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The chapter opens with Dorothea, Celia, their uncle (Mr. Brooke), Sir James Chettam, and Mr. Casaubon (an old scholar/minister who lives nearby) all sitting down to dinner together.
Mr. Brooke keeps going on about the different books he read as a young man, and the different writers and poets he met. He can't seem to form a coherent thought, and rambles a lot.
Sir James Chettam picks up on one book Mr. Brooke has mentioned, Agricultural Chemistry by Sir Humphry Davy, and says that he's been reading it so that he'll be better able to help his tenants learn how to farm better.
Time out for a Brief Historical Context Lesson: At this point in English history (around 1830), most land in the country was owned in large chunks by wealthy noble families, and they passed the land down from father to son. They made their money by renting out individual farms on their property to tenant farmers. Of course, some of these rural landlords were better than others: some of them, like Sir James here, tried to educate their tenants and help them make the most of their land. Some of them (like Mr. Brooke, as you'll see) let the farmhouses that they rent out go to rack and ruin, and charged too much rent for bad land.
Back to the story: Dorothea's happy to hear that Sir James Chettam is going to help his tenants make a better living (remember, she's obsessed with helping the poor).
Mr. Casaubon is impressed at her passion and intelligence.
Mr. Brooke brushes her off, and says that women don't understand such things.
Dorothea is impressed by Mr. Casaubon's precise manner of speaking.
Sir James keeps trying to impress Dorothea, and keeps failing – she thinks he's trying to impress Celia.
They discuss horseback riding – Dorothea used to ride a lot, and still loves it, but has given it up because she'd rather spend her time on little projects to help the poor instead of on activities for her own enjoyment.
The conversation turns to Mr. Casaubon's great scholarly project (he's trying to discover the "Key to all Mythologies," and it's been his life's work).
Mr. Brooke asks him how he organizes his desk, and Dorothea's knowledge of how to organize papers impresses Mr. Casaubon.
After dinner, Dorothea and Celia talk about Mr. Casaubon and Sir James.
Dorothea likes Mr. Casaubon much more: she thinks he's got "a great soul," but Celia can't see past the hairy moles on his face.
Once the men have joined Dorothea and Celia, Sir James has the opportunity of talking more with Celia, and decides she's all right, too – but not as pretty or smart as Dorothea.