Читать книгу A Treatise on Mechanics онлайн

87 страница из 91

(89.) The properties of compounded motions cause some of the equestrian feats exhibited at public spectacles to be performed by a kind of exertion very different from that which the spectators generally attribute to the performer. For example, the horseman standing on the saddle leaps over a garter extended over the horse at right angles to his motion; the horse passing under the garter, the rider lights upon the saddle at the opposite side. The exertion of the performer, in this case, is not that which he would use were he to leap from the ground over a garter at the same height. In the latter case, he would make an exertion to rise, and, at the same time, to project his body forward. In the case, however, of the horseman, he merely makes that exertion which is necessary to rise directly upwards to a sufficient height to clear the garter. The motion which he has in common with the horse, compounded with the elevation acquired by his muscular power, accomplishes the leap.

To explain this more fully, let ABC, fig.19., be the direction in which the horse moves, A being the point at which the rider quits the saddle, and C the point at which he returns to it. Let D be the highest point which is to be cleared in the leap. At A the rider makes a leap towards the point E, and this must be done at such a distance from B, that he would rise from B to E in the time in which the horse moves from A to B. On departing from A, the rider has, therefore, two motions, represented by the lines AE and AB, by which he will move from the point A to the opposite angle D of the parallelogram. At D, the exertion of the leap being overcome by the weight of his body, he begins to return downward, and would fall from D to B in the time in which the horse moves from B to C. But at D he still retains the motion which he had in common with the horse; and therefore, in leaving the point D, he has two motions, expressed by the lines DF and DB. The compounded effects of these motions carry him from D to C. Strictly speaking, his motion from A to D, and from D to C, is not in straight lines, but in a curve. It is not necessary here, however, to attend to this circumstance.