498 THE CONSERVATION OF ENERG"5G 



the energies due to heat, vibrations, etc., and add these to the energy 

 of the bodies considei'ed as wholes, that the sum. would be the total 

 energy before impact. I do not think that an.y scientific man of the 

 present day would controvert this. 



It may be said that the more perfect the elasticity of a body is, 

 the greater is its tendency to yield up the motion of its parts before 

 contact ceases, and that if perfectly elastic, it would be perfectly at 

 rest in its interior when contact ceased. 



If a helical spring be suspended horizontally as a pendulum, and 

 be allowed to fall endwise against a vertical wall, its coils will be 

 noticed to be in a state of intense vibration after contact ceases, and 

 I think no one would assert that it is possible to conceive it to be so 

 elastic as not to vibrate. The assertion would even involve a con- 

 tradiction of terms. 



The fact is, that a perfectly elastic body would vibrate for eveis, 

 external resistances being supposed removed ; and that this is not 

 the case in imperfectly elastic bodies, is simply because their vibrations 

 are gradually destroyed by internal friction being converted into heat, 

 which is in turn communicated to surrounding bodies. 



Again, take a number of balls placed very close together, and con- 

 nected two and two by elastic strings of such tension that if the end 

 ball be pulled away from the others, the motion is communicated 

 through the system with the same velocity as it is when the end ball 

 is struck towards the others ; and imagine two such systems with a 

 different number of balls in each to collide endwise in the line of 

 their common axis. Calculate now the motion on the supposition of 

 the conservation of relative motion as between each ball, and it will 

 be found that the relative motion of the sys.tems as wholes after 

 impact is less than it was before impact, and that the motion of the 

 parts will exactly account for the difference. 



Thus we have an example of bodies made up of perfectly elasti*^ 

 parts in the sense in which the word has hitherto been used, which 

 as wholes collide like imperfectly elastic bodies. 



Now in all these cases, what is it that we see invariably to accom- 

 pany the loss of relative motion. Is it not motion among the parts 1 



Do we not see that as the motion of the parts is diminished the 

 relative motion becomes greater] Is not the loss of relative motion 

 less when the bodies are harder, more able to retain their form,.ajid 



