DA TE NDIS IS BETON NEWLY DIgh to dang suplimet al scent: men of 24 Tull of the dazzine thus be the number mi cartes of the emanacions is very Bella"Lant They menât the vai teč rugs viði at seen with the madores of fore; the rooms produced 1o a dew betweeL. TV & prezes ✔ past will asking a the the vg, should moquar when the thicksame of the puna is a times that of ta ples, and which do so; the Ghatge Falting from the employment of che füis that water; taa etun of arg the puses: also the fringes and bands which wanapati Balova the phenomena observed by Grnači, Newton, Maruth, and gilera, and i thero bever at all reduced to rule. Young varva, very judy, "whatever may be thought of the theory, we bars got a simple and genera, law” of the phenomena. He moreover Katie Man Kaum Murth of an undulation from the measurements of Jongea of shawowe, as be had done before from the colors of thin y what and found a very close accordance of the results of the various A with mother.

Phil. Trans. Memoir, read Nov. 24.

There is one difficulty, and one inaccuracy, in Young's views at this period, which it may be proper to note. The difficulty was, that he found it necessary to suppose that light, when reflected at a rarer medium, is retarded by half an undulation. This assumption, though often urged at a later period as an argument against the theory, was fully justified as the mechanical principles of the subject were unfolded; and the necessity of it was clear to Young from the first. On the strength of this, says he, "I ventured to predict, that if the reflections were of the same kind, made at the surfaces of a thin plate, of a density intermediate between the densities of the mediums surrounding it, the central spot would be white; and I have now the pleasure of stating, that I have fully verified this prediction by interposing a drop of oil of sassafras between a prism of flint-glass and a lens of crown-glass."

The inaccuracy of his calculations consisted in his considering the external fringe of shadows to be produced by the interference of a ray reflected from the edge of the object, with a ray which passes clear of it; instead of supposing all the parts of the wave of light to corroborate or interfere with one another. The mathematical treatment of the question on the latter hypothesis was by no means easy. Young was a mathematician of considerable power in the solution of the problems which came before him: though his methods possessed none of the analytical elegance which, in his time, had become general in France. But it does not appear that he ever solved the problem of undulations as applied to fringes, with its true conditions. He did, however, rectify his conceptions of the nature of the interference; and we may add, that the numerical error of the consequences of the defective hypothesis is not such as to prevent their confirming the undulatory theory.'

But though this theory was thus so powerfully recommended by experiment and calculation, it met with little favor in the scientific world. Perhaps this will be in some measure accounted for, when we come, in the next chapter, to speak of the mode of its reception by

I may mention, in addition to the applications which Young made of the principle of interferences, his Eriometer, an instrument invented for the purpose of measuring the thickness of the fibres of wood; and the explanation of the supernumerary bands of the rainbow. These explanations involve calculations founded on the length of an undulation of light, and were confirmed by experiment, as far as experiment went.

the

the supposed judges of science and letters. Its author wem on labormuy at the completion and application of the theory in ciber parts of subject; but his extraordinary success in unraveling the OUGZEUGI phenomena of which we have been speaking, appears to have exsued wone of the notice and admiration which property belonged to it til Fresnel's Memoir On Diffraction was delivered to the Institute, in October, 1815.

MM. Arago and Poinsot were commissioned to make a report upo the Memoir; and the former of these philosophers threw himself upon the subject with a zeal and intelligence which peculiarly belonged to bom. He verified the laws announced by Fresnel: laws" he says, “which appear to be destined to make an epoch in science." He then cool rapid glance at the history of the subject, and recognized, at ome, the place which Young occupied in it. Grimaldi, Newton, Muraldi, he states, had observed the facts, and tried in vain to reduce them to rule or cause, "Such was the state of our knowledge on this difficult question, when Dr. Thomas Young made the very remarkable exponent which is described in the Philosophical Transactions for 1808" namely, that to obliterate all the bands within the shadow, we mod only stop the ray which is going to graze, or has grazed, one border of the object. To this, Arago added the important observabon, that the same obliteration takes place, if we stop the ray, with a transparent plate; except the plate be very thin, in which case the bands are displaced, and not extinguished. "Fresnel," says he, "guessed the effect which a thin plate would produce, when I had told him of the effect of a thick glass." Fresnel himself declares that he was not, at the time, aware of Young's previous labors. After stating nearly the same reasonings concerning fringes which Young had put forward in 1801, he adds, "it is therefore the meeting, the actual crossing of the rays, which produces the fringes. This consequence, which is only, so to speak, the translation of the phenomena, seems to me entirely opposed to the hypothesis of emission, and confirms the system which makes es light consist in the vibrations of a peculiar fluid." And thus the Principle of Interferences, and the theory of undulations, so far as that principle depends upon the theory, was a second time established by Fresnel in France, fourteen years after it had been discovered, fully proved, and repeatedly published by Young in England.

