The chapter opens with Mr. Vincy going to see Mr. Bulstrode to ask him to write that letter for Fred.
The narrator describes Mr. Bulstrode as a sickly, pale man, whose soft voice had something untrustworthy in it, somehow.
Mr. Bulstrode is just finishing up with another visitor when Mr. Vincy arrives. It's Mr. Lydgate, and they're discussing plans to open a new fever hospital in the area. Mr. Bulstrode would fund it, and Mr. Lydgate would be the head doctor.
During their chat, Mr. Bulstrode admits to Mr. Lydgate that the medical profession in Middlemarch is rather behind the times. Lydgate plans to change that and get Middlemarch up to date.
Bulstrode says that their hospital will need a chaplain, and he wants to appoint Mr. Tyke, even though everyone will expect it to go to Mr. Farebrother.
Lydgate knows and likes Mr. Farebrother, and has never met Mr. Tyke, but, as a doctor, he doesn't really see how the appointment of the chaplain is any of his business.
As he's leaving Mr. Bulstrode's house, Lydgate passes Mr. Vincy, and receives a dinner invitation. That should make Rosamond happy.
Mr. Vincy starts to explain the situation to Mr. Bulstrode, and has to keep himself from being snippy when Bulstrode starts to lecture him about the mistakes he's made in raising his children.
Bulstrode at first refuses to write the letter, and finally agrees to think it over.