that the function of natural bodies is selec-| flashing of those colors over the surface of tive, not creative; that they extinguish cer- the water. On a small scale we produce them tain constituents of the white solar light, and thus: A common tea-tray is filled with water, appear in the colors of the unextinguished beneath the surface of which dips the end of light. It must at once flash upon your minds a pipette. A beam of light falls upon the that, inasmuch as we have in interference an water, and is reflected by it to the screen. agency by which light may be self-extin- Spirit of turpentine is poured into the pipette; quished, we may have in it the conditions it descends, issues from the end in minute for the production of color. But this would drops, which rise in succession to the surface. imply that certain constituents are quenched On reaching it, each drop spreads suddenly by interference, while others are permitted to out as a film, and glowing colors immediately remain. This is the fact; and it is entirely flash forth upon the screen. The colors due to the difference in the lengths of the change as the thickness of the film changes waves of light. by evaporation. They are also arranged in zones in consequence of the gradual diminution of thickness from the centre outwards.

The subject is most easily illustrated by the class of phenomena which first suggested the undulatory theory to the mind of Hooke. Any film whatever will produce these colors. These are the colors of thin films of all kinds, The film of air between two plates of windowwhich are known as the colors of thin plates. | glass, squeezed together, exhibits rich fringes In this relation no object in the world pos- of color. Nor is even air necessary; the sesses a deeper scientific interest than a com- mere rupture of optical continuity suffices. mon soap-bubbie. And here let me say Smite with an axe the black, transparent iceemerges one of the difficulties which the stu- black, because it is transparent and of great dent of pure science encounters in the pres-depth-under the moraine of a glacier; you ence of practical" communities like those readily produce in the interior flaws which no of America and England; it is not to be ex-air can reach, and from these flaws the colors pected that such communities can entertain any profound sympathy with labors which seem so far removed from the domain of practice as many of the labors of the man of science are. Imagine Dr. Draper spending his days in blowing soap-bubbles and in studying their colors! Would you show him the necessary patience, or grant him the necessary support? And yet, be it remembered, it was thus that Newton spent a large portion of his time; 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 labors you ought to abide.

of thin plates sometimes break like fire. The colors are commonly seen in flawed crystals; they are also formed by the film of oxide which collects upon molten lead. It is the colors of thin plates that guide the tempering of steel. But the origin of most historic interest is, as already stated, the soap-bubble. With one of those 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 twelve or fifteen inches in diameter. You may look at the bubble itself, or you may look at its projection upon the screen, rich colors 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 color overspread the screen, which rotate as the beam is carried round the circumference of the bubble. By this experiment the internal motions of the film are also strikingly displayed.

Whence, then, are derived the colors 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 Newton sought to measure the thickness of its second surface, and is again in part re- the bubble corresponding to each of these flected. The waves from the second surface colors; in fact, he sought to determine genthus turn back and hotly pursue the waves erally the relation of color to thickness. His from the first surface. And, if the thickness first care was to obtain a film of variable and of the film be such as to cause the necessary calculable depth. On a plano-convex glass retardation, the two systems of waves inter-lens of very feeble curvature he laid a plate of fere 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 self-extinction in the case of the longer waves, a greater thickness of film is necessary than in the case of the shorter ones. Different colors, therefore, appear at different thicknesses of the film.

glass with a plane surface, thus obtaining a film of air of gradually increasing depth from the point of contact outwards. On looking at the film in monochromatic light he saw sur rounding 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. When he employed red light, his rings had certain diameters; when he employed blue light, the diameters were less. Causing his glasses to pass through the spes

trum from red to blue, the rings contracted; when the passage was from blue to red, the rings expanded. When white light fell upon the glasses, inasmuch as the colors were not superposed, a series of iris-colored circles were obtained. They became paler as the film became thicker, until finally the colors became so intimately reblended as to produce white light. 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.

itself. The self-same particle, he affirmed, was affected by "fits" of easy transmission and reflection.

If you are willing to follow me while I unravel this theory of fits, the most subtle, perhaps, that ever entered the human mind, the intellectual discipline will 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 cannot be a doubt that his mind rested on a mechanical cause. Nor can there be a doubt that, as in all attempts at theorizing, he was compelled to. fall back upon experience for the materials of his theory. His course of observation and of thought may have been this: From a magnet he might obtain the notion of attracted and repelled poles. What more natural than that he should endow his lightparticles 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 parti. cle at different times might be accounted for.

Regard 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 dj then Newton found the distance corresponde ing to the second dark ring 2 d; the thick ness corresponding to the third dark ring 3 d; the thickness corresponding to the tenth dark

He compared the tints thus obtained with the tints of the 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 cne 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 great-ring 10 d, and so on. Surely there must be est 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 lightparticles 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. Thus 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 be through me change in the condition of the particle

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 probably outcome of his thought. He had endowed his light-particles with poles, but now he is forced to introduce the notion of periodic recurrence. How was this to be done? By supposing the light-particles animated, not only with

a motion of translation, but also with a motion of rotation. Newton's astronomical knowledge would render all such conceptions familiar to him. The earth has such a 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 must 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 con- | sumed that the action which produces the alceptions are, in point of intellectual quality, ternate bright and dark rings took place at a identical. 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 proper devices we may abolish reflection from one of the surfaces of the film, and when this is done the rings vanish altogether.

