He was born on 1 January 1795. Davies made his earliest communications to the
Leeds Correspondent in July 1817 and the ''
Gentleman's Diary for 1819. He subsequently contributed largely to the Gentleman's and Lady's Diary'', Clay's
Scientific Receptacle, the
Monthly Magazine, the
Philosophical Magazine, the
Bath and Bristol Magazine, and the ''Mechanics' Magazine''. Davies was elected a
Fellow of the Society of Antiquaries of London, 19 March 1840 Davies's early acquaintance with Dr.
William Trail, the author of the
Life of Dr. Robert 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''. In 1831 he was elected a Fellow of the
Royal Society of Edinburgh his proposer being
John Shoolbred. In April, 1833 he was elected a
Fellow of the Royal Society. In 1834, he was appointed one of the mathematical masters in the
Royal Military Academy at
Woolwich. Among the numerous subjects that 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 presentation "On the Velocipede" in May 1837 is extant as a manuscript and gives a vivid testimony of the rise and putting down of the draisines aka hobby-horses. He must have been an early hobby-horse rider himself according to that (transcript in
The Boneshaker #108(1985) pp. 4–9 and #111(1986) pp. 7–12)) His death, after six years of illness, took place at Broomhall Cottage,
Shooter's Hill,
Kent, on 6 January 1851, when he was in his fifty-seventh year. ==Publications==