THE MECHANICAL SYSTEM AND ITS LIMITS 381 



combination of ultimate things ; in other words, we can 

 express all bodies in arithmetic formulae. Numbers are 

 always comprehensible ; they have no particular features 

 in themselves, and so lack the diversity of forms that is 

 found in reality. We know, especially, that we can 

 count in a series as long as we like, and we will never 

 come to anything essentially new. Like bodies, we can 

 also represent all phenomena by certain arithmetic 

 formulations of the one law, which is all we have to 

 grasp. 



But this comprehension of the world will only be 

 possible if the " ultimate things " are fundamentally 

 distinct from the bodies that we know. All the objects 

 known to us change. Each of these changes passes 

 through an incalculable number of stages, and the 

 ultimate things, which must be calculable, cannot be 

 changeable. They must not be transitory. They must 

 also be indivisible, as all division is change. Finally, 

 they must be exactly alike in size and quality. Each 

 ultimate thing must be capable of being replaced by 

 another without the least change taking place ; other- 

 wise they cannot be used in mathematical formulae. 



Mechanism endeavours to realise this ideal of know- 

 ledge. There is only one thing that is common to 

 all others and enters into the composition of all that 

 begins to exist ether. There is only one law that 

 embraces all phenomena the movements of ether. 

 Ether is a space-filling but imponderable medium, con- 

 sisting of minute particles, which are simple, immutable, 

 indivisible and homogeneous. All the phenomena in the 