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 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 somersaults within the film; when the thickness is 3 d, three complete somersaults; when 10 d, ten complete somersaults 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.

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 wich have suffered two reflections within the film. They are thus completely accounted for.

Newton, by the foregoing exceedingly subtle assumption, vaulted over the difficulty prese ted by the colors of thin plates. And, as further difficulties in process of time thickened round the theory, his disciples tried to sustain it with an ingenuity worthy of their master. The new difficulties were not anticipated by the theory, but were met by new assumptions, until at length the Emission Theory became what a distinguished writer calls a "mob of hypotheses." In the presence of the phenomena of interference, the theory finally broke down, while the whole of these phenomena lie, as it were, latent in the theory of undulation. Newton's "fits," for example, are immediately translatable into the lengths of the ether-waves. We have the observed periodic recurrence as the thickness varies so as to produce a retardation of an odd or even number of semi-undulations.*

Numerous other colors are due to interfer

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 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, ence. Fine scratches drawn upon glass of therefore, driven back and reaches the eye. polished metal reflect the waves of light from At all distances round the centre correspond- their sides; and some, being reflected from ing to this thickness the same effect is pro- opposite sides of the same furrow, interfere duced, and the consequence is a ring of with and quench each other. But the ob brightness. The other bright rings are sim-liquity of reflection which extinguishes the ilarly 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, producing the impression of brightness. Here, then, we have unravelled the most subtle application that Newton ever made of the Emission Theory.

These

shorter waves does not extinguish the longer
ones, hence the phenomena of color.
are called the colors of striated surfaces.
They are well illustrated by mother-of-pearl..
This shell is composed of exceedingly thin
layers, which, when cut across by the polish.
ing of the shell, expose their edges and fur-
nish the necessary small and regular grooves.
The most conclusive proof that the colors are
due to the mechanical state of the surface is
to be found in the fact, established by Brew-
ster, that, by stamping the shell carefully

In the

In the explanation of Newton's rings, something besides thickness is to be taken into account. case of the first surface of the film of air, the waves pass from a denser to a rarer medium, while in the case of the second surface, the waves pass from a This difference at the

It has been stated in the early part of this lecture, that the Emission Theory assigned a greater velocity to light in glass and water, than in air or stellar space. Here it was at direct issue with the theory of undulation, which makes the velocity in air or stellar space less than in glass or water. By an experiment proposed by Arago, and executed with comsummate skill by Foucault and to the addition of half a wave-length to the thicktwo reflecting surfaces can be proved to be equivalent Fizeau, this question was bought to a crucial ness of the film. To the absolute thickness, as detest, and decided in favor of the theory of termined by Newton, half a wave-length is in each undulation. In the present instance also the bright rings follow each other in exact accordance case to be added. When this is done, the dark and two theories are at variance. Newton as-with the law of interference already enunciated.

rarer to a denser medium.

upon black sealing-wax, we transfer the grooves, and produce upon the wax the colors of mother-of-pearl.

LECTURE III.

Relation of Theories to Experience: Origin of the
Notion of the Attraction of Gravitation: Notion
of Polarity, how generated: Atomic Polarity:
Structural Arrangements due to Polarity: Archi-
tecture of Crystals considered as an Introduction to
their Action upon Light: Notion of Atomic Po-
larity applied to Crystalline Structure: Experi-
mental Illustrations: Crystallization of Water:
Expansion by Heat and by Cold: Deportment of
Water considered and explained: Molecular Ac-
tion illustrated by a Model: Force of Solidifica-
tion:
Bearings of Crystallization on Optical Phe-
nomena: Refraction: Double Refraction: Po-
larization: Action of Tourmaline: Character of
the Beams emergent from Iceland Spar: Polariza-
tion by ordinary Refraction and Reflection: De-
polarization.

not create, but that it expands, diminishes, moulds, and refines, as the case may be, mater als derived from the world of fact and observation.

This is more evidently the case in a theory like that of light, where the motions of a subsensible medium, the ether, are presented to the mind. But no theory escapes the condition. Newton took care not to encumber gravitation with unnecessary physical conceptions; but we have reason to know that he indulged in them, though he did not connect them with his theory. But even the theory as it stands did not enter the mind as a revelation dissevered from the world of experience. The germ of the conception that the sun and planets are held together by a force of attraction is to be found in the fact that a magnet had been previously seen to attract iron. The notion of matter attracting matter came thus from without, not from within. In our present lecture the magnetic force must serve us till further; but here we must master its elementary phenomena.

