Obtiene su título de doctor en medicina en 1844, en Dublín. Fue tesorero colonial en ciudad del Cabo de 1836 a 1842 donde recolecta muchos especímenes vegetales.
En 1844, es curador del herbario del "Colegio Trinity de Dublín", y, en 1848, profesor de botánica en la "Sociedad Real de Dublín", y, en 1856, en el "Colegio Trinity".
Se interesa particularmente de las algas marinas. Harvey se opuso a la teoría de la evolución propuesta por Charles Darwin (1809-1882).
Algunas publicaciones
Cubierta de Nereis Boraeli-Americana or Contributions to a History of the Marine Algæ of North America, 1853.
1833. Div. II. Confervoideae. Div. III. Gloiocladeae. En Hooker, W.J. (ed.) The English flora of Sir James Edward Smith5. Londres
1834. Algologhical illustrations. No. 1 Remarks on some British algae and descriptions of a new species recently added to our flora. J. Bot. Hooker 1: 296 - 305
1838. The genera of South African plants. Ciudad del Cabo, 429 pp
Description of Ballia, a new genus of Algae. Hooker's J. Bot. 2
1841. Manual of British Algae
1844. Description of a minute alga from the coast of Ireland. Ann. and Magagazine of Natural History 14: 27 - 28
1844. Description of a new British species of Callithamnion (C. pollexfenii)Ann. and Magagazine of Natural History 14: 109 - 131
1844. Algae of Tasmania, J. of Bot. Londres, 3: 428 - 454
1850. Observations on the Marine Flora of the Atlantic States. Proc. Am. Assn. Adv. Sci.: 79 - 80
1851. Nereis Boreali-Americana:... Parte I. Melanospermaea. Smithsonian Institution
1853. Nereis Boreali-Americana:... Parte II. Rhodospermeae
1855. Some account of the marine botany of the colony of Western Australia. Trans. of the Royal Irish Acad. 22: 525-566
1855. Algae. En J.D.Hooker, The Botany of the Antarctic Voyage 2: Flora Nova-Zelandiae II. Londres, 211 - 266, pl. 107 - 121
1857. Nereis Boreali-Americana:... Parte III. Chlorospermeae
1857. Sea-side Book 1849, 4ª ed.
1857. Short description of some new British algae, with two plates. Nat. Hist. Rev.4: 201 - 204
1858. List of Arctic Algae, Chiefly Compiled from Collections Brought Home by Officers of the Recent Searching Expeditiions. Smithsonian Contrib. to Knowledge. Parte III, Supl. 2: 132 - 134
1860. Algae. pp. 242 - 383, pl. 185- 196 in: The Botany of the Antarctic Voyage, Parte III. Flora Tasmaniae. Vol. 2 (ed. J.D. Hooker) L. Reeve, Londres
1862. Phycologia Australica. Vol 4, Pl. 181-240. Londres
1862. Notice of a collection of algae made on the northwest coast of North America, chiefly at Vancouver's Island, por David Lyall, Esq., M.D., R.N., en los años 1859 - 1861. J. Linn. Soc. Bot.6: 157 - 177
1868. The Genera of South African Plant. (2.ª ed. aumentada, ed. Sir J.D. Hooker) Londres
Ray Desmond (1994). Dictionary of British and Irish Botanists and Horticulturists including Plant Collectors, Flower Painters and Garden Designers. Taylor & Francis, & The Natural History Museum (Londres)
