SCIENTIFIC MATERIALISM. 309 
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 Dotent 
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 v or those of others, the inves- 
tigator 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 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 profoundest rninds 
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, audits incessant correction and 
realization. His experiments constitute a body, of which 
his purified intuitions are, as it were, the soul, 
