He was deeply affected by the religious revival at Oxford, and was much influenced by Isaac Williams, then a tutor of Trinity.
He successfully contested as a Democratic-Republican the election of Federalist John M. Bowers to the 13th United States Congress to fill the vacancy caused by the death of Representative-elect William Dowse (1770–1813), and served from January 24, 1814, to March 3, 1815.
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He was then elected again, to the 18th United States Congress, holding office from March 4, 1823, to March 3, 1825.
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Williams was elected again, to the 15th United States Congress, holding office from March 4, 1817 to March 3, 1819.
Isaac Newton | John Williams | Isaac Asimov | Robin Williams | Robbie Williams | Tennessee Williams | Williams College | Ralph Vaughan Williams | Isaac Stern | Ted Williams | Vanessa L. Williams | Isaac Hayes | William Carlos Williams | Hank Williams, Jr. | Hank Williams | Don Williams | Williams | Shirley Williams | Isaac | Lucinda Williams | Andy Williams | Victoria Williams | Serena Williams | Isaac Bashevis Singer | Brian Williams | Vanessa Williams | Esther Williams | Paul Williams | Bert Williams | Rowan Williams |
He was declared elected as a Federalist to the 13th United States Congress to fill the vacancy caused by the death of Representative-elect William Dowse and served as United States Representative for the fifteenth district of New York from June 21, 1813 to December 20, 1813; when Isaac Williams, Jr., who had contested the election, was declared entitled to the seat.
In conjunction with Isaac Williams, "then the proprietor of the Chino," Wheeler began his trading career, at first with "a train of merchandise and supplies," with headquarters at Agua Caliente, California, followed by a trading expedition across the Colorado Desert to Fort Yuma, Arizona.