320 THE PRINCIPLES OF SCIENCE. 



fingers, and senses, and instruments must stop somewhere, 

 there is no reason why the mind should not go on. We 

 can see that a proof which is only carried through a few 

 steps, in fact, might be carried on without limit, and it is 

 this consciousness of no stopping place, which renders 

 Euclid's proof of his 1 1 7th 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 which immediately follows from these con- 

 siderations is, that we cannot possibly adjust any two 

 quantities in absolute equality. The suspension of Ma- 

 homet'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 displace- 

 ment. It might be possible to balance an egg on its end 

 practically, because no egg has a surface of perfect curva- 

 ture. 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, quantity, 

 or magnitude of any phenomenon. The eye cannot cor- 

 rectly estimate the comparative brightness of two lumi- 

 nous bodies which differ much in brilliancy ; for we know 

 that the iris is constantly adjusting itself to the intensity 



8 Lacroix, 'Essai sur 1'Enseignement ou manifere d'dtudier les Mathe- 

 matiques/ 2nd ed. Paris, 1816, pp. 292-294. 



