102 Young’s first published statement of the doctrine of transverse vibrations was given in the explanation of the phenomena of dipolarization, of which we shall have to speak in the next Section. But the primary and immense value of this conception, as a step in the progress of the undulatory theory, was the connexion which it established between polarization and double refraction; for it held forth a promise of accounting for polarization, if any conditions could be found which might determine what was the direction of the transverse vibrations. The analysis of these conditions is, in a great measure, the work of Fresnel; a task performed with profound philosophical sagacity and great mathematical skill.
Since the double refraction of uniaxal crystals could be explained by undulations of the form of a spheroid, it was perhaps not difficult to conjecture that the undulations of biaxal crystals would be accounted for by undulations of the form of an ellipsoid, which differs from the spheroid in having its three axes unequal, instead of two only; and consequently has that very relation to the other, in respect of symmetry, which the crystalline and optical phenomena have. Or, again, instead of supposing two different degrees of elasticity in different directions, we may suppose three such different degrees in directions at right angles to each other. This kind of generalization was tolerably obvious to a practised mathematician.
But what shall call into play all these elasticities at once, and produce waves governed by each of them? And what shall explain the different polarization of the rays which these separate waves carry with them? These were difficult questions, to the solution of which mathematical calculation had hitherto been unable to offer any aid.
It was here that the conception of transverse vibrations came in, like a beam of sunlight, to disclose the possibility of a mechanical connexion of all these facts. If transverse vibrations, travelling through a uniform medium, come to a medium not uniform, but constituted so that the elasticity shall be different in different directions, in the manner we have described, what will be the course and condition of the waves in the second medium? Will the effects of such waves agree with the phenomena of doubly-refracted light in biaxal crystals? Here was a problem, striking to the mathematician for its generality and difficulty, and of deep interest to the physical philosopher, because the fate of a great theory depended upon its solution.
The solution, obtained by great mathematical skill, was laid before the French Institute by Fresnel in November, 1821, and was carried 103 further in two Memoirs presented in 1822. Its import is very curious. The undulations which, coming from a distant centre, fall upon such a medium as we have described, are, it appears from the principles of mechanics, propagated in a manner quite different from anything which had been anticipated. The “surface of the waves” (that is, the surface which would bound undulations diverging from a point), is a very complex, yet symmetrical curve surface; which, in the case of uniaxal crystals, resolves itself into a sphere and a spheroid; but which, in general, forms a continuous double envelope of the central point to which it belongs, intersecting itself and returning into itself. The directions of the rays are determined by this curve surface in biaxal crystals, as in uniaxal crystals they are determined by the sphere and the spheroid; and the result is, that in biaxal crystals, both rays suffer extraordinary refraction according to determinate laws. And the positions of the planes of polarization of the two rays follow from the same investigation; the plane of polarization in every case being supposed to be that which is perpendicular to the transverse vibrations. Now it appeared that the polarization of the two rays, as determined by Fresnel’s theory, would be in directions, not indeed exactly accordant with the law deduced by M. Biot from experiment, but deviating so little from those directions, that there could be small doubt that the empirical formula was wrong, and the theoretical one right.
The theory was further confirmed by an experiment showing that, in a biaxal crystal (topaz), neither of the rays was refracted according to the ordinary law, though it had hitherto been supposed that one of them was so; a natural inaccuracy, since the error was small.85 Thus this beautiful theory corrected, while it explained, the best of the observations which had previously been made; and offered itself to mathematicians with an almost irresistible power of conviction. The explanation of laws so strange and diverse as those of double refraction and polarization, by the same general and symmetrical theory, could not result from anything but the truth of the theory.
“Long,” says Fresnel,86 “before I had conceived this theory, I had convinced myself by a pure contemplation of the facts, that it was not possible to discover the true explanation of double refraction, without explaining, at the same time, the phenomena of polarization, which always goes along with it; and accordingly, it was after having found 104 what mode of vibration constituted polarization, that I caught sight of the mechanical causes of double refraction.”
