Arthur Goodger passed the examination for the Certificate of proficiency in the Theory of Land Surveying of the University of the Cape of Good Hope in 1883 and was admitted as a land surveyor in the Cape Colony in 1885. From about 1894 he worked mainly in Griqualand East, the Transkei and Pondoland (now parts of the Eastern Cape) surveying and drawing up plans of Mount Ayliff (1894), Qumbu (1894-1896 and 1904), Tsolo (1897, with C.P. Watermeyer*), Mount Fletcher (1897), Umtata (1898), Matatiele (1898), Flagstaff (1902), Ngqeleni (1902), Tabankulu (1902), Mqanduli (1903), and Elliotdale (1903-1904). Towards the end of 1902 he was employed on the secondary triangulation of East Griqualand under the direction of J.J. Bosman*, his tasks being to reconnoitre, erect beacons, and make observations.
In 1884 Goodger presented a large number of Karoo fossils from the neighbourhood of Alice and Fort Beaufort to the Albany Museum, Grahamstown. They were said to be mainly Dicynodon and Saurian remains. In 1888 he was present at the first meeting of the short-lived South African Geological Association in Grahamstown and was elected a member of its committee.