'Running Race for Young Ladies' (1828)

'Running Race for Young Ladies at Tenterden' by Robert Cruickshank is an 1828 illustration from Pierce Egan's 'Life in London or, the Day and Night Scenes of Jerry Hawthorn, esq., and his elegant friend, Corinthian Tom, accompanied by Bob Logic, the Oxonian, in their rambles and sprees through the Metropolis'. This fictional account of London adventures was first published as a monthly serial from 1821. 

In reality races involving women would have been a rarity in this period, though not unknown. I don't know whether Cruickshank based his illustration on any real event, but it would have been hard going too far or fast in dresses like these!