Civilian and academic career
William resigned his commission in the U.S. Army on December 1, 1856, to accept a professorship of mathematics at the University of Michigan. A year later, he returned to the U.S. Coast Survey as a civilian scientific adviser, where he was employed on Gulf Stream observations and in magnetic work at Key West, Florida. From 1862 to 1865, during the Civil War, he was in charge of the engineer agency in New York City and oversaw the construction of the fort at Willets Point as well as repairs to New York Harbor.
After the war, he was vice-president of the Novelty Iron Works in New York City until 1871, when he returned to academia as first mechanical engineering professor at Yale, where he took the post of Professor of Dynamical Engineering in the Sheffield Scientific School. While at Yale, he served the State of Connecticut as Adjutant General from 1872 to 1876, commissioner of the building of the Connecticut State Capitol and as commissioner for establishing harbor lines at New Haven. In 1877 he accepted a position as chair of the engineering department at the School of Mines at Columbia College, where he remained until his death in 1892. While serving at Columbia College, Professor Trowbridge took charge of the Tenth Census of the department of power and machinery employed in manufactures.
He was associate editor with Johnson’s Universal Cyclopaedia and author of “Heat and Heat-Engines” (1874) as well as numerous contributions to the Academy of Sciences of New York. The degree of A.M. was conferred upon him by University of Rochester in 1856 and by Yale in 1870. He was awarded a Ph.D. by Princeton College in 1880 and an LL.D. by Trinity College in 1883 and by the University of Michigan in 1887. He was a member of the New York Academy of Sciences, the American Association for the Advancement of Science and was elected a member of the National Academy in 1872.