to a series of circular waves. This is the important point up to which I wish to lead you. Every particle of the wave m n does act in this way. Taking each particle as a centre, and surrounding it by a circular wave with a radius equal to the distance between m n and m’ n’, the coalescence of all these little waves would build up the large ridge m’ n’ exactly as we find it built up in nature. Here, in fact, we resolve the wave-motion into its elements, and having succeeded in doing this we shall have no great difficulty in applying our knowledge to optical phenomena.

Now let us return to our slit, and, for the sake of simplicity, we will first consider the case of monochromatic light. Conceive a series of waves of ether advancing from the first slit towards the second, and finally filling the second slit. When each wave passes through the latter it not only pursues its direct course to the retina, but diverges right and left, tending to throw into motion the entire mass of the ether behind the slit. In fact, as already explained, every point of the wave which fills the slit is itself a centre of a new wave system which is transmitted in all directions through the ether behind the slit. This is the celebrated principle of Huyghens: we have now to examine how these secondary waves act upon each other.

Let us first regard the central band of the series. Let AP (fi be the width of the aperture held before the eye, grossly exaggerated of course, and let the dots across the aperture represent ether particles, all in the same phase of vibration. Let E T represent a portion of the retina. From O, in the centre of the slit, let a perpendicular O R be imagined drawn upon the retina. The motion communicated to the point R will then be the sum of all the motions emanating in this direction from the ether particles in the slit. Considering the extreme narrowness of the aperture, we may, without sensible error, regard all points of the wave A P as equally distant from R. No one of the partial waves lags sensibly behind the others: hence, at R, and in its immediate neighbourhood, we have no sensible reduction of the light by interference. This undiminished light produces the brilliant central band of the series.

Let us now consider those waves which diverge laterally behind the second slit. In this case the waves from the two sides of the slit have, in order to converge upon the retina, to pass over unequal distances. Let A P (fi represent, as before, the width of the second slit. We have now to consider the action of the various parts of the wave A P upon a point R’ of the retina, not situated in the line joining the two slits.

Let us take the particular case in which the difference of path from the two marginal points A, P, to the retina is a whole wave-length of the red light; how must this difference affect the final illumination of the retina?

Let us fix our attention upon the particular oblique line that passes through the centre O of the slit to the retina at R’. The difference of path between the waves which pass along this line and those from the two margins is, in the case here supposed, half a wavelength. Make e R’ equal to P R’, join P and e, and draw O d parallel to P e. A e is then the length of a wave of light, while A d is half a wave-length. Now the least reflection will make it clear that not only is there discordance between the central and marginal waves, but that every line of waves such as x R’, on the one side of O R’, finds a line x’ R’ upon the other side of O R’, from which its path differs by half an undulation-with which, therefore, it is in complete discordance. The consequence is, that the light on the one side of the central line will completely abolish the light on the other side of that line, absolute darkness being the result of their coalescence. The first dark interval of our series of bands is thus accounted for. It is produced by an obliquity of direction which causes the paths of the marginal waves to be a whole wave-length different from each other.

When the difference between the paths of the marginal waves is half a wave-length, a partial destruction of the light is effected. The luminous intensity corresponding to this obliquity is a little less than one-half-accurately 0.4-that of the undiffracted light. If the paths of the marginal waves be three semi-undulations different from each other, and if the whole beam be divided into three equal parts, two of these parts will, for the reasons just given, completely neutralize each other, the third only being effective. Corresponding, therefore, to an obliquity which produces a difference of three semi-undulations in the marginal waves, we have a luminous band, but one of considerably less intensity than the undiffracted central band.

With a marginal difference of path of four semi-undulations we have a second extinction of the entire beam, because here the beam can be divided into four equal parts, every two of which quench each other. A second space of absolute darkness will therefore correspond to the obliquity producing this difference. In this way we might proceed further, the general result being that, whenever the direction of wave-motion is such as to produce a marginal difference of path of an even number of semi-undulations, we have complete extinction; while, when the marginal difference is an odd number of semi-undulations, we have only partial extinction, a portion of the beam remaining as a luminous band.

