Truman was buried in the Churchyard of St Mary's, Hertingfordbury, Hertfordshire.
Cowpers eldest son William Cowper was clerk of parliament and the father of General William Cowper of Hertingfordbury Park (MP).
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Cowper died on 10 December 1728 and was buried at the family seat Hertingfordbury where a monument to him by Louis-François Roubiliac was erected.