Sir William Rowan Hamilton', a British philosopher, born in Dublin, Aug. 4, 1805, died at Dunsink, near Dublin, Sept. 2, 1865. He gave early indications of extraordinary intellectual powers, and when 13 years old he was in different degrees acquainted with 13 languages, including French, Italian, Spanish, German, Syriac, Persian, Sanskrit, Hindostanee, and Malay. At 14 years of age he addressed a letter of greeting in the Persian language to the Persian ambassador, Mirza Abu Hassan Khan. Falling in with a Latin copy of Euclid when 10 years old, he soon became interested in geometry, and at 12 he was fully confirmed in his taste for algebra. He studied the Arith-metica Universalis and the Principia of Newton, and the Mecanique celeste of Laplace, while in his 18th year, and about the same time entered upon his investigations in optics. In 1823 he entered the university of Dublin, where he at once gained the first place, and at every quarterly examination obtained the chief honor in science and the classics. In 1827, while still an undergraduate, he was appointed Andrews professor of astronomy in the university and astronomer royal of Ireland. In 1837 he was elected president of the royal Irish academy.

The honor of knighthood was conferred upon him at the meeting of the British association for the advancement of science at Dublin in 1835, when Hamilton held the post of secretary and delivered the annual address. He engaged in numerous investigations on scientific subjects, published in the "Transactions" and "Proceedings" of the royal Irish academy and royal society, in the "Proceedings" of the British association, in the " London and Edinburgh Philosophical Magazine," etc. In 1828 he published in the "Transactions" of the royal Irish academy an "Essay on the Theory of Systems of Kays," which accomplished for optics what Descartes has done for geometry and Lagrange for mechanics; that is, the application of algebra, including the differential calculus, to those problems in the science of optics which spring from the hypothesis of transverse vibrations, or what is more generally called the undulatory theory of light. By a peculiar analysis, developed in this theory, he generalized the most complicated cases of common geometrical optics; and his prediction of the most singular and critical of all the results of Fresners theory, the conical refraction in biaxal crystals, amply rewarded his labors.

Dr. Lloyd, of Trinity college, Dublin, verified this result in the case of aragonite, which is a biaxal crystal; he found the position, dimensions, and conditions of polarization of the emerging cone of light to be exactly such as Hamilton's prediction assigned. Airy has designated it as "perhaps the most remarkable prediction that has ever been made." For this discovery Sir William received the Cunninghame gold medal from the royal Irish academy, and the royal gold medal of King William IV. from the royal society of London. In 1834 he published two papers in the " Philosophical Transactions" of the royal society, " On a General Method in Dynamics, by which the study of the motions of all free systems of attracting or repelling points is reduced to the search and differentiation of one central relation or characteristic function." The most elaborate of Hamilton's writings is his "Method or Calculus of Quaternions" (8vo, Dublin, 1853), which formed the subject of successive courses of lectures delivered in 1848 and subsequent years at Trinity college.

He aimed in this to show that " expressions which seem, according to common views, to be merely symbolical and quite incapable of being interpreted, may pass into the world of thoughts, and acquire reality and significance, if algebra be viewed, not as a mere art or language, but as the science of pure time." The fundamental geometrical view, adopted and developed in the "Lectures," is that according to which a quaternion is considered as the quotient of two directed lines in tridimensional space; and the motive (in this view) for calling such a quotient a quaternion, or the ground for connecting its conception with the number four, is derived from the consideration, that while the relative length of the two lines compared depends only on one number, expressing their ratio, their relative direction depends on a system of three numbers - one denoting the angle between the two lines, and the two others determining the aspect of the plane of that angle, or the direction of the axis of the positive rotation in that plane.

His "Elements of Quaternions" appeared in 1866.