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divinity and graduated M.A. It was intended that he should become a minister, but he chose to follow his father's profession. Through the interest of the Earl of Kinnoul, then chancellor of the university, he was nominated by Lord Adam Gordon a cadet of artillery at Woolwich. On the outbreak of the American war in 1775, Glenie embarked with his regiment for Canada, becoming second lieutenant on 3 Nov. 1776. He so distinguished himself that he was transferred from the artillery to the engineers as practitioner engineer and second lieutenant on 23 Feb. 1779. While engaged in his professional duties he found time to write some scientific essays which were submitted by his friend Francis Maseres to the Royal Society. His dissertations on ‘The Division of Right Lines, Surfaces, and Solids’ (‘Phil. Trans.’ lxvi. 73), and on ‘The General Mathematical Laws which Regulate and Extend Proportion Universally’ (ib. lxvii. 450), were deemed valuable enough to procure him election as fellow on 18 March 1779 without fees (Thomson, Hist. of Roy. Soc. app. iv. p. lvii.) Towards the close of 1780 Glenie returned to England, and soon afterwards married Mary Anne Locke, a daughter of the storekeeper at Plymouth, by whom he had three children. The Duke of Richmond, who became master-general of the ordnance in 1783, conceived the idea of fortifying all the naval arsenals and of forming lines of defence on the coast, and was anxious to obtain Glenie's approbation of his plans. Glenie rashly declared them absurd and impracticable, and advised their total abandonment. Mr. Courtenay, the secretary of Lord Townshend, the duke's predecessor as master-general of the ordnance, invited Glenie to his house for a few days, and asked him to write a pamphlet condemning the duke's schemes. Thereupon Glenie issued ‘A Short Essay on the Modes of Defence best adapted to the Situation and Circumstances of this Island … by an Officer,’ 8vo, London, 1785. The duke published an ‘Answer,’ to which Glenie replied. The proposals were negatived in parliament in 1786. Though Glenie was promoted to a first lieutenancy in 1787 (Army List, 1787, p. 372), he retired from the army during the same year, and subsequently emigrated to New Brunswick. Here he purchased a tract of land, and was elected a representative of the House of Assembly. He became a contractor for ship timber and masts for government, but the speculation failed, and both Glenie and his partner were ruined. Forced to return to England, Glenie applied to the Earl of Chatham, who, unable to find him regular employment, retained him as engineer extraordinary. By his recommendation, however, Glenie was appointed in 1806 instructor to the East India Company's young artillery officers with salary and fees amounting to 400l. a year. Unluckily for him he was summoned as a witness for the crown at the prosecution of G. L. Wardle, M.P., on 10 Dec. 1809, and his evidence having called forth the severe censure of Chief-justice Ellenborough (Trial, pp. 42–3), he was soon afterwards dismissed from his situation. In November 1812 Glenie went to Copenhagen to negotiate for an ex-member of parliament the purchase of a large plantation in Denmark. He never received any compensation for his trouble. As a last resource he attempted to procure a few mathematical pupils, but did not meet with much success. He died in poverty at Chelsea on 23 Nov. 1817, and was buried in the churchyard of St. Martin-in-the-Fields. He was also author of: 1. ‘The History of Gunnery, with a new method of deriving the theory of projectiles in vacuo from the properties of the square and rhombus,’ 8vo, Edinburgh, 1776. 2. ‘The Doctrine of Universal Comparison, or General Proportion,’ 4to, London, 1789. 3. ‘Observations on Construction,’ 8vo, London, 1793. 4. ‘The Antecedental Calculus, or a Geometrical Method of Reasoning, without any consideration of motion or velocity applicable to every purpose to which fluxions have been or can be applied, with the geometrical principles of increments,’ &c., 4to, London, 1793. 5. ‘Observations on the Duke of Richmond's Extensive Plans of Fortification, and the new works he has been carrying on since these were set aside by the House of Commons in 1786, including the Short Essay which chiefly occasioned the famous debate and division in the House of Commons on his Grace's projected works for Portsmouth and Plymouth,’ 8vo, London, 1805. 6. ‘Observations on the Defence of Great Britain and its Principal Dockyards,’ 8vo, London, 1807. To the ‘Transactions’ of the Royal Society of Edinburgh he contributed papers ‘On the Principles of the Antecedental Calculus,’ iv. 65, ‘On the Circle,’ vi. 21, and ‘On a Boy born Blind and Deaf,’ vii. 1. In F. Maseres's ‘Scriptores Logarithmici’ will be found his ‘Problem concerning the Construction of a certain Triangle by means of a Circle only,’ vol. iv., commented on by Maseres in vol. vi., and ‘A Demonstration of Sir I. Newton's Binomial Theorem,’ vol. v. Glenie was at all times a prominent fellow of the Royal Society, and, at the meeting convened on 12 Feb. 1784 to consider the conduct of Sir J. Banks with regard to Dr. Hutton, distinguished himself by a vigorous speech in