Haines has basically ordered Mulligan and Stephen to pay their milk tab, which otherwise they would probably have been happy to delay for several months. Mulligan reluctantly scrounges up money to pay her, and recites some Swinburne to make it classy.
Rob has taken pains to show us a detail from the narration of this moment–Mulligan comes up with the coin from his trousers, but it’s Stephen who actually hands the coin to the milkwoman. It’s a concrete illustration of the difference in caste between Stephen and Mulligan, but also Stephen’s role as the “server of a servant.”
Looking back over the last few pages, what does the milkwoman get from each of the men in the tower, and what might each of those gifts say about them? From Haines the Englishman? A speech in Irish that she can’t understand. From Mulligan the aristocrat with family money? A poem about how poor he is. From Stephen? A coin that isn’t really his. Is this any way to treat Athena in disguise?