Chapter III: Part 3

He extends his observations to essential oils and spirits of wine, 'which being shaken till they have good store of bubbles, those bubbles will (if attentively considered) appear adorned with various and lovely colours, which all immediately vanish upon the retrogressing of the liquid which affords these bubbles their skins into the rest of the oil.' He also refers to the colour of glass films. 'I have seen one that was skilled in fashioning glasses by the help of a lamp blowing some of them so strongly as to burst them; whereupon it was found that the tenacity of the metal was such that before it broke it suffered itself to be reduced into films so extremely thin that they constantly showed upon their surface the varying colours of the rainbow.'[14]

Subsequent to Boyle the colours of thin plates occupied the attention of Robert Hooke, in whose writings we find a dawning of the undulatory theory of light. He describes with great distinctness the colours obtained with thin flakes of 'Muscovy glass' (talc), also those surrounding flaws in crystals where optical continuity is destroyed. He shows very clearly the dependence of the colour upon the thickness of the film, and proves by microscopic observation that plates of a uniform thickness yield uniform colours. 'If,' he says, 'you take any small piece of the Muscovy glass, and with a needle, or some other convenient instrument, cleave it oftentimes into thinner and thinner laminæ, you shall find that until you come to a determinate thinness of them they shall appear transparent and colourless; but if you continue to split and divide them further, you shall find at last that each plate shall appear most lovely tinged or imbued with a determinate colour. If, further, by any means you so flaw a pretty thick piece that one part begins to cleave a little from the other, and between these two there be gotten some pellucid medium, those laminated or pellucid bodies that fill that space shall exhibit several rainbows or coloured lines, the colours of which will be disposed and ranged according to the various thicknesses of the several parts of the plate.' He then describes fully and clearly the experiment with pressed glasses already referred to:--

'Take two small pieces of ground and polished looking-glass plate, each about the bigness of a shilling: take these two dry, and with your forefingers and thumbs press them very hard and close together, and you shall find that when they approach each other very near there will appear several irises or coloured lines, in the same manner almost as in the Muscovy glass; and you may very easily change any of the colours of any part of the interposed body by pressing the plates closer and harder together, or leaving them more lax--that is, a part which appeared coloured with a red, may presently be tinged with a yellow, blue, green, purple, or the like. 'Any substance,' he says, 'provided it be thin and transparent, will show these colours.' Like Boyle, he obtained them with glass films; he also procured them with bubbles of pitch, rosin, colophony, turpentine, solutions of several gums, as gum arabic in water, any glutinous liquor, as wort, wine, spirit of wine, oyl of turpentine, glare of snails, &c.

Hooke's writings show that even in his day the idea that both light and heat are modes of motion had taken possession of many minds. 'First,' he says, 'that all kind _of fiery burning bodies_ have their parts in motion I think will be easily granted me. That the spark struck from a flint and steel is in rapid agitation I have elsewhere made probable;... that heat argues a motion of the internal parts is (as I said before) generally granted;... and that in all extremely hot shining bodies there is a very quick motion that causes light, as well as a more robust that causes heat, may be argued from the celerity wherewith the bodies are dissolved. Next, it must be _a vibrative motion.'_ His reference to the quick motion of light and the more robust motion of heat is a remarkable stroke of sagacity; but Hooke's direct insight is better than his reasoning; for the proofs he adduces that light is 'a vibrating motion' have no particular bearing upon the question.

Still the Undulatory Theory had undoubtedly dawned upon the mind of this remarkable man. In endeavouring to account for the colours of thin plates, he again refers to the relation of colour to thickness: he dwells upon the fact that the film which shows these colours must be transparent, proving this by showing that however thin an opaque body was rendered no colours were produced. 'This,' he says, 'I have often tried by pressing a small globule of mercury between two smooth plates of glass, whereby I have reduced that body to a much greater thinness than was requisite to exhibit the colours with a transparent body.' Then follows the sagacious remark that to produce the colours 'there must be a considerable reflecting body adjacent to the under or further side of the lamina or plate: for this I always found, that the greater that reflection was the more vivid were the appearing colours. From which observation,' he continues, 'it is most evident, _that the reflection from the further or under side of the body is the principal cause of the production of these colours._'

He draws a diagram, correctly representing the reflection at the two surfaces of the film; but here his clearness ends. He ascribes the colours to a coalescence or confusion of the two reflecting pulses; the principal of interference being unknown to him, he could not go further in the way of explanation.

