Hamilton, SIR WILLIAM ROWAN, one of the few really great mathematicians of the 19th century, was born in Dublin on August 3-4, 1805. From his infancy he displayed extraordinary talents, and at thirteen had a good knowledge of thirteen languages. Having at an unusually early age taken to the study of mathematics, in his fifteenth year he had mastered thoroughly all the ordinary university course, and commenced original investigations of so promising a kind that Dr Brinkley, himself a very good mathematician, took him under his especial patronage. His earlier essays connected with caustics and contact of curves grew by degrees into an elaborate treatise on the Theory of Systems of Rays, published by the Royal Irish Academy in 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 the experimental verification of which by Lloyd still forms one of the most convincing proofs of the truth of the Undulatory Theory of Light. 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. He 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 coefficients. This paper produced a profound sensation, especially among continental mathematicians. Jacobi of Königsberg took up the purely mathematical side of Hamilton's method, and considerably extended it; and of late years the dynamical part has been richly commented on and elaborated by mathematicians of all nations, 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 varying 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 Differences, his great paper on Fluctuating Functions, and his Examination 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 Science of Pure 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 Lectures, which, as the unaided work of one man in a few years, has perhaps hardly been surpassed. Another immense volume on the same subject, containing his more recent improvements and extensions of his calculus, as well as a somewhat modified view of the general theory, was published after his death, which took place 2d September 1865.
While yet an undergraduate of Trinity College, Dublin, he was appointed in 1827 successor to Dr Brinkley in the Andrews chair of Astronomy in the university of Dublin, to which is attached the astronomer-royalship of Ireland. This post he held till his death. 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; he was an honorary 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 distinguished. See his Life by Graves (3 vols. 1883-89).