Muir was a chartered accountant.
He was admitted on 28 February 1887 as a lay member of Glasgow Art Club. He was among those Glasgow painters and architects and art club members who in 1891 appended their names to a list requesting that the Corporation of Glasgow buy JW's Arrangement in Grey and Black, No. 2: Portrait of Thomas Carlyle (YMSM 137) (#12326). He lived at 27 Huntley Gardens, Glasgow.
Records of Glasgow Art Club.