296 Darwinism and Other Essays. 



studies " discipline the mind." Though exqui- 

 sitely vague, as thus expressed, this favourite 

 apology is doubtless essentially valid. The al- 

 most universal distaste for mathematics, 1 co-exist- 

 ing as it does in many persons with excellent 

 reasoning powers, proves that the faculty of 

 imagining abstract relations is ordinarily quite 

 feebly developed. Not reason, but imagination, 

 is at fault. The passage from premise to con- 

 clusion could easily be made, if the abstract rela- 

 tions of position or quantity which are involved 

 could be accurately conceived and firmly held in 

 the mind. Now the ability to imagine relations 

 is one of the most indispensable conditions of all 

 precise thinking. No subject can be named, in 

 the investigation of which it is not imperatively 

 needed ; but it can nowhere else be so thoroughly 

 acquired as in the study of mathematics. This 

 fact alone is sufficient to justify the university in 

 requiring its students to devote some attention to 

 such a study. But the excellence of mathematics 

 as an instrument of mental discipline by no means 



1 Which probably attained its sublimest expression some years ago 

 in the case of a Sophomore who, coming from Harvard Hall, where 

 his " annual " had goaded him to desperation, was heard to declare, 

 in language equally with Caligula's deserving immortality, his wish 

 that the whole of mathematical science might be condensed into a sin- 

 gle lesson, that he might " dead " on it all at once! 



