206 PROFESSOR WHEWELL's DEMONSTRATION 



truths of which we afterwards see the necessity. This is the case with 

 the laws of motion, as I have repeatedly endeavoured to shew. The same 

 will appear to be the case with the proposition, that bodies of different 

 kinds have their inertia proportional to their weight. 



For bodies of the same kind have their inertia proportional to their 

 weight, both quantities being proportional to the quantity of matter. 

 And if we compress the same quantity of matter into half the space, 

 neither the weight nor the inertia is altered, because these depend on 

 the quantity of matter alone. But in this way we obtain a body of 

 twice the density ; and in the same manner we obtain a body of any other 

 density. Therefore whatever be the density, the inertia is proportional 

 to the quantity of matter. But the mechanical relations of bodies cannot 

 depend upon any difference of kind, except a difference of density. For 

 if we suppose any fundamental difference of mechanical nature in the 

 particles or component elements of bodies, we are led to the same con- 

 clusion, of arbitrary, and therefore impossible, results, which we deduced 

 from this supposition with regard to weight. Therefore all bodies of 

 different density, and hence, all bodies whatever, must have their inertia 

 proportional to their weight. 



Hence we see, that the propositions, that all bodies are heavy, and that 

 inertia is proportional to weight, necessarily follow from those fundamental 

 ideas which we unavoidably employ in all attempts to reason concerning 

 the mechanical relations of bodies. This conclusion may perhaps appear the 

 more startling to many, because they have been accustomed to expect that 

 fundamental ideas and their relations should be self-evident at our first 

 contemplation of them. This, however, is far from being the case, as I have 

 already shewn. It is not the first, but the most complete and developed 

 condition of our conceptions which enables us to see what are axiomatic 

 truths in each province of human speculation. Our fundamental ideas 

 are necessary conditions of knowledge, universal forms of intuition, 

 inherent types of mental developement ; they may even be termed, if 

 any one chooses, results of connate intellectual tendencies ; but we cannot 

 term them innate ideas, without calling up a large array of false opinions. 

 For innate ideas were considered as capable of composition, but by no 

 means of simplification : as most perfect in their original condition ; as to 



