160 INDUCTION. 



consideration more than two or three essential influences."* 

 Of this, the problem of the Three Bodies has already been 

 cited, more than once, as a remarkable instance ; the complete 

 solution of so comparatively simple a question having vainly 

 tried the skill of the most profound mathematicians. We 

 may conceive, then, how chimerical would be the hope that 

 mathematical principles could be advantageously applied to 

 phenomena dependent on the mutual action of the innume- 

 rable minute particles of bodies, as those of chemistry, and 

 still more, of physiology; and for similar reasons those 

 principles remain inapplicable to the still more complex in- 

 quiries, the subjects of which are phenomena of society and 

 government. 



The value of mathematical instruction as a preparation for 

 those more difficult investigations, consists in the applicability 

 not of its doctrines, but of its method. Mathematics will ever 

 remain the most perfect type of the Deductive Method in 

 general ; and the applications of mathematics to the deductive 

 branches of physics, furnish the only school in which philo- 

 sophers can effectually learn the most difficult and important 

 portion of their art, the employment of the laws of simpler 

 phenomena for explaining and predicting those of the more 

 complex. These grounds are quite sufficient for deeming 

 mathematical training an indispensable basis of real scientific 

 education, and regarding (according to the dictum which an 

 old but unauthentic tradition ascribes to Plato) one who is 

 ayew/uiTpriTog, as wanting in one of the most essential qualifi- 

 cations for the successful cultivation of the higher branches of 

 philosophy. 



* Philosophic Positive, iii. 414-416. 



