glass capable of rotation. A beam of light is received upon the glass and reflected back upon the line of its incidence. Though the incident and the reflected beams pass in opposite directions, they do not jostle or displace each other. The index being turned, the mirror turns along with it, and at each side of the index the incident and the reflected beams are seen tracking themselves through the dust of the room. The mere inspection of the two angles enclosed between the index and the two beams suffices to show their equality. The same simple apparatus enables us to illustrate a law of great practical importance, name y, that, when a mirror rotates, the angular velocity of a beam reflected from it is twice that of the reflecting mirror. One experiment wil make this plan to you. The mirror is now vertical, and both the incident and the reflected beams are horizontal. Turning the mirror through an angle of 45° the reflected beam is vertical; that is to say, it has moved 90", or through twice the angle of the mirror. One of the problems of science, on which scientific progress mainly depends, is to help the senses of man by carrying them into regions which could never be attained without such help. Thus we arm the eye with the telescope when we want to sound the depths of space, and with the miscroscope when we want to explore motion and structure in their infinitesimal dimensions. Now, this law of angular reflection, coupled with the fact that a beam of light possesses no weight, gives us the means of magnifying small motions to an extraordinary degree. Thus, by attaching mirrors to his suspended magnets, and by wa ching the images of scales reflected from the mirrors, the celebrated Gauss was able to detect the slightest thrill or variation on the part of the earth's magnetic force. The minute elongation of a bar of metal by the mere warmth of the hand may be so magnified by this method as to cause the index-beam to move from the ceiling to the floor of this room. The elongation of a bar of iron when it is magnetized may be thus demonstrated. By a similar arrangement the feeble attractions and repulsions of the diamagnetic force have been made manifest; while in Sir William Thompson's reflecting galvanometer the prin-dence into a refracted and a reflected portion. ciple receives one of its latest applications.

theirs warmly, and show scant respect for those who dissent from their views.* As regards the refraction of light, the course of real inquiry was resumed in 1100 by an Arabian philosopher named Alhazen. Then it was taken up in succession by Roger Bacon, Vitellio, and Kepler. One of the most im-' portant occupations of science is the determination, by precise measurements, of the quantitative relations of phenomena. The value of such measurements depends upon the skill and conscientiousness of the man who! makes them. Vitellio appears to have been both skilful and conscientious, while Kepler's habit was to rummage through the observations of his predecessors, look at them in all lights, and thus distill from them the principles which united them. He had done this with the astronomical measurements of Tycho Brahe, and had extracted from them the celebrated "laws of Kepler." He did it also with the measurements of Vitellio. But in the case of refraction he was not successful. The principle, though a simple one, escaped him. It was firs discovered by Willebrod Snell, about the year 1621.

For more than 1,000 years no step was taken in optics beyond this law of reflection. The men of the Middle Ages, in fact, endeavored on the one hand to develop the laws of the universe out of their own consciousness, while many of them were so occupied with the concerns of a future world that they looked with a lofty scorn on all things pertaining to this one. Notwithstanding its demonstrated failure during 1,500 years of trial, there are still men among us who think the riddle of the universe is to be solved by this appeal to consciousness. And, like most people who support a delusion, they maintain

Less with the view of dwelling upon the phenomenon itself than of introducing it to you in a form which will render intelligible the play of theoretic thought in Newton's mind, I will show you the fact of refraction. The dust of the air and the turbidity of a liquid may here be turned to account. A shallow circula: vessel with a glass face, half filled with water, rendered barely turbed by the precipitation of a little mastic, is placed upon its edge with its glass face vertical. Through a slit in the hoop surrounding the vessel a beam of light is admitted. It impinges upon the water, enters it, and tracks itself through the liquid in a sharp, bright band. Meanwhite the beam passes unseen through the air above the water, for the air is not competent to scatter the light. A puff of tobacco smoke into this space at once reveals the track of the incident-beam. If the incidence be vertical, the beam is unrefracted. If oblique, its refraction at the common surface of air and water is rendered clearly visible. It is also seen that reflection accompanies refraction, the beam dividing itself at the point of inci

The law by which Snell connected together all the measurements executed up to his time, is this: Let A B C D represent the outline of our circular vessel (Fig. 1), A C being the" water-line. When the beam is incident along B E, which is perpendicular to A C, there is no refraction. When it is incident along m E, there is refraction: it is bent at E and strikes the circle at n. When it is incident

