On his way out the gate of Mr. Brooke's estate in his carriage, Mr. Casaubon passes another lady in a smaller carriage on her way in.
The lady isn't dressed very well, but she's clearly important socially – the lodge-keeper's wife curtseys to her as she opens the gate.
It's Mrs. Cadwallader, the wife of the vicar. They aren't very well off (and have lots of children), but Mrs. Cadwallader is the descendent of earls and dukes. She's also very opinionated and stubborn, and more than willing to give a piece of her mind to anyone who disagrees with her.
Mr. Brooke isn't too happy when he sees Mrs. Cadwallader arrive – he knows she's going to scold him about allowing Dorothea to marry Mr. Casaubon.
Mrs. Cadwallader begins by scolding Mr. Brooke on political questions, but quickly reverts to the question of Dorothea's marriage. She assumes that she'll marry Sir James.
Mr. Brooke sets her straight, but doesn't mention who the preferred suitor is.
Celia comes into the room, and Mr. Brooke takes the opportunity of escaping.
Celia tells Mrs. Cadwallader that Dorothea's engaged to Mr. Casaubon.
Mrs. Cadwallader is disappointed for Sir James' sake – she was partly responsible for setting them up.
Mrs. Cadwallader excuses herself to go break the news to Sir James.
He doesn't take it well, partly because he's disappointed (of course), and partly because Casaubon is such an old "mummy."
Mrs. Cadwallader hints that Sir James would be better off with Celia, anyway.
Eliot's narrator then goes off on one of her famous tangents, philosophizing about how difficult it is to judge people and the reasons they do the things they do. She uses the metaphor of the microscope to illustrate her point – see the "Science" theme under "Quotes and Thoughts" for more on that.
The chapter closes with a description of Sir James' disappointment when he next goes to lunch at Tipton Grange (that's the name of Mr. Brooke's house). Sir James, however, hides his disappointment, and resolves to pay more attention to Celia.