times slow, sometimes rapid, and at all times | can maintain itself against the voice of Nature a source of intellectual joy. When rapid, the speaking through experiment. But the voice pleasure is concentrated and becomes a kind of Nature may be an uncertain voice, through of ecstasy or intoxication. To any one who the scantiness of data. This was the case at has experienced this pleasure, even in a mod- the period now referred to, and at such a peerate degree, the action of Archimedes when riod by the authority of Newton all antagohe quitted the bath, and ran naked, crying nists were naturally overborne. "Eureka!" through the streets of Syracuse, becomes intelligible. How, then, did it fare with the theory of Newton, when the deductions from it were brought face to face with natural phenomena ? To the mind's eye, Newton's elastic particles present themselves like particles of sensible magnitude. The same reasoning applies to both; the same experimental checks exist for both. Tested by experiment, then, Newton's theory 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. Still, even at an early period of the existence of the Emission Theory, one or two great names were found recording a protest against it; and 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: ound is conveyed in waves or pu'ses through the air; and no sooner was this truth well housed in the mind than it was transformed into 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 guilty of so clumsy a contrivance as the filling of space with ether in order 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 other 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 indeed applied to various phenomena of optics by the celebrated astronomer, Huyghens. It 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 I 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, Still, this great Emission Theory, which held its ground so long, resembled one of those circles which, according to your countryman Emerson, the 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, one of the most remarkable men that England ever produced. 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-moti n; 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 his 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. Permit me, by a kind of geometrical construction which I once employed 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, which shall form a 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. He would not, in my opinion, reach the line; for if he did he would be taller intellectually than Young, and there was, I believe, 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 ide s 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 countrymen-deemed in fact a dreamer, through the vigorous audacity 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, remade independently, as Helmholtz_says, 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 turn filled with the fame of Young's colleague at the Royal In stitution, Davy, and afterwards with the fame of Faraday. Carlyle refers to the remark of Novalis, that a man's self-trust is enormously increased the moment he finds that others believe 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. Our hardest work is now before us. And, as I have often had occasion to notice that capacity for hard work depends in a great measure on the antecedent winding up of the will and determination, I would call upon you to gird up your loins for our coming labors. If we succeed in climbing the hill which faces us to-night, our future efforts will be comparatively light. 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 sea-shore 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 passed 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 onward 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 parti cles of water are made to vibrate across the line of propagation.* And now we have to take a step forward, 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 hold 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, the wave is lifted to a double height; if furrow coincide with crest, the motions are in opposition, and thei. sum is zero. We have then still water, which we shall learn presently corresponds to what we call darkness in reference to our present subject. This action of wave upon wave is technically called interference, a term to be remembered. Thomas Young's fundamental discovery in optics was that the principle of Interference applied 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 with the details of the motion, but I may draw atten*I do not wish to encumber the conception here tion to the beautiful model of Professor Lyman, wherein waves are shown to be produced by the cir the brothers Weber, is the real motion in case of cular motion of the particles. This, as proved by water-waves. light. They are parts of a spiral, drawn upon a circle of blackened glass, and, when the circle rotates, the spots move in successive pulses over the screen. You have here clearly set before you how the pulses travel incessantly forward, while the particles that compose them perform oscillations to and fro. This is the picture of a sound-wave, in which the vibrations are longitudinal. By another glass wheel, we produce an image of a transverse wave, and here we observe the waves travelling in succession over the screen, while each individual spot of light performs an excursion to and fro across