|Born||9 December 1863|
|Died||6 July 1931(aged 67)|
|Fields||Mathematics and physics|
|Institutions||University of Tasmania
University of Melbourne
|Alma mater||University of Cambridge
University of Manchester
|Doctoral advisor||Ernest Rutherford|
|Doctoral students||Neville Ronsley Parsons|
|Known for||Work on quaternions|
He is the brother of Francis Macaulay.
McAulay was born December 9, 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". 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" he suggested improvements to the texts then in use. He also wrote a technical article on integration.
Departing for Australia, he lectured at Ormond College, University of Melbourne from 1893 to 1895. As a distant correspondent, he participated in a vigorous debate about the place of quaternions in physics education. In 1893 his book Utility of Quaternions in Physics was published. A. S. Hathaway contributed a positive review and Peter Guthrie Tait praised it in these terms:
- Here, at last, we exclaim, is a man who has caught the full spirit of the quaternion system: the real aestus, the awen of the Welsh Bards, the divinus afflatus that transports the poet beyond the limits of sublunary things! Intuitively recognizing its power, he snatches up the magnificent weapon which Hamilton tenders us all, and at once dashes off to the jungle on the quest of big game.
McAulay took up the position of Professor of Physics in Tasmania from 1896 until 1929, at which time his son Alexander Leicester McAulay took over the position for the next thirty years.
Following William Kingdon Clifford who had extended quaternions to split-biquaternions, 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.
McAulay died 6 July 1931. His brother Francis Macaulay, who stayed in England, also contributed to ring theory. The University of Tasmania has commemorated the McAulays' contributions in Winter Public Lectures.
- A. McAulay (1883) Messenger of Mathematics 13:26 to 37
- "McAulay, Alexander (FML883A)". A Cambridge Alumni Database. University of Cambridge.
- McAulay (1888) Messenger of Mathematics 18:131 to 136
- A. McAulay (1888) "The transformation of multiple surface integrals into multiple line integrals", Messenger of Mathematics 18:139 to 45
- M.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.
- A. S. Hathaway (1894) Review: Utility of Quaternions in Physics, Bulletin of the American Mathematical Society 3(8):179–85
- PG Tait (1893) Nature 28 December
- University of Tasmania: McAulay Lectures
- Rev N. M. Ferres (1892), Review of "On the Mathematical Theory of Electromagnetism", in Proceedings of the Royal Society, London, v.51,p. 400
- A. McAulay (1893) Utility of Quaternions in Physics, originally published in London, now available online from Project Gutenberg.
- Rev N. M. Ferres (1895) Preview of Octonions, Proceedings of the Royal Society 59: 169, weblink from Archive.org.
- A. McAulay (1900) "Notes on the Electromagnetic Theory of Light", Philosophical Magazine 49(5):228–242.