198 



ACTION AND REACTION. 



part of the velocity of A before it. Thus A loses by the impact ten eleventh 

 parts of its motion, which are precisely what B receives. 



Again, if the masses of A and B be 5 and 7, then the united mass after im- 

 pact will be 12. The motion of A before impact will be equally distributed 

 between these 12 parts, so that each part will have a 12th of it ; but 5 of these 

 parts belong to the mass A, and 7 to B. Hence, B will receive -j 7 ^, while A 

 retains T 5 ^. 



In general, therefore, when a mass, A, in motion impinges on a mass, B, at 

 rest, to find the motion of the united mass after impact, divide the whole motion 

 of A into as many equal parts as there are equal component masses in A and 

 B together, and then B will receive by the impact as many parts of this motion 

 as it has equal component masses. 



This is an immediate consequence of the property of inertia. If we were 

 to suppose that, by their mutual impact, A were to give to B either more or 

 less motion than that which it, A, loses, it would necessarily follow that either 

 A or B must have a power of producing or of resisting motion, which would be 

 inconsistent with the quality of inertia already defined. For, if A give to B 

 more motion than it loses, all the overplus or excess must be excited in B by 

 the action of A ; and therefore A is not inactive, but is capable of exciting mo- 

 tion which it does not possess. On the other hand, B cannot receive from A 

 less motion than A loses, because then B must be admitted to have the power 

 by its resistance of destroying all the deficiency ; a power essentially active, 

 and inconsistent with the quality of inertia. 



If we contemplate the effects of impact, which we have now described, as 

 facts ascertained by experiment (which they may be), we may take them as 

 further verification of the universality of the quality of inertia. But, on the 

 other hand, we may view them as phenomena which may certainly be pre- 

 dicted from the previous knowledge of that quality ; and this is one of many 

 instances of the advantage which science possesses over knowledge merely 

 practical. Having obtained by observation or experience a certain number of 

 simple facts, and thence deduced the general qualities of bodies, we are ena- 

 bled, by demonstrative reasoning, to discover other facts which have never 

 fallen under our observation, or, if so, may have never excited attention. In 

 this way philosophers have discovered certain small motions and slight chan- 

 ges which have taken place among the heavenly bodies, and have directed 

 the attention of astronomical observers to them, instructing them with the 

 greatest precision as to the exact moment of time, and the point of the firma- 

 ment to which they should direct the telescope, in order to witness the pre- 

 dicted event. 



Since, by the quality of inertia, a body can neither generate nor destroy mo- 

 tion, it follows that when two bodies act upon each other, in any way what- 

 ever, the total quantity of motion in a given direction, after the action takes 

 place, must be the same as before it, for otherwise some motion would be pro- 

 duced by the action of the bodies, which would contradict the principle that 

 they are inert. The word " action" is here applied, perhaps improperly, but 

 according to the usage of mechanical writers, to express a certain phenomenon 

 or effect. It is, therefore, not to be understood as implying any active princi- 

 ple in the bodies to which it is attributed. 



In the cases of collision of which we have spoken, one of the masses, B, was 

 supposed to be quiescent before the impact. We shall now suppose it to be 

 moving in the same direction as A, that, is, toward C, but with a less velocity, 

 so that A shall overtake it, and impinge upon it. After the impact, the two 

 masses will move toward C with a common velocity, the amount of which we 

 now propose to determine. 



