infinite ways, as one is a multiple or sub-multiple of another. Thus we have one-fourth, one-half, equal to, twice, four times, etc. Mass is a sum of units measured in terms of force, and such units may become constituent parts in higher orders of units. One number is thus a measure of another. Out of these relations ratios and proportions arise. It seems unnecessary to enter into a discussion of the relations of numbers, as they are developed in the science of arithmetic and algebra.
III
Extension is exclusive occupancy of space. As there is more than one extension, and every one excludes all others, there is relative position. Thus we have positions derived from many extensions. Position is the relation of one extension to another. Space is founded on extension, for if a particle had no extension it could not be an element of space; a plurality of particles, each having extension, constitutes space. If they are in juxtaposition the space is the sum of their extensions. If they are separated by a medium, as for example an intervening fluid, the space is marked by their position and in this sense is related position; position, therefore, depends upon relation, but there can be no related positions if the extensions are annihilated. Extension is absolute, position is relative and space is absolute in extension and relative in position; extension is constant or persistent in ultimate particles.
In space one particle may be related to another in distance and in direction. These relations give rise to geometry and trigonometry and are the relations chiefly dealt with in astronomy.