* Schelling thus expresses his contempt for experimental knowledge: Newton's Optics is the greatest illustration of a whole structure of fallacies, which in all its parts is founded on observation and experi ment. There are some small imitators of Schelling still in Germany.

along E, there is also refraction at E, the certain that he did not enunciate the true beam striking the point n'. From the ends law. This was reserved for Newton, who of the incident beams, let the perpendiculars went to work in this way: Through the closed mo, m'o' be drawn upon B D, and from the window-shutter of a room he pierced an oriends of the refracted beams let the perpen-fice, and allowed a thin sunbeam to pass diculars pn, p'n' be also drawn. Measure through it. The beam stamped a round the lengths of o m and of p n. and divide the

B

D

FIG. I.

image of the sun on the opposite white wall of the room. In the path of this beam Newton placed a prism, expecting to see the beam refracted, but also expecting to see the image of the sun, after refraction, round; to his astonishment, it was drawn out to an image whose length was five times its breadth; and this image was divided into bands of different colors. Newton saw immediately that solar light was composite, not simple. His image revealed to him the fact that some constituents of the solar light were more deflected by the prism than others, and he concluded, therefore, that white solar light was a mixture of lights of different colors and of different degrees of refrangibility.

Let us reproduce this celebrated experiment. On the screen is now stamped a luone by the other. You obtain a certain quo- minous disk, which may stand for Newton's tient. In like manner divide m'o' by the image of the sun. Causing the beam which corresponding perpendicular pn'; you ob- produces the disk to pass through a prism, tain in each case the same quotient. Snell, in we obtain Newton's elongated colored image, fact, found this quotient to be a constant which he called a spectrum. Newton divided quantity for each particular substance, though the spectrum into seven parts-red, orange, it varied in amount from substance to sub-yellow, green, blue, indigo, violet-which stance. He called the quotient the index of are commonly called the seven primary or refraction. prismatic colors. This drawing out of the white light into its constituent colors is called dispersion.

This was the first analysis of solar light by Newton; but the scientific mind is fond of verification, and never neglects it where it is possible. It is this stern conscientiousness in testing its conclusions that gives adamantine strength to science, and renders all assaults on it unavailing. Newton completed his proof by synthesis in this way: The spectrum now before you is produced by a glass

This law is oue of the corner-stones of optical science, and its applications to-day are million-fold. Immediately after its discovery, Descartes applied it to the explanation of the rainbow. The bow is seen when the back is turned to the sun. Draw a straight line through the spectator's eye and the sun, the bow is always seen at the same angular distance from this line. This was the great difficulty. Why shouid the bow be always and at all its parts, forty-one degrees from this line? Taking a pen and calculat-prism. Causing the decomposed beam to ing the track of every ray through a raindrop, Descartes found that, at one particular angle, the rays emerged from the drop almost parallel to each other; being thus enabled to preserve their intensity through long atmospheric distances; at all other angles the rays quitted the drop divergent, and through this divergence became so enfeebled as to be practically lost to the eye. The particular angle here referred to was the foregoing angle of forty-one degrees, which observation had proved to be invariably that of the

rainbow.

But in the rainbow a new phenomenon was introduced-the phenomenon of color. And here we arrive at one of those points in the history of science, when men's labors so intermingle, that it is difficult to assign to each worker his precise meed of honor. Descartes was at the threshold of the discovery of the composition of solar light. But he failed to attain perfect clearness, and it is

pass through a second similar prism, but so placed that the colors are refracted back and reblended, the perfectly white image of the slit is restored. Here, then, refraction and dispersion are simultaneously abolished. Are they always so? Can we have the one without the other? It was Newton's conclusion that we could not. Here he erred, and his error, which he maintained to the end of his life, retarded the progress of optical discovery. Dolland subsequently proved that, by combining two different kinds of glass, the colors could be extinguished, still leaving a residue of refraction, and he employed this residue in the construction of achromatic lenses-lenses which yield no color-which Newton thought an impossibility. By setting a waterprism-water contained in a wedge-shaped vessel with glass sides-in opposition to a prism of glass, this point can be illustrated before you. We have first the position of the unrefracted beam marked upon the screen;

then we produce the water-spectrum; finally, | To it we owe all the phenomena of color; by introducing a flint glass prism, we refract and yet not to it alone, for there must be a the beam back, until the color disappears. The image of the slit is now white; but you see that, though the dispersion is abolished, the refraction is not.

