Does each verse use the same tune? The one I know changed at the end (hence why the scanning is so completely different).

It's interesting that she's called 'Jemima' - when I was looking online, there was one site that said:

"This actually isn't a nursery rhyme. It is a poem written by Henry Wadsworth Longfellow. The line "she was very, very good" should actually be "she was very good indeed". Longfellow's second son Ernest says of this poem: "It was while walking up and down with his second daughter, then a baby in his arms, that my father composed and sang to her the well-known lines .... Many people think this a Mother Goose rhyme, but this is the true version and history"

But I'm not sure that's from a reliable source...