ON ACCELERATING FORCE?. JJ 



diminish it in any degree that is required. Two boxes, which are attached to a 

 thre 1(1 passing over a pulley, may be filled with different vveights, wliich coun- 

 terbalance each other, and constitute, together with the pulley, an inert mass, 

 which is put into motion by a small weight added to one of them. The time 

 of descent is measured by a second or lialf second pendulum, the space de- 

 scribed being ascertained by the place of a moveable stage, against which the 

 bottom of the descending box strijses: and when we wish to determine imme- 

 diately the velocity acquired at any point, by measuring the space uniforndy 

 described in a given time, the accelerating force is removed, by means of a ring, 

 which intercepts the preponderating weight, and the box proceeds with a uni- 

 form velocity, except so far as the friction of the machine retards: it. By 

 changing the proportion of the preponderating weight to the whole weight of 

 the boxes, it is obvious that we may change the velocity of the descent, and 

 thus exhibit the effects of forces of different magnitudes. The most conveni- 

 ent mode of letting the weights go, without danger of disturbance from their 

 vibrations, is to hold the lowest weight only, and to allow it to ascend at the 

 instant of a beat of the pendulum. (Plate I. Fig. 11.) 



That the velocity generated is proportional to the time of the action of the 

 force, or that the force of gravitation, thus modified, is properly called a uni- 

 form accelerating force, .may be shown by placing the moveable ring so as to 

 intercept the same bar successively at two different points: thus the spact; uni- 

 formly described in a second, by the box alone, is twice as great, when the force 

 is withdrawn after a descent of ten half seconds, as it is after a descent of five.. 

 And if we chose to vary the weight of the bar, we might show in a similar 

 manner, that the velocity gcDcrated in a given time is proportional to the force 

 employed. 



We are neJit to determine the magnitude of the whole space described in a 

 given time with a velocity thus uniformly increasing. The la;W discovered by 

 Galileo, that the space described is as the square of the time of descent, and 

 that it is also equal to half the space which would be described in the same time 

 with the final velocity, is one of the most useful and interesting propositions 

 in the whole science of mechanics. Its truth is easily shown from mathema- 

 tical considerations, by comparing the time with the base, and the velocity 

 with the perpendicular of a triangle gradually increasing, of which the area 



