Professor Minott is a mathematician at Robinson College in Fredericksburg, Virginia who has determined that an apocalyptic cataclysm is fast approaching that could destroy the entire universe.
The cataclysm manifests itself on June 5, 1935 (one year in the future of the story's original publication) when sections of the Earth's surface begin changing places with their counterparts in alternate timelines.
A ferry approaching San Francisco finds the flag of Tsarist Russia flying from a grim fortress dominating the city.
Leinster's story, conversely, introduced the concept to the pulp science fiction readership, bringing about the creation of one of the field's subgenres.
Lawrence Watt-Evans' story "Storm Trooper" (1992) is set in world whose inhabitants, like those of "Sidewise in Time", must cope with the sudden appearance of sections of other timelines.
The anime series Orguss took "Sidewise in Time" as one of its inspirations, and showed the world caught in a trap of constantly changing territories of alternate-Earths.
The setting of Fred Hoyle's October the First Is Too Late (1966) is similar to that of Leinster's story, except that the segments of Earth which are brought together and interact with each other are from different historical periods, rather than from different parallel histories.
The idea of a scholar using a cataclysmic event to make himself the ruler of primitive people was taken up by S. M. Stirling in the Nantucket and Emberverse series, where the main villains do this repeatedly.