The aspect of these curves so fascinated Faraday that the greater portion of his intellectual life was devoted to pondering over them.

He invested the s.p.a.ce through which they run with a kind of materiality; and the probability is that the progress of science, by connecting the phenomena of magnetism with the luminiferous ether, will prove these 'lines of force,' as Faraday loved to call them, to represent a condition of this mysterious substratum of all radiant action.

It is not, however, the magnetic curves, as such, but their relationship to theoretic conceptions, that we have now to consider.

By the action of the bar magnet upon the needle we obtain the notion of a polar force; by the breaking of the strip of magnetized steel we attain the notion that polarity can attach itself to the ultimate particles of matter. The experiment with the iron filings introduces a new idea into the mind; the idea, namely, of _structural arrangement_.

Every pair of filings possesses four poles, two of which are attractive and two repulsive. The attractive poles approach, the repulsive poles retreat; the consequence being a certain definite arrangement of the particles with reference to each other.

-- 2. _Theory of Crystallization._

Now this idea of structure, as produced by polar force, opens a way for the intellect into an entirely new region, and the reason you are asked to accompany me into this region is, that our next inquiry relates to the action of crystals upon light. Prior to speaking of this action, I wish you to realise intellectually the process of crystalline architecture. Look then into a granite quarry, and spend a few minutes in examining the rock. It is not of perfectly uniform texture. It is rather an agglomeration of pieces, which, on examination, present curiously defined forms. You have there what mineralogists call quartz, you have felspar, you have mica. In a mineralogical cabinet, where these substances are preserved separately, you will obtain some notion of their forms. You will see there, also, specimens of beryl, topaz, emerald, tourmaline, heavy spar, fluor-spar, Iceland spar--possibly a full-formed diamond, as it quitted the hand of Nature, not yet having got into the hands of the lapidary.

[Ill.u.s.tration: Fig. 24.]

These crystals, you will observe, are put together according to law; they are not chance productions; and, if you care to examine them more minutely, you will find their architecture capable of being to some extent revealed. They often split in certain directions before a knife-edge, exposing smooth and shining surfaces, which are called planes of cleavage; and by following these planes you sometimes reach an internal form, disguised beneath the external form of the crystal.

Ponder these beautiful edifices of a hidden builder. You cannot help asking yourself how they were built; and familiar as you now are with the notion of a polar force, and the ability of that force to produce structural arrangement, your inevitable answer will be, that those crystals are built by the play of polar forces with which their molecules are endowed. In virtue of these forces, molecule lays itself to molecule in a perfectly definite way, the final visible form of the crystal depending upon this play of its ultimate particles.

Everywhere in Nature we observe this tendency to run into definite forms, and nothing is easier than to give scope to this tendency by artificial arrangements. Dissolve nitre in water, and allow the water slowly to evaporate; the nitre remains and the solution soon becomes so concentrated that the liquid condition can no longer be preserved.

The nitre-molecules approach each other, and come at length within the range of their polar forces. They arrange themselves in obedience to these forces, a minute crystal of nitre being at first produced. On this crystal the molecules continue to deposit themselves from the surrounding liquid. The crystal grows, and finally we have large prisms of nitre, each of a perfectly definite shape. Alum crystallizes with the utmost ease in this fashion. The resultant crystal is, however, different in shape from that of nitre, because the poles of the molecules are differently disposed. When they are _nursed_ with proper care, crystals of these substances may be caused to grow to a great size.

The condition of perfect crystallization is, that the crystallizing force shall act with deliberation. There should be no hurry in its operations; but every molecule ought to be permitted, without disturbance from its neighbours, to exercise its own rights. If the crystallization be too sudden, the regularity disappears. Water may be saturated with sulphate of soda, dissolved when the water is hot, and afterwards permitted to cool. When cold the solution is supersaturated; that is to say, more solid matter is contained in it than corresponds to its temperature. Still the molecules show no sign of building themselves together.

