When Claudia and Jamie reach the sidewalk, Claudia plans to take a taxi to the Met; however, Jamie talks her out of it, explaining that they are on a very limited budget. He demands that they walk to save money, much to Claudia's annoyance.
Claudia is cold and uncomfortable, and becomes more and more irritated. She mocks Jamie when he pulls out a compass to ascertain the direction they need to travel in. Jamie calms her down by noting that her plan to travel to New York, where no one will take any notice of two kids alone - no one takes notice of anything in New York - was very brilliant. This compliment boosts Claudia's spirits.
At last they arrive at the museum, where they blend in easily with all the crowds of schoolchildren carrying notebooks. They are stopped by the guard, who tells them that they must check their instrument cases. Jamie is anxious about this: his pajamas are in his trumpet case; how is he supposed to change into them?! Claudia explains the rest of her plan: they will check out of the museum at 4:30, leave the museum by the front door, and then re-enter from the back door that leads from the parking lot to the Children's Museum.
Jamie also decides that they will eat at the snack bar rather than the restaurant in order to save money, but he is frustrated when they spend $1.50 and leave feeling hungry. The two begin to become concerned about the amount of money they have. Jamie asks Claudia if she thinks the guards will play a game of war with him - he has even brought his cards. Claudia is very skeptical that they will, and thinks that this would blow their cover. Jamie confesses that he always cheats at cards with Bruce, which is how he has earned so much money.
Claudia ignores Jamie’s comment and continues explaining her plan. During the dangerous time between the closing of the museum and the time when all the guards and helpers leave, they will stand on toilets in the bathroom to avoid detection. Claudia is certain that guards only peek under the doors of the stalls to see if there are feet.
Jamie suggests that they should be wary of the night watchman, but Claudia points out that his job is mainly to prevent people from getting in - she and Jamie are already in, so they'll probably escape his notice.
The two tour the galleries, and Claudia stares longingly at a lounge chair that once belonged to Marie Antoinette. She cannot wait until the museum is closed, when she can finally sit in it herself.
At last, Claudia finds a gorgeous canopy bed from the sixteenth century that she decides they will sleep in that night. Jamie is annoyed that they are going to sleep in such luxury; as runaways, he thinks they should sleep on floors or in the woods. When Claudia points out a small sign next to the bed explaining that the bed was the sight of a grisly murder, Jamie is pleased. At that moment, the two of them truly become partners.
Their plan to check out of the museum and sneak back in goes well, as does their strategy of standing on toilets to evade the last sweep of the guards. Despite being very hungry, they change into their pajamas in the dark and hop into the heat canopy bed - which is much more dusty and musty-smelling than they anticipated.
Claudia and Jamie have some trouble falling asleep, but then they collapse from exhaustion. The night watchman passes by, but does not notice them. The two sleep soundly.
Jamie and Claudia wake at dawn, feeling horribly hungry. They dress in the cold, hide their possessions in museum artifacts, and then go back to the bathrooms to hide in the stalls during the perilous time between the arrival of the guards and the opening of the museum to guests.
All goes according to plan...except when Jamie hears running water about ten minutes after the museum opens and reveals himself, assuming it's another museum guest. It turns out to be a janitor, who is shocked to see Jamie. Jamie makes a flippant comment and walks away quickly, though Claudia is extremely concerned about this breach of their plan.
Claudia also decides that she and Jamie will use their time at the Met to learn more about art. Every day, they will pick a different gallery to explore and will learn everything about it. Teasingly, Jamie decides to tour the Hall of the Italian Renaissance because there are so many paintings of naked women there.
The two children find a great crowd in the hall, but they don't think much of it. In fact, this crowd has gathered to see the exhibition of a new statue, a beautiful angel. Claudia is immediately enraptured by the statue. Jamie is more intrigued by the newspaper photographers taking photos - he wants to get his picture in the paper. Claudia shoves him out of the range of the photographer.
The statue seems to have an almost magnetic power. Claudia wants to buy a copy of The New York Times to learn more about it, but Jamie vetoes this expense. Claudia is still determined to find a way to learn more about Angel.
The two children head to the Egyptian wing next, blending in with a group of schoolchildren on a tour. The guide tells them about mummies and Egyptian art, but most of the other schoolchildren are not listening to her. Jamie, though, asks a question about the cost of making a mummy, irritating Claudia by bringing attention to them again.
Jamie considers buying a pamphlet about the Egyptian exhibit; the guide says that some of them are as inexpensive as a copy of The New York Times. Claudia looks smug.
The next day, Claudia and Jamie snatch a copy of The New York Times from a distracted businessman. The children read it as they eat a hearty breakfast. They learn that the statue is simply called Angel, and that there is speculation that it may have been carved by Michelangelo. The statue was purchased for only $225, and it came from the private art collection of Mrs. Basil E. Frankweiler, a wealthy widow.
Elsewhere in the paper, though the children don't see it, is a news piece describing the disappearance of two children from Connecticut - the parents of Claudia and Jamie are desperately looking for them. However, the children are too wrapped up in the statue to notice.
Claudia decides that she will solve the mystery of the statue and discover whether or not Michelangelo created it. Jamie is rather dismissive of this idea. They visit the statue again the next day, but they are frustrated to see that the crowd around it is even larger than it was yesterday, so they join a school group in the colonial America wing of the museum.
The siblings irritate each other, but they also know how to compromise and make each other laugh. When Claudia becomes extremely angry at having been forced to walk forty blocks, Jamie points out how brilliant her plan is, knowing that this flattery will make her happy. There are a number of moments that draw the two siblings together and make them a true team; this culminates with Claudia's observation that an ornate bed was the site of a grisly murder, which delights Jamie.
Some of Claudia's interest in the statue comes from the fact that she thinks it looks like her, which is implied by a scene on page 63: “‘Jamie,’ she said, ‘do you think the statue looks like anyone special?’ She folded her arms and gazed into the distance. ‘No one I know looks like an angel.’ ‘Think a minute.’ She cleared her throat and lifted her chin slightly and gazed into the distance. ‘Don’t think about the hair style or the clothes or anything. Just think about the face.’ She nudged the page of the New York Times closer under Jamie’s nose and resumed her pose. Jamie looked at the picture. ‘Nope,’ he said looking up. ‘Can’t you see any resemblance?’ ‘Nope.’”
Chapter 4 introduces an important symbol: Angel. This small, beautiful, and very mysterious statue represents Claudia's desire to be different and unique. For the rest of the novel, Claudia will pursue her interest, because the fulfillment of her goal of being different is wrapped up in Angel.
These chapters also contain instances of verbal humor. While the children are in the Egyptian wing with another school group, Jamie asks the guide how much it cost to become a mummy. One of the students on another tour group replies, “You might even say it costs him his life" (pg. 55). This playful pun turns on the meaning of cost, which is generally used to indicate the amount of money one needs to pay for something, but sometimes also refers to the more invisible costs. In this case, a person does need to be dead in order to be turned into a mummy.