James attended Daniel Stewart's College in Edinburgh, being dux of the school in 1885. He then was an undergraduate at the University of Edinburgh, where he was awarded an M.A., then went to Emmanuel College, Cambridge, where he was a Wrangler in the Mathematical Tripos. In 1893 he was appointed as a Master at Eton, then as a master in Winchester two years later. In 1896 he entered the services of the Egyptian Government. He married Isabella Wilson in 1897.
He was employed at the Ministry of Food in London during the last phase of World War I, then he became Food Controller in 1918-20 to the Upper Silesia Plebiscite Commission. He served with the Egyptian Ministry of Finance as Controller General 1925-8, then as Financial Secretary to the Egyptian Census 1928-34. He was UK Government Commissioner of Customs 1934-47.
He was elected a Fellow of the Royal Society of Edinburgh on 17 February 1908 having been proposed by George Chrystal, William J Macdonald, John Alison, and John Brown Clark. He was a member of the International Statistical Institute and of the Hungarian Statistical Institute. He published General Theory of Map Projections. In 1909 he invented the Craig retroazimuthal map projection. It is a cylindrical projection preserving the direction from any place to other predetermined place. It is sometimes known as the Mecca projection because Craig invented it while working in Egypt to help Muslims find their qibla.
Craig was killed when an Egyptian mob set fire to the Turf Club in Cairo.
His obituary in the Edinburgh Mathematical Notes is at THIS LINK
Article by: J J O'Connor and E F Robertson