In Sphinx, Nicholas Cabot has come to a countryhouse called Mereway where he plans to work on a machine he has invented that records dreams. He encounters a family with three marriageable daughters, and takes refuges from them in the company of some neighbors, including the calculating Celia Hantish and the well-known composer Lore Jensen, who has written a tune called "Sphinx" which hints at the riddle of existence. Meanwhile as Cabot experiments with his machine, he finds that dreams give access to a deeper meaning of life.