RESULTS AND LIMITS OF SCIENTIFIC METHOD. 467 



dictory results. The very nature of continuous quantity 

 leads us into extreme difficulties. Any finite length is 

 composed of an infinite number of infinitely small spaces, 

 each of which, again, is composed of an infinite number of 

 spaces of a second order of infinite smallness ; these spaces 

 of the second order are composed, again, of infinitely small 

 spaces of the third order. Even these spaces of the third 

 order are not absolute geometrical points answering to 

 Euclid's definition of a point, as position without mag- 

 nitude. Go on as far as we will, in the subdivision of 

 continuous quantity, yet we never get down to the ab- 

 solute point. Thus Scientific Method leads us to the 

 inevitable conception of an infinite series of successive 

 orders of infinitely small quantities. If so. there is nothing 

 impossible in the existence of a myriad universes within 

 the compass of a needle's point, each with its stellar sys- 

 tems, and its suns and planets, in number and variety 

 unlimited. Science does nothing to reduce the number 

 of strange things that we may believe. When fairly 

 pursued it makes large drafts upon our powers of com- 

 prehension and belief. 



Some of the most precise and beautiful theorems in 

 mathematical science seem to me to involve apparent con- 

 tradiction. Can we imagine that a point moving along 

 a perfectly straight line towards the west, would ever 

 get round to the east and come back again, having 

 performed a circuit through infinite space, as it were, 

 yet without ever diverging from a perfectly straight 

 direction ? Yet this is what happens to the intersecting 

 point of two straight lines, when, being in the same 

 plane, one line revolves about a fixed point. The same 

 principle is exhibited in the hyperbola, which may be 

 regarded as an infinite ellipse, one extremity of which 

 has passed to an infinite distance and come back in 

 the opposite direction. A varying quantity may change 



H h 2 



