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THREE:In 1720 Colin Maclaurin, the successor of James Gregory in the mathematical chair at Edinburgh, published his "Geometrical Organica," a treatise on curves; in 1742 his admirable treatise on Fluxions; and in 1748 his treatise on Algebra. Dr. Robert Simson, professor of mathematics at Glasgow, published a restoration of the "Loci" of Apollonius, and an English translation of Euclid, which continued down to a late period in use, both in Scotland and England. In 1717 James Stirling published a Latin treatise on lines of the third order, and another on Fluxions, called "Methodus Differentialis," in 1730. William Emerson, a mathematician and mechanist, wrote on fluxions, trigonometry, mechanics, navigation, algebra, optics, astronomy, geography, dialling, etc., but a considerable portion was only in part published during this period. Thomas Simpson, a weaver, of Market Bosworth, at the age of seven-and-twenty suddenly discovered himself as an extraordinary mathematician, and went on till his death, in 1761, publishing works on fluxions, the nature and laws of chance, on mixed mathematics, on the doctrine of annuities and reversions, on algebra, elementary geometry, trigonometry, etc. James Ferguson, also, the son of a day-labourer, in Banffshire, studied mathematics whilst tending sheep, and published a number of works on the phenomena of the harvest moon, astronomy, mechanics, hydrostatics,[154] pneumatics, and optics. Ferguson had a remarkably lucid and demonstrative style, both in writing and lecturing, and his example excited a keen spirit of inquiry amongst the working classes, so that he is said to have diffused the knowledge of physical science amongst the class from which he sprang more than any other man.The expedition against England was at this moment actually in motion. The squadrons of Brest and Rochefort were already united under the command of Admiral Roquefeuille, and sailing up the Channel to clear the way for the transports containing the soldiers. Sir John Norris had been appointed Admiral of our Channel fleet, consisting of twenty-one ships of the line. He had lain at Spithead, but had quitted that station and sailed into the Downs, where he was joined by other ships from Chatham; and thus was not only superior in number to the French, but had the advantage of being well acquainted with the coasts, he having long been Captain of Deal Castle. Roquefeuille sailed right up to the Isle of Wight, and, observing no vessels off Spithead, he, in his French egotism, concluded that the fleet had sought shelter in Portsmouth harbour. He therefore lost no time in despatching a small vessel to Dunkirk to hasten on his armament. Seven thousand men were instantly sent on board transports, and the prince and Marshal Saxe, who was to take command of the land force, accompanied them. Roquefeuille, meanwhile, proceeding on his voyage, came to anchor off Dungeness, which he had no sooner done than he beheld the British fleet bearing down upon him in much greater force than his own, for he had only fifteen ships of the line and five frigates. The destruction of the French fleet appeared inevitable, but Sir John Norris this time justly incurred the censure of lingering. He thought, from the state of the tide and the approach of night, it was better to defer the attack till morning; and, when morning came, no Frenchmen were to be seen. The French admiral, much more active than poor old Sir John, had slipped his cables and made the best of his way homewards.