216 



COMPOSITION AND RESOLUTION OF FORCE. 



direction E P Q. The foot P of the tower will, therefore, in one day, move 

 over the circle E P Q, while the top T moves over the greater circle T T' R. 

 Hence it is evident that the top of the tower moves with greater speed than 

 the foot, and therefore in the same time moves through a greater space. Now 

 suppose a body placed at the top ; it participates in the motion which the top 

 of the tower has in common with the earth. If it be disengaged, it also re- 

 ceives the descending motion T P. Let us suppose that the body would take 

 five seconds to fall from T to P, and that in the same time the top T is moved 

 by the rotation of the earth from T to T', the foot being moved from P to P'. 

 The falling body is therefore endued with two motions, one expressed by T T', 

 and the other by T P. The combined effect of these will be found in the usual 

 way by the parallelogram. Take T />, equal to T T', the body will move from 

 T to p in the time of the fall, and will meet the ground at p. But since T T' 

 is greater than P P / , it follows that p must be at a distance from P' equal to 

 the excess of T T' above P P'. Hence the body will not fall exactly at the 

 foot of the tower, but at a certain distance from it, in the direction of the earth's 

 motion, that is, eastward. This is found, by experiment, to be actually the 

 case ; and the distance from the foot of the tower, at which the body is ob- 

 served to fall, agrees with that which is computed from the motion of the earth, 

 to as great a degree of exactness as could be expected from the nature of the 

 experiment. 



The properties of compounded motions cause some of the equestrian feats 

 exhibited at public spectacles to be performed by a kind of exertion very dif- 

 ferent from that the spectators generally attribute to the performer. For ex- 

 ample, 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 per- 

 former, 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 ne- 

 cessary to rise directly upward to a sufficient height to clear the garter. The 

 motion which he has in common with the horse, compounded with the eleva- 

 tion acquired by his muscular power, accomplishes the leap. 



To explain this more fully, let ABC, fig. 13, be the direction in which the 



Fig. 13. 



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 toward 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 A E and A J3, 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 



