What is true of the carbon is true in a still more striking degree of the metals, the most refractory of which can be fused, boiled, and reduced to vapour by the electric current. From the incandescent vapour the light, as a general rule, flashes in groups of rays of definite degrees of refrangibility, spaces existing between group and group, which are unfilled by rays of any kind. But the contemplation of the facts will render this subject more intelligible than words can make it. Within the camera is now placed a cylinder of carbon hollowed out at the top; in the hollow is placed a fragment of the metal thallium. Down upon this we bring the upper carbon-point, and then separate the one from the other. A stream of incandescent thallium-vapour passes between them, the magnified image of which is now seen upon the screen. It is of a beautiful green colour. What is the meaning of that green? We answer the question by subjecting the light to prismatic analysis. Sent through the prism, its spectrum is seen to consist of a single refracted band. Light of one degree of refrangibility—that corresponding to this particular green—is emitted by the thallium-vapour.

We will now remove the thallium and put a bit of silver in its place. The are of silver is not to be distinguished from that of thallium; it is not only green, but the same shade of green. Are they then alike? Prismatic analysis enables us to answer the question. However impossible it is to distinguish the one colour from the other, it is equally impossible to confound the spectrum of incandescent silver-vapour with that of thallium. In the case of silver, we have two green bands instead of one.

If we add to the silver in our camera a bit of thallium, we shall obtain the light of both metals. After waiting a little, we see that the green of the thallium lies midway between the two greens of the silver. Hence this similarity of colour.

But why have we to 'wait a little' before we see this effect? The thallium band at first almost masks the silver bands by its superior brightness. Indeed, the silver bands have wonderfully degenerated since the bit of thallium was put in, and for a reason worth knowing. It is the resistance offered to the passage of the electric current from carbon to carbon, that calls forth the power of the current to produce heat. If the resistance were materially lessened, the heat would be materially lessened; and if all resistance were abolished, there would be no heat at all. Now, thallium is a much more fusible and vaporizable metal than silver; and its vapour facilitates the passage of the electricity to such a degree, as to render the current almost incompetent to vaporize the more refractory silver. But the thallium is gradually consumed; its vapour diminishes, the resistance rises, until finally you see the two silver bands as brilliant as they were at first.[24]

We have in these bands a perfectly unalterable characteristic of the two metals. You never get other bands than these two green ones from the silver, never other than the single green band from the thallium, never other than the three green bands from the mixture of both metals. Every known metal has its own particular bands, and in no known case are the bands of two different metals alike in refrangibility. It follows, therefore, that these spectra may be made a sure test for the presence or absence of any particular metal. If we pass from the metals to their alloys, we find no confusion. Copper gives green bands; zinc gives blue and red bands; brass—an alloy of copper and zinc—gives the bands of both metals, perfectly unaltered in position or character.

But we are not confined to the metals themselves; the salts of these metals yield the bands of the metals. Chemical union is ruptured by a sufficiently high heat; the vapour of the metal is set free, and it yields its characteristic bands. The chlorides of the metals are particularly suitable for experiments of this character. Common salt, for example, is a compound of chlorine and sodium; in the electric lamp it yields the spectrum of the metal sodium. The chlorides of copper, lithium, and strontium yield, in like manner, the bands of these metals.

When, therefore, Bunsen and Kirchhoff, the illustrious founders of spectrum analysis, after having established by an exhaustive examination the spectra of all known substances, discovered a spectrum containing bands different from any known bands, they immediately inferred the existence of a new metal. They were operating at the time upon a residue, obtained by evaporating one of the mineral waters of Germany. In that water they knew the unknown metal was concealed, but vast quantities of it had to be evaporated before a residue could be obtained sufficiently large to enable ordinary chemistry to grapple with the metal. They, however, hunted it down, and it now stands among chemical substances as the metal Rubidium. They subsequently discovered a second metal, which they called Caesium. Thus, having first placed spectrum analysis on a sure foundation, they demonstrated its capacity as an agent of discovery. Soon afterwards Mr. Crookes, pursuing the same method, discovered the bright green band of Thallium, and obtained the salts of the metal which yielded it. The metal itself was first isolated in ingots by M. Lamy, a French chemist.

All this relates to chemical discovery upon earth, where the materials are in our own hands. But it was soon shown how spectrum analysis might be applied to the investigation of the sun and stars; and this result was reached through the solution of a problem which had been long an enigma to natural philosophers. The scope and conquest of this problem we must now endeavour to comprehend. A spectrum is pure in which the colours do not overlap each other. We purify the spectrum by making our beam narrow, and by augmenting the number of our prisms. When a pure spectrum of the sun has been obtained in this way, it is found to be furrowed by innumerable dark lines. Four of them were first seen by Dr. Wollaston, but they were afterwards multiplied and measured by Fraunhofer with such masterly skill, that they are now universally known as Fraunhofer's lines. To give an explanation of these lines was, as I have said, a problem which long challenged the attention of philosophers, and to Professor Kirchhoff belongs the honour of having first conquered this problem.

(The positions of the principal lines, lettered according to Fraunhofer, are shown in the annexed sketch (fig. 55) of the solar spectrum. A is supposed to stand near the extreme red, and J near the extreme violet.)



The brief memoir of two pages, in which this immortal discovery is recorded, was communicated to the Berlin Academy on October 27, 1859. Fraunhofer had remarked in the spectrum of a candle flame two bright lines, which coincide accurately, as to position, with the double dark line D of the solar spectrum. These bright lines are produced with particular intensity by the yellow flame derived from a mixture of salt and alcohol. They are in fact the lines of sodium vapour. Kirchhoff produced a spectrum by permitting the sunlight to enter his telescope by a slit and prism, and in front of the slit he placed the yellow sodium flame. As long as the spectrum remained feeble, there always appeared two bright lines, derived from the flame, in the place of the two dark lines D of the spectrum. In this case, such absorption as the flame exerted upon the sunlight was more than atoned for by the radiation from the flame. When, however, the solar spectrum was rendered sufficiently intense, the bright bands vanished, and the two dark Fraunhofer lines appeared with much greater sharpness and distinctness than when the flame was not employed.

This result, be it noted, was not due to any real quenching of the bright lines of the flame, but to the augmentation of the intensity of the adjacent spectrum. The experiment proved to demonstration, that when the white light sent through the flame was sufficiently intense, the quantity which the flame absorbed was far in excess of that which it radiated.

Here then is a result of the utmost significance. Kirchhoff immediately inferred from it that the salt flame, which could intensify so remarkably the dark lines of Fraunhofer, ought also to be able to produce them. The spectrum of the Drummond light is known to exhibit the two bright lines of sodium, which, however, gradually disappear as the modicum of sodium, contained as an impurity in the incandescent lime, is exhausted. Kirchhoff formed a spectrum of the limelight, and after the two bright lines had vanished, he placed his salt flame in front of the slit. The two dark lines immediately started forth. Thus, in the continuous spectrum of the lime-light, he evoked, artificially, the lines D of Fraunhofer.

Kirchhoff knew that this was an action not peculiar to the sodium flame, and he immediately extended his generalisation to all coloured flames which yield sharply defined bright bands in their spectra. White light, with all its constituents complete, sent through such flames, would, he inferred, have those precise constituents absorbed, whose refrangibilities are the same as those of the bright bands; so that after passing through such flames, the white light, if sufficiently intense, would have its spectrum furrowed by bands of darkness. On the occasion here referred to Kirchhoff also succeeded in reversing a bright band of lithium.

The long-standing difficulty of Fraunhofer's lines fell to pieces in the presence of facts and reflections like these, which also carried with them an immeasurable extension of the chemist's power. Kirchhoff saw that from the agreement of the lines in the spectra of terrestrial substances with Fraunhofer's lines, the presence of these substances in the sun and fixed stars might be immediately inferred. Thus the dark lines D in the solar spectrum proved the existence of sodium in the solar atmosphere; while the bright lines discovered by Brewster in a nitre flame, which had been proved to coincide exactly with certain dark lines between A and B in the solar spectrum, proved the existence of potassium in the sun.

All subsequent research verified the accuracy of these first daring conclusions. In his second paper, communicated to the Berlin Academy before the close of 1859, Kirchhoff proved the existence of iron in the sun. The bright lines of the spectrum of iron vapour are exceedingly numerous, and 65 of them were subsequently proved by Kirchhoff to be absolutely identical in position with 65 dark Fraunhofer's lines. Angstroem and Thalen pushed the coincidences to 450 for iron, while, according to the same excellent investigators, the following numbers express the coincidences, in the case of the respective metals to which they are attached:—

Calcium 75 Barium 11 Magnesium 4 Manganese 57 Titanium 118 Chromium 18 Nickel 33 Cobalt 19 Hydrogen 4 Aluminium 2 Zinc 2 Copper 7

The probability is overwhelming that all these substances exist in the atmosphere of the sun.

