158 BULLETIN OF THE 



any finite velocity, or of any finite change in veloeity. Only an 

 infinite force could generate motion instantaneously, and this 

 acting for any finite time would produce an infinite velocity. Now 

 the impact of a moving body upon a body at rest, must occur in the 

 absolute instant of contact. No motion could be transmitted before 

 contact, for this would be the chimera — actio in distans. No motion 

 could be transmitted after contact, for then the impinging body 

 could evidently have no more motion than the body impinged upon. 

 And no motion could be transmitted at the instant of contact, for 

 this occupies but an infinitesimal of time. But if no motion could 

 be communicated either before, or at, or after contact, it is very 

 clearly established that no motion whatever could possibly be de- 

 rived from impact pure and simple. This conclusion — applicable 

 alike to an atom or a planet — remains equally unassailable what- 

 ever be the magnitudes of the bodies in action. 



We are thus strongly reminded of Zeno's celebrated paradox as 

 to the impossibility of motion. For while the kinematist very posi- 

 tively assures us that action at a distance is a metaphysical impos- 

 sibility, the dynamist assures us no less positively that action at no 

 distance is a demonstrated physical impossibility.* But if mere 

 kinetic energy cannot be transferred excepting through a vacant 



* This position is so forcibly stated by Prof. Joseph Bayma in his able 

 Treatise on Molecular Physics, that a quotation from that work seems here 

 especially appropriate. " Finite velocity cannot be communicated in an 

 indivisible instant, as we have seen. - - - Nor can the demonstration be 

 evaded bv having recourse to the multitude of points among which the 

 contact would be supposed to take place. For - - - if each individ- 

 ual point of matter only acquires an infinitesimal velocity (vdt), the whole 

 multitude will acquire only an infinitesimal velocity ; that is, there will be 

 no motion caused at all. Nor can it be said that the motion is communi- 

 cated by means of a prolonged contact. A prolonged contact is impossi- 

 ble unless the velocities have become equal at the very commencement of 

 the contact. Therefore if velocity were communicated by the contact of 

 matter with matter, it would have to be communicated in the very first 

 instant of the contact, not in its prolongation. - - - Therefore dis- 

 tance is a necessary condition of the action of matter upon matter. There- 

 fore the contact between the agent and, the object acted upon is not material 

 but virtual, inasmuch as it is by its active power (virtus), not byits matter, 

 that the agent reaches the matter of the object acted upon." (Molecular 

 Mechanics. 8vo. London, 1866 : book I, prop. 3, pp. 14, 15.) 