Having thus got possession of the principle of the mechanism of polarization, Fresnel proceeded to apply it to the other cases of polarized light, with a rapidity and sagacity which reminds us of the spirit in which Newton traced out the consequences of the principle of universal gravitation. In the execution of his task, indeed, Fresnel was forced upon several precarious assumptions, which make, even yet, a wide difference between the theory of gravitation and that of light. But the mode in which these were confirmed by experiment, compels us to admire the happy apparent boldness of the calculator.
The subject of polarization by reflection was one of those which seemed most untractable; but, by means of various artifices and conjectures, it was broken up and subdued. Fresnel began with the simplest case, the reflection of light polarized in the plane of reflection; which he solved by means of the laws of collision of elastic bodies. He then took the reflection of light polarized perpendicularly to this plane; and here, adding to the general mechanical principles a hypothetical assumption, that the communication of the resolved motion parallel to the refracting surface, takes place according to the laws of elastic bodies, he obtains his formula. These results were capable of comparison with experiment; and the comparison, when made by M. Arago, confirmed the formulæ. They accounted, too, for Sir D. Brewster’s law concerning the polarizing angle (see Chap. vi.); and this could not but be looked upon as a striking evidence of their having some real foundation. Another artifice which MM. Fresnel and Arago employed, in order to trace the effect of reflection upon common light, was to use a ray polarized in a plane making half a right angle with the plane of reflection; for the quantities of the oppositely87 polarized light in such an incident ray are equal, as they are in common light; but the relative quantities of the oppositely polarized light in the reflected ray are indicated by the new plane of polarization; and thus these relative quantities become known for the case of common light. The results thus obtained were also confirmed by facts; and in this manner, all that was doubtful in the process of Fresnel’s reasoning, seemed to be authorized by its application to real cases.
105 These investigations were published88 in 1821. In succeeding years, Fresnel undertook to extend the application of his formulæ to a case in which they ceased to have a meaning, or, in the language of mathematicians, became imaginary; namely, to the case of internal reflection at the surface of a transparent body. It may seem strange to those who are not mathematicians, but it is undoubtedly true, that in many cases in which the solution of a problem directs impossible arithmetical or algebraical operations to be performed, these directions may be so interpreted as to point out a true solution of the question. Such an interpretation Fresnel attempted89 in the case of which we now speak; and the result at which he arrived was, that the reflection of light through a rhomb of glass of a certain form (since called Fresnel’s rhomb, would produce a polarization of a kind altogether different from those which his theory had previously considered, namely, that kind which we have spoken of as circular polarization. The complete confirmation of this curious and unexpected result by trial, is another of the extraordinary triumphs which have distinguished the history of the theory at every step since the commencement of Fresnel’s labors.
But anything further which has been done in this way, may be treated of more properly in relating the verification of the theory. And we have still to speak of the most numerous and varied class of facts to which rival theories of light were applied, and of the establishment of the undulatory doctrine in reference to that department; I mean the phenomena of depolarized, or rather, as I have already said, dipolarized light.
When Arago, in 1811, had discovered the colors produced by polarized light passing through certain crystals,90 it was natural that attempts should be made to reduce them to theory. M. Biot, animated by the success of Malus in detecting the laws of double refraction, and Young, knowing the resources of his own theory, were the first persons to enter upon this undertaking. M. Biot’s theory, though in the end displaced by its rival, is well worth notice in the history of the subject. It was what he called the doctrine of moveable polarization. He conceived that when the molecules of light pass through 106 thin crystalline plates, the plane of polarization undergoes an oscillation which carries it backwards and forwards through a certain angle, namely, twice the angle contained between the original plane of polarization and the principal section of the crystal. The intervals which this oscillation occupies are lengths of the path of the ray, very minute, and different for different colors, like Newton’s fits of easy transmission; on which model, indeed, the new theory was evidently framed.91 The colors produced in the phenomena of dipolarization really do depend, in a periodical manner, on the length of the path of the light through the crystal, and a theory such as M. Biot’s was capable of being modified, and was modified, so as to include the leading features of the facts as then known; but many of its conditions being founded on special circumstances in the experiments, and not on the real conditions of nature, there were in it several incongruities, as well as the general defect of its being an arbitrary and unconnected hypothesis.
