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 Roman legion from a timeline where the Roman Empire never fell appears on the outskirts of St. Louis, Missouri. Viking longships from a timeline where the Vikings settled North America raid a seaport in Massachusetts. A traveling salesman from Louisville, Kentucky, whose van bears a commercial logo including Uncle Sam with the Stars and Stripes, finds himself in trouble with the law when he travels into an area where the South won the American Civil War. A ferry approaching San Francisco finds the flag of Tsarist Russia flying from a grim fortress dominating the city.
When a forest of sequoias appears north of Fredericksburg, Professor Minott leads an expedition of seven students from Robinson College to explore it. They reach the Potomac River, and find on its banks a Chinese village surrounded by rice paddies. At this point, Minott reveals the true situation to the students: he knew in advance that the timeline exchanges were going to take place, and he intends to lead the students to a timeline where he can use his scientific knowledge to gain wealth and power. The party returns to Fredericksburg, which in their absence has been replaced by wilderness, and Minott informs the students that they cannot return to their original timeline.
That night, an airplane from their own timeline makes a crash landing near Minott's party. Before the pilot dies, they learn from him that Washington, D.C. from their timeline was still in place. A student named Blake wants to make for Washington, but Minott refuses. The forest catches fire from the burning airplane, and the party flees to a Roman villa. They are captured by the villa's owner, except for Blake, who escapes. Later that night Blake secretly returns to the villa and frees the others from the slave pen, shooting the owner in the process. The next morning, the party finds itself near a section of their own timeline. Blake leads the other students there, but Minott refuses to come; he still intends to travel to a more primitive timeline and make himself its ruler. One of the women in the party joins him, while the rest of the students return to their timeline.
The students are able to contact the rest of the world and inform them of Minott's deductions about the event. Within two weeks, the timeline exchanges trail off, leaving bits and pieces of other timelines embedded in our own.