The second part of the chant that opens Oxen of the Sun invokes some god to bless women's wombs with new life: "Send us bright one, light one, Horhorn, quickening and wombfruit." Under one aspect, this deity is simply Dr. Andrew J. Horne, the master of the maternity hospital. But the play on his name to suggest an animal's "horn," and the mentions of "light," pull in the Homeric motif from which this chapter derives its name: cattle sacred to the sun god Helios.
In Book 12 of the Odyssey, the voyagers are forced to land on an island that they have been warned to avoid, because it contains cattle sacred to Helios (a sun god who later became identified with Apollo), and the god will punish any harm that comes to them. When they run out of food, the men break their vow to Odysseus and slaughter some of the cattle. Helios appeals to Zeus, who destroys the Greek warriors' ship with a lightning bolt when they depart.
Joyce certainly intended the link between Horne and Helios: Gilbert's schema identifies the Irish doctor as the counterpart of the Homeric god. But the anger of Homer's god introduces a new element into what so far has been an evocation of human worship and divine benevolence. By killing the sacred oxen, Odysseus' men commit an offense against life. The theme of a god being displeased because men disrespect the fertility that he sanctions will be picked up in the chastising tone of paragraphs 4-6, and in many later sections of the episode.