This consensus of evidence is one of the strongest points of the undulatory theory. The shortest waves of the visible spectrum are those of the extreme violet; the longest, those of the extreme red; while the other colours are of intermediate pitch or wavelength. The length of a wave of the extreme red is such, that it would require 39,000 such waves, placed end to end, to cover one inch, while 64,631 of the extreme violet waves would be required to span the same distance.

Now, the velocity of light, in round numbers, is 186,000 miles per second. Reducing this to inches, and multiplying the number thus found by 39,000, we find the number of waves of the extreme red, in 186,000 miles, to be four hundred and sixty millions of millions. _All these waves enter the eye, and strike the retina at the back of the eye in one second_. In a similar manner, it may be found that the number of shocks corresponding to the impression of violet is six hundred and seventy-eight millions of millions.

All s.p.a.ce is filled with matter oscillating at such rates. From every star waves of these dimensions move, with the velocity of light, like spherical sh.e.l.ls in all directions. And in ether, just as in water, the motion of every particle is the algebraic sum of all the separate motions imparted to it. One motion does not blot out the other; or, if extinction occur at one point, it is strictly atoned for, by augmented motion, at some other point. Every star declares by its light its undamaged individuality, as if it alone had sent its thrills through s.p.a.ce.

-- 6. _Interference of Light_.

[Ill.u.s.tration: Fig. 11.]

The principle of interference, as just stated, applies to the waves of light as it does to the waves of water and the waves of sound. And the conditions of interference are the same in all three. If two series of light-waves of the same length start at the same moment from a common origin (say A, fig. 11), crest coincides with crest, sinus with sinus, and the two systems blend together to a single system (A _m_ _n_) of double amplitude. If both series start at the same moment, one of them being, at starting, a whole wavelength in advance of the other, they also add themselves together, and we have an augmented luminous effect. The same occurs when the one system of waves is any _even_ number of semi-undulations in advance of the other. But if the one system be half a wave-length (as at A' _a_', fig. 12), or any _odd_ number of half wavelengths, in advance, then the crests of the one fall upon the sinuses of the other; the one system, in fact, tends to _lift_ the particles of ether at the precise places where the other tends to _depress_ them; hence, through the joint action of these opposing forces (indicated by the arrows) the light-ether remains perfectly still. This stillness of the ether is what we call darkness, which corresponds with a dead level in the case of water.

[Ill.u.s.tration: Fig. 12.]

It was said in our first lecture, with reference to the colours produced by absorption, that the function of natural bodies is selective, not creative; that they extinguish certain const.i.tuents of the white solar light, and appear in the colours of the unextinguished light. It must at once occur to you that, inasmuch as we have in interference an agency by which light may be self-extinguished, we may have in it the conditions for the production of colour. But this would imply that certain const.i.tuents are quenched by interference, while others are permitted to remain. This is the fact; and it is entirely due to the difference in the lengths of the waves of light.

-- 7. _Colours of thin Films. Observations of Boyle and Hooke_.

This subject may be ill.u.s.trated by the phenomena which first suggested the undulatory theory to the mind of Hooke. These are the colours of thin transparent films of all kinds, known as the _colours of thin plates_. In this relation no object in the world possesses a deeper scientific interest than a common soap-bubble. And here let me say emerges one of the difficulties which the student of pure science encounters in the presence of 'practical' communities like those of America and England; it is not to be expected that such communities can entertain any profound sympathy with labours which seem so far removed from the domain of practice as are many of the labours of the man of science. Imagine Dr. Draper spending his days in blowing soap-bubbles and in studying their colours! Would you show him the necessary patience, or grant him the necessary support? And yet be it remembered it was thus that minds like those of Boyle, Newton and Hooke were occupied; and that on such experiments has been founded a theory, the issues of which are incalculable. I see no other way for you, laymen, than to trust the scientific man with the choice of his inquiries; he stands before the tribunal of his peers, and by their verdict on his labours you ought to abide.

Whence, then, are derived the colours of the soap-bubble? Imagine a beam of white light impinging on the bubble. When it reaches the first surface of the film, a known fraction of the light is reflected back.

But a large portion of the beam enters the film, reaches its second surface, and is again in part reflected. The waves from the second surface thus turn back and hotly pursue the waves from the first surface. And, if the thickness of the film be such as to cause the necessary r.e.t.a.r.dation, the two systems of waves interfere with each other, producing augmented or diminished light, as the case may be.

But, inasmuch as the waves of light are of different lengths, it is plain that, to produce extinction in the case of the longer waves, a greater thickness of film is necessary than in the case of the shorter ones. Different colours, therefore, must appear at different thicknesses of the film.

