Moreover, Casey's star that he had used to mark the spot moved over to the west and finally slid out of sight altogether.

But Casey felt sure of the direction and he kept going doggedly toward the point where the light had been.

He says there wasn't a rod where a snail couldn't have outrun him, and when the sky streaked red and orange and the sun came up, he stood still and looked for a camp, and when he saw nothing at all but bare rock and bushes of the kind that love barrenness, he crawled under the nearest shade, tied William fast to the bush and slept.
You don't realize your thirst so much when you are asleep, and you are saving your strength instead of wearing it out in the hot sun.

He remained there until the sun was almost out of sight behind a high peak.

Then he got up, untied William, mounted him without argument from either, and went on, keeping to the direction in which he had seen the light.
Even the little brown mule was having trouble now.