Kirchhoff's discovery profoundly modified the conceptions previously entertained regarding the constitution of the sun, leading him to views which, though they may be modified in detail, will, I believe, remain substantially valid to the end of time. The sun, according to Kirchhoff, consists of a molten nucleus which is surrounded by a flaming atmosphere of lower temperature. The nucleus may, in part, be clouds, mixed with, or underlying true vapour. The light of the nucleus would give us a continuous spectrum, like that of the Drummond light; but having to pass through the photosphere, as Kirchhoff's beam passed through the sodium flame, those rays of the nucleus which the photosphere emit are absorbed, and shaded lines, corresponding to the rays absorbed, occur in the spectrum. Abolish the solar nucleus, and we should have a spectrum showing a bright line in the place of every dark line of Fraunhofer, just as, in the case of Kirchhoff's second experiment, we should have the bright sodium lines of the flame if the lime-light were withdrawn. These lines of Fraunhofer are therefore not absolutely dark, but dark by an amount corresponding to the difference between the light intercepted and the light emitted by the photosphere.

Almost every great scientific discovery is approached contemporaneously by many minds, the fact that one mind usually confers upon it the distinctness of demonstration being an illustration, not of genius isolated, but of genius in advance. Thus Foucault, in 1849, came to the verge of Kirchhoff's discovery. By converging an image of the sun upon a voltaic arc, and thus obtaining the spectra of both sun and arc superposed, he found that the two bright lines which, owing to the presence of a little sodium in the carbons or in the air, are seen in the spectrum of the arc, coincide with the dark lines D of the solar spectrum. The lines D he found to he considerably strengthened by the passage of the solar light through the voltaic arc.

Instead of the image of the sun, Foucault then projected upon the arc the image of one of the solid incandescent carbon points, which of itself would give a continuous spectrum; and he found that the lines D were thus generated in that spectrum. Foucault's conclusion from this admirable experiment was 'that the arc is a medium which emits the rays D on its own account, and at the same time absorbs them when they come from another quarter.' Here he stopped. He did not extend his observations beyond the voltaic arc; he did not offer any explanation of the lines of Fraunhofer; he did not arrive at any conception of solar chemistry, or of the constitution of the sun. His beautiful experiment remained a germ without fruit, until the discernment, ten years subsequently, of the whole class of phenomena to which it belongs, enabled Kirchhoff to solve these great problems.

Soon after the publication of Kirchhoff's discovery, Professor Stokes, who also, ten years prior to the discovery, had nearly anticipated it, borrowed an illustration from sound, to explain the reciprocity of radiation and absorption. A stretched string responds to aerial vibrations which synchronize with its own. A great number of such strings stretched in space would roughly represent a medium; and if the note common to them all were sounded at a distance they would take up or absorb its vibrations.

When a violin-bow is drawn across this tuning-fork, the room is immediately filled with a musical sound, which may be regarded as the radiation or emission of sound from the fork. A few days ago, on sounding this fork, I noticed that when its vibrations were quenched, the sound seemed to be continued, though more feebly. It appeared, moreover, to come from under a distant table, where stood a number of tuning-forks of different sizes and rates of vibration. One of these, and one only, had been started by the sounding fork, and it was the one whose rate of vibration was the same as that of the fork which started it. This is an instance of the absorption of the sound of one fork by another. Placing two unisonant forks near each other, sweeping the bow over one of them, and then quenching the agitated fork, the other continues to sound; this other can re-excite the former, and several transfers of sound between the two forks can be thus effected. Placing a cent-piece on each prong of one of the forks, we destroy its perfect synchronism with the other, and no such communication of sound from the one to the other is then possible.

I have now to bring before you, on a suitable scale, the demonstration that we can do with light what has been here done with sound. For several days in 1861 I endeavoured to accomplish this, with only partial success. In iron dishes a mixture of dilute alcohol and salt was placed, and warmed so as to promote vaporization. The vapour was ignited, and through the yellow flame thus produced the beam from the electric lamp was sent; but a faint darkening only of the yellow band of a projected spectrum could be obtained. A trough was then made which, when fed with the salt and alcohol, yielded a flame ten feet thick; but the result of sending the light through this depth of flame was still unsatisfactory. Remembering that the direct combustion of sodium in a Bunsen's flame produces a yellow far more intense than that of the salt flame, and inferring that the intensity of the colour indicated the copiousness of the incandescent vapour, I sent through the flame from metallic sodium the beam of the electric lamp. The success was complete; and this experiment I wish now to repeat in your presence.[25]

Firstly then you notice, when a fragment of sodium is placed in a platinum spoon and introduced into a Bunsen's flame, an intensely yellow light is produced. It corresponds in refrangibility with the yellow band of the spectrum. Like our tuning-fork, it emits waves of a special period. When the white light from the electric lamp is sent through that flame, you will have ocular proof that the yellow flame intercepts the yellow of the spectrum; in other words, that it absorbs waves of the same period as its own, thus producing, to all intents and purposes, a dark Fraunhofer's band in the place of the yellow.

In front of the slit (at L, fig. 56) through which the beam issues is placed a Bunsen's burner (b) protected by a chimney (C). This beam, after passing through a lens, traverses the prism (P) (in the real experiment there was a pair of prisms), is there decomposed, and forms a vivid continuous spectrum (S S) upon the screen. Introducing a platinum spoon with its pellet of sodium into the Bunsen's flame, the pellet first fuses, colours the flame intensely yellow, and at length bursts into violent combustion. At the same moment the spectrum is furrowed by an intensely dark band (D), two inches wide and two feet long. Introducing and withdrawing the sodium flame in rapid succession, the sudden appearance and disappearance of the band of darkness is shown in a most striking manner. In contrast with the adjacent brightness this band appears absolutely black, so vigorous is the absorption. The blackness, however, is but relative, for upon the dark space falls a portion of the light of the sodium flame.



I have already referred to the experiment of Foucault; but other workers also had been engaged on the borders of this subject before it was taken up by Bunsen and Kirchhoff. With some modification I have on a former occasion used the following words regarding the precursors of the discovery of spectrum analysis, and solar chemistry:—'Mr. Talbot had observed the bright lines in the spectra of coloured flames, and both he and Sir John Herschel pointed out the possibility of making prismatic analysis a chemical test of exceeding delicacy, though not of entire certainty. More than a quarter of a century ago Dr. Miller gave drawings and descriptions of the spectra of various coloured flames. Wheatstone, with his accustomed acuteness, analyzed the light of the electric spark, and proved that the metals between which the spark passed determined the bright bands in its spectrum. In an investigation described by Kirchhoff as "classical," Swan had shown that 1/2,500,000 of a grain of sodium in a Bunsen's flame could be detected by its spectrum. He also proved the constancy of the bright lines in the spectra of hydrocarbon flames. Masson published a prize essay on the bands of the induction spark; while Van der Willigen, and more recently Pluecker, have also given us beautiful drawings of spectra obtained from the same source.

'But none of these distinguished men betrayed the least knowledge of the connexion between the bright bands of the metals and the dark lines of the solar spectrum; nor could spectrum analysis be said to be placed upon anything like a safe foundation prior to the researches of Bunsen and Kirchhoff. The man who, in a published paper, came nearest to the philosophy of the subject was Angstroem. In that paper, translated by myself, and published in the "Philosophical Magazine" for 1855, he indicates that the rays which a body absorbs are precisely those which, when luminous, it can emit. In another place, he speaks of one of his spectra giving the general impression of the reversal of the solar spectrum. But his memoir, philosophical as it is, is distinctly marked by the uncertainty of his time. Foucault, Thomson, and Balfour Stewart have all been near the discovery, while, as already stated, it was almost hit by the acute but unpublished conjecture of Stokes.'

Mentally, as well as physically, every year of the world's age is the outgrowth and offspring of all preceding years. Science proves itself to be a genuine product of Nature by growing according to this law. We have no solution of continuity here. All great discoveries are duly prepared for in two ways; first, by other discoveries which form their prelude; and, secondly, by the sharpening of the inquiring intellect. Thus Ptolemy grew out of Hipparchus, Copernicus out of both, Kepler out of all three, and Newton out of all the four. Newton did not rise suddenly from the sea-level of the intellect to his amazing elevation. At the time that he appeared, the table-land of knowledge was already high. He juts, it is true, above the table-land, as a massive peak; still he is supported by the plateau, and a great part of his absolute height is the height of humanity in his time. It is thus with the discoveries of Kirchhoff. Much had been previously accomplished; this he mastered, and then by the force of individual genius went beyond it. He replaced uncertainty by certainty, vagueness by definiteness, confusion by order; and I do not think that Newton has a surer claim to the discoveries that have made his name immortal, than Kirchhoff has to the credit of gathering up the fragmentary knowledge of his time, of vastly extending it, and of infusing into it the life of great principles.

