ACHILLES AND THE TORTOISE. 



ment that Achilles could not pass the tortoise, 

 but we make it plain also how he necessarily 

 will do so. As no other explanation can be 

 given which is not an illegitimate and un- 

 illuminating juggle with words, and as we know 

 from the facts of observation (corroborated by 

 the reasoning of our friend the learned mathe- 

 matician) that the swifter actually does pass 

 the slower in a race, we have no choice but to 

 accept the explanation as true, and to believe 

 that there is a limit to the smallness of things, 

 spaces, and motion. 



This postulate, however, is so much at 

 variance with our accustomed habits of thought, 

 that it cannot be expected to pass without 

 itself receiving careful consideration and 

 an attempt at explanation. When we think 

 of the flight of a bird or a bullet from place 

 to place, the attribute we would most con- 

 fidently assign to such flight is its continuity. 

 Admitting that the speed of flight may have 

 increased or decreased, either progressively or 

 intermittently, we cannot, without special con- 

 sideration, imagine that any portion of the 

 space included in the flight could be too small 

 to have been separately passed through after 

 the preceding and before the succeeding spaces 

 have been entered upon. 



To understand that there may be spaces 

 too small for separate movement that is, 

 that movement may not be continuous, we 



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