Eight lines of courtesy, and underneath them a love story the poem refuses to tell. Robert Burns writes as someone who has been told, or has told himself, that an old feeling must now go by a smaller name. The first line holds past and present in a single breath: "Once fondly lov'd, and still remember'd dear." The rest of the poem is the struggle between those two halves.
The central idea is love forced to pass itself off as friendship. The speaker offers "this mark of friendship, warm, sincere," and then repeats the word with an exclamation mark: "Friendship! 'tis all cold duty now allows." That abrupt pause is the hinge of the poem. The first time, friendship is warm. The second time, it is only what is left once "cold duty" has taken everything else. We are never told whose duty this is or what forbids more. Judging by the wording, some obligation now stands between the two people, but the poem leaves it unnamed, and the silence makes the line sting more.
The form is tidy and controlled. It is a single stanza of iambic pentameter, rhymed ABAB CDCD: dear and sincere, vows and allows, then rhymes and climes, more and roar. The apostrophes in "lov'd," "remember'd" and "th' Atlantic" squeeze the syllables into a steady ten-beat line. The pairing of "vows" with "allows" sums up the whole situation. Vows are what was promised, and allows is what is now permitted. The distance between those two words is the poem's real subject. Burns is best known for his Scots-language verse, but here he writes in polished standard English, with words like "object," "haply" and "climes." The feeling is kept in its best clothes, which suits a speaker who must stay formal while saying something close to a confession.
The second half changes the point of view. The speaker has been "I" and "my," but he now steps back into the third person: "One friendly sigh for him—he asks no more." The dash works like a breath taken before humility. Calling himself "him" makes him seem already far away, a figure for the reader to pity, and the next word is "distant." The distance is geographical, but it is emotional too.
The final two lines hold the poem's most vivid imagery. The man "burns in flaming torrid climes, / Or haply lies beneath th' Atlantic roar." Fire sits opposite water, and these two extreme fates answer the "cold duty" of line four. Cold has been replaced by heat, then by drowning. The verb "burns" has a small curiosity of its own, since it is also the poet's surname. Whether that is a deliberate wink or a coincidence, the poem doesn't say. "Haply" is an old word for "perhaps," and it lets the thought of death slip in as a mere possibility. "Lies" is a gentle verb for it, almost a euphemism. The poem then ends not on the sigh it asks for but on "roar," the sound of the sea. The modest request "he asks no more" is rhymed with, and nearly drowned by, that noise.
There is some irony in the phrase "simple artless rhymes." The speaker presents his verses as a plain, unpolished gift, a familiar gesture of modesty. Yet the poem is anything but artless. Its rhyme scheme is exact, its contrasts of warm and cold, near and far, fire and water are carefully balanced, and its last word is placed for effect. The humility is itself a kind of craft, and it lets the speaker say something intense while appearing to ask for almost nothing.
That restraint is what makes the poem worth reading. It is short and occasional, almost a note slipped inside a gift, and it does not try to argue with duty or protest against fate. It asks for one sigh. The smallness of the request makes the unspoken feeling behind it seem larger, and the poem shows how much emotion a few polite lines can carry when the speaker is not allowed to say more.