the line of propagation. quenched each other and darkened the spot. | gation. The vibrations of the air are longiThis was a statement of fundamental signifi- tudinal, the vibrations of the ether are transcance, but it required the discoveries and the versal. genius of Young to give it meaning. How It is my desire that you should realize with he did so, I will now try to make clear to clearness the character of wave-motion, both you. You know that air is compressible; in ether and in air. And, with this view, I that by pressure it can be rendered more bring before you an experiment wherein the dense, and that by dilatation it can be ren-air-particles are represented by small spots of dered 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 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 conse quence of this coincidence would be a louder sound than that produced by either system of Notice what follows when the glass wheel waves taken singly. But you can also ima- is turned very quickly. Objectively considgine a state of things where the condensa-ered, the transverse waves propagate themtions of the one system fall upon the rarefac-selves as before, but subjectively the effect is tions of the other system. In this case 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. totally changed. Because of the retention of impressions upon the retina, the spots of light simply describe a series of parallel luminous lines upon the screen, the length of these lines marking the amplitude of the vibration. The impression of wave-motion has totally disappeared. The most familiar illustration of the interThe analogy between sound and light here ference of sound-waves is furnished by the at once flashes upon the mind. Young gen beats produced by two musical sounds slightly eralized this observation. He discovered a out of unison. These two tuning-forks are multitude of similar cases, and determined now in perfect unison, and when they are their precise conditions. On the assumption agitated together the two sounds flow without that light was wave-motion, all his experi- roughness, as if they were but one. But, by ments on interference were explained; on the attaching to one of the forks a two-cent piece, assumption that light was flying particles, we cause it to vibrate a little more slowly nothing was explained. In the time of Huy- than its neighbor. Suppose that one of them ghens and Euler a medium had been assumed performs 101 vibrations in the time required for the transmission of the waves of light; by the other to perform 100, and suppose but Newton raised the objection that, if light that at starting the condensations and rareconsisted of the waves of such a medium, factions of both forks coincide. At the 101st shadows could not exist. The waves, he vibration of the quickest fork they will again contended, would bend round opaque bodies coincide, the quicker fork at this point havand produce the motion of light behind them, ing gained one whole vibration, or one whole as sound turns a corner, or as waves of water wave upon the other. But a little reflection wash round a rock. It was proved that the will make it clear that, at the 50th vibration, bending round referred to by Newton actually the two forks are in opposition; here the one occurs, but that the inflected waves abolish tends to produce a condensation where the each other by their mutual interference. other tends to produce a rarefaction; by the Young also discerned a fundamental differ- united action of the two forks, therefore, the ence between the waves of light and those of sound is quenched, and we have a pause of sound. Could you see the air through which silence. This occurs where one fork has sound-waves are passing, you would observe gained half a wave-length upon the other. every individual particle of air oscillating to At the 101st vibration we have again coinci and fro in the direction of propagation. dence, and, therefore, augmented sound; at Could you see the ether, you would also find the 150th vibration we have again a quenchevery individual particle making a small ex-ing of the sound. Icre the one fork is three cursion to and fro, but here the motion, like half-waves in advance of the other. In genthat assigned to the water-particles above re-eral terms, the waves conspire when the one ferred to, would be across the line of propa-series is an even number of half-wave lengths, and they are destroyed 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. I new wish to show you what may be called the optical expression of those beats. Attached to a large tuning-fork, F (Fig. 2), is a small mirror, which shares the vibrations of the fork, and on to the mirror is thrown a thin beam of light, which shares the vibrations of the mirror. The beam reflected from the fork is received upon a piece of looking-glass, and thrown back upon the screen, where it stamps itself as a small luminous disk. The agitation of the fork by a violin-bow converts that disk into a band of light, and if yo1 simply move your heads to and fro you cause the image of the band to sweep over the retina, drawing it out to a sinuous line, thus proving the periodic character of the motion which produces it. By a sweep of the looking-glass, we can also cover the screen from side to side by a luminous scroll, mn, Fig. 2, the depth of the sinuosities indicating the amplitude of the vibration. band of light gradually shortening as the otion subsides, until, when the