In considering the next point, we will operate, for the sake of simplicity, with monochromatic light--with red light, for example, which is easily obtained pure by red gla.s.s. Supposing a certain thickness of the gypsum produces a r.e.t.a.r.dation of half a wave-length, twice this thickness will produce a r.e.t.a.r.dation of two half wave-lengths, three times this thickness a r.e.t.a.r.dation of three half wave-lengths, and so on. Now, when the Nicols are parallel, the r.e.t.a.r.dation of half a wave-length, or of any _odd_ number of half wave-lengths, produces extinction; at all thicknesses, on the other hand, which correspond to a r.e.t.a.r.dation of an _even_ number of half wave-lengths, the two beams support each other, when they are brought to a common plane by the a.n.a.lyzer. Supposing, then, 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 r.e.t.a.r.dations of one, three, five, etc., half wave-lengths, while the bright bands occur between the dark ones. Experiment proves the wedge-shaped film to show these bands. They are also beautifully shown by a circular film, so worked as to be thinnest at the centre, and gradually increasing in thickness from the centre outwards. A splendid series of rings of light and darkness is 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 be now inferred; inasmuch as the red and the blue fall in different places, we have _iris-coloured_ rings produced by the white light.

Some of the chromatic effects of irregular crystallization are beautiful in the extreme. Could I introduce between our two Nicols a pane of gla.s.s covered by those frost-ferns which your cold weather renders now so frequent, rich colours would be the result. The beautiful effects of the irregular crystallization of tartaric acid and other substances on gla.s.s plates now presented to you, ill.u.s.trate what you might expect from the frosted window-pane. 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 thus upon light; for their architecture implies an arrangement of the molecules, and of the ether a.s.sociated with the molecules, which involves double refraction. A film of horn, or the section of a sh.e.l.l, for example, yields very beautiful colours in polarized light. In a tree, the ether certainly possesses different degrees of elasticity along and across the fibre; and, were wood transparent, this peculiarity of molecular structure would infallibly reveal itself by chromatic phenomena like those that you have seen.

-- 4. _Colours produced by Strain and Pressure._

Not only do natural bodies behave in this way, but it is possible, as shown by Brewster, to confer, by artificial strain or pressure, a temporary double refracting structure upon non-crystalline bodies such as common gla.s.s. This is a point worthy of ill.u.s.tration. When I place a 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 of the wood the ether is thrown into a condition which would render the wood, were it transparent, double-refracting. For, in cases like the present, the drawing of the molecules asunder longitudinally is always accompanied by their approach to each other laterally; while the longitudinal squeezing is accompanied by lateral retreat. Each half of the bar of wood exhibits this ant.i.thesis, and is therefore double-refracting.

Let us now repeat this experiment with a bar of gla.s.s. 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 gla.s.s, but it has no effect upon the light. I simply bend the gla.s.s 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 pa.s.sing from longitudinal strain to longitudinal pressure, we cross a portion of the gla.s.s where neither is exerted. This is the so-called neutral axis of the bar of gla.s.s, and along it you see a dark band, indicating that the gla.s.s along this axis exercises no action upon the light. By employing 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 gla.s.s which can be inserted into a press of another kind. Introducing the uncompressed square between the prisms, its neutrality is declared; but it can hardly be held sufficiently loosely in the press to prevent its 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 gla.s.s. On turning a screw, the image of the square of gla.s.s flashes out upon the screen. Luminous s.p.a.ces are seen separated from each other by dark bands.

Every two adjacent s.p.a.ces are in opposite mechanical conditions. On one side of the dark band we have strain, on the other side pressure, the band marking the neutral axis between both. I now tighten the vice, and you see colour; tighten still more, and the colours appear as rich as those presented by crystals. Releasing the vice, the colours suddenly vanish; tightening suddenly, they reappear. From the colours of a soap-bubble Newton was able to infer the thickness of the bubble, thus uniting by the bond of thought apparently incongruous things. From the colours here presented to you, the magnitude of the pressure employed might be inferred. Indeed, the late M. Wertheim, of Paris, invented an instrument for the determination of strains and pressures, by the colours of polarized light, which exceeded in accuracy all previous instruments of the kind.

And now we have to push these considerations to a final ill.u.s.tration.

Polarized light may be turned to account in various ways as an a.n.a.lyzer of molecular condition. It may, for instance, be applied to reveal the condition of a solid body when it becomes sonorous. A strip of gla.s.s six feet long, two inches wide and a quarter of an inch thick, is held at the centre between the finger and thumb. On sweeping a wet woollen rag over one of its halves, you hear an acute sound due to the vibrations of the gla.s.s. What is the condition of the gla.s.s 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 from each other. Between their opposing actions, the gla.s.s at the centre is kept motionless: but, on the other hand, it is alternately strained and compressed. In fig. 38, A B may be taken to represent the gla.s.s rectangle with its centre condensed; while A' B'

represents the same rectangle with its centre rarefied. The ends of the strip suffer neither condensation nor rarefaction.

