23 II. Having shewn what takes place in naming simple SENSATIONS, and simple IDEAS, in pairs, both as 24 such and such, and as antecedent and consequent, we come to the second case of relative terms, that of naming the clusters, called EXTERNAL OBJECTS, in pairs. The principal occasions of doing so we have said are four.
1. When we speak of them, as they exist in the synchronous order, that is, the order in space, we use such relative terms as the following: high, low; east, west; right, left; hind, fore; and so on.
It is necessary to carry along with us a correct idea of what is meant by synchronous order, that is, the order of simultaneous, in contradistinction to that of successive, existence. The synchronous order is much more complex than the successive. The successive 25 order is all, as it were, in one direction. The synchronous is in every possible direction. The following seems to be the best mode of conceiving it.
Take a single particle of matter as a centre. Other particles may be aggregated to it, in the line of every possible radius; and as the radii diverge, and other lines, tending to the centre, may be continually interposed, to any number, particles may be aggregated in those numberless directions. They may also be aggregated in those directions to a less or a greater extent. And they may be aggregated to an equal extent in every direction; or to a greater extent in some of the directions, a less extent in others. In the first case of aggregation they compose a globe; in the last, any other shape.
Every one of the particles in this aggregate, has a certain order; first with respect to the centre particle; next with respect to every other particle. This order is also called, the Position of the particle. In such an aggregate, therefore, the positions are innumerable. It is thence observable, that position is an exceedingly complex idea; for the position of each of those particles is its order with respect to every one of the other innumerable particles; it includes, therefore, innumerable ingredients. Hence it is not wonderful that, while viewed in the lump, it should seem obscure and mysterious.
Of positions, thus numberless, it is a small portion, only that have names. Bulk is a name for an aggregate of particles, greater, or less. Figure is only a modification, or case, of bulk; it is more or fewer particles in such and such directions.
These things being explained, it now remains to 26 shew, of what copies of sensations, peculiarly combined, the complex ideas in question are composed.
The simplest case of position, or synchronous order, is that of two or more particles in one direction. Let us take the particle, conceived as the centre particle, in a preceding supposition, and let us aggregate to it a number of particles, all in the direction of a single radius, one by one. We have first the centre particle, and one other, in juxta-position. This is the simplest case of synchronous order, and this is the simplest of all positions. Let us next aggregate a second particle; we have now the centre particle, and two more. The position of the first of the aggregated particles with respect to the centre particle is contact, or juxta-position; that of the second is not juxta-position, but position at the distance of a particle; the next which is aggregated, is at the distance of two; the next of three particles, and so on, to any extent.
Particles thus aggregated, all in the direction of a single radius from the first, constitute a line of less or greater length, according to the number of aggregated particles.
Line is a word of great importance; because it is by that, chiefly, we express ourselves concerning synchronous order; or frame names for positions. Now it happens, that Line has a duplicity of meaning, most unfortunate, because it has confounded two meanings, which it is of the highest importance to preserve distinct.