SCIENTIFIC MATERIALISM. 399 



whole, faces physical nature on all sides, and pushes knowl- 

 edge centrifugally outward, the sum. of its labors con- 

 stituting 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. 



Mathematics and Physics have been long accustomed to 

 coalesce, and here they form a single section. 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 are all-powerful as an instrument of deduction. 

 The command of Geometry over the relations of space, and 

 the far-reaching power which Analysis confers, are potent 

 both as means of physical discovery, and of reaping the 

 entire fruits of discovery. Indeed, without mathematics, 

 expressed or implied, our knowledge of physical science 

 would be both friable and incomplete. 



Side by side with the mathematical method we have the 

 method of experiment. Here from a starting-point fur- 

 nished by his own researches or those of others, the inves- 

 tigator proceeds by combining intuition and verification. 

 lie 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 of 

 intellectual penetration into this penumbral region which 

 surrounds actual knowledge is not, as some seem to think, 

 dependent upon method, but upon the genius of the inves- 

 tigator. There is, however, no genius so gifted as not to 

 need control and verification. The profound eat 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. Thus the vocation of the 

 true experimentalist may be defined as the continued exer- 

 cise of spiritual insight, and its incessant correction and 

 realization. His experiments constitute a body, of which 

 his purified intuitions are, as it were, the soul. 



