Chapter VII: Part 7

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, Cunæus, 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 Göttingen, 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°, all trace
of colour disappears; and also that when the angle amounts to 90°,
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° 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°. 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 versâ_, 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 æther; 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°; 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 versâ_), we have only to turn
the plate round through 90°. 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°
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°, 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° 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°, 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°.

'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 versâ_, 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° 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 Wünsch, Leipzig 1792, in which the author announces the proposition that there are neither five nor seven, but only three simple colours in white light. Wünsch 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, Wünsch 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, Wünsch'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 reconnaître que parmi les peuples civilisés de nos jours il en est pen chez qui les hautes sciences aient fait moins de progrès qu'aux États-Unis, ou qui aient fourni moins de grands artistes, de poëtes illustres et de célèbres écrivains.' (_De la Démocratie en Amérique_, 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

Ångström, his paper on spectrum analysis, 202

Arago, François, 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

Bérard 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

Cæsium, discovery of, 193

Calorescence, 174

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