With one additional point we will wind up our illustrations of the principles of solar chemistry. Owing to the scattering of light by matter floating mechanically in the earth's atmosphere, the sun is seen not sharply defined, but surrounded by a luminous glare. Now, a loud noise will drown a whisper, an intense light will overpower a feeble one, and so this circumsolar glare prevents us from seeing many striking appearances round the border of the sun. The glare is abolished in total eclipses, when the moon comes between the earth and the sun, and there are then seen a series of rose-coloured protuberances, stretching sometimes tens of thousands of miles beyond the dark edge of the moon. They are described by Vassenius in the 'Philosophical Transactions' for 1733; and were probably observed even earlier than this. In 1842 they attracted great attention, and were then compared to Alpine snow-peaks reddened by the evening sun. That these prominences are flaming gas, and principally hydrogen gas, was first proved by M. Janssen during an eclipse observed in India, on the 18th of August, 1868.

But the prominences may be rendered visible in sunshine; and for a reason easily understood. You have seen in these lectures a single prism employed to produce a spectrum, and you have seen a pair of prisms employed. In the latter case, the dispersed white light, being diffused over about twice the area, had all its colours proportionately diluted. You have also seen one prism and a pair of prisms employed to produce the bands of incandescent vapours; but here the light of each band, being absolutely monochromatic, was incapable of further dispersion by the second prism, and could not therefore be weakened by such dispersion.

Apply these considerations to the circumsolar region. The glare of white light round the sun can be dispersed and weakened to any extent, by augmenting the number of prisms; while a monochromatic light, mixed with this glare, and masked by it, would retain its intensity unenfeebled by dispersion. Upon this consideration has been founded a method of observation, applied independently by M. Janssen in India and by Mr. Lockyer in England, by which the monochromatic bands of the prominences are caused to obtain the mastery, and to appear in broad daylight. By searching carefully and skilfully round the sun's rim, Mr. Lockyer has proved these prominences to be mere local juttings from a fiery envelope which entirely clasps the sun, and which he has called the Chromosphere.

It would lead us far beyond the object of these lectures to dwell upon the numerous interesting and important results obtained by Secchi, Respighi, Young, and other distinguished men who have worked at the chemistry of the sun and its appendages. Nor can I do more at present than make a passing reference to the excellent labours of Dr. Huggins in connexion with the fixed stars, nebulae, and comets. They, more than any others, illustrate the literal truth of the statement, that the establishment of spectrum analysis, and the explanation of Fraunhofer's lines, carried with them an immeasurable extension of the chemist's range. The truly powerful experiments of Professor Dewar are daily adding to our knowledge, while the refined researches of Capt. Abney and others are opening new fields of inquiry. But my object here is to make principles plain, rather than to follow out the details of their illustration.

SUMMARY AND CONCLUSION.

My desire in these lectures has been to show you, with as little breach of continuity as possible, something of the past growth and present aspect of a department of science, in which have laboured some of the greatest intellects the world has ever seen. I have sought to confer upon each experiment a distinct intellectual value, for experiments ought to be the representatives and expositors of thought—a language addressed to the eye as spoken words are to the ear. In association with its context, nothing is more impressive or instructive than a fit experiment; but, apart from its context, it rather suits the conjurer's purpose of surprise, than the purpose of education which ought to be the ruling motive of the scientific man.

And now a brief summary of our work will not be out of place. Our present mastery over the laws and phenomena of light has its origin in the desire of man to know. We have seen the ancients busy with this problem, but, like a child who uses his arms aimlessly, for want of the necessary muscular training, so these early men speculated vaguely and confusedly regarding natural phenomena, not having had the discipline needed to give clearness to their insight, and firmness to their grasp of principles. They assured themselves of the rectilineal propagation of light, and that the angle of incidence was equal to the angle of reflection. For more than a thousand years—I might say, indeed, for more than fifteen hundred years—the scientific intellect appears as if smitten with paralysis, the fact being that, during this time, the mental force, which might have run in the direction of science, was diverted into other directions.

The course of investigation, as regards light, was resumed in 1100 by an Arabian philosopher named Alhazen. Then it was taken up in succession by Roger Bacon, Vitellio, and Kepler. These men, though failing to detect the principles which ruled the facts, kept the fire of investigation constantly burning. Then came the fundamental discovery of Snell, that cornerstone of optics, as I have already called it, and immediately afterwards we have the application, by Descartes, of Snell's discovery to the explanation of the rainbow. Following this we have the overthrow, by Roemer, of the notion of Descartes, that light was transmitted instantaneously through space. Then came Newton's crowning experiments on the analysis and synthesis of white light, by which it was proved to be compounded of various kinds of light of different degrees of refrangibility.

Up to his demonstration of the composition of white light, Newton had been everywhere triumphant—triumphant in the heavens, triumphant on the earth, and his subsequent experimental work is, for the most part, of immortal value. But infallibility is not an attribute of man, and, soon after his discovery of the nature of white light, Newton proved himself human. He supposed that refraction and chromatic dispersion went hand in hand, and that you could not abolish the one without at the same time abolishing the other. Here Dollond corrected him.

But Newton committed a graver error than this. Science, as I sought to make clear to you in our second lecture, is only in part a thing of the senses. The roots of phenomena are embedded in a region beyond the reach of the senses, and less than the root of the matter will never satisfy the scientific mind. We find, accordingly, in this career of optics the greatest minds constantly yearning to break the bounds of the senses, and to trace phenomena to their subsensible foundation. Thus impelled, they entered the region of theory, and here Newton, though drawn from time to time towards truth, was drawn still more strongly towards error; and he made error his substantial choice. His experiments are imperishable, but his theory has passed away. For a century it stood like a dam across the course of discovery; but, as with all barriers that rest upon authority, and not upon truth, the pressure from behind increased, and eventually swept the barrier away.

In 1808 Malus, looking through Iceland spar at the sun, reflected from the window of the Luxembourg Palace in Paris, discovered the polarization of light by reflection. As stated at the time, this discovery ushered in the darkest hour in the fortunes of the wave theory. But the darkness did not continue. In 1811 Arago discovered the splendid chromatic phenomena which we have had illustrated by the deportment of plates of gypsum in polarized light; he also discovered the rotation of the plane of polarization by quartz-crystals. In 1813 Seebeck discovered the polarization of light by tourmaline. That same year Brewster discovered those magnificent bands of colour that surround the axes of biaxal crystals. In 1814 Wollaston discovered the rings of Iceland spar. All these effects, which, without a theoretic clue, would leave the human mind in a jungle of phenomena without harmony or relation, were organically connected by the theory of undulation.

The wave theory was applied and verified in all directions, Airy being especially conspicuous for the severity and conclusiveness of his proofs. A most remarkable verification fell to the lot of the late Sir William Hamilton, of Dublin, who, taking up the theory where Fresnel had left it, arrived at the conclusion that at four special points of the 'wave-surface' in double-refracting crystals, the ray was divided, not into two parts but into an infinite number of parts; forming at these points a continuous conical envelope instead of two images. No human eye had ever seen this envelope when Sir William Hamilton inferred its existence. He asked Dr. Lloyd to test experimentally the truth of his theoretic conclusion. Lloyd, taking a crystal of arragonite, and following with the most scrupulous exactness the indications of theory, cutting the crystal where theory said it ought to be cut, observing it where theory said it ought to be observed, discovered the luminous envelope which had previously been a mere idea in the mind of the mathematician.

Nevertheless this great theory of undulation, like many another truth, which in the long run has proved a blessing to humanity, had to establish, by hot conflict, its right to existence. Illustrious names were arrayed against it. It had been enunciated by Hooke, it had been expounded and applied by Huyghens, it had been defended by Euler. But they made no impression. And, indeed, the theory in their hands lacked the strength of a demonstration. It first took the form of a demonstrated verity in the hands of Thomas Young. He brought the waves of light to bear upon each other, causing them to support each other, and to extinguish each other at will. From their mutual actions he determined their lengths, and applied his knowledge in all directions. He finally showed that the difficulty of polarization yielded to the grasp of theory.

After him came Fresnel, whose transcendent mathematical abilities enabled him to give the theory a generality unattained by Young. He seized it in its entirety; followed the ether into the hearts of crystals of the most complicated structure, and into bodies subjected to strain and pressure. He showed that the facts discovered by Malus, Arago, Brewster, and Biot were so many ganglia, so to speak, of his theoretic organism, deriving from it sustenance and explanation. With a mind too strong for the body with which it was associated, that body became a wreck long before it had become old, and Fresnel died, leaving, however, behind him a name immortal in the annals of science.