Young’s mode of accounting for the brilliant phenomena of dipolarization appeared in the Quarterly Review for 1814. After noticing the discoveries of MM. Arago, Brewster, and Biot, he adds, “We have no doubt that the surprise of these gentlemen will be as great as our own satisfaction in finding that they are perfectly reducible, like other causes of recurrent colors, to the general laws of the interference of light which have been established in this country;” giving a reference to his former statements. The results are then explained by the interference of the ordinary and extraordinary ray. But, as M. Arago properly observes, in his account of this matter,92 “It must, however, be added that Dr. Young had not explained either in what circumstances the interference of the rays can take place, nor why we see no colors unless the crystallized plates are exposed to light previously polarized.” The explanation of these circumstances depends on the laws of interference of polarized light which MM. Arago and Fresnel established in 1816. They then proved, by direct experiment, that when polarized light was treated so as to bring into view the most marked phenomena of interference, namely, the bands of shadows; pencils of light which have a common origin, and which are polarized in the parallel planes, interfere completely, while those which are 107 polarized in opposite (that is, perpendicular,) planes do not interfere at all.93 Taking these principles into the account, Fresnel explained very completely, by means of the interference of undulations, all the circumstances of colors produced by crystallized plates; showing the necessity of the polarization in the first instance; the dipolarizing effect of the crystal; and the office of the analysing plate, by which certain portions of each of the two rays in the crystal are made to interfere and produce color. This he did, as he says,94 without being aware, till Arago told him, that Young had, to some extent, anticipated him.
When we look at the history of the emission-theory of light, we see exactly what we may consider as the natural course of things in the career of a false theory. Such a theory may, to a certain extent, explain the phenomena which it was at first contrived to meet; but every new class of facts requires a new supposition,—an addition to the machinery; and as observation goes on, these incoherent appendages accumulate, till they overwhelm and upset the original frame-work. Such was the history of the hypothesis of solid epicycles; such has been the history of the hypothesis of the material emission of light. In its simple form, it explained reflection and refraction; but the colors of thin plates added to it the hypothesis of fits of easy transmission and reflection; the phenomena of diffraction further invested the particles with complex hypothetical laws of attraction and repulsion; polarization gave them sides; double refraction subjected them to peculiar forces emanating from the axes of crystals; finally, dipolarization loaded them with the complex and unconnected contrivance of moveable polarization; and even when all this had been assumed, additional mechanism was wanting. There is here no unexpected success, no happy coincidence, no convergence of principles from remote quarters; the philosopher builds the machine, but its parts do not fit; they hold together only while he presses them: this is not the character of truth.
In the undulatory theory, on the other hand, all tends to unity and simplicity. We explain reflection and refraction by undulations; when we come to thin plates, the requisite “fits” are already involved in our fundamental hypothesis, for they are the length of an undulation; the phenomena of diffraction also require such intervals; and the intervals thus required agree exactly with the others in magnitude, 108 so that no new property is needed. Polarization for a moment checks us; but not long; for the direction of our vibrations is hitherto arbitrary;—we allow polarization to decide it. Having done this for the sake of polarization, we find that it also answers an entirely different purpose, that of giving the law of double refraction. Truth may give rise to such a coincidence; falsehood cannot. But the phenomena become more numerous, more various, more strange; no matter: the Theory is equal to them all. It makes not a single new physical hypothesis; but out of its original stock of principles it educes the counterpart of all that observation shows. It accounts for, explains, simplifies, the most entangled cases; corrects known laws and facts; predicts and discloses unknown ones; becomes the guide of its former teacher, Observation; and, enlightened by mechanical conceptions, acquires an insight which pierces through shape and color to force and cause.
We thus reach the philosophical moral of this history, so important in reference to our purpose; and here we shall close the account of the discovery and promulgation of the undulatory theory. Any further steps in its development and extension, may with propriety be noticed in the ensuing chapters, respecting its reception and verification.
[2nd Ed.] [In the Philosophy of the Inductive Sciences, B. xi. ch. iii. Sect. 11, I have spoken of the Consilience of Inductions as one of the characters of scientific truth. We have several striking instances of such consilience in the history of the undulatory theory. The phenomena of fringes of shadows and colored bands in crystals jump together in the Theory of Vibrations. The phenomena of polarization and double refraction jump together in the Theory of Crystalline Vibrations. The phenomena of polarization and of the interference of polarized rays jump together in the Theory of Transverse Vibrations.
