During a freezing December in the Thames Valley, Hollywood actress Marcia Blystone travels to White Priory, the country estate of Maurice Bohun, a theatrical impresario and antiquarian. Bohun has convened an eccentric house party consisting of his brother, several theatrical colleagues, and personal associates to negotiate production rights. The focal point of the estate grounds is the Queen's Mirror, an isolated, octagonal historical pavilion built in the seventeenth century, situated in the center of an expansive open lawn covered by an unblemished layer of fresh winter snow.

In the early hours of the morning, Marcia Blystone is discovered bludgeoned to death on the pavilion floor. Physical inspection of the surrounding terrain reveals an insoluble environmental puzzle: several inches of snow fell during the night, ending well before the estimated hour of death, leaving the expanse surrounding the pavilion completely undisturbed. Only a single track of footprints traverses the lawn from the main house to the pavilion door, and these match the victim's evening shoes precisely. No other footsteps, ski tracks, vehicle marks, or aerial contrivances exist within fifty yards of the structure, leaving no observable physical route by which a human assailant could approach or withdraw from the scene.

Chief Inspector Humphrey Masters of Scotland Yard arrives to find local constabulary efforts impeded by the apparent impossibility of the physical footprint evidence. Accompanied by American diplomat James Bennett, Masters requests the intervention of Sir Henry Merrivale, whose investigative approach emphasizes practical mechanics and thermodynamic analysis. With the suspects confined to the estate and mutual accusations mounting among the theatrical company, Merrivale must determine the exact timing of the weather conditions and deduce how an external weapon could inflict fatal blunt-force trauma across an untouched snowfield.