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The events of the thirty-fourth day—specifically the giving of the gifts to Odysseus and his departure by ship original: "embarkation" at sunset—are described in Book 13, lines 18–92.
On the thirty-fifth day, Odysseus wakes up in Ithaca and visits Eumaeus his loyal swineherd, while the goddess Athena seeks out Telemachus Odysseus's son in Sparta and sends him on his journey home as far as Pherae (Book 13, line 93—Book 15, line 188).
The thirty-sixth day is taken up with the continuation of Telemachus’s voyage and the second day of Odysseus’s stay original: "sojourn" with Eumaeus (Book 15, lines 189–494). Early in the morning of the thirty-seventh day, Telemachus arrives in Ithaca, goes to the hut of Eumaeus, and meets his father (Book 15, line 495—Book 16, line 481).
The thirty-eighth day includes Telemachus’s visit to the palace; the fight with the beggar Irus; and the moment Odysseus is recognized by his old nurse, Eurycleia (Book 17, line 1—Book 20, line 90). The contest original: "ordeal" of the bow and the axes; the slaughter of the suitors the noblemen who had spent years occupying Odysseus's palace; and Odysseus’s recognition by his wife, Penelope, all occur on the thirty-ninth day (Book 20, line 91—Book 23, line 299). Finally, the fortieth day includes the visit to his father, Laertes, and the establishment of peace between the combatants (Book 23, line 300—Book 24).