One word more I should like to say regarding Fresnel. There are things better even than science. Character is higher than Intellect, but it is especially pleasant to those who wish to think well of human nature when high intellect and upright character are found combined. They were combined in this young Frenchman. In those hot conflicts of the undulatory theory, he stood forth as a man of integrity, claiming no more than his right, and ready to concede their rights to others. He at once recognized and acknowledged the merits of Thomas Young. Indeed, it was he, and his fellow-countryman Arago, who first startled England into the consciousness of the injustice done to Young in the 'Edinburgh Review.'

I should like to read to you a brief extract from a letter written by Fresnel to Young in 1824, as it throws a pleasant light upon the character of the French philosopher. 'For a long time,' says Fresnel, 'that sensibility, or that vanity, which people call love of glory has been much blunted in me. I labour much less to catch the suffrages of the public, than to obtain that inward approval which has always been the sweetest reward of my efforts. Without doubt, in moments of disgust and discouragement, I have often needed the spur of vanity to excite me to pursue my researches. But all the compliments I have received from Arago, De la Place, and Biot never gave me so much pleasure as the discovery of a theoretic truth or the confirmation of a calculation by experiment.'

* * * * *

This, then, is the core of the whole matter as regards science. It must be cultivated for its own sake, for the pure love of truth, rather than for the applause or profit that it brings. And now my occupation in America is well-nigh gone. Still I will bespeak your tolerance for a few concluding remarks, in reference to the men who have bequeathed to us the vast body of knowledge of which I have sought to give you some faint idea in these lectures. What was the motive that spurred them on? What urged them to those battles and those victories over reticent Nature, which have become the heritage of the human race? It is never to be forgotten that not one of those great investigators, from Aristotle down to Stokes and Kirchhoff, had any practical end in view, according to the ordinary definition of the word 'practical.' They did not propose to themselves money as an end, and knowledge as a means of obtaining it. For the most part, they nobly reversed this process, made knowledge their end, and such money as they possessed the means of obtaining it.

We see to-day the issues of their work in a thousand practical forms, and this may be thought sufficient to justify, if not ennoble, their efforts. But they did not work for such issues; their reward was of a totally different kind. In what way different? We love clothes, we love luxuries, we love fine equipages, we love money, and any man who can point to these as the result of his efforts in life, justifies these results before all the world. In America and England, more especially, he is a 'practical' man. But I would appeal confidently to this assembly whether such things exhaust the demands of human nature? The very presence here for six inclement nights of this great audience, embodying so much of the mental force and refinement of this vast city,[26] is an answer to my question. I need not tell such an assembly that there are joys of the intellect as well as joys of the body, or that these pleasures of the spirit constituted the reward of our great investigators. Led on by the whisperings of natural truth, through pain and self-denial, they often pursued their work. With the ruling passion strong in death, some of them, when no longer able to hold a pen, dictated to their friends the last results of their labours, and then rested from them for ever.

Could we have seen these men at work, without any knowledge of the consequences of their work, what should we have thought of them? To the uninitiated, in their day, they might often appear as big children playing with soap-bubbles and other trifles. It is so to this hour. Could you watch the true investigator—your Henry or your Draper, for example—in his laboratory, unless animated by his spirit, you could hardly understand what keeps him there. Many of the objects which rivet his attention might appear to you utterly trivial; and if you were to ask him what is the use of his work, the chances are that you would confound him. He might not be able to express the use of it in intelligible terms. He might not be able to assure you that it will put a dollar into the pocket of any human being present or to come. That scientific discovery may put not only dollars into the pockets of individuals, but millions into the exchequers of nations, the history of science amply proves; but the hope of its doing so never was, and it never can be, the motive power of the investigator.

I know that some risk is run in speaking thus before practical men. I know what De Tocqueville says of you. 'The man of the North,' he says, 'has not only experience, but knowledge. He, however, does not care for science as a pleasure, and only embraces it with avidity when it leads to useful applications.' But what, I would ask, are the hopes of useful applications which have caused you so many times to fill this place, in spite of snow-drifts and biting cold? What, I may ask, is the origin of that kindness which drew me from my work in London to address you here, and which, if I permitted it, would send me home a millionaire? Not because I had taught you to make a single cent by science am I here to-night, but because I tried to the best of my ability to present science to the world as an intellectual good. Surely no two terms were ever so distorted and misapplied with reference to man, in his higher relations, as these terms useful and practical. Let us expand our definitions until they embrace all the needs of man, his highest intellectual needs inclusive. It is specially on this ground of its administering to the higher needs of the intellect; it is mainly because I believe it to be wholesome, not only as a source of knowledge but as a means of discipline, that I urge the claims of science upon your attention.

But with reference to material needs and joys, surely pure science has also a word to say. People sometimes speak as if steam had not been studied before James Watt, or electricity before Wheatstone and Morse; whereas, in point of fact, Watt and Wheatstone and Morse, with all their practicality, were the mere outcome of antecedent forces, which acted without reference to practical ends. This also, I think, merits a moment's attention. You are delighted, and with good reason, with your electric telegraphs, proud of your steam-engines and your factories, and charmed with the productions of photography. You see daily, with just elation, the creation of new forms of industry—new powers of adding to the wealth and comfort of society. Industrial England is heaving with forces tending to this end; and the pulse of industry beats still stronger in the United States. And yet, when analyzed, what are industrial America and industrial England?

If you can tolerate freedom of speech on my part, I will answer this question by an illustration. Strip a strong arm, and regard the knotted muscles when the hand is clenched and the arm bent. Is this exhibition of energy the work of the muscle alone? By no means. The muscle is the channel of an influence, without which it would be as powerless as a lump of plastic dough. It is the delicate unseen nerve that unlocks the power of the muscle. And without those filaments of genius, which have been shot like nerves through the body of society by the original discoverer, industrial America, and industrial England, would be very much in the condition of that plastic dough.

At the present time there is a cry in England for technical education, and it is a cry in which the most commonplace intellect can join, its necessity is so obvious. But there is no such cry for original investigation. Still, without this, as surely as the stream dwindles when the spring dies, so surely will 'technical education' lose all force of growth, all power of reproduction. Our great investigators have given us sufficient work for a time; but if their spirit die out, we shall find ourselves eventually in the condition of those Chinese mentioned by De Tocqueville, who, having forgotten the scientific origin of what they did, were at length compelled to copy without variation the inventions of an ancestry wiser than themselves, who had drawn their inspiration direct from Nature.

Both England and America have reason to bear those things in mind, for the largeness and nearness of material results are only too likely to cause both countries to forget the small spiritual beginnings of such results, in the mind of the scientific discoverer. You multiply, but he creates. And if you starve him, or otherwise kill him—nay, if you fail to secure for him free scope and encouragement—you not only lose the motive power of intellectual progress, but infallibly sever yourselves from the springs of industrial life.

What has been said of technical operations holds equally good for education, for here also the original investigator constitutes the fountain-head of knowledge. It belongs to the teacher to give this knowledge the requisite form; an honourable and often a difficult task. But it is a task which receives its final sanctification, when the teacher himself honestly tries to add a rill to the great stream of scientific discovery. Indeed, it may be doubted whether the real life of science can be fully felt and communicated by the man who has not himself been taught by direct communion with Nature. We may, it is true, have good and instructive lectures from men of ability, the whole of whose knowledge is second-hand, just as we may have good and instructive sermons from intellectually able and unregenerate men. But for that power of science, which corresponds to what the Puritan fathers would call experimental religion in the heart, you must ascend to the original investigator.

To keep society as regards science in healthy play, three classes of workers are necessary: Firstly, the investigator of natural truth, whose vocation it is to pursue that truth, and extend the field of discovery for the truth's own sake and without reference to practical ends. Secondly, the teacher of natural truth, whose vocation it is to give public diffusion to the knowledge already won by the discoverer. Thirdly, the applier of natural truth, whose vocation it is to make scientific knowledge available for the needs, comforts, and luxuries of civilized life. These three classes ought to co-exist and interact. Now, the popular notion of science, both in this country and in England, often relates not to science strictly so called, but to the applications of science. Such applications, especially on this continent, are so astounding—they spread themselves so largely and umbrageously before the public eye—that they often shut out from view those workers who are engaged in the quieter and profounder business of original investigation.

Take the electric telegraph as an example, which has been repeatedly forced upon my attention of late. I am not here to attenuate in the slightest degree the services of those who, in England and America, have given the telegraph a form so wonderfully fitted for public use. They earned a great reward, and they have received it. But I should be untrue to you and to myself if I failed to tell you that, however high in particular respects their claims and qualities may be, your practical men did not discover the electric telegraph. The discovery of the electric telegraph implies the discovery of electricity itself, and the development of its laws and phenomena. Such discoveries are not made by practical men, and they never will be made by them, because their minds are beset by ideas which, though of the highest value from one point of view, are not those which stimulate the original discoverer.

