DEDUCTIVE HABITS. 3'27 



longer contested, are riot felt to need a lengthened 

 proof. But their consequences require far more 

 room and far more intellectual labour. If we 

 take, for example, the laws of motion and the law 

 of universal gravitation, we can express in a few 

 lines, that which, when developed, represents and 

 explains an innumerable mass of natural pheno- 

 mena. But here the course of developement is 

 necessarily so long, the reasoning contains so 

 many steps, the considerations on which it rests 

 are so minute and refined, the complication of 

 cases and of consequences is so vast, and even 

 the involution arising from the properties of space 

 and number is so serious, that the most consum- 

 mate subtlety, the most active invention, the most 

 tenacious power of inference, the widest spirit of 

 combination, must be tasked and tasked severely, 

 in order to solve the problems which belong to 

 this portion of science. And the persons who 

 have been employed on these problems, and who 

 have brought to them the high and admirable 

 qualities which such an office requires, have 

 justly excited in a very eminent degree the ad- 

 miration which mankind feel for great intellectual 

 powers. Their names occupy a distinguished 

 place in literary history ; and probably there are 

 no scientific reputations of the last century higher, 

 and none more merited, than those earned by the 

 great mathematicians who have laboured with 

 such wonderful success in unfolding the me- 



