that we take a plate of a wedge-form, which grows gradually thicker from edge to back, we ought to expect in red light a series of recurrent bands of light and darkness; the dark bands occurring at thicknesses which produce retardations of one, three, five, etc., half wave-lengths, while the light bands occur between the dark ones. Experiment proves the wedge-shaped crystal to show these bands; but they are far better shown by this circular film, which is so worked as to be thinnest at the centre, gradually increasing in thickness from the centre outwards. These splendid rings of light and darkness are thus produced. When, instead of employing red light, we employ blue, the rings are also seen; but as they occur at thinner portions of the film, they are smaller than the rings obtained with the red light. The consequence of employing white light may now be inferred: inasmuch as the red and the blue fall in different places, we have iris-colored rings produced by the white light. the glass bar with my finger and thumb, keeping its length oblique to the directions of vibration in the Nicols. Instantly light flashes out upon the screen. The two sides of the bar are illuminated, the edges most, for here the strain and pressure are greatest. In passing from strain to pressure, we cross a portion of the glass where neither is exerted. This is the so-called neutral axis of the bar of glass, and along it you see a dark band, indicating that the glass along this axis exercises no action upon the light. By employ. ing the force of a press, instead of the force of my finger and thumb, the brilliancy of the light is greatly augmented. Again, I have here a square of glass which can be inserted into a press of another kind. Introducing the square between the prisms, its neutrality is declared; but it can hardly be held sufficiently loosely to prevent as action from manifesting itself. Already, though the pressure is infinitesimal, you see spots of light at the points where the press is in contact with the glass. I now turn this screw. Instantly the image of the square of glass flashes out upon the screen. You see luminous spaces separated from each other by dark bands. Every pair of adjacent luminous spaces is in opposite mechanical conditions. On one side of the dark band we have strain, on the other side pressure; while the dark band marks the neutral axis between both. I now tighten the vise, and you see color; tighten still more, and the colors appear as rich as those presented by crystals. Releasing the vise, the colors suddenly vanish; tightening suddenly, they reappear. From the colors of a soap-bubble Newton was able to infer the thickness of the Some of the chromatic effects of irregular crystallization are beautiful in the extreme. Could I introduce between our Nicols a pane of glass covered by those frost-ferns which the cold weather renders now so frequent, rich colors would be the result. The beautiful effects of irregular crystallization on glass plates, now presented to you, illustrate what you might expect from the frosted windowpane. And not only do crystalline bodies act thus upon light, but almost all bodies that 'possess a definite structure do the same. As a general rule, organic bodies act in this way; for their architecture implies an arrangement of the ether which involves double refraction. A film of horn, or the section of a shell, for example, yields very beautiful colors in polar-bubble, thus uniting by the bond of thought ized light. In a tree, the ether certainly pos- apparently incongruous things. From the sesses different degrees of elasticity along and colors here presented to you, the magnitude across the fibre; and, were wood transparent, of the pressure employed might be inferred. this peculiarity of molecular structure would Indeed, the late M. Wertheim, of Paris, ininfallibly reveal itself by chromatic phe-vented an instrument for the determination nomena like those that you have seen. But not only do todies built permanently by Nature behave in this way, but it is possible, as shown by Brewster, to confer, by strain or by pressure, a temporary double-refracting structure upon non-crystalline bodies, such as common glass. When I place this bar of wood across my knee and seek to break it, what is the mechanical condition of the bar? It bends, and its convex surface is strained longitudinally; its concave surface, that next my knee, is longitudinally pressed. Both in the strained portion and in the pressed portion the ether is thrown into a condition which would render the wood, were it transparent, double refracting. Let us repeat the experiment with a bar of glass. Between the crossed Nicols I introduce such a bar. By the dim residue of light lingering upon the screen, you see the image of the glass, but it has no effect upon the light. I simply bend of strains and pressures by the colors of polarized light, which exceeded in accuracy · all other instruments of the kind. You know that bodies are expanded by heat and contracted by cold. If the heat be applied with perfect uniformity, no local strains or pressures come into play; but, if one portion of a solid be heated and others not, the expansion of the heated portion introduces strains and pressures which reveal themselves under the scrutiny of polarized light. When a square of common windowglass is placed between the Nicols, you see its dim outline, but it exerts no action on the polarized light. Held for a moment over the flame of a spirit-lamp, on reintroducing it between the Nicols, light flashes out upon the screen. Here, as in the case of mechanical action, you have spaces of strain divided by neutral axes from spaces of pressure. Let us apply the heat more symmetrically. This small square of glass is perforated at the centre, and into the orifice a bit