He was married to Margaret Polson Murray who founded the Imperial Order Daughters of the Empire.

[3] Murray stayed at Queen's until 1871 when he accepted a position at McGill University as their Frothingham Professor of Mental and Moral Philosophy.

[6] At McGill, Murray was not deterred from continuing to advocate for women to attend university, despite pushback from fellow professors.

[7] He also lectured at the Montreal Ladies' Educational Association, the Kingston Ladies Educational Association, the Glenmore Summer School of Philosophy, the Cooper Union and the People's Institute in New York City, and the Presbyterian College of Montreal.

[5] His continued advocacy caused problems between him and McGill Principal John William Dawson, which forced Murray to retire from teaching in 1903.