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On the Optical Writings of Sir William Rowan Hamilton

Published online by Cambridge University Press:  03 November 2016

G. C. Steward
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Extract

The study of Geometrical Optics has not attracted much interest or attention for some years now. at all events until recently, save only among a quite small company of specialists, and, as but one particular result of this, the divorce between optical theory and optical practice has been lamentable, as, for example, in that problem of so great practical importance, the design of the symmetrical optical system. For the one part, the subject has been regarded as isolated and of little theoretical interest, and scarcely susceptible of wide and profound generalisations, then, too, and this more especially from the point of view of university teaching, geometrical optics has seemed to stand apart from the path to a general mathematical education and training, and, in consequence, in several universities the study of it has been almost abandoned, save only in its most elementary aspects.

Type
Research Article
Information
The Mathematical Gazette , Volume 16 , Issue 219 , July 1932 , pp. 179 - 191
Copyright
Copyright © Mathematical Association

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References

page no 179 note * The Mathematical Papers of Sir William Wowan Hamilton: Volume I, Geometrical Optics. Edited for the Royal Irish Academy by Conway, A. W and Synge, J. L.. Pp. xxviii, 534. 50s. 1931. (Cambridge university Press.)Google Scholar

page no 187 note * An outline sketch of the properties of the symmetrical optical system, from the purely geometrical and also from the physical (diffraction) points of view, will be found in The Symmetrical Optical System, Cambridge Tracts in Mathematics and Mathematical Physics, No. 25, by the present writer.

page no 188 note * Cf. Trans. Camb. Phil. Soc. xxiii, No. ix (1926).

page no 188 note † Due to Smith, T.: cf. “The Optical Cosine Law”, Trans. Opt. Soc. xxiv (1922-3), No. 1 Google Scholar; and, for another proof, Proc. Camb. Phil. Soc. xxiii, vi, p. 703, “On Herschel’s Condition and the Optical Cosine Law”, by the present writer; or, Camb. Math. and Phys. Tracts, No. 25, ch. iv, §§ 6 and 7.

page no 189 note * Cf. Trans. Camb. Phil. Soc. xxiii, No. ix (1926), § 26, by the present writer.

page no 189 note † The usual treatment of (first order) coma is but a special case of Hamilton’s investigation, given in § 60, sect, xii, on Aberrations, in Part I of the Theory of Systems of Rays; for here Hamilton considers the distribution of near rays around any ray having what he defines as a principal focus, i.e. a ray for which the usual two foci coincide; and the optical system is in no way symmetrical. He finds a family of ellipses enveloped by two straight lines passing through the principal focus; a somewhat similar phenomenon to that found by the present writer to hold for symmetrical systems and for aberrations of the second and higher orders, which he has named “elliptical coma” (Trans. Camb. Phil. Soc. xxiii, No. ix, § 8). And there are also more generalised types of coma.

page no 191 note * Phil. Trans. Roy. Soc. A, 225 (1925).