226-228] COLLISION. 257 



are others in which the recovery of form is practically complete. 

 Now it is clear that if the bodies are rigid no deformation can 

 take place, and accordingly we shall be unable to give an account 

 of the circumstances if we treat the bodies as rigid. On the other 

 hand, the problem of calculating the deformation from the elastic 

 properties of the bodies is generally beyond our power. Further, 

 we shall find that one inevitable result of every impulsive action 

 between parts of a system is a loss of kinetic energy in the system, 

 and this apparent loss of energy can frequently be calculated. 

 Considering the bodies as elastic we might expect to find the 

 energy transformed partly into potential energy of strain, and 

 partly into kinetic energy of relative motions of the parts of the 

 bodies. Now there is one particular case in which the calculation 

 can be made by means of the Theory of Elasticity, the case of the 

 longitudinal impact of thin elastic bars, and in that case it is 

 found that the apparent loss of energy as calculated depends on 

 the masses of the bars in a way quite different to that which is 

 experimentally found to hold good. It appears to follow that, 

 even if we could in every case calculate from the Theory of 

 Elasticity the deformations of impinging bodies, we should never- 

 theless not be in a position to give a complete account of the 

 nature of the action that takes place in impact, and we are led 

 to expect, in impulsive changes of motion, a transformation of 

 energy into some other form than kinetic and potential energies 

 of the bodies and their parts, regarded as continuous. Nor 

 have we far to seek for the form of energy that is developed in 

 compensation for the apparent loss. It is a fact of observation 

 that when one body strikes against another the temperature 

 of both is raised, and it has been abundantly proved that the 

 production of thermal effects of this kind is of the nature of 

 just such a transformation of energy as we have described. We 

 must therefore expect that in impulsive changes of motion some 

 mechanical energy will be transformed into heat. In order to 

 formulate in a simple and general manner the mechanical effects 

 produced in two bodies by collision it is necessary to have recourse 

 to special experiments and subsidiary hypotheses. 



228. Newton's experimental Investigation. Newton 

 made an elaborate series of experiments* on the impact of 



* Pnncipia, Lib. i., Axiomata sive Leges Motus. 

 L. 17 



