Joseph was the 10th graduate of the United States Military Academy, one of a class of three graduating in 1805. After assisting his maternal uncle Jared Mansfield surveying the Northwest Territory, Joseph served with the Army Corps of Engineers building Castle Williams and Castle Clinton in New York Harbor. He saw combat in the War of 1812. After overseeing construction of Fort Adams in Newport, Rhode Island, Joseph was appointed Chief Engineer of the United States Army in 1838, and served in that capacity until his death in 1864. He was elected an Associate Fellow of the American Academy of Arts and Sciences in 1841.
While building Fort Montgomery on Lake Champlain in upstate New York, Joseph invented an iron-reinforced embrasure for cannon, known as Totten shutters. These shutters were hinged swinging doors installed on cannon openings of forts between the mortar and brick facade. These iron shutters were balanced to swing freely to be forced open by the gas expelled from the cannon, and then rebound shut immediately afterwards, shielding the gunners from incoming fire.
Joseph directed the siege of Veracruz as General Winfield Scott's chief engineer during the Mexican–American War.
One of Totten's most significant achievements was the design and construction of the Minot's Ledge Light near Cohasset, Massachusetts. Previous efforts to build a lighthouse on the small ledge of rock had failed but Totten conceived a plan whereby the lighthouse would be pinned by its own weight to the ledge, making it able to withstand the harshest extremes of weather and survive into the 21st century.
Joseph was regent of the Smithsonian Institution and cofounder of the National Academy of Sciences. The Civil War-era Fort Totten was named for him when built as part of the Defenses of Washington, D.C. A few earthworks remain in Fort Totten Park. Another Fort Totten similarly named for him is the historic former U.S. Army fort maintained by New York City in Queens.
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