CHAPTER X
Extension may be defined as exclusive occupancy of space. The particles having extension exclude others from that extension, and thus extension has also been called impenetrability. The particle having motion changes its position to occupy space vacated; hence, change of position is always exchange of position. As the particles are all in motion at an inconceivable rate of speed, one evacuates its position as another enters.
The idea of a plenum of substance was entertained by philosophers in the early history of civilization. Gradually this was abandoned by many, but lately it has been revived as best explaining the phenomena of the ether, and countenance is given to the hypothesis by the demonstration that molecular bodies have internal motions and interspatial ether.
Space is the relation of extension which particles bear to one another in position, when considered without regard to their incorporation in a higher body. If the particles be not ultimate a medium of smaller particles is intercalated. Space, therefore, is the extension of positions.
While space is the relation of positions, positions and relations must vanish if the extensions vanish. These relations may be relations of direction, or they may be relations of distance, but as particles are in motion the relations of direction are changed. In the same manner the relations of distance may change. Thus the boy and the dog may change relation of direction, when one or both move, and they may or may not change relations of distance at the same time. These space relations do not change by reason of intervening bodies. The boy may be a yard from the dog though a wall intervenes.
When positions are considered as established by incorporation, forms are observed having the relations of the particles established, and these established relations constitute structure and figure; thus form is figure and structure. When space becomes form, extension becomes figure and position becomes structure.
By incorporation particles retain in a qualified degree their space relations; that is, the space relations must be fixed within such limits that the incorporation is preserved, for if dissolution supervenes form relations are dissolved. Still, form relations are not fixed with such rigidity as to prevent internal motion. A body may still remain a body within certain degrees of temperature, passing through stages of bulk by contraction and expansion, but if the expansion is increased beyond the critical point the body is dissolved.
We consider bodies as particles when we consider their space relations, and we consider them as forms when we consider their corporeal relations as units. Habits of thought are formed in such a manner that some bodies are usually considered as particles, while other bodies are usually considered as bodies. By like habits of thought it is customary to consider the solar system, not as a body, but as an assemblage of orbs, for the science of astronomy has not yet successfully attacked the problem of the relation of the solar system to other stellar systems. When a body is considered as an individual in shape and structure, form is presented; but when a body is considered as a community of particles, space is considered. Thus it is seen that what is called space in the relations of particles, is called structure in the relations of form. In this treatise the term space is never used to denote the void—the nothing—but is always used to denote something real; so that space relations are the reciprocals of structure relations.
When we consider stars as such they are bodies, the particles of which are molecules. If we could study them as molecules they would present relations of structure; so we may conceive of such relations, though we cannot actually observe them; but we can observe the figures of the bodies. Stars are embodied into systems when they, in turn, become particles and have space relations to one another; this is structure from the standpoint of the system, but the systems as bodies have form as figure and structure. Here in the celestial realm is found a series or hierarchy of individuals and communities.
When we come to the study of the earth as a body, we find it composed of four particles: the atmosphere, the hydrosphere, the lithosphere, and the centrosphere. When we consider it as a body we consider form and structure; when we consider the spheres as particles their relations are those of space, one above another; thus in the body there is form, in the particles there is position, and that which is position in the particle constitutes structure in the body.