42t OUTLINES OF NATURAL PHILOSOPHY. 



When the bodies are imperfectly elastic, the sum of 

 the products of the bodies into the squares of their 

 velocities does not continue the same after collision 

 that it was before it. The quantity of motion, 

 however, estimated in a given direction, remains 

 the same in every case. 



There is another law which extends to the collision of 

 all bodies, whether elastic, unelastic, or imperfect- 

 ly elastic. It is, that if each body be multiplied 

 into the square of the change that has taken place 

 in its velocity by the collision, the sum of these 

 products is a minimum ; that is, using the prece- 

 ding notation A (a a') 2 -f B (b b') 9 is the least 

 possible, or is less in the case which actually takes 

 place in nature, than if the difference between a 

 and a', b and &', were other than they are. This 

 law was discovered by MAUPERTUIS. It is not de- 

 monstrated from principle, but is collected from the 

 preceding propositions by induction. 



SECT. 



