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Paton spent his artistic career in London, where he is said to have been born, although no record of his birthplace or parentage is known. He is said to have grown up in poverty, and he is described as "self-taught". Some critics have discerned an influence of Samuel Scott's works, and also of Charles Brooking. Any such influence is hardly evident.
According to an account by Harry Parker, in "The Mariner's Mirror", March 1912, p 85, while Paton was begging "on Tower Hill, he attracted the attention of Admiral Sir Charles Knowles (died 1777), who happened to be passing that way, and who, taking a fancy to the boy, offered to take him to sea". He was assistant to the ship’s painter on Knowles' ship, gaining knowledge in both painting and seamanship. In 1742, he started working at the Excise Office.
Paton's specialities were marine and naval paintings. He painted naval actions of wars ongoing at the time of painting such as the Seven Years' War of 1756–1763 and later The American Revolutionary War, as well as earlier events such as the battles of the War of the Quadruple Alliance which took place when he was a baby. The paintings include many dramatic effects such as battles at night, the shooting of cannons and the effect of bombardments. There are, however, also less militant themes such as ships becalmed. His "sublime depiction of the sky" was considered especially noteworthy. Prints of his works, made among others by Pierre-Charles Canot, made them widely known.
His work was judged "uneven in quality, possibly reflecting his lack of proper training." His career, with its emphasis on the favourable depiction of British war ships and battles at sea, was simultaneous with the publication and immediate popularity of the still well-known song "Rule Britannia." Like that song, Paton's marine paintings both reflected the growth of British sea power throughout the 18th century and helped gain public support and backing for that process.
Among his most well-known works is the Action Between the Serapis and Bonhomme Richard, depicting the famous confrontation of the British Richard Pearson and the American John Paul Jones, occurring on 23 September 1779, off Flamborough Head. It ended with a British defeat; nevertheless, the painting achieved success when included among the prints published within a year of the battle, while the war was still going on, by James Fittler and Daniel Lerpinière. The painting is at present in the museum of the United States Naval Academy at Annapolis.
- Benezit Dictionary of British Graphic Artists and Illustrators, Volume I. Oxford University Press. 21 June 2012. p. 195. ISBN 978-0-19-992305-2. Retrieved 2 February 2013.