Hamilton's first years of mathematical research were dedicated to the creation of a theory of geometric optics, whose fundamental principles were based on the use of a characteristic function. This theory was expounded and developed in four substantial papers:---
Hamilton's first published paper was Part First of
Theory of Systems of Rays.which appeared in the Transactions of the Royal Irish Academy, volume 15 (1828), pp. 69-174.
The Theory of Systems of Rays (Part First) is available here in the following formats:
This paper was written whilst Hamilton was an undergraduate at Trinity College, Dublin. (He had earlier submitted for publication a paper entitled On Caustics, but this was not accepted by the Royal Irish Academy in the form in which it was presented: the referees felt that the methods by which some of the conclusions had been arrived at needed to be explained in more detail.)
The Theory of Systems of Rays was originally intended to consist of three parts, and the analytical table of contents describes all three parts. However only Part First was published in Hamilton's lifetime. (Part Second appeared posthumously in The Mathematical Papers of Sir William Rowan Hamilton, Volume I: Geometrical Optics, edited by A. W. Conway and J. L. Synge, and published by Cambridge University Press in 1931.)
An Account of a Theory of Systems of Rays, written by Hamilton himself, is to be found in chapter VI of the Life of Sir William Rowan Hamilton by R. P. Graves.
Hamilton subsequently published three supplements to this essay.
Hamilton developed his approach to geometrical optics in the
Supplement to an Essay on the Theory of Systems of Rays.which appeared in the Transactions of the Royal Irish Academy, volume 16, part 1 (1830), pp. 1-61.
The Supplement to an Essay on the Theory of Systems of Rays is available here in the following formats:
Hamilton subsequently published two further supplements to this essay.
The methods of the Supplement to an Essay on the Theory of Systems of Rays were further developed in the
Second Supplement to an Essay on the Theory of Systems of Rays.which appeared in the Transactions of the Royal Irish Academy, volume 16, part 2 (1831), pp. 93-125.
The Second Supplement to an Essay on the Theory of Systems of Rays is available here in the following formats:
The Second Supplement was followed by a further supplement.
The most developed presentation of Hamilton's approach to geometrical optics is to be found in the
Third Supplement to an Essay on the Theory of Systems of Rays.which appeared in the Transactions of the Royal Irish Academy, volume 17, (1837), pp. 1-144.
The Third Supplement to an Essay on the Theory of Systems of Rays is available here in the following formats:
The Third Supplement was completed in 1832. It commences with an exposition of the theory of Hamilton's characteristic function V (considered as a function of the coordinates both the initial and final point of the light ray) and the auxiliary functions W (first introduced in the Supplement to an Essay on the Theory of Systems of Rays) and T. This is followed by a detailed discussion of aberration. The paper concludes with a discussion of the relationship between Hamilton's theory of the characteristic function and the wave theory of light. The theory is applied to the refraction of light in biaxal crystals (such as arragonite), further developing the theory of refraction in such crystals formulated by Fresnel, and Hamilton predicts the occurrence of the phenomenon of conical refraction, a prediction that was subsequently verified experimentally by Humphrey Lloyd.
Hamilton published in 1833 an expository article, entitled On an General Method of expressing the Paths of Light and of the Planets by the Coefficients of a Characteristic Function, in the Dublin University Review. This article provides an introduction to the theory of the characteristic function with which the Third Supplement commences.
Links:
D.R. Wilkins