Following completion of those studies he worked under Robert Stephenson for two years, before returning to Tasmania on 18 October 1842.
Archer studied botany in England between the years 1856 and 1858 and was elected a Fellow of the Linnean Society before returning to Tasmania.
Sir Joseph Dalton Hooker wrote a dedication to him (and jointly to Ronald Campbell Gunn) in his Flora Tasmaniae (1859).
Archer composed illustrations of orchids and collected and sent numerous Tasmanian plant specimens to the Royal Botanical Gardens in Kew.
[1] He was the appointed architect to the Anglican Diocese of Tasmania, and designed The Hutchins School located in Hobart (1848–49), additions to the world heritage listed Woolmers and Brickendon estates, the calendar house "Mona Vale" (1865–68) in Ross, his own home Cheshunt, Fairfield for his brother.