Celia finally sets Dorothea straight: Sir James is intending to propose to "the eldest Miss Brooke."
Dorothea is very irritated by the news – she'll have to give up discussing her cottage plans with him.
Mr. Brooke comes home and asks to speak with Dorothea in his library.
He says that he'd had lunch with Mr. Casaubon on his way home, and that Mr. Casaubon had asked his permission to propose to Dorothea.
(Remember, Mr. Brooke is Dorothea's uncle and legal guardian, so it was traditional for the man to get the permission of the woman's parents before even proposing to the woman in question.)
Dorothea tells her uncle that, when and if Mr. Casaubon proposes to her, she'll accept him.
Mr. Brooke is totally blown away by the news, and rambles on about how maybe Mr. Casaubon will suit her better than a younger man, after all, since she's so interested in books and ideas and stuff. (He's not a very articulate speaker.)
Dorothea leaves Mr. Brooke bewildered about women. He really doesn't get Dorothea at all.