PROGRESS IN KNO WLEDGE 2 1 9 



within the past three generations. The only thing Book in 

 that has increased has been the concentration on the 

 ordinary man's productive talents of the productive 

 talents of the exceptional man. The talents of the 

 exceptional man, in fact, have been the only variant 

 in the problem ; and, accordingly, the minimum which 

 these talents produce is the total difference between 

 ,14 and ^"35. This sum is no mere piece of fanci- 

 ful ingenuity. Parts of it are being done daily before 

 our eyes, and its practical character is being shown 

 in the most conclusive manner, when the profits of 

 a business decline on the death of some head or 

 partner, or when some declining town is restored 

 to its old prosperity by some man of industrial 

 genius, who starts in it some new manufacture. 



And now let us pass from industrial activity to TO the 

 intellectual, and apply to this our second method progress in 

 of analysis. Of purely intellectual results, or, as Mill J 



calls them, ''advances in speculative knowledge" the methodof 



f > ' inquiring what 



the most striking examples are to be found in faculties are 



rr* 1 involved in it. 



the mathematical sciences. To the advances made 

 in these it is not only certain but obvious, that the 

 many have contributed nothing, because even of 

 that section of mankind which has some mathe- 

 matical aptitude the majority are unable even to 

 appreciate them completely when they are made ; 

 much less do they possess the powers to make them. 

 No one would contend that the books of Euclid are These are 

 the result of the faculties possessed by every average e^ r ei es con _ 

 school-boy, or of the kind of man into which the fined to the 



f few. 



average school-boy grows. We may indeed dismiss 



