Alexander McAulay (9 November 1863 – 5 July 1931) was a mathematician and physicist who was the first professor of mathematics and physics at the University of Tasmania, Hobart, Australia. He was also a proponent of dual quaternions, which he termed "octonions" or "Clifford biquaternions".
Life McAulay was born on 9 November 1863 and attended Kingswood School in Bath. He proceeded to Caius College, Cambridge, there taking up a study of the quaternion algebra. In 1883 he published an article "Some general theorems in quaternion integration".A. McAulay (1883) Messenger of Mathematics 13:26 to 37 McAulay took his degree in 1886, and began to reflect on the instruction of students in quaternion theory. In an article "Establishment of the fundamental properties of quaternions",McAulay (1888) Messenger of Mathematics 18:131 to 136 he suggested improvements to the texts then in use. He also wrote a technical articleA. McAulay (1888) "The transformation of multiple surface integrals into multiple line integrals", Messenger of Mathematics 18:139 to 45 on integration.
Departing for Australia, he became a lecturer and tutor in mathematics at Ormond College, University of Melbourne, from 1888 to 1895, being appointed first lecturer of mathematics in 1893. As a distant correspondent, he participated in a vigorous debate about the place of quaternions in physics education.Michael J. Crowe (1967) A History of Vector Analysis, U. Notre Dame Press. Chapter 6 details McAulay's four contributions in 1893 and 94 to the debate on vectors and quaternions. In 1893 his book Utility of Quaternions in Physics was published. A. S. Hathaway contributed a positive reviewA. S. Hathaway (1894) Review: Utility of Quaternions in Physics, Bulletin of the American Mathematical Society 3(8):179–85 and Peter Guthrie Tait praised it in these terms:
In 1896, McAulay took up the position of first professor of mathematics and physics at the newly-founded University of Tasmania. He ceased teaching in 1924 due to incipient blindness and was selected as research professor until his retirement in 1929.
Following William Kingdon Clifford, who had extended quaternions to dual quaternions, McAulay made a special study of this hypercomplex number system. In 1898 McAulay published, through Cambridge University Press, his Octonions: a Development of Clifford's Biquaternions.Rev N. M. Ferres (1895). Preview of Octonions. Proceedings of the Royal Society. 59: 169, weblink from Archive.org
McAulay died from cerebral haemorrhage on 5 July 1931, in his home at Sandy Bay, Tasmania, and was buried in Hobart.
His brother Francis Sowerby Macaulay, who stayed in England, also contributed to ring theory. The University of Tasmania has commemorated the McAulays' contributions in Winter Public Lectures.University of Tasmania: McAulay Public Lectures archived from 2007-06-13
Works 1893: Utility of Quaternions in Physics, link from Project Gutenberg. 1898: Octonions: a development of Clifford's Biquaternions, link from Internet Archive 1900: "Notes on the Electromagnetic Theory of Light", Philosophical Magazine 49(5):228–242.Rev N. M. Ferres (1892). Review of "On the Mathematical Theory of Electromagnetism". Proceedings of the Royal Society, London. v. 51, p. 400.
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