Page:Kant's Prolegomena etc (1883).djvu/294

 only these two kinds of forces, as such, to which all the forces of motion in material nature must he reduced, are capable of being conceived.

Matter fills its spaces by the repulsive forces of all its parts, i.e., by its own force of extension, which has a definite degree, beyond which smaller or larger [degrees] can be conceived to infinity.

Demonstration.

Matter fills a space only by moving force (proposition 1), this being such as to resist the impression, that is, the approach of others. Now this is a repulsive force (explanation II.). Thus matter fills its space, and indeed all the parts thereof, by repulsive forces only, because otherwise a part of its space would not be filled (against the assumption), but would only be enclosed. But the force of an extended by virtue of the repulsion of all its parts is a force of extension (expansive). Thus matter fills its space by its own force of extension; which was the first point. Beyond every given force a greater must be conceived, for that beyond which there is no greater possible would be one, whereby, in a finite time, an infinite space would be passed over (which is impossible). Further, beyond every given moving force a smaller must be able to be conceived (for the smallest would be that, by the infinite addition of which to itself, throughout any given time, no finite velocity could be generated, but this signifies the lack of all moving force). Thus below every given degree of a moving force, a smaller must always be able to be given; which is the second [point]. The force of extension, therefore, whereby all matter fills its space, has its degree, which is never the greatest or smallest; but beyond which, greater as well as smaller, may be found to infinity.

Note 1.

The expansive force of a matter is termed elasticity. Now as the former is the basis on which the filling of