422 Observatio7is on Mr. Herapath's Theory. [Dec, 



impulse of the ball ; then because that part of the intermediate 

 hody which is against the fixture is not urged any way by that 

 fixture, the force with which the ball comes in contact with the 

 other side is the force with which the sides of this intermediate 

 body are driven together ; but this force is the momentum of 

 the ball ; therefore, that momentum is the force of constipation 

 in this case." 



But Mr. H. has just before stated, that the plane "re-acts 

 upon the ball at the instant of contact" " in a direction opposite 

 to its motion," with a force " just equal to its momentum ; " 

 and consequently the intermediate body would be acted on upon 

 one side by the momentum of the ball, and on the other by the 

 reaction of the plane, which he has stated to be, and which is in 

 fact, equal to the momentum. The force of constipation must 

 necessarily, therefore, be the sum of the forces of the momentum 

 of the ball, and the reaction of the plane. 



Mr. H. proceeds : " But if we now fix the intermediate body, 

 and instead of the fixed body on one side of it, imagine another 

 equal ball to come in contact with it at the same time as the 

 former, and with an equal momentum, then the force with which 

 each surface of this intermediate body is urged towards its 

 centre, is equal to the momentum of each of the balls ; and, 

 therefore, the force with which the two surfaces are urged toge- 

 ther is equal to the sum of these momenta, or to twice one of 

 them ; but this force is manifestly the force with which the two 

 balls would have come in contact if there had been no interme- 

 diate body ; therefore, that force is» the double of the force with 

 which either body would have struck a fixed plane." No doubt 

 it is so, and also double the force with which either one ball 

 strikes the other. And as " action and re-action are equal, and 

 contrary," the plane resists the stroke with a force " just equal 

 to its momentum," and the one body resists the other with a 

 force just equal to its momentum. So, if one ball, A, be fixed, 

 and an intermediate body of such a nature as that it shall not be 

 necessary for its vis inertia to be noticed, be placed in contact 

 with it, if another body, B, with any given momentum, comes in 

 contact with the intermediate body, the two surfaces of the inter- 

 mediate body will be urged towards its centre with a foroe 

 exactly as great as if each side had been struck with a momen- 

 tum equal to that of B. This, besides its being an actual fact, 

 as Mr. Herapath may at any time prove by experiment, neces- 

 sarily follows from the axiom which he himself has mentioned, 

 that action and re-action are equal ; for if that axiom be true, 

 the re-action of the fixed ball must be exactly equal to the action 

 of the ball in motion; and that it is so, is also proved by the 

 fact that the ball requires to be fixed with strength sufficient to 

 afford such a resistance, otherwise it would be driven away. 

 Mr. Herapath, however, from the reasoning in the foregoing 

 pxlract, immediately concludes; " Hence if two hard and equal 



