HAMILTON, SIR WILLIAM ROWAN Scottish mathematician, was born in Dublin on Aug. 4, 1805. His great mathematical intelligence was awakened by the reading of Newton's Arit/imetica universalis when he was 12 years old. He went on to the Principia, and when he was 17 attacked La place's Mecanique celeste. In this he detected an error, which was communicated to John Brinkley, then royal astronomer in Ireland, who at once recognized one of the first mathematical minds of the age. Hamilton had a brilliant career at Trinity col lege, Dublin, but before it was completed, he was appointed, at the age of 22 to the Andrews chair of astronomy in succession to Brinkley. The rest of his life was spent at the observatory at Dunsink, near Dublin, in the close study of mathematics. He was knighted in 1835. At the time of his death, Sept. 2, 1865, he was working on his Elements of Quaternions, on which the last six years of his life had been spent.
His earliest papers were the "Theory of Systems of Rays" (Trans. Roy. Irish Acad., 1828-32); in the last of these, by the aid of mathematics, he predicted conical refraction. These were followed by papers on "The Principle of Varying Action" and in 1834 and 1835 by two memoirs "On a General Method in Dynam ics." The latter papers made a great addition to the methods of inquiry in dynamics; they have been of great value in mathemat ical physics and particularly in the Quantum theory. His Lectures on Quaternions were published in 1853 and his great book, The Elements of Quaternions, posthumously in 1866. In the preface to the Lectures he describes the steps by which he reached his important conclusions, a full description of which is given in the article QUATERNIONS. It has been said of his work on this sub ject that the methods of analysis elaborated by him "are as great an advance over those of analytical geometry, as the latter were over those of Euclidean geometry." The discoveries, papers and treatises mentioned might well have formed the whole work of a long and laborious life. But he left an enormous collection of ms. books, full to overflowing with new and original matter, which were handed over to Trinity college, Dublin. His investigations connected with the solution of algebraic equations of the fifth degree form a great contribution to science. His paper on Fluctuating Functions and his extremely ingenious invention of the hodograph must also be mentioned. Of his investigations into the solution (especially by numerical approximation) of certain classes of differential equations only a few items were published at intervals in the Philosophical Maga zine. Hamilton was a neat, precise and fastidious writer, and it was probably for this reason that he published so little compared with the extent of his investigations.