# Algebraic methods for the determination of the geometrical higher order aberrations of optical systems ; On tensors arising from coordinate-invariant and gauge-invariant action integrals ; Two papers concerned with the axiomatic treatment of the second law of thermodynamics

Buchdahl, HA 1949 , 'Algebraic methods for the determination of the geometrical higher order aberrations of optical systems ; On tensors arising from coordinate-invariant and gauge-invariant action integrals ; Two papers concerned with the axiomatic treatment of the second law of thermodynamics', DSc thesis, University of Tasmania.

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## Abstract

The following thesis, submitted to the University of Tasmania for the degree of Doctor of Science, consists of two main sections, complete details of which may be found on pp. (ii)-(v). The parts marked [1]-[5] represent published papers, whilst [6]-[8] have been submitted for publication to the Acta Mathematica and the Annals of Mathematics respectively. The rest consists of a number of hitherto unpublished papers.
The work was carried out indeendently by the candidate, and the various ideas underlying the construction of the algebraic optics here presented, as well as the methods of dealing with invariant action principles are due to him. Further details may be found on pp. 3, 34 ff., 149 ff., etc.
Of two papers photostatic copies of proofs are given, as reprints have not yet been received. In accordance with the rules governing the degree, two papers on the Axiomatic Treatment of the Second Law of Thermodynamics, (due to appear in the American Journal of Physics in December 1948), have also been included.

Item Type: Thesis - DSc Buchdahl, HA Optics, Integrals, Thermodynamics Copyright 1949 the author - The University is continuing to endeavour to trace the copyright owner(s) and in the meantime this item has been reproduced here in good faith. We would be pleased to hear from the copyright owner(s). Article VI appears to be the equivalent of a post-print version of an article published as: Buchdahl, H. A., 1948. On Eddington's higher order equations of the gravitational field, Proceedings of the Edinburgh Mathematical Society, 8(2), 89-94Article VII appears to be the equivalent of a pre-copyedited, author-produced version of an article accepted for publication in Quarterly journal of mathematics following peer review. The version of record, Buchdahl, H. A., 1948, The Hamiltonian derivatives of a class of fundamental invariants, Quarterly journal of mathematics, os-19(1), 150-159, is available online at: https://doi.org/10.1093/qmath/os-19.1.150Article IX appears to be the equivalent of a pre-print version of an article published as: Buchdahl, H. A., 1951. Über die Variationsableitung von Fundamental-Invarianten beliebig hoher Ordnung, Acta Mathematica, 85, 63-72Article X appears to be the equivalent of a pre-print version of an article published as: Buchdahl, H. A., 1951. On the Hamiltonian derivatives arising from a class of gauge‐invariant action principles in a W$$_n$$, Journal of the London Mathematical Society, s1-26(2), 139-149Article XI appears to be the equivalent of a pre-print version of an article published as: Buchdahl, H. A., 1951. An identity between the Hamiltonian derivatives of certain fundamental invariants in a W$$_4$$, Journal of the London Mathematical Society, s1-26(2), 150-152Article XII appears to be the equivalent of a pre-print version of an article published as: Buchdahl, H. A., 1948. On a set of conform-invariant equations of the gravitational field, Proceedings of the Edinburgh Mathematical Society, 8(2), 89-94Article XIII appears to be the equivalent of a pre-print version of an article published as: Buchdahl, H. A., 1949. On the principle of Carathéodory, American journal of physics, 17, 41-43Article XIV appears to be the equivalent of a pre-print version of an article published as: Buchdahl, H. A., 1949. On the Theorum of Carathéodory, American journal of physics, 17, 44-46 View statistics for this item