DEDUCTIVE HABITS. 341 



piety, as it often has been. And an entire com- 

 mand of the conceptions and processes of mathe- 

 matics is not only consistent with, but is the 

 necessary condition and principal instrument of 

 every important step in the discovery of physical 

 principles. Newton was eminent above the philo- 

 sophers of his time, in no one talent so much as 

 in the power of mathematical deduction. When 

 he had caught sight of the law of universal 

 gravitation, he traced it to its consequences with 

 a rapidity, a dexterity, a beauty of mathematical 

 reasoning which no other person could approach ; 

 so that on this account, if there had been no 

 other, the establishment of the general law was 

 possible to him alone. He still stands at the 

 head of mathematicians as well as of philoso- 

 phical discoverers. But it never appeared to 

 him, as it may have appeared to some mathe- 

 maticians who have employed themselves on his 

 discoveries, that the general law was an ultimate 

 and sufficient principle ; that the point to which 

 he had hung his chain of deduction was the 

 highest point in the universe. Lagrange, a mo- 

 dern mathematician of transcendent genius, was 

 in the habit of saying, in his aspirations after 

 future fame, that Newton was fortunate in having 

 had the system of the world for his problem, 

 since its theory could be discovered once only. 

 But Newton himself appears to have had no such 

 persuasion that the problem he had solved was 



