In 1857-1863, Murray was as principal of The Albany Academy in New York. From 1863 to 1873,
he was a professor of mathematics, natural philosophy and astronomy at
Rutgers College in New Jersey.
Together with George Cook, Murray developed a full science curriculum at Rutgers, and successfully lobbied for Rutgers to be named the state's land grant college.
Their 1864-67 surveys established the marine boundary between New York and New Jersey, and their
1872 survey fixed the land boundary between New York and New Jersey. Murray was also responsible for the building of Rutgers' first astronomical observatory, the Daniel S. Schanck Observatory. In 1873, Murray departed Rutgers to become the educational advisor for the Japanese government. After his return, Murray served on the Rutgers College board of trustees from 1892 until his death in 1905.
Chamberlain, William Isaac. (1915). In Memoriam, David Murray, Ph.D., LL. D., Superintendent of Educational Affairs in the Empire of Japan, and Adviser to the Japanese Imperial Minister of Education, 1873-1879. New York: private printing. U.S. Library of Congress, online full-text; OCLC 7578354