He and his brother William founded the Craven Hunt, and he appears in James Seymour's 1743 A Kill at Ashdown Park, a picture owned by the Craven family until 1968.
Though ultimately his love for horseracing led to his financial ruin, Seymour still ranks among the most important early sporting artists, together with John Wootton and Peter Tillemans being considered one of the three founders of the sporting school.
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Swyer made a single first-class appearance, in a County Championship match in 1923 against Kent, in which he bowled thirteen overs in a match which saw centuries from Kent pair Wally Hardinge and James Seymour.