Died: 7 June 1937 in Peebles, Scotland

James Macdonald was educated at Duncan Place School in Leith, spending ten years there from 1874 to 1884. At this time his address was 8 Noble Place, Leith. He first matriculated at Edinburgh University in October 1884. He graduated with an M.A. with First Class Honours in Mathematics and Natural Philosophy in 1895, obtaining a B.Sc. (Pure) in the same year after taking B.Sc. courses in Mathematics, Natural Philosophy, Botany, Zoology, including Comparative Anatomy, Chemistry and Practical Chemistry.

It is not entirely clear [to the writers of this biography] why he graduated eleven years after first matriculating, but given that he became a rector and was made a fellow of the Royal Society of Edinburgh two years after graduating, it is reasonable to assume that he must have taught in schools during these eleven years. Certainly the record of courses he took at Edinburgh University contains a break between session 1887-88 and session 1893-94 and there is no record of him attending any courses in the five intervening sessions. At Edinburgh he was awarded the Fergusson Scholarship in Mathematics, the Neil Arnott Scholarship in Physics and the Maclaren Scholarship in Mathematics and Natural Philosophy.

Macdonald was the first Rector of Leith Academy, appointed to the role in 1897. In December 1899 he submitted his thesis Certain Properties of the "C" Discriminant, a Treatment of the subject from a Kinematical and Analytical Point of View for the degree of D.Sc. at the University of Edinburgh. Chrystal and Gibson examined the thesis, Chrystal as Internal Examiner and Gibson from Glasgow as External Examiner, and rejected it in January 1900. Macdonald did not try again for this degree. In 1901 he became one of His Majesty's Inspectors of Schools. He lived first in Kelvinside, Glasgow, then from 1903 in Dingwall. In 1910 he moved to Stewarton, Kilmacolm, and then in the following year to Inverness. In 1921 he became Chief Inspector of Schools for the Highland Division. He retired in 1930 and went to live at Rothes, Frankscroft, Peebles.

In 1908 Macdonald's son, also named James Alexander Macdonald, was born in Dingwall, Ross-shire. This son went on to become a botanist and was Professor of Botany at the University of St Andrews from 1961 to 1977. For several years around 1970, he was my [EFR] golfing partner playing for the University of St Andrews staff golf team.

A member of the Edinburgh Mathematical Society, Macdonald joined in February 1896 while teaching in Leith but before his appointment as Headmaster there. He remained in the Society throughout his life. He was elected to the Royal Society of Edinburgh on 7 June 1897, his proposers being George Chrystal, Peter Guthrie Tait, Alexander Crum Brown, Cargill Gilston Knott.

An obituary, written anonymously, appears in the Proceedings of the Royal Society of Edinburgh, Volume 57 (1936-37), 436. 
We give a version of this obituary at THIS LINK.

The Scotsman published an obituary of Macdonald in June 1937:-

THE LATE MR JAMES A MACDONALD

Former Chief Inspector of Schools in Highlands
The death has occurred, at his home at Rothes, Peebles, of Mr James Alexander Macdonald, a well-known figure in Scottish education circles, and formerly His Majesty's Chief Inspector of Schools for the Highland Division.

1. , M.A., B.Sc., Proc. Roy. Soc. Edinburgh 57 (1936-37), 436.
2. Graduates in Arts, 1884-1925 (University of Edinburgh).
3. Graduates in Arts (University of Edinburgh).
4. Graduates in Science (University of Edinburgh).