LIMITS OF OUR KNOWLEDGE OF NATURE. 21 



knowledge at all. The conception of the world as consisting of mi- 

 nute 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 quan- 

 tity 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 w^hile ; 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 physico- 

 mathematical studies, but that when we overtax it, and make demands 

 upon it that it is not intended to meet, then as a corpuscular philoso- 

 phy 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, regard- 

 less 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 con- 

 gruous in itself, and under certain conditions a useful fiction in mathe- 

 matical physics. But, latterly, atoms have been as far as possible dis- 

 carded in favor of volume-elements of bodies regarded as continuous. 



A philosophical atom, on the other hand, i. e., a presumably indi- 

 visible 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 men- 

 tion 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 investi- 

 gators of Nature. If with Descartes and Leibnitz we consider all 



