While flying to an international news conference in Melbourne, radio commentator Mark Bradley and his pilot, Joe Walker, are forced to crash land on an uncharted island in the Pacific Ocean. They find this island is inhabited by Dr. Paul Lujan and his three beautiful daughters: Venus, Mercuria, and Urana. Lujan, a nuclear scientist, has fled here to escape from a world which is like "a horrible great snowball rolling faster and faster toward extinction." He doesn't want his two visitors to leave, lest they reveal his whereabouts, so he destroys their plane. With help from the two older daughters, however, the men begin to construct a raft. (Mark and Venus have fallen in love as have Joe and Mercuria). A fire in Lujan's solar furnace now causes an explosion which nearly wrecks the island but which attracts the attention of a search plane. Mark, Joe, and the three young women look forward to being rescued; Lujan has doubts but is resigned.