196 THE GRAMMAR OF SCIENCE 



how long the man took to go from one landing to another, 

 and when he was going quickly, when slowly. But it is 

 still far from clear how we are to describe the motion of 

 the button, so that we could conceive its motion repeated 

 by aid of our description. The button, like the man, has 

 many elements, and the question again arises how we are 

 to describe the motions of them all. 



Let us now stretch our imaginations a little further ; 

 let us suppose the staircase to be embedded in a great 

 mass of soft wax, and suppose the button, guided still by 

 the spirit hand, to move up the staircase precisely as it 

 did on the man's waistcoat, but now pushing its way 

 through the wax. The passage of the button would now 

 form a long tube-like hollow in our mass of wax extend- 

 ing from the bottom to the top of the staircase. This 

 tube would not necessarily be of equal bore throughout, 

 because, owing to the motion of the man, the button 

 might occasionally move more or less sideways. Still, the 

 smaller the button the smaller would be the bore of the 

 tube cut through the wax. We will now suppose a long 

 piece of stiff wire passed through the tube and firmly fixed 

 at its ends. The wax, and even the staircase, may now 

 be removed, and then, if a small bead be slung on the 

 wire and move up the wire in the same manner as the 

 button moved up the tube, we shall be able to describe a 

 eood deal of the motion of the button from that of the 

 bead. Now in conception we may suppose the wire to 

 get thinner and thinner, and the bead smaller and smaller, 

 till in conception the wire ends in a geometrical line 

 or curve, and the bead in a geometrical point. The 

 motion of the ideal point along the ideal curve will repre- 

 sent with a great degree of accuracy the motion of an 

 extremely small button up a tube of an extremely small 

 bore through the wax. The reader may feel inclined to 

 ask why we did not commence by saying : " Consider a 

 point of the man ; its motion must give a curve passing 

 from top to bottom of the staircase." The answer lies in 

 this : that we cannot peixeive a point. In conception we 

 reach a point by carrying to a limit the perceptual process 



