He was born in Magherahamlet, County Down, the eldest son of Rev Richard Archer, vicar of Clonduff.
He was one of the twelve founder (1849) members of the Dublin Microscopical Club. Between 1858 and 1885 he wrote over 230 scientific papers in the Quarterly Journal of Microscopical Science, Proceedings of the Natural History Society of Dublin, the vast majority are short notes on desmids collected in Ireland.Sometimes the same article was published in two or more journals.
He was appointed Librarian of the National Library of Ireland from 1877 to 1895. "Archer was my chief in the National Library of Ireland during my first three years of service there - a rather dreamy man, prematurely old (for he took no care of his health), living in a small house in Hatch-street with a scapegrace young nephew and a would-be housekeeper, and spending his off-time chiefly in the reading-room of the Royal Dublin Society next door to the National Library. He forgot even his meals sometimes. Once when he had gone on leave a marked odour began to pervade the Librarian’s office, which grew so insistent as the days went by that the Head Attendant and I were forced to investigate. We eventually found in his private drawer two herrings, very much the worse for wear!" Robert Lloyd PraegerSome Irish naturalists: A Biographical Note-book W.Tempest, Dundalgan Press, Dundalk, 1949
Prescott G.W., 1984 Bibliographia Desmidiacearum Universalis (A Contribution to a Bibliography of Desmid Systematics, Biology and Ecology from 1774-1982). Koeltz Scientific Books, Koenigstein. 612 pp. Full list of papers on desmids.