The proof of what is above said of the undulatory theory is contained in the previous history. This theory has “accounted for, explained, and simplified the most entangled cases;” as the cases of fringes of shadows; shadows of gratings; colored bands in biaxal crystals, and in quartz. There are no optical phenomena more entangled than these. It has “corrected experimental laws,” as in the case of M. Biot’s law of the direction of polarization in biaxal crystals. It has done this, “without making any new physical hypothesis;” for the transverse direction of vibrations, the different optical elasticities of crystals in different directions, and (if it be adopted) the hypothesis of finite 109 intervals of the particles (see chap. x. and hereafter, chap. xiii.), are only limitations of what was indefinite in the earlier form of the hypothesis. And so far as the properties of visible radiant light are concerned, I do not think it at all too much to say, as M. Schwerd has said, that “the undulation theory accounts for the phenomena as completely as the theory of gravitation does for the facts of the solar system.”
This we might say, even if some facts were not yet fully explained; for there were till very lately, if there are not still, such unexplained facts with regard to the theory of gravitation, presented to us by the solar system. With regard to the undulatory theory, these exceptions are, I think, disappearing quite as rapidly and as completely as in the case of gravitation. It is to be observed that no presumption against the theory can with any show of reason be collected from the cases in which classes of phenomena remain unexplained, the theory having never been applied to them by any mathematician capable of tracing its results correctly. The history of the theory of gravitation may show us abundantly how necessary it is to bear in mind this caution; and the results of the undulatory theory cannot be traced without great mathematical skill and great labor, any more than those of gravitation.
This remark applies to such cases as that of the transverse fringes of grooved surfaces. The general phenomena of these cases are perfectly explained by the theory. But there is an interruption in the light in an oblique direction, which has not yet been explained; but looking at what has been done in other cases, it is impossible to doubt that this phenomenon depends upon the results of certain integrations, and would be explained if these were rightly performed.
The phenomena of crystallized surfaces, and especially their effects upon the plane of polarization, were examined by Sir D. Brewster, and laws of the phenomena made out by him with his usual skill and sagacity. For a time these were unexplained by the theory. But recently Mr. Mac Cullagh has traced the consequences of the theory in this case,95 and obtained a law which represents with much exactness, Sir D. Brewster’s observation.
The phenomena which Sir D. Brewster, in 1837, called a new property of light, (certain appearances of the spectrum when the pupil of the eye is half covered with a thin glass or crystal,) have been explained by Mr. Airy in the Phil. Trans. for 1840.
Mr. Airy’s explanation of the phenomena termed by Sir D. 110 Brewster a new property of light, is completed in the Philosophical Magazine for November, 1846. It is there shown that a dependence of the breadth of the bands upon the aperture of the pupil, which had been supposed to result from the theory, and which does not appear in the experiment, did really result from certain limited conditions of the hypothesis, which conditions do not belong to the experiment; and that when the problem is solved without those limitations, the discrepance of theory and observation vanishes; so that, as Mr. Airy says, “this very remarkable experiment, which long appeared inexplicable, seems destined to give one of the strongest confirmations to the Undulatory Theory.”
I may remark also that there is no force in the objection which has been urged against the admirers of the undulatory theory, that by the fulness of their assent to it, they discourage further researches which may contradict or confirm it. We must, in this point of view also, look at the course of the theory of gravitation and its results. The acceptance of that theory did not prevent mathematicians and observers from attending to the apparent exceptions, but on the contrary, stimulated them to calculate and to observe with additional zeal, and still does so. The acceleration of the Moon, the mutual disturbances of Jupiter and Saturn, the motions of Jupiter’s Satellites, the effect of the Earth’s oblateness on the Moon’s motion, the motions of the Moon about her own centre, and many other phenomena, were studied with the greater attention, because the general theory was deemed so convincing: and the same cause makes the remaining exceptions objects of intense interest to astronomers and mathematicians. The mathematicians and optical experimenters who accept the undulatory theory, will of course follow out their conviction in the same manner. Accordingly, this has been done and is still doing, as in Mr. Airy’s mathematical investigation of the effect of an annular aperture; Mr. Earnshaw’s, of the effect of a triangular aperture; Mr. Talbot’s explanation of the effect of interposing a film of mica between a part of the pupil and the pure spectrum, so nearly approaching to the phenomena which have been spoken of as a new Polarity of Light; besides other labors of eminent mathematicians, elsewhere mentioned in these pages.