[Ill.u.s.tration: Fig. 38]

If we introduce the strip of gla.s.s (_s_ _s'_, fig. 39) between the crossed Nicols, taking care to keep it oblique to the directions of vibration of the Nicols, and sweep our wet rubber over the gla.s.s, this is what 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 gla.s.s is sounded. That it is so, experiment testifies: at every sweep of the rubber (_h_, fig. 39) a fine luminous disk (O) flashes out upon the screen. The experiment may be varied in this way: Placing in front of the polarizer a plate of unannealed gla.s.s, you have a series of beautifully coloured 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 a beautiful experiment which we owe to Biot. His apparatus, however, confined the observation of it to a single person at a time.

[Ill.u.s.tration: Fig. 39.]

-- 5. _Colours of Unannealed Gla.s.s_.

Bodies are usually 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 another portion 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 window-gla.s.s 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 luminous s.p.a.ces of strain divided by dark neutral axes from s.p.a.ces of pressure.

[Ill.u.s.tration: Fig. 40.]

[Ill.u.s.tration: Fig. 41.]

Let us apply the heat more symmetrically. A small square of gla.s.s 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 wire, the heat pa.s.ses by conduction to the gla.s.s, through which it spreads from the centre outwards. You immediately see four luminous quadrants and a dim cross, which becomes gradually blacker, by comparison with the adjacent brightness. And as, in the case of pressure, we produced colours, so here also, by the proper application of heat, gorgeous chromatic effects may be evoked. The condition necessary to the production of these colours may be rendered permanent by first heating the gla.s.s sufficiently, and then cooling it, so that the chilled ma.s.s shall remain in a state of permanent strain and pressure. Two or three examples will ill.u.s.trate this point. Figs. 40 and 41 represent the figures obtained with two pieces of gla.s.s thus prepared; two rectangular pieces of unannealed gla.s.s, crossed and placed between the polarizer and a.n.a.lyzer, exhibit the beautiful iris fringes represented in fig. 42.

[Ill.u.s.tration: Fig. 42.]

-- 6. _Circular Polarization._

But we have to follow the ether still further into its hiding-places.

Suspended before you is a pendulum, which, when drawn aside and liberated, oscillates to and fro. If, when the pendulum is pa.s.sing 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 still 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.

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. The 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 refrangible the light the greater is the amount of twisting; so that, when white light is employed, its const.i.tuent colours are thus drawn asunder. Placing the quartz plate between the polarizer and a.n.a.lyzer, this vivid red appears; and, turning the a.n.a.lyzer in front from right to left, the other colours of the spectrum appear in succession. Specimens of quartz have been found which require the a.n.a.lyzer to be turned from left to right to obtain the same succession of colours. Crystals of the first cla.s.s are therefore called right-handed, and of the second cla.s.s, left-handed crystals.

With profound sagacity, Fresnel, 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 circ.u.mstance 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 opposite directions, when brought to interference by the a.n.a.lyzer, are demonstrably competent to produce all the observed phenomena.

-- 7. _Complementary Colours of Bi-refracting Spar in Circularly Polarized Light. Proof that Yellow and Blue are Complementary._

I now remove the a.n.a.lyzer, and put in its place the piece of Iceland spar with which we have already ill.u.s.trated double refraction. The two images of the carbon-points are now before you, produced, as you know, by two beams vibrating at right angles to each other. Introducing a plate of quartz between the polarizer and the spar, the two images glow with complementary colours. Employing the image of an aperture instead of that of the carbon-points, we have two coloured circles. As the a.n.a.lyzer is caused to rotate, the colours pa.s.s through various changes: but they are always complementary. When the one is red, the other is green; when the one is yellow, the other is blue. Here we have it in our power to demonstrate afresh a statement made in our first lecture, that 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 image is now a vivid yellow, the other a vivid blue, and you notice that where these colours are superposed we have a pure white. (See fig. 43, where N is the end of the polarizer, Q the quartz plate, L a lens, and B the bi-refracting spar. The two images overlap at O, and produce white by their mixture.)

[Ill.u.s.tration: Fig. 43.]

-- 8. _The Magnetization of Light._

This brings us to a point of our inquiries which, though rarely ill.u.s.trated in lectures, is nevertheless so likely to affect profoundly the future course of scientific thought that I am unwilling to pa.s.s it over without reference. I refer to the experiment which Faraday, its discoverer, called the 'magnetization of light.' The arrangement for this celebrated experiment is now before you. We have, first, our electric lamp, then a Nicol prism, to polarize the beam emergent from the lamp; then an electro-magnet, then a second Nicol, 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 gla.s.s, first made by Faraday, and called Faraday's heavy gla.s.s. Through this gla.s.s the beam from the polarizer now pa.s.ses, being intercepted by the Nicol in front. On exciting the magnet light instantly appears upon the screen.

