64 



THE ACCELERATION OF GRAVITY. 



a body are, as has been already stated, perfectly similar 

 to those now discussed, but the acceleration is much 

 greater. Our mass, weighing 588^, was acted on by a 

 force represented by 6^; but if we allow the same mass 

 to fall freely, so that no other mass is set in motion by 

 it, the force which acts upon it is 588 = 6 x 98^. 

 Now it has been shown that the velocities acquired in 

 equal times, or in other words the accelerations, are pro- 

 portional to the forces. A force 98 times greater will 

 hence produce an acceleration 98 times greater; the 

 freely falling body would have therefore an acceleration 

 of 98 x l decirn = 9^-8; and since all bodies which have 

 not to overcome the resistance of the air fall with equal 

 velocity, it follows generally that 9 m *8 is the accelera- 

 tion which the force of gravity imparts to falling bodies: 

 this is the acceleration of gravity. It is hence possible 

 to calculate for a small body which possesses great 

 weight but a small surface, such as a leaden bullet or 

 stone, the space traversed in a given time. Thus if a 

 stone dropped from a tower reaches the ground in 2*5 

 seconds, the height of the tower is equal to the 

 square of the time multiplied by half the acceleration 



of gravity, or = 2-5 x 2'5 x I* 8 = 3CT625. 



jB 



The velocities acquired by a freely falling body and 

 the spaces traversed for the first 6 seconds are given in 

 the following little table : 



