272 Prof. WhewelVs Demonstration, S^c. 



our convictions do not rest upon experiment. We learn by observation 

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

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

 same will appear to be the case with the proposition, that bodies of dif- 

 ferent 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 

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

 other density. Therefore whatever be the density, the inertia is pro- 

 portional 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 mechan- 

 ical nature in the particles or component elements of bodies, we are 

 led to the same conclusion, of arbitrary, and therefore, impossible, re- 

 sults, which we deduced from this supposition with regard to weight. 

 Therefore all bodies of different density, and hence, all bodies what- 

 ever, 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 fun- 

 damental 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 frst, 

 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 know- 

 ledge, universal forms of intuition, inherent types of mental develop- 

 ment ; 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 con- 

 sidered as capable of composition, but by no means of simplification ; 

 as most perfect in their original condition ; as to be found, if any where, 

 in the most uneducated and most uncultivated minds ; as the same in 

 all ages, nations, and stages of intellectual culture ; as capable of being 

 referred to at once, and made the basis of our reasonings, without any 

 special acuteness or effort : in all which circumstances the fundamental 

 ideas of which we have spoken, are opposed to innate ideas so under- 

 stood. 



