Force of Inertia. \ 79 



Now every resistance does not always imply an actual motion 

 in the residing body. If the body A, for example, be drawn at 

 the same time by two equal and opposite forces represented by 

 AB, AC, it would evidently have no motion. But it is not less Fig.145. 

 evident that if a force equal to G# were to act upon it in the 

 direction CB, this force would be destroyed by the effort AC, 

 and the body would yield in virtue of the force AB, equal to that 

 just applied. 



We do not pretend to decide whether the resistance which 

 bodies oppose to motion, does or does not arise from a cause of 

 this kind. However the fact may be, the resistance in question 

 which we call the force of inertia, differs from the resistance op- 

 posed by active forces (as that of bodies which impinge against 

 each other in opposite directions) in this, that these last annihi- 

 late a part of the motion ; whereas, with respect to the force of 

 inertia, while it destroys a part of the motion in the impinging 

 body, this motion passes wholly into the impinged body, as is 

 clearly shown by the equation 



m (u u') = n (u f v), 



above obtained for determining the motion after collision of 

 two bodies which move in the same direction ; for u u' is 287. 

 the velocity lost by the impinging body, and consequently 

 m (u u') is the quantity of motion which this body loses by 

 collision. We have, in like manner, seen, that u' v, is the ve- 

 locity, and n (u' v) the quantity of motion, gained by the im- 

 pinged body. Now we have shown that these two quantities 

 must necessarily be equal. 



The force of inertia, therefore, is, properly speaking, the 

 means of the communication of motion from one body to another. 

 Every body resists motion, and it is by resisting that it receives 

 motion ; it receives also just so much as it destroys in the body 

 that acts upon it. 



We hence see that, every obstacle being removed, however 

 small we suppose the impinging body, and however great the 

 mass impinged, motion will always take place upon collision. 

 When, for example, one of the two bodies is at rest, the velocity 

 which has for its expression 



