Archer is stunned upon leaving Mrs. Mingott's. He reasons that Ellen's decision to stay in New York must be an indication that she has resolved to have an affair with him. While Archer is somewhat relieved that she will be staying, he is also afraid that their affair will be no different than those of his peers and that it will dissolve into a pathetic pack of lies. Yet he consoles himself with the thought that he and Ellen are different from the rest of New York society and that their unique situation puts them above the judgment of their clan. That evening, he waits in front of Beaufort's house for Ellen, who we learn has come to console Regina Beaufort in the midst of her troubles. They agree to meet the next day at the Metropolitan Museum.
The following day, Archer meets Ellen in the antiquities gallery of the museum. Ellen explains that she has decided to stay near her grandmother because she feels she will be safe there from the temptation of Archer. She begs him not to let them become like the other adulterers they know. Yet she hesitates and asks him if she should just come to him once and then leave New York. Archer agrees, and they plan to meet two days later. Back home that evening, Archer learns from May that she too has seen Ellen that afternoon. May claims that the two of them have had a long talk and that May has decided to befriend Ellen despite her eccentricities.
The next night, the van der Luydens host a pre-opera dinner at their exclusive Madison Avenue home. At dinner, the topic of discussion is again the Beauforts' financial failure. The van der Luydens are dismayed to learn that Ellen had been to see Mrs. Beaufort, an action they conceive of as imprudent, considering the Beauforts' fall from good society. At the opera, Archer feels guilty about his intended tryst with Ellen. At his side, May is wearing her wedding dress, as is the custom for young married women. Archer suddenly feels the urge to confess to her, and he persuades May to leave the opera early. Back home, Archer is on the verge of confessing when May interrupts him by mentioning that Ellen has decided to return to Europe. Archer is stunned and excuses himself for bed.
After learning from Mrs. Mingott that Ellen will be remaining in New York, Archer's joy is tempered with a growing sense of anxiety. He is not so much worried about the actual moral questions raised in having an affair, but more about the bad appearance it would make. In explaining the codes of adultery, Wharton gives us a sense of how truly complex, and even contradictory, gender relations are in New York. While Archer argued in Book One that women face more restraints and judgment than men if they have love affairs, he now seems to reverse this opinion. A woman, he muses, is considered weak and subject to fits of nerves. Therefore, any marital infidelity on her part only makes her husband look foolish for being cuckolded. But a married man who initiates an affair is viewed with contempt, for he is expected to be responsible to his duty. In such cases, the man's wife is pitied and supported. This commentary foreshadows the scene in Chapter 33, when the Archers throw a dinner party. The guests, assuming May to have been wronged by Archer's supposed infidelity, tacitly support her.
Archer's meeting with Ellen in the antiquities wing of the Museum gives Wharton a chance to again compare Old New York to dead, ancient cultures. Ellen remarks that it is sad to see that all these artifacts from old cultures now have no use or meaning. Things that were once so important to a group of people now have no relevance in 1870. When Wharton wrote The Age of Innocence following the First World War, Old New York was itself a defunct society. Being an historical curiosity rather than a current reality, its individual artifacts and customs now seemed as obsolete as those represented in the glass cases of the Metropolitan Museum.
In the Museum, Archer and Ellen find themselves torn on both an emotional and physical level. While Archer until this point has restrained his erotic feelings, he is now impatient to arrange a more intimate rendezvous with Ellen. Both are still afraid that if their relationship is consummated, there will be nothing that sets them above the infidelities of Beaufort and Larry Lefferts. However, Ellen does suggest that they meet once and that afterwards she will leave him for good. Archer is daunted by the idea of parting permanently, but he recklessly agrees to meet her anyway. It is significant that after they agree to meet, Archer and Ellen stand facing each other "almost like enemies." Both realize that their relationship is disturbingly close to becoming a typical affair. The thought that they will not be able to escape the trappings of an affair (the furtiveness, the inevitable disillusion, and judgment) is enough to make them feel antagonistic towards each other.