For three months, Anna and Vronsky have been traveling around Europe.
They have arrived in a small Italian town where they intend to settle down for a while.
Vronsky is chatting with the headwaiter about renting a palazzo when Vronsky sees an old friend named Golenishchev, who had heard that Vronsky was in town.
Although they had parted on bad terms the last time they were together, Vronsky and Golenishchev get along fine now. Vronsky in particular is excited to have someone else to interrupt the monotony of his life.
In order to hide what he's saying from the servants, Vronsky speaks in French and tells Golenishchev that he is traveling with Madame Karenina. Based on Golenishchev's reaction, Vronsky concludes that he can introduce his friend to Anna because he "takes it the right way."
People who "take it the right way" are politely indifferent to the obvious relationship between Anna and Vronsky. They don't mention it at all.
This is the case when Vronsky introduces Golenishchev to Anna.
Golenishchev is taken with Anna's beauty and the simplicity with which she accepts her situation.
Golenishchev mentions that there's a fine painting by Tintoretto in the palazzo that Vronsky is about to rent. The three decide to go over and take a look. Anna goes inside to get a hat.
Vronsky and Golenishchev talk about Golenishchev's book, about which, to Vronsky's discomfort, Golenishchev becomes excited. Vronsky disapproves of Golenishchev, who comes from a good family, placing himself on the same level as common, low-class scholars. Vronsky sympathizes with Golenishchev's obvious unhappiness, but finds Golenishchev's feverish excitement on the subject of Russia's origins to be almost insane.
Golenishchev doesn't even notice when Anna comes back into the room.
After they come back from the palazzo, Anna notes that she's pleased the house has a little studio. To Anna's pleasure, Vronsky has started painting.