GRAVITATION. 



by the presence, and contemporaneous action of various 

 other principles. 



There is only one class of these effects, which proper- 

 ly comes within the scope of our present design ; and 

 that is the case of bodies falling freely. This subject we 

 shall proceed briefly to investigate. The result to which 

 we shall come, and which is called the general law of 

 falling bodies is this 



The spaces passed over by falling bodies are as the 

 squares of the times. 



That is, if one body is falling one minute, and another 

 two minutes, the spaces which they will respectively de- 

 scribe, will be as the squares of those numbers, so that the 

 second will not fall simply twice as far as the first, but 

 four times as far. For as the square of 1 is 1, and of 2, 

 4, the spaces will be as 1 to 4. In the same manner, if 

 one body fall 2 seconds, and another 3, the number of 

 feet of the respective descents will be as 4 to 9, for 4 is 

 the square of 2, and 9 of 3. 



We cannot here give the mathematical demonstration 

 of this principle, but to illustrate it a little, let the reader 

 imagine a mass of rock loosed from the edge of an over- 

 hanging cliff. No one doubts that the impetuosity of its 

 descent will be increased by the distance it has to fall, 

 but every one has not a distinct idea of the nature and 

 cause of this acceleration. In order to understand this, 

 let us think of its condition after it has fallen through the 

 first ten feet of its descent. Suppose that, at this point, 

 the force of gravitation should suddenly cease, would the 

 rock stop in its descent 1 By no means ; it would go for- 

 ward with the velocity which it had previously acquired, 

 precisely as the cannon ball continues to move swiftly 

 through the air, after the explosive force of gunpowder 

 ceases to operate upon it. The impulse given in this 

 latter case is over in an instant, but the motion continues 

 until the resistance of the air extinguishes it. In the 

 same manner, if the force of gravity were to cease at the 

 end of the first ten feet of the fall of the rock, the mass 

 would move on, with the velocity which it had already 

 acquired, to the earth, excepting that it might lose a little 

 by the resistance of the air. But gravitation does not 