certain relationship between the ultimate particles of natural bodies and light to enable them to extract from it the luxuries of color. But the function of natural bodies is here selective, not creative. There is no color genem-erated by any natural body whatever. Natural bodies have showered upon them, in the white light of the sun, the sum total of all possible colors, and their action is limited to the sifting of that total, the appropriating from it of the colors which really belong to them, and the rejecting of those which do not. It will fix this subject in your minds if I say that it is the portion of light which they reject, and not that which belongs to them, that gives bodies their colors.

This is the place to illustrate another point bearing upon the instrumental means ployed in these lectures. Note the position of the water-spectrum upon the screen. Altering, in no particular, the wedge-shaped vessel, but simply substituting for the water the transparent bisulphide of carbon, you notice how much higher the beam is thrown, and how much richer is the display of color. This will explain to you the use of this substance in our subsequent experiments.

The synthesis of white light may be effected in three ways, which are now worthy Let us begin our experimental inquiries here of special attention: Here, in the first in- by asking, What is the meaning of blackness? stance, we have a rich spectrum produced by Pass a black ribbon in succession through the a prism of bisulphide of carbon. One face colors of the spectrum; it quenches all. of the prism is protected by a diaphragm This is the meaning of blackness-it is the with a longitudinal slit, through which the result of the absorption of all the constituents beam passes into the prism. It emerges de- of solar light. Pass a red ribbon through the composed at the other side. I permit the spectrum. In the red light the ribbon is a colors to pass through a cylindrical lens, | vivid red. Why? Because the light that which so squeezes them together as to pro- enters the ribbon is not quenched or absorbed, duce upon the screen a sharply-defined rect- but sent back to the eye. Place the same rib angular image of the longitudinal slit. In bon in the green or blue of the spectrum; that image the colors are re-blended, and you is black as jet. It absorbs the green and see it perfectly white. Between the prism blue light, and leaves the space on which they and the cylindrical lens may be seen the fall a space of intense darkness. Place a colors tracking themselves through the dust green ribbon in the green of the spectrum. of the room. Cutting off the more rerangi-It shines vividly with its proper color; transfer ble fringe by a card, the rectangle is seen red; cutting off the less refrangiole fringe, the rectangle is seen blue. By means of a thin glass prism, I deflect one portion of the colors, and leave the residual portion. On the screen are now two colored rectangles produced in this way. These are complementary colors-colors which, by their union, produce white. Note that, by judicious management, one of these colors is rendered yellow, and the other blue. I withdraw the thin prism; yellow falls upon blue, and we have white as the result of their union. On our way, we thus abolish the fallacy, first exposed by Helmholtz, that the mixture of blue and yellow lights produces green.

Again, restoring the circular aperture, we, obtain once more a spectrum like that of Newton. By means of a lens, we gather up these colors, and build them together not to an image of the aperture, but to an image of the carbon points themselves. Finally, in virtue of the persistence of impressions upon the retina, by means of a rotating disk, on which are spread in sectors the colors of the spectrum, we blend together the prismatic colors in the eye itself, and thus produce the impression of whiteness.

it to the red, it is black as jet. Here it absorbs all the light that falls upon it, and offers mere darkness to the eye. When white light is employed, the red sifts it by quenching the green, and the green sifts it by quenching the red, both exhibiting the residual color. Thus the process through which natural bodies acquire their colors is a negative one. The colors are produced by subtraction, not by addition. This red glass is red because it destroys all the more refrangible rays of the spectrum. This blue liquid is blue because it destroys all the less refrangible rays. Both together are opaque because the light transmitted by the one is quenched by the other. In this way by the union of two transparent substances we obtain a combination as dark as pitch to solar light. This other liquid finally is purple because it destroys the greea and the yellow, and allows the terminal colors of the spectrum to pass unimpeded. From the blending of the blue and the red this gorgeous color is produced.

