500 THE CONSERVATION OP ENERGY 



What is meant by the motion of a moving point at a given instant ? 

 Properly speaking, there is no such thing; but what we mean in 

 speaking thus is the motion which takes place in an indefinitely short 

 time in which that instant lies. 



Similarly the motion of a moving point, at a given point in space, 

 is understood to mean the motion which takes place through an 

 indefinitely small space in which the fixed point lies. 



Having now gained some definite notions, we are ready to answer 

 some objections which have been made to the law of conservation on 

 the contact theory. 



It has been objected that when two rigid atoms rebound from each 

 other, the motion of each must have been totally destroyed when 

 impact took place, and immediately recreated. 



We may reply thus : If the motion had been destroyed, there 

 must at least have been an indefinitely short time during which 

 there was no motion, duration being absolutely necessary to motion ; 

 but the contact was instantaneous, it did not occupy time, hence the 

 motion was never destroyed. 



Again : the two atoms passed through no space while in contact, for 

 the same reason, hence they cannot acquire a common motion. If 

 this were not so, what would the result hel If adjacent surfaces of 

 two atoms were in contact, that is, coincided, and they had no 

 relative motion, there would be no real division between them. In 

 passing from the interior of one atom to the interior of the other, we 

 should come across nothing whei-eby we could assert that they were 

 not continuous ; in fact, they would form one rigid atom. But if 

 we consider the matter, we shall see that it would be perfectly 

 impossible, by any force, however great, to press the atoms together 

 so that they can form one continuous atom. The only forces with 

 which we are acquainted being blows or collisions, we should have 

 to strike the atoms together ; they would rebound ; and no matter 

 how hard or how fast we struck them, they would rebound at every 

 blow. All pressures consist of a rapid succession of minute blows, 

 We recognize no such thing as dead pressure, or a force acting with- 

 out being the result of motion. That pressure is possible between 

 two surfaces which are not constantly striking and rebounding, is, 

 from our point of view, absolutely inconceivable. All our forces are 

 the result of relative motion in the direction of the space betwe^^n 

 the bodies considered. 