of copper wire is introduced. Placing the square between the prisms, and heating the copper, the heat passes by conduction along the wire to the glass, through which it spreads from the centre outwards. You see a dim cross bounding four luminous quadrants growing up and becoming gradually black by comparison with the adjacent brightness. And as, in the case of pressure, we produced colors, so here alsɔ, by the proper application of heat, gorgeous chromatic effects may be produced, and they may be rendered permanent by first heating the glass sufficiently, and then cooling it, so that the chilled mass shall remain in a state of strain and pressure. Two or three examples will illustrate this point. The colors, you observe, are quite as rich as those obtained in the case of crystals. And now we have to push these considerations to a final illustration. Polarized light may be turned to account in various ways as an analyzer of molecular condition. A strip of glass six feet long, two inches wide, and a quarter of an inch thick, is held at the centre between my finger and thumb. I sweep over one of its halves a wet woolen rag; you hear an acute sound, due to the vibrations of the glass. What is the condition of the glass while the sound is heard? This its two halves lengthen and shorten in quick succession. Its two ends, therefore, are in a state of quick vibration; but at the centre the pulses from the two ends alternately meet and retreat. Between their opposing actions, the glass at the centre is kept motionless; but, on the other hand, it is alternately strained and compressed. The state of the glass may be illustrated by a row of spots of light, as the propagation of a sonorous pulse was illustrated in a former of vibration, while those at the centre are alternately crowded together and torn asunder, the centre one not moving at all. The condition of the sounding strip of glass is here correctly represented. In Fig. 18, A B represents the glass rectangle with its centre condensed; while A'B' represents the same rectangle with its centre rarefied. If we introduce the glass ss' (Fig. 19) be tween the crossed Nicols, taking care to keep the strip oblique to the direction of vibration of the Nicols, and sweep our wet rubber over the glass, this may be expected to occur: At every moment of compression the light will flash through; at every moment of strain the light will also flash through; and these states of strain and pressure will follow each other so rapidly that we may expect a permanent luminous impression to be made upon the eye. By pure reasoning, therefore, we reach the conclusion that the light will be revived whenever the glass is sounded. That it is so, experiment testifies: at every sweep of the rubber, a fine luminous disk (o) flashes out upon the screen. The experiment may be varied in this way: Placing in fron of the polarizer a plate of unannealed glass, you have those beautiful colored rings, intersected by a black cross. Every sweep of the rubber not only abolishes the rings, but introduces complementary ones, the black cross being for the moment supplanted by a white one. This is a modification of an experiment which we owe to Biot. His apparatus, however, confined the observation of it to a single person at a time. But we have to follow the ether still further. Suspended before you is a pendulum, which, when drawn aside and then liberated, oscillates to and fro. If when the pendulum is passing the middle point of its excursion, I impart a shock to it tending to drive it at right angles to its present course, what occurs? The two impulses compound themselves to a vibration oblique in direction to the former one, but the pendulum oscillates in a plane. But, if the rectangular shock be imparted to the pendulum when it is at the limit of its swing, then the compounding of the two impulses causes the suspended ball to describe not a straight line, but an ellipse; and, if the shock be competent of itself to produce a vibration of the same amplitude as the first one, the ellipse becomes a circle. But why do I dwell upon these things? Simply to make known to you the resemblance of these gross mechanical vibrations to the vibrations of light. I hold in my hand a plate of quartz cut from the crystal perpendicular to its axis. This crystal thus cut possesses the extraordinary power of twisting the plane of vibration of a polarized ray to an extent dependent on the thickness of the crystal. And the more refrangilecture. By a simple mechanical contrivance ble the light the greater is the amount of the spots are made to vibrate to and fro. twisting, so that, when white light is emThe terminal dots have the largest amplitudeployed, its constituent colors are thus drawn L FIG. 18. asunder. Placing the quartz between the polarizer and the analyzer, you see this splendid color, and, turning the analyzer in front, from right to left, the other colors appear in succession. Specimens of quartz have been found which require the analyzer to be turned from left to right, to obtain the same succession of colors. Crystals of the first class are therefore called right-handed, and, of the second class, left handed crystaís. With profound sagacity, Fresne, to whose genius we mainly owe the expansion and final triumph of the undulatory theory of light, reproduced mentally the mechanism of these crystals, and showed their action to be due to the circumstance that, in them, the waves of ether so act upon each other as to produce the condition represented by our rotating pendulum. Instead of being plane polarized, the light in rock crystal is circularly polarized. Two such rays transmitted along the axis of the crystal, and rotating in although the mixture of blue and yellow pigments produces green, the mixture of blue and yellow lights produces white. By