In the descent of the lever from _b_ to _c_ the power will only be transmitted through the arc between _d_ and _e_; taking an equal arc from _f_ to _g_ for the power given on the other side, we have the two small arcs _f d_ and _g e_, all of whose points are dead points, and we might say we have a dead line. Upon the other hand, if the machine happens to be driven in the opposite direction from that of which we have been speaking, or, in other words, if the pedal is in advance of instead of in the rear of the driving-axle, as seen in Fig. 5, we have an advantage, since the arcs _f d_ and _g e_ would represent arcs in which the rider has power on both treadles instead of on neither, and it might be said that, instead of having an arc of dead centre or no power, we have considerably less than no dead centre at all. The lever and crank, Fig. 5, is a device used on some rear-driving machines,—the pedal descends slowly and ascends rapidly; certainly a desirable arrangement. That is to say, if the arc _d e_ raises and _d f g e_ lowers the pedal, it will then raise quickly and lower slowly; whereas, if _d e_ lowers and _d f g e_ raises the pedal, it will raise slowly and lower quickly. The study of wheels in the market made with front-driving mechanism, on the plan of Fig. 4, suggests an incontrovertible argument in favor of getting over the work, in spite of the difficulty noticed in respect to dead centres; such machines actually have a creditable reputation as powerful hill-climbers and rough-road machines, which can only be explained on the theory that the vertical application of power more than makes up the deficiency caused by the arc of no power at all. In speaking of the second group, Figs. 4 and 5, it must be understood that the matter of driving from either the front or the rear wheel has nothing to do with the principle, except in so far as it regulates the arrangement of the pedal and the direction of translation appertaining thereto. The difference in principle depends on whether the driving or the returning arc of the crank is towards or farther from the pedal. It strikes me that the style of lever and crank of the first group is a kind of cross between the direct crank and the pivoted lever and crank of Group II., and especially of Fig. 4 of that group, since it possesses some of the advantages and some of the objections found in both. I find from observations, which will be spoken of later, that the ankle-power in the direct crank is very considerable, and that it is diminished in the oval-motion lever, Group I., and that it disappears absolutely in the pivoted lever, Group II. These facts are really evident, but as they came within the domain of other experiment, I merely state the result. CHAPTER VI. GRAPHIC ILLUSTRATION OF THE APPLICATION OF POWER TO CYCLES—KINEMATICS.