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and pointed to a diagram where the curvilinear course of the diffracted bands, which was the subject of the discussion, is theoretically established.”*

In a word, the claims of Young were at once recognised by Arago; and by none more freely than by Fresnel himself; and between these two eminent fellow-labourers a correspondence and even intimacy was soon established. They constantly communicated their ideas as new points of investigation pressed on their notice, and each contributed, in some instances, to clear up the difficulties which presented themselves to the other. Yet the announcement of Fresnel’s researches excited violent hostility among a considerable section of the savans of the Institute, consisting of devoted adherents to Laplace, who continued to uphold the theory of emission; and this great mathematician in particular used his utmost influence to discourage and suppress the new doctrine. The fate of the undulatory theory on its first announcement was thus remarkably and similarly unfortunate, from different causes, in England and in France; and considering the very abstract nature of the subject, and how apparently remote it is from any thing which could be supposed to involve the interests or passions of men, it is not less singular to observe the bitterness and acrimony of the hostility which it had to encounter. The British reviewer and the French academician seemed to vie with each other in malignity; and the two great discoverers, Young and Fresnel, were both for a long time destined to the mortification of neglect and discouragement. The only cheering feature was certainly in favour of British science; the several papers of Young, successively communicated to the Royal Society, having been not only printed in its Transactions, but also in two instances selected as the Bakerian lectures; a compliment which the council has the power of bestowing annually, from a small bequest, on one of the papers communicated to the Society. In 1809 Young published an elaborate refutation of Laplace's memoir on double refraction; showing that its laws could be much more satisfactorily explained on the wave system. This may be regarded as the most signal blow directed against the lingering credit of the molecular theory. It stood its ground among the French academicians longer than elsewhere, from the predominant influence of Laplace, who, with an obstimacy which formed part of his character, continued to the last to cling to the doctrine he had so long upheld, in the face of all the new facts and reasonings which were now enlightening the world of science. It has been well observed, that “simplicity is not always a

* Arago's Biog. Notice of Young, CEuvres, tom. i. p. 292.

fruit of the first growth;” and accordingly some of the earliest of Young's researches were complicated by unnecessary conditions afterwards easily removed, but which in some instances continued long to embarrass the subject and furnish sources of objection to the wave hypothesis. One such difficulty for a long time pressed upon the completeness of theory in regard to the explanation of the thin plates. According to the law of the thickness, it followed that at the point of actual contact at the centre the rays would be in accordance, and the centre ought to be a point of brightness; it is however, in fact, always black when the extreme limit is reached. Hence Dr. Young, and those who followed him for a long time afterwards, supposed that in this, as well as in some other cases which seemed analogous, we must suppose half an undulation to be by some means gained by one ray or lost by the other; and this seemed an arbitrary or empirical assumption, which the theory did not account for. We shall presently see how the difficulty was obviated. Other cases involving the principle of interference were also investigated by Dr. Young; which are not without a practical bearing. Every one may have remarked the threads of a spider’s web occasionally exhibiting brilliant colours in the sunshine. The same thing is seen in fine scratches on the surface of polished metal, and may be artificially produced in several ways. These colours Dr. Young showed were due to interference of the portions of light reflected from the sides of the groove, or narrow transparent thread. His attention was also particularly directed to the more complex tints produced when light was transmitted through a texture of fine threads, such as gauze, or even loose fibres of wool, cotton, silk, &c. Here a similar theoretical explanation was found to apply; and when the fibres were tolerably uniformly spread, a bright point of light seen through them appeared surrounded by a halo of coloured rings. The diameters of these rings varied with the fineness of the fibres; and were theoretically shown to depend on the interference of the portions of light passing through the transparent fibres and the interstices. He was able to show by theory the relation between the diameters of the rings and the thickness of the fibres; but the former could be easily measured by an appropriate apparatus of a very simple construction. Hence the diameters of those minute fibres could be immediately determined, and thus differences among them rendered appreciable which were quite imperceptible to the eye. He proposed this practical consideration as likely to be of importance to those interested in estimating the fineness of wool, cotton, &c. for commercial purposes. It does not appear, so far as we know, whether such a method has ever been found practically available. But we should imagine it could not be undeserving of attention; and in the hands of a person of moderate skill would certainly confer new powers of discrimination in such CaSeS. The undulatory doctrine, however, was long embarrassed by several objections which it required more extended consideration to remove. Thus, it had long since been remarked by Newton that waves spread round an obstacle, and on the same principle the rectilinear propagation of light is a difficulty; light ought to bend round the edges of any intercepting body. But the very principle suggested by Huyghens afforded in some sense an answer; and a fuller examination of the nature and mode of propagation of the waves showed that the oblique and diverging portions will in general interfere with and neutralise each other, so that the main effect will be confined to that part which is in the direct line of the proportion. Youngo dwelt much at first on this objection; and afterwards, in a letter to Arago, he renews a similar expression of the difficulties he felt in another point of view : “If light has so great a tendency to diverge into the path of neighbouring rays, and to interfere with them, as Huyghens supposes, I do not see how it escapes being totally extinguished in a very short space, even in the most transparent medium.” But the principle just adverted to shows that the middle portion of the light coming from a point of any physical magnitude is not subject to these mutual interferences, and does not diverge, but is perpetually reinforced by the supply of fresh waves incessantly propagated from the original source. In these explanations Young at length expressed his full concurrence in a letter to Fresnel. The capital discovery of the polarisation of light by reflection made by Malus in 1810 formed a remarkable epoch in the history of optical research. The same idea of sides or poles imagined by Newton seemed to be involved. The reflected ray acquired the same character and properties as each of the rays in the doubly refracting crystal, though their planes of polarisation are at right angles to each other, and in determinate directions with respect . to the crystal. A ray polarised in one plane will neither be transmitted through the crystal nor reflected from glass, when the planes in which they are respectively presented to it are at right angles to its own plane of polarisation. A ray may also be polarised by other methods: by transmission through a number of parallel plates of glass, or through a plate of tourmaline, or certain other substances. Hence any of these methods may be used convertibly to test the polarisation of a ray, and the plates or crystals employed are then termed analysers. A particular angle of incidence is necessary to give the maximum effect; different for each reflecting substance; and this subject to a law whose subsequent disclosure constituted one of the most beautiful discoveries of Sir D. Brewster, viz. that it takes place at that incidence at which the refracted ray is perpendicular to the reflected; or, which is mathematically the same thing otherwise expressed, when the tangent of the angle of incidence is the Ånder of refraction of the substance. Such were some of the leading points successively disclosed; and they soon engaged the attention of Young, as well as Fresnel, who afterwards so largely contributed to the development and extension of them in connection with the doctrine of undulations, of which they were destined to form one of the strongest supports. Yet so little was the value and tendency of Malus' discovery at first perceived, that it was regarded as quite at variance with the wave theory. Young himself went so far as to predict that it was a problem which “would probably long remain to mortify the vanity of an ambitious philosophy, completely unresolved by any theory.” Again, in a review of Malus' paper (in 1811), he considers it “conclusive with respect to the insufficiency of the undulatory theory in its present state for explaining all the phemomena of light.” And, again, in a letter to Sir D. Brewster, five years later, he expresses himself thus: “With respect to my fundamental hypotheses respecting the nature of light (i. e. the wave theory), I become less and less fond of dwelling on them, as I learn more and more facts like those which M. Malus discovered; because though they may not be incompatible with those facts, they certainly give no assistance in earplaining them.” Even Malus himself was at first of opinion that the phenomena of polarisation were equally irreconcilable with both the undulatory and molecular theories; an opinion which he distinctly expressed in a letter to Young.” Somewhat later, however, we find Young beginning to entertain a more satisfactory view of the case, as appears by the

