Brainworm delivers the letter to Edward, immediately and deliberately informing him that Old Knowell has read its contents. Stephen comes in, still annoyed about the servant earlier. Edward reads the letter, laughing heartily. Stephen worries that his cousin is laughing at him.
It’s never explained why, but Brainworm shows more loyalty to Edward than to Old Knowell, acting as an informant. Edward’s laughter indicates that he is used to this kind of behavior from his father.
Edward explains to Stephen that there is no need for him to be “melancholy”—he was laughing at the letter, not him. He explains that he will go to meet his friend at the Old Jewry by crossing over Moorfields, and invites Stephen to accompany him. His cousin enthusiastically agrees. Edward sarcastically praises Stephen’s character—though the latter doesn’t pick up on the sarcasm.
Stephen’s worry that he is being laughed indicates the fragile state of his ego—a fair criticism for many of the characters of the play. He is constantly looking for external verification about who he is—and, vice versa, always on the look-out for ridicule (which, ironically, he often misses). The Old Jewry is a street in London, which at the time was the site of the Windmill Tavern. Melancholy was representative of one of the four humours, which was the medical theory that the human body depended on a balance between blood, phlegm, yellow bile, and black bile. An excess of these produced a defect often manifested as an undesirable character trait (e.g. black bile and melancholy).