The phenomena of the absorption of light have no especial bearing upon the undulatory theory. There is not much difficulty in explaining the possibility of absorption upon the theory. When the light is absorbed, it ceases to belong to the theory. 111
For, as I have said, the theory professes only to explain the phenomena of radiant visible light. We know very well that light has other bearings and properties. It produces chemical effects. The optical polarity of crystals is connected with the chemical polarity of their constitution. The natural colors of bodies, too, are connected with their chemical constitution. Light is also connected with heat. The undulatory theory does not undertake to explain these properties and their connexion. If it did, it would be a Theory of Heat and of Chemical Composition, as well as a Theory of Light.
Dr. Faraday’s recent experiments have shown that the magnetic polarity is directly connected with that optical polarity by which the plane of polarization is affected. When the lines of magnetic force pass through certain transparent bodies, they communicate to them a certain kind of circular polarizing power; yet different from the circular polarizing power of quartz, and certain fluids mentioned in chapter ix.
Perhaps I may be allowed to refer to this discovery as a further illustration of the views I have offered in the Philosophy of the Inductive Sciences respecting the Connexion of Co-existent Polarities. (B. v. Chap. ii.)]
WHEN Young, in 1800, published his assertion of the Principle of Interferences, as the true theory of optical phenomena, the condition of England was not very favorable to a fair appreciation of the value of the new opinion. The men of science were strongly pre-occupied in favor of the doctrine of emission, not only from a national interest in Newton’s glory, and a natural reverence for his authority, but also from deference towards the geometers of France, who were looked up to as our masters in the application of mathematics to physics, and who were understood to be Newtonians in this as in other subjects. A general tendency to an atomic philosophy, which had begun to appear from the time of Newton, operated powerfully; and 112 the hypothesis of emission was so easily conceived, that, when recommended by high authority, it easily became popular; while the hypothesis of luminiferous undulations, unavoidably difficult to comprehend, even by the aid of steady thought, was neglected, and all but forgotten.
Yet the reception which Young’s opinions met with was more harsh than he might have expected, even taking into account all these considerations. But there was in England no visible body of men, fitted by their knowledge and character to pronounce judgment on such a question, or to give the proper impulse and bias to public opinion. The Royal Society, for instance, had not, for a long time, by custom or institution, possessed or aimed at such functions. The writers of “Reviews” alone, self-constituted and secret tribunals, claimed this kind of authority. Among these publications, by far the most distinguished about this period was the Edinburgh Review; and, including among its contributors men of eminent science and great talents, employing also a robust and poignant style of writing (often certainly in a very unfair manner), it naturally exercised great influence. On abstruse doctrines, intelligible to few persons, more than on other subjects, the opinions and feelings expressed in a Review must be those of the individual reviewer. The criticism on some of Young’s early papers on optics was written by Mr. (afterwards Lord) Brougham, who, as we have seen, had experimented on diffraction, following the Newtonian view, that of inflexion. Mr. Brougham was perhaps at this time young enough96 to be somewhat intoxicated with the appearance of judicial authority in matters of science, which his office of anonymous reviewer gave him: and even in middle-life, he was sometimes considered to be prone to indulge himself in severe and sarcastic expressions. In January, 1803, was published97 his critique on Dr. Young’s Bakerian Lecture, On the Theory of Light and Colors, in which lecture the doctrine of undulations and the law of interferences was maintained. This critique was an uninterrupted strain of blame and rebuke. “This paper,” the reviewer said, “contains nothing which deserves the name either of experiment or discovery.” He charged the writer with “dangerous relaxations of the principles of physical logic.” “We wish,” he cried, “to recall philosophers to the strict and severe methods of investigation,” describing them as those pointed out by Bacon, Newton, and the like. Finally, Dr. Young’s speculations 113 were spoken of as a hypothesis, which is a mere work of fancy; and the critic added, “we cannot conclude our review without entreating the attention of the Royal Society, which has admitted of late so many hasty and unsubstantial papers into its Transactions;” which habit he urged them to reform. The same aversion to the undulatory theory appears soon after in another article by the same reviewer, on the subject of Wollaston’s measures of the refraction of Iceland spar; he says, “We are much disappointed to find that so acute and ingenious an experimentalist should have adopted the wild optical theory of vibrations.” The reviewer showed ignorance as well as prejudice in the course of his remarks; and Young drew up an answer, which was ably written, but being published separately had little circulation. We can hardly doubt that these Edinburgh reviews had their effect in confirming the general disposition to reject the undulatory theory.
