and the Conservation of Energy. 41 



It seems desirable, before leaving the subject, to say a few- 

 words upon a theory which has been set up as a rival to that 

 of central forces, and in some quarters has met with consider- 

 able favour. This theory supposes that bodies can act on each 

 other only when in absolute contact; and that all the pheno- 

 mena of the universe may be accounted for by the knockings 

 together of a number of ultimate atoms, considered as very 

 small impenetrable bodies, moving with high velocities in 

 space. 



It might be urged that before such a theory can be seriously 

 discussed, it must be shown capable of explaining (as the 

 theory of central forces certainly does explain) the facts and 

 principles of Mechanics. I am not aware that this has been 

 done. I may, however, point out that the theory is not incon- 

 sistent with the conservation of energy ; that is to say, it can 

 be reconciled with it by certain special assumptions. For the 

 proof of that principle, as given above, does not necessarily 

 imply that the forces acting are continuous. If the attraction 

 of A be supposed to act on B by equal impulses at certain 

 intervals of space, or distances from A, which distances remain 

 always the same, then the proof will still hold ; for B will be 

 acted upon by exactly the same number of impulses, and at 

 exactly the same places, on its return journey as on its outward 

 journey, and the effects will therefore be the same. Now the 

 " collision " theory above mentioned may be taken to repre- 

 sent the extremest possible case of this discontinuous action — 

 there being then but one impulse, and that acting when A and 

 B are in absolute contact. 



Let us, however, consider the assumptions involved, if the 

 conservation of energy is to hold in this extreme case. Imagine 

 two " ultimate atoms," of equal mass, to meet each other with 

 equal velocities in the same straight line. This is clearly a 

 possible case under the theory; and the conservation of energy 

 must therefore be consistent with it. Then the instant before 

 the atoms meet they have no action upon each other, and the 

 instant after, by symmetry, they must either be at rest or 

 must have passed through one another. As the latter is con- 

 trary to the hypothesis, they must be at rest. Hence a finite 

 mass moving with a finite velocity has been brought to rest 

 in a space infinitely small ; and therefore the impulse acting 

 upon it must have been strictly infinite in amount. This col- 

 lision therefore (and it is easily seen that the same will be true 

 of all collisions) occasions the instantaneous development of a 

 strictly infinite force. The atoms being brought to rest, there 

 is no reason to be given why any thing further should happen. 

 But we must assume it as an axiom that a further mutual im- 



