After completing his school education, Macdonald entered the University of St Andrews, giving the Latin version of his name "Gulielmus Jacobus Macdonald" when he matriculated. In his first year 1868-9 he studied English Literature, Greek 1, Latin 1, and Mathematics 1; in 1869-70 he studied Logic, Greek 2, Latin 2, and Mathematics 2; in 1870-71 he studied Moral Philosophy, Political Economy and Mathematics 3; in 1871-72 he studied Natural Philosophy and Chemistry; finally in 1872-73 he studied Natural Philosophy and Mathematics 3. He graduated M.A. on 30 April 1873. Macdonald showed his outstanding abilities by gaining prizes in almost all the classes he took. He was awarded the Miller prize, which was awarded for the best work by a student in their year, in 1870, 1871 and 1872. He was also awarded the Gray Prize in 1872 for his essay on Spectrum Analysis and in the same year he was awarded the Arnott prize.
After graduating, Macdonald was appointed as an assistant in the Mathematics Department in Madras College. He only taught there for a short time before accepting an appointment as Mathematics Master at Merchiston Castle School in Edinburgh. In 1880 he moved schools, but remained in Edinburgh, when he went to Daniel Stewart's College. He spent the rest of his career at this College.
He was a pioneer in the introduction of modern geometry into the mathematical curriculum, and his book A Higher Geometry was widely used in schools and colleges. Macdonald also acted as an external examiner in mathematics for the University of St Andrews for two periods of three years.
In June 1914 the Senatus Academicus of the University of St Andrews resolved to confer the degree of LL.D. to William James MacDonald, M.A., F.R.S.E. The citation for the award noted that MacDonald was:-
... lately Mathematical master in Daniel Stewart's College, Edinburgh. A graduate in Arts of St Andrews, he had held the mathematical mastership in Daniel Stewart's College for upwards of thirty years. He is author of "A Higher Geometry." He was President of the Edinburgh Mathematical Society 1888 - 9, and President of the Scottish Secondary School Teachers' Association 1898 - 9.However, Macdonald respectfully declined the honour. He did accept a fellowship of the Royal Society of Edinburgh, becoming a fellow on 1 February 1886. He was proposed by William Swan, John Sturgeon Mackay, George Chrystal, and Sir Thomas Muir.
Macdonald was a founder member of the Edinburgh Mathematical Society, joining at the first meeting of the Society in February 1883. He was honoured by the Society when elected president for session 1887-88. Examples of papers Macdonald read to the Society are: An account of Pascal's "Essais pour les Coniques" (Friday 14 March 1884); A proof of a geometrical theorem (Friday 11 February 1887); and A Suggestion for Improvement of Mathematical Tables (Friday 8 March 1895). He also acted as editor of the Proceedings of the Edinburgh Mathematical Society in 1896-97.
Macdonald's death was recorded with the following announcement on Wednesday 31 December 1941:-
Macdonald - At 15 Comiston Drive. Edinburgh, on 29th December 1941. William James Macdonald, in his 91st year, late mathematical master, Daniel Stewart's College. Funeral today (Wednesday), 31 December to Morningside Cemetery. Friends wishing to attend please meet at the cemetery gate at 3.20 pm.
Article by: J J O'Connor and E F Robertson