Muir received an appointment to the United States Military Academy (USMA) at West Point, New York in 1881, graduating eighth in his class in 1885.

Brown, Robert Lee Bullard, William F. Martin, Daniel B. Devore and Willard A. Holbrook.

After receiving his commission as a second lieutenant in the United States Army, Muir was sent to Dakota Territory and later to Fort D. A. Russell in Wyoming.

His final duty assignment was at the War Department in Washington, D.C., after which he retired from the army with the permanent rank of major general.

They were the parents of three sons and a daughter, including James I. Muir, who was a career army officer and attained the rank of major general as commander of the 44th Infantry Division during World War II.