Take with you a little bottle of spirit of turpentine, and pour it into one of your country ponds. You will then see the glowing of those colours over the surface of the water. On a small scale we produce them thus: A common tea-tray is filled with water, beneath the surface of which dips the end of a pipette. A beam of light falls upon the water, and is reflected by it to the screen. Spirit of turpentine is poured into the pipette; it descends, issues from the end in minute drops, which rise in succession to the surface. On reaching it, each drop spreads suddenly out as a film, and glowing colours immediately flash forth upon the screen. The colours change as the thickness of the film changes by evaporation. They are also arranged in zones, in consequence of the gradual diminution of thickness from the centre outwards.

Any film whatever will produce these colours. The film of air between two plates of gla.s.s squeezed together, exhibits, as shown by Hooke, rich fringes of colour. A particularly fine example of these fringes is now before you. Nor is even air necessary; the rupture of optical continuity suffices. Smite with an axe the black, transparent ice--black, because it is pure and of great depth--under the moraine of a glacier; you readily produce in the interior flaws which no air can reach, and from these flaws the colours of thin plates sometimes break like fire. But the source of most historic interest is, as already stated, the soap-bubble. With one of the mixtures employed by the eminent blind philosopher, Plateau, in his researches on the cohesion figures of thin films, we obtain in still air a bubble ten or twelve inches in diameter. You may look at the bubble itself, or you may look at its projection upon the screen; rich colours arranged in zones are, in both cases, exhibited. Rendering the beam parallel, and permitting it to impinge upon the sides, bottom, and top of the bubble, gorgeous fans of colour, reflected from the bubble, overspread the screen, rotating as the beam is carried round. By this experiment the internal motions of the film are also strikingly displayed.

Not in a moment are great theories elaborated: the facts which demand them become first prominent; then, to the period of observation succeeds a period of pondering and of tentative explanation. By such efforts the human mind is gradually prepared for the final theoretic illumination. The colours of thin plates, for example, occupied the attention of Robert Boyle. In his 'Experimental History of Colours' he contends against the schools which affirmed that colour was 'a penetrative quality that reaches to the innermost parts of the object,' adducing opposing facts. 'To give you a first instance,' he says, 'I shall need but to remind you of what I told you a little after the beginning of this essay, touching the blue and red and yellow that may be produced upon a piece of tempered steel; for these colours, though they be very vivid, yet if you break the steel they adorn, they will appear to be but superficial.' He then describes, in phraseology which shows the delight he took in his work, the following beautiful experiment:--

'We took a quant.i.ty of clean lead, and melted it with a strong fire, and then immediately pouring it out into a clean vessel of convenient shape and matter (we used one of iron, that the great and sudden heat might not injure it), and then carefully and nimbly taking off the sc.u.m that floated on the top, we perceived, as we expected, the smooth and glossy surface of the melted matter to be adorned with a very glorious colour, which, being as transitory as delightful, did almost immediately give place to another vivid colour, and that was as quickly succeeded by a third, and this, as it were, chased away by a fourth; and so these wonderfully vivid colours successively appeared and vanished till the metal ceasing to be hot enough to hold any longer this pleasing spectacle, the colours that chanced to adorn the surface when the lead thus began to cool remained upon it, but were so superficial that how little soever we sc.r.a.ped off the surface of the lead, we did, in such places, sc.r.a.pe off all the colour.' 'These things,' he adds, 'suggested to me some thoughts or ravings which I have not now time to acquaint you with.'[13]

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 gla.s.s films. 'I have seen one that was skilled in fashioning gla.s.ses 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 gla.s.s' (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 gla.s.s, and with a needle, or some other convenient instrument, cleave it oftentimes into thinner and thinner laminae, 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 s.p.a.ce 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 gla.s.ses already referred to:--

'Take two small pieces of ground and polished looking-gla.s.s 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 gla.s.s; 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 gla.s.s 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 gla.s.s, 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 princ.i.p.al 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 princ.i.p.al 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_.

[Ill.u.s.tration: Fig. 13]

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 gla.s.s lens (D B E, fig. 13) of very feeble curvature he laid a plate of gla.s.s (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 gla.s.ses to pa.s.s through the spectrum from red to blue, the rings gradually contracted; when the pa.s.sage 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 gla.s.ses, 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.

[Ill.u.s.tration: Fig. 14]

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 gla.s.s 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 gla.s.s 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 exact.i.tude.

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 gla.s.s 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 pa.s.sing over a million and a half of miles of its...o...b..t--that is, in twenty-four hours--our planet performs a complete rotation; and in the time required to pa.s.s 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 gla.s.s 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 _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 1_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 a.n.a.lysis, 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 a.s.signed a greater velocity to light in gla.s.s and water than in air or stellar s.p.a.ce; and that on this point it was at direct issue with the theory of undulation, which makes the velocity in air or stellar s.p.a.ce greater than in gla.s.s 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 a.s.sumed 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 pa.s.sed _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 r.e.t.a.r.ded 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 'r.e.t.a.r.dation' 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 cla.s.ses 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 const.i.tutes a suitable point of light. The image of the sun formed on the convex surface of a gla.s.s bead, or of a watch-gla.s.s 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 gla.s.s 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.