This Tale originally appeared as a serial in The Monthly Packet, beginning in April, 1880. The writer's intention was to embody in each Knot (like the medicine so dextrously, but ineffectually, concealed in the jam of our early childhood) one or more mathematical questions---in Arithmetic, Algebra, or Geometry, as the case might be---for the amusement, and possible edification, of the fair readers of that Magazine.