Protuberance? Fingering the sweetness of Shakespeare's potato

Potato fact #1 - There are two references to the potato in the works of Shakespeare. The first in the Merry Wives of Windsor (Act 5, Scene V); the second in Troilus and Cressida (Act 5, Scene II).

This suits as #potatofact #1, as the potato is believed to have been imported into Europe around a century before these two Shakespeare plays were published (1602 and 1609, respectively), but the plant's introduction and spread toward Northern Europe in the intervening period was both relatively unremarked and unremarkable.

But was it really the common potato, the spud, the tater, that we now know, adore and consume by the kilo, to which Shakespeare was referring?

And by "common potato" I refer to practically all of the supra 1000 potato varieties (99% in fact)  that share common germplasm with a variety that at some time in the species' early history of domestication grew in the Chiloé Archipelago in South-central Chilé.

In both references, Shakespeare's characters allude to the potato's aphrodisiac, even phallic, properties. In Merry Wives, Falstaff tries it on with Mistress Ford:

  My doe with the black scut! Let the sky rain
  potatoes; let it thunder to the tune of Green
  Sleeves, hail kissing-comfits and snow eringoes; let
  there come a tempest of provocation, I will shelter me here.

Whilst Thersites, the scurrilous Greek, is ostentatiously lewd:

  How the devil Luxury, with his fat rump and
  potato-finger, tickles these together! Fry, lechery, fry!

In a letter to the Editor of the London Times, of August 28, 1882, an anonymous writer asserted that at the time of the plays' publication the word potato had a double meaning, referring both to the solanum (our common potato) and to a convolvulus (the ipomoea batatas, or "sweet potato"). Whilst John Gerard's Herball or Generalle Historie of Plantes (1597) refers to the potato as the "batatas", this is more likely a reference only to the imported potato, as opposed to Britain's homegrown variety (the sweet potato being too tender for the British climate).

Thus the protuberances on display in Shakespeare's works, whilst less tuberant in nature, are likely to be all the sweeter for it.