Third Supplement to An Essay on the Theory of Systems of Rays. From the Seventeenth Volume of the Transactions of the Royal Irish Academy. INSCRIBED BY WILLIAM ROWAN HAMILTON TO AUGUSTIN-LOUIS CAUCHY.

HAMILTON, William R. [CAUCHY, Augustin-Louis]

Published by Dublin: P. Dixon Hardy, Printer to the Royal Irish Society.

About this Item

1 leaf [title page], [v]-ix, 144 pp. Later cloth. Very Good. First Separate Edition. INSCRIBED BY WILLIAM ROWAN HAMILTON TO AUGUSTIN-LOUIS CAUCHY: "To M. Cauchy/ from the author." Inscription very slightly trimmed at right edge. "Hamilton wrote the 'Theory of Systems of Rays' in three parts. . . . He published only the first part, on reflected rays. . . . He probably decided not to publish the second and third parts because they had become obsolete by the time the Royal Irish Academy had room for them in their Transactions. Instead he published two 'supplements' in 1830 . . . and a third supplement [offered here], in 1833, which was a complete treatise in itself and the most advanced version of his optical theory. The third supplement contained the startling prediction of conical refraction in biaxial crystals, a discovery that did more than all his other mathematical labors to bring him to the attention of the scientific community. . . . As Hamilton made his theory more general in successive supplements to the 'Theory of Systems of Rays,' he also constructed a mathematical formalism that came closer and closer to satisfying the needs of mechanics. The transition from the 'Third Supplement' in 1833 to the 'General System of Dynamics' in 1834 was relatively easy. The greatest amount of mathematical labor went into the optics--not the dynamics (Hankins, Sir William Rowan Hamilton, pp. 67-68). . . . The third supplement is not really a supplement at all, but a complete treatise in its own right. . . . it develops the theory in its greatest generality. . . . The method that Hamilton worked out in his third supplement is still the most general method available for analyzing the properties of optical instruments. . . . Hamilton advertised his third supplement by sending copies directly to a large number of scientists, but these were soon filed away, so that after Hamilton's death in 1865 the optical papers were again unknown or certainly little known (ibid., p. 86). . . . Hamilton's 'General Method in Dynamics' is the most important of all his major mathematical discoveries; it is also the one on which he spent the least time. It grew directly out of his 'Theory of Systems of Rays' (ibid., p. 172). . . . Hamilton's optical papers . . . gradually sank from view and were little known in Germany, where much of the advanced work on mechanics and theoretical physics was taking place. With the advent of the quantum theory in the twentieth century, Hamilton's theory found new value, because it was the one form of classical mechanics that could be transferred almost directly to quantum mechanics. In the second part of his famous paper of 1926 on wave mechanics, Erwin Schrödinger wrote at length about the optical theory that Hamilton had published almost a century earlier. What Schrödinger found of greatest importance was Hamilton's discovery that the laws of geometrical optics and the laws governing the motion of particles could be expressed in the same mathematical form. . . . In his paper of 1926 Schrödinger exploited the Hamiltonian analogy to show how his famous wave equation was related to the principles of classical mechanics and optics" (ibid., pp. 199-200).

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Bibliographic Details

• Title: Third Supplement to An Essay on the Theory of Systems of Rays. From the Seventeenth Volume of the Transactions of the Royal Irish Academy. INSCRIBED BY WILLIAM ROWAN HAMILTON TO AUGUSTIN-LOUIS CAUCHY.
• Publisher: Dublin: P. Dixon Hardy, Printer to the Royal Irish Society.
• Binding: Hardcover
• Edition: 1st Edition
• Condition: Very Good
• Signed: Signed by Author(s)