Brinkley, John (1766?–1835), astronomer and bishop, was born in Woodbridge, Suffolk, England, and baptised 31 January 1767, illegitimate son of John Toler and Sarah Brinkley, who later married James Boulter. He was educated by clergymen in Suffolk (it is not known at whose expense), and was then taught by the Rev. Tilney of Harleston, Northants., a well known schoolmaster, who apparently arranged means of support for him at Caius College, Cambridge, from which he graduated BA in 1788 as senior wrangler and first Smith's prizeman. He was a fellow of Caius (1788/9–1792), but even before graduation he wrote on astronomy for the Ladies' Diary, and worked under Neville Maskelyne at Greenwich observatory. In 1790 Maskelyne recommended the young man as successor to Henry Ussher (qv), the Andrews professor of astronomy in TCD. Although some at Trinity would have preferred an Irish candidate, Brinkley was appointed in December 1790, was ordained priest in England in 1791, and moved to Dunsink observatory in that year. In 1792, by issue of letters patent, the title ‘royal astronomer of Ireland’ was attached to the Andrews' professorship, and Brinkley was the first to bear that title. He received in 1791 an MA from Cambridge, in 1792 an MA ad eundem from Dublin, and in 1806 he was awarded a DD by Dublin, where he remained professor until 1827. Since Dunsink lacked adequate instruments until 1808, when a long-ordered 8-ft (2.43 m) meridian circle was finally delivered, Brinkley concentrated on mathematical astronomy, and published several papers and an important textbook, Elements of plane astronomy, one of the first to be intended for college students, and used widely for many years. He revised and reissued this in five editions from 1808; after his death, three further editions appeared, the last in 1886. He pioneered the application to astronomical observation of the mathematical technique of least-squares analysis (derived from the work of Gauss), and apparently was the first mathematician in Ireland to use, in a paper in the RIA's Transactions (1817), the notation of differential and integral calculus, developed by Leibniz and used by mathematicians elsewhere in Europe.
His observations with the meridian circle provided him with the opportunity to try to detect stellar parallax, and in 1810 he reported to Maskelyne that he had measured a parallax of 1.3 arc seconds for α Lyrae. Maskelyne published this communication in the proceedings of the Royal Society (of which Brinkley had been a fellow since 1803). Similar results, indicating annual parallaxes for four bright stars, were announced before the RIA in 1814, but the Dunsink observations were irreconcilable with those of astronomers at Greenwich, and a controversy arose between Brinkley and John Pond, astronomer royal in England, which lasted for many years. His other observations and calculations at Dunsink on solar and lunar nutation, on the determination of astronomical refraction, and on the constant of aberration were so accurate that Brinkley convinced himself that his parallax observations could not be mistaken. Eventually Brinkley's parallaxes were disproved; the failure lay in his instrument, which was not well suited to the task. He was first to observe the minute effect of the sun on the earth's axis, known as solar nutation, which had been predicted by theory, and the Astronomical Society's catalogue of stars made use of the constants of aberration and of lunar nutation which he had established. The instruments, as well as the state of theoretical knowledge of the period, did not permit parallax to be accurately ascertained, but the controversy over stellar parallax led to a greatly increased awareness among astronomers of the importance of allowing for instrumental errors.
Other papers appeared on such topics as the precession of the equinoxes and the mean motion of the lunar perigee. Brinkley's contributions to astronomy were honoured by the RIA with the Cunningham medal (1818) and by the Royal Society with the Copley medal (1824). He was president of the RIA from 1822 until his death, and president of the Astronomical Society of London 1831–4. His work was known internationally, greatly increasing the status of Dunsink observatory, and was recognised by promotions within the church to be prebend of Kilgoghlin (1806), the archdiaconate of Clogher (1808), and the see of Cloyne (1826), an unusual level of attainment for someone of illegitimate birth. Increased ecclesiastical duties curtailed astronomical activity; indeed, it is said he refused to allow a telescope into the episcopal palace at Cloyne, lest he be distracted from his religious responsibilities, and he published little more. He was also expert in botany, and as a member of the commission on Irish records displayed considerable knowledge of the history of the Church of Ireland, ecclesiastical law, and allied subjects. He died 14 September 1835, after several years of ill-health, at the house of a relative of his wife in Leeson St., Dublin, and was buried in the vaults of TCD.
He married (12 July 1792) Esther Weld of Dublin, daughter of Matthew Weld, and had two sons, John (b. 1793), a clergyman, and Matthew (b. 1797), a lay vicar-choral of Cloyne. His daughter Sarah married Robert James Graves (qv). There is a portrait of Brinkley in the RIA, reproduced in Wayman, Dunsink observatory (1984).