155

G133

include all the characters that are common to every line of the described family and which belongs to each line in itself considered. Yet I should have much sympathy with a mind that should doubt this, inasmuch as the description applies to every oval, or simple self-returning line. For the motion of a particle along such a line until it returns to its original point on any one of the lines of the family is related to the motion of a point along ordinary ovals until it returns to its place precisely as the simple turning over of the common plane of two sheets of paper that are stuck together, so as to bring that plane of separation back to its original place, is related to a complete revolution of [a] pair of sheets. Suppose, Reader, take a yard of ribbon of paper, for example, and mark with lead pencil a line along the middle of one side of it, and then simply turning over one end of the ribbon, so paste the two ends together so that upon one end having the mark on its upper side shall be pasted down the other end with the mark upon its lower side (so as to bring not merely the two ends of the ribbon