Seaton, Crane and their wives depart the Green system in the hugely powerful Skylark Three but are waylayed by the "pure intellectual" beings first seen in Skylark of Space. To escape them, the Earthlings take a jaunt through the fourth dimension.
Meanwhile, Duquesne conquers Earth.
"I've been thinking, Rufus, and if you don't believe that it's hard work, you'd better try it sometime. I won't have to do it any more though -- got a machine to do my thinking for me now."
"Human? It's a lot more than that. It can outthink and outperform even those pure intellectuals-- 'and that,' as the poet feelingly remarked, 'is going some'!"
This book is unusual in that it discusses computing devices, a topic Smith otherwise missed almost entirely. Throughout the guy's work, scientists design ships and weapons, deploy them and navigate the universe with the help of only a slide rule. In this book, the protagonists rely on a mechanical computational device to help them find their way back to Earth after their disorienting trip through higher dimensions (a seemingly modern concept, but one Smith used quite often).
Seaton appears to vanquish Duquesne for real here, zapping the man's consciousness out of his body and sending his intelligence floating away through the universe. It's kind of like the opening scene of Superman: The Movie, in which Zod and his cohorts are banished to another dimension for their crimes against Krypton. As in the Superman flick, the reader can rely upon the bad guy returning in a sequel.
"The courage which dictates the useless sacrifice of a life ceases to be courage at all, but becomes sheerest folly."