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Sir James and Mr. Brooke are arguing about Casaubon's will.
Apparently there's something in the will that Dorothea won't like, and they're trying to decide if there's any way of keeping it from her. But she's an executrix, so she's bound to find out.
The part of the will in question has something to do with Will Ladislaw. Sir James asks Mr. Brooke to send Will away for the sake of Dorothea's "dignity," but Mr. Brooke refuses – he likes Will, and thinks he's been useful to the newspaper.
At the end of the chapter, it's made clear: Casaubon added a codicil in his will (a codicil is like a P.S. at the end of a will) that says that Dorothea will lose all her inheritance from Casaubon (which is considerable) if she were to marry Will Ladislaw.
And of course, Sir James and Mr. Brooke think that this is a slap in the face to Dorothea.
Everyone will think that she wanted to marry Will, or that he wanted to marry her. In any case, people will think that there was a reason for Mr. Casaubon to be jealous.
Brooke points out that if they sent Will away, people would think that her own friends didn't trust her.
They finally agree that Dorothea should go to Freshitt (the Chettams' house) as soon as possible to stay with Celia and Sir James.