He studied from the works of Sir Peter Lely, and under Joseph van Aken acquired facility in painting satin.
[1] Through a Masonic lodge, Davison became acquainted with James Murray, 2nd Duke of Atholl, and painted his portrait.
Under the patronage of the Duke and Duchess he went to Scotland, and obtained a good practice as a portrait-painter in Edinburgh, and London.
At Greenwich Hospital is a full-length portrait by him of Admiral George Byng, 1st Viscount Torrington; in the National Gallery of Scotland is a head of Richard Cooper, the elder; and in the Merchants' Hall, Edinburgh, is a half-length of Elizabeth Macdonald of Largie, wife of Charles Lockhart of Lee and Carnwath.
[1] A group representing James Douglas, 14th Earl of Morton and his family is now in the Scottish National Portrait Gallery.