24 MECHANICS. 



an exact second each if the cord be Sd^ inches long, or of 

 half a second each if it be about 9f inches long. 



The velocity increases simply as the time, that is, the 

 speed in falling is twice as great in two seconds as in one ; 

 three times as great in three seconds ; four times as great 

 in four seconds, and so forth. A stone will fall four times 

 as far in two as in one second, while its velocity will be 

 doubled ; nine times as far in three seconds, while its 

 velocity will be tripled, etc. 



If a stone is thrown upward, its motion continues 

 gradually to decrease, at the same rate as it increases in 

 falling ; hence the same time is required to reach its 

 highest point, as to fall from that point back to the earth. 

 Therefore the velocity with which it is first projected up- 

 ward is equal to the velocity w^hich it attains at the 

 moment of striking the ground. There is an exception, 

 however, to this general rule. In a vacuum it w^ould be 

 perfectly correct, but in ordinary practice the resistance 

 of the air tends to diminish the velocity while ascending, 

 and still further to retard it while descending. For this 

 reason, it will fall with less speed than it first arose. For 

 heavy bodies and small distances, this exception would be 

 imperceptible ; but with small bodies falling from great 

 heights, the difference will be considerable. 



The velocity of a stone after falling one second, or six- 

 teen feet, is at the rate of thirty-tw^o feet per second; 

 hence, if thrown upward at that rate, it will rise just six- 

 teen feet high. After falling three seconds, the rate is 

 ninety-six feet ; and hence, if projected upward at ninety- 

 six feet per second, it will rise nine times sixteen feet, or 

 one hundred and forty-four feet high. And so of otlier 

 heights. 



Were it not for the resistance of the air, a feather would 

 fall as swiftly as a leaden ball. This is conclusively shown 

 by an interesting experiment. A tall glass jar (fig. 11), 

 open at the bottom, is covered with a brass cap, fitting it 



