A lot of hot air has been generated in an attempt to solve the riddle first proposed in Word Ways in 1981. I believe that Ronnie Kon has unwittingly given us the clue that will reveal the riddle's answer. He notes that it first appeared in Dickson's Balloon Almanac in 1801, and we need to discover what kind of publication that was.
Eckler, Faith W.
"A Lot of Hot Air,"
Word Ways: Vol. 44
, Article 6.
Available at: https://digitalcommons.butler.edu/wordways/vol44/iss1/6