Eddard talks with Pycelle about Jon Arryn's death. Apparently Jon asked for a book one day and then died soon after; his last words were "the seed is strong." What does that mean?
Pycelle doesn't think it was poisoning and warns Eddard not to trust the eunuch,Varys.
Eddard talks to Arya about how Bran can never be a knight because he's crippled, but might be a great councillor or builder; while Arya, because she's a girl, can't be anything. (See our discussion of "Gender" and/or get mad.)
Eddard talks – boy, he does that a lot – to Petyr who has found four people from the Arryn household who are still in the city, including Jon Arryn's squire who is now a knight (Ser Hugh). Petyr also notes that Eddard shouldn't trust anyone, not even Petyr himself.