PHYSIOLOGICAL. PARADOXES. 



grain of crystalline formation. Edges appar- 

 ently clear and sharp show jagged and notched 

 serrations when sufficiently magnified. It is 

 with the sense of touch as with the other senses : 

 to its imperfection only is due any evidence 

 that we have, in things natural or artificial, of 

 perfectly smooth continuity. 



5. Achilles and the Tortoise. 



We have had several occasions to consider 

 cases of a deceptive appearance of continuity 

 where things were not really continuous ; and 

 this will be a fitting place to consider the false 

 continuity of motion, which may be suitably 

 introduced by the classical puzzle of Achilles 

 and the tortoise. 



Achilles, having a world-wide reputation 

 as a sprinter, was greatly surprised to receive 

 from the champion of slowness, the tortoise, a 

 challenge for a hundred yards' race on handicap 

 terms a start of 50 per cent. Being more 

 amused than piqued, however, at what he 

 considered the challenger's impudence, he readily 

 consented to a meeting. He made no diffi- 

 culty of granting the very long start of half 

 the course, believing himself easily able to 

 cover more than nine yards for the tortoise's 

 one, and so to concede, if required, a start of 

 90 per cent, and win. To his astonishment, 

 however, he found, when the race actually 



266 



