I agree with Messrs MacKintosh & Imlach on the progression from "older" to "old", but otherwise I think Mr Seeger has the better of it.

As to the tune, it does resemble that of (the chorus of) "Officer Krupke" at the beginning, but the latter goes off on quite a different tack. The mention of "Fair Harvard" (whose tune is stolen from "Believe me, if all those endearing young charms") is pleasantly satirical on the hazards of trying to trace tunes.