The diagrams show the paths of the point in the various machines passing over a four-inch obstruction; _F_ designates the front and _R_ the rear wheel, and the arrows indicate the direction of translation,—that is, the way the machine is running. The degrees designate the angle between lines from the drive-wheel axle, one extending vertically and the other through the saddle; sometimes also expressed in inches of horizontal distance between verticals through the rear axle and saddle. The heights or top points of the curves from the base line show the amount the machine is raised at the saddle as each wheel passes over the obstruction; these heights give inferentially the position of the saddle between the wheels, or, rather, between the vertical lines through the respective axles thereof, since the nearer over a wheel the saddle is placed the more it will be elevated when the wheel passes over the obstruction. Again, from the location of the saddle with reference to the axles we can determine the amount of weight carried by each wheel, the weight each carries being proportional to the respective distances from the saddle horizontally. The sum of the heights of the two curves from the general level will be the height of the obstacle. Theoretically there is no difference in the amount of work required to pass over an impediment, no matter where the saddle is placed, as the man must be raised in all to the height of the same, and it does not matter whether he is lifted up half way twice or all the way once in so far as the amount of labor is concerned. The man and the machine must be lifted up to a certain height in some way; as it happens, it is more comfortable to be lifted twice through half the distance than all at once; but this should not affect the actual work done nor the energy expended. Our scale in the study of this question is one-sixteenth of an inch to the inch; therefore in these diagrams one-eighth of an inch represents two inches in the full-size bicycle. In this connection also it must be taken into consideration that the effect upon momentum is not shown entirely by the contour of these lines; the sudden stoppage or checking of the system is generally shown by a vertical tendency in the curve, but a very disagreeable shock to the body may occur and momentum be lost without any deviation in the curve whatever when, for instance, in the most pronounced case, the saddle goes straight back upon its course. This is shown by means of the short vertical or diverging lines upon the curves. These short lines show the distance forward the point in the saddle travels in proportion to the advance of the wheels in a forward direction in space; each short line indicates an advance of two inches in the wheels. When the lines are below the curve, the saddle has actually dropped backward,—that is, it has been directly reversed in its course.