208 DISCOURSE ON THE STUDY 



(219.) Theories are best arrived at by the con- 

 sideration of general laws ; but most securely verified 

 by comparing them with particular facts, because 

 this serves as a verification of the whole train of 

 induction, from the lowest term to the highest. 

 But then, the comparison must be made with facts 

 purposely selected so as to include every variety of 

 case, not omitting extreme ones, and in sufficient 

 number to afford every reasonable probability of 

 detecting error. A single numerical coincidence in 

 a final conclusion, however striking the coincidence 

 or important the subject, is not sufficient. Newton's 

 theory of sound, for example, leads to a numerical 

 expression for the actual velocity of sound, differing 

 but little from that afforded by the correct theory 

 afterwards explained by La Grange, and (when cer- 

 tain considerations not contemplated by him are 

 allowed for) agreeing with fact ; yet this coincidence 

 is no verification of Newton's view of the general 

 subject of sound, which is defective in an essential 

 point, as the great geometer last named has very 

 satisfactorily shown. This example is sufficient to 

 inspire caution in resting the verification of theories 

 upon any thing but a very extensive comparison with 

 a great mass of observed facts. 



(220.) But, on the other hand, when a theory 

 will bear the test of such extensive comparison, 

 it matters little how it has been originally framed. 

 However strange and, at first sight, inadmissible its 

 postulates may appear, or however singular it may 

 seem that such postulates should have been fixed 

 upon, if they only lead us, by legitimate reasonings, 

 to conclusions in exact accordance with numerous 



