Obstetric surgeon and medical lecturer. Hamilton was the son of a retired army surgeon, who practiced at Fordoun (Kincardineshire). In 1780, Hamilton was appointed the fourth Professor of Midwifery at the University of Edinburgh. He held the Chair jointly with his predecessor until 1783. In 1793, with his son, James (1767 - 1839), Hamilton founded a maternity (or 'lying-in') hospital for the poor of Edinburgh, which also proved valuable in teaching.
His son succeeded to his Chair in 1800.