Arthur Turnour Atchison was born on May 16, 1848, in Bath, Somerset County, England.

He was educated in Brighton College and in 1866, he went to Christ’s College, Cambridge. During his residence at Cambridge, he acquired considerable distinction as an oarsman and a gymnast. There he received both his B.A. (1870) and his M.A. (1873) degrees in Civil engineering and became a member of the Association of Civil Engineers. He assisted in superintending the construction of the Alexandra Docks in Wales. After spending some time in the office of Mr. Bailey Denton, a surveyor and civil engineer, he started his own company in London in 1877. His chief work related to the preparation of reports and plans for parliamentary deposit in connection with railways, tramways, and schemes for water supply. He assisted in the construction of the Shanghai Waterworks and in the preparation of a scheme for the water supply of St. Vincent. In 1872, Atchison became a member of the British Association and in 1874, he undertook the duties of Secretary of Section G (Mechanics). He filled the same office again in 1877, and from that time continuously until 1886, accompanying his Section to Montreal in 1884. He contributed articles on mechanical subjects to Nature. He was also a Secretary of the Association at Birmingham, 1886; Manchester, 1887; Bath, 1888, and Newcastle, 1889. In 1875, he visited Ceylon and in 1881, Florida to report on some proposed work.

In 1876, he married Rachel Rogers (1853–1940). He died of consumption on April 21, 1891, in Mentone, Provence-Alpes-Côte d'Azur, France.