In Part III, which mostly takes place in the feverishly-paced imagination of Peyton Farquhar during his fall from the bridge to the end of his literal rope, Farquhar imagines that the "rope [has] broken" and that he has fallen into the river beneath the bridge. Thus, the circle of the noose would be, in his imagination, still pulled tightly around his neck, the rope having snapped higher up. This is why he feels that it "was already suffocating him." The narrator tells us Farquhar's thoughts in this moment, saying,

To die of hanging at the bottom of a river!—the idea seemed to him ludicrous.

Thus, it is not the idea of hanging, or even of drowning, that strikes him as ridiculous, but, rather, it is the idea of dying of hanging while he is not actually hanging but is submerged underwater at the bottom of the river. To die of hanging while one is actually hanging would not be ludicrous, but to die of hanging while one is not actually hanging strikes Farquhar in this moment as absurd. Such a thought at such a time might be read as one of many clues for us that not everything is as it seems.