34 Prof. Oliver Lodge on 



out again in the kinetic form, or unless by means of slip a 

 good deal of energy is dissipated. But some dissipation is 

 essential anyhow : a certain fraction, equal to the ratio of the 

 moving mass to the whole mass, must assume a vibrational 

 form of some kind. 



It is instructive to recollect certain elementary facts, such 

 as that in the impact of two perfectly elastic bodies, one 

 moving, one stationary, all the energy and all the momentum 

 may be transmitted complete, but that in this case the 

 resulting motion of the two bodies cannot be the same. 

 Whereas, if by reason of elastic vibrations, or by reason of 

 heat dissipation, it is arranged that two equal bodies shall 

 after impact move together, then only one half the momentum 

 and only one quarter of the energy is transmitted, the re- 

 maining half of the energy having been diverted or wasted in 

 heat or vibration. 



So it is with any system of shafting or mill-gearing to 

 which motion has to be communicated from a revolving fly- 

 wheel. The conservation of moment of momentum gives part of 

 the circumstances; the refusal of ultimate mutual recoil gives 

 the other part. And the amount of ultimate vibrational dissipa- 

 tion of energy is precisely the same, under these circum- 

 stances, for perfectly elastic as for perfectly inelastic bodies. 

 The case is not unlike the opening of a stopcock between a full 

 and empty pair of reservoirs. A certain fraction of the energy 

 is necessarily either dissipated in heat or left as permanent 

 vibration. 



« d cba a'b'c' *' 



r i mm 



Consider the circumstance of the impact of a couple of 

 equal elastic rods moving end-on. Conceive them in trans- 

 verse strata labelled a, b, c, . . . z for each rod. Let one rod be 

 stationary, and the other strike it longitudinally with velocity v. 

 At the beginning of the impact a strikes a!, and the two move 

 on in contact with the speed £r. b now strikes the mass aa' } 

 and would accelerate it, but at the same instant a! strikes b f , 

 communicating the motion to it and neutralizing the accelera- 

 tion on itself; so that now the four strata are all moving with 

 speed |v, while all the rest of one rod is still stationary, and 

 all the rest of the other rod is still moving with original 

 velocity v. The length of the half-speed piece about the 

 point of contact continually increases, and behaves as a body 

 under gradually increasing compression as it receives blow 

 after blow on either end. At length z and z' strike, and the 

 recoil is ready to begin. This is the middle of the impact, 