enlarging our aperture, the two images produced by the spar are caused to approach each other, and finally to overlap. The one is now a vivid yellow, the other a vivid blue, and you notice that where the colors are superposed we have a pure white. (See Fig. 20, where N is the nozzle of the lamp, Q the quartz plate, L a lens, and B the birefracting spar. The two images overlap at O, and produce white by their mixture.) This brings us to a point of our inquiries which, though not capable of brilliant illustration, is nevertheless so likely to affect profoundly the future course of scientific thought that I am unwilling to pass it over without reference. I refer to the experiment which Faraday, its discoverer, called the magnetization of light. The arrangement for thi celebrated experiment is now before you. opposite directions, when brought to interference by the analyzer, are demonstrably competent to produce the observed phe nomena. We have first our electric lamp, then a Nicot prism, to polarize the beam emergent from the lamp; then an electro-magnet, then a second Nicol prism, and finally our screen. At the present moment the prisms are crossed, and the screen is dark. I place from pole to pole of the electro-magnet a cylinder of a peculiar kind of glass, first made by Faraday, and called Faraday's heavy glass. Through this glass the beam from the polarizer now passes, being intercepted by the Nicol in front. I now excite the magnet, and instantly light appears upon the screen. On examination, we find that, by the action of the magnet upon the ether contained within the heavy glass, the plane or vibration is caused to rotate, thus enabling the light to get through the analyzer. I now abandon the analyzer, and put in its place the piece of Iceland spar with which we have already illustrated double refraction. The two images of the carbon-points are now before you. Introducing a plate of quartz between the polarizer and the spar, the two images glow with complementary colors. Employing the image of an aperture instead of that of the carbon-points, we have two complementary colored circles. As the analyzer is caused to rotate, the colors pass through various changes; but they are always complementary to each other. If the one be red, the other will be green; if the one be yellow, the other will be blue. Here The two classes into which quartz-crystals we have it in our power to demonstrate afresh are divided have been already mentioned. a statement made in a former lecture, that, i In my hand I hold a compound piate, one half of it taken from a right-handed and the molecular arrangement implies symmetry on other from a left-handed crystal. Placing the part of the ether; atomic dissymmetry, the plate in front of the polarizer, we turn on the other hand, involves the dissymmetry one of the Nicols until the two halves of the of the ether, and, as a consequence, double plate show a common puce color. This refraction. In a certain class of crystals the yields an exceedingly sensitive means of ren-structure is homogeneous, and such crystals dering the action of a magnet upon light produce no double refraction. sible. By turning either the polarizer or In certain FIG. 20. around others. Along the former, therefore, the ray is undivided, while along all the others we have double refraction. Ice is a familiar example; it is built with perfect symmetry around the perpendiculars to the planes of freezing, and a ray sent through ice in this direction is not doubly refracted; whereas, in all other directions, it is. Iceland spar is another example of the same kind: its molecules are built symmetrically round the line uniting the two blunt angles of the rhomb. In this direction a ray suffers no double refraction, in all others it does. This direction of double refraction is called the optic axis of the crystal. the analyzer through the smallest angle, the other crystals the mole ules are ranged symuniformity of the color disappears, and the metrically around a ertain line, and not two halves of the quartz show different colors. | The magnet also produces this effect. The puce-colored circle is now before you on the screen. (See Fig. 21 for the arrangement of the experiment. N is the nozzle of the lamp, H the first Nicol, Q the biquartz plate, L a lens, M the electro-magnet, and P the second Nicol.) Exciting the magnet, one half of the image becomes suddenly red, the other half green. Interrupting the current, the two colors fade away, and the primitive puce is restored. The action, moreover, depends upon the polarity of the magnet, or, in other words, on the direction of the current which surrounds the magnet. Reversing the current, the red and green reappear, but they have changed places. The red was formerly to the right, and the green to the left; the green is now to the right, and the red to the left. With the most exquisite ingenuity, Faraday analyzed all those actions and stated their laws. This experiment, however, long remained rather as a scientific curiosity than as a fruitful germ. That it would bear fruit of the highest importance, Faraday felt profoundly convinced, and recent researches are on the way to verify his conviction. Hence, if a plate be cut from a crystal of Iceland spar perpendicular to the axis, all rays sent across this plate in the dirction of the axis will produce but ene image. But, the moment we deviate from the parallelism with the axis, double refraction sets in. If, therefore, a beam that has been rendered conical by a converging lens be rent through the spar so that the central ray of the cone passes along the axis, this ray only will escape double refraction. Each of the others will be divided into an ordinary and extraor A few words more are necessary to com- dinary ray, the one moving more slowly plete our knowledge