APPENDIX A XLVII 
before. Any fresh application calls for observation and experiment, 
with reasoning similar to that of abstract science. Abstract science 
seeks for general properties, applied science for the particular properties 
of the materials at hand, but there is no hard and fast distinction be- 
tween general and particular properties in a given case. If an ex- 
perimenter measures the electrical resistance of a metallic wire at the 
different temperatures at which it is to be used, he is applying science; 
if he formulates a rule which will connect the resistance with the tem- 
perature, he is touching the domain of abstract science. To draw an 
arbitrary line, and prevent the investigator from crossing it, would be 
mischievous, if it were not impracticable. 
The abstract, if it can be reached, is more useful than the concrete 
for it comprehends it, and much besides. It results in economy of 
thought, time and labor. Compare the table of “instances agreeing 
in the form of heat” in the Novum Organum, which is a list of sources 
of heat, with the brief comprehensive statement which could now be 
made. A text book of physics is a compendium of principles which 
may be applied to innumerable particular cases. The higher the ab- 
straction the more useful it is, for it comprehends a wider range of 
knowledge. 
The real distinction between abstract and applied science lies in 
the purpose of the investigator. Generalizations usually ascend from 
the less to the more general. If the investigator is looking for utility 
his first minor generalizations are likely to lead him away from his 
quest for higher ones, to seek practical applications. The motive of 
abstract science is an «esthetic one, the search for knowledge as a thing 
desirable in itself and for the beauty of the abstract, that is, of the 
harmony of nature. Other considerations would only distract, and it is 
the disregard of such that characterizes, to use Hawthorne’s words, 
“the deep philosophers who think the thought in one generation that 
will revolutionize society in the next.” 
Human progress has always followed the growth of abstract science, 
yet there have been people in every age who have thought that science 
was complete, or sufficiently near completion, and that all useful prin- 
ciples were known. To say this is of course tantamount to saying that 
all principles are known, for it is clearly impossible to foresee the utility, 
or otherwise, of principles which have not yet been discovered. 
The cosmogony of Ptolemy held its ground for a millennium and a 
half and men thought they knew all that could be known about the 
heavenly bodies. Comte, seventy years ago, thought that useful 
science was in his time all but complete. John Stuart Mill seems to have 
held the same view in some degree, and even Tyndall thought that the 
remaining problems of science were minor ones, whereas the progress 
