A scientifically minded professor is stumped by a case involving séances and an inexplicable inheritance . . .   After drifting apart from Sir John Claverton, Dr. Lancelot Priestley is finally visiting his old friend for dinner. But Claverton's situation is worrying. He's surrounded by relatives, among them a sister who speaks to the dead--but not to him--and a niece who may or may not be a qualified nurse. Based on Claverton's odd behavior, Priestley and a mutual friend suspect that someone is slipping him arsenic.   But when Priestley discovers that Claverton has died just a week later and shares his concerns with the police, no trace of arsenic--or anything else untoward--is found during the autopsy. Still, the perceptive professor can't shake his sense that something isn't right, and Claverton's recently revised will only adds to the mystery . . .   "The puzzle is sound, the atmosphere menacing in a splendidly gloomy way." --Jacques Barzun and Wendell Hertig Taylor, A Catalogue of Crime   "You can never go far wrong with a Dr. Priestley story." --The New York Times