Actually, the full title is The Gaping, Wide-mouthed, Waddling Frog: A New and Entertaining Game of Questions and Commands: With Proper Directions for Playing the Game, and Crying Forfeits: Embellished with Sixteen Colored Engravings (London: Printed for A.K. Newman and Co. Leadenhall-street, [between 1814 and 1822]; London: Dean and Munday, printers, Threadneedle-street).
A long-winded title for what is a fairly simple counting and recitation game for children. The rules state that the Treasurer (appointed by the group) begins the game. "He holds a penknife, pocket-book, thimble, or some other trifling article in his hand, and addressing the person who sets next to him, gives the command - Take this; - the person spoken to asks the question - What's this? - the Treasurer answers, A gaping, wide-mouthed, waddling Frog." This question and answer continues round the circle until it reaches the Treasurer who adds a second verse to the recital.
The game "manual" reveals fourteen of these verses, each with an appropriate illustration. Shown here is the illustration for the verse "Six beetles against the wall, Close to an old woman's apple-stall."
Once the game is finished the Treasurer appoints a Dictator "whose office it is to to direct what is to be done by each person in order to redeem their forfeits." Forfeits are incurred when any player fails to remember a verse or recites it incorrectly. Suggestions for possible penalties include submitting to be tickled by all players and to "Heat a cinder." The latter is apparently cause for great hilarity since "this sounding like eat, causes some mirth before it is discovered it only means to throw it into the fire."
Ask for Rare Book GV 150 .W8 G36 to read all fourteen verses and discover additional ideas for forfeit penalties.