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This is an allusion to a mythological drug that you might take to forget your grief. From what we can tell, we think our narrator might really need some of this stuff.
Lines 82-83: The idea of nepenthe occurs to our speaker in a kind of daydream/hallucination. He imagines that the room is filling with some sort of perfume, and thinks that God himself has decided to help him forget his misery. In the Odyssey, Homer describes nepenthe in exactly this way, as a drink that will take away all sadness.