1847[March]        Melville, Herman. _Omoo: A Narrative of Adventures in the South Seas_. London: John Murray.

Written in 1846. Melville's sea experience was 1841-42, in whaling ship to South Pacific (Marquesas). He'd also seen Liverpool.

The chanteying references are consistent with what we know about chanteying for the time period, i.e. the popularity of "Cheer'ly Man," the vague "singing" of untitled (and perhaps non-distinct) songs, and, indeed, the overall lack of references to familiar chanteys. Melville was such a richly descriptive writer, and it would be surprising if there was lots of notable chanteying going on but he did not make effort to explain it. On the other hand, maybe he just wasn't interested in dotting his prose with verse all the time, unlike lots of other 19th century authors.

First reference is to [CHEERLY] while catting anchor. [151]
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The decks were all life and commotion; the sailors on the forecastle singing, "Ho, cheerly men!" as they catted the anchor;
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In the other reference, sailors ashore are "Farming in Polynesia." They decide to try to make the work of clearing land go more smoothly by brining in one of their windlass songs. "Shorty" in the passage is a Cockney character. [206]
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"Give us a song, Shorty," said the doctor, who was rather sociable, on a short acquaintance. Where the work to be accomplished is any way difficult, this mode of enlivening toil is quite efficacious among sailors. So, willing to make every thing as cheerful as possible, Shorty struck up, "Were you ever in Dumbarton?" a marvellously inspiring, but somewhat indecorous windlass chorus.
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Stuart Frank notes that Doerflinger collected "Were you ever in Dumbarton?" from a lumberjack. But while the line is reminiscent of "Highland Laddie" and other chanties, they don't resemble each other in other ways that I can see. Rather, Doerflinger notes the similarity between this and the song in 1832's _The Quid_, i.e.

"Oh! if I had her,
Eh then if I had her,
Oh! how I could love her,
Black although she be."

The similarity comes in the chorus of "Dumbarton." I must say that the "Quid" lyrics do scan quite nicely over the version of "Dumbarton" collected by Doerflinger. I'm even more enthusiastic about the similarity than Doerflinger seemed to be. Doerflinger's is in 3/4 meter. Though tempo comes into play as a variable, my guess is that such a song would not have worked well at the brake/pump windlass, but would have been just fine at the spoke windlass. My hunch is that Melville's ship(s) would have still been fitted with the spoke windlass. I've said before the idea that the adoption of the new brake windlass may have been a factor in ushering in the new kind of worksongs. Perhaps, by the same token, the obsolescence of the old windlass contributed to older songs dying out.

Doerflinger called "Dumbarton" a Scottish folk song, which seems reasonable based on its content, however, I'm not finding any info on the song outside of references to Omoo and Doerflinger's book.