Silber's Songs of the Civil War has two very different "Billy Barlow" songs, but they share the same tune. Q posted the first in the first message of this thread. Here's the second:

BILLY BARLOW-ON THE TIMES
Words by H. Angelo
Music: "Billy Barlow"

1. I beg your attention, kind gentlefolks all,
I hope no intrusion in making this call;
It's been a long time since you've seen me, I know,
But I'm the identical Billy Barlow.
Oh! dear, I'm ragged, I know,
But the times have affected poor Billy Barlow.

2. Our country's excited 'bout this thing and that,
Both North and the South hardly know what they're at.
They secession, coercion, and compromise blow,
But it's talk and no cider, thinks Billy Barlow.
Oh! dear, I'm ragged I know,
But "Stand by the Union" will Billy Barlow.

3. If I had but the power I'd soon bring 'em to,
Though this may be nonsense I'm singing to you.
I'd hang of ringleaders a hundred or so,
And choke off secession, would Billy Barlow.
Oh! dear, I'm ragged, I know,
Then times would be better, thinks Billy Barlow.

4. Our cities are flooded with traitors and spies,
And our papers are filled with a strange pack of lies;
They'll agitate questions for friend or a foe.
Whilst they pocket the rhino, says Billy Barlow.
Oh! dear, I'm ragged, I know,
Self-interest they go for, thinks Billy Barlow.

5. Our members of Congress have plenty to do,
But it's seldom, if ever, they do it, 'tis true.
Political speeches for hours they'll blow,
But it all 'mounts to nothing, says Billy Barlow.
Oh! dear, I'm ragged, I know,
Why don't they do something? says Billy Barlow.

6. Believe me, my friend, in my song I don't err,
But the poor have to suffer when such things occur;
And as I belong to that class, you must know,
I'd fight for the Union, would Billy Barlow.
Oh! dear, I'm ragged, I know,
Hurrah for the Union! says Billy Barlow