2 REPORT—1868. 
problems. Indeed 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 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 
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 pro- 
foundest 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 ex- 
periments finally constituting a body, of which his purified intuitions are, as it 
were, the soul. 
Partly through mathematical and partly through experimental research, physi- 
cal 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 produced, and it is destined 
to produce, immense changes,—vast social ameliorations, and vast alterations in the 
popular conception of the origin, rule, and governance of things. Miracles are 
wrought by science in the physical world, while philosophy is forsaking its ancient 
metaphysical channels and pursuing those opened or indicated by scientific re- 
search. This must become more and more the case as philosophic writers become 
more deeply imbued with the methods of science, better acquainted with the facts 
whee cee men have won, and with the great theories which they have ela- 
orated, 
If you look at the face of a watch, you see the hour- and minute-hands, and 
possibly also a second-hand, moving over the graduated dial. Why do these hands 
move? and why are their relative motions such as they are observed to be? These 
questions cannot be answered without opening the watch, mastering its various 
arts, and ascertaining their relationship to each other. When this is done, we 
find that the observed motion of the hands follows of necessity from the inner me- 
chanism of the watch when acted upon by the force invested in the spring. 
This motion of the hands may be called a phenomenon of art, but the case is 
similar with the phenomena of nature. These also have their inner mechanism, 
and their store of force to set that mechanism going. The ultimate problem of 
physical science is to reveal this mechanism, to discern this store, and to show that 
from the combined action of both the phenomena of which they constitute the 
basis must of necessity flow. 
I thought that an attempt to give you even a brief and sketchy illustration of the 
manner in which scientific thinkers regard this problem would not be uninteresting 
to you on the present occasion ; more especially as it will give me occasion to say a 
word or two on the tendencies and limits of modern science, to point out the region 
which men of science claim as their own, and where it ismere waste of time to op- 
pose their advance, and also to define, if possible, the bourn between this and that 
other region to which the questionings and yearnings of the scientific intellect are 
directed in vain. 
But here your tolerance will be needed. It was the American Emerson, I think, 
who said that it is hardly possible to state any truth strongly without apparent in- 
jury to some other truth. Under the circumstances, the proper course appears to 
be to state both truths strongly, and allow each its fair share in the formation of 
the resultant conviction. For truth is often of a dual character, taking the form of 
a magnet with two poles; and many of the differences which agitate the thinking 
part of mankind are to be traced to the exclusiveness with which different parties 
affirm one half of the duality in forgetfulness of the other half. But this waiting 
for the statement of the two sides of a question implies patience. It implies a reso- 
