Buchanan received from McMaster University B.A. in 1906, from Hamilton College B.A. in 1906 and M.A. in 1908, and from the University of Chicago Ph.D. in 1911. He was a professor of astronomy and mathematics from 1911 to 1920 at Queen's University, Kingston, Ontario. He was elected in 1921 a Fellow of the Royal Society of Canada. At the University of British Columbia he became in 1920 professor and head of the department of mathematics and astronomy and in 1928 dean of the faculty of arts and sciences.
