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BIO his instrument on the mountain Desierto de las Palmas, Biot accompanied Rodrignez to the island of Yvica, in the hope of finding a mountain from which the signal on the Desierto could be seen. After leaving Rodriguez at Campvey, Biot returned to Spain to join his colleagues on the Pyrenees; but he was seized with fever, and obliged to repair to Tarragona for the recovery of his health. In April, 1807, all the triangles in the island were finished, and the whole chain of triangulation about the end of autumn. Biot went to Paris in April to have a new circle constructed, and afterwards joined his friends in Spain at Valence. After spending the winter in the island of Formentara, our astronomer embarked for Spain in a small Algerine ship, leaving with Arago the Spanish vessel and the English safe passport. He was, however, captured by the pirates of Ragusa, from whom he purchased his liberty, and afterwards landed at Denia, where he performed a short quarantine in a ruined chateau that had once been the residence of the dukes of Medina Cœli. Leaving Arago to complete his labours, Biot returned to Paris and submitted his observations to the board of longitude.—(See Arago's Biography of Distinguished Men; Autobiog. of Arago, pp. 12-24, for some anecdotes of Biot. London, 1827. See also Biot's notice—"Sur les operations faites en Espagné pour prolonger la Meridienne de France jusqu'aux Isles Pythiuses," which though read to the Academy in 1810, was not published till 1820, in the Memoirs of the Academy for 1818, tom. iii. p. 73.)

After the publication of Dr. Young's papers on the Huygenian theory of light (the undulatory theory, as it is now called), and of Dr. Wollaston's experimental confirmation of Huygens' explanation of the double refraction of Iceland spar, the attention of continental philosophers was drawn to the subject of double refraction. In 1808 the Institute of France proposed it as the subject of a prize, to be adjudged in 1810. The prize was gained by M. Malus, colonel of the imperial corps of engineers, who, in the course of his researches, made the important discovery of the polarization of light by reflection from the surfaces of transparent bodies, a property of light which Huygens had discovered in doubly refracting crystals more than a hundred years before the attention of the members of the Institute was drawn to this remarkable discovery. In 1811 M. Arago communicated to the Academy of Sciences his important discovery of the colours of thin plates of crystallized bodies when examined in polarized light, a discovery made independently by Sir David Brewster. M. Biot saw the extent and importance of this new branch of optics, and devoted to it all the energies of his powerful mind. In 1812 he communicated to the Academy a memoir of one hundred and forty-five pages, "On the new relations which exist between the reflection and the polarization of light by crystallized bodies," in which he made many important experiments on the colour of thin plates of sulphate of lime and quartz, by means of a divided apparatus and a spherometer, for measuring the thickness of the thinnest plates; and from these experiments he concluded, that the polarization of light in these two minerals follows exactly the same laws and the same periods as ordinary reflection in thin plates of air or glass, with this difference only, that the two classes of phenomena take place at different thicknesses. In a second memoir, read in the same year, he announced that he has found in the polarization of light a law analogous to that of the conservation of living forces in mechanics, which he derived from the fact that the same tint is produced by any number of laminæ combined, whatever be the order of their combination, provided that their axes are parallel.

In order to explain the remarkable phenomena of coloured polarization, our author devised what he has called the theory of moveable polarization, which he communicated to the Academy of Sciences in November, 1812, with the title of "A new kind of oscillation which the molecules of light experience in traversing certain crystals." In this profound and ingenious memoir, which forms a quarto volume of three hundred and seventy-one pages, he supposes light to consist of separate particles, which oscillate round their centres of gravity in virtue of attractive and repulsive forces, and that after these oscillations have gone on to a certain depth in the crystal, the particles acquire a fixed polarization, by which their axes are arranged in two rectangular directions.

