What does the rope connect to in The Cay?
Good question! Somewhat mysteriously, we see in Chapter Nine that Timothy insists on making a rope out of the thick vines that are scattered across the island. Phillip helps him, realizing that the rope will connect the upper hill (where they camp out at night) to the lower beach (where they have a signal fire ready to be set at any moment).
The rope's purpose is to help Phillip, who is blind, make his way quickly and safely from one location to another—especially if he hears a plane going by and needs to light the signal fire in a hurry. He can hold onto the rope and use it to walk in the right direction.
Considering the plot, the rope is also an important object. As they are weaving the rope, Phillip gets frustrated with his inability to see his work. He takes out his anger on Timothy, calling him an "ugly black man" and "stupid," in response to which Timothy promptly slaps him. Immediately afterward, Timothy gently says that it's time to get back to work. This early conflict helps us understand how much development Phillip really needs: he needs to become patient, for one thing, and to adjust to his blindness, and he also needs to shake off the racial prejudices that have gripped him since earlier childhood. Phillip does show a glimmer of growth right after this incident when he recalls that the rope is for his own benefit and feels ashamed of his outburst.
You can also consider the rope an important symbol in the novel. Toward the middle of the story, Phillip clings desperately to the rope as a means of getting around safely. But toward the end of the story, he becomes more assured of himself and his movements and relies less on the rope. The rope, then, symbolizes dependence: the less Phillip relies on it, the more he is growing into an independent person despite his blindness.