MUTUAL CHANGES COMMON TO ALL MATTER 53 



any vertical displacement is followed by a return to the 

 original relative positions. 



37. The Manner in which a Displaced Body returns to 

 the Earth. The Time of Fall. A body allowed to fall from a 

 height of 16 feet reaches the ground in one second. 



A body allowed to fall from a height of 64 feet reaches the 

 ground in two seconds. In the last second it must therefore 

 fall through 48 feet, if it takes, as may be proved, the first 

 second in falling through 16 feet. 1 



The first fact may be demonstrated by suspending the body 

 by an electro-magnet. Then break the current, and thus 

 remove the support, at one tick of the seconds-pendulum. The 

 body will reach the ground at the next tick. 



The second fact is not always easy to demonstrate on 

 account of the distance being inconveniently great, but it may 

 be accepted as the result of many experiments. 



More accurate measurements show that, if the resistance of 

 the air be allowed for, the fall in a second is 490*5 centimetres, 

 and in two seconds 1,962 centimetres. 



The result of all observations of the fall of bodies to the 

 earth is to show that the rate of fall gradually increases along 

 the course, and that the longer the course or, in other words, 

 the greater the original displacement the greater the speed 

 with which they reach the earth. 



38. When a Body is displaced from the Surface of the Earth 

 and then set free, it returns with a Uniformly Accelerated 

 Speed in a Straight Line, That a body, displaced a short 

 distance from the surface of the earth and allowed to fall, 

 returns in a straight line, is a matter of direct observation. 



That it returns with a uniformly accelerated speed is in- 

 convenient to prove directly, on account of the magnitude being 

 too great to measure in a room. The law may, however, be 

 proved by retarding the motion and then measuring. This is 

 best arranged by using Atwood's machine in conjunction with 

 a pendulum beating seconds, or a clock. 



1 It would not necessarily follow that it took one second to fall 

 through 16 feet at the greater distance from the earth, but experiment 

 shows that this is true within a moderate range. 



