284 Mr. Herapath on the Causes, Laws, and principal [April, 



time is always consumed. If now, other things being ahke, we 

 suppose the bodies to increase in hardness, then, since their 

 parts have a less disi)osition to yield to the force of percussion, 

 the intensity of the impulses (if we suppose the stroke to be 

 given in impulses) will be stronger, the quantity of motion com- 

 municated by each greater, and the time of the whole stroke, 

 therefore, shorter. And if we suppose, cateris paribus, the hard- 

 ness to increase still more, the duration of the stroke will be 

 still less, until, if the hardness be perfect, there will be no yield* 

 ing of figure, and no duration for the strokes. And since this 

 is the case with every stroke between perfectly hard bodies, it 

 follows that all the strokes between bodies absolutely hard have 

 no duration, and are thence equally smart. 



Cor, — Hence we gather, that in perfectly hard bodies, the 

 intensity of the impulse depends on the violence or momentum, 

 of contact, and is independent of the velocity of contact, except 

 inasmuch as it is augmented or diminished by that velocity. 



Prop. II. 



If a hard spherical body impinge perpendicularly on a 

 hard fixed plane, the body will, after the stroke, remain at rest 

 on the plane. 



For the plane having no motion of its own, and being fixed, 

 the force with which the bodies come in contact will be equal to 

 the momentum of the ball ; and because action and reiiction are 

 equal and contrary, this momentum is the force with which the 

 ball acts upon the plane, and the plane reacts upon the ball at 

 the instant of contact. The force, therefore, with which the 

 ball is acted on by the plane at the time of the contact in a 

 direction opposite to its motion is just equal to its momentum ; 

 consequently the momentum and action of the plane being equal 

 and opposite destroy one another ; and the ball having no other 

 tendency continues at rest on the plane. 



Cor. 1. — Hence a hard ball impinging obliquely upon a fixed 

 hard smooth plane slides along the surface of it in a determinate 

 direction with a determinate velocity. For if the motion of the 

 body previous to the contact be resolved into two, one perpendi- 

 cular and the other parallel to the plane, the perpendicular part 

 will be entirely destroyed by the contact, but the other part 

 being that with which the body would neither recede from, nor 

 approach the plane, will continue the same after as before the 

 stroke, and will induce the body to slide along the surface of 

 the plane in its direction, and with its entire force. 



Cor. 2. — From this proposition it appears that if, instead of 

 the plane, the body meets with another equal and hard body 

 moving equally in an opposite direction, the intensity of the 

 stroke will be twice as great as between the body and the plane ; 

 for the plane being fixed contributes nothing to the violence of 

 the blow, but the other body coming with an equal force in a 

 contrary direction, adds its whole motion to the force with which 