The ancients discovered the electricity of amber; and Gilbert, in the year 1600, extended the discovery to other bodies. Then followed Boyle, Von Guericke, Gray, Canton, Du Fay, Kleist, Cunaeus, and your own Franklin. But their form of electricity, though tried, did not come into use for telegraphic purposes. Then appeared the great Italian Volta, who discovered the source of electricity which bears his name, and applied the most profound insight, and the most delicate experimental skill to its development. Then arose the man who added to the powers of his intellect all the graces of the human heart, Michael Faraday, the discoverer of the great domain of magneto-electricity. OErsted discovered the deflection of the magnetic needle, and Arago and Sturgeon the magnetization of iron by the electric current. The voltaic circuit finally found its theoretic Newton in Ohm; while Henry, of Princeton, who had the sagacity to recognize the merits of Ohm while they were still decried in his own country, was at this time in the van of experimental inquiry.

In the works of these men you have all the materials employed at this hour, in all the forms of the electric telegraph. Nay, more; Gauss, the illustrious astronomer, and Weber, the illustrious natural philosopher, both professors in the University of Goettingen, wishing to establish a rapid mode of communication between the observatory and the physical cabinet of the university, did this by means of an electric telegraph. Thus, before your practical men appeared upon the scene, the force had been discovered, its laws investigated and made sure, the most complete mastery of its phenomena had been attained—nay, its applicability to telegraphic purposes demonstrated—by men whose sole reward for their labours was the noble excitement of research, and the joy attendant on the discovery of natural truth.

Are we to ignore all this? We do so at our peril. For I say again that, behind all our practical applications, there is a region of intellectual action to which practical men have rarely contributed, but from which they draw all their supplies. Cut them off from this region, and they become eventually helpless. In no case is the adage truer, 'Other men laboured, but ye are entered into their labours,' than in the case of the discoverer and applier of natural truth. But now a word on the other side. While practical men are not the men to make the necessary antecedent discoveries, the cases are rare, though, in our day, not absent, in which the discoverer knows how to turn his labours to practical account. Different qualities of mind and habits of thought are usually needed in the two cases; and while I wish to give emphatic utterance to the claims of those whose position, owing to the simple fact of their intellectual elevation, is often misunderstood, I am not here to exalt the one class of workers at the expense of the other. They are the necessary complements of each other. But remember that one class is sure to be taken care of. All the material rewards of society are already within their reach, while that same society habitually ascribes to them intellectual achievements which were never theirs. This cannot but act to the detriment of those studies out of which, not only our knowledge of nature, but our present industrial arts themselves, have sprung, and from which the rising genius of the country is incessantly tempted away.

Pasteur, one of the most illustrious members of the Institute of France, in accounting for the disastrous overthrow of his country, and the predominance of Germany in the late war, expresses himself thus: 'Few persons comprehend the real origin of the marvels of industry and the wealth of nations. I need no further proof of this than the employment, more and more frequent, in official language, and in writings of all sorts, of the erroneous expression applied science. The abandonment of scientific careers by men capable of pursuing them with distinction, was recently deplored in the presence of a minister of the greatest talent. The statesman endeavoured to show that we ought not to be surprised at this result, because in our day the reign of theoretic science yielded place to that of applied science. Nothing could be more erroneous than this opinion, nothing, I venture to say, more dangerous, even to practical life, than the consequences which might flow from these words. They have rested in my mind as a proof of the imperious necessity of reform in our superior education. There exists no category of the sciences, to which the name of applied science could be rightly given. We have science, and the applications of science, which are united together as the tree and its fruit.'

And Cuvier, the great comparative anatomist, writes thus upon the same theme: 'These grand practical innovations are the mere applications of truths of a higher order, not sought with a practical intent, but pursued for their own sake, and solely through an ardour for knowledge. Those who applied them could not have discovered them; but those who discovered them had no inclination to pursue them to a practical end. Engaged in the high regions whither their thoughts had carried them, they hardly perceived these practical issues though born of their own deeds. These rising workshops, these peopled colonies, those ships which furrow the seas—this abundance, this luxury, this tumult—all this comes from discoveries in science, and it all remains strange to the discoverers. At the point where science merges into practice they abandon it; it concerns them no more.'

When the Pilgrim Fathers landed at Plymouth Rock, and when Penn made his treaty with the Indians, the new-comers had to build their houses, to cultivate the earth, and to take care of their souls. In such a community science, in its more abstract forms, was not to be thought of. And at the present hour, when your hardy Western pioneers stand face to face with stubborn Nature, piercing the mountains and subduing the forest and the prairie, the pursuit of science, for its own sake, is not to be expected. The first need of man is food and shelter; but a vast portion of this continent is already raised far beyond this need. The gentlemen of New York, Brooklyn, Boston, Philadelphia, Baltimore, and Washington have already built their houses, and very beautiful they are; they have also secured their dinners, to the excellence of which I can also bear testimony. They have, in fact, reached that precise condition of well-being and independence when a culture, as high as humanity has yet reached, may be justly demanded at their hands. They have reached that maturity, as possessors of wealth and leisure, when the investigator of natural truth, for the truth's own sake, ought to find among them promoters and protectors.

Among the many problems before them they have this to solve, whether a republic is able to foster the highest forms of genius. You are familiar with the writings of De Tocqueville, and must be aware of the intense sympathy which he felt for your institutions; and this sympathy is all the more valuable from the philosophic candour with which he points out not only your merits, but your defects and dangers. Now if I come here to speak of science in America in a critical and captious spirit, an invisible radiation from my words and manner will enable you to find me out, and will guide your treatment of me to-night. But if I in no unfriendly spirit—in a spirit, indeed, the reverse of unfriendly—venture to repeat before you what this great historian and analyst of democratic institutions said of America, I am persuaded that you will hear me out. He wrote some three and twenty years ago, and, perhaps, would not write the same to-day; but it will do nobody any harm to have his words repeated, and, if necessary, laid to heart.

In a work published in 1850, De Tocqueville says: 'It must be confessed that, among the civilized peoples of our age, there are few in which the highest sciences have made so little progress as in the United States.'[27] He declares his conviction that, had you been alone in the universe, you would soon have discovered that you cannot long make progress in practical science without cultivating theoretic science at the same time. But, according to De Tocqueville, you are not thus alone. He refuses to separate America from its ancestral home; and it is there, he contends, that you collect the treasures of the intellect, without taking the trouble to create them.

De Tocqueville evidently doubts the capacity of a democracy to foster genius as it was fostered in the ancient aristocracies. 'The future,' he says, 'will prove whether the passion for profound knowledge, so rare and so fruitful, can be born and developed as readily in democratic societies as in aristocracies. For my part,' he continues, 'I can hardly believe it.' He speaks of the unquiet feverishness of democratic communities, not in times of great excitement, for such times may give an extraordinary impetus to ideas, but in times of peace. There is then, he says, 'a small and uncomfortable agitation, a sort of incessant attrition of man against man, which troubles and distracts the mind without imparting to it either loftiness or animation.' It rests with you to prove whether these things are necessarily so—whether scientific genius cannot find, in the midst of you, a tranquil home.

I should be loth to gainsay so keen an observer and so profound a political writer, but, since my arrival in this country, I have been unable to see anything in the constitution of society, to prevent a student, with the root of the matter in him, from bestowing the most steadfast devotion on pure science. If great scientific results are not achieved in America, it is not to the small agitations of society that I should be disposed to ascribe the defect, but to the fact that the men among you who possess the endowments necessary for profound scientific inquiry, are laden with duties of administration, or tuition, so heavy as to be utterly incompatible with the continuous and tranquil meditation which original investigation demands. It may well be asked whether Henry would have been transformed into an administrator, or whether Draper would have forsaken science to write history, if the original investigator had been honoured as he ought to be in this land. I hardly think they would. Still I do not imagine this state of things likely to last. In America there is a willingness on the part of individuals to devote their fortunes, in the matter of education, to the service of the commonwealth, which is probably without a parallel elsewhere; and this willingness requires but wise direction to enable you effectually to wipe away the reproach of De Tocqueville.

Your most difficult problem will be, not to build institutions, but to discover men. You may erect laboratories and endow them; you may furnish them with all the appliances needed for inquiry; in so doing you are but creating opportunity for the exercise of powers which come from sources entirely beyond your reach. You cannot create genius by bidding for it. In biblical language, it is the gift of God; and the most you could do, were your wealth, and your willingness to apply it, a million-fold what they are, would be to make sure that this glorious plant shall have the freedom, light, and warmth necessary for its development. We see from time to time a noble tree dragged down by parasitic runners. These the gardener can remove, though the vital force of the tree itself may lie beyond him: and so, in many a case you men of wealth can liberate genius from the hampering toils which the struggle for existence often casts around it.

