298 Darwinism and Other Essays. 



in, by deducing all human phenomena first from 

 the unchecked action of selfishness and then from 

 the unchecked action of sympathy, he arrives at 

 mutually - limiting conclusions of transcendent 

 practical importance, furnish for all time a bril- 

 liant illustration of the value of mathematical 

 methods and mathematical discipline. 



If magnitudes and quantities thus contemplated 

 in the abstract yield such wholesome pabulum for 

 the intellect, no less beneficial in many respects 

 is the study of the direct applications of mathe- 

 matics to the concrete phenomena of mechanics, 

 astronomy, and physics. Not only do the numer- 

 ous devices by which algebraic expressions are 

 utilized in the solution of physical problems af- 

 ford extensive scope for inventive ingenuity, but 

 some familiarity with quantitative conceptions of 

 the action and interaction of forces is eminently 

 conducive to the entertainment of sound philo- 

 sophic views. The reorganization of mechanics 

 by Lagrange, and the beautiful construction by 

 Fourier of a mathematical doctrine of heat, were 

 . innovations in philosophy as well as in science ; 

 and although the student can hardly be expected 

 to gain even a rudimentary knowledge of these 

 recondite subjects, he may at least with profit to 

 himself be enabled to form some general notion 



