Having regenerated in order to recover from the Toxoemia, the new Doctor starts acting erratically, he nearly strangles Peri and then decides to become a hermit on the Titan 3 Asteroid. But his quiet existence is soon to be disturbed by an enormous dome on the distant horizon. The mysterious inhabitants have been linked with the kidnapping of the twins Romulus and Remus. The pair are extraordinary mathematicians with power to move planets.