Logopolis

Logopolis is the seventh and final serial of the 18th season in the British science fiction television series Doctor Who, which was first broadcast in four weekly parts from 28 February to 21 March 1981. It was Tom Baker's last story as the Fourth Doctor and marks the first appearance of Peter Davison as the Fifth Doctor. This serial also marks the first appearance of Janet Fielding as new companion Tegan Jovanka, whilst Nyssa, played by Sarah Sutton and seen in previous serial The Keeper of Traken, returns and also joins the Doctor as a companion.

Plot

Warned of upcoming danger by the TARDIS's Cloister Bell, the Doctor decides to stay out of trouble, and instead spends time fixing his broken chameleon circuit by extracting the measurements of a true police box on Earth in order to give to the mathematicians of the planet Logopolis. He is unaware that the Master is aware of his plan, and materialises his own TARDIS in a recursive loop with the Doctor's. The Doctor and Adric work out the recursion, and attempt to flush the Master out by materialising the TARDIS in the River Thames, but instead land on a boat on the river with no sign of the Master's TARDIS. Outside, the Doctor sees a glowing white figure, the Watcher, who directs him to hurry to Logopolis. In flight, they discover they have picked up a passenger, Tegan Jovanka, an airline stewardess who wandered into the TARDIS to call for help to fix her aunt's flat tyre; the Doctor informs her the Master has killed her aunt with his Tissue Compression Eliminator.