He then rose and said among the Argives, "Stand forward, you who will essay this contest." Forthwith uprose fleet Ajax son of Oileus, with cunning Ulysses, and Nestor's son Antilochus, the fastest runner among all the youth of his time.

They stood side by side and Achilles showed them the goal.

The course was set out for them from the starting-post, and the son of Oileus took the lead at once, with Ulysses as close behind him as the shuttle is to a woman's bosom when she throws the woof across the warp and holds it close up to her; even so close behind him was Ulysses--treading in his footprints before the dust could settle there, and Ajax could feel his breath on the back of his head as he ran swiftly on.

The Achaeans all shouted applause as they saw him straining his utmost, and cheered him as he shot past them; but when they were now nearing the end of the course Ulysses prayed inwardly to Minerva.
"Hear me," he cried, "and help my feet, O goddess." Thus did he pray, and Pallas Minerva heard his prayer; she made his hands and his feet feel light, and when the runners were at the point of pouncing upon the prize, Ajax, through Minerva's spite slipped upon some offal that was lying there from the cattle which Achilles had slaughtered in honour of Patroclus, and his mouth and nostrils were all filled with cow dung.
Ulysses therefore carried off the mixing-bowl, for he got before Ajax and came in first.

But Ajax took the ox and stood with his hand on one of its horns, spitting the dung out of his mouth.