Simson,’ materially influenced his course of study, and made him familiar with the old as well as with the modern professors of geometry. He became a fellow of the Royal Society of Edinburgh in 1831, and he contributed several original and elaborate papers to its ‘Transactions.’ He also published ‘Researches on Terrestrial Magnetism’ in the ‘Philosophical Transactions,’ ‘Determination of the Law of Resistance to a Projectile’ in the ‘Mechanics' Magazine,’ and other papers in the ‘Cambridge and Dublin Mathematical Journal,’ the ‘Civil Engineer,’ the ‘Athenæum,’ the ‘Westminster Review,’ and ‘Notes and Queries.’ He was elected a fellow of the Society of Antiquaries 19 March 1840. In 1834 he was appointed one of the mathematical masters in the Royal Military Academy at Woolwich. Among the very numerous subjects which engaged his attention were researches on the properties of the trapezium, Pascal's hexagramme mystique, Brianchon's theorem, symmetrical properties of plane triangles, and researches into the geometry of three dimensions. His new system of spherical geometry preserves his name in the list of well-known mathematicians. His death, after six years of illness, took place at Broomhall Cottage, Shooter's Hill, Kent, on 6 Jan. 1851, when he was in his fifty-seventh year.
Davies edited the following works: 1. ‘A Course of Mathematics for the use of the Royal Military Academy, by Charles Hutton. The eleventh edition by Olinthus Gregory,’ 1837, 2 vols.; the principal alterations, additions, and improvements in this work were made by Davies. 2. ‘Solutions of the Principal Questions in Dr. Hutton's “Course of Mathematics,”’ 1840. 3. ‘A Course of Mathematics, by C. Hutton, continued by O. Gregory; twelfth edition by T. S. Davies,’ 1841–3, 2 vols. 4. ‘The Mathematician,’ ed. by T. S. Davies and others, 1845, 1847, and 1850. Of the above, No. 2, ‘Solutions of the Principal Questions,’ is the most important work. It is a large octavo of 560 pages, enriched with four thousand solutions on nearly all subjects of mathematical interest and of various degrees of difficulty. A long catalogue of Davies's writings is printed in the ‘Westminster Review,’ April 1851, pp. 70–83.
[Gent. Mag. May 1851, p. 559; Illustrated London News, xviii. 38 (1851); Mechanics' Mag. 11 Jan. 1851, pp. 33–5; The Expositor, an Illustrated Recorder (London, 1851), i. 284, with portrait.]
DAVIES, WALTER (1761–1849), Welsh bard and essayist, was born on 15 July 1761 at Wern in the parish of Llanfechan, Montgomeryshire, and with reference to his native parish he assumed in afterlife the bardic name of Gwallter Mechain. His parents were poor, and when they could keep him no longer at school he was obliged to have recourse to mechanical employment in the first instance, but subsequently he became a schoolmaster. In 1789 he was the successful competitor for the best Welsh essay on the ‘Life of Man,’ and in the following year he gained a premium at the St. Asaph Eisteddfod for an essay on ‘Liberty.’ About 1791 he obtained a clerkship at All Souls' College, Oxford, and while resident in the university he held office at the Ashmolean Museum. He graduated B.A. at Oxford in 1795, but took the degree of M.A. in 1803 at Cambridge, as a member of Trinity College (Cat. of Oxford Graduates, ed. 1851, p. 176; Graduati Cantab. ed. 1856, p. 103). On taking orders he became curate of Meivod, Montgomeryshire, and in 1799 he was nominated to the perpetual curacy of Yspytty Ivan, Denbighshire, which he held till his death. Subsequently he was collated by Bishop Horsley to the rectory of Llanwyddelan, Montgomeryshire, which he resigned in 1807, on being collated by Bishop Cleaver to the rectory of Manafon in the same county, in consequence, it was understood, of the assistance he rendered in correcting the orthography of the Welsh Bible, published about that time by the Society for Promoting Christian Knowledge. He resigned Manafon in 1837, on his collation to the vicarage of Llanrhaiadyr-yn-Mochnant, Denbighshire. He died at the latter place on 5 Dec. 1849.
Davies ranks high among Welsh scholars and bards. He gained numerous prizes for poetical and prose compositions at the Eisteddfodau, but at those held in 1793 and 1794 he and Davydd Ddu Eryri, the Snowdon bard, were suspended from being competitors for bardic prizes, on the ground that, if admitted, they were almost certain to leave no chance of success to others. Most of his poems are written in the ancient bardic style, only a small portion of them being Dyrivan, lyrical compositions in a style less severe, and more adapted to popular singing. His prose writings consist chiefly of prize essays and contributions to periodical publications on subjects connected with the topography, history, and language of Wales. He also wrote a ‘General View of the Agriculture and Domestic Economy of North Wales and South Wales,’ 3 vols. 1810, 1813, and 1816, 8vo, published by order of the Board of Agriculture; and prepared editions of the Welsh poems of Hugh Morris, 2 vols. 1823, 12mo, and (conjointly with the Rev. John Jones) the ‘Poetical Works of Lewis Glyn Cothi,’
