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They key thing that happens on this page (so to speak) is Mulligan asking for the key to the tower. We know that Stephen has paid the rent, we know that he’s the real intellectual, we know that Mulligan has been overplaying their friendship to Haines for the sake of squeezing some money out of the Englishman, we know that Mulligan’s real interest in Stephen pales in comparison to his more craven or conniving plans.
By giving up the key, Stephen is relinquishing control of the tower to an untrustworthy friend. As he does so, he knows it’s a turning point in his relationship with Mulligan and in his life. By handing over the key, he is freeing himself from the “third master” who wants him for the “odd jobs.”
And of course, Haines, the Englishman, prudently shows himself to be afraid of swimming on a full stomach. Or maybe the sight of naked Mulligan disheartened him.