58 



knowledge now in our hands ; yet it would be difficult 

 to overstate the almost miraculous increase which may- 

 be produced by a liberal distribution of what we already 

 have, and by a restriction of our cravings within the 

 limits of possibility. 



In proportion as method is better than impulse, 

 deliberate purpose than erratic action, the clear glow of 

 sunshine than irregular reflexion, and definite utterances 

 than an uncertain sound ; in proportion as knowledge 

 is better than surmise, proof than opinion ; in that pro- 

 portion will the mathematician value a discrimination 

 between the certain and the uncertain, and a just estimate 

 of the issues which depend upon one motive power or the 

 other. While on the one hand he accords to his neighbours 

 full lil^erty to regard the unknown in whatever way they 

 are led by the noblest powers that they possess ; so 

 on the other he claims an equal right to draw a clear 

 line of demarcation between that which is a matter of 

 knowledge, and that which is at all events something 

 else, and to treat the one category as fairly claiming our 

 assent, the other as open to further evidence. And yet, 

 when he sees around him those whose aspirations are 

 so fair, whose impulses so strong, whose receptive 

 faculties so sensitive, as to give objective reality to 

 what is often but a reflex from themselves, or a pro- 

 jected image of their own experience, he will be willing 

 to admit that there are influences which he cannot as 

 yet either fathom or measure, but whose operation he 

 must recognize among the facts of our existence. 



