112 THE WOKLD-ENEEGY 



It may be, indeed, that even such external change 

 necessarily involves internal change also, though that is 

 not immediately apparent. Nevertheless, as was already 

 seen at an earlier stage of the argument, any change in 

 the relative position of any given force-center must in- 

 volve a change in the strains to which it is subjected, and 

 hence must develop greater or less modification within 

 the force-center itself; and not only so, but it would 

 seem that the continuity of substance must render such 

 interrelation inevitable in every sphere of existence. Of 

 this we will see more as we proceed. 



Another form of Zeno's argument is as follows: Grant- 

 ing that motion is possible, an arrow, for example, can 

 never actually pass through any assigned space. For 

 since space is infinitely divisible, there will be an infinite 

 number of divisions or spaces between the point of be- 

 ginning and the assigned terminus of its flight. At the 

 same time, it must occupy a definite portion of time in 

 passing through each of these spaces. But, as there is 

 an infinite number of spaces to be passed over, the arrow 

 will necessarily occupy in its flight an infinite number of 

 moments or divisions of time. That is, an infinite time 

 will be required for the arrow to reach its terminus. 

 Therefore no assigned space can be traversed by any 

 object in any finite time. 



It is as if all velocities were subdivided into what the 

 acute eye of modern science has been able to recognize as 

 "infinitely small" velocities, which in truth is but a 

 calm adoption, with or without recognition, of the dread- 

 fully metaphysical conception of the infinite divisibility 

 of both time and space ; f or " velocity" is just the product 

 of space and time. 



