Although he was not an astronomer, on the strength of his mathematical ability he was appointed first assistant at the Royal Observatory, Cape of Good Hope in April 1873, under the direction of Edward James Stone.
[6] His chief interest was comets and in March 1880 he presented a paper on them before the South African Philosophical Society.
He was the first astronomer to record observations of the "Great Comet of 1882" (C/1882 R1), and he presented his findings to the South African Philosophical Society in October 1882.
[6] His other astronomical work included the preparation of star correction tables and determination of Stellar parallaxes, in collaboration with David Gill.
He also was involved in the determination of the relative longitudes of Cape Town, Aden, Delagoa Bay, Quelimane and Zanzibar.
[6] Finlay became chief assistant at the Royal Observatory in 1897 but was forced to retire in August 1898 owing to poor health.