A tour group of older Americans descend on the Randolph Hotel, including a woman who is about to donate a priceless artefact, the Wolvercote Tongue, to the Ashmolean Museum. When she is found dead shortly after arriving and the Tongue is missing from her hotel room, Morse suspects foul play, despite the hotel doctor's insistence that she died from natural causes. The chief suspect is the woman's husband, Eddie Poindexter, who soon disappears.
The following evening, Morse and Lewis's attention is diverted to Theodore Kemp, the colourful museum curator whose naked body is found floating in the River Cherwell. Morse is convinced that these are two murders connected to the theft, but he has no evidence. Kemp's disabled wife commits suicide after learning of his death, and Morse stumbles into a new line of inquiry by considering the movements of the other expert connected to the tour, Cedric Downes, and his wife, whom Morse and Lewis happen to intercept as she makes her way to London with a suitcase. Later that day, they confront Downes on the platform of Oxford station. His account of when he learned of Kemp's death does not match his wife's, and when Lewis and Morse are distracted by seeing Poindexter step off a train, Downes make an unsuccessful attempt to escape.
Poindexter and Downes confess. Poindexter admits that his wife's death, unsurprising given her heart condition, occurred in his presence, and that he took the Tongue in order to throw it into the river and collect the insurance money. During his disappearance he connected with his long-lost daughter. Downes claims that Kemp's death was an accident and occurred after a confrontation when he had returned home to collect his notes for his lecture, only to find his wife with Kemp in flagrante. After some bending of the truth from Morse, Downes admits to killing his wife in London where she had gone to dispose of Kemp's clothing.
The Wolvercote Tongue is retrieved from the river, and Morse admits that, despite his prior insistence, there were two cases here rather than one: the original death was indeed of natural causes, and the subsequent murders were not related to the theft.
Based on an original story by Colin Dexter, which he subsequently novelised as The Jewel That Was Ours.