180 INDUCTION. 



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 mathe- 

 matical principles could ever be advantageously applied 

 to phenomena dependent upon the mutual action of 

 the innumerable minute particles of bodies, as those of 

 chemistry, and still more, of physiology ; and for 

 similar reasons those principles must be for ever 

 inapplicable to the still more complex inquiries, the 

 subjects of which are phenomena of society and 

 government. 



The value of mathematical instruction as a prepa- 

 ration for those more difficult investigations, consists 

 in the applicability not of its doctrines, but of its 

 method. Mathematics will ever remain the most per- 

 fect type of the Deductive Method in general ; and 

 the applications of mathematics to the simpler 

 branches of physics, furnish the only school in which 

 philosophers 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, with Plato, one who is ayewfierprjros^ as want- 

 ing in one of the most essential qualifications for 

 the successful cultivation of the higher branches of 

 philosophy. 



