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William Houston was born about 1746 to Margaret and Archibald Houston. He attended the College of New Jersey (later Princeton) and graduated in 1768 and became master of the college grammar school and then its tutor. In 1771 he was appointed professor of mathematics and natural philosophy.
From 1775 to 1776 Houston was deputy secretary of the Continental Congress. He also saw active military service in 1776 and 1777 when, as captain of the foot militia of Somerset County, he engaged in action around Princeton. During the Revolution, Houston also served in the New Jersey Assembly (1777) and the New Jersey Council of Safety (1778). In 1779 he was once again elected to the Continental Congress, where he worked mainly in the areas of supply and finance. In addition to serving in Congress, Houston remained active in the affairs of the College of New Jersey and also found time to study law. He was admitted to the bar in 1781 and won the appointment of clerk of the New Jersey Supreme Court in the same year. Houston resigned from the college in 1783 and concentrated on his Trenton law practice. He represented New Jersey in Congress once again in 1784 and 1785.
Houston represented New Jersey at both the Annapolis and Philadelphia conventions. Though illness forced him to leave after 1 week, he did serve on a committee to consider the distribution of seats in the lower house. Houston did not sign the Constitution, but he signed the report to the New Jersey legislature.
On August 12, 1788, William Houston succumbed to tuberculosis and died in Frankford, PA., leaving his wife Jane, two daughters, and two sons. His body was laid to rest in the Second Presbyterian Churchyard in Philadelphia.