We may add, however, that Young’s mode of presenting his opinions was not the most likely to win them favor; for his mathematical reasonings placed them out of the reach of popular readers, while the want of symmetry and system in his symbolical calculations, deprived them of attractiveness for the mathematician. He himself gave a very just criticism of his own style of writing, in speaking on another of his works:98 “The mathematical reasoning, for want of mathematical symbols, was not understood, even by tolerable mathematicians. From a dislike of the affectation of algebraical formality which he had observed in some foreign authors, he was led into something like an affectation of simplicity, which was equally inconvenient to a scientific reader.”
Young appears to have been aware of his own deficiency in the power of drawing public favor, or even notice, to his discoveries. In 1802, Davy writes to a friend, “Have you seen the theory of my colleague, Dr. Young, on the undulations of an ethereal medium as the cause of light? It is not likely to be a popular hypothesis, after what has been said by Newton concerning it. He would be very much flattered if you could offer any observations upon it, whether for or against it.” Young naturally felt confident in his power of refuting objections, and wanted only the opportunity of a public combat.
Dr. Brewster, who was, at this period, enriching optical knowledge with so vast a train of new phenomena and laws, shared the general aversion to the undulatory theory, which, indeed, he hardly overcame 114 thirty years later. Dr. Wollaston was a person whose character led him to look long at the laws of phenomena, before he attempted to determine their causes; and it does not appear that he had decided the claims of the rival theories in his own mind. Herschel (I now speak of the son) had at first the general mathematical prejudice in favor of the emission doctrine. Even when he had himself studied and extended the laws of dipolarized phenomena, he translated them into the language of the theory of moveable polarization. In 1819, he refers to, and corrects, this theory; and says, it is now “relieved from every difficulty, and entitled to rank with the fits of easy transmission and reflection as a general and simple physical law;” a just judgment, but one which now conveys less of praise than he then intended. At a later period, he remarked that we cannot be certain that if the theory of emission had been as much cultivated as that of undulation, it might not have been as successful; an opinion which was certainly untenable after the fair trial of the two theories in the case of diffraction, and extravagant after Fresnel’s beautiful explanation of double refraction and polarization. Even in 1827, in a Treatise on Light, published in the Encyclopædia Metropolitana, he gives a section to the calculations of the Newtonian theory; and appears to consider the rivalry of the theories as still subsisting. But yet he there speaks with a proper appreciation of the advantages of the new doctrine. After tracing the prelude to it, he says, “But the unpursued speculations of Newton, and the opinions of Hooke, however distinct, must not be put in competition, and, indeed, ought scarcely to be mentioned, with the elegant, simple, and comprehensive theory of Young,—a theory which, if not founded in nature, is certainly one of the happiest fictions that the genius of man ever invented to grasp together natural phenomena, which, at their first discovery, seemed in irreconcileable opposition to it. It is, in fact, in all its applications and details, one succession of felicities; insomuch, that we may almost be induced to say, if it be not true, it deserves to be so.”