of the wonderful inter- through the crystal than the other; the one, action between ponderable molecules and the therefore, retarded with reference to the ether interfused among them. Symmetry of other. Here, then, we have the conditions FIG. 21. for interference, when the waves are reduced | and, enlightened by mechanical conceptions, by the analyzer to a common plane. A acquires an insight which pierces through highly beautiful and important source of shape and color to force and cause. chromatic phenomena is thus revealed. Placing the plate of spar between the crossed prisms, we have upon the screen a beautiful system of iris rings surrounding the end of the optic axis, the circular bands of color being intersected by a black cross. The arms of this cross are parallel to the two directions of vibration in the polarizer and analyzer. It is easy to see that those rays whose planes of vibration within the spar coincide with the plane of vibration of either prism, cannot get through both. This complete interception produces the arms of the With mono-chromatic light the rings would be simply bright and black-the bright rings occurring at those thicknesses of the spar which cause the rays to conspire; the black rings at those thicknesses which cause them to quench each other. Here, however, as elsewhere, the different lengths of the light-waves give rise to iris-colors when white light is employed. cross. But, while I have thus endeavored to illustrate before you the power of the undulatory theory as a solver of all the difficulties of optics, do I therefore wish you to close your eyes to any evidence that may arise against it? By no means. You may urge, and justly urge, that a hundred years ago another theory was held by the most eminent men, and that, as the theory then held had to yield, the undulatory theory may have to yield also. This is perfectly logical; but let us understand the precise value of the arg ment. In similar language a person in the time of Newton, or even in our time, might reason thus: "Hipparchus and Ptolemy, and numbers of great men after them, believed that the earth was the centre of the solar system. But this deep-set theoretic notion had to give way, and the theory of gravitation may, in its turn, have to give way also." This is just as logical as the first argument. Wherein consists the strength of the theory of gravitation? Solely in its competence to account for all the phenomena of the solar system. Wherein consists the strength of the theory of undulation? Solely in its competence to disentangle and explain phetnomena a hundred-fold more complex than those of the solar system. Be as skeptical, if you like, regarding the undulatory theory; but if your skepticism be philosophical, it will wrap the theory of gravitation in the same or greater doubt.t Besides the regular crystals which produce double refraction in no direction, and the uniaxal crystals which produce it in all directions but one, Brewster discovered that in a large class of crystals there are two directions which double refraction does not take place. These are called biaxal crystals. When plates of these crystals, suitably cut, are placed betwee. the polarizer and analyzer, the axes are seen su rounded, not by circles, but by curves of and her order and of a perfectly definite mathema ical character. Each band, as proved experimentally by Herschel, forms a lemniscata; but the experimental proof was here, as in numberless other cases, preceded by the deduction which showed that, Range of vision incommensurate with Range of Radiaccording to the undulatory theory, the bands must possess this special character. I have taken this somewhat wide range over polarization itselt and over the phenomena exhibited by crystals in polarized light, in order to give you some notion of the firmness and completeness of the theory which grasps them all. Starting from the single assumption of transverse undulations, we first of all determine the wave-lengths, and find all the phenomena of color dependent on this element. The wave-lengths may be determined in many independent ways, and, when the lengths so determined are compared ogether, the strictest agreement is found to xist between them. We follow the ether nto the most complicated cases of interacon between it and ordinary matter, the heory is equal to them all. It makes not a ingle new hypothesis; but out of its original tock of principles it educes the counterparts of all that observation shows. It accounts or, explains, simplifies the most entangled bases; corrects known laws and facts; prelicts and discloses unknown ones; becomes he guide of its former teacher Observation; ation: LECTURE V. Fluorescence: The Ultra-Violet Rays: Rendering Invisible Rays visible: Vision not the only Sense appealed to by the Solar and Electric Beam: Heat of Beam: Combustion by Total Beam at the Foci of Mirrors and Lenses: Combustion through Ice-Lens: Ignition of Diamond: Search for the Kays here effective: Sir William Herschel's Discovery of Dark Solar Rays: Invisible Rays the Basis of the Visible: Detachment by a Ray-Filter of the Invisible Rays from the Visible: Combustion at Dark Foci: Conversion of Heat-Rays into Light-Rays: Calorescence: Part played in Nature by Dark Rays: Identity of Light and Radiant Heat: Invisible Images: Reflection, Refraction, Plane Polarization, Depolarization, Circular Polarization, Double Refraction, and Magnetization of Radiant Heat. THE first question that we have to con sider to-night is this: Is the eye, as an organ of vision, commensurate with the whole range of solar radiation-is it capable of receiving visual impressions from all the rays emitted by the sun? The answer is nega tive. If we allowed ourselves to accept for a * Whewell. Theory, from the pen of an American writer, is an |