Alexander Macfarlane FRSE (April 21, 1851 – August 28, 1913) was a Scottish logician, physicist, and mathematician.
Macfarlane was born in Blairgowrie, Scotland and studied at the University of Edinburgh. His doctoral thesis, on the conditions governing the electric spark, was subsequently published in the Transactions of the Royal Society of Edinburgh. It brought him to the notice of James Clerk Maxwell, and in 1878 Macfarlane was elected a Fellow of the Royal Society of Edinburgh
During his life, Macfarlane played a prominent role in research and education. He taught at the universities of Edinburgh and St Andrews, was physics professor at the University of Texas (1885 – 1894)^{[2]}, professor of Advanced Electricity, and later of mathematical physics, at Lehigh University. MacFarlane was the secretary of the Quaternion Society and compiler of its publications.
Macfarlane was also the author of a popular 1916 collection of mathematical biographies (Ten British Mathematicians), a similar work on physicists (Lectures on Ten British Physicists of the Nineteenth Century, 1919), and he compiled a bibliography on quaternions in 1904. Significantly, by exploiting the concept of hyperbolic versor originating with James Cockle, he invented hyperbolic quaternions, which anticipated Minkowski space. (He was imbued with hyperbolic geometry through his brotherinlaw G. B. Halsted while they taught in Austin.)
Macfarlane actively participated in several International Congresses of Mathematicians including the primordial meeting in Chicago, 1893, and the Paris meeting of 1900 where he spoke on "Application of space analysis to curvilinear coordinates".
Macfarlane retired to Chatham, Ontario, where he died in 1913.
