Which John Milton?

According to the news, a dirty poem has been discovered with John Milton's name attached. The poem runs:

Have you not in a Chimney seen
A Faggot which is moist and green
How coyly it receives the Heat
And at both ends do's weep and sweat?
So fares it with a tender Maid
When first upon her Back she's laid
But like dry wood th'experienced Dame
Cracks and rejoices in the Flame.

Though it comes from a 1709 collection of verses, not even Dr Batt, who found the poem, believes that it's by Milton. The working theory is that somebody attributed it to Milton in order to sully, smear and besmirch his reputation. That seems a trifle unlikely to me. By the standards of the late sixteenth century this isn't a particularly dirty rhyme. Certainly if your main aim was to traduce Milton by writing the muckiest rhyme you could imagine, you could have done something an awful lot saucier.

It might be worth noting that John has always been one of the commonest Christian names in England, and Milton one of the commonest surnames. Any medieval chap from a town with a mill could acquire the moniker. Wikipedia has four John Miltons, Facebook two thousand.

Faggot, of course, used to be a pejorative term for a woman, until in the early twentieth century the baton was passed to homosexuals. The poem is also quite neat in its misapplied words: in the first half the wood is, improbably, coy; and this is answered in the second half by the experienced dame's cracking (although at the time a fallen woman could be referred to as a crack).

Milton was rather keen on rumpy-pumpy, but I don't think he would have made a joke about it. The beast with two backs was to him a sacred animal. There was solemnity in his sexuality, if not grandeur in his groin.

They're also a kind of food