Wikipedia has a brief article about her, as does thepeerage, but The Duchess of Devonshire's Gossip Guide good article about her with illustrations (including two seen in this Subalbum) includes more - including this: "Another drama quickly followed Betsy's broken engagement with Thomas Long. Sheridan saw his chance and swept Betsy off her feet. She agreed to marry him and the two eloped to France in 1772. Since both were underage, the marriage was invalid, and neither father approved. To save his daughter's reputation Thomas gave his blessing a month later and the two were accepted into polite society as a very talented and good-looking young couple."
Elizabeth Linley was a female intellectual of the day - they were then called Bluestockings.
Gainsborough portrayed her several times, as will be seen.