OF NATURAL PHILOSOPHY. 199 



ticularizing the law, and trying the truth of it by 

 following out its consequences and comparing them 

 with facts; or, 3dly, By a process partaking of 

 both these, and combining the advantages of both 

 without their defects, viz. by assuming indeed the 

 laws we would discover, but so generally expressed, 

 that they shall include an unlimited variety of 

 particular laws ; following out the consequences 

 of this assumption, by the application of such general 

 principles as the case admits; comparing them 

 in succession with all the particular cases within our 

 knowledge ; and, lastly, on this comparison, so modi- 

 fying and restricting the general enunciation of our 

 Jaws as to make the results agree. 



(211.) AH these three processes for the discovery 

 of those general elementary laws on which the 

 higher theories are grounded are applicable with 

 different advantage in different circumstances. We 

 might exemplify their successive application to 

 the case of gravitation : but as this would rather 

 lead into a disquisition too particular for the ob- 

 jects of this discourse, and carry us too much 

 into the domain of technical mathematics, we shall 

 content ourselves with remarking, that the method 

 last mentioned is that which mathematicians (espe- 

 cially such as have a considerable command of those 

 general modes of representing and reasoning on 

 quantity, which constitute the higher analysis,) find 

 the most universally applicable, and the most effica- 

 cious; and that it is applicable with especial ad- 

 vantage in cases where subordinate inductions of 

 the kind described in the last section have already 

 led to laws of a certain generality admitting of 

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