# Dictionary of National Biography, 1901 supplement/Hirst, Thomas Archer

​HIRST, THOMAS ARCHER (1830–1892), mathematician, born at Heckmondwike in Yorkshire on 22 April 1830, was the youngest son of Thomas Hirst (d. 1842), a woolstapler, by his wife, a daughter of John Gates, a blanket manufacturer of Heckmondwike. About 1835 his father retired from business and removed to Fieldhead near Wakefield. In 1840 Thomas entered the West Riding proprietary school at Wakefield, and in 1846 was articled to Richard Carter, a land agent and surveyor at Halifax. At Carter's office he met John Tyndall [q. v.], who was then Carter's principal assistant. Tyndall became his lifelong friend, and exercised a deep influence on his scientific studies. In 1849 Hirst followed Tyndall to Marburg to study mathematics, physics, and chemistry. After three years at that university he obtained the degree of Ph.D. Subsequently, after spending a short time at Gottingen, where he made the acquaintance of Carl Friedrich Gauss, and worked at magnetism under Wilhelm Eduard Weber, he went to Berlin, and in the session of 1852-3 attended lectures by Peter Gustav Lejeune Dirichlet, Jakob Steiner, and Ferdinand Joachimstal. His intercourse with Steiner did much to determine the ultimate bent of his mathematical investigations.
In 1853 Hirst succeeded Tyndall at Queenwood College in Hampshire as lecturer in mathematics and natural philosophy. He married in 1854, and resigned his post on account of his wife's ill-health in 1856. He spent the winter of 1857-8 at Paris, attending lectures by Michel Chasles and Gabriel Lame, and passed the following winter at Rome. While travelling in Italy he made the acquaintance of Luigi Cremona, with whom he became intimate. Returning to England in 1860 he was appointed mathematical master of University College School. The experience in educational methods which he gained there, and his experiments on teaching geometry apart from Euclid, led ​him to join the Association for the Improvement of Geometrical Teaching on its formation in 1871, and for the first seven years of its existence he filled the office of president.
On 6 June 1861 Hirst was elected a fellow of the Royal Society, and in 1866 of the Royal Astronomical Society. In 1865 he was appointed professor of physics at University College. On the resignation of Augustus De Morgan [q. v.] in 1866, he succeeded to the professorship of pure mathematics ; this chair he resigned in 1870 to become assistant registrar in the university of London, giving up at the same time the general secretaryship of the British Association which he had held for four years. On the establishment of the Royal Naval College at Greenwich in 1873 he was appointed director of naval studies, and he continued to discharge the duties of that office for ten years.
Most of Hirst's earlier papers are devoted to researches in mathematical physics, but from 1861 he turned his chief attention to pure geometry. He took a prominent part in the foundation of the London Mathematical Society in 1865, served as its president from 1872 to 1874, and was a member of its council from 1864 to 1883. His papers on pure geometry were largely contributed to the proceedings of this society. The work with which his name will be most definitely associated is contained in his papers on the correlation of planes and the correlation of space of three dimensions. A few properties of correlative planes were proved by Chasles in his 'Traité de Geometric Supérieure' (Paris, 1852), but Hirst first constructed the theory of the correlation of planes and developed it to a great degree of perfection. The extension of the theory of correlation to space of three dimensions was adverted to by Chasles in his 'Aperçu Historique sur l'Origine et le Développement des Méthodes de la Geometric' (Brussels, 1837); but the full extension was carried out by Hirst, whose investigations, together with those of Rudolf Sturm, Cremona, and others, have resulted in substantial additions to the theory of pure geometry. In 1882 Hirst was elected a fellow of the university of London, and in 1883 he received a royal medal for his researches from the Royal Society. In the same year ill-health compelled him to resign his post at Greenwich. He received a pension and subsequently lived in retirement, spending most of his winters abroad. He died in London on 16 Feb. 1892 at 7 Oxford and Cambridge Mansions. He married in 1854 Anna (d. 1857), youngest daughter of Samuel Martin of Longhorne, co. Down, and sister of John Martin (1812-1875) [q. v.], the Irish nationalist. He was an honorary member of the Cambridge Philosophical Society and of several foreign scientific institutions.
Besides contributing papers to the 'Proceedings' of the London Mathematical Society, Hirst also wrote several of importance for the 'Philosophical Transactions' of the Royal Society. He edited 'The Mechanical Theory of Heat' (London, 1867, 8vo), translated from the German of Rudolf Julius Emmanuel Clausius; wrote a preface to Richard P. Wright's 'Elements of Plane Geometry' (London, 1868, 12mo); and contributed a paper 'On the Complexes generated by two Correlative Planes' to the collection of mathematical papers edited by Cremona, 'In Memoriam D. Chelini,' Milan. 1881, 8vo.
[Proc. of the Royal Soc. 1892-3, vol. Hi. pp. xii-xviii; Monthly Notices of the Royal Astron. Soc. 1893, liii. 218-19; Biograph, 1881, vi. 252-6; Men and Women of the Time, 1891.]
E. I. C.