He was born in
Edinburgh in 1767, the son of
Dr Alexander Hamilton. He attended the High School in Edinburgh, and then studied medicine at the
University of Edinburgh (in part under his father). He also studied at
Paris,
Leiden and the
University of St Andrews receiving his
MD from the latter in 1792. In 1824, he was elected a fellow of the
Royal Society of Edinburgh, his proposer being
Andrew Coventry. In 1825, he fell out with fellow Edinburgh doctor
James Crawford Gregory as to whether or not midwifery should be a compulsory component of the University course. He bypassed the Senate of the
Royal College of Physicians of Edinburgh on this issue and received consent directly from the
Lord Provost, William Trotter. When Gregory next met him he beat him ferociously with his cane. He was fined £100 for the assault. After he died, he was succeeded in his professorship by
James Young Simpson. ==Private life and death==