A moment’s reflection will make it plain that the wider the slit the less will be the obliquity of direction needed to produce the necessary difference of path. With a wide slit, therefore, the bands, as observed, will be closer together than with a narrow one. It is also plain that the shorter the wave, the less will be the obliquity required to produce the necessary retardation. The maxima and minima of violet light must therefore fall nearer to the centre than the maxima and minima of red light. The maxima and minima of the other colours fall between these extremes. In this simple way the undulatory theory completely accounts for the extraordinary appearance above referred to.

When a slit and telescope are used, instead of the slit and naked eye, the effects are magnified and rendered more brilliant. Looking, moreover, through a properly adjusted telescope with a small circular aperture in front of it, at a distant point of light, the point is seen encircled by a series of coloured bands. If monochromatic light be used, these bands are simply bright and dark, but with white light the circles display iris-colours. If a slit be shortened so as to form a square aperture, we have two series of spectra at right angles to each other. The effects, indeed, are capable of endless variation by varying the size, shape, and number of the apertures through which the point of light is observed. Through two square apertures, with their corners touching each other as at A, Schwerd observed the appearance shown in fi. Adding two others to them, as at B, he observed the appearance represented in fi. The position of every band of light and shade in such figures has been calculated from theory by Fresnel, Fraunhofer, Herschel, Schwerd, and others, and completely verified by experiment. Your eyes could not tell you with greater certainty of the existence of these bands than the theoretic calculation.

The street-lamps at night, looked at through the meshes of a handkerchief, show diffraction phenomena. The diffraction effects obtained in looking through a bird’s feathers are, as shown by Schwerd, very brilliant. The iridescence of certain Alpine clouds is also an effect of diffraction which may be imitated by the spores of Lycopodium. When shaken over a glass plate these spores cause a point of light, looked at through the dusted plate, to be surrounded by coloured circles, which rise to actual splendour when the light becomes intense. Shaken in the air the spores produce the same effect. The diffraction phenomena obtained during the artificial precipitation of clouds from the vapours of various liquids in an intensely illuminated tube are, as I have elsewhere shewn, exceedingly fine.

One of the most interesting cases of diffraction by small particles that ever came before me was that of an artist whose vision was disturbed by vividly coloured circles. He was in great dread of losing his sight; assigning as a cause of his increased fear that the circles were becoming larger and the colours more vivid. I ascribed the colours to minute particles in the humours of the eye, and ventured to encourage him by the assurance that the increase of size and vividness on the part of the circles indicated that the diffracting particles were becoming smaller, and that they might finally be altogether absorbed. The prediction was verified. It is needless to say one word on the necessity of optical knowledge in the case of the practical oculist.

Without breaking ground on the chromatic phenomena presented by crystals, two other sources of colour may be mentioned here. By interference in the earth’s atmosphere, the light of a star, as shown by Arago, is self-extinguished, the twinkling of the star and the changes of colour which it undergoes being due to this cause. Looking at such a star through an opera-glass, and shaking the glass so as to cause the image of the star to pass rapidly over the retina, you produce a row of coloured beads, the spaces between which correspond to the periods of extinction. Fine scratches drawn upon glass or polished metal reflect the waves of light from their sides; and some, being reflected from the opposite sides of the same scratch, interfere with and quench each other. But the obliquity of reflection which extinguishes the shorter waves does not extinguish the longer ones, hence the phenomena of colours. These are called the colours of striated surfaces. They are beautifully illustrated by mother-of-pearl. This shell is composed of exceedingly thin layers, which, when cut across by the polishing of the shell, expose their edges and furnish the necessary small and regular grooves. The most conclusive proof that the colours are due to the mechanical state of the surface is to be found in the fact, established by Brewster, that by stamping the shell carefully upon black sealing-wax, we transfer the grooves, and produce upon the wax the colours of mother-of-pearl.