Began his professional career as a clerk in the Customs Office at Liverpool when he collected, arranged and named all the specimens of the imports into Liverpool for the Great Exhibition of 1851. Subsequently took to lecturing in local institutions and educational establishments and became a Professor in the Liverpool Institution. In June 1860 he was appointed Superintendent of the Technological Museum in Edinburgh and from January 1866 Director. During his directorship he did much to shape the appearance of this institution now famous as the Royal Scottish Museum. In 1876 he travelled to the USA as joint Executive Commissioner of the Phildaelphia Centennial Exhibition. He was a FRS (Edinburgh).
Archer published various papers on natural history subjects including one on beetles entitled 'On the ravages of Scolytus destructor. Cossus ligniperdus, and other insects on forest trees' in Transactions Botanical Society of Edinburgh, 8, 1866, 4-20).
There is an account of Archer in the Graphic, 13, 1876, 542, which also includes a portrait (p.552) and an obituary in the Athenaeum, 28 February 1885, 283. (MD 8/17)