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gaged, the Royal Society awarded in 1811 the Rumford medal to Malus for his researches, the decision being notified to him in a letter of the most complimentary character from Dr. T. Young (then the foreign secretary of the Society) enhancing the acknowledgment of Malus's merits by the candid confession that his discovery seemed to subvert Dr. Young's own theory of waves. Such was the impression at first produced by a phenomenon soon after destined to afford the strongest confirmation of that theory. We cannot follow the minute points connected with this capital discovery, many of which continued to engage Malus's attention in conjunction with that of Arago and Fresnel, until his constitution, already broken by the fearful sufferings and toils he had undergone, finally gave way, under the inroads of a consumption which terminated his life towards the close of 1811, at the early age of thirtysix. Fresnel and Arago were thus left to pursue the research with only the aid of correspondence with Young. Fresnel, always in delicate health, still devoted his energies with a singular success and felicity of resources (only to be appreciated by those who profoundly study the mathematical theory) until, sinking under the pressure of disease, he just lingered to receive on his dying bed the valued testimonial of the Royal Society's Rumford medal in 1827.

The various properties of polarised light were soon successively disclosed:-its relation to double refraction; the reverse experiment of applying the reflector or the doublerefracting crystal to test or analyse the polarisation; the use of tourmaline for the same purpose; the laws of the variation of intensity of the light at different azimuths of the analyser; and lastly Sir D. Brewster's law, that the maximum polarising effect takes place at the angle whose tangent is the index of refraction of the substance.


There is an innate love of the marvellous and mysterious in the human mind, and it seems there is something in the term polarisation' in a high degree calculated to command public reverence and awe. In any branch of science the experimentalist, when he meets with any new but obscure phenomenon, has only to look solemn, and pronounce it to be a species of polarity,' and the popular voice immediately accords to him the credit of a profound discovery. When the Library of Useful Knowledge' came out in numbers, we remember hearing it stated, that of all the scientific tracts, that on Polarisation' had by far the largest sale. The many thought there was some occult mystery in it, and that in proportion as it was incomprehensible it must be more deeply

philosophical. Nor was this altogether without foundation in the perplexity and obscurity in which the first announcement of this property seemed to be involved even among philosophers, and in some measure even in the minds of those who discovered and investigated it. And it is by no means one of the least curious circumstances in the history of this theory that it was soon found itself to furnish the solution of those difficulties, which at first seemed so fatal to its admission.

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In 1811 Arago published a discovery of an entirely new class of facts connected with polarisation: and doubtless from the same want of communication with the Continent, already referred to in a similar case, it occurred that Sir D. Brewster was at the same time independently working on the same subject, though his results were not published till 1813. These phenomena have been distinguished by the names of depolarisation, or, as suggested by Professor J. Forbes, more expressively dipolarisation, or more commonly polarised tints,' polarised rings, that is, the succession of tints of colour displayed by plates of various crystals, such as those of mica and selenite, or calcspar cut perpendicular to its axis, when polarised light is transmitted through them and examined by an analyser. Similar phenomena were discovered by Brewster in glass artificially compressed, or in an unanealed condition; and in certain cases of crystals with two axes, where the rings assume peculiar forms, by Sir J. Herschel. These tints were employed by Arago to detect the existence of polarisation in light from various sources, as for instance, in that of the planets and comets, proving it to be reflected, and in the diffuse light of the atmosphere dependent on the place of the sun; an idea which Professor Wheatstone has so ingeniously applied to the construction of a polariscopic dial.

The explanation of these phenomena was not for some time apparent. Young, in 1814, ascribed them generally to interference: but Arago soon noticed that this explanation was incomplete. It remained so until he and Fresnel jointly succeeded in demonstrating a new law, that two polarised rays cannot interfere unless polarised in parallel planes.' This afforded the clue to the polarised tints, though at first sight seeming to have little connexion with them. It directly involved the idea of vibrations transverse to the direction of the ray. The two rays into which the light is divided in traversing the plate of crystal have their vibrations at right angles to each other; and therefore cannot interfere. But the application of the analyser resolves each ray into two, one parallel to its own plane, and one perpendicular, which it suppresses. The two which reach the

eye are in the same plane, and thus directly manifest their interference, and produce the periodical colours.

Yet to reconcile the idea of these transverse vibrations with the dynamical conditions of a wave was long a serious difficulty in the minds of the philosophers who adopted it. Fresnel would hardly venture to embrace, still less to announce, an idea which he believed so much at variance with dynamical principles.

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Dr. Whewell mentions from personal information, that

Arago was wont to relate that when he and Fresnel had obtained their joint experimental results, of the non-interference of oppositely polarised pencils, and that when Fresnel had pointed out that transverse vibrations were the only possible translation of this fact into the undulatory theory, he himself protested that he had not the courage to publish such a conception; and accordingly the second part of the memoir was published in Fresnel's name alone. What renders this more remarkable is, that it occurred when Arago had in his possession the very letter of Young (1818), in which he proposed the same suggestion.'*

We have, however, a familiar though rough illustration in a rope fastened at one end and agitated at the other by the hand, when we can easily cause a series of waves to run along it; but the particles of the rope really retain their original distances from the hand, and merely move up and down in directions transverse to its length. In a somewhat similar way the ethereal molecules are, according to this theory, made to vibrate, or, as Fresnel graphically expressed it, to tremble laterally.'

