How does Rainsford end up on the island?

At the beginning of the short story, Rainsford is sitting on the top deck of the yacht alongside Whitney as the two hunters sail to the Amazon, where they plan to hunt jaguars. After Whitney goes to bed below deck, Rainsford stays awake and smokes his pipe on the top deck. Suddenly, Rainsford hears the sound of gunshots coming from the direction of the nearby island. Rainsford immediately springs from his seat and stands on the rail looking out into the darkness. While Rainsford is balancing on the rail, his pipe accidentally hits a rope and is knocked out of his mouth. Rainford then reaches for his pipe, loses his balance, and falls into the dark Caribbean Sea.
After falling into the water, Rainsford yells at the top of his lungs for someone to come to his aid but the yacht continues to sail away. He then remembers that the sound of the gunshots came from the right and begins to swim in that direction. After a "seemingly endless time," Rainsford reaches the rocky, jagged coast of the island and climbs the massive boulders onto dry land, where he immediately collapses at the edge of the dense jungle.

Rainsford ends up on the island, the notorious Ship-Trap Island, completely by accident. He is initially on a yacht bound for Rio de Janeiro. The yacht passes by Ship-Trap Island. The crew are highly nervous; they can almost sense the evil emanating from the mysterious island. However, Rainsford is suitably intrigued. As a big-game hunter, he has a taste for danger.
It is night, and Rainsford is standing on the afterdeck smoking a pipe. Suddenly, the sound of gunshots cut through the darkness; they are coming from the vicinity of Ship-Trap Island. Rainsford wants to find out what is happening, so he hoists himself onto the yacht's guard rail to see if he can get a better look. As he does so, he drops his pipe, tries to make a grab for it, and then promptly falls into the water. Despite repeated cries for help, the yacht continues on its voyage without him. Rainsford has no choice but to swim to Ship-Trap Island and bed down for the night. Rainsford has just experienced the start of the most thrilling adventure of his life.