This is a very remarkable, though a very common fact. The molecules in the centre of the liquid are so hampered by the action of their neighbours that freedom to follow their own tendencies is denied to them. Fix your mind's eye upon a molecule within the ma.s.s. It wishes to unite with its neighbour to the right, but it wishes equally to unite with its neighbour to the left; the one tendency neutralizes the other and it unites with neither. But, if a crystal of sulphate of soda be dropped into the solution, the molecular indecision ceases. On the crystal the adjacent molecules will immediately precipitate themselves; on these again others will be precipitated, and this act of precipitation will continue from the top of the flask to the bottom, until the solution has, as far as possible, a.s.sumed the solid form. The crystals here produced are small, and confusedly arranged.

The process has been too hasty to admit of the pure and orderly action of the crystallizing force. It typifies the state of a nation in which natural and healthy change is resisted, until society becomes, as it were, supersaturated with the desire for change, the change being then effected through confusion and revolution.

Let me ill.u.s.trate the action of the crystallizing force by two examples of it: Nitre might be employed, but another well-known substance enables me to make the experiment in a better form. The substance is common sal-ammoniac, or chloride of ammonium, dissolved in water. Cleansing perfectly a gla.s.s plate, the solution of the chloride is poured over the gla.s.s, to which when the plate is set on edge, a thin film of the liquid adheres. Warming the gla.s.s slightly, evaporation is promoted, but by evaporation the water only is removed.

The plate is then placed in a solar microscope, and an image of the film is thrown upon a white screen. The warmth of the illuminating beam adds itself to that already imparted to the gla.s.s plate, so that after a moment or two the dissolved salt can no longer exist in the liquid condition. Molecule then closes with molecule, and you have a most impressive display of crystallizing energy overspreading the whole screen. You may produce something similar if you breathe upon the frost ferns which overspread your window-panes in winter, and then observe through a pocket lens the subsequent recongelation of the film.

In this case the crystallizing force is hampered by the adhesion of the film to the gla.s.s; nevertheless, the play of power is strikingly beautiful. Sometimes the crystals start from the edge of the film and run through it from that edge; for, the crystallization being once started, the molecules throw themselves by preference on the crystals already formed. Sometimes the crystals start from definite nuclei in the centre of the film, every small crystalline particle which rests in the film furnishing a starting-point. Throughout the process you notice one feature which is perfectly unalterable, and that is, angular magnitude. The spiculae branch from the trunk, and from these branches others shoot; but the angles enclosed by the spiculae are unalterable. In like manner you may find alum-crystals, quartz-crystals, and all other crystals, distorted in shape. They are thus far at the mercy of the accidents of crystallization; but in one particular they a.s.sert their superiority over all such accidents--_angular magnitude_ is always rigidly preserved.

My second example of the action of crystallizing force is this: By sending a voltaic current through a liquid, you know that we decompose the liquid, and if it contains a metal, we liberate this metal by electrolysis. This small cell contains a solution of acetate of lead, which is chosen for our present purpose, because lead lends itself freely to this crystallizing power. Into the cell are dipped two very thin platinum wires, and these are connected by other wires with a small voltaic battery. On sending the voltaic current through the solution, the lead will be slowly severed from the atoms with which it is now combined; it will be liberated upon one of the wires, and at the moment of its liberation it will obey the polar forces of its atoms, and produce crystalline forms of exquisite beauty. They are now before you, sprouting like ferns from the wire, appearing indeed like vegetable growths rendered so rapid as to be plainly visible to the naked eye. On reversing the current, these wonderful lead-fronds will dissolve, while from the other wire filaments of lead dart through the liquid. In a moment or two the growth of the lead-trees recommences, but they now cover the other wire.

In the process of crystallization, Nature first reveals herself as a builder. Where do her operations stop? Does she continue by the play of the same forces to form the vegetable, and afterwards the animal?

Whatever the answer to these questions may be, trust me that the notions of the coming generations regarding this mysterious thing, which some have called 'brute matter,' will be very different from those of the generations past.

There is hardly a more beautiful and instructive example of this play of molecular force than that furnished by water. You have seen the exquisite fern-like forms produced by the crystallization of a film of water on a cold window-pane.[15] You have also probably noticed the beautiful rosettes tied together by the crystallizing force during the descent of a snow-shower on a very calm day. The slopes and summits of the Alps are loaded in winter with these blossoms of the frost. They vary infinitely in detail of beauty, but the same angular magnitude is preserved throughout: an inflexible power binding spears and spiculae to the angle of 60 degrees.

