152 PSYCHOLOGY. 



probably not an absolutely true opinion, but for our pres- 

 ent purpose that is immaterial. So far as the subdivisions 

 of a sense -space are to be measured exactly against each 

 other, objective forms occupying one subdivision must 

 directly or indirectly be superposed upon the other, and 

 the mind must get the immediate feeling of an outstanding 

 plus. And even where we only feel one subdivision to be 

 vaguely larger or less, the mind must pass rapidly between 

 it and the other subdivision, and receive the immediate sen- 

 sible shock of the more. 



We seem, thus to have accounted for all space-relations, and 

 made them clear to our understanding. They are nothing hut 

 sensations of particular lines, particular angles, particular forms 

 of transition, or (in the case of a distinct more) of particular 

 outstanding portions of space after tivo figures have been super- 

 posed. These relation-sensations may actually be produced 

 as such, as when a geometer draws new lines across a figure 

 with his pencil to demonstrate the relations of its parts, 

 or they may be ideal representations of lines, not really 

 drawn. But in either case their entrance into the mind is 

 equivalent to a more detailed subdivision, cognizance, and 

 measurement of the space considered. The bringing of sub- 

 divisions to consciousness constitutes, then, the entire process 

 by ivhich we pass from our first vague feeling of a total 

 vastness to a cognition of the vastness in detail. The more 

 numerous the subdivisions are, the more elaborate and per- 

 fect the cognition becomes. But inasmuch as all the sub- 

 divisions are themselves sensations, and even the feeling 

 of ' more ' or ' less ' is, where not itself a figure, at least a 

 sensation of transition between two sensations of figure, 

 it follows, for aught we can as yet see to the contrary, 

 that all spatial hiowledge is sensational at bottom, and that, 

 as the sensations lie together in the unity of consciousness, 

 no new material element whatever comes to them from a 

 supra-sensible source.* 



* In the eyes of many it will have seemed strange to call a relation a 

 mere line, and a line a mere sensation. We may easily learn a great deal 

 about any relation, say that between two points: we may divide the line 

 wliich joins these, and distinguish it, and classify it, and find out its rela- 



