Brief Encounters: Cambridge Previsited
So... since when can the First Doctor navigate the TARDIS so accurately? Not only do we get a short hop from the library to Chronotis' office, but we get the Doctor's ridiculous extravagance of asking the Professor to meet him in the College library "fifteen minutes ago". If Ian and Barbara are amongst the companions sleeping the TARDIS, it's to hoped that they didn't wake up and catch him flitting about...
Why exactly does the Doctor visit Chronotis? All he seems to do is make small talk before clearing off! [The impression given throughout is that this story is set fairly early in the continuity of the television series, so it's possible that, still a relatively new exile from Gallifrey, the Doctor wants to meet a kindred spirit, although this still doesn't explain the fact that all he does is recommend a book to him].
Continuity: Time Lords can recognise other Time Lords regardless of incarnation.
The Doctor is travelling with companions, who remain sleeping in the TARDIS whilst he visits Chronotis. The First Doctor meets Professor Chronotis for the first time here and knows of him by reputation, apparently from before he left Gallifrey. The Doctor has already read The Time Machine by this point (see The TV Movie). The Doctor hasn't read Treasure Island, and after his meeting with Chronotis, he materialises the TARDIS in the Professor's rooms and exchanges a copy for a copy of The Time Machine.
Chronotis dislikes Earth music, including Buddy Holly. He finds Earth and humans "irritatingly fascinating". Although the First Doctor meets him for the first time here, Chronotis has recently seen the Third or Fourth Doctor and Sarah Jane Smith and is aware of the Doctor's period of exile on Earth (The War Games). He desperately tries to pretend not to the know the Doctor to avoid damaging the time lines. The Doctor recommended that he read H.G. Wells' The Time Machine. Chronotis seemingly uses his gift for mental projection to make students realise when they have made errors in their work (see Shada). He is sure that he has read every book in the college library. Amongst the books in his rooms are biographies, children's story books, science and nature books, and a first edition Peter Rabbit.
The Ancient and Worshipful Law of Gallifrey is possibly sentient.
Links: Shada. The Doctor notes that he settled on Earth for a while in "a few years" time (An Unearthly Child). Chronotis mentions Rassilon.
Location: Cambridge, a few years before 1963.
The Bottom Line: Nice idea, sloppy execution. There's no real reason for the Doctor's vanishingly brief meeting with Chronotis and for a story so dependent on continuity it gets far too much wrong (see Goofs)