Remark how the rider must be lifted from the level _c_ to _b_ and be thrown forward from _a_ to _b_. Fig. 5 shows the curve of a No. 2 machine, with the anti-header device, on a level road. The elevation and forward throw are represented by the same letters as in Fig. 4; it will be noticed that the distance from _a_ to _b_ is very much increased. Figs. 6 and 7 show the curves or necessary projection, forward and upward, of the saddle in the header act of a No. 2 machine upon four- and eight-inch obstructions respectively. The feature of a non-backward revolution of the drive-wheel through the fork is a natural consequence in some lever and clutch machines. This element of anti-header has been the subject of an invention in the way of an attachment to the Ordinary, contrived with a view to reaching the same result, but it cannot be said to be a successful venture in the market, the probable reasons being, first, that it interferes, to a slight extent, in managing the dismounted wheel, the operator being unable to run it backward, as is sometimes desirable; second, that the anti-header element has not been really understood or appreciated among the fraternity, as it does not appeal to the judgment of the casual observer that any such element results from the fact “that a wheel won’t run back.” In the lever and clutch machine a third objection is raised,—the rider cannot back-pedal, but must depend entirely on the brake in descending hills. [Illustration: Fig. 8 Header Rational Ordinary.] [Illustration: Fig. 9 Header Kangaroo.] [Illustration: Fig. 10 Kangaroo anti-header, four-inch obstruction.] [Illustration: Fig. 11 Header Star rear-driver lever machine.] [Illustration: Fig. 12 Header Rover rear-driver type of machine.] Fig. 8 shows the Rational Ordinary curve; Fig. 9, the curve made by the well-known Kangaroo; Fig. 10, the Kangaroo with clutch or anti-header attachment; Fig. 11, the American Star combination of wheels; Fig. 12, the curve of the regular crank Rover machine. The Rover type of safety machine is practically free from the liability to direct headers, for the reason that the centre of gravity of the system has to be raised to such a height that the rider swerves around sideways before he can go over; nevertheless, a modified form of the same might be possible through some remote concatenation of circumstances causing the machine to stop and throw the rider bodily over the handle-bar without keeping him company on the trip as usual, in which case he, at least, escapes the usual subsequent annoyance of being pounded by the rear wheel.