HAMILTON, Sir William Rowan (1805-1865). "Theory of Quaternions", in: Proceedings of the Royal Irish Academy, volume III, pp.1-16, 109, 273-92 and xxx-lx. Dublin: M.H. Gill, 1847. FIRST EDITION. Hamilton's major contribution to mathematics, quaternions, the linear algebra of rotations in space of three dimensions, came to him in a flash of inspiration on 16 October 1843, after 22 years spent searching for a system of expressing hypercomplex numbers that would give a 'natural' algebraic representation of three-dimensional space. Hamilton's quaternions were important in the development of later noncommutative algebra such as matrices and vector analysis. PMM 334; Norman 985.
HAMILTON, Sir William Rowan. "Theory of Systems of Rays", in: The Transactions of the Royal Irish Academy, volume XV, pp.69-174; XVI, (parts 1 & 2), 4-64 & 129-30 and XVII, 1-144. Dublin: various printers, 1828-37. 4 volumes, 4° (270 x 208). (Some browning and foxing). Contemporary cloth (a few repairs). FIRST EDITION of Hamilton's important work in which he predicted conical refraction. 'Applying the laws of optics he proved that under certain circumstances a ray of light passing through a crystal ball will emerge not as a single or double ray but as a cone of rays. This theoretical deduction involved the discovery of two laws of light, and under the mathematical aspect was pronounced by Sir John Herschel to be "a powerful and elegant piece of analysis" while Professor Airy, on the physical side, said "it had made a new science of optics"' (DNB). (5)