Hi Lighter,

Smith could be the author, but considering the range and scope of the ballad it's more likely his arrangement or perhaps something he copied from print-- as it is the same text given by Rimbault from the mystery broadside (if the broadside is after 1655 Smith could be the source). Anything he submitted whether he wrote it or not would have his name attached. So yes, it's possible he wrote it, I just don't think so. Child says:

Both of these name "Mr. Smith" as the author; that is, Dr. James Smith, a well-known writer of humorous verses, to whom the larger part of the pieces in Wit Restor'd has been attributed. If the ballad were ever in Smith's hands, he might possibly have inserted the three burlesque stanzas, 11-13; but similar verses are found in another copy (L a), and might easily be extemporized by any singer of sufficiently bad taste.

Richie