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 const.i.tution 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 inst.i.tutions, 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 G.o.d; 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 n.o.ble 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 ama.s.sed 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 a.s.sured 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 Inst.i.tution, 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 a.n.a.lyzer, 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 pa.s.sage 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 a.n.a.lyzer, 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 a.n.a.lyzer 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 a.n.a.lyzer 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 a.n.a.lyzer 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 a.n.a.lyzer 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 a.n.a.lyzer 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 a.n.a.lyzer 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 cla.s.s 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 s.p.a.ce, so that they will be differently affected by different positions of the a.n.a.lyzer. 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 a.n.a.lyzer. This statement merely recapitulates a fundamental point in polarization. In fact, plane-polarized light is alternately transmitted and extinguished by the a.n.a.lyzer 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 pa.s.sed 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 a.n.a.lyzer. The general effect to the eye will consequently be a general shifting of the bands through one-fourth of the s.p.a.ce 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. 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 a.n.a.lyzer 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 a.n.a.lyzer 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 pa.s.sage. 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 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 a.n.a.lysis 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 circ.u.mference, is easily connected with a similar effect obtained with Newton's rings. Let a thin slice of light fall upon the gla.s.ses which show the rings, so as to cover a narrow central vertical zone pa.s.sing 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 a.n.a.lysis, 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 pa.s.s 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 pa.s.ses 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 gla.s.s, when they can be looked at through a magnifying lens from behind, or they can be observed in the air when the ground gla.s.s 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 quant.i.ty.

[Ill.u.s.tration: Fig. 57.]

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 gla.s.s, 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 gla.s.s 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 Wunsch, Leipzig 1792, in which the author announces the proposition that there are neither five nor seven, but only three simple colours in white light. Wunsch 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, Wunsch 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, Wunsch'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 Inst.i.tution:--