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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.

THREE:Argyll, who received the news of the retreat about four in the afternoon of that day, occupied Perth with Dutch and English troops by ten o'clock the next morning. They had quitted Stirling on the 29th, and that night they encamped on the snow amid the burnt remains of the village of Auchterarder. Argyll and Cadogan followed the advanced guard and entered Perth on[32] the evening of the 1st of February; but the remainder of the troops did not arrive till late at night, owing to the state of the roads and the weather. Some few of the rebels, who had got drunk and were left behind, were secured. The next day Argyll and Cadogan, with eight hundred light foot and six squadrons of dragoons, followed along the Carse of Gowrie to Dundee. Cadogan, in a letter to Marlborough, complained of the evident reluctance of Argyll to press on the rebels. When he arrived at Dundee on the 3rd, the rebel army was already gone. He and Cadogan then separated, taking different routes towards Montrose. Cadogan, whose heart was in the business, pushed on ahead, and on the 5th, at noon, reached Arbroath, where he received the news that the Pretender had embarked at Montrose and gone to France. In this manner did the descendant of a race of kings and the claimant of the Crown of Great Britain steal away and leave his unhappy followers to a sense of his perfidious and cruel desertion. His flight, no doubt, was necessary, but the manner of it was at once most humiliating and unfeeling. The consternation and wrath of the army on the discovery were indescribable. They were wholly broken up when Argyll reached Aberdeen on the 8th of February.

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