§ 8. _Newton's Rings. Relation of Colour to Thickness of Film_.

In this way, then, by the active operation of different minds, facts are observed, examined, and the precise conditions of their appearance determined. All such work in science is the prelude to other work; and the efforts of Boyle and Hooke cleared the way for the optical career of Newton. He conquered the difficulty which Hooke had found insuperable, and determined by accurate measurements the relation of the thickness of the film to the colour it displays. In doing this his first care was to obtain a film of variable and calculable depth. On a plano-convex glass lens (D B E, fig. 13) of very feeble curvature he laid a plate of glass (A C) with a plane surface, thus obtaining a film of air of gradually increasing depth from the point of contact (B) outwards. On looking at the film in monochromatic light he saw, with the delight attendant on fulfilled prevision, surrounding 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 (as in fig. 14). When he employed red light, his rings had certain diameters; when he employed blue light, the diameters were less. In general terms, the more refrangible the light the smaller were the rings. Causing his glasses to pass through the spectrum from red to blue, the rings gradually contracted; when the passage was from blue to red, the rings expanded. This is a beautiful experiment, and appears to have given Newton the most lively satisfaction. When white light fell upon, the glasses, inasmuch as the colours were not superposed, a series _of iris-coloured_ circles was obtained. 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. You notice that in monochromatic light the rings run closer and closer together as they recede from the centre. This is due to the fact that at a distance the film of air thickens more rapidly than near the centre. When white light is employed, this closing up of the rings causes the various colours to be superposed, so that after a certain thickness they are blended together to white light, the rings then ceasing altogether. It needs but a moment's reflection to understand that the colours of thin plates, produced by white light, are never unmixed or monochromatic.

Newton compared the tints obtained in this way with the tints of his 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 one. 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 greatest optical 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 light-particles 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. 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 he through _some change in the condition of the particle itself_. The self-same particle, he affirmed, was affected by 'fits' of easy transmission and reflection.

§ 9. _Theory of 'Fits' applied to Newton's Rings_.

If you are willing to follow me in an attempt to reveal the speculative groundwork of this theory of fits, the intellectual discipline will, I think, 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 can hardly be a doubt that his mind rested on a physical cause. Nor can there be a doubt that here, as in all attempts at theorising, he was compelled to fall back upon experience for the materials of his theory. Let us attempt to restore his course of thought and observation. A magnet would furnish him with the notion of attracted and repelled poles; and he who habitually saw in the visible an image of the invisible would naturally endow his light-particles 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 particle at different times might be accounted for.

Consider 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 _d_; then Newton found the distance corresponding to the second dark ring 2 _d_; the thickness corresponding to the third dark ring 3 _d_; the thickness corresponding to the tenth dark ring 10 _d_, and so on. Surely there must be 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 probable outcome of his thought. He had endowed his light-particles with poles, but now he is forced to introduce the notion of _periodic recurrence_. Here his power of transfer from the sensible to the subsensible would render it easy for him to suppose the light-particles animated, not only with a motion of translation, but also with a motion of rotation. Newton's astronomical knowledge rendered all such conceptions familiar to him. The earth has such a double 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 might 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 conceptions are, in point of intellectual quality, identical.

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 therefore 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 rotations within the film; when the thickness is 3 _d, three_ complete rotations; when 10 _d, ten_ complete rotations 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.

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 ½_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, therefore, driven back and reaches the eye. At all distances round the centre corresponding to this thickness the same effect is produced, and the consequence is a ring of brightness. The other bright rings are similarly accounted for. At the second one, where the thickness is 1½_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, and produce there the impression of brightness. This analysis, though involving difficulties when closely scrutinised, enables us to see how the theory of fits may have grown into consistency in the mind of Newton.

It has been already stated that the Emission Theory assigned a greater velocity to light in glass and water than in air or stellar space; and that on this point it was at direct issue with the theory of undulation, which makes the velocity in air or stellar space greater than in glass or water. By an experiment proposed by Arago, and executed with consummate skill by Foucault and Fizeau, this question was brought to a crucial test, and decided in favour of the theory of undulation.

In the present instance also the two theories are at variance. Newton assumed that the action which produces the alternate bright and dark rings took place at a _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 a proper arrangement, as we shall afterwards learn, we may abolish reflection from one of the surfaces of the film, and when this is done the rings vanish altogether.

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 which have suffered _two_ reflections within the film, and are thus completely accounted for.

§ 10. _The Diffraction of Light_.

