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16 PEOF. W. JAMES : particular forms of transition, dr, in the case of a distinct more, of particular outstanding portions of space after two figures have been superposed. 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 &c. not really drawn. But in either case their entrance into the mind is equivalent to a more detailed subdivision, cognisance and measurement of the space con- sidered. The bringing of subdivisions to consciousness constitutes then the entire process by which we pass from our first vague feeling of a total vastness to a cognition of the vast- ness in detail. The more numerous the subdivisions are, the more elaborate and perfect the cognition becomes. But inasmuch as all the subdivisions 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 knowledge 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. 1 The bringing of subdivisions to consciousness ! This then is our next topic. They may be brought to consciousness under three aspects, in respect of their locality, in respect of their size, in respect of their shape. 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 which joins these, and distinguish it, and classify it, and find out its rela- tions by drawing or representing new lines, and so on. But all this further industry has naught to do with our acquaintance with the relation itself, in its first intention. So cognised, the relation is the line and nothing more. It would indeed be fair to call it something less ; and in fact it is easy to understand how most of us come to feel as if the line were a much grosser thing than the relation. The line is broad or narrow, blue or red, made by this object or by that alternately, in the course of our experience ; it is independent of any of these accidents ; and so, from viewing it as 110 one of such sensible qualities, we may end by thinking of it as something which cannot be denned, except as the negation of all sensible quality whatever, and which needs to be put into the sensations by a mysterious act of ' relating thought '. Another reason why we get to feel as if a space-relation must be some- thing other than the mere feeling of a line or angle, is that between two positions we can potentially make any number of lines and angles, or find, to suit our purposes, endlessly numerous relations. The sense of this indefi- nite potentiality cleaves to our words when we speak in a general way of ' relations of place,' and misleads us into supposing that not even any single one of them can be exhaustively equated by a single angle or a single line.