CHAPTEE XII 

 GENERALIZED COORDINATES 



258. So far we have dealt with the mechanics (dynamics and 

 statics) of material bodies on the supposition that these bodies 

 consist of innumerable small particles which, in the case of a rigid 

 body, are held firmly in position and serve the purpose of trans- 

 mitting force from one part of the body to another. 



259. Even when dealing with rigid bodies this conception of the 

 structure of matter has not led to entirely consistent results. Tor 

 instance, we have found that after an impact between two im- 

 perfectly elastic bodies, or after sliding between two imperfectly 

 smooth bodies, a certain amount of energy disappears from view, 

 and we have had to suppose that this energy is used in starting 

 small motions, relative to one another, of the ultimate particles of 

 which the bodies are composed. In other words, after an impact 

 or sliding has taken place, a rigid body can no longer be supposed 

 to satisfy the conditions postulated for a rigid body. 



When dealing with bodies which are obviously not rigid the case 

 is worse. Here the conceptions which we have introduced into the 

 study of rigid bodies do not help at all, and very little progress is 

 possible without introducing some other conceptions to replace these. 



260. There are two ways of proceeding at this stage. We may 

 introduce new conceptions which seem plausible, and in this way 

 try to form a picture of the structure of the matter with which we 

 are dealing. We cannot be certain that the results obtained in this 

 way will be true, for we can never be sure that our conceptions of 

 the nature of the ultimate structure of matter are accurate. But 

 it may be worth trying what results are obtained by introducing a 

 set of provisional conceptions as to the structure of matter. If 

 these results are in agreement with the phenomena observed in 



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