knowledge at all. The conception of the world as consisting of minute parts that have always existed, and that are indestructible, and whose central forces produce all motion, is only a sort of substitute for an explanation. As has been remarked, it reduces all changes in the physical world to a constant sum of forces and a constant quantity of matter, and thus leaves in the changes themselves nothing that requires explanation. Given the existence of this constant, we can, in our joy for this new insight, be content for a little while; but soon we long to penetrate deeper, and to comprehend it in its own substance. The result is, as all know, that within certain limits the atomic theory is serviceable, and even indispensable for our physicomathematical studies, but that when we overtax it, and make demands upon it that it is not intended to meet, then as a corpuscular philosophy it leads to interminable contradictions.
A physical atom, i. e., a mass which, as compared with bodies with which we are acquainted, is held to be infinitesimal, but yet, regardless of its name, ideally divisible, and to which properties or a state of motion is attributed, whereby the behavior of a mass consisting of countless such atoms is explained—such a notion is a fiction quite congruous in itself, and under certain conditions a useful fiction in mathematical physics. But, latterly, atoms have been as far as possible discarded in favor of volume-elements of bodies regarded as continuous.
A philosophical atom, on the other hand, i. e., a presumably indivisible mass of inert and inefficient substratum, from which proceed through vacant space efficient forces, is, on closer consideration, a chimera.
For, if this indivisible, inert, by itself ineffective, substratum is to have any actual existence, it must occupy a certain space, however small; and, in that case, we cannot see how it can be indivisible. Then, too, it can occupy space only on condition that it possesses perfect hardness, i. e., that it resists the intrusion into the same space of any other body, in virtue of a force exerted out to its own limits, though not overstepping them, which excludes all other bodies, and which must therefore be greater than any other given force. Not to mention any of the other difficulties which meet us here, we may observe that the substratum is thus represented as no longer inefficient.
But if with the dynamists we conceive of the substratum as being only the middle point of the central forces, then the substratum does not occupy space, for a point is the very negation of space in space. Hence we have nothing from which the central forces spring; nothing that could be inert, like matter.
The idea of forces operating at a distance through vacant space is unthinkable, nay, even self-contradictory; though, since Newton's day, owing to a misunderstanding of his doctrine, and in the face of his express warning, it has been a current conception among investigators of Nature. If with Descartes and Leibnitz we consider all