He was educated at the University of St. Andrews, where during Jacobite rebellion of 1715, he headed a riot of some students of the college, who rang the college bells on the day that the Old Pretender was proclaimed.
[2] In October 1740 Martine accompanied Charles Cathcart, 8th Lord Cathcart, as physician to the forces on the British expedition during the War of Jenkins' Ear, to attack the Spanish possessions in America.
After the death of Lord Cathcart, on Dominica, 20 December 1740, he was attached as first physician to the expedition against Cartagena under Edward Vernon (see Battle of Cartagena de Indias).
[2] The Examination of the Newtonian Argument for the Emptiness of Space London, 1740, was also by Martine.
It led him into controversy with Colin Maclaurin, who replied with Account of Sir Isaac Newton's Discoveries (1748), defending Newton's assertion of the existence of the vacuum.