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Kitty's begins asking her mother if she can be friends with Varenka.
Her mother is initially resistant, since she is sure that Varenka is just Madame Stahl's paid companion. Princess Shcherbatsky was acquainted with Madame Stahl's sister-in-law, and Princess Shcherbatsky is offended that Madame Stahl has not approached her to make her acquaintance.
Finally, Princess Shcherbatsky assents after they learn that Varenka intervened and made peace between Nicholas Levin and his doctor. Nicholas behaved badly when he felt that the doctor was not treating him correctly, going so far as to raise his stick at the doctor threateningly. Varenka took Nicholas's arm and led him away before he could do any more damage.
Princess Shcherbatsky decides that there is no harm in their friendship, and that it will perhaps do Kitty some good.
Princess Shcherbatsky approaches Varenka directly and mentions that Kitty's taken with her, and wants to become friends. After the introduction, Kitty feels free to join Varenka for a chat. The two express mutual interest in friendship.
We finally find out the relationship between Varenka and Madame Stahl: they are not related by blood, but Madame Stahl raised Varenka.