AND THE NATURE OF FORCE. 499 



afc the same time less elastic (in the sense of being subject to vibra- 

 tions) and less liable to be heated ; and in this case, also is not the 

 time taken up by impact less ? 



What is the proper inference ] Is it not that in the case of bodies 

 whose parts are incapable of motion among themselves, the relative 

 velocity after impact will be the same as before impact, and the 

 impact will be instantaneous. 



Hence rigidity, instead of being inconsistent with the doctrine of 

 conservation of energy, is the very condition necessary to its exist- 

 ence as regards the relative motions of the bodies as wholes. 



From a remark Newton makes in his illustrations of the third law 

 of motion, it seems that Huyghens and Wren held this idea concern- 

 ing rigid bodies, but since their time it seems to have fallen com- 

 pletely out of view. 



The greatest change of form always occurs when relative motion 

 is destroyed. Is it natural to suppose that where no change of form 

 occurs the same result would follow. And yet this has always been, 

 assumed. 



This conclusion as to rigid bodies is the very foundation of the- 

 action by contact theory, without which it would only result inv 

 absurdities. 



We now proceed to discuss some cases of collision of rigid bodies, 

 but first it will be necessary to gain perfectly clear ideas respecting 

 space, time and motion. What is the difierence between the follow- 

 ing terms: "A geometrical point," "an indefinitely short line," 

 " an indefinitely small surface," " an indefinitely small, solid." It is 

 a difierence of kind — they are not homogeneous. No amount of 

 multiplication or division of any one of these will change its kind. 

 An infinite number of geometrical points cannot occupy the smallest 

 part of space of any dimensions ; they cannot constitute a line, a 

 surface, or a solid. 



The summation, of indefinitely short lines, indefinitely small sur- 

 faces or solids will' produce lines, surfaces and solids respectively, and 

 nothing else. So with time. An instant, in the sense in which we 

 shall use it, corresponds to a geometrical point, separating two parts 

 of a line. 



It has no duration, and differs totally from an indefinitely short 

 period of time. An infinite number of instants thus defined can 

 occupy no time. 



