perception of shape however elementary; which is the same as saying that for an utterly oblivious mind there could be no relationships, and therefore no meaning. In the case of Symmetry the relations are not merely the lengths and directions of the single lines, that is to say their relations to ourselves, and the relation established by comparison between these single lines; there is now also the relation of both to a third, itself of course related to ourselves, indeed, as regards visible shape, usually answering to our own axis. The expectation which is liable to fulfilling or balking is therefore that of a repetition of this double relationship remembered between the lengths and directions on one side, by the lengths and directions on the other; and the repetition of a common relation to a central item.

The case of RYTHM is more complex. For, although we usually think of Rythm as a relation of two items, it is in reality a relation of four (or more ); because what we remember and expect is a mixture of similarity with dissimilarity between lengths, directions or impacts. OR IMPACTS. For with Rythm we come to another point illustrative of the fact that all shape-elements depend upon our own activity and its modes. A rythmical arrangement is not necessarily one between objectively alternated elements like objectively longer or shorter lines of a pattern, or objectively higher or lower or longer and shorter notes. Rythm exists equally where the objective data, the sense stimulations, are uniform, as is the case with the ticks of a clock. These ticks would be registered as exactly similar by appropriate instruments. But our mind is not such an impassive instrument: our mind (whatever our mind may really be) is subject to an alternation of more and less, of vivid and less vivid, important and less important, of strong and weak; and the objectively similar stimulations from outside, of sound or colour or light, are perceived as vivid or less vivid, important or less important, according to the beat of this mutual alternation with which they coincide: thus the uniform, ticking of the clock will be perceived by us as a succession in which the stress, that is the importance, is thrown upon the first or the second member of a group; and the recollection and expectation are therefore of a unity of dissimilar importance. We hear STRONG-WEAK; and remembering strong-weak, we make a new strong-weak out of that objective uniformity. Here there is no objective reason for one rythm more than another; and we express this by saying that the tickings of a clock have no intrinsic form. For Form, or as I prefer to call it, Shape, although it exists only in the mind capable of establishing and correlating its constituent relationships, takes an objective existence when the material stimulations from the outer world are such as to force all normally constituted minds to the same series and combinations of perceptive acts; a fact which explains why the artist can transmit the shapes existing in his own mind to the mind of a beholder or hearer by combining certain objective stimulations, say those of pigments on paper or of sound vibrations in time, so as to provoke perceptive activities similar to those which would, ceteris paribus, have been provoked in himself if that shape had not existed first of all only in his mind.

A further illustration of the principle that shape-perception is a combination of active measurements and comparisons, and of remembrance and expectations, is found in a fact which has very great importance in all artistic dealings with shapes. I have spoken, for simplicity's, sake, as if the patches of colour on a blank (i.e. uninteresting) ground along which the glance sweeps, were invariably contiguous and continuous. But these colour patches, and the sensations they afford us, are just as often, discontinuous in the highest degree; and the lines constituting a shape may, as for instance in constellations, be entirely imaginary. The fact is that what we feel as a line is not an objective continuity of colour-or-light-patches, but the continuity of our glance's sweep which may either accompany this objective continuity or replace it. Indeed such imaginary lines thus established between isolated colour patches, are sometimes felt as more vividly existing than real ones, because the glance is not obliged to take stock of their parts, but can rush freely from extreme point to extreme point. Moreover not only half the effectiveness of design, but more than half the efficiency of practical life, is due to our establishing such imaginary lines. We are inevitably and perpetually dividing visual space (and something of the sort happens also with "musical space") by objectively non-existent lines answering to our own bodily orientation. Every course, every trajectory, is of this sort. And every drawing executed by an artist, every landscape, offered us by "Nature," is felt, because it is measured, with reference to a set of imaginary horizontals or perpendiculars. While, as I remember the late Mr G. F. Watts showing me, every curve which we look at is felt as being part of an imaginary circle into which it could be prolonged. Our sum of measuring and comparing activities, and also our dramas of remembrance and expectation, are therefore multiplied by these imaginary lines, whether they connect, constellation-wise, a few isolated colour indications, or whether they are established as standards of reference (horizontals, verticals, etc.) for other really existing lines; or whether again they be thought of, like those circles, as wholes of which objectively perceived series of colour patches might possibly be parts. In all these cases imaginary lines are felt, as existing, inasmuch as we feel the movement by which we bring them into existence, and even feel that such a movement might be made by us when it is not.

So far, however, I have dealt with these imaginary lines only as an additional proof that shape-perception is an establishment of two dimensional relationships, through our own activities, and an active remembering, foreseeing and combining thereof.

CHAPTER VII

FACILITY AND DIFFICULTY OF GRASPING

OF this we get further proof when we proceed to another and less elementary relationship implied in the perception of shape: the relation of Whole and Parts.

In dealing with the ground upon which we perceive our red and black patches to be extended, I have already pointed out that our operations of measuring and comparing are not applied to all the patches of colour which we actually see, but only to such as we look at; an observation equally applicable to sounds. In other words our attention selects certain sensations, and limits to these all that establishing of relations, all that measuring and comparing, all that remembering and expecting; the other sensations being excluded. Now, while whatever is thus merely seen, but not looked at, is excluded as so much blank or otherness; whatever is, on the contrary, included is thereby credited with the quality of belonging, that is to say being included, together. And the more the attention alternates between the measuring of included extensions and directions and the expectation of equivalent (symmetrical or rythmical) extensions or directions or stresses, the closer will become the relation of these items included by our attention and the more foreign will become the excluded otherness from which, as we feel, they detach themselves. But—by an amusing paradox—these lines measured and compared by our attention, are themselves not only excluding so much otherness or blank; they also tend, so soon as referred to one another, to include some of this uninteresting blankness; and it is across this more or less completely included blankness that the eye (and the imagination!) draw such imaginary lines as I