These experiments prepare us for the further consideration of a point already adverted to, and regarding which error has found cur rency for ages. You will find it stated in books that blue and yellow lights mixed toHaving unravelled the interwoven con-gether produce green. But blue and yellow stituents of white light, we have next to have been just proved to be complementary inquire, What part the constitution so colors, producing white by their mixture. revealed enables this agent to play in Nature? The mixture of blue and yellow pigments un

He had been

Be that

both in the ranks of science and out of them, of elastic collision. The fact of optical reuncomfortable. That men in the ranks of flection certainly occurred as if light consistscience should feel thus is, I think, a proofed of elastic particles, and this was Newton's that they have suffered themselves to be mis-sole justification for introducing them. led by the popular definition of a great But this is not all. In another important faculty instead of observing its operation in particular, also. Newton's conceptions retheir own minds. Without imagination we garding the nature of light were influenced cannot take a step beyond the bourne of the by his previous knowledge. mere animal world, perhaps not even to the working at the phenomena of gravitation. edge of this. But, in speaking thus of and had made himself at home amid the operImagination, I do not mean a riotous power ations of this universal power. Perhaps his which deals capriciously with facts, but a mind at this time was too freshly and too well-ordered and disciplined power, whose deeply imbued with these notions to permit sole function is to form conceptions which of his forming an unfettered judgment rethe intellect imperatively demands. Imagina-garding the nature of light. tion thus exercised never really severs itself as it may, Newton saw in refraction from the world of fact. This is the store- the action of an attractive force exerted He carried his house from which all its pictures are drawn; on the light-particles. and the magic of its art consists, not in conception out with the most severe concreating things anew, but in so changing the sistency. Dropping vertically downwards magnitude, position, and other relations of towards the earth's surface, the motion of a sensible things, as to render them fit for the body is accelerated as it approaches the earth. requirements of the intellect in the subsen- Dropping in the same manner downwards on sible world.* a horizontal surface, say through air on glass I will take, as an illustration of this sub- or water, the velocity of the light-particles, Ject, the case of Newton. Before he began when they come close to the surface, was, to deal with light, he was intimately ac- according to Newton, also accelerated. Apquainted with the laws of elastic collision, proaching such a surface obliquely, he supwhich all of you have seen more or less per- posed the particles, when close to it, to be fectly illustrated on a billiard-table. As re- drawn down upon it, as a projectile is gards the coilision of sensible masses, New-drawn by gravity to the surface of the earth. ton 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, 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. He supposed light to consist of elastic particles of inconceivable minuteness shot out with inconceivable rapidity by luminous bodies. Such particles impinging upon smooth surfaces were reflected in accordance with the ordinary law

*The following charming extract, bearing upon this point, was discovered and written out for me by my friend, Dr. Bence Jones, Hon. Secretary to the Royal Institution.

This deflection was, according to Newton, the refraction seen in our last lecture. Finally, it was supposed that differences of color might be due to differences in the sizes 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 rigid deduction what are the phenomena which must of necesIf the phenomena sity grow out of this root. thus deduced agree with those of the actual world, it is a presumption in favor of the theory. If as new classes of phenomena arise "In every kind of magnitude there is a degree or sort to which our sense is proportioned, the percep- they also are found to harmonize with theotion and knowledge of which is of the greatest use to retic deduction, the presumption becomes still mankind. The same is the groundwork of philosophy: for, though all sorts and degrees are equally stronger. If, finally, the theory confers prothe object of philosophical speculation, yet it is from phetic vision upon the investigator, enabling those which are proportioned to sense that a philoso-him to predict the existence of phenomena pher must set out in his inquiries, ascending or de- which have never yet been seen, and if those scending afterwards, as his pursuits may require. He does well indeed to take his views from many points predictions be found on trial to be rigidly corof sight, and supply the defects of sense by a well-rect, the persuasion of the truth of the theory regulated imagination; nor is he to be confined by becomes overpowering. Thus working backany limit in space or time; but, as his knowledge of Nature is founded on the observation of sensible wards from a limited number of phenomena, things, he must begin with these, and must often re- genius, by its own expansive force, reaches a turn to them to examine his progress by them. conception which covers all the phenomena. Here is his secure hold; and as he sets out from There is no more wonderful performance of thence, so if he likewise trace not often his steps backwards with caution, he will be in hazard of losing the intellect than this. And we can render his way in the labyrinths of Nature."-(Maclaurin: no account of it. Like the scriptural gift of An Account of Sir I. Newton's Philosophical Dis- the Spirit, no man can tell whence it cometh. coveries. Written 1728; second edition, 1750; PP. The passage from fact to principle is some

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