110 FRAGMENTS OF SCIENCE. 



chemist pursues his atoms, while the physical investigator 

 has his own large field in optical, thermal, electrical, 

 acoustical, and other phenomena. The British Associa- 

 tion then, as a whole, faces physical Nature on all sides 

 and pushes knowledge centrifugally outward, the sum of 

 its labors constituting what Fichte might call the sphere of 

 natural knowledge. In the meetings of the Association it 

 is found necessary to resolve this sphere into its component 

 parts, which take concrete form under the respective letters 

 of our Sections. 



This is the Mathematical and Physical Section. Mathe- 

 matics and physics have been long accustomed to coalesce. 

 For, no matter how subtle a natural phenomenon may be, 

 whether we observe it in the region of sense, or follow it 

 into that of imagination, it is in the long-run reducible to 

 mechanical laws. But the mechanical data once guessed 

 or given, mathematics become all-powerful as an instru- 

 ment of deduction. The command of geometry over the 

 relations of space, the far-reaching power which organized 

 symbolic reasoning confers, are potent both as means of 

 physical discovery, and of reaping the entire fruits of dis- 

 covery. Indeed, without mathematics, expressed or im- 

 plied, 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 in- 

 vestigator proceeds by combining intuition and verification. 

 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 discovery so limited 

 as not to illuminate something beyond itself. The force 



