Hart wrote this paper after an carrying out an investigation suggested by William Rowan Hamilton in a letter to Hart. In addition, Hart corresponded with George Salmon on the same topic. This paper contains the result which became known as Hart's Theorem, which is a generalisation of Feuerbach's Theorem. Hart's Theorem states:  In "Principles of geometry" (1925), Henry Baker sums up Hart's Theorem as follows:  Hart was co-opted as a Senior Fellow of TCD on 10 July 1858. In February 1873, Hart made up part of the delegation sent to London on behalf of TCD to lobby members of parliament to vote against the Irish University Bill  He was elected Vice-Provost of TCD in 1876, and at this time undertook many of the duties of the then provost, Humphrey Lloyd, that ill health had permitted him from carrying out. He married in 1840 Frances, daughter of Sir Henry McDougall, Q.C., of Dublin; she died in 1876. Two sons, George Vaughan Hart (1841-1912), a barrister, and Henry Chichester Hart (1847-1908), a botanist and explorer, of Carrablagh House, Donegal, survived him. The youngest son, William Hume Hart (1852-1887) predeceased Sir Andrew. Sir Andrew Hart took an active interest in the affairs of the Irish Church, and was for many years a member of the general synod and representative church body. On 25 January 1886 he was knighted at Dublin Castle by the lord-lieutenant, Lord Carnarvon, ""in recognition of his academic rank and attainments."" Sir Andrew Hart died suddenly at the house of his brother-in-law and cousin (his sister had married her cousin), George Vaughan Hart, of Kilderry, County Donegal, on . Left to right: "Norah Searle Hart (1879-1965), Adelaide (Ada) Hart (1876-197?), George Vaughan (Vaughan) Hart (1877-1928), Hilda Chichester Hart (1882-1967), Tristram Beresford Hart (1884-1963), Ruth Hart (1886-1977), Sir Andrew Searle Hart, Ethel Hart (1875-1964). All the minors shown except Ada were children of George Vaughan Hart. Ada was the daughter of William Hume Hart."