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As Dr. Reed, the head of the physics department at Trent University makes his retirement speech at commencement, four professors wonder who will succeed him. Susan Nash realizes that a woman would not have a chance, but colleagues Marvin Griswald, John Lamont and Alan Shaw are all hopeful. Alan and Lamont both love Reed's granddaughter Deb, while Susan is in love with Lamont. Griswald's wife Janet, though not a faculty member, is a brilliant physicist whose theory about the variable speed of light has propelled Griswald to his present position. When Janet discovers that Griswald has been having an affair with his assistant, Tonya Van Horne, she plans to leave him and take her notes with her. That night, during a party at their home, she suspects that Griswald will do anything to get her notebook, so she hides it in a coat which she thinks is hers, but is actually Deb's. When Griswald confronts her in their second story bedroom, she refuses to surrender the notebook, so he throws a ball out the window and her beloved little dog falls to his death chasing it. The shock then causes Janet to have a fatal heart attack. Griswald summons help and pretends to be a grieving widower, and only Rudolph Brehmer, Janet's faithful assistant, who has found Janet's dead dog in the garden, suspects the truth. After everyone leaves, Tonya and Griswald look in vain in for the notebook, which Deb unknowingly has in her coat pocket. Griswald then goes to Alan's house to look, but is interrupted by Lamont, who had sneaked in to steal some of the artifacts from Alan's research trip to prove that they are fakes. Griswald then kills Lamont and stuffs his body into the dumbwaiter. Meanwhile, Alan and Deb quarrel and she leaves him in a subway station. Next, Susan goes to Lamont's house and finds the body wearing one of Alan's exotic masks. Frightened, she rushes home and her mother tells her to say nothing. Later, Griswald goes to a tavern and runs into Detective Christopher Cross, a Trent alumni who came to town for commencement. Pretending that he is too upset to go home, Griswald suggests that they visit Lamont's house for "the best brandy in town" and, once there, Chris discovers Lamont's body. Griswald is shocked to see the body there, and when the police arrive, he speculates that Lamont's wound could have been caused by a spear. Through various clues, Chris deduces that Lamont must have been transported after death and Griswald suggests that a strong, athletic man, such as Alan, could have done it. When Alan arrives, he admits that he moved the body, but says that he did it because he was afraid to be falsely accused of the murder. The police arrest Alan, but later, Deb suggests to Chris that Susan, who is a fairly large woman, might have moved the body. When the police go to question Susan, they find the body of Susan's mother, and later find Susan's body. At first Alan appears to be in the clear because he was in jail, but Chris soon learns that Alan has escaped from the police. A short time later, Deb discovers Janet's notebook in her pocket and goes to Griswald with it, not realizing that he is the killer. At the same time, Chris and Sergeant Luks of the police department go to a Turkish bank and find Alan. While they are there, they talk about Lamont, and Chris discovers that Lamont did not drink. Chris now suspects Griswald, who insisted they go to Lamont's for a drink. Chris then talks with Rudolph and learns about the missing notebook. Finally realizing that Janet, too, has been murdered, Chris sorts the clues and goes to Griswald's. When he arrives, Griswald has already drugged Deb and is about to kill her. Though he pretends to be innocent, Griswald soon lets remarks slip that reveal that he has killed all of the murder victims. The police arrive just then and chase him to a window ledge. Griswald falls to his death while grabbing for a tree, and Rudolph throws a ball after him. With the case solved, Deb and Alan are reunited.