Born in Leeds in 1721, Wilson moved to London after his father's business failed, and may have studied under Thomas Hudson. He painted portraits in Dublin in 1746, 1748-50, then returned to London. A very successful portrait painter, he is also known to have painted scenes for the Duke of York's private plays.
Wilson was also a scientist, who experimented with electricity, and published a treatise on the subject in 1746, which Franklin is known to have read and praised in 1752. On Franklin's arrival in London, the two men became associated in a quasi-friendly scientific rivalry, attending demonstrations and conducting experiments. They held differing opinions about the design of lightning rods; that and other differences eventually cooled the friendship.
He was made a Fellow of the Royal Society in 1751, enjoyed a long and prosperous career as a painter, and died in London in 1788.
Sellers, pp. 54-55, 331-332, 409-414 Pls. 2, 3.