How did rainford end up on ship trap island?

The poor guy fell overboard because off loss of balance while cruising the Caribbean in his yacht one night. The engines were noisy, and no one could hear him so he had to swim ashore to the island or risk drowning. Once ashore, he falls asleep on the beach.

Explanation:

21 balloons is the story of professor william sherman's travels.

in 1883, he set off from san francisco for a balloon ride over the pacific and was found a month later floating with 21 balloons in the atlantic ocean. this seemed an astounding feat and everyone wanted to know what had happened.    

professor sherman was loyal, however, and said he would tell his tale first to the western american explorers club in san francisco, of which he was a member. this built up suspense for several chapters before he began to tell of the wonders of his adventures and the amazing island of krakatoa, an island which had just been blown up by a volcano.  

the residents of krakatoa are all millionaires who live under a "gourmet government" of their own devising. we get to see all the incredible adventures that creative people with unlimited resources would create according to the author.