[1] Davies made his earliest communications to the Leeds Correspondent in July 1817 and the Gentleman's Diary for 1819.
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 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.
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.
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.