Dr. Livesey is worried about fever, dysentery, and a lack of clean water.
As chapter 16 opens, John Silver and the mutineers head for shore, leaving only six men on board. The captain, the doctor, and a few other men occupy the Hispaniola's cabin and gallery while the mutineers occupy the deck. The captain and his men consider attacking the six men left on board and leaving the island, but the wind is calm and they are therefore unable to sail.
The doctor, who narrates this chapter, says that the anchorage in which the Hispaniola lies is terrible. The water is stagnant and the weather is hot--perfect conditions for dysentery and fever. Also, the Hispaniola has insufficient drinkable water on board. Thus, when the doctor heads to shore to scout the stockade, he notices a spring with fresh water and makes the case to the captain that they should abandon the Hispaniola for the stockade.