Hornsby became a Fellow of Corpus Christi College, Oxford in 1760.
Hornsby was especially concerned with the observation of the transit of Venus. In 1761, he observed the transit of Venus from Shirburn Castle, in Oxfordshire, the possession of the Earl of Macclesfield. George Parker, 2nd Earl of Macclesfield (ca. 1695-1764), celebrated as an astronomer, had spent most of his time conducting astronomical observations at Shirburn Castle; here he had built an observatory and a chemical laboratory.
In the periodical Philosophical Transactions, Hornsby published a comparative analysis of 1761 transit (1763); a plan for suitable viewing stations for 1769, including possible locations in the Pacific (1765); a description of organising and reporting observing groups in Oxford (1769); and a comparative analysis of the 1769 transit (1771).
Hornsby was instrumental in the establishment of the Radcliffe Observatory at Oxford in 1772, and was made Radcliffe Observer in the same year. In 1782, he was appointed Sedleian Professor of Natural Philosophy. In 1783, he became Radcliffe Librarian. He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1788.
Hornsby made tens of thousands of astronomical observations. These were not published, however, until 1932.
- "Book of Members, 1780–2010: Chapter H". American Academy of Arts and Sciences. Retrieved 28 July 2014.
- Thomas Harriot's manuscripts
- History of transit observing
- Stephen Johnston, "Blast from the Past: Measurement and morals in the early Transits of Venus," Museum of the History of Science, University of Oxford, at http://www.physics.ox.ac.uk/phystat05/Talks/johnston.ppt (accessed July 2006)