150 PSYCHOLOGY. 



before 3'ou in all its completeness, witli nothing further to 

 be done. Just so the relation of direction between two lines 

 is identical wdth the peculiar sensation of shape of the 

 space enclosed between them. This is commonly called 

 an angular relation. 



If these relations are sensations, no less so are the rela- 

 tions of position. The relation of position hetiveen the top and 

 bottom points of a vertical line is that line, and nothing else. 

 The relations of position between a point and a horizontal 

 line below it are potentially numerous. There is one more 

 important than the rest, called its distance. This is the 

 sensation, ideal or actual, of a perpendicular drawn from the 

 point to the line.* Two lines, one from each extremity of 

 the horizontal to the point, give us a peculiar sensation of 

 triangularity. This feeling may be said to constitute the 

 locus of all the relations of position of the elements in ques- 

 tion, tightness and leffness, npness and doicnness, are again 

 pure sensations differing specifically from each other, and 

 generically from everything else. Like all sensations, they 

 can only be indicated, not described. If we take a cube and 

 label one side top, another bottom, a third front, and a fourth 

 back, there remains no form of words hj which we can de- 

 scribe to another person which of the remaining sides is right 

 and which left. We can only point and say here is right 

 and there is left, just as we should say this is red and that 

 blue. Of two points seen beside each other at all, one is 

 always affected by one of these feelings, and .the other by 

 the opposite ; the same is true of the extremities of any 

 line.t 



* The whole scieuce of geometry may be said to owe its being to the 

 exorbitant interest which the human mind takes in lines. We cut space 

 up in every direction in order to manufacture them. 



f Kant was, 1 believe, the tirst to call attention to this last order of facts. 

 After pointing out that two opposite spherical triangles, two gloves of a 

 pair, two spirals wound in contrary directions, have identical inward de- 

 terminations, that is, have their parts defined with relation to each other by 

 the sam3 law, and so must be conceived as identical, he showed that the im- 

 possibility of their mutual superposition obliges us to assign to each figure 

 of a symmetrical pair a peculiar difference of its own which can only con- 

 sist in an outward determination or relation of its parts, no longer to each 

 other, but to the whole of an objectively outlying space with its points of the 

 compass given absolutely. This inwwceivable difference is perceived only 