By the action of the magnet upon the heavy gla.s.s the plane of vibration is caused to rotate, the light being thus enabled to get through the a.n.a.lyzer.

The two cla.s.ses into which quartz-crystals are divided have been already mentioned. In my hand I hold a compound plate, one half of it taken from a right-handed, and the other from a left-handed crystal.

Placing the plate in front of the polarizer, I turn one of the Nicols until the two halves of the plate show a common puce colour. This yields an exceedingly sensitive means of rendering visible the action of a magnet upon light. By turning either the polarizer or the a.n.a.lyzer through the smallest angle, the uniformity of the colour disappears, and the two halves of the quartz show different colours.

The magnet produces an effect equivalent to this rotation. The puce-coloured circle is now before you on the screen. (See fig. 44, where N is the nozzle of the lamp, H the first Nicol, Q the biquartz plate, L a lens, M the electro-magnet, with the heavy gla.s.s across its perforated poles, 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 colours 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 a.n.a.lyzed all those actions and stated their laws. This experiment, however, long remained a scientific curiosity rather than a fruitful germ. That it would bear fruit of the highest importance, Faraday felt profoundly convinced, and present researches are on the way to verify his conviction.

[Ill.u.s.tration: Fig. 44]

-- 9. _Iris-rings surrounding the Axes of Crystals._

A few more words are necessary to complete our knowledge of the wonderful interaction between ponderable molecules and the ether interfused among them. Symmetry of molecular arrangement implies symmetry on the part of the ether; atomic dissymmetry, on the other hand, involves the dissymmetry of the ether, and, as a consequence, double refraction. In a certain cla.s.s of crystals the structure is h.o.m.ogeneous, and such crystals produce no double refraction. In certain other crystals the molecules are ranged symmetrically round a certain line, and not around others. Along the former, therefore, the ray is undivided, while along all the others we have double refraction. Ice is a familiar example: its molecules are 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 no double refraction is called the _optic axis_ of the crystal.

Hence, if a plate be cut from a crystal of Iceland spar perpendicular to the axis, all rays sent across this plate in the direction of the axis will produce but one 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 sent through the spar so that the central ray of the cone pa.s.ses along the axis, this ray only will escape double refraction. Each of the others will be divided into an ordinary and an extraordinary ray, the one moving more slowly through the crystal than the other; the one, therefore, r.e.t.a.r.ded with reference to the other. Here, then, we have the conditions for interference, when the waves are reduced by the a.n.a.lyzer to a common plane.

Placing the plate of Iceland spar between the crossed Nicol prisms, and employing the conical beam, we have upon the screen a beautiful system of iris-rings surrounding the end of the optic axis, the circular bands of colour being intersected by a black cross (fig. 45).

The arms of this cross are parallel to the two directions of vibration in the polarizer and a.n.a.lyzer. 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 cross.

[Ill.u.s.tration: Fig. 45.]

With monochromatic 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. Turning the a.n.a.lyzer 90 round, we obtain the complementary phenomena. The black cross gives place to a bright one, and every dark ring is supplanted also by a bright one (fig. 46). Here, as elsewhere, the different lengths of the light-waves give rise to iris-colours when white light is employed.

[Ill.u.s.tration: Fig. 46.]

[Ill.u.s.tration: Fig. 47.]

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 cla.s.s of crystals there are _two_ directions in which double refraction does not take place. These are called _biaxal_ crystals. When plates of these crystals, suitably cut, are placed between the polarizer and a.n.a.lyzer, the axes (A A', fig. 47) are seen surrounded, not by circles, but by curves of another order and of a perfectly definite mathematical 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, according to the undulatory theory, the bands must possess this special character.

-- 10. _Power of the Wave Theory_.

I have taken this somewhat wide range over polarization itself, 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 a.s.sumption of transverse undulations, we first of all determine the wave-lengths, and find that on them all the phenomena of colour are dependent. The wavelengths may be determined in many independent ways. Newton virtually determined them when he measured the periods of his Fits: the length of a fit, in fact, is that of a quarter of an undulation.

The wave-lengths may be determined by diffraction at the edges of a slit (as in the Appendix to these Lectures); they may be deduced from the interference fringes produced by reflection; from the fringes produced by refraction; also by lines drawn with a diamond upon gla.s.s at measured distances asunder. And when the length determined by these independent methods are compared together, the strictest agreement is found to exist between them.