Newton's espousal of the Emission Theory is said to have retarded scientific discovery. It might, however, be questioned whether, in the long run, the errors of great men have not really their effect in rendering intellectual progress rhythmical, instead of permitting it to remain uniform, the 'retardation' in each case being the prelude to a more impetuous advance. It is confusion and stagnation, rather than error, that we ought to avoid. Thus, though the undulatory theory was held back for a time, it gathered strength in the interval, and its development within the last half century has been so rapid and triumphant as to leave no rival in the field. We have now to turn to the investigation of new classes of phenomena, of which it alone can render a satisfactory account.

Newton, who was familiar with the idea of an ether, and who introduced it in some of his speculations, objected, as already stated, that if light consisted of waves shadows could not exist; for that the waves would bend round the edges of opaque bodies and agitate the ether behind them. He was right in affirming that this bending ought to occur, but wrong in supposing that it does not occur. The bending is real, though in all ordinary cases it is masked by the action of interference. This inflection of the light receives the name of _Diffraction_.

To study the phenomena of diffraction it is necessary that our source of light should be a physical point, or a fine line; for when a luminous surface is employed, the waves issuing from different points of the surface obscure and neutralize each other. A _point_ of light of high intensity is obtained by admitting the parallel rays of the sun through an aperture in a window-shutter, and concentrating the beam by a lens of short focus. The small solar image at the focus constitutes a suitable point of light. The image of the sun formed on the convex surface of a glass bead, or of a watch-glass blackened within, though less intense, will also answer. An intense _line_ of light is obtained by admitting the sunlight through a slit and sending it through a strong cylindrical lens. The slice of light is contracted to a physical line at the focus of the lens. A glass tube blackened within and placed in the light, reflects from its surface a luminous line which, though less intense, also answers the purpose.

In the experiment now to be described a vertical slit of variable width is placed in front of the electric lamp, and this slit is looked at from a distance through another vertical slit, also of variable aperture, and held in the hand.

The light of the lamp being, in the first place, rendered monochromatic by placing a pure red glass in front of the slit, when the eye is placed in the straight line drawn through both slits an extraordinary appearance (shown in fig. 15) is observed. Firstly, the slit in front of the lamp is seen as a vivid rectangle of light; but right and left of it is a long series of rectangles, decreasing in vividness, and separated from each other by intervals of absolute darkness.

The breadth of these bands is seen to vary with the width of the slit held before the eye. When the slit is widened the bands become narrower, and crowd more losely together; when the slit is narrowed, the individual bands widen and also retreat from each other, leaving between them wider spaces of darkness than before.

Leaving everything else unchanged, let a blue glass or a solution of ammonia-sulphate of copper, which gives a very pure blue, be placed in the path of the light. A series of blue bands is thus obtained, exactly like the former in all respects save one; the blue rectangles are _narrower_, and they are _closer together_ than the red ones.

If we employ colours of intermediate refrangibilities, which we may do by causing the different colours of a spectrum to shine through the slit, we obtain bands of colour intermediate in width, and occupying intermediate positions, between those of the red and blue. The aspect of the bands in red, green, and violet light is represented in fig. 16. When _white light_, therefore, passes through the slit the various colours are not superposed, and instead of a series of monochromatic bands, separated from each other by intervals of darkness, we have a series of coloured spectra placed side by side. When the distant slit is illuminated by a candle flame, instead of the more intense electric light, or when a distant platinum wire raised to a white heat by an electric current is employed, substantially the same effects are observed.

§ 11. _Application of the Wave-theory to the Phenomena of Diffraction_.

Of these and of a multitude of similar effects the Emission Theory is incompetent to offer any satisfactory explanation. Let us see how they are accounted for by the Theory of Undulation.

And here, with the view of reaching absolute clearness, I must make an appeal to that faculty the importance of which I have dwelt upon so earnestly here and elsewhere--the faculty of imagination. Figure yourself upon the sea-shore, with a well-formed wave advancing. Take a line of particles along the front of the wave, all at the same distance below the crest; they are all rising in the same manner and at the same rate. Take a similar line of particles on the back of the wave, they are all falling in the same manner and at the same rate. Take a line of particles along the crest, they are all in the same condition as regards the motion of the wave. The same is true for a line of particles along the furrow of the wave.

