MECHANICS. 



time, and that \vhen G' strikes the ball 

 it shall move along AD in the same 

 time. Now, if both the guns strike X 

 at the same instant, it will be found to 

 move along the diagonal, and to do so 



fa*. 



exactly in the same time as, by the im- 

 pulse of each gun separately it moved 

 along the sides. In order that the ball 

 X should move along the sides A B and 

 AD in the same time, it is necessary 

 that the force of the springs should be 

 proportional to the lengths of the sides. 

 In constructing such a table it is usual 

 to make it square, and, therefore, to 

 make the springs of equal force. 



In like manner, if several impulses, 

 which, communicated separately to a 

 body, would make it move parallel to 

 the several sides of a polygon taken in 

 order, the last side alone excepted, and 

 with velocities proportional to those 

 sides, be communicated to it at the 

 same instant, it will move in the direc- 

 tion of the last side, with a velocity pro- 

 portional to that side. 



There are numerous effects, fami- 

 liar to every one, which are exam- 

 ples of the composition and resolution 

 of motion. If, in walking along one 

 side of a street, we desire to reach a 

 distant point at the opposite side ; the 

 direct method would be to pass in a 

 straight line to the point, moving diago- 

 nally across the street; but wishing 

 to be for as short a space as possible oif 

 the foot-path, we first pass across 

 the street in a direction perpendicular 

 to the foot-path, and then pass down 

 the opposite side to the desired point. 

 This is, in facl, nothing more than a 

 resolution of the diagonal motion first 

 mentioned into its two components, viz. 

 the sides of the parallelogram. 



Again, if a boat be rowed directly 

 across a river, when there is no current, 

 it will pass over in a straight line, per- 

 pendicular to the banks. But, if there 

 be a current, the boat will be carried by 

 the current parallel to the banks, while 

 it is impelled by the oars in a direction 

 perpendicular to the banks : the con- 



sequence will be, that it will pass across 

 in a diagonal direction, arriving at the 

 other bank not at the point immedi- 

 ately opposite to where it started, but 

 at a point considerably below it : it 

 moves, in fact, in the diagonal of a paral- 

 lelogram, one side of which is a straight 

 line drawn across the river from the 

 point where it started perpendicular to 

 the banks ; and the other side is so much 

 of the bank itself measured from the 

 point where it started as the current 

 moved with the boat down the river in 

 the time taken to cross it. This, there- 

 fore, is an example of the composition 

 of motion, as the former was of its re- 

 solution. 



The facility with which many of the 

 feats of horsemanship exhibited in the 

 circus are performed may be accounted 

 for on this principle. When the man and 

 horse are moving with great speed, it 

 sometimes excites surprise, that when 

 the man leaps directly upward, the horse 

 does not pass from under him, and that 

 he does not, in descending, alight upon 

 the ground perpendicularly under the 

 point at which he sprang from the 

 saddle. But it should be considered, 

 that, on leaving the saddle, the body of 

 the rider has the same velocity as that 

 of the horse : the spring which he takes 

 perpendicularly upward in no degree 

 diminishes this velocity ; so that, while 

 he is ascending from the saddle, he is 

 still advancing with the same speed as 

 the horse, and continues so advancing 

 until his return to the saddle. In this 

 case, the body of the rider describes the 

 diagonal of a parallelogram, one side of 

 which is in the direction of the horse's 

 motion, and the other perpendicularly 

 upward, in the direction in which he 

 makes the leap. 



In the common feat of jumping 

 through a hoop, and alighting again 

 on the saddle, an inexperienced rider 

 would be likely to project his body for- 

 ward in the same manner as he would 

 do in leaping through the same hoop 

 from the ground. In such a case, instead 

 of alighting on the saddle, he would 

 alight either before the horse or on his 

 head or neck ; for he would, in fact, 

 then advance forward more rapidly 

 than the horse, his body having, be- 

 sides the speed of the horse, in which it 

 always partakes, the additional speed 

 derived from the muscular exertion 

 by which the rider projects his body 

 forward. All that is requisite to exe- 

 cute this feat is, to leap directly up- 



