William Henry Finlay received his schooling in Liverpool and then entered Trinity College, Cambridge, where he was awarded the Bachelor of Arts (BA) degree with honours in mathematics in 1873. In April that year he was appointed first assistant at the Royal Observatory, Cape of Good Hope, then under the direction of E.J. Stone*. Finlay assumed duty in June and initially spent much time on the reduction of the meridian observations of Stone's predecessor, Thomas Maclear*. He was elected a Fellow of the Royal Astronomical Society in Novermber 1873.
Although he was inexperienced in practical astronomy he soon acquired the necessary skills and in time proved himself an expert in the use of the heliometer. However, feeling the need for a higher income he started to take on private pupils for the examination in surveying of the University of the Cape of Good Hope. As this began to affect his observatory work, Stone put a stop to it in 1876. Finlay and George W.H. Maclear*, the second assistant, were responsible for most of the transit circle observations on which Stone's Cape Catalogue of stars (1880) was based. Finlay's paper "On the variations of level of the Cape transit circle" was published in the Transactions of the South African Philosophical Society (Vol. 4, pp. 6-10) in 1884.
Finlay was particularly interested in comets and in March 1880 read a paper on the subject before the South African Philosophical Society. At least 10 papers by him dealt with observations and orbits of comets. He independently discovered the Great Comet of 1882, which was so bright that it could be seen in daytime, and was the first to measure its position accurately. The elements of its orbit were communicated by him to the South African Philosphical Society in October 1882. Dr David Gill*, who had taken over the direction of the observatory in 1879, then sent Finlay and the third assistant, Robert T. Pett*, to Aberdeen Road, where they erected a temporary observatory, determined its longitude, and observed the transit of Venus on 6 December 1882. In September 1886 Finlay discovered another comet, which was named Comet Finlay in his honour, and computed its orbit. His other astronomical work, reported in at least 15 papers, included the preparation of star correction tables, and assisting Gill in his determination of stellar parallaxes.
In 1887 Finlay undertook an analysis of the tidal records of Table Bay and Algoa Bay and published the results in the Transactions of the South African Philosophical Society. He also played a major role in the determination of the relative longitudes of Cape Town and Aden (now 'Adan, Yemen), which formed part of the geodetic work that Gill initiated and directed. On his voyages to and from Aden he took advantage of short stoppages at Delagoa Bay (now Baia de Maputo), Quelimane, the port city Mozambique, and Zanzibar to determine local time with portable instruments and exchange telegraph time signals with Cape Town to determine their longitude. The results were published in the Monthly Notices of the Royal Astronomical Society. He also reported his "Preliminary results for the longitude of Bloemfontein, from an occultation" in the Transactions of the South African Philosophical Society for 1890-1895 (Vol. 8, pp. 77-79). In 1891 he and Gill participated in the measurement of a baseline near Kimberley, as part of the geodetic survey of South Africa.
Finlay was elected a Fellow of the Royal Astronomical Society before 1880. In 1875 he became a member of the reorganised Meteorological Commission of the Cape of Good Hope and served it continuously to 1897. In its report for 1883 he published a "Table of mean monthly temperature at the Royal Observatory, 1871-1882", which supplemented the meteorological observations for earlier years published by Stone. He was a member of the South African Philosophical Society from 1877 (the year of its formation) and played an active role in its management, serving as general secretary from 1881, as president from 1887 to 1889, and as a member of council to 1898. From 1880 to 1898 he was an examiner in various branches of mathematics and physics, and from 1913 to 1915 in mathematics only, for the University of the cape of Good Hope. Meanwhile he had been awarded the degree Master of Arts (MA) by the University of Cambridge. On the basis of this qualification the University of the Cape of Good Hope admitted him to the MA degree in 1886.
When the staff of the observatory was reorganised in 1897 Finlay was promoted to chief assistant, following many years of invaluable service. However, ill health led to his retirement in August 1898 and his departure for England. He spent several years there, during which he regained his health, and upon his return to Cape Town again took up teaching. In 1909 he stood in for T.P. Kent*, professor of mathematics at the South African College, for a few months. In 1914 he took the place of professor David Williams* of Rhodes University College to teach mathematics and surveying. He remained there when Williams returned, and continued working to within a few days of his death in 1923.