The particles referred to in each of these cases respectively, being in the same condition as regards the motion of the wave, are said to be in the same _phase_ of vibration. But if you compare a particle on the front of the wave with one at the back; or, more generally, if you compare together any two particles not occupying the same position in the wave, their conditions of motion not being the same, they are said to be in different phases of vibration. If one of the particles lie upon the crest, and the other on the furrow of the wave, then, as one is about to rise and the other about to fall, they are said to be in _opposite_ phases of vibration.

There is still another point to be cleared up--and it is one of the utmost importance as regards our present subject. Let O (fig. 17) be a spot in still water which, when disturbed, produces a series of circular waves: the disturbance necessary to produce these waves is simply an oscillation up and down of the water at O. Let _m_ _n_ be the position of the ridge of one of the waves at any moment, and _m'_ _n'_ its position a second or two afterwards. Now every particle of water, as the wave passes it, oscillates, as we have learned, up and down. If, then, this oscillation be a sufficient origin of wave-motion, each distinct particle of the wave _m_ _n_ ought to give birth, to a series of circular waves. This is the important point up to which I wish to lead you. Every particle of the wave _m_ _n_ _does_ act in this way. Taking each particle as a centre, and surrounding it by a circular wave with a radius equal to the distance between _m_ _n_ and _m'_ _n'_, the coalescence of all these little waves would build up the large ridge _m'_ _n'_ exactly as we find it built up in nature. Here, in fact, we resolve the wave-motion into its elements, and having succeeded in doing this we shall have no great difficulty in applying our knowledge to optical phenomena.

Now let us return to our slit, and, for the sake of simplicity, we will first consider the case of monochromatic light. Conceive a series of waves of ether advancing from the first slit towards the second, and finally filling the second slit. When each wave passes through the latter it not only pursues its direct course to the retina, but diverges right and left, tending to throw into motion the entire mass of the ether behind the slit. In fact, as already explained, _every point of the wave which fills the slit is itself a centre of a new wave system which is transmitted in all directions through the ether behind the slit_. This is the celebrated principle of Huyghens: we have now to examine how these secondary waves act upon each other.

Let us first regard the central band of the series. Let AP (fig. 18) be the width of the aperture held before the eye, grossly exaggerated of course, and let the dots across the aperture represent ether particles, all in the same phase of vibration. Let E T represent a portion of the retina. From O, in the centre of the slit, let a perpendicular O R be imagined drawn upon the retina. The motion communicated to the point R will then be the sum of all the motions emanating in this direction from the ether particles in the slit. Considering the extreme narrowness of the aperture, we may, without sensible error, regard all points of the wave A P as equally distant from R. No one of the partial waves lags sensibly behind the others: hence, at R, and in its immediate neighbourhood, we have no sensible reduction of the light by interference. This undiminished light produces the brilliant central band of the series.

Let us now consider those waves which diverge laterally behind the second slit. In this case the waves from the two sides of the slit have, in order to converge upon the retina, to pass over unequal distances. Let A P (fig. 19) represent, as before, the width of the second slit. We have now to consider the action of the various parts of the wave A P upon a point R' of the retina, not situated in the line joining the two slits.

Let us take the particular case in which the difference of path from the two marginal points A, P, to the retina is a whole wave-length of the red light; how must this difference affect the final illumination of the retina?

Let us fix our attention upon the particular oblique line that passes through the _centre_ O of the slit to the retina at R'. The difference of path between the waves which pass along this line and those from the two margins is, in the case here supposed, half a wavelength. Make _e_ R' equal to P R', join P and _e_, and draw O _d_ parallel to P e. A e is then the length of a wave of light, while A _d_ is half a wave-length. Now the least reflection will make it clear that not only is there discordance between the central and marginal waves, but that every line of waves such as _x_ R', on the one side of O R', finds a line _x_' R' upon the other side of O R', from which its path differs by half an undulation--with which, therefore, it is in complete discordance. The consequence is, that the light on the one side of the central line will completely abolish the light on the other side of that line, absolute darkness being the result of their coalescence. The first dark interval of our series of bands is thus accounted for. It is produced by an obliquity of direction which causes the paths of the marginal waves to be _a whole wave-length_ different from each other.

When the difference between the paths of the marginal waves is _half a wave-length,_ a partial destruction of the light is effected. The luminous intensity corresponding to this obliquity is a little less than one-half--accurately 0.4--that of the undiffracted light. If the paths of the marginal waves be three semi-undulations different from each other, and if the whole beam be divided into three equal parts, two of these parts will, for the reasons just given, completely neutralize each other, the third only being effective. Corresponding, therefore, to an obliquity which produces a difference of three semi-undulations in the marginal waves, we have a luminous band, but one of considerably less intensity than the undiffracted central band.

