20 ON THE RELATION OF 



stand the test of application to more complex cases. Accord- 

 ingly the physical sciences, when once the right methods have 

 been discovered, have made proportionately rapid progress. 

 Not only have they allowed us to look back into primaeval 

 chaos, where nebulous masses were forming themselves into 

 suns and planets, and becoming heated by the energy of their 

 contraction ; not only have they permitted us to investigate 

 the chemical constituents of the solar atmosphere and of the 

 remotest fixed stare, but they have enabled us to turn the 

 forces of surrounding nature to our own uses and to make them 

 the ministers of our will. 



Enough has been said to show how widely the intellectual 

 processes involved in this group of sciences differ, for the most 

 part, from those required by the moi'al sciences. The mathe- 

 matician need have no memory whatever for detached facts, the 

 physicist' hardly any. Hypotheses based on the recollection of 

 similar cases may, indeed, be useful to guide one into the right 

 track, but they have no real value till they have led to a precise 

 and strictly defined law. Nature does not allow us for a moment 

 "to doubt that we have to do with a rigid chain of cause and 

 effect, admitting of no exceptions. Therefore to us, as her 

 students, goes forth the mandate to labour on till we have dis- 

 covered unvarying laws ; till then we dare not rest satisfied, for 

 then only can our knowledge grapple victoriously with time 

 and space and the forces of the universe. 



The iron labour of conscious logical reasoning demands great 

 perseverance and great caution ; it moves on but 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 concen- 

 trated 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 cele- 

 brated logician, Mr. John Stuart Mill, expresses his conviction 

 that the inrluctive sciences have of late done more for the advance 



