for him a clerkship under the East India Company. The mathematical bent of his mind, however, was presently to assert itself. In his tenth year he was matched in public with Zerah Colburn, the American 'calculating boy,' retiring from the arithmetical duels not without honour. About the same time he fell upon a Latin copy of Euclid, and studied it with' such effect that within two years he read the 'Arithmetica Universalis' of Newton, and soon after began the 'Principia.' In 1822 good evidence shows that he understood much of that work, and had acquired such command of mathematical methods as to speedily master several modern books on analytical geometry and the differential calculus. Hamilton thus appears 'to have been mainly self-taught in mathematical learning. In his seventeenth year, when reading the 'Mécanique Céleste' of Laplace, he found an error in the reasoning on which one of the propositions was based. This discovery led to Hamilton's introduction to Dr. Brinkley, the astronomer royal for Ireland, afterwards bishop of Cloyne, whom he still further surprised by an original paper on osculation of certain curves of double curvature. The discipline of Newton and Laplace had already brought into relief the marked features of a mathematical genius of very rare quality and power.
In 1823 Hamilton became a student of Trinity College, Dublin. His achievements in mathematics alone implied great and continuous mental effort, but his success in other departments of thought was scarcely less remarkable. First in all subjects and at all examinations, twice gaining the vice-chancellor's prize for English verse, decorated with the 'double optime' (almost unprecedented), and, but for the appointment to which his special qualifications entitled him, certain to gain both gold medals (a thing quite unprecedented), he was characterised by a candour and enthusiastic eloquence that well became him as scholar, poet, and metaphysician, not less than as mathematician or natural philosopher.
In 1824, when only a second year's student, Hamilton read before the Royal Irish Academy a 'Memoir on Caustics,' and being invited to develop the subject, he some time after produced a celebrated paper on systems of rays, and predicted 'conical refraction.' Applying the laws of optics he proved that under certain circumstances a ray of light passing through a crystal will emerge not as a single or double ray but as a cone of rays. This theoretical deduction involved the discovery of two laws of light; and under the mathematical aspect was pronounced by Sir John Herschel to be 'a powerful and elegant piece of analysis,' while Professor Airy, on the physical side, said 'it had made a new science of optics.' This result, that light refracts as a conical pencil both internally and externally, obtained on purely theoretical grounds, was soon after verified for universal acceptance, when Professor Humphrey Lloyd, at Hamilton's suggestion, put the new law to the test by means of a plate of arragonite (Transactions of the Royal Irish Academy, xvii. 145). The ray of light either issues as a cone with its vertex at the surface of emission, or issues as a cylinder after being converted on entering the crystal into a cone whose vertex is at the point of incidence.
Hamilton, when still an undergraduate, was appointed in 1827 Andrews professor of astronomy and superintendent of the observatory, and soon after astronomer royal for Ireland. He was twice honoured with the gold medal of the Royal Society, first for his optical discovery, and secondly, in 1834, for his theory of a general method of dynamics, which resolves an extremely abstruse problem relating to a system of bodies in motion. Next year, on the occasion of the British Association visiting Dublin, Hamilton was knighted by the lord-lieutenant. In 1837 he was chosen president of the Royal Irish Academy, and had the rare distinction of becoming a corresponding member of the academy of St. Petersburg.
About 1843 Hamilton began more or less clearly to shape out the new mathematical method which when perfected was to give him right to rank in originality and insight with Diophantus, Descartes, and La Grange—a method which, as set forth and illustrated in his own writings, can 'only be compared with the "Principia" of Newton and the "Mécanique Céleste " of La Place as a triumph of analytical and geometrical power' (Professor Tait in North British Review, September 1866). In 1844, before the Royal Irish Academy, of which he was still president, he formally defined the term 'quaternions,' by which the new calculus was to be known; but not till 1848 can the method be considered as systematically established, when he began, in Trinity College, Dublin, the 'Lectures on Quaternions,' which were published in 1853. Nearly the whole of this bulky octavo, occupying 808 pages, besides an introduction of 64 pages, can be understood only by advanced mathematicians. But for Professor Tait of Edinburgh, who interpreted the new science for more common-place mathematicians, Hamilton's merits must long have remained unrealised or absolutely unknown. The truth is that this great book