The common ice of our lakes is also ruled in its formation by the same angle. You may sometimes see in freezing water small crystals of stellar shapes, each star consisting of six rays, with this angle of 60 between every two of them. This structure may be revealed in ordinary ice. In a sunbeam, or, failing that, in our electric beam, we have an instrument delicate enough to unlock the frozen molecules, without disturbing the order of their architecture. Cutting from clear, sound, regularly frozen ice, a slab parallel to the planes of freezing, and sending a sunbeam through such a slab, it liquefies internally at special points, round each point a six-petalled liquid flower of exquisite beauty being formed. Crowds of such flowers are thus produced. From an ice-house we sometimes take blocks of ice presenting misty s.p.a.ces in the otherwise continuous ma.s.s; and when we inquire into the cause of this mistiness, we find it to be due to myriads of small six-petalled flowers, into which the ice has been resolved by the mere heat of conduction.

A moment's further devotion to the crystallization of water will be well repaid; for the sum of qualities which renders this substance fitted to play its part in Nature may well excite wonder and stimulate thought. Like almost all other substances, water is expanded by heat and contracted by cold. Let this expansion and contraction be first ill.u.s.trated:--

A small flask is filled with coloured water, and stopped with a cork.

Through the cork pa.s.ses a gla.s.s tube water-tight, the liquid standing at a certain height in the tube. The flask and its tube resemble the bulb and stem of a thermometer. Applying the heat of a spirit-lamp, the water rises in the tube, and finally trickles over the top.

Expansion by heat is thus ill.u.s.trated.

Removing the lamp and piling a freezing mixture round the flask, the liquid column falls, thus showing the contraction of the water by the cold. But let the freezing mixture continue to act: the falling of the column continues to a certain point; it then ceases. The top of the column remains stationary for some seconds, and afterwards begins to rise. The contraction has ceased, and _expansion by cold_ sets in. Let the expansion continue till the liquid trickles a second time over the top of the tube. The freezing mixture has here produced to all appearance the same effect as the flame. In the case of water, contraction by cold ceases, and expansion by cold sets in at the definite temperature of 39 Fahr. Crystallization has virtually here commenced, the molecules preparing themselves for the subsequent act of solidification, which occurs at 32, and in which the expansion suddenly culminates. In virtue of this expansion, ice, as you know, is lighter than water in the proportion of 8 to 9.[16]

A molecular problem of great interest is here involved, and I wish now to place before you, for the satisfaction of your minds, a possible solution of the problem:--

Consider, then, the ideal case of a number of magnets deprived of weight, but retaining their polar forces. If we had a mobile liquid of the specific gravity of steel, we might, by making the magnets float in it, realize this state of things, for in such a liquid the magnets would neither sink nor swim. Now, the principle of gravitation enunciated by Newton is that every particle of matter, of every kind, attracts every other particle with a force varying inversely as the square of the distance. In virtue of the attraction of gravity, then, the magnets, if perfectly free to move, would slowly approach each other.

But besides the unpolar force of gravity, which belongs to matter in general, the magnets are endowed with the polar force of magnetism.

For a time, however, the polar forces do not come sensibly into play.

In this condition the magnets resemble our water-molecules at the temperature say of 50. But the magnets come at length sufficiently near each other to enable their poles to interact. From this point the action ceases to be solely a general attraction of the ma.s.ses.

Attractions of special points of the ma.s.ses and repulsions of other points now come into play; and it is easy to see that the rearrangement of the magnets consequent upon the introduction of these new forces may be such as to require a greater amount of room. This, I take it, is the case with our water-molecules. Like our ideal magnets, they approach each other for a time _as wholes_. Previous to reaching the temperature 39 Fahr., the polar forces had doubtless begun to act, but it is at this temperature that their claim to more room exactly balances the contraction due to cold. At lower temperatures, as regards change of volume, the polar forces predominate. But they carry on a struggle with the force of contraction until the freezing temperature is attained. The molecules then close up to form solid crystals, a considerable augmentation of volume being the immediate consequence.