Drawn by your kindness, I have come here to give these lectures, and now that my visit to America has become almost a thing of the past, I look back upon it as a memory without a single stain. No lecturer was ever rewarded as I have been. From this vantage-ground, however, let me remind you that the work of the lecturer is not the highest work; that in science, the lecturer is usually the distributor of intellectual wealth amassed by better men. And though lecturing and teaching, in moderation, will in general promote their moral health, it is not solely or even chiefly, as lecturers, but as investigators, that your highest men ought to be employed. You have scientific genius amongst you—not sown broadcast, believe me, it is sown thus nowhere—but still scattered here and there. Take all unnecessary impediments out of its way. Keep your sympathetic eye upon the originator of knowledge. Give him the freedom necessary for his researches, not overloading him, either with the duties of tuition or of administration, nor demanding from him so-called practical results—above all things, avoiding that question which ignorance so often addresses to genius: 'What is the use of your work?' Let him make truth his object, however unpractical for the time being it may appear. If you cast your bread thus upon the waters, be assured it will return to you, though it be after many days.



APPENDIX.

ON THE SPECTRA OF POLARIZED LIGHT.

Mr. William Spottiswoode introduced some years ago to the members of the Royal Institution, in a very striking form, a series of experiments on the spectra of polarized light. With his large Nicol prisms he in the first place repeated and explained the experiments of Foucault and Fizeau, and subsequently enriched the subject by very beautiful additions of his own. I here append a portion of the abstract of his discourse:—

'It is well known that if a plate of selenite sufficiently thin be placed between two Nicol's prisms, or, more technically speaking, between a polarizer and analyzer, colour will be produced. And the question proposed is, What is the nature of that colour? is it simply a pure colour of the spectrum, or is it a compound, and if so, what are its component parts? The answer given by the wave theory is in brief this: In its passage through the selenite plate the rays have been so separated in the direction of their vibrations and in the velocity of their transmission, that, when re-compounded by means of the analyzer, they have in some instances neutralized one another. If this be the case, the fact ought to be visible when the beam emerging from the analyzer is dispersed by the prism; for then we have the rays of all the different colours ranged side by side, and, if any be wanting, their absence will be shown by the appearance of a dark band in their place in the spectrum. But not only so; the spectrum ought also to give an account of the other phenomena exhibited by the selenite when the analyzer is turned round, viz. that when the angle of turning amounts to 45 deg., all trace of colour disappears; and also that when the angle amounts to 90 deg., colour reappears, not, however, the original colour, but one complementary to it.

'You see in the spectrum of the reddish light produced by the selenite a broad but dark band in the blue; when the analyzer is turned round the band becomes less and less dark, until when the angle of turning amounts to 45 deg. it has entirely disappeared. At this stage each part of the spectrum has its own proportional intensity, and the whole produces the colourless image seen without the spectroscope. Lastly, as the turning of the analyzer is continued, a dark band appears in the red, the part of the spectrum complementary to that occupied by the first band; and the darkness is most complete when the turning amounts to 90 deg.. Thus we have from the spectroscope a complete account of what has taken place to produce the original colour and its changes.

'It is further well known that the colour produced by a selenite, or other crystal plate, is dependent upon the thickness of the plate. And, in fact, if a series of plates be taken, giving different colours, their spectra are found to show bands arranged in different positions. The thinner plates show bands in the parts of the spectrum nearest to the violet, where the waves are shorter, and consequently give rise to redder colours; while the thicker show bands nearer to the red, where the waves are longer and consequently supply bluer tints.

'When the thickness of the plate is continually increased, so that the colour produced has gone through the complete cycle of the spectrum, a further increase of thickness causes a reproduction of the colours in the same order; but it will be noticed that at each recurrence of the cycle the tints become paler, until when a number of cycles have been performed, and the thickness of the plate is considerable, all trace of colour is lost. Let us now take a series of plates, the first two of which, as you see, give colours; with the others which are successively of greater thickness the tints are so feeble that they can scarcely be distinguished. The spectrum of the first shows a single band; that of the second, two; showing that the second series of tints is not identical with the first, but that it is produced by the extinction of two colours from the components of white light. The spectra of the others show series of bands more and more numerous in proportion to the thickness of the plate, an array which may be increased indefinitely. The total light, then, of which the spectrum is deprived by the thicker plates is taken from a greater number of its parts; or, in other words, the light which still remains is distributed more and more evenly over the spectrum; and in the same proportion the sum total of it approaches more and more nearly to white light.

'These experiments were made more than thirty years ago by the French philosophers, MM. Foucault and Fizeau.

'If instead of selenite, Iceland spar, or other ordinary crystals, we use plates of quartz cut perpendicularly to the axis, and turn the analyzer round as before, the light, instead of exhibiting only one colour and its complementary with an intermediate stage in which colour is absent, changes continuously in tint; and the order of the colour depends partly upon the direction in which the analyzer is turned, and partly upon the character of the crystal, i.e. whether it is right-handed or left-handed. If we examine the spectrum in this case we find that the dark band never disappears, but marches from one end of the spectrum to another, or vice versa, precisely in such a direction as to give rise to the tints seen by direct projection.

'The kind of polarization effected by the quartz plates is called circular, while that effected by the other class of crystals is called plane, on account of the form of the vibrations executed by the molecules of aether; and this leads us to examine a little more closely the nature of the polarization of different parts of these spectra of polarized light.

'Now, two things are clear: first, that if the light be plane-polarized—that is, if all the vibrations throughout the entire ray are rectilinear and in one plane—they must in all their bearings have reference to a particular direction in space, so that they will be differently affected by different positions of the analyzer. Secondly, that if the vibrations be circular, they will be affected in precisely the same way (whatever that may be) in all positions of the analyzer. This statement merely recapitulates a fundamental point in polarization. In fact, plane-polarized light is alternately transmitted and extinguished by the analyzer as it is turned through 90 deg.; while circularly polarized light [if we could get a single ray] remains to all appearance unchanged. And if we examine carefully the spectrum of light which has passed through a selenite, or other ordinary crystal, we shall find that, commencing with two consecutive bands in position, the parts occupied by the bands and those midway between them are plane-polarized, for they become alternately dark and bright; while the intermediate parts, i.e. the parts at one-fourth of the distance from one band to the next, remain permanently bright. These are, in fact, circularly polarized. But it would be incorrect to conclude from this experiment alone that such is really the case, because the same appearance would be seen if those parts were unpolarized, i.e. in the condition of ordinary lights. And on such a supposition we should conclude with equal justice that the parts on either side of the parts last mentioned (e.g. the parts separated by eighth parts of the interval between two bands) were partially polarized. But there is an instrument of very simple construction, called a "quarter-undulation plate," a plate usually of mica, whose thickness is an odd multiple of a quarter of a wave-length, which enables us to discriminate between light unpolarized and circularly polarized. The exact mechanical effect produced upon the ray could hardly be explained in detail within our present limits of time; but suffice it for the present to say that, when placed in a proper position, the plate transforms plane into circular and circular into plane polarization. That being so, the parts which were originally banded ought to remain bright, and those which originally remained bright ought to become banded during the rotation of the analyzer. The general effect to the eye will consequently be a general shifting of the bands through one-fourth of the space which separates each pair.

'Circular polarization, like circular motion generally, may of course be of two kinds, which differ only in the direction of the motion. And, in fact, to convert the circular polarization produced by this plate from one of these kinds to the other (say from right-handed to left-handed, or vice versa), we have only to turn the plate round through 90 deg.. Conversely, right-handed circular polarization will be changed by the plate into plane-polarization in one direction, while left-handed will be changed into plane at right angles to the first. Hence if the plate be turned round through 90 deg. we shall see that the bands are shifted in a direction opposite to that in which they were moved at first. In this therefore we have evidence not only that the polarization immediately on either side of a band is circular; but also that that immediately on the one side is right-handed, while that immediately on the other is left-handed[28].

'If time permitted, I might enter still further into detail, and show that the polarization between the plane and the circular is elliptical, and even the positions of the longer and shorter axes and the direction of motion in each case. But sufficient has, perhaps, been said for our present purpose.

'Before proceeding to the more varied forms of spectral bands, which I hope presently to bring under your notice, I should like to ask your attention for a few minutes to the peculiar phenomena exhibited when two plates of selenite giving complementary colours are used. The appearance of the spectrum varies with the relative position of the plates. If they are similarly placed—that is, as if they were one plate of crystal—they will behave as a single plate, whose thickness is the sum of the thicknesses of each, and will produce double the number of bands which one alone would give; and when the analyzer is turned, the bands will disappear and re-appear in their complementary positions, as usual in the case of plane-polarization. If one of them be turned round through 45 deg., a single band will be seen at a particular position in the spectrum. This breaks into two, which recede from one another towards the red and violet ends respectively, or advance towards one another according to the direction in which the analyzer is turned. If the plate be turned through 45 deg. in the opposite direction, the effects will be reversed. The darkness of the bands is, however, not equally complete during their whole passage. Lastly, if one of the plates be turned through 90 deg., no bands will be seen, and the spectrum will be alternately bright and dark, as if no plates were used, except only that the polarization is itself turned through 90 deg..

