To represent this variation of power by actual length of lines, appended will be found a diagram, Fig. 2, showing the tangential resultant or force to turn the wheel, imparted by a one-hundred-and-fifty-pound man with and without the use of ankle-motion. _A A_ is a line showing the divisions of the angles through which the crank passes in its revolution around the axle. The line _a f i_ is a sine curve. Using the middle section and beginning at the point _a_, which is that at which the crank crosses the vertical above the axle, making a zero angle therewith, we have a direct downward pressure and, without ankle-motion, zero power. Now, by means of ankle-motion on one crank at this point we get thirty pounds of power, represented by the length of the line from _a_ to _b_; and by ankle-motion on both cranks we have sixty pounds, represented by the total length of the line from _a_ to _c_. After the crank has advanced forward fifteen degrees, we have thirty-nine pounds of direct power (_m n_), and then adding the ankle-power of twenty-three pounds (_n o_), we have a total resultant of sixty-two pounds, represented by the length of the next line (_m o_), and so on up, the direct power increasing and the ankle-power diminishing till we come to the top of the curve _f_, when we have one hundred and fifty pounds of direct power. Passing through the angle of ninety degrees, and now counting from the vertical below the axle, we decrease in power inversely as we increased before. Fig. 1 will show a little more graphically to the eyes of some casual readers how the power expands. Take _d a f i e_ as the regular swing of the crank with no power at _a_, then _d b f h e_ as the increase of power on one and the dotted lines _c_ and _g_ as the auxiliary ankle-power on the other crank added. [Illustration: Fig. 2. Ankle-power sine curve.] [5] Observe Fig. 1, p. 58. CHAPTER VII. BALANCING, AND SOME QUESTIONS OF POTENTIAL ENERGY—HILL-CLIMBING. It seems pertinent at this point to make some further distinction between two distinctive classes of road wheels. The conception in the mind of man of road carriages which require an element of balancing was a recent event in the development of vehicles in general, and the similarity of the words bicycle and tricycle, together with the fact that both are included in the generic term velocipede, has led many to overlook a distinction of balancing, which should class them under very different heads. Both are velocipedes if we mean machines run by foot-power; both are man-motors in the light that human force or energy actuates them; but the two-wheel single-track machine must employ a particular faculty on the part of the rider, not required in running one of stable equilibrium.