24 ON THE RELATION OP 



slowly, and is rarely illuminated by brilliant flashes of 

 genius. It knows little of that facility with which the 

 most varied instances come thronging into the memory of 

 the philologist or the historian. Rather is it an essential 

 condition of the methodical progress of mathematical 

 reasoning that the mind should remain concentrated on a 

 single point, undisturbed alike by collateral ideas on the 

 one hand, and by wishes and hopes on the other, and 

 moving on steadily in the direction it has deliberately 

 chosen. A celebrated logician, Mr. John Stuart Mill, 

 expresses his conviction that the inductive sciences have 

 of late done more for the advance of logical methods than 

 the labours of philosophers properly so called. One essen- 

 tial ground for such an assertion must undoubtedly be that 

 in no department of knowledge can a fault in the chain of 

 reasoning be so easily detected by the incorrectness of the 

 results as in those sciences in which the results of reason- 

 ing can be most directly compared with the facts of nature. 

 Though I have maintained that it is in the physical 

 sciences, and especially in such branches of them as are 

 treated mathematically, that the solution of scientific 

 problems has been most successfully achieved, you will 

 not, I trust, imagine that I wish to depreciate other 

 studies in comparison with them. If the natural and 

 physical sciences have the advantage of great perfection 

 in form, it is the privilege of the moral sciences to deal 

 with a richer material, with questions that touch more 

 nearly the interests and the feelings of men, with the 

 human mind itself, in fact, in its motives and the 

 different branches of its activity. They have, indeed, 

 the loftier and the more difficult task, but yet they 

 cannot afford to lose sight of the example of their rivals, 

 which, in form at least, have, owing to the more ductile 

 nature of their materials, made greater progress. Not 

 only have they something to learn from them in point of 