motion ceases, we have our luminous disk restored. Weighting one of the forks as we did before, with a two-cent piece, sometimes the forks conspire, and then you have the band of light drawn out to its maximum length; sometimes they oppose each other, and then you have the band of light diminished to a circle. Thus, the beats which address the ear express themselves optically as the alternate elongation and shortening of the band of light. If I move the mirror of this second fork, you have a sinuous line, as before; but the sinuosities are sometimes deep, and sometimes they al most disappear, as in Fig. 3, thus expressing the alternate increase and diminution of the sound, the intensity of which is expressed by the depth of the sinuosities. To Lissajous we owe this mode of illustration. FIG. 2. Instead of receiving the beam reflected from the fork on a piece of looking-glass, we now receive it upon a second mirror attached to a second fork, and cast by it upon the screen. Both forks now act in combination upon the beam. The disk is drawn out, as before, the The pitch of a sound is wholly determined by the rapidity of the vibration, as the inten sity is by the amplitude. The rise of pitch with the rapidity of the impulses may be illustrated by the syren, which consists of a perforated disk rotating over a cylinder into which air is forced, and the end of which is also perforated. When the perforations of the disk coincide with those of the cylinder, a puff escapes; and, when the puffs succeed each other with sufficient rapidity, the impressions upon the auditory nerve link themselves together to a continuous musical note. The more rapid the rotation of the disk the quicker is the succession of the impulses, and the higher the pitch of the note. Indeed, by FIG. 3. means of the syren the number of vibrations | compared, the strictest harmony is found to due to any musical no e, whether it be that of an instrument, of the human voice, or of a flying insect, may be accurately determined. ter. FIG. 4. exist between them. The shortest waves of the visible spectrum are those of the extreme violet; the longest, those of the extreme red; while the other colors are of intermediate pitch or wave-length. The length of a wave of the extreme red is such that it would require 36,918 of them 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 190,000 miles per second. Reducing this to inches, and multiplying the number thus found by 36,918, we obtain the number of waves of the extreme red in 190,000 miles. All these waves enter the eye, and hit the retina at the back of the eye in one second. The number of shocks per second necessary to the production of the impression of red is, therefore, four hundred and fifty-one millions of millions. In a similar manner, it may be found that the number of shocks corresponding to the impression of violet is seven hundred and eighty-nine 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 outwards. And in the ether, just as in the water, the mction of every particle is the algebraic sum of all the separate motions imparted to it. Still, one extinction occur at one point, it is atoned for at some other point. Every star declares by its light its undamaged individuality, as if it alone had sent its thrills through space. In front of our lamp now stands a very homely instrument, S, Fig. 4, of this charac-motion does not blot the other out; or, if The perforated disk is turned by a wheel and band, and, when the two sets of perforations coincide, a series of spots of light, sharply defined by the lens L, ranged on the circumference of a circle, is seen upon the screen. On slowly turning the disk, a flicker is produced by the alternate stoppage and transmission of the light. At the same time air is urged into the syren, and you hear a fluttering sound corresponding to the flickering light. But, by augmenting the rapidity of rotation, the light, though intercepted as before, appears perfectly steady, through the persistence of impressions upon the retina; and, about the time when the optical impression becomes continuous, the auditory impression becomes equally so; the puffs from the syren linking themselves then together to a continuous musical note, which rises in pitch with the rapidity of the rotation. A movement of the head causes the image of the spots to sweep over the retina, producing beaded lines: the same effect is produced upon our screen by the sweep of a looking glass which has received the thin beams from the syren. In the undulatory theory, what pitch is to the ear, color is to the eye. 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 The principle of interference 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, crest coincides with crest, sinus with sinus, and the two systems blend together to a single system of double amplitude. If both series start at the same moment, one of them being, at starting, a whole wave-length in advance of the other, they also add themselves together, and we have an augmented luminous effect. Just as in the case of sound, 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, or any odd number of half wave-lengths 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 their joint action the ether remains perfectly still. This stillness of the ether is what we call darkness, which corresponds, as already stated, with a dead level in the case of water. It was said in our first lecture, with reference to the colors produced by absorption, |