How do the doctor and his companions escape from the Hispaniola, and where do they go?

In Chapter Sixteen, Dr. Livesey begins his narration by explaining that, although the good men on board wanted to attack the pirates, they could not because Jim was on shore and they could not leave them behind. Instead, the two men, Livesey and Hunter, decide to take a boat to shore and go to a place that is around the bend, and consequently, out of the guards' sight.

The captain, the squire, and I were talking matters over in the cabin. Had there been a breath of wind, we should have fallen on the six mutineers who were left aboard with us, slipped our cable, and away to sea. But the wind was wanting; and to complete our helplessness, down came Hunter with the news that Jim Hawkins had slipped into a boat and was gone ashore with the rest.

It never occurred to us to doubt Jim Hawkins, but we were alarmed for his safety. With the men in the temper they were in, it seemed an even chance if we should see the lad again. We ran on deck. The pitch was bubbling in the seams; the nasty stench of the place turned me sick; if ever a man smelt fever and dysentery, it was in that abominable anchorage. The six scoundrels were sitting grumbling under a sail in the forecastle; ashore we could see the gigs made fast and a man sitting in each, hard by where the river runs in. One of them was whistling "Lillibullero."

Waiting was a strain, and it was decided that Hunter and I should go ashore with the jolly-boat in quest of information.