In France, Young’s theory was little noticed or known, except perhaps by M. Arago, till it was revived by Fresnel. And though Fresnel’s assertion of the undulatory theory was not so rudely received as Young’s had been, it met with no small opposition from the older mathematicians, and made its way slowly to the notice and comprehension of men of science. M. Arago would perhaps have at once adopted the conception of transverse vibrations, when it was suggested by his fellow-laborer, Fresnel, if it had not been that he was a member of the 115 Institute, and had to bear the brunt of the war, in the frequent discussions on the undulatory theory; to which theory Laplace, and other leading members, were so vehemently opposed, that they would not even listen with toleration to the arguments in its favor. I do not know how far influences of this kind might operate in producing the delays which took place in the publication of Fresnel’s papers. We have seen that he arrived at the conception of transverse vibrations in 1816, as the true key to the understanding of polarization. In 1817 and 1818, in a memoir read to the Institute, he analysed and explained the perplexing phenomena of quartz, which he ascribed to a circular polarization. This memoir had not been printed, nor any extract from it inserted in the scientific journals, in 1822, when he confirmed his views by further experiments.99 His remarkable memoir, which solved the extraordinary and capital problem of the connexion of double refraction and crystallization, though written in 1821, was not published till 1827. He appears by this time to have sought other channels of publication. In 1822, he gave,100 in the Annales de Chimie et de Physique, an explanation of refraction on the principles of the undulatory theory; alleging, as the reason for doing so, that the theory was still little known. And in succeeding years there appeared in the same work, his theory of reflection. His memoir on this subject (Mémoire sur la Loi des Modifications que la Réflexion imprime à la Lumière Polarisée,) was read to the Academy of Sciences in 1823. But the original paper was mislaid, and, for a time, supposed to be lost; it has since been recovered among the papers of M. Fourier, and printed in the eleventh volume of the Memoirs of the Academy.101 Some of the speculations to which he refers, as communicated to the Academy, have never yet appeared.102
Still Fresnel’s labors were, from the first, duly appreciated by some of the most eminent of his countrymen. His Memoir on Diffraction was, as we have seen, crowned in 1819: and, in 1822, a Report upon his Memoir on Double Refraction was drawn up by a commission consisting of MM. Ampère, Fourier, and Arago. In this report103 Fresnel’s theory is spoken of as confirmed by the most delicate tests. The reporters add, respecting his “theoretical ideas on the particular kind of undulations which, according to him, constitute light,” that “it would be impossible for them to pronounce at present a decided 116 judgment,” but that “they have not thought it right to delay any longer making known a work of which the difficulty is attested by the fruitless efforts of the most skilful philosophers, and in which are exhibited in the same brilliant degree, the talent for experiment and the spirit of invention.”
In the meantime, however, a controversy between the theory of undulations and the theory of moveable polarization which M. Biot had proposed with a view of accounting for the colors produced by dipolarizing crystals, had occurred among the French men of science. It is clear that in some main features the two theories coincide; the intervals of interference in the one theory being represented by the intervals of the oscillations in the other. But these intervals in M. Biot’s explanations were arbitrary hypotheses, suggested by these very facts themselves; in Fresnel’s theory, they were essential parts of the general scheme. M. Biot, indeed, does not appear to have been averse from a coalition; for he allowed104 to Fresnel that “the theory of undulations took the phenomena at a higher point and carried them further.” And M. Biot could hardly have dissented from M. Arago’s account of the matter, that Fresnel’s views “linked together”105 the oscillations of moveable polarization. But Fresnel, whose hypothesis was all of one piece, could give up no part of it, although he allowed the usefulness of M. Biot’s formulæ. Yet M. Biot’s speculations fell in better with the views of the leading mathematicians of Paris. We may consider as evidence of the favor with which they were looked upon, the large space they occupy in the volumes of the Academy for 1811, 1812, 1817, and 1818. In 1812, the entire volume is filled with a memoir of M. Biot’s on the subject of moveable polarization. This doctrine also had some advantage in coming early before the world in a didactic form, in his Traité de Physique, which was published in 1816, and was the most complete treatise on general physics which had appeared up to that time. In this and others of this author’s writings, he expresses facts so entirely in the terms of his own hypothesis, that it is difficult to separate the two. In the sequel M. Arago was the most prominent of M. Biot’s opponents; and in his report upon Fresnel’s memoir on the colors of crystalline plates, he exposed the weaknesses of the theory of moveable polarization with some severity. The details of this controversy need not occupy us; but we may observe that this may be considered as the last struggle 117 in favor of the theory of emission among mathematicians of eminence. After this crisis of the war, the theory of moveable polarization lost its ground; and the explanations of the undulatory theory, and the calculations belonging to it, being published in the Annales de Chimie et de Physique, of which M. Arago was one of the conductors, soon diffused it over Europe.