Andrew Henry Farrell Duncan served in the Royal Navy from 1868 to 1883. In the latter year he passed the examination for the Certificate of proficiency in the theory of land surveying of the University of the Cape of Good Hope and in 1884 was admitted as a land surveyor in the Cape Colony. He, S.G.A. Shippard and J.J. Leverton were appointed as commissioners to determine land claims and effect land settlement in British Bechuanaland (now part of the Northern Cape and North-West) and reported on these matters in 1886. Duncan then served as surveyor-general of British Bechuanaland from 1886 to 1891. He also surveyed and compiled plans of the townships Ekowa (1885-1886) and Elliot (1885-1904) in the Transkei and Vryburg (1897, with J. Fleming) in North-West. In 1893 he was chief magistrate in Bulawayo and on 10 September 1894 was appointed as the first surveyor-general of Rhodesia (now Zimbabwe), a post from which he resigned in July 1897 and in which he was succeeded by Joseph Millerd Orpen*. He was on active service during the Matabele rebellion of 1896 and was awarded the Matabele War medal.
When the Anglo-Boer War (1899-1902) broke out Duncan volunteered for service and served with the Royal Engineers and the Intelligence Department. Shortly after the British assumed control of the Orange Free State (now the Free State) during the Anglo-Boer War (1899-1902) Duncan supervised the compilation of the Orange River Colony Degree Sheet Series of maps, published in 1901 on a scale of 1000 Cape roods to the inch (c 1:149 000). The project was initiated in 1900 by the British occupation forces. The 25 maps were based on the farm diagrams available in the office of the surveyor-general of the territory. They were revised after 1902 by the surveyor-general's staff and remained in use for many years.
In 1906 Duncan was listed as a government land surveyor admitted to practice in the Transvaal Colony and was associated with the Swaziland Commission. During 1906 he surveyed a chain of triangles in Swaziland. His survey was later incorporated in the primary triangulation along the northern border of Swaziland, carried out by the Trigonometrical Survey of the Union of South Africa between 1920 and 1936. In 1928 he received a Crown grant of portion F of the farm Hartebeestfontein No. 592, Pretoria.