The inoffensive Reverend Babbington chokes to death at a cocktail party he is attending with his wife at the home of famous actor Sir Charles Cartwright. Some time later Sir Bartholomew Strange, an eminent doctor and friend of Cartwright, also dies of poisoning at a dinner party he is giving miles away. There appears to be no link between the two deaths but Poirot, assisted by Cartwright, offers to help Superintendent Crossfield in the investigation and discovers that a mysterious butler with a birthmark on his wrist was hired for the night and appeared to share a joke with the dead doctor. This man has now vanished and would seem to the killer. A third death, that of a sanatorium patient who has written to Poirot, would appear to link to the doctor's murder and there is certainly a secret which somebody will go to any lengths to conceal - but who would gain from the death of a harmless old vicar?