Historical. That the problems of plane kinematics should have been studied for a long period is natural; they present themselves quite easily, and in simple fashion. At the end of the seventeenth century, and the beginning of the eighteenth century, De La Hire investigated roulettes, and to him also is due the introduction of the inflexion circle, as the aggregate of the points of a plane, subject to coplanar motion, which are instantaneously at inflexions of their paths. At a much later date, Ball (1) drew attention to that one point of the moving plane—upon the inflexion circle—which, in quite general motion, has four point contact with its approximately straight line path; or, has four consecutive positions in line.