-- 3. _Ordinary Refraction of Light explained by the Wave Theory_.

We have now to exhibit the bearings of this act of crystallization upon optical phenomena. According to the undulatory theory, the velocity of light in water and gla.s.s is less than in air. Consider, then, a small portion of a wave issuing from a point of light so distant that the minute area may be regarded as practically plane.

Moving vertically downwards, and impinging on a horizontal surface of gla.s.s or water, the wave would go through the medium without change of direction. As, however, the velocity in gla.s.s or water is less than the velocity in air, the wave would be r.e.t.a.r.ded on pa.s.sing into the denser medium.

[Ill.u.s.tration: Fig. 25.]

But suppose the wave, before reaching the gla.s.s, to be _oblique_ to the surface; that end of the wave which first reaches the medium will be the first r.e.t.a.r.ded by it, the other portions as they enter the gla.s.s being r.e.t.a.r.ded in succession. It is easy to see that this r.e.t.a.r.dation of the one end of the wave must cause it to swing round and change its front, so that when the wave has fully entered the gla.s.s its course is oblique to its original direction. According to the undulatory theory, light is thus _refracted_.

With these considerations to guide us, let us follow the course of a beam of monochromatic light through our gla.s.s prism. The velocity in air is to its velocity in gla.s.s as 3: 2. Let A B C (fig. 25) be the section of our prism, and _a_ _b_ the section of a plane wave approaching it in the direction of the arrow. When it reaches _c_ _d_, one end of the wave is on the point of entering the gla.s.s. Following it still further, it is obvious that while the portion of the wave still in the air pa.s.ses over the distance _c_ _e_, the wave in the gla.s.s will have pa.s.sed over only two-thirds of this distance, or _d_ _f_. The line _e_ _f_ now marks the front of the wave. Immersed wholly in the gla.s.s it pursues its way to _g_ _h_, where the end _g_ of the wave is on the point of escaping into the air. During the time required by the end _h_ of the wave to pa.s.s over the distance _h_ _k_ to the surface of the prism, the other end _g_, moving more rapidly, will have reached the point _i_. The wave, therefore, has again changed its front, so that after its emergence from the prism it will pa.s.s on to _l_ _m_, and subsequently in the direction of the arrow.

The refraction of the beam is thus completely accounted for; and it is, moreover, based upon actual experiment, which proves that the ratio of the velocity of light in gla.s.s to its velocity in air is that here mentioned. It is plain that if the change of velocity on entering the gla.s.s were greater, the refraction also would be greater.

-- 4. _Double Refraction of Light explained by the Wave Theory_.

The two elements of rapidity of propagation, both of sound and light, in any substance whatever, are _elasticity_ and _density_, the speed increasing with the former and diminishing with the latter. The enormous velocity of light in stellar s.p.a.ce is attainable because the ether is at the same time of infinitesimal density and of enormous elasticity. Now the ether surrounds the atoms of all bodies, but it is not independent of them. In ponderable matter it acts as if its density were increased without a proportionate increase of elasticity; and this accounts for the diminished velocity of light in refracting bodies. We here reach a point of cardinal importance. In virtue of the crystalline architecture that we have been considering, the ether in many crystals possesses different densities, and different elasticities, in different directions; the consequence is, that in such crystals light is transmitted with different velocities. And as refraction depends wholly upon the change of velocity on entering the refracting medium, being greatest where the change of velocity is greatest, we have in many crystals two different refractions. By such crystals a beam of light is divided into two. This effect is called _double refraction_.

In ordinary water, for example, there is nothing in the grouping of the molecules to interfere with the perfect h.o.m.ogeneity of the ether; but, when water crystallizes to ice, the case is different. In a plate of ice the elasticity of the ether in a direction perpendicular to the surface of freezing is different from what it is parallel to the surface of freezing; ice is, therefore, a double refracting substance.

Double refraction is displayed in a particularly impressive manner by Iceland spar, which is crystallized carbonate of lime. The difference of ethereal density in two directions in this crystal is very great, the separation of the beam into the two halves being, therefore, particularly striking.