'If a wedge-shaped crystal be used, the bands, instead of being straight, will cross the spectrum diagonally, the direction of the diagonal (dexter or sinister) being determined by the position of the thicker end of the wedge. If two similar wedges be used with their thickest ends together, they will act as a wedge whose angle and whose thickness is double of the first. If they be placed in the reverse position they will act as a flat plate, and the bands will again cross the spectrum in straight lines at right angles to its length.

'If a concave plate be used the bands will dispose themselves in a fanlike arrangement, their divergence depending upon the distance of the slit from the centre of concavity.

'If two quartz wedges, one of which has the optic axis parallel to the edge of the refractory angle, and the other perpendicular to it, but in one of the planes containing the angle (Babinet's Compensator), the appearances of the bands are very various.

'The diagonal bands, besides sometimes doubling themselves as with ordinary wedges, sometimes combine so as to form longitudinal (instead of transverse) bands; and sometimes cross one another so as to form a diaper pattern with bright compartments in a dark framework, and vice versa, according to the position of the plates.

'The effects of different dispositions of the interposed crystals might be varied indefinitely; but enough has perhaps been said to show the delicacy of the method of spectrum analysis as applied to the examination of polarized light.'

* * * * *

The singular and beautiful effect obtained with a circular plate of selenite, thin at the centre, and gradually thickening towards the circumference, is easily connected with a similar effect obtained with Newton's rings. Let a thin slice of light fall upon the glasses which show the rings, so as to cover a narrow central vertical zone passing through them all. The image of this zone upon the screen is crossed by portions of the iris-rings. Subjecting the reflected beam to prismatic analysis, the resultant spectrum may be regarded as an indefinite number of images of the zone placed side by side. In the image before dispersion we have iris-rings, the extinction of the light being nowhere complete; but when the different colours are separated by dispersion, each colour is crossed transversely by its own system of dark interference bands, which become gradually closer with the increasing refrangibility of the light. The complete spectrum, therefore, appears furrowed by a system of continuous dark bands, crossing the colours transversely, and approaching each other as they pass from red to blue.

In the case of the plate of selenite, a slit is placed in front of the polarizer, and the film of selenite is held close to the slit, so that the light passes through the central zone of the film. As in the case of Newton's rings, the image of the zone is crossed by iris-coloured bands; but when subjected to prismatic dispersion, the light of the zone yields a spectrum furrowed by bands of complete darkness exactly as in the case of Newton's rings and for a similar reason. This is the beautiful effect described by Mr. Spottiswoode as the fanlike arrangement of the bands—the fan opening out at the red end of the spectrum.

* * * * *

MEASUREMENT OF THE WAVES OF LIGHT.

The diffraction fringes described in Lecture II., instead of being formed on the retina, may be formed on a screen, or upon ground glass, when they can be looked at through a magnifying lens from behind, or they can be observed in the air when the ground glass is removed. Instead of permitting them to form on the retina, we will suppose them formed on a screen. This places us in a condition to understand, even without trigonometry, the solution of the important problem of measuring the length of a wave of light.

We will suppose the screen so distant that the rays falling upon it from the two margins of the slit are sensibly parallel. We have learned in Lecture II. that the first of the dark bands corresponds to a difference of marginal path of one undulation; the second dark band to a difference of path of two undulations; the third dark band to a difference of three undulations, and so on. Now the angular distance of the bands from the centre is capable of exact measurement; this distance depending, as already stated, on the width of the slit. With a slit 1.35 millimeter wide,[29] Schwerd found the angular distance of the first dark band from the centre of the field to be 1'38"; the angular distances of the second, third, fourth dark bands being twice, three times, four times this quantity.



Let A B, fig. 57, be the plate in which the slit is cut, and C D the grossly exaggerated width of the slit, with the beam of red light proceeding from it at the obliquity corresponding to the first dark band. Let fall a perpendicular from one edge, D, of the slit on the marginal ray of the other edge at d. The distance, C d, between the foot of this perpendicular and the other edge is the length of a wave of the light. The angle C D d, moreover, being equal to R C R', is, in the case now under consideration, 1'38". From the centre D, with the width D C as radius, describe a semicircle; its radius D C being 1.35 millimeter, the length of this semicircle is found by an easy calculation to be 4.248 millimeters. The length C d is so small that it sensibly coincides with the arc of the circle. Hence the length of the semicircle is to the length C d of the wave as 180 deg. to 1'38", or, reducing all to seconds, as 648,000" to 98". Thus, we have the proportion—

648,000 : 98 :: 4.248 to the wave-length C d.

Making the calculation, we find the wave-length for this particular kind of light to be 0.000643 of a millimeter, or 0.000026 of an inch.

FOOTNOTES:

[Footnote 1: Among whom may be especially mentioned the late Sir Edmund Head, Bart., with whom I had many conversations on this subject.]

[Footnote 2: At whose hands it gives me pleasure to state I have always experienced honourable and liberal treatment.]

[Footnote 3: One of the earliest of these came from Mr. John Amory Lowell of Boston.]

[Footnote 4: It will be subsequently shown how this simple apparatus may be employed to determine the 'polarizing angle' of a liquid.]

[Footnote 5: From this principle Sir John Herschel deduces in a simple and elegant manner the fundamental law of reflection.—See Familiar Lectures, p. 236.]

[Footnote 6: The low dispersive power of water masks, as Helmholtz has remarked, the imperfect achromatism of the eye. With the naked eye I can see a distant blue disk sharply defined, but not a red one. I can also see the lines which mark the upper and lower boundaries of a horizontally refracted spectrum sharp at the blue end, but ill-defined at the red end. Projecting a luminous disk upon a screen, and covering one semicircle of the aperture with a red and the other with a blue or green glass, the difference between the apparent sizes of the two semicircles is in my case, and in numerous other cases, extraordinary. Many persons, however, see the apparent sizes of the two semicircles reversed. If with a spectacle glass I correct the dispersion of the red light over the retina, then the blue ceases to give a sharply defined image. Thus examined, the departure of the eye from achromatism appears very gross indeed.]

[Footnote 7: Both in foliage and in flowers there are striking differences of absorption. The copper beech and the green beech, for example, take in different rays. But the very growth of the tree is due to some of the rays thus taken in. Are the chemical rays, then, the same in the copper and the green beech? In two such flowers as the primrose and the violet, where the absorptions, to judge by the colours, are almost complementary, are the chemically active rays the same? The general relation of colour to chemical action is worthy of the application of the method by which Dr. Draper proved so conclusively the chemical potency of the yellow rays of the sun.]

[Footnote 8: Young, Helmholtz, and Maxwell reduce all differences of hue to combinations in different proportions of three primary colours. It is demonstrable by experiment that from the red, green, and violet all the other colours of the spectrum may be obtained.

Some years ago Sir Charles Wheatstone drew my attention to a work by Christian Ernst Wuensch, Leipzig 1792, in which the author announces the proposition that there are neither five nor seven, but only three simple colours in white light. Wuensch produced five spectra, with five prisms and five small apertures, and he mixed the colours first in pairs, and afterwards in other ways and proportions. His result is that red is a simple colour incapable of being decomposed; that orange is compounded of intense red and weak green; that yellow is a mixture of intense red and intense green; that green is a simple colour; that blue is compounded of saturated green and saturated violet; that indigo is a mixture of saturated violet and weak green; while violet is a pure simple colour. He also finds that yellow and indigo blue produce white by their mixture. Yellow mixed with bright blue (Hochblau) also produces white, which seems, however, to have a tinge of green, while the pigments of these two colours when mixed always give a more or less beautiful green, Wuensch very emphatically distinguishes the mixture of pigments from that of lights. Speaking of the generation of yellow, he says, 'I say expressly red and green light, because I am speaking about light-colours (Lichtfarben), and not about pigments.' However faulty his theories may be, Wuensch's experiments appear in the main to be precise and conclusive. Nearly ten years subsequently, Young adopted red, green, and violet as the three primary colours, each of them capable of producing three sensations, one of which, however, predominates over the two others. Helmholtz adopts, elucidates, and enriches this notion. (Popular Lectures, p. 249. The paper of Helmholtz on the mixture of colours, translated by myself, is published in the Philosophical Magazine for 1852. Maxwell's memoir on the Theory of Compound Colours is published in the Philosophical Transactions, vol. 150, p. 67.)]

