From the Internet Movie Database: Emma, 1996
During the dance sequence between Emma and Mr. Knightly, the music being played is "Mr. Beveridge's Maggot" ("maggot" meaning "to fancy or like something"). This is the same music used in the famous scene at Netherfield Hall in A&E's Pride and Prejudice, another screen adaptation of a Jane Austen novel.
This scene from Emma leads up to the dance. You can hear the music start up at the end of it.
Click here to hear "Mr. Beveridge's Maggot" in the Pride & Prejudice 1995 dance scene.