Sir William Rowan Hamilton

By John Francis Waller, LL. D.; M.R.I.A.,
Honorary Secretary to the Royal Dublin Society.

[The Imperial Dictionary of Universal Biography, vol. II, p. 801.]

HAMILTON, SIR WILLIAM ROWAN, Royal Astronomer of Ireland, one of the most distinguished of living men of science, was born in Dublin on the 4th of August, 1805. There are few instances on record of more vast development of intellectual power than he early exhibited. At the age of six he had acquired the elements of Greek and Latin, and at thirteen he was acquainted with thirteen languages, including Syriac, Persian, Arabic, Sanscrit, Hindostanee, and Malay. When the Persian ambassador, Mirza Abou Hassan Khan, was in Dublin in 1819, young Hamilton addressed to him a congratulatory letter, of which the latter observed that he did not think there was a man in these countries who could write such a composition. At the age of ten an accident directed his attention to mathematics, in which he became profoundly interested; and at fifteen he had mastered the ordinary amount of what was known in every department of science. In 1822 he presented to Dr. Brinkley, then astronomer-royal, a paper ``On Contacts between Algebraic Curves and Surfaces,'' which was shortly after followed by one on the same subject, entitled ``Developments,'' both of which elicited the admiration and procured him the friendship of that eminent man. ``This young man I do not say will be,'' was his remark, ``but is the first mathematician of his age.'' He entered college in 1823, obtaining the first place and the first Hebrew premium; and throughout his course never failed in taking all the highest honours, and obtained two ``optimes,'' an honour extremely rare in Dublin college. Meantime he had occupied himself in the application of algebraic geometry to optics, by which he had arrived at new and important results. These he communicated in a paper on caustics to the Royal Irish Academy, subsequently enlarged under the title of ``Theory of Systems of Rays,'' published in 1828. But his academical course and honours were brought to a sudden close, more honourable than their most successful prosecution could have been. Dr. Brinkley vacated the chair of astronomy on his elevation to the see of Cloyne in 1827, and amongst the candidates for the chair was Airy, afterwards astronomer-royal of England. Hamilton was induced to offer himself, and was appointed while still an undergraduate, and before he had attained his twenty-second year. Hamilton now devoted himself entirely to science. His astronomical lectures were highly popular and eloquent, and he was ardent and assiduous as a professor. To mathematics, however, his mind turned with a peculiar predilection, and he has since devoted himself with distinguished success to investigations in that department of science. He has been an eminent member of the British Association since its formation, contributing on all occasions valuable papers - at Oxford in 1832 one on his system of optics; at Cambridge in the following year, on his discovery of conical refraction. In the year 1834 he contributed to the Philosophical Transactions his paper on a ``General Method in Dynamics.'' The originality and power displayed in this memoir would have secured for the author a place amongst the greatest mathematicians of Europe, even if it had been his only contribution to mathematical science. Since that time he has continued to apply himself to these pursuits with diligence and success. Taking up and elucidating the celebrated argument of Abel against the possibility of finding a general and algebraic solution for equations of the fifth degree, he discussed this question by a method of his own, and showed that various proposed methods of reduction and solution involved fallacies. Perhaps his most remarkable discovery was that of the calculus of quaternions. A quaternion, as its name imports, consists of four parts, one of which is real, the three others are imaginary. When interpreted geometrically, the real part answers to undirected quantity, the imaginary parts to linear magnitude directed along three rectangular axes; and the entire quaternion expresses by one combined symbol, capable of addition, subtraction, multiplication, and division, the direction as well as the magnitude of a geometrical quantity, as compared with an unit of magnitude and a fixed direction. The calculus furnishes rules and methods for operating upon quantities of this kind, and has been used by its inventor in the discussion of a variety of questions both geometrical and analytical. Sir W. Hamilton has applied it with success in his invention and proof of theorems relating to surfaces of all kinds, and especially to those of the second order. He has used it in the theory of rotation, and expressed in its language several of the leading principles and results of physical astronomy. Hitherto but few mathematicians have attempted to use this new instrument of research; but its power is beginning to be understood, and there is little doubt that Sir W. Hamilton will be remembered as one of the few who have furnished new methods for the advancement of mathematical science. The calculus of quaternions is explained by its inventor in a separate work on that subject. A popular explanation of it, from the pen of the disoverer, will be found in the late Professor Nichol's Cyclopedia of Physical Sciences. It would be impossible to give in a short compass even the titles of the papers contributed by Sir W. Hamilton to the scientific journals of his time. In addition to the subjects already mentioned, he has written upon the dynamics of light, fluctuating functions, the calculus of probabilities, definite integrals, &c. One of his latest inventions is a system of anharmonic co-ordinates, which he has employed with great elegance and skill in the discussion of various geometrical problems in space as well as on the plane. To general literature, also, Sir William has been a contributor, and his poetical compositions have high merit for their elegance of diction and depth of thought. Few philosophers have been more honoured. In 1835, on the occasion of the meeting of the British Association in Dublin, he delivered, as its secretary, the annual address, and received the honour of knighthood; he has obtained the gold medals of the Royal Society, the Royal Irish Academy, and various other high institutions. Sir William occupied for several years the presidential chair of the Royal Irish Academy, which he resigned in 1846, having been elected in 1837. He is a member of most of the great scientific societies of Europe and America, and was enrolled amongst the members of the Imperial Academy of St. Petersburg for his services in ``the integration of dynamical equations.''


D.R. Wilkins
School of Mathematics
Trinity College, Dublin