[Footnote 9: The following charming extract, bearing upon this point, was discovered and written out for me by my deeply lamented friend Dr. Bence Jones, when Hon. Secretary to the Royal Institution:—

'In every kind of magnitude there is a degree or sort to which our sense is proportioned, the perception and knowledge of which is of the greatest use to mankind. The same is the groundwork of philosophy; for, though all sorts and degrees are equally the object of philosophical speculation, yet it is from those which are proportioned to sense that a philosopher must set out in his inquiries, ascending or descending afterwards as his pursuits may require. He does well indeed to take his views from many points of sight, and supply the defects of sense by a well-regulated imagination; nor is he to be confined by any limit in space or time; but, as his knowledge of Nature is founded on the observation of sensible things, he must begin with these, and must often return to them to examine his progress by them. Here is his secure hold: and as he sets out from thence, so if he likewise trace not often his steps backwards with caution, he will be in hazard of losing his way in the labyrinths of Nature.'—(Maclaurin: An Account of Sir I. Newton's Philosophical Discoveries. Written 1728; second edition, 1750; pp. 18, 19.) ]

[Footnote 10: I do not wish to encumber the conception here with the details of the motion, but I may draw attention to the beautiful model of Prof. Lyman, wherein waves are shown to be produced by the circular motion of the particles. This, as proved by the brothers Weber, is the real motion in the case of water-waves.]

[Footnote 11: Copied from Weber's Wellenlehre.]

[Footnote 12: See Lectures on Sound, 1st and 2nd ed., Lecture VII.; and 3rd ed., Chap. VIII. Longmans.]

[Footnote 13: Boyle's Works, Birch's edition, p. 675.]

[Footnote 14: Page 743.]

[Footnote 15: The beautiful plumes produced by water-crystallization have been successfully photographed by Professor Lockett.]

[Footnote 16: In a little volume entitled 'Forms of Water,' I have mentioned that cold iron floats upon molten iron. In company with my friend Sir William Armstrong, I had repeated opportunities of witnessing this fact in his works at Elswick, 1863. Faraday, I remember, spoke to me subsequently of the perfection of iron castings as probably due to the swelling of the metal on solidification. Beyond this, I have given the subject no special attention; and I know that many intelligent iron-founders doubt the fact of expansion. It is quite possible that the solid floats because it is not wetted by the molten iron, its volume being virtually augmented by capillary repulsion. Certain flies walk freely upon water in virtue of an action of this kind. With bismuth, however, it is easy to burst iron bottles by the force of solidification.]

[Footnote 17: This beautiful law is usually thus expressed: The index of refraction of any substance is the tangent of its polarizing angle. With the aid of this law and an apparatus similar to that figured at page 15, we can readily determine the index of refraction of any liquid. The refracted and reflected beams being visible, they can readily be caused to inclose a right angle. The polarizing angle of the liquid may be thus found with the sharpest precision. It is then only necessary to seek out its natural tangent to obtain the index of refraction.]

[Footnote 18: Whewell.]

[Footnote 19: Removed from us since these words were written.]

[Footnote 20: The only essay known to me on the Undulatory Theory, from the pen of an American writer, is an excellent one by President Barnard, published in the Smithsonian Report for 1862.]

[Footnote 21: Boyle's Works, Birch's edition, vol. i. pp, 729 and 730.]

[Footnote 22: Werke, B. xxix. p. 24.]

[Footnote 23: Defined in Lecture I.]

[Footnote 24: This circumstance ought not to be lost sight of in the examination of compound spectra. Other similar instances might be cited.]

[Footnote 25: The dark band produced when the sodium is placed within the lamp was observed on the same occasion. Then was also observed for the first time the magnificent blue band of lithium which the Bunsen's flame fails to bring out.]

[Footnote 26: New York: for more than a decade no such weather had been experienced. The snow was so deep that the ordinary means of locomotion were for a time suspended.]

[Footnote 27: 'Il faut reconnaitre que parmi les peuples civilises de nos jours il en est pen chez qui les hautes sciences aient fait moins de progres qu'aux Etats-Unis, ou qui aient fourni moins de grands artistes, de poetes illustres et de celebres ecrivains.' (De la Democratie en Amerique, etc. tome ii. p. 36.)]

[Footnote 28: At these points the two rectangular vibrations into which the original polarized ray is resolved by the plates of gypsum, act upon each other like the two rectangular impulses imparted to our pendulum in Lecture IV., one being given when the pendulum is at the limit of its swing. Vibration is thus converted into rotation.]

[Footnote 29: The millimeter is about 1/25th of an inch.]



INDEX.

Absorption, principles of, 199

Airy, Sir George, severity and conclusiveness of his proofs, 209

Alhazen, his inquiry respecting light, 14, 207

Analyzer, polarizer and, 127 ——recompounding of the two systems of waves by the analyzer, 129

Angstroem, his paper on spectrum analysis, 202

Arago, Francois, and Dr. Young, 50 ——his discoveries respecting light, 208

Atomic polarity, 93-96

Bacon, Roger, his inquiry respecting light, 14, 207

Bartholinus, Erasmus, on Iceland spar, 112

Berard on polarization of heat, 180

Blackness, meaning of, 32

Boyle, Robert, his observations on colours, 65, 66 ——his remarks on fluorescence, 163, 164

Bradley, James, discovers the aberration of light, 21, 22

Brewster, Sir David, his chief objection to the undulatory theory of light, 47

Brewster, Sir David, his discovery in biaxal crystals, 209

Brougham, Mr. (afterwards Lord), ridicules Dr. T. Young's speculations, 50, 51

Caesium, discovery of, 193

Calorescence, 174

Clouds, actinic, 152-154 ——polarization of, 155

Colours of thin plates, 64 ——Boyle's observations on, 65, 66 ——Hooke on the colours of thin plates, 67 ——of striated surfaces, 89, 90

Comet of 1680, Newton's estimate of the temperature of, 168

Crookes, Mr., his discovery of thallium, 193

Crystals, action of, upon light, 98 ——built by polar force, 98 ——illustrations of crystallization, 99 ——architecture of, considered as an introduction to their action upon light, 98 ——bearings of crystallization upon optical phenomena, 106

Crystals, rings surrounding the axes of, uniaxal and biaxal, 145

Cuvier on ardour for knowledge, 220

De Tocqueville, writings of, 215, 222, 223

Descartes, his explanation of the rainbow, 24, 25 ——his ideas respecting the transmission of light, 43 ——his notion of light, 207

Diamond, ignition of a, in oxygen, 169

Diathermancy, 173

Diffraction of light, phenomena of, 78 ——bands, 78, 79 ——explanation of, 80 ——colours produced by, 89

Dollond, his experiments on achromatism, 28

Draper, Dr., his investigation on heat, 172

Drummond light, spectrum of, 195

Earth, daily orbit of, 74

Electric beam, heat of the, 168

Electricity, discoveries in, 217, 218

Emission theory of light, bases of the, 45 ——Newton espouses the theory, and the results of this espousal, 77

Ether, Huyghens and Euler advocate and defend the conception of an, 48, 58 ——objected to by Newton, 58

Euler espouses and defends the conception of an ether, 48, 58

Eusebius on the natural philosophers of his time, 13

Expansion by cold, 104

Experiment, uses of, 3

Eye, the, its imperfections, grown for ages towards perfection, 8 ——imperfect achromatism of the, 29, note

Faraday, Michael, his discovery of magneto-electricity, 218

'Fits,' theory of, 73 ——its explanation of Newton's rings, 74 ——overthrow of the theory, 77

Fizeau determines the velocity of light, 22

Fluorescence, Stokes's discovery of, 161 ——the name, 174

Forbes, Professor, polarizes and depolarizes heat, 180

Foucault, determines the velocity of light, 22 ——his experiments on absorption, 197, 198

Fraunhofer, his theoretical calculations respecting diffraction, 87 ——his lines, 193 ———their explanation by Kirchhoff, 193

Fresnel, and Dr. Young, 50 ——his theoretical calculations respecting diffraction, 87 ——his mathematical abilities and immortal name, 210

Goethe on fluorescence, 165

Gravitation, origin of the notion of the attraction of, 92 ——strength of the theory of, 148

Grimaldi, his discovery with respect to light, 56 ——Young's generalizations of, 56

Hamilton, Sir William, of Dublin, his discovery of conical refraction, 209

Heat, generation of, 6 ——Dr. Draper's investigation respecting, 171

Helmholtz, his estimate of the genius of Young, 50 ——on the imperfect achromatism of the eye, 29 note, 31 ——reveals the cause of green in the case of pigments, 37

Henry, Professor Joseph, his invitation, 2

Herschel, Sir John, his theoretical calculations respecting diffraction, 87 ——first notices and describes the fluorescence of sulphate of quinine, 165 ——his experiments on spectra, 201

Herschel, Sir William, his experiments on the heat of the various colours of the solar spectrum, 171

Hooke, Robert, on the colours of thin plates, 67 ——his remarks on the idea that light and heat are modes of motion, 68