the Foundations of Dynamics. 35 



half the momentum has been transmitted and half the energy ; 

 but of the transmitted half energy, one-half again, or a quarter 

 of the original only is in the kinetic form, the other quarter is 

 in the potential or elastic-stress form. 



If the rods are inelastic everything so far has happened 

 similarly, but nothing further happens ; what I have called 

 the middle of the elastic impact is the end of the inelastic 

 one. Kinetic energy from iv and y has been transmitted to 

 w' and y' through the intervention of the quasi-rigid com- 

 pressed portion of each rod, and energy from z has reached z\ 

 A quarter of the whole energy has been transmitted direct as 

 kinetic, and there is no potential because there is no recoil. 

 One half the original energy has been lost. 



If the rods are elastic the recoil brings z to rest and flings 

 z 1 on with the original velocity v ; then y stops and y' flies on 

 after z', and so on, till at the end of the impact the rods part 

 asunder, the first one completely stationary, the second one 

 completely moving with all the energy simply kinetic. 



If the rods are partially elastic some of the potential energy 

 is dissipated and some utilised, while if they are of unequal 

 length or material the pulses are not timed similarly in both ; 

 the shorter one (supposed the striker) is struck dead as before, 

 the longer one is left with a pulse in it after they have sepa- 

 rated, and its residual potential energy then assumes the sound- 

 vibrational form : the strata progressing jerkily for some 

 time. 



If the rod to be moved is incompressible, its pulse travels 

 instantaneously and it all gets moved at once. A blow to 

 such a rod transmits energy instantaneously, and all in the 

 kinetic form, but there is nothing in mere speed to affect the , 

 amount transmitted. 



By the consideration of instances we have thus been led to 

 the induction that energy can be transmitted without obvious 

 change of form by substances with infinite properties, e. g. by 

 an incompressible solid ; all molecular processes being either 

 non-existent or being ignored ; but that with ordinary matter 

 there is always some percentage of obvious transformation, 

 though we may apparently have all grades of it from com- 

 plete to very small. 



Thinking of these impact cases alone, it might appear as if 1 

 had been overhasty in saying that the whole of energy must be 

 transformed when it is transferred. Yet observe that it has 

 to pass through the intermediate condition. A row of ivory 

 balls in contact has another thrown against one end, and from 

 the other end one leaps off. The energy has been transmitted 

 through the row somewhat as it is transmitted through the 



D2 



