The chapter begins with the Professor eating breakfast at a Chinese restaurant. After breakfast, Mr. F and the Professor go to a "fine coral beach" in order to do some swimming. After the swim, the Professor starts asking Mr. F some questions about life on the island. One such question is about why the people live there at all.
"Why," I asked Mr. F., "do you people live here on top of this dormant volcano when with a handful of diamonds you could live a life of lavish ease and comfort in any other country?"
Mr. F gives a fairly lengthy answer, but ultimately, he says they live there because they are happy on the island. The Professor expresses his concern about living on a volcano that might explode in cataclysmic fashion. Mr. F then explains their escape plan and device. He describes a huge flying platform that is lifted aloft by balloon power.
"It's a flying platform, a huge platform big enough to take us all swiftly into the air within ten minutes of a warning from the mountain."
Much of the chapter after this point is Mr. F giving mathematical details about the size of the platform, the lifting strength of the balloons, and the mechanism by which all of the balloons get rapidly inflated with hydrogen. The chapter ends with Mr. F recommending that the Professor secure himself a parachute in case he ever has to flee the island on the giant platform.