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instruments in the solution of natural problems. In- 

 deed, without mathematics, expressed or implied, our 

 knowledge of physical science would be friable in the 

 extreme. 



Side by side with the mathematical method, we have 

 the method of experiment. Here, from a starting-point 

 furnished by his own researches or those of others, the 

 investigator proceeds by combining intuition and verifi- 

 cation. He ponders the knowledge he possesses and 

 tries to push it further, he guesses and checks his guess, 

 he conjectures and confirms or explodes his conjecture. 

 These guesses and conjectures are by no means leaps in 

 the dark ; for knowledge once gained casts a faint light 

 beyond its own immediate boundaries. There is no dis- 

 covery so limited as not to illuminate something beyond 

 itself. The force of intellectual penetration into this 

 penumbral region which surrounds actual knowledge is 

 not dependent upon method, but is proportional to the 

 genius of the investigator. There is, however, no genius 

 so gifted as not to need control and verification. The 

 profoundest minds know best that nature's ways are not 

 at all times their ways, and that the brightest flashes in 

 the world of thought are incomplete until they have 

 been proved to have their counterparts in the world of 

 fact. The vocation of the true experimentalist is the 

 incessant correction and realization of his insight ; his 

 experiments finally constituting a body, of which his 

 purified intuitions are, as it were, the soul. 



Partly through mathematical, and partly through ex- 

 perimental research, physical science has of late years 

 assumed a momentous position in the world. Both in 

 a material and in an intellectual point of view it has pro- 

 duced, and it is destined to produce, immense, changes, 



