Burns begins by saying goodbye to a place, but the real subject is something the speaker can't leave behind. The stream that "winding flows / Around Eliza's dwelling" is addressed first, yet within four lines he is begging memory itself to "spare the cruel thoes / Within my bosom swelling." The printed "thoes" looks like a slip for "throes", and the rhyme with "flows" supports that reading. The farewell is geographical, but the torment travels with him.
What follows is the portrait of a secret, unreturned love. The speaker is "condemn'd to drag a hopeless chain" and to "feel a fire in every vein", so he is both imprisoned and burning, held still and consumed at once. He insists he is "unseen, unknown" and wants to "cover" his griefs, but the second stanza admits the attempt is failing. "The bursting sigh, th' unweeting groan, / Betray the hapless lover." "Unweeting" means unknowing, so the body gives him away without his consent. The poem is about the failure of self-control as much as about love.
The most surprising move comes at the end of that stanza. He doesn't ask Eliza to love him or even to pity him first. He accepts that she "Nor wilt, nor canst relieve me", a phrase that lets her off the hook on both counts, and then asks to be forgiven. He treats his own feeling as an offence against her. That humility, and the restraint of a lover who never blames the person he can't have, keeps the poem from sounding like a mere complaint.
The form is made for singing, as the title "Song" signals. There are three eight-line stanzas, each rhymed ABABCDCD. The longer lines are steady four-beat iambics ("Farewell, thou stream that winding flows"), while the shorter lines end on an extra unstressed syllable: "dwelling," "swelling," "languish," "anguish," "cover," "lover." Those soft endings create a falling, sighing cadence, as if each short line were a breath let out. Often the soft ending is the word "me": "relieve me" and "forgive me" in the second stanza, "enslav'd me" and "sav'd me" in the third. The speaker keeps closing his lines on himself, and the rhymes repeat that small, helpless pronoun.
The third stanza explains how he came to be trapped, and it is the most inventive part. He heard her voice, "Nor wist while it enslav'd me", meaning he did not know what was happening. He saw her eyes and "nothing fear'd, / Till fears no more had sav'd me." That line is a little knotted, and the knot is the point. Fear would have protected him, but it arrived only when protection was useless. The word "enslav'd" also links back to the "chain" of the first stanza, so the opening condition is now traced to its cause.
Then comes the simile of the "unwary sailor" who watches a "wheeling torrent" and sinks "'Mid circling horrors". Here the water imagery has quietly changed character. The poem opened with a gentle, winding stream, a pretty piece of landscape, and ends with a whirlpool that kills. Hearing the whirlpool's circles against the earlier "winding" is my reading, but it fits the poem's logic. What looks harmless from the bank is the thing that pulls a person under. The last line, "In overwhelming ruin", gives no reply from Eliza and no consolation. The poem simply stops where the sailor goes down.
Burns wrote a great many songs, and this one shows his craft in a conventional mood. Phrases like "hapless lover" and "Love's veriest wretch" belong to a familiar language of sentimental verse, and the poem is in smooth English rather than Scots. It is lifted out of cliché by its structure and its psychology: the body that betrays its owner, the fear that comes too late, the apology where a demand might be expected, and the scenery that turns lethal. It is a small poem, but it understands how love can feel like an accident that has already happened.