Here's another application of the tune, also in a New York paper, this time the November 5, 1842 edition of the Poughkeepsie Eagle (reprinted, apparently, from the New Bedford Mercury). It lacks the genuine folk quality (sardonic air quotes optional) of the last piece, but has some wit. I have endeavored to transcribe it accurately, errors of punctuation and all.

Light Reading.
From, the New Bedford Mercury.
OIL SONG
A LAMP-OON ;
OR, PIG'S FAT VERSUS WHALE'S OIL
By a Sau-sage
Air—"Derry Down."

A cry from the West has reached us down East—
New light's the cause of a squeal from the beast—
Fish-oil has lost its once far-famed repute,
And must yield to hog's fat beyond a dispute.
Derrydown, down, down, derry down.

That the fat of the pig, Western savans affirm,
With a wick (of hog's bristles?) does brilliantly burn;
Sperm candles or oil are poor trash at best,
Compar'd with the hog-fat that's raised at the West.
Derry down, &c.

That the old lights have ever come out of the East,
From the first of sun rising, (as a data the least,)
And as the world goes upside down at the best,
The hogs have determined to illumine the West.
Derry down, &c.

That the virtue of pig-tail our forefathers knew,
When they wove it behind and term'd it a queue,
But in those dark ages, most writers agree,
They slighted the hogs for the fish of the sea.
Derry down, &c.

Had they but known what a pig-tail has done.
When steep'd in hog's lard, how it rivall'd the sun,
No drawing-room lusters, assemblies, or feasts,
Would be any great shakes without tails of the beasts.
Derry down, &c.

The West had indignantly rais'd to a man,
To throw fat on the lights of the East, if they can;
And their ends to attain, at no trifles will stick,
They will go the whole hog and use bristles for wick
Derry down, down, down, derry down.