276 THE PRINCIPLES OF SCIENCE. [CHAP. 



this consciousness of no stopping-place, which renders 

 Euclid's proof of his n/th proposition so impressive. Try 

 how we will to circumvent the matter, we cannot really 

 avoid the consideration of the infinitely small and the 

 infinitely great. The same methods of approximation 

 which seem confined to the finite, mentally extend them- 

 selves to the infinite. 



One result of these considerations is, that we cannot 

 possibly adjust two quantities in absolute equality. The 

 suspension of Mahomet's coffin between two precisely 

 equal magnets is theoretically conceivable but practically 

 impossible. The story of the Merchant of Venice turns 

 upon the infinite improbability that an exact quantity of 

 flesh could be cut. Unstable equilibrium cannot exist in 

 nature, for it is that which is destroyed by an infinitely 

 small displacement. It might be possible to balance an 

 egg on its end practically, because no egg has a surface of 

 perfect curvature. Suppose the egg shell to be perfectly 

 smooth, and the .feat would become impossible. 



The Fallacious Indications of the Senses. 



I may briefly remind the reader how little we can trust 

 to our unassisted senses in estimating the degree or 

 magnitude of any phenomenon. The eye cannot correctly 

 estimate the comparative brightness of two luminous 

 bodies which differ much in brilliancy ; for we know 

 that the iris is constantly adjusting itself to the intensity 

 of the light received, and thus admits more or less light 

 according to circumstances. The rnoon which shines with 

 almost 'dazzling brightness by night, is pale and nearly 

 imperceptible while the eye is yet affected by the vastly 

 more powerful light of day. Much has been recorded 

 concerning the comparative brightness of the zodiacal 

 light at different times, but it would be difficult to prove 

 that these changes are not due to the varying darkness 

 at the time, or the different acuteness of the observer's 

 eye. For a like reason it is exceedingly difficult to esta- 

 blish the existence of any change in the form or compara- 

 tive brightness of nebulae ; the appearance of a nebula 

 greatly depends upon the keenness of sight of the 

 observer, or the accidental condition of freshness or 



