## Acta Mathematica

- Acta Math.
- Volume 67 (1936), 213-250.

### On invariant and semi-invariant aberrations of the symmetrical optical system

**Full-text: Open access**

#### Article information

**Source**

Acta Math., Volume 67 (1936), 213-250.

**Dates**

First available in Project Euclid: 31 January 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.acta/1485888151

**Digital Object Identifier**

doi:10.1007/BF02401742

**Mathematical Reviews number (MathSciNet)**

MR1555420

**Zentralblatt MATH identifier**

0015.42904

**Rights**

1936 © Almqvist & Wiksells Boktryckeri-A.-B.

#### Citation

Steward, G. C. On invariant and semi-invariant aberrations of the symmetrical optical system. Acta Math. 67 (1936), 213--250. doi:10.1007/BF02401742. https://projecteuclid.org/euclid.acta/1485888151

#### Literaturverzeichnis

*Aberration Diffraction Effects*: Phil. Trans. Royal Soc. (Lond.) A. 225.- see, for example,
*The Aberrations of a Symmetrical Optical Systems*, Trans. Camb. Phil. Soc. XXIII, No. IX, and also*The Symmetrical Optical System*: Camb. Tracts in Mathematics and Mathematical Physics, No. 25. - The surprising extent to which Sir William Hamilton had applied his very general theory to the actual consideration of particular optical systems, whether symmetrical or quite unsymmetrical, is only revealed by a careful perusal of his celebrated Papers on
*The Theory of Systems of Rays*. These have recently been published in the Edition of his Collected Works, Volume I,*Geometrical Optics*, by the Cambridge University Press, under the very able and joint Editorship of Professors Conway and Synge: here certain papers are published for the first time. And in them the general functions introduced by Hamilton are applied to the symmetrical optical system, a project which frequently he mentioned in his published works, but to which, in them, he never seems to have addressed himself. But even in the papers published, for example, in 1833–34 there is given an investigation of the aberration known afterwards as*coma*, and this for a system quite unsymmetrical; and the discovery of this aberration has commonly been attributed to Kirchhoff, at a much later date, who himself was working with functions akin to those introduced by Hamilton. For additional information concerning these matters, and other matters connected with them, reference may be made to a paper, by the present writer,*On the Optical Writings of Sir William Rowan Hamilton*, Mathematical Gazette, July 1932, Vol. XVI, No. 219, pp. 179–191. *The Symmetrical Optical System*: Camb. Tracts in Mathematics and Mathematical Physics, No. 25.*The Symmetrical Optical System*, Camb. Tracts in Mathematics and Mathematical Physics, No. 25, Ch. V.- This invariant relation, the simplest of its type, is, of course, the ‘Petzvalsum’.
- Θ/
*v*is in fact the modified and reduced eikonal for a single spherical surface, separating media of optical indices μ and μ′, the base-points being coincident at the centre of curvature of the surface. *The Aberrations of a Symmetrical Optical System*: Trans. Camb. Phil. Soc. XXIII. No IX.- Trans. Camb. Phil. Soc. XXIII. No. IX. § 3.
- Trans. Camb. Phil. Soc. XXIII. No. IX. § 17.
- Trans. Camb. Phil. Soc. XXIII. No IX. §§ 7, 8, 9.
- Trans. Camb. Phil. Soc. XXIII. No IX, § 27.

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