156 . • LECTURE XIII. 



makes the resistance of their lower parts to any lateral motion almost in- 

 superable. 



When a hard body penetrates another, or when a substance is ground away 

 by the attrition of another, the force, which opposes the motion, is to be con- 

 sidered, like the force of friction, as a uniformly retarding force. There is no 

 reason for imagining the stiffness of a bar, whether longer or shorter, to de- 

 pend on the velocity of the body that bends it, and the space through which 

 it may be bent, without breaking, is also limited only by the toughness of 

 the materials. In the same manner, when the internal parts of a solid are 

 broken and displaced by the penetration of another, or its external parts 

 abraded by its attrition, the resistance is the same, whatever the velocity 

 may be, and the space described by the body, before its velocity is destroyed, 

 is always proportional to the square of that velocity, or to the energy which 

 ' results from a combination of the proportions of the velocity and the mo- 

 mentum. 



