go LECTURE VIII. 



obtain a certain velocit}', by means of tbe descent of a beavy body fiom a 

 beigbt, to wliicb we carry it by a fligbt of steps, we must ascend, if we wish 

 to double the velocity, a quadruple number of steps, and this will cost us 

 nearly four times as much labour. In the same manuer, if we press with a 

 g-iven force on the shorter end of a lever, in order to move a weight at a 

 greater distance on the other side of the fulcrum, a certain portion of the 

 force is expended i.n the pressure which is supported by tlie fulcrum, and we 

 by no means produce the same momentum, as would have been obtained, by 

 the immediate action of an equal force, on the body to be moved. 



An elastic ball, of 2 ounces weight, moving with a velocity of 3 feet in a 

 second, possesses an energy, as we have already seen, which ma}- be ex- 

 pressed by 18. If it strike a ball of 1 ounce which is at rest, its velocity 

 will be reduced to 1 foot in a second, and the smaller ball will receive a 

 velocity of 4 feet: the energy of the first ball Avill then be expressed by 2, 

 and that of the second by 16, making together 18, as before. The momentum 

 of the larger ball after collision is 2, that of the smaller 4, and the sum of 

 these is equal to the original momentum of the first ball. 



Supposing the magnitude of an elastic body, which is at rest, to be infinite, 

 it will receive twice the momentum of a small body that strikes it ; but its 

 velocity, and consequently its energy, will be inconsiderable, since the 

 energy is expressed by the product of the momentum into the velocity. And 

 if the larger body be of a finite magnitude, but still much greater than the 

 smaller, its energy will be very small ; that of the smaller, which rebounds 

 with a velocity not much less than its original velocity, being but little di- 

 minished. It is for this reason, that a man, having a heavy anvil placed on 

 his chest, can bear, without much inconvenience, the blow of a large hammer 

 striking on the anvil, while a much slighter blow of the hammer, acting im- 

 mediately on his body, would have fractured his ribs, and destroyed his life. 

 The anvil receives a momentum nearly twice as great as that of the hammer; 

 but its tendency to overcome the strength of the bones, and to crush the man, 

 is only proportional to its energy, which is nearly as much less than that of 

 the hammer, as four times the weight of the hammer is less than the weight 

 of the anvil. Thus, if the weight of the hammer were 5 pounds, and that of 

 the anvil 100, the energy of the anvil would be less than one fifth as great as 