IN our last lecture we sought to familiarize our minds with the characteristics of wavemotion. We drew a clear distinction between the motio of the wave itself and the motion of its constituent particles. Passing through The general facts of magnetism are most water-waves and air-waves, we prepared our simply illustrated by a magnetized bar of minds for the conception of light-waves prop-steel, commonly called a bar magnet. Placing agated through the luminiferous ether. The such a magnet urght upon a table, and analogy of sound will fix the whole mechan- bringing a magne eedle near its bottom, im in your minds. Here we have a vibrat- one end of the ne promptly retreats from g body which originates the wave motion, the magnet, w the other as promptly we have, in the air, a vehicle which conveys approaches. needle is held quivering it, and we have the auditory nerve which re- there by some visible influence exerted ceives the impressions of the sonorous waves. upon it. Raising the needle along the magIn the case of light we have in the vibrating net, but still avoiding contact the rapidity atoms of the luminous body the originators of of its oscillations decreases, because the force At the the wave-motion, we have in the ether its acting upon it becomes weaker. Above the vehicle, while the optic nerve receives the im- centre the oscillations cease. pression of the luminiferous waves. We centre, the end of the needle which had been learned, also, that color is the analogue of previously drawn towards the magnet repitch, that the rapidity of atomic vibration treats, and the opposite end approaches. As augmented, and the length of the ether-waves we ascend higher, the oscillations become decreased, in passing from the red to the blue mcre violent, because the force becomes end of the spectrum. The fruitful principle stronger. At the upper end of the magnet, of interference we also found applicable to the phenomena of light; and we learned that, in consequence of the different lengths of the ether-waves, they were extinguished by different thicknesses of a transparent film, the particular thickness which quenched one color glowing, therefore, with the complementary

one.

Thus the colors of thin plates were ac

counted for.

But one of the objects of our last lecture, ad that not the least important, was to illusrate the manner in which scientific theories re formed. They, in the first place, take heir rise in the desire of the mind to penerate to the sources of phenomena. This deire has long been a part of human nature. It prompted Cæsar to say that he would exhange his victories for a glimpse of the burces of the Nile; it may be seen working ʼn Lucretius; it impels Darwin to those darng speculations which of late years have so gitated the public mind. We have learned hat in framing theories the imagination does

FIG. 5.

S

N

as at the lower, the force reaches a maximum. but all the lower half of the magnet, from E to S (Fig. 5), attracts one end of the

needle, while all the upper half, from E to N, attracts the opposite end. This doubleness of the magnetic force is called polarity, and the points near the ends of the magnet in which the forces seem concentrated are called its poles.

rection of the needle, and no other. A needle of iron will answer as well as the magnetic needle; for the needle of iron is magnetized by the magnet, and acts exactly like a needle independently magnetized.

If we place two or more needles of iron near the magnet, the action becomes more, complex, for the the iron needles are not only acted on by the magnet, but they act upon each other. And if we pass to smaller masses of iron-to iron filings, for example-we find that they act substantially as the needles, arranging themselves in definite forms, in obe

What, then, will occur if we break this magnet in two at the centre E? Will each of the separate halves act as it did when it formed part of the whole magnet? No; each half is in itself a perfect magnet, pos sessing two poles. This may be proved by breaking something of less value than the magnet-the steel of a lady's stays, for ex-dience to the magnetic action. example, hardened and magnetized. It acts like the magnet. When broken, each half acts like the whole; and when these parts are again broken, we have still the perfect magnet, possessing, as in the first instance, two poles. Push your breaking to its utmost limit; you will be driven to prolong your

Placing a sheet of paper or glass over this bar magnet and showering iron filings upon the paper, I notice a tendency of the filings to arrange themselves in determinate lincs. They cannot freely follow this tendency, for they are hampered by the friction against the paper, They are helped by tapping the

JI

FIG. 6.

is the nozzle of the lamp; M a plane mirror, reflecting the beam upwards. At P, the magnets and iron filings are placed; L is a lens which forms an image of the magnets and filings; and R is a totally-reflecting prism which casts the image, G, upon the screen.

vision beyond that limit, and to contemplate | paper: each tap releases them for a moment' this thing that we call magnetic polarity as resident in the ultimate particles of the magEach atom is endowed with this polar

net. force.

Like all other forces, this force of magnetism is amenable to mechanical laws; and knowing the direction and magnitude of the force, we can predict its action. Placing a small magnetic needle near a bar magnet, it takes up a determinate position. That position might be deduced theoretically from the mutual action of the polcs. Moving the needle round the magnet, for each point of the surrounding space there is a definite di

and enables them to follow their bias. Bu this is an experiment which can only be seen by myself. To enable you to see it, I take a pair of small magnets and by a simple optical, arrangement throw the images of the magnets upon the screen. Scattering iron filings over the glass plate to which the small magnets are attached, and tapping the plate, you see the arrangement of the iron filings in those magnetic curves which have been so long familiar to scientific men.*

been recently obtained, and fixed, by Prof. Mayer, *Very beautiful specimens of these curves have of Hoboken."