Citation needed! This sounds like the "Cow Tools" of the nineteenth century, but I can't find it or anyone else talking about it online. Internal evidence from TOBoHP says the cartoon is from 1841 or 1842, and all of 1841 is on Project Gutenberg. But I don't see the point of most old Punch cartoons, which makes it impossible for me to see the one that never made sense to anybody.
Update, much later: Mystery solved!
(1) Sat Jul 14 2007 10:23:
I'm reading The Oxford Book of Humorous Prose and on page 295 Frank Muir drops a maddening hint:
Thackeray contributed hundreds of short prose items and drawings to Punch in its early years. These attracted little notice except for one drawing: this became famous because nobody then or since has been able to see the point of it. A rival magazine helpfully offered five hundred pounds to anybody who could explain the drawing. Nobody could.