* Life, p. 140.

following passage from a letter addressed by him to Arago in 1817:

“I have been reflecting upon the possibility of giving an imperfect explanation of the affection of light, which constitutes polarisation, without departing from the genuine doctrine of undulations. It is a principle of this theory that all undulations are simply propagated through homogeneous mediums in concentric spherical surfaces, like the undulations of sound, consisting simply of the direct and retrograde motions of their particles in the direction of the radius, with their concomitant condensations and rarefactions. And yet it is possible to explain in this theory a transverse vibration, propagated also in the direction of the radius, and with equal velocity, the motions of

* Works, vol. i. p. 248, note.

the particles bearing a certain constant direction with respect to that radius; and this is polarisation.”

The conception of transverse vibrations, now that the idea has become familiarised, seems to present little difficulty; yet it was at first opposed to the prepossessions cven of the most zealous undulationists. Fresnel long hesitated fully to adopt the idea, although admitting it to be the only mode of representing polarisation,-on the ground of being unable to reconcile it with mechanical principles; and this more preciscly as to the motion of transverse vibrations alone being produced, which constituted this theory in all its simplicity; whereas Young had (as we have just seen) believed both these and longitudinal vibrations to co-exist. To establish this point, he expressly says, was the main difficulty which embarrassed him.* This idea of vibrations performed in directions at right angles to the line of the ray received at length its decisive proof from the phenomena of the coloured tints developed in polarised light by the interposition of plates of crystals (such as those of mica, selenite, &c.), when examined by an analyser. Young ascribed these colours generally to interference; but both Fresnel and Arago pointed out that this explanation was incomplete. Why did it only take place in polarised light, and even then not until the analyser had been applied? These questions could not be answered until another important law had been established by the joint researches of Fresnel and Arago; and this consisted in the experimental conclusion, that when two rays are, in other respects, in a condition to interfere, but are polarised in planes at right angles to each other, they cannot interfere: they can only do so when polarised in parallel planes. Now this result, of necessity, implics that in rays polarised in different planes the vibrations must be executed in different planes; and this involves the admission that the vibrations must be transverse to the ray. This principle was at length seen to complete the explanation so long sought of the polarised tints. The light originally polarised in one plane was, in traversing the doubly refracting crystal, divided into two portions in planes at right angles, which, as Young had shown in regard to position, were in a condition to interfere; (the ordinary ray of one such pair coinciding in direction with the extraordinary of some other pair :) were it not that being polarised in these rectangular planes, they could not interfere. It only required, then, the action of the analyser to resolve, each portion into two, suppressing those in one plane, and transmitting those in the other, which, having their vibrations now parallel,

* Ann. de Chimie, 1831, tom. xvii. p. 184.

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