OF NATURAL PHILOSOPHY. 179 



each describes about the sun's centre equal areas in 

 equal times ; and that in the orbits of different pla- 

 nets the squares of the periodical times are propor- 

 tional to the cubes of the distances ; were the results 

 of inconceivable labour of calculation and compari- 

 son: but they amply repaid the labour bestowed 

 on them, by affording afterwards the most conclusive 

 and unanswerable proofs of the Newtonian system. 

 On the other hand, when empirical laws are unduly 

 relied on beyond the limits of the observations from 

 which they were deduced, there is no more fertile 

 source of fatal mistakes. The formulae which have 

 been empirically deduced for the elasticity of steam 

 (till very recently), and those for the resistance of 

 fluids, and other similar subjects, have almost inva- 

 riably failed to support the theoretical structures 

 which have been erected on them. 



(188.) It is a remarkable and happy fact, that 

 the shortest and most direct of all inductions 

 should be that which has led at once, or by very 

 few steps, to the highest of all natural laws, 

 we mean those of motion and force. Nothing can 

 be more simple, precise, and general, than the 

 enunciation of these laws ; and, as we have once 

 before observed, their application to particular facts 

 in the descending or deductive method is limited 

 by nothing but the limited extent of our mathe- 

 matics. It would seem, then, that dynamical science 

 were taken thenceforward out of the pale of in- 

 duction, and transformed into a matter of absolute 

 u priori reasoning, as much as geometry ; and so it 

 would be, were our mathematics perfect, and all the 

 data known. Unhappily, the first is so far from being 

 x 2 