With a marginal difference of path of four semi-undulations we have a second extinction of the entire beam, because here the beam can be divided into four equal parts, every two of which quench each other. A second space of absolute darkness will therefore correspond to the obliquity producing this difference. In this way we might proceed further, the general result being that, whenever the direction of wave-motion is such as to produce a marginal difference of path of an _even_ number of semi-undulations, we have complete extinction; while, when the marginal difference is an _odd_ number of semi-undulations, we have only partial extinction, a portion of the beam remaining as a luminous band.

A moment's reflection will make it plain that the wider the slit the less will be the obliquity of direction needed to produce the necessary difference of path. With a wide slit, therefore, the bands, as observed, will be closer together than with a narrow one. It is also plain that the shorter the wave, the less will be the obliquity required to produce the necessary retardation. The maxima and minima of violet light must therefore fall nearer to the centre than the maxima and minima of red light. The maxima and minima of the other colours fall between these extremes. In this simple way the undulatory theory completely accounts for the extraordinary appearance above referred to.

When a slit and telescope are used, instead of the slit and naked eye, the effects are magnified and rendered more brilliant. Looking, moreover, through a properly adjusted telescope with a small circular aperture in front of it, at a distant point of light, the point is seen encircled by a series of coloured bands. If monochromatic light be used, these bands are simply bright and dark, but with white light the circles display iris-colours. If a slit be shortened so as to form a square aperture, we have two series of spectra at right angles to each other. The effects, indeed, are capable of endless variation by varying the size, shape, and number of the apertures through which the point of light is observed. Through two square apertures, with their corners touching each other as at A, Schwerd observed the appearance shown in fig. 20. Adding two others to them, as at B, he observed the appearance represented in fig. 21. The position of every band of light and shade in such figures has been calculated from theory by Fresnel, Fraunhofer, Herschel, Schwerd, and others, and completely verified by experiment. Your eyes could not tell you with greater certainty of the existence of these bands than the theoretic calculation.

The street-lamps at night, looked at through the meshes of a handkerchief, show diffraction phenomena. The diffraction effects obtained in looking through a bird's feathers are, as shown by Schwerd, very brilliant. The iridescence of certain Alpine clouds is also an effect of diffraction which may be imitated by the spores of Lycopodium. When shaken over a glass plate these spores cause a point of light, looked at through the dusted plate, to be surrounded by coloured circles, which rise to actual splendour when the light becomes intense. Shaken in the air the spores produce the same effect. The diffraction phenomena obtained during the artificial precipitation of clouds from the vapours of various liquids in an intensely illuminated tube are, as I have elsewhere shewn, exceedingly fine.

One of the most interesting cases of diffraction by small particles that ever came before me was that of an artist whose vision was disturbed by vividly coloured circles. He was in great dread of losing his sight; assigning as a cause of his increased fear that the circles were becoming larger and the colours more vivid. I ascribed the colours to minute particles in the humours of the eye, and ventured to encourage him by the assurance that the increase of size and vividness on the part of the circles indicated that the diffracting particles were becoming _smaller_, and that they might finally be altogether absorbed. The prediction was verified. It is needless to say one word on the necessity of optical knowledge in the case of the practical oculist.

Without breaking ground on the chromatic phenomena presented by crystals, two other sources of colour may be mentioned here. By interference in the earth's atmosphere, the light of a star, as shown by Arago, is self-extinguished, the twinkling of the star and the changes of colour which it undergoes being due to this cause. Looking at such a star through an opera-glass, and shaking the glass so as to cause the image of the star to pass rapidly over the retina, you produce a row of coloured beads, the spaces between which correspond to the periods of extinction. Fine scratches drawn upon glass or polished metal reflect the waves of light from their sides; and some, being reflected from the opposite sides of the same scratch, interfere with and quench each other. But the obliquity of reflection which extinguishes the shorter waves does not extinguish the longer ones, hence the phenomena of colours. These are called the colours of _striated surfaces_. They are beautifully illustrated by mother-of-pearl. This shell is composed of exceedingly thin layers, which, when cut across by the polishing of the shell, expose their edges and furnish the necessary small and regular grooves. The most conclusive proof that the colours are due to the mechanical state of the surface is to be found in the fact, established by Brewster, that by stamping the shell carefully upon black sealing-wax, we transfer the grooves, and produce upon the wax the colours 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
ARCHITECTURE OF CRYSTALS CONSIDERED AS AN INTRODUCTION
TO THEIR ACTION UPON LIGHT
NOTION OF ATOMIC POLARITY APPLIED TO CRYSTALLINE STRUCTURE
EXPERIMENTAL ILLUSTRATIONS
CRYSTALLIZATION OF WATER
EXPANSION BY HEAT AND BY COLD
DEPORTMENT OF WATER CONSIDERED AND EXPLAINED
BEARINGS OF CRYSTALLIZATION ON OPTICAL PHENOMENA
REFRACTION
DOUBLE REFRACTION
POLARIZATION
ACTION OF TOURMALINE
CHARACTER OF THE BEAMS EMERGENT FROM ICELAND SPAR
POLARIZATION BY ORDINARY REFRACTION AND REFLECTION
DEPOLARIZATION

