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Barlow of Dr. Hutton, professor of mathematics at Woolwich. By Hutton's advice he sought, and after a severe competitive examination obtained, in 1801, the post of assistant mathematical master, from which he was subsequently advanced to that of professor, in the Royal Military Academy. His first book, ‘An Elementary Investigation of the Theory of Numbers,’ was published in 1811, and was succeeded in 1814 by ‘A New Mathematical and Philosophical Dictionary.’ In the same year appeared his ‘New Mathematical Tables,’ giving the factors, squares, cubes, square and cube roots, reciprocals and hyperbolic logarithms of all numbers from 1 to 10000, together with the first ten powers of numbers under 100, and the fourth and fifth of all from 100 to 1000. The principal part of this vast mass of accurate and highly useful numerical information was reprinted in stereotype (1856) by the Society for the Diffusion of Useful Knowledge, under the supervision of Professor De Morgan. Barlow's merits, however, were first rendered conspicuous by the publication, in 1817, of an ‘Essay on the Strength of Timber and other Materials’ (6th ed. 1867), supplying, as the results of numerous experiments in Woolwich dockyard, much-needed data for the calculations of engineers. The experiments upon the resistance of iron which formed the basis of the design for the Menai suspension bridge were submitted by Telford to his examination, and were printed as an appendix to the third edition of his ‘Essay’ (1826). His services to the profession were acknowledged by admission, in 1820, as an honorary member, to the Institution of Civil Engineers.

In 1819, with a view to devising a remedy for the large deviations of the compass due to the increasing quantities of iron used in the construction and fittings of ships, he undertook the first experimental investigation ever attempted of the phenomena of induced magnetism. The remarkable fact that the intensity of magnetic effects depends not on mass, but on extent of surface, established by his observations on the deflections produced in a magnetised needle by vicinity to an iron globe, as well as an empirical law of such deflections, were shown by Poisson in 1824 to be mathematically deducible from Coulomb's hypothesis of magnetic action (Mém. de l'Institut, v. 261, 336). In his ‘Essay on Magnetic Attractions’ (1820), Barlow gave the details of his experiments, and described a simple method of correcting ships' compasses by fixing a small iron plate in such a position as to compensate all other local attractions. After successful trial in various latitudes, it was adopted by the admiralty, but has not proved adequate to its purpose in ships built wholly of iron. For this invention he received from the board of longitude a grant of 500l., besides presents from the chief naval boards; from the Emperor Alexander, on its introduction into the Russian navy in 1824, a gold watch and chain; and in 1821 the gold medal of the Society of Arts.

In a second enlarged edition of his work, published in 1823, Barlow succeeded in connecting the whole of his experimental results by a mathematical theory based on a few simple assumptions; the effects of varying temperature on the magnetic power of iron were first recorded in detail (see also his paper ‘On the anomalous Magnetic Action of Hot Iron between the White and Blood-red Heat,’ Phil. Trans. cxii. 117), while additional sections were introduced for the theoretical and experimental illustration of the new science of electro-magnetism. In an essay ‘On the probable Electric Origin of all the Phenomena of Terrestrial Magnetism,’ communicated to the Royal Society on 27 Jan. 1831, he described an ingenious experiment (strikingly confirmatory of Ampère's theory) showing the precise similarity between the action of the earth on the magnetic needle and that of a wooden globe coiled round with copper wire carrying a galvanic current (Phil. Trans. cxxi. 104). He moreover employed a neutralised needle in his magnetic researches (Phil. Trans. cxiii. 327), and made an early attempt at signalling by electricity. The publication in 1833 of a variation chart embodying a large amount of new information (Phil. Trans. cxxiii. 667) closed the list of his contributions to this branch of science.

His optical experiments began about 1827. In the course of some efforts to reduce to practice rules for the curvatures of achromatic object-glasses given by him in vol. cxvii. of the ‘Philosophical Transactions,’ he was met with the difficulty of procuring suitable flint-glass, and immediately set himself to devise a substitute. This he found in disulphide of carbon, a perfectly colourless liquid, with about the same refractive, and more than twice the dispersive power of flint-glass. He accordingly constructed two telescopes, of respectively 3 and 6 inches aperture, in which the corrections both for colour and curvature were effected by a concavo-convex lens composed of this substance enclosed in glass, of half the diameter of the plate-lens, and fixed at a distance within it of half its focal length (Phil. Trans. cxviii. 107; see also in Astronomische Nachrichten, No. 127). Aided by a grant from the board of longitude, he shortly after advanced to an