He was recommended to Thomas Whichcote of Harpeswell, MP for Lincolnshire, who had him tested by the master of Brigg school, following which he nominated Watson to the Royal Military Academy at Woolwich.
He received training from Professor Thomas Simpson who became a close friend and contributed articles to The Ladies' Diary, a mathematical periodical.
Watson was unable to do this; he was posted to Belleisle under Commodore Keppel and General Hodgson and then to Havana under Admiral Sir George Pocock.
He designed and proposed dry and wet docks at Calcutta but this was not completed due to lack of funds.
He became a lieutenant colonel in January 1775 and returned to England, where he translated Euler's Compleat Theory of the Construction and Properties of Vessels (1776).