Compton is the home of Mr. Smith, Mr. Rushworth's friend. He admires Mr. Smith's renovation of the grounds at Compton and desires to remodel his own home of Sotherton in the same way. It is now a parish and has two manors on it: Compton East and Compton West. The image is of the old Compton Inn found in the village. 

https://www.british-history.ac.uk/vch/surrey/vol3/pp16-24