62 ELEMENTS OF SCIENCE 



It also follows from the foregoing facts that the velo 

 city a body acquires in falling, is as the square root of the 

 height fallen through. Thus, to acquire a velocity of 

 32 feet per second it must fall a distance of 4 2 feet ; for 

 a velocity of 64 feet per second, 48 feet ; and for 96 feet 

 per second, 80 feet and so on. The distances fallen 

 through during equal successive intervals are as the 

 series of odd numbers i, 3, 5, 7, &c. 



These laws apply not only to the motion of Jailing but 

 also to all uniformly accelerated motions ; only the rate 

 of acceleration is never so rapid on inclined planes or in 

 any other conditions, as when falling freely. All freely 

 falling bodies are accelerated at the same rate, because 

 however they may differ in mass, the force of gravity 

 acts on them in exact proportion thereto acting twelve 

 times more forcibly on a mass of twelve pounds, than on 

 a mass of one pound. 



The pendulum, while one of the simplest of scientific 

 instruments, is also one of the most valuable. If a 

 small, heavy body be suspended by a thread from a fixed 

 point, that will form an instrument of the kind of a most 

 simple description. 



When at rest, the line from the point of suspension S 

 (Fig. 13), to the weight A, serves to indicate the line along 

 which gravity acts the "plumb-line" or vertical line. 



When the weight is drawn on one side, and then let 

 go e.g., if A be drawn to C and then allowed to 

 fall in a vertical plane it will, after descending to its 

 former position, ascend on the other side as far as B 

 that is, nearly as far from A on one side as C was on 

 the other. It will then descend again and afterwards 

 ascend nearly as high as was the point B, and so on. 

 Its entire sweep from C to B is called one vibration, 

 or oscillation of the pendulum, and its extent or anipli- 



