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HAMILTON, SIR WILLIAM ROWAN (1805-1865)
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See also: He soon commenced to read the Principia, and at sixteen he had mastered a See also:great See also:part of that See also:work, besides some more modern See also:works on See also:analytical See also:geometry and the See also:differential calculus.
About this See also:period he was also engaged in preparation for entrance at Trinity See also:College, Dublin, and had therefore to devote a portion of his time to See also:classics. In the summer of 1822, in his seventeenth See also:year, he began a systematic study of See also:Laplace's
Mecanique See also:Celeste. Nothing could be better fitted to See also:call forth such mathematical See also:powers as those of Hamilton; for Laplace's great work, See also:rich to profusion in analytical processes alike novel and powerful, demands from the most gifted student careful and often laborious study. It was in the successful effort to open this treasure-See also:house that Hamilton's mind received its final See also:temper, " See also:Des-lors it commenca a marcher soul," to use the words of the biographer of another great mathematician. From that time he appears to have devoted himself almost wholly to See also:original investigation (so far at least as regards See also:mathematics), though he ever kept himself well acquainted with the progress of See also:science both in See also:Britain and abroad.
Having detected an important defect in one of Laplace's demonstrations, he was induced by a friend to write out his remarks, that they might be shown to Dr See also: This was his See also:appointment to the See also:Andrews professorship of See also:astronomy in the university of Dublin, vacated by Dr Brinkley in 1827. The See also:chair was not exactly offered to him, as has been sometimes asserted, but the See also:electors, having met and talked over the subject, authorized one of their number, who was Hamilton's See also:personal friend, to urge him to become a See also:candidate, a step which his modesty had prevented him from taking. Thus, when barely twenty-two, he was established at the See also:Observatory, Dunsink, near Dublin. He was not specially fitted for the See also:post, for although he had a profound acquaintance with theoretical astronomy, he had paid but little See also:attention to the See also:regular work of the See also:practical astronomer. And it must be said that his time was better employed in original investigations than it would have been had he spent it in observations made even with the best of See also:instruments,—infinitely better than if he had spent it on those of the observatory, which, however See also:good originally, were then totally unfit for the delicate requirements of modern astronomy. Indeed there can be little doubt that Hamilton was intended by the university authorities who elected him to the professorship of astronomy to spend his time as he best could for the See also:advancement of science, without being tied down to any particular branch. Had he devoted himself to practical astronomy they would assuredly have furnished him with modern instruments and an adequate See also:staff of assistants. In 1835 , being secretary to the See also:meeting of the See also:British Association which was held that year in Dublin, he was knighted by the See also:lord-See also:lieutenant. But far higher honours rapidly succeeded, among which we may merely mention his See also:election in 1837 to the See also:president's chair in the Royal Irish See also:Academy, and the rare distinction of being made corresponding member of the academy of St See also:Petersburg. These are the few salient points (other, of course, than the epochs of his more important discoveries and inventions presently to be considered) in the uneventful life of this great man. He retained his wonderful faculties unimpaired to the very last, and steadily continued till within a See also:day or two of his See also:death, which occurred on the 2nd of See also:September 1865, the task (his Elements of See also:Quaternions) which had occupied the last six years of his life. The germ of his first great See also:discovery was contained in one of those See also:early papers which in 1823 he communicated to Dr Brinkley, by whom, under the See also:title of " Caustics," it was presented in 1824 to the Royal Irish Academy. It was referred as usual to a See also:committee, Their See also:report, while acknowledging the novelty and value of its
contents, and the great mathematical skill of its author, recommended that, before being published, it should be still further See also:developed and simplified. During the next three years the See also:paper See also:grew to an immense bulk, principally by the additional details which had been inserted at the See also:desire of the committee. But it also assumed a much more intelligible form, and the See also:grand features of the new method were now easily to be seen. Hamilton himself seems not till this period to have fully understood either the nature or the importance of his discovery, for it is only now that we find him announcing his intention of applying his method to See also:dynamics. The paper was finally entitled " Theory of Systems of Rays," and the first part was printed in 1828 in the Transactions of the Royal Irish Academy. It is understood that the more important contents of the second and third parts appeared in the three voluminous supplements (to the first part) which were published in the same Transactions, and in the two papers " On a See also:General Method in Dynamics," which appeared in the Philosophical Transactions in 1834-1835. The principle of " Varying See also:Action " is the great feature of these papers; and it is See also:strange, indeed, that the one particular result of this theory which, perhaps more than anything else that Hamilton has done, has rendered his name known beyond the little See also:world of true philosophers, should have been easily within the reach of Augustin See also:Fresnel and others for many years before, and in no way required Hamilton's new conceptions or methods, although it was by them that he was led to its discovery. This singular result is still known by the name " conical See also:refraction," which he proposed for it when he first predicted its existence in the third supplement to his " Systems of Rays," read in 1832.