The dynamical views of the subject followed out by Fresnel were more systematic than those of Young; yet neither of them were so fully developed as to be free from obscurities and they still involved assumptions which seemed in some degree gratuitous. Nevertheless the idea of transverse vibrations once admitted, its consequences were readily seen to influence the whole conception of the theory of waves. By the application of the theory of transverse vibrations the mysterious agency of polarisation was reduced to the simplest of all mechanical conceptions-a resolution of rectilinear motion into two components at right angles. A ray impinging on a plane surface at a certain angle, with its transverse vibrations in all possible planes round the line of its direction, has every one of them resolved into two: one parallel to the surface, the other perpendicular to it; one set are reflected, the other transmitted. The same thing happens in transmitting a ray through a doubly-refracting crystal, each set

* Hist. of Inductive Sciences, vol. ii. p. 418.

forming a separate ray; in passing through a tourmaline, one set is suppressed or absorbed.

Fresnel's investigations have in fact formed the basis of all subsequent mathematical views of the theory. From the general idea of transverse vibrations he advanced to the deduction of formulas of a very comprehensive character, embracing all the laws of polarised light, including Brewster's law of the tangent (before mentioned), which was thus shown to be a consequence from theory, as were several other observed facts which had occasioned considerable perplexity in the first instance.

One other result was the singular anticipation, from a mere interpretation of an algebraical symbol, made by Fresnel, that a ray polarised at half-right angles to the plane of incidence, after two internal reflexions in glass, will emerge with vibrations no longer rectilinear, but performed in circles; if at any other inclination, in ellipses. Experiment confirmed the remarkable prediction: such a ray differs both from common and plane polarised light, and is said to be circularly or elliptically polarised. It was some time after proved to be the same modification which Brewster had found to be imparted to light by reflexion from metals, and had, on a different analogy, called by the same name. This subject of circular and elliptic polarisation, especially in the reflexion of metals, has opened a wide field of research. The polarised rings in such light undergo a curious dislocation in their form, which is fully explained by the formulas of theory, and has been used to detect such polarisation in a variety of cases, especially in some investigations of Mr. Airy. The effect was always supposed due to some peculiarity in metals. But Professor Powell found it in the reflexion from some substances not metallic, a fact further generalised by Mr. J. A. Dale in a valuable research (to which, we think, due justice has not been done*), by which he showed the existence of elliptic polarisation, in the reflexion from a number of substances wholly non-metallic but agreeing with metals in having very high refractive powers; this then is the immediate cause of ellipticity, and not metallic character as such, as commonly asserted.

To return: Arago was the first who observed a yet more remarkable case of polarised tints, presented by plates of quartz, or rock crystal, cut perpendicular to the axis; they were analysed by Biot, up to the essential fact that a series of tints are developed in a certain order, as the analyser is made to revolve, the cause of which is that as the polarised ray traverses

See British Association Report, 1846, section A.

the crystal its plane of polarisation is continually changing, and this in a different degree for each primary ray. Thus, on emergence the analyser transmits a ray of that colour whose vibrations accord with its position, and consequently different tints as it rotates. The tint will also vary with a different thickness of the plate. This twisting of the plane of polarisation takes place in some specimens of rock crystal towards the right hand, in others towards the left; and this has been found by Sir J. Herschel to correspond to a like peculiarity in the disposition of the natural facets round the summit of the crystal. The same property was observed by Biot and Seebeck in certain liquids, and even vapours.

The peculiar phenomena exhibited by quartz, in polarised light, above mentioned, were subjected to theoretical inquiry in the first instance by Fresnel, who proved that along the axis the light consists of two circularly polarised portions superimposed; and afterwards by Mr. Airy, who showed that in other directions the two corresponding portions are elliptically polarised, in opposite directions. The theory was still further followed out in connexion with mathematical considerations by Professor Maccullagh. This investigation is perhaps on the whole the most difficult and complex of any which the theory of undulations presents, and can hardly yet be said to have been fully elucidated in all points, especially in its connexion with a dynamical theory. The phenomenon is expressively designated by the term rotatory polarisation.' It is this property which has been so marvellously shown by Professor Faraday to be communicated to glass by magnetism.

Another remarkable class of phenomena, first examined by Arago in 1817, were the changes in the colours of thin films in polarised light. Some analogous inquiries were afterwards pursued by Mr. Airy, which have an important bearing on the confirmation of the theory; and some similar experiments were made by Nobili, especially on the beautiful coloured metallic films which he had produced by galvanic deposition. These researches are closely connected with the general question of the reflexion from metallic' surfaces which is still surrounded with difficulties that have exercised the talents of several eminent mathematicians; and in relation to which the late Professor Maccullagh produced some very elaborate and profound researches, of which his deeply lamented premature death prevented the completion. But the subject has been much elucidated and brought into closer relation to the formulas of Fresnel, by the recent investigations of M. Jamin, and in a different point of view, by those of Professor Stokes.

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