HAMILTON, Sir ROWAN, LL.D., one of the few really great mathema ticians of the present c., was b. in Dublin in Aug., 1805. From his infancy he dis played extraordinary talents, having at the age of 13 a good knowledge of thirteen languages. Having at an unusually early age taken to the study of mathematics, in his 15th year he had mastered thoroughly all the ordinary university course, and com menced original investigations of so promising a kind that Dr. Brinkley, himself a very good mathematician, took him under his especial patronage. His earlier essays, con nected with contact of curves, and caustics, grew by degrees into an elaborate treatise on the Theory of Systems of Rays, published by the royal Irish academy iu 1828. To this he added various supplements, in the last of which, published in 1833, he predicted the existence of the two kinds of conical refraction (see REFRACTION), the experimental verification of which by Lloyd still forms one of the most convincing proofs of the truth of the undulatory theory of light. See LIGIIT. The great feature of his Systems of Rays is the employment of a single function, upon whose differential coefficients (taken on various hypotheses) the whole of any optical problem is made to depend.. lie seems to have been led by this to his next great work, A General Method in Dynamics, published in the Philosophical Transactions for 1834. Here, again, the whole of any dynamical problem is made to depend upon a single function and its differential coeffi cients. This paper produced a profound sensation, especially among continental mathe maticians. Jacobi of Kbnigsberg took up the purely mathematical part of Hamilton's method, and considerably extended it; and of late years the dynamical part has been richly commented on and elaborated by several French mathematicians, all uniting in their admiration of the genius displayed in the original papers. For these researches, Hamilton was elected an honorary member of the academy of St. Petersburg, a rare
and coveted distinction. The principle of retrying action, which forms the main feature of the memoirs, is hardly capable, at all events in few words, of popular explanation. Among Hamilton's other works, which are very numerous, we may mention particularly a very general Theorem in the Separation of Symbols in Finite Diprences, and his Exami nation of Abel's Argument concerning the Impossibility of solving the General Equation of the Fifth Degree.
We may also particularly allude to his memoir on Algebra as the of Pare Time, one of the first steps to his grand invention of quaternions. The steps by which he was led to this latter investigation, which will certainly, when better known, give him even a greater reputation than conical refraction or varying action has done, will be more properly treated under QUATERNIONS. On the latter subject he published, in 1853, a large volume of Lectui;es, which, as the unaided work of a single man in a few years, has perhaps hardly been surpassed. Another volume of a more elementary character, on the same containing in addition his more recent improvements and exten sions of his calculus, was published aft& his death, which took place Sept. 2, 1865.
While yet an undergraduate of Trinity college, Dublin, he was appointed, in 1827, successor to Dr. Brinkley in the Andrew's chair of astronomy in the university of Dublin, to which is attached the astronomer-royalship of Ireland. In 1835 he was knighted on his delivering the address as secretary to the British association for its Dublin meeting. He occupied for many years the post of president of the royal Irish academy, and was a member of most of the great scientific academies of Europe. He held during his life, not in Dublin alone, but in the world of science, a position as merited as it was dis tinguished