Lines 37-38

And every day that quiet clay seemed to heavy and heavier grow;
And on I went, though the dogs were spent and the grub was getting low;

• The miserable trip continues. The speaker starts to imagine that the body – which he poetically calls "that quiet clay" – is getting heavier all the time, that it’s dragging the sled down.
• The dogs are "spent" (completely exhausted) and there isn’t much food left. Things are looking bad for out speaker, but he's still determined to keep his word.

Lines 39-40

The trail was bad, and I felt half mad, but I swore I would not give in;
And I'd often sing to the hateful thing, and it hearkened with a grin.

• Things just get weirder and tougher. Not only is he hungry and tired, but the road is bad, and he feels nearly crazy. Still, he refuses to give up. We get the impression that he’s a pretty tough dude.
• To pass the time, he sings to his friend’s corpse, imagining that it is listening to him and grinning.
• That’s a super-creepy image, isn’t it? Service really wants us to feel the pain and the awfulness of this moment, to sense the little tingle of madness that’s building here.