McQuistan went from Whitehill School, Glasgow, to the University of Glasgow in 1896 with a Marshall Bursary. His position as fifth in the bursary list for the year was an indication of the brilliant career to follow. In April 1899 he obtained honours in Greek and Latin; in the summer of the same year he was awarded the Joseph Black Medal for Physics; in 1901 he graduated M.A. with First-Class Honours in Mathematics and Natural Philosophy, and was awarded the Thomas Logan Medal and Prize as the most distinguished Arts graduate of the year. In the following year he was appointed William Houldsworth Research Scholar in Natural Philosophy, and in 1903 he obtained the degree of B.Sc. with Special Distinction in Mathematics, Natural Philosophy, and Astronomy. From Glasgow he went to the Cavendish Laboratory, Cambridge, as Carnegie Research Fellow for the years 1904-6.
After leaving Cambridge McQuistan devoted himself to teaching, his first appointment being in the Natural Philosophy Department of the Royal Technical College, Glasgow. This he held until 1912, when he decided to take up school work, and served on the staffs of three of the large Glasgow schools - Whitehill, Allan Glen's, and the High School. In 1925 he was recalled to the College as Associate Professor of Natural Philosophy, and on the retiral of Professor Muir in 1938 he was appointed Freeland Professor and head of the department. After only four years ill-health compelled him to resign.
Many generations of students will remember him as a brilliant teacher and demonstrator, while he was in demand as a popular lecturer on scientific subjects. He took a great interest in students' activities and other extra-mural work, and his keen insight and logical mind made him a valuable member of the many academic, scientific, and local government bodies on which he served. To those who were privileged to know him intimately the outstanding memory will be of the kindness, gentleness, and courtesy he always showed, and of his wonderful patience in the long years of failing health and enforced inactivity.
He was elected a Fellow of the Society in 1921.