An. Chim. išiã, Febr.

4 Ib. tom. xvii. p. 402.

In this Memoir of Fresnel's, he takes very nearly the same course as Young had done; considering the interference of the direct light with that reflected at the edge, as the cause of the external fringes; and he observes, that in this reflection it is necessary to suppose half an undulation lost: but a few years later, he considered the propagation of undulations in a more true and general manner, and obtained the solution of this difficulty of the half-undulation. His more complete Memoir on Diffraction was delivered to the Institute of France, July 29, 1818; and had the prize awarded it in 1819: but by the delays which at that period occurred in the publication of the Parisian Academical Transactions, it was not published' till 1826, when the theory was no longer generally doubtful or unknown in the scientific world. In this Memoir, Fresnel observes, that we must consider the effect of every portion of a wave of light upon a distant point, and must, on this principle, find the illumination produced by any number of such waves together. Hence, in general, the process of integration is requisite; and though the integrals which here offer themselves are of a new and difficult kind, he succeeded in making the calculation for the cases in which he experimented. His Table of the Correspondences of Theory and Observation,' is very remarkable for the closeness of the agreement; the errors being generally less than one hundredth of the whole, in the distances of the black bands. He justly adds, "A more striking agreement could not be expected between experiment and theory. If we compare the smallness of the differences with the extent of the breadths measured; and if we remark the great variations which a and b (the distance of the object from the luminous point and from the screen) have received in the different observations, we shall find it difficult not to regard the integral which has led us to these results as the faithful expression of the law of the phenomena."

A mathematical theory, applied, with this success, to a variety of cases of very different kinds, could not now fail to take strong hold of the attention of mathematicians; and accordingly, from this time, the undulatory doctrine of diffraction has been generally assented to, and the mathematical difficulties which it involves, have been duly studied and struggled with.

Among the remarkable applications of the undulatory doctrine to diffraction, we may notice those of Joseph Fraunhofer, a mathemati

6

'Ann. Chim. May, 1819. Mém. Inst. for 1821-2. * Mém. Inst. p. 420–424. VOL. IL-7.

cal optician of Munich. He made a great number of experiments on the shadows produced by small holes, and groups of small holes, very near each other. These were published' in his New Modifications of Light, in 1823. The greater part of this Memoir is employed in tracing the laws of phenomena of the extremely complex and splendid appearances which he obtained; but at the conclusion he observes, "It is remarkable that the laws of the reciprocal influence and of the diffraction of the rays, can be deduced from the principles of the undulatory theory: knowing the conditions, we may, by means of an extremely simple equation, determine the extent of a luminous wave for each of the different colors; and in every case, the calculation corresponds with observation." This mention of "an extremely simple equation," appears to imply that he employed only Young's and Fresnel's earlier mode of calculating interferences, by considering two portions of light, and not the method of integration. Both from the late period at which they were published, and from the absence of mathematical details, Fraunhofer's labors had not any strong influence on the establishment of the undulatory theory; although they are excellent verifications of it, both from the goodness of the observations, and the complexity and beauty of the phenomena.

We have now to consider the progress of the undulatory theory in another of its departments, according to the division already stated.

Sect. 3.-Explanation of Double Refraction by the Undulatory

Theory.

We have traced the history of the undulatory theory applied to diffraction, into the period when Young came to have Fresnel for his fellow-laborer. But in the mean time, Young had considered the theory in its reference to other phenomena, and especially to those of double refraction.

In this case, indeed, Huyghens's explanation of the facts of Iceland spar, by means of spheroidal undulations, was so complete, and had been so fully confirmed by the measurements of Hay and Wollaston, that little remained to be done, except to connect the Huyghenian hypothesis with the mechanical views belonging to the theory, and to extend his law to other cases. The former part of this task Young executed, by remarking that we may conceive the elasticity of the

In Schumacher's Astronomische Abhandlungen, in French; earlier in German.