We meet Anne's friend, Mrs. Smith
While Sir Walter and Elizabeth enjoy their lodgings in Camden Place and crow about their connection to the tedious Dalrymples, Anne has started visiting people she actually likes: her former governess, and her friend from her school days, Mrs. Smith, with whom she had lost touch for a while. Last Anne knew, her friend had married Mr. Smith, a man with a good fortune, but it turns out that these days, Mrs. Smith is a widow whose husband left his estate in disarray, so now she's poor. And due to an unfortunate bout of rheumatic fever, she is also lame - at least for the time being - and living in Westgate Buildings.
Now, allow me to put this into perspective for you: Camden Place (now Camden Crescent) was located up the hill and near the highest point in Bath at that time, so that Sir Walter and Elizabeth were quite literally looking down on pretty much everyone else in Bath; at the same time, planned construction on Camden Place had to be given up because the terrain was unstable - so our financially shaky baronet is also quite literally on shaky ground. The Westgate Buildings, by contrast, are located quite low down in the City - not far from the baths, which is why Mrs. Smith selected them. They are quite unfashionable, and Anne has Lady Russell drop her a short distance away, probably so as not to embarrass Mrs. Smith by pulling up in a fancy carriage, essentially rubbing her friend's nose in the difference in their present economic condition.
If Sir Walter and Elizabeth is all that is foolish, small-minded and silly, Mrs. Smith is the opposite:
Anne found in Mrs. Smith the good sense and agreeable manners which she had almost ventured to depend on, and a disposition to converse and be cheerful beyond her expectation. Neither the dissipations of the past--and she had lived very much in the world--nor the restrictions of the present, neither sickness nor sorrow seemed to have closed her heart or ruined her spirits.
We hear that Anne has paid Mrs. Smith several additional visits, learning still more about Mrs. Smith's situation. One of the people we hear of Nurse Rooke, who is helping to tend to Mrs. Smith, and has taught her to knit - Mrs. Smith now fashions small needlecases and whatnot, which Nurse Rook sells to her recovering patients who can afford them, and Mrs. Smith thereby obtains money to help people who are poorer than she. Nurse Rooke is quite well-connected, and provides Mrs. Smith with news (gossip) that she picks up around town. This is a clever introduction to a character who we don't meet in person, and we are told as well that she is tending a Mrs. Wallis just now. If that name sounds vaguely familiar, it is because Mrs. Wallis is the knocked-up wife of Colonel Wallis, whom Sir Walter is so keen to meet. Is this quite a coincidence? Yes, but it's not at the deus ex machina level on Austen's part - and it proves to be quite a helpful and informative sort of connection later in the book.
When Sir Walter eventually learns of Anne's visits to her friend - because Anne refuses to visit the Dowager Viscountess Dalrymple one evening owing to a pre-existing appointment to visit Mrs. Smith - he ridicules Anne and her friend. I adore this particular section, which shows Sir Walter's and Anne's true characters quite well, while amusing the hell out of me:
" . . . A widow Mrs. Smith lodging in Westgate Buildings! A poor widow barely able to live, between thirty and forty; a mere Mrs. Smith, an every-day Mrs. Smith, of all people and all names in the world, to be the chosen friend of Miss Anne Elliot, and to be preferred by her to her own family connections among the nobility of England and Ireland! Mrs. Smith! Such a name!"
Mrs. Clay, who had been present while all this passed, now thought it advisable to leave the room, and Anne could have said much, and did long to say a little in defense of her friend's not very dissimilar claims to theirs, but her sense of personal respect to her father prevented her. She made no reply. She left it to himself to recollect, that Mrs. Smith was not the only widow in Bath between thirty and forty, with little to live on, and no sirname of dignity.
The snarkiness of Anne's thoughts here, correct as they are, cracks me up. And Mrs. Clay's sensitivity to the topic (and Sir Walter's complete disregard for how she might interpret his rantings) is brilliant as well.
Lady Russell's and Anne's opinions on Mr. Elliot
While Anne was off visiting Mrs. Smith, Sir Walter and Elizabeth rounded up Lady Russell and Mr. Elliot and carted them off to visit the Dowager Viscountess. Lady Russell spent quite a bit of time chatting with Mr. Elliot, who seems to have a large amount of respect and (perhaps) affection for Anne. Lady Russell's yenta tendencies rush to the fore, and she starts calculating how many more days Mr. Elliot has to stay in mourning for his dead wife, hoping that Anne will marry him.
Anne, however, is certain they would not make a good match. For one, she's still carrying a torch for Captain Wentworth. Secondly, she can't make out Mr. Elliot's character, a word which encompasses both his true nature and his reputation. She suspects him of having a rather wild past, and is uncertain that he would not return to his wild ways; she also finds him to be very guarded, and his closed nature makes her believe he's holding something back. On the one hand, he doesn't do anything impulsive and he never mis-speaks, but she finds that cause for concern - she'd rather deal with an open person who occasionally has an outburst that might be questionable than a careful person who never misspeaks at all.