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Hamilton's first ever publication of his Second Supplement to an Essay on the Theory of Systems of Rays - a "Statement and Integration of the Partial Equation, which determines the Characteristic Function of Ordinary Systemsof Rays, produced by any number of successive Reflexions or Refractions" originally first read at the Royal Irish Academy in Dublin on October 25, 1830 & published for the first time in the Science section of this R.I.A. official publication of Volume 16 Part 2, of the Transactions of the Royal Irish Academy, pp. 93-125. Pp. 129-130 are also by Hamilton & are titled: " Note to a Paper on the Error of a received Principle of Analysis" by Wm. R. Hamilton, & c. Read April 18, 1831. Thes are preceded in the Science section by a paper by James McCullagh: On the double Refraction of Lightin a crystallized Medium, according to the Principles of Fresnel (1830); In between the two Hamilton papers is: James Townsend MacKay. Note of an Indigenous Heath, found in Connemara. (1830); Section 2: Polite Literature contains: (1) William Hamilton Drummond. Dubject proposed by the Royal Irish Academy, to investigate the Authenticity of the Poems of Ossian, both as given in MacPerson's translation, and as published in Gaelic.1807 under the .Highland Society of London.to assign a probable Era and Country of the original Poet or Poets. Prize Essay. (1829): (2) Edward O'Reilly. A Prize Essay on the same subject. (1829). Contemporary boards. Partial spine, most lacking. Covers loose. Top edge of pages uncut. Signature top r/h corner of f.f.e.p. in pen is W. Betham. Sir William Betham (1779-1853) was a Herald and Antiquarian & Ulster King of Arms. Interesting Association Copy. William Rowan Hamilton (1805-1865) was born in Dublin and spent his childhood in Trim, Co. Meath was perhaps Ireland's greatest polymath, made contributions to many areas of mathematics. The invention of quaternions, an extension of complex numbers, is the achievement for which he is most often remembered. Hamilton?s first published mathematical paper, His Theory of Systems of Rays, begins by proving that a system of light rays filling a region of space can be focused down to a single point by a suitably curved mirror if and only if those light rays are orthogonal to some series of surfaces. Moreover, the latter property is preserved under reflection in any number of mirrors. Hamilton?s innovation was to associate with such a system of rays a characteristic function, constant on each of the surfaces to which the rays are orthogonal, which he employed in the mathematical investigation of the foci and caustics of reflected light. The theory of the characteristic function of an optical system was further developed in three supplements. In the third of these, the characteristic function depends on the Cartesian coordinates of two points (initial and final) and measures the time taken for light to travel through the optical system from one to the other. If the form of this function is known, then basic properties of the optical system (such as the directions of the emergent rays) can easily be obtained. In applying his methods in 1832 to the study of the propagation of light in anisotropic media, in which the speed of light is dependent on the direction and polarization of the ray, Hamilton was led to a remarkable prediction: if a single ray of light is incident at certain angles on a face of a biaxial crystal (such as aragonite), then the refracted light will form a hollow cone. Hamilton?s colleague Humphrey Lloyd, professor of natural philosophy at Trinity College, sought to verify this prediction experimentally. Lloyd had difficulty obtaining a crystal of aragonite of sufficient size and purity, but eventually he was able to observe this phenomenon of conical refraction. This discovery excited considerable interest within the scientific commun.
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