140 THE GENESIS OF SCIENCE. 



possible to present, with great plausibility, just the opposite 

 generalization to that which he enunciates. While he as- 

 serts that the rational order of the sciences, like the ordei 

 of their historic development, " is determined by the de- 

 gree of simplicity, or, what comes to the same thing, of 

 generality of their phenomena ; " it might contrariwise be 

 asserted, that, commencing with the complex and the spe- 

 cial, mankind have progressed step by step to a knowledge 

 of greater simplicity and wider generality. So much evi- 

 dence is there of this as to have drawn from Whewell, in 

 his History of the Inductive Sciences, the general remark 

 that " the reader has already seen repeatedly in the course 

 of this history, complex and derivative principles present- 

 ing themselves to men's minds before simple and elemen- 

 tary ones." 



Even from M. Comte's ovna work, numerous facts, ad 

 missions, and arguments, might be picked out, tending to 

 show this. We have already quoted his words in proof 

 that both abstract and concrete mathematics have pro- 

 gressed towards a higher degree of generality, and that he 

 looks forward to a higher generality still. Just to strength- 

 en this adverse hypothesis, let us take a further instance. 

 From the particular case of the scales, the law of equilibri- 

 um of which was familiar to the earliest nations known, Ar- 

 chimedes advanced to the more general case of the unequal 

 lever with unequal weights; the law of equilibrium of 

 which includes that of the scales. By the help of Galileo's 

 discovery concerning the composition of forces, D'Alembert 

 *' established, for the first time, the equations of equilibrium 

 of any system of forces applied to the different points of a 

 solid body " — equations which include all cases of levers 

 and an infinity of cases besides. Clearly this is progress 

 towards a higher generality — towards a knowledge more 

 independent of special circumstances — towards a study of 

 phenomena " the most disengaged from the incidents of 



