522 
old enough to have lived in the pre-scien- 
tific, as well as in the present epoch, feel as 
if a millennium were close at hand. Indeed, 
such a wealth of good scientific literature 
is just now thrust before us and such a 
wealth of praise is just now bestowed on 
scientific achievement that the modest man 
of science must hesitate before adding a 
word to that literature or a qualification to 
that praise. 
The requirements of official position are 
remorseless, however, and one must speak 
his thought, although silence with respect 
to science may appear to be the most urgent 
need of the hour. In view of these circum- 
stances, it seems best to avoid topics of 
eurrent interest and to invite your atten- 
tion to a brief consideration of the elements 
which lie at the basis of scientific investiga- 
tion and scientific progress. A recurrence 
to the slow and painful beginnings of knowl- 
edge and the first principles evolved there- 
from is always instructive ; and it is espe- 
cially fitting at a time, like the present, 
when the ardor of research is somewhat in 
danger of the sedative influences which 
spring from the popular glorification of 
triumphant successes. 
The fundamental data from which all 
scientific knowledge grows are furnished by 
observation and experiment. After these 
come the higher steps of comparison, hy- 
pothesis, and finally the correlation and 
unification of phenomena under theory. 
Even pure mathematics, though long held 
apart from the other sciences, must be 
founded, I think, in the last analysis, on ob- 
servation and experiment. 
Of the infinite variety of phenomena 
which appeal to our senses, some, like those 
of sideral astronomy, are subject, in the 
main, to observation only ; while others, 
like those of terrestrial physics, chemistry 
and biology, are subject to both observa- 
tion and experiment. All phenomena are 
SCIENCE. 
[N.S. Vou. XIII. No. 327. 
more or less entangled. They point back- 
ward and forward in time; any one of 
them appears and disappears only in con- 
nection with others; and the record any 
one of them leaves is known only by its 
interaction with others. Out of this piexus 
of relations and interrelations it is the busi- 
ness of science to discover the conditions of 
occurrence and the laws of continuity. 
Happily for man, although the ultimate 
complexity of phenomena is everywhere 
very great, it is frequently possible to 
discern those conditions and occasionally 
possible to trace out those laws. But the 
results we reach are essentially first ap- 
proximations, depending, in general, on the 
extent to which we may ignore other phe- 
nomena than those specially considered. 
In fact, a first step towards the solution of 
a problem in science consists in determin- 
ing how much of the universe may be safely 
left out of account. Thus the method of 
approximating to a knowledge of the laws, 
of nature is somewhat like the method of 
infinite series so much used by mathema- 
ticians in numerical calculations; and as it 
is a condition of success in the use of such 
series that they be convergent rather than 
divergent, so is it an essential of scientific 
sanity that the mind be restricted by ob- 
served facts rather than diverted by pleas- 
ing fancies. 
The prime characteristic of the kind of 
knowledge that leads up to science is its 
dependence on facts which are permanent, 
and hence verifiable. In the course of the 
progress of our race there have been cer- 
tain Juminous epochs during which ob- 
servers and experimentalists have revealed 
more or less of such knowledge. These 
epochs have been followed, generally, by 
others of comparative dullness, or positive 
darkness, during which fact has been re- 
placed by fancy and what is permanent 
and verifiable has been eclipsed by what is 
ephemeral and illusory. It is my purpose 
