Alexander McAulay (9 December 1863 – 6 July 1931) was the first professor of mathematics and

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

at the

University of Tasmania The University of Tasmania (UTAS) is a public research university, primarily located in Tasmania, Australia. Founded in 1890, it is Australia's fourth oldest university. Christ College, one of the university's residential colleges, first prop ...

, Hobart,

Tasmania ) , nickname = , image_map = Tasmania in Australia.svg , map_caption = Location of Tasmania in AustraliaCoordinates: , subdivision_type = Country , subdi ...

. He was also a proponent of

dual quaternion In mathematics, the dual quaternions are an 8-dimensional real algebra isomorphic to the tensor product of the quaternions and the dual numbers. Thus, they may be constructed in the same way as the quaternions, except using dual numbers instead of ...

s, which he termed "octonions" or "Clifford biquaternions". McAulay was born on 9 December 1863 and attended

Kingswood School (''In The Right Way Quickly'') , established = , closed = , type = Independent , religious_affiliation = Methodist , president = , head_label = Headmaste ...

in Bath. He proceeded to

Caius College, Cambridge Gonville and Caius College, often referred to simply as Caius ( ), is a constituent college of the University of Cambridge in Cambridge, England. Founded in 1348, it is the fourth-oldest of the University of Cambridge's 31 colleges and one of th ...

, 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 The University of Melbourne is a public research university located in Melbourne, Australia. Founded in 1853, it is Australia's second oldest university and the oldest in Victoria. Its main campus is located in Parkville, an inner suburb no ...

from 1893 to 1895. As a distant correspondent, he participated in a vigorous debate about the place of quaternions in

physics education Physics education refers to the methods currently used to teach physics. Physics Education Research refers to an area of pedagogical research that seeks to improve those methods. Historically, physics has been taught at the high school and colle ...

. In 1893 his book ''Utility of Quaternions in Physics'' was published. A. S. Hathaway contributed a positive review and

Peter Guthrie Tait Peter Guthrie Tait FRSE (28 April 1831 – 4 July 1901) was a Scottish mathematical physicist and early pioneer in thermodynamics. He is best known for the mathematical physics textbook ''Treatise on Natural Philosophy'', which he co-wrote wi ...

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 is a Latin term used by Cicero in , ("The Nature of the Gods") and has been translated as "inspiration". Cicero's usage was a literalising of "inspiration", which had already become figurative. As "inspiration" had come to mean simply the gathe ...

'' 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

s, McAulay made a special study of this

hypercomplex number In mathematics, hypercomplex number is a traditional term for an element of a finite-dimensional unital algebra over the field of real numbers. The study of hypercomplex numbers in the late 19th century forms the basis of modern group represen ...

system. In 1898 McAulay published, through

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, his ''Octonions: a Development of Clifford's Biquaternions''. McAulay died on 6 July 1931. His brother Francis Macaulay, who stayed in England, also contributed to

ring theory In algebra, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers. Ring theory studies the structure of rings, their r ...

. The University of Tasmania has commemorated the McAulays' contributions in ''Winter Public Lectures''.

McAulay Public Lectures archived from 2007-06-13
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Works

* 1893
Utility of Quaternions in Physics
link from

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. * 1898
Octonions: a development of Clifford's Biquaternions
link from

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* 1900: "Notes on the Electromagnetic Theory of Light",

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49(5):228–242.

References

* Rev N. M. Ferres (1892), Review of "On the Mathematical Theory of Electromagnetism", in

Proceedings of the Royal Society ''Proceedings of the Royal Society'' is the main research journal of the Royal Society. The journal began in 1831 and was split into two series in 1905: * Series A: for papers in physical sciences and mathematics. * Series B: for papers in life s ...

, London, v.51,p. 400 * Rev N. M. Ferres (1895
Preview of ''Octonions''
''Proceedings of the Royal Society'' 59: 169, weblink from

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External links

* Bruce Scott (1986
McAulay, Alexander (1863 – 1931)
from Australian Dictionary of Biography. * * {{DEFAULTSORT:McAulay, Alexander 1863 births 1931 deaths British physicists 19th-century British mathematicians 19th-century Australian mathematicians 20th-century Australian mathematicians Historical treatment of quaternions