Basically, Chapter 7 and 8 are both about the Professor exploring more of the island, the people that live there, and the society that they have built.
Chapter 7 begins with the Professor and Mr. F on their way to Mr. M's house. As they walk, the Professor asks what the people of Krakatoa do with their spare time, and the people of Krakatoa have a lot of spare time.
"You have nineteen days out of each of your months in which, according to your Constitution, you have no work to do—are you bored, or have you interests here which keep you busy?"
The first answer that the Professor receives is about the homes that the people live in. Mr. F says that the people have spent a ton of time making their homes as magnificent as possible, and they try to emulate a beautiful house from the country that the family originated from. The people also spend a great deal of time inventing things for their homes that will make their lives simpler, easier, and more relaxing.
Chapter 8 begins with the Professor relaxing like so many of the inhabitants do so frequently. Not long after that, the Professor's tour of the island resumes. He is told that he is going to go see the "Balloon Merry-Go-Round." He states that it sounds like part of an amusement park, and Mr. F confirms that notion. Mr. F also explains that the entire idea has been conceived and executed by the children of the island.
"It is part of an amusement park," said Mr. F., "which the children of Krakatoa are planning for themselves. . .We agreed to give them two boatloads a year, so all of the children held a meeting to decide how best to fill their freighters. This amusement park they have started to build is the result of their planning. The Balloon Merry-Go-Round is their own invention, designed with but little help from us."
The rest of the chapter is about the Professor, Mr. F, and the children using the Balloon Merry-Go-Round. It uses hydrogen to inflate its balloons, and it has small boats attached to it. As it rises into the air, it spins around the central launch pole. The entire contraption then rises above the pole and heads out over the island and toward the ocean. Once over the water, the balloons are deflated, packed up into the boats, and the boats sail back to the island.