1821.] Observatiom on Mr. Herapath's Theory. 423 



balls come in contact with equal and opposite momenta, they 

 will separate after the stroke with the same velocity with which 

 they met. For since the intensity of the stroke is the force with 

 which each of the halls is acted on in a direction opposite to that in 

 which it came at the time of the contact ; and since that intensity 

 is, by the preceding cor. equal to twice the momentum of either 

 ball, eaeh ball at the time of the contact might be conceived to 

 be acted on by two opposite forces, one its momentum, impelling 

 it towards the other ball ; and the other, the force of the contact 

 equal to twice its momentum impelling it in an opposite direc- 

 tion. The difference between these two forces, therefore, or the 

 value of one momentum is the force with which each ball 

 retraces its path; and, consequently, the velocity of the separa- 

 tion of the balls is equal to the velocity of their approach." 

 How Mr. H. proves, " that the intensity of the stroke is the 

 force with which each of the balls is acted on in a direction oppo- 

 site to that in which it came at the time of the contact," I am at 

 a loss to discover ; there certainly is nothing suggested in the 

 paper under observation even pretending to be an argument to 

 that effect. The intensity of the force is " equal to the sum of 

 the momenta " " with which both balls come in contact," half 

 of which is in one direction, and half in the opposite ; so that the 

 intensity of the force of contact, according to his own previous 

 reasoning, is exactly double to that of each ball in the direction 

 in which it came at the time of contact ; consequently, " if each 

 ball at the time of the contact be conceived to be acted on by 

 two opposite forces, one its momentum impelling it towards the 

 other ball, and the other the force" at the time " of the contact 

 impelling it in an opposite direction," which will be half the sum 

 of the momenta; that is, exactly equal to the momentum of one 

 ball, each ball will remain at rest, instead of separating in oppo- 

 site directions. 



Thus if a man push with all his strength against a wall, say 

 with a force as 10, action and re-action being equal, the wail 

 resists with a force as 10, exactly in a similar manner to the fixed 

 plane in Mr. H.'s proposition. If, instead of the wall, there be 

 an opposing active force, another person, for instance, pushing 

 against the first with an exactly equal force, the effect to the 

 first will be just the same as the wall, and neither person will be 

 able to move the other. But by Mr. Herapath's reasoning each 

 person would be acted on in a direction opposite to that towards 

 which he pushed, by a force equal to twice the force of either 

 one ; that is, with a force as 20, and consequently both must be 

 pushed backwards ; a conclusion notoriously contrary to fact. 

 And yet this is the reasoning by which are to be overturned, in 

 one short page, the doctrines of Newton, Maclaurin, Hutton, 

 Playfair, and innumerable other mathematicians, in relation t<* 

 the collision of hard bodies ; the fust principles of winch too are 

 its nearly as possible self evident. 



