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The exposition of these definitions and the preliminary explanations necessary will, I hope, serve as a general explanation of the function of event-particles in the analysis of nature. We note that event-particles have 'position' in respect to each other. In the last lecture I explained that 'position' was quality gained by a spatial element in virtue of the intersecting moments which covered it.

This is the essential difference between painting and sculpture; the painted thing is always a part of a larger spatial whole within which it exists in relation to other things, while the sculptured thing exists by itself; the space of the statue is the space which it fills; there is no further space to which it belongs, no background in which it lies.

But it will perhaps be argued that our ordinary sensations carry with them a spatial meaning and implication, and that indirectly, therefore, our sensations do supply us with the idea of Space. It will readily be agreed that if this is so of any sensations it is pre-eminently true of the sensations of vision and touch.

At a given time, it requires that, from all the tendencies that are partially called out, those be selected which center energy upon the point of need. Successively, it requires that each act be balanced with those which precede and come after, so that order of activity is achieved. Focusing and ordering are thus the two aspects of direction, one spatial, the other temporal.

Specially is it necessary to keep our heads, and refuse to be led away by the constant modern talk of the primitive, unconscious, foreconscious instinctive and other minds which are so prominent in modern psychological literature, or by the spatial suggestions of such terms as threshold, complex, channel of discharge: remembering always the central unity and non-material nature of that many-faced psychic life which is described under these various formulæ.

It will be convenient to reserve the ordinary spatial terms 'plane, 'straight line, 'point' for the elements of the timeless space of a time-system.

The spatial, the temporal, the hillside, the passing seconds, the vibrations and material atoms stimulating my five senses, all were tropical, quickened with the unbelievable vitality of equatorial life. A rustling came to my ears, although the breeze was still little more than a sensation of coolness.

Berkeley, whose interests lay in a different quarter, used the same critical method in support of a different dogmatism; armed with the traditional pietistic theory of Providence he undertook with a light heart to demolish the whole edifice which reason and science had built upon spatial perception.

If one carries his study far enough, he will find even the properties which are significant for spatial knowledge giving way to those which facilitate knowledge of other things perhaps a knowledge of the general relations of number. There will be nothing in the conceptual definitions even to suggest spatial form, size, or direction.

Now if the actual velocities of the stars, which can, of course, be measured, were smaller than the calculated velocities, we should have a proof that the actual attractions at great distances are smaller than by Newton's law. From such a deviation it could be proved indirectly that the universe is finite. It would even be possible to estimate its spatial magnitude.