§ 1. _Derivation of Theoretic Conceptions from Experience._

One of the objects of our last lecture, and that not the least important, was to illustrate the manner in which scientific theories are formed. They, in the first place, take their rise in the desire of the mind to penetrate to the sources of phenomena. From its infinitesimal beginnings, in ages long past, this desire has grown and strengthened into an imperious demand of man's intellectual nature. It long ago prompted Cæsar to say that he would exchange his victories for a glimpse of the sources of the Nile; it wrought itself into the atomic theories of Lucretius; it impelled Darwin to those daring speculations which of late years have so agitated the public mind. But in no case, while framing theories, does the imagination _create_ its materials. It expands, diminishes, moulds, and refines, as the case may be, materials 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 the idea of gravitation with unnecessary physical conceptions; but we 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 as the portal into a new domain; but in the first place we must master its elementary phenomena.

The general facts of magnetism are most simply illustrated by a magnetized bar of steel, commonly called a bar magnet. Placing such a magnet upright upon a table, and bringing a magnetic needle near its bottom, one end of the needle is observed to retreat from the magnet, while the other as promptly approaches. The needle is held quivering there by some invisible influence exerted upon it. Raising the needle along the magnet, but still avoiding contact, the rapidity of its oscillations decreases, because the force acting upon it becomes weaker. At the centre the oscillations cease. Above the centre, the end of the needle which had been previously drawn towards the magnet retreats, and the opposite end approaches. As we ascend higher, the oscillations become more violent, because the force becomes stronger. At the upper end of the magnet, as at the lower, the force reaches a maximum; but all the lower half of the magnet, from E to S (fig. 22), 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_.

What, then, will occur if we break this magnet in two at the centre E? Shall we obtain two magnets, each with a single pole? No; each half is in itself a perfect magnet, possessing two poles. This may be proved by breaking something of less value than the magnet--the steel of a lady's stays, for 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 sensible limit--you cannot stop there. The bias derived from observation will infallibly carry you beyond the bourne of the senses, and compel you to regard this thing that we call magnetic polarity as resident in the ultimate particles of the steel. You come to the conclusion that each molecule of the magnet is endowed with this polar 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 a determinate position. That position might be deduced theoretically from the mutual action of the poles. Moving the needle round the magnet, for each point of the surrounding space there is a definite direction 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 steel needle independently magnetized.

If we place two or more needles of iron near the magnet, the action becomes more complex, for then the 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 obedience to the magnetic action.

Placing a sheet of paper or glass over a bar magnet and showering iron filings upon the paper, I notice a tendency of the filings to arrange themselves in determinate lines. They cannot freely follow this tendency, for they are hampered by the friction against the paper. They are helped by tapping the paper; each tap releasing them for a moment, and enabling them to follow their tendencies. But this is an experiment which can only be seen by myself. To enable you all to see it, I take a pair of small magnets and by a simple optical arrangement throw the magnified 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 (fig. 23).

N 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.]

(By a very ingenious device, Professor Mayer, of Hoboken, has succeeded in fixing and photographing the magnetic curves. I am indebted to his kindness for the annexed beautiful illustration, fig. 24.)

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 space 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.

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 mass. 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, assumed 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 illustrate 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 glass plate, the solution of the chloride is poured over the glass, to which when the plate is set on edge, a thin film of the liquid adheres. Warming the glass 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 glass 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 glass; 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 spiculæ branch from the trunk, and from these branches others shoot; but the angles enclosed by the spiculæ 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 assert 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 spiculæ to the angle of 60 degrees.