160 BULLETIN OF THE 



another ball no larger than itself? The two possessing the same 

 inertia, why did not A expend just half its motion on collision with 

 B, giving the latter its equal share ; and thus conserve the original 

 momentum by the double mass moving conjointly with half the 

 velocity ? This very simple question — it is safe to affirm — can never 

 be answered by any principles of the science of kinematics. 



By the principles of dvnamics, these three queries admit of a 

 very satisfactory solution. At the moment of physical contact be- 

 tween the two balls, (there being still an assignable space between 

 them,) their approaching surfaces commence mutually to encroach 

 upon a powerful molecular repulsion crowding back and compress- 

 ing more closely together vast multitudes of resisting layers of 

 molecules on either side, until their combined pressure gradually 

 absorbs and destroys the momentum of J., while simultaneously ex- 

 erting an equal stress on the inertia of B. And thus by the neces- 

 sary equality of action and re-action, the centers of inertia of the 

 two balls pass successively through the same reversed phases of ap- 

 proach and recession during the brief finite interval of physical 

 contact, attaining a relative velocity of separation precisely equal 

 to that of the encounter : the deformations of the balls, or their 

 compressions, being as the squares of the absorbed velocity, and 

 their energy of recovery being as the square roots of the restored 

 velocity. So far therefore from the original motion of A being 

 transferred to B (as often loosely stated), it really passes continu- 

 ously through every stage of decline to actual rest; and a new 

 motion commencing from zero is gradually started in B, by the con- 

 tinued application of an elastic pressure, during a finite time. 



To take one more example in illustration of the impossibility of 

 action at no distance, let us suppose an ivory ball weighing one 

 ounce to be centrally struck while at rest by another ivory ball 

 weighing four ounces, and moving with a velocity of 10 feet per 

 second. If we were to ignore the " occult " force of elasticity, and 

 neglect the difficulties already exposed, kinematics would give the 

 simple result of a common velocity of the two balls after impact, of 

 8 feet per second : 4 X 10 being equal to 5 X 8. But this is not 

 what would happen. We should find instead that the four-ounce 

 ball has its velocity reduced to 6 feet per second, while the one- 

 ounce ball takes up a velocity of 16 feet per second ; — just double 

 that it should have taken were action at no distance a natural pos- 

 sibility : the latter ball absorbing (so to speak) the whole velocity 