The step from See also:optics to dynamics in the application of the method of " Varying Action " was made in 1827, and communicated to the Royal Society, in whose Philosophical Transactions for 1834 and 1835 there are two papers on the subject. These display, like the Systems of Rays," a mastery over symbols and a flow of mathematical See also:language almost unequalled. But they contain what is far more valuable still, the greatest addition which dynamical science had received since the grand strides made by Sir See also:Isaac Newton and See also:Joseph See also: G. J. See also:Jacobi and other mathematicians have developed to a great extent, and as a question of pure mathematics only, Hamilton's processes, and have thus made extensive additions to our knowledge of differential equations. But there can be little doubt that we have as yet obtained only a See also:mere glimpse of the vast See also:physical results of which they contain the germ. And though this is of course by far the more valuable aspect in which any such contribution to science can be looked at, the other must not be despised. It is characteristic of most of Hamilton's, as of nearly all great discoveries, that even their indirect consequences are of high value. The other great contribution made by Hamilton to mathematical science, the invention of Quaternions, is treated under that heading. The following characteristic See also:extract from a See also:letter shows Hamilton's own See also:opinion of his mathematical work, and also gives a hint of the devices which he employed to render written language as expressive as actual speech. His first great work, Lectures on Quaternions (Dublin, 1852), is almost painful to read in consequence of the frequent use of italics and capitals. " I See also:hope that it may not be considered as unpardonable vanity or presumption on my part, if, as my own See also:taste has always led me to feel a greater See also:interest in methods than in results, so it is by METHODS, rather than by any THEOREMS, which can be separately quoted, that I desire and hope to be remembered. Nevertheless it is only human nature, to derive some See also:pleasure from being cited, now and then, even about a '_Theorem '; especially where . the quoter can enrich the subject, by combining it with researches of his own." The discoveries, papers and See also:treatises we have mentioned might well have formed the whole work of a long and laborious life. But not to speak of his enormous collection of MS. books, full to over-flowing with new and original See also:matter, which have been handed over to Trinity College, Dublin, the works we have already called attention to barely form the greater portion of what he has published. His extraordinary investigations connected with the See also:solution of algebraic equations of the fifth degree, and his examination of the results arrived at by N. H. See also:Abel, G. B. Jerrard, and others in their researches on this subject, form another grand contribution to science. There is next his great paper on Fluctuating Functions, a subject which, since the time of J. See also:Fourier, has been of immense and ever increasing value in physical applications of mathematics. There is also the extremely ingenious invention of the See also:hodograph. Of his extensive investigations into the solution " (especially by numerical approximation) of certain classes of differential equations which constantly occur in the treatment of physical questions, only a few items have been published, at intervals, in the Philosophical See also:Magazine. Besides all this, Hamilton was a voluminous correspondent. Often a single letter of his occupied from fifty to a See also:hundred or more closely written pages, all devoted to the See also:minute See also:consideration of every feature of some particular problem; for it was one of the See also:peculiar characteristics of his mind never to be satisfied with a general understanding of a question; he pursued it until he knew it in all its details. He was ever courteous and See also:kind in answering applications for assistance in the study of his works,even when his compliance must have cost him much time. He was excessively precise and hard to please with reference to the final See also:polish of his own works for publication; and it was probably for this See also:reason that he published so little compared with the extent of his investigations. Like most men of great originality, Hamilton generally matured his ideas before putting See also:pen to paper. " He used to carry on," says his See also:elder son, William See also:Edwin Hamilton, " long trains of algebraical and arithmetical calculations in his mind, during which he was unconscious of the earthly See also:necessity of eating; we used to bring in a ' snack ' and leave it in his study, but a brief nod of recognition of the intrusion of the chop or cutlet was often the only result, and his thoughts went on soaring upwards." For further details about Hamilton (his See also:poetry and his association with poets, for instance) the reader is referred to the Dublin University Magazine (See also:Jan. 1842), the See also:Gentleman's Magazine (Jan. 1866), and the Monthly Notices of the Royal Astronomical Society (Feb. 1866) ; and also to an See also:article by the See also:present writer in the North British See also:Review (See also:Sept. 1866), from which much of the above See also:sketch has been taken. His works have been collected and published by R. P. See also:Graves, Life of Sir W. R. Hamilton (3 vols., 1882, 1885, 1889). (P. G. Additional information and CommentsThere are no comments yet for this article.
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