I am unwilling to quit this subject before raising it to unmistakable clearness in your minds. The vibrations of light being transversal, the elasticity concerned in the propagation of any ray is the elasticity at right angles to the direction of propagation. In Iceland spar there is one direction round which the crystalline molecules are symmetrically built. This direction is called the axis of the crystal.

In consequence of this symmetry the elasticity is the same in all directions perpendicular to the axis, and hence a ray transmitted along the axis suffers no double refraction. But the elasticity along the axis is greater than the elasticity at right angles to it.

Consider, then, a system of waves crossing the crystal in a direction perpendicular to the axis. Two directions of vibration are open to such waves: the ether particles can vibrate parallel to the axis or perpendicular to it. _They do both_, and hence immediately divide themselves into two systems propagated with different velocities.

Double refraction is the necessary consequence.

[Ill.u.s.tration: Fig. 26.]

By means of Iceland spar cut in the proper direction, double refraction is capable of easy ill.u.s.tration. Causing the beam which builds the image of our carbon-points to pa.s.s through the spar, the single image is instantly divided into two. Projecting (by the lens E, fig. 26) an image of the aperture (L) through which the light issues from the electric lamp, and introducing the spar (P), two luminous disks (E O) appear immediately upon the screen instead of one.

The two beams into which the spar divides the single incident-beam have been subjected to the closest examination. They do not behave alike. One of them obeys the ordinary law of refraction discovered by Snell, and is, therefore, called the _ordinary ray_: its index of refraction is 1.654. The other does not obey this law. Its index of refraction, for example, is not constant, but varies from a maximum of 1.654 to a minimum of 1.483; nor in this case do the incident and refracted rays always lie in the same plane. It is, therefore, called the _extraordinary ray_. In calc-spar, as just stated, the ordinary ray is the most refracted. One consequence of this merits a pa.s.sing notice. Pour water and bisulphide of carbon into two cups of the same depth; the cup that contains the more strongly refracting liquid will appear shallower than the other. Place a piece of Iceland spar over a dot of ink; two dots are seen, the one appearing nearer than the other to the eye. The nearest dot belongs to the most strongly refracted ray, exactly as the nearest cup-bottom belongs to the most highly refracting liquid. When you turn the spar round, the extraordinary image of the dot rotates round the ordinary one, which remains fixed.

This is also the deportment of our two disks upon the screen.

-- 5. _Polarization of Light explained by the Wave Theory_.

The double refraction of Iceland spar was first treated in a work published by Erasmus Bartholinus, in 1669. Huyghens sought to account for this phenomenon on the principles of the wave theory, and he succeeded in doing so. He, moreover, made highly important observations on the distinctive character of the two beams transmitted by the spar, admitting, with resigned candour, that he had not solved the difficulty, and leaving the solution to future times. Newton, reflecting on the observations of Huyghens, came to the conclusion that each of the beams transmitted by Iceland spar had two sides; and from the a.n.a.logy of this _two-sidedness_ with the _two-endedness_ of a magnet, wherein consists its polarity, the two beams came subsequently to be described as _polarized_.

We may begin the study of the polarization of light, with ease and profit, by means of a crystal of tourmaline. But we must start with a clear conception of an ordinary beam of light. It has been already explained that the vibrations of the individual ether-particles are executed _across_ the line of propagation. In the case of ordinary light we are to figure the ether-particles as vibrating in all directions, or azimuths, as it is sometimes expressed, across this line.

Now, in the case of a plate of tourmaline cut parallel to the axis of the crystal, a beam of light incident upon the plate is divided into two, the one vibrating parallel to the axis of the crystal, the other at right angles to the axis. The grouping of the molecules, and of the ether a.s.sociated with the molecules, reduces all the vibrations incident upon the crystal to these two directions. One of these beams, namely, that whose vibrations are perpendicular to the axis, is quenched with exceeding rapidity by the tourmaline. To such vibrations many specimens of the crystal are highly opaque; so that, after having pa.s.sed through a very small thickness of the tourmaline, the light emerges with all its vibrations reduced to a single plane. In this condition it is what we call _plane polarized light_.

[Ill.u.s.tration: Fig. 27.]