60 ORIGIN AND SIGNIFICANCE OP 



than natural bodies do ever in fact correspond exactly 

 to the abstract notion we have obtained of them by in- 

 duction. Taking the notion of rigidity thus as a mere 

 ideal, a strict Kantian might certainly look upon the 

 geometrical axioms as propositions given, a priori, by 

 transcendental intuition, which no experience could 

 either confirm or refute, because it must first be decided 

 by them whether any natural bodies can be considered 

 as rigid. But then we should have to maintain that the 

 axioms of geometry are not synthetic propositions, as 

 Kant held them ; they would merely define what quali- 

 ties and deportment a body must have to be recognised 

 as rigid. 



But if to the geometrical axioms we add proposi- 

 tions relating to the mechanical properties of natural 

 bodies, were it only the axiom of inertia, or the single 

 proposition, that the mechanical and physical proper- 

 ties of bodies and their mutual reactions are, other 

 circumstances remaining the same, independent of 

 place, such a system of propositions has a real import 

 which can be confirmed or refuted by experience, but 

 just for the same reason can also be gained by expe- 

 rience. The mechanical axiom, just cited, is in fact of 

 the utmost importance for the whole system of our 

 mechanical and physical conceptions. That rigid solids, 

 as we call them, which are really nothing else than elas- 

 tic solids of great resistance, retain the same form in 