In two memoirs read to the Academy of Sciences in 1814, Biot has given an account of his important discovery of two kinds of polarization, which he calls polarization quartzeuse, from its being found in quartz, and the other polarization berilleuse, from its being found in beryl. In the former the extraordinary ray is supposed to be produced by an attractive force drawing it to the axis of the crystal, and in the latter by a repulsive force, which drives it from the axis. In quartz the phenomena are represented by the variable radii of a prolate spheroid, and in beryl by those of an oblate spheroid. In his early experiments M. Arago had observed a particular kind of polarized tints along the axes of quartz, but did not study them with attention. M. Biot, however, undertook the examination of them, under the name of successive polarization, and ascribed the phenomena to the continual rotation of the luminous particles round their axes. In the end of 1815 and the beginning of 1816, he and M. Seebeck of Berlin discovered about the same time an analogous property, now called circular polarization, in a number of essential oils, vegetable juices, and other fluids—in oil of turpentine, oil of laurel, and various saccharine solutions—some of which turned the planes of polarization from left to right, and others from right to left. In the uncrystallizable syrup called dextrine, from its turning the planes of polarization from right to left, M. Biot found circular polarization so strong, that it surpassed, in this respect, all other substances excepting rock crystal.

With the view of proving that this property of certain solids and fluids resided in the individual molecules of which the bodies were composed, and not to their mode of aggregation (Sir D. Brewster found that quartz lost the rotatory property after fusion), our author resolved to make the experiment with the vapour of turpentine. A suitable apparatus for this purpose was accordingly erected in an old church, which had become the orangerie of the chamber of peers. It consisted of a furnace and boiler to produce the vapour, of a double tube about one hundred feet long to hold it, of a plate of glass at one end of the tube to polarize the light of a lamp, and of a divided circle and an achromatised prism at the other end to show and measure the rotation. With the help of two assistants, Biot observed that the image of the Iceland spar, which had disappeared when the tube was filled with air, assumed a slightly bluish-green tint, while the other image changed into a reddish yellow, a result which indicated the existence of a full rotation, produced by one hundred feet of the vapour of turpentine. Our author then proceeded to turn the analysing prism from right to left, in order to see if the rotation was in the same direction as in the fluid essence of turpentine, when a tremendous explosion took place. The cover of the boiler was blown into the air, the vapour of the fluid turpentine was set on fire, and the column of fire was so alarming that the distracted philosopher was obliged to call in the nearest fire-engine to extinguish the flames. The escape of the two assistants was most providential, for if Biot had not called them to the end of the tube most distant from the boiler, in order to see the result of the experiment, they would both have been killed. These experiments are described in a bulky memoir of nearly one hundred pages, entitled "On the Rotations which certain substances impress on the axes of polarization of the luminous rays."—(Mem. de l'Academie de Sciences, 1818, tom. ii. p. 41.)

In the year 1818 M. Biot communicated to the Academy of Sciences a long but interesting memoir "On the utility of the Laws of the Polarization of Light for recognizing the state of crystallization and combination in a great number of cases where the crystalline system is not immediately observable." In this memoir he showed, from the analyses of Vauquelin, that in micas with two axes of different inclinations, or with one axis of different characters, the chemical composition is different. In the uniaxal crystals Vauquelin found a considerable quantity of magnesia, of which there was no trace in those which were biaxal, while in the biaxal crystals with different angles between the optic axes there was a great difference in the silica, alumina, and oxide of iron which they contained. In the same year he published a long and valuable memoir "On the rotations which certain substances impress on the axes of polarization of the luminous rays" (Mem. Acad. Paris, 1818, tom. ii. pp. 41-137), a subject which he resumed at various times, both in separate memoirs, and in reports on the discoveries of M. Pasteur.

In order to execute a map of Great Britain and Ireland, General Roy and Colonel Mudge had measured an arc of the meridian from the south of England to the north of Scotland. The French board of longitude were desirous of joining to this arc the one measured in France and Spain, and to take measures of the length of the pendulum along the arc in Britain,