386 THE SCIENTIFIC MONTHLY 



in the search many unexpected secrets are found. Once a body of facts 

 has been accumulated, correlation follows. The attempt is made to 

 find something common to them all and it is at this stage that science, 

 in the modern sense, may perhaps be said to have its birth. But this is 

 only a beginning. The mind that can grasp correlation can soon pro- 

 ceed to go further and try to find a formula which will not only be a 

 common property, but which will completely embrace the facts; that 

 is, in modern parlance, a law which groups all the phenomena under 

 one head. 



The formula or law once discovered, consequences other than those 

 known are sought, and the process of scientific discovery begins. 

 Realms which could never have been opened up by observation alone 

 are revealed to the mind which has the ability to predict results as con- 

 sequences of the law, and thence is found the means by which the 

 truth of the law is tested. If the further consequences are shown to 

 be in agreement with what may be observed, the evidence is favorable. 

 If the contrary, the law must be abandoned or changed so as to embrace 

 the newly discovered phenomena. The process of trial and error, or 

 of hypothesis and test, is a recurring one which embraces a large pro- 

 portion of the scientific work of to-day. 



Scientific development has two main aspects. One is the framing 

 of laws in order to discover new phenomena and develop the subject 

 forward so as to open out new roads into the vast forest of the secrets 

 of nature. The other is the turning backward in order to discover the 

 foundations on which the science rests. Just as no teacher would think 

 it wise to start the young pupil in chemistry or physics by introducing 

 him at the outset to the fundamental unit of matter or energy as it is 

 known at the time, but will rather start in the middle of the subject with 

 facts which are within the comprehension of his mind and the exper- 

 ience of his observation, science itself has been and must necessarily be 

 developed in the same manner. We proceed down to the foundations 

 as well as up to the phenomena. 



This two-fold aspect of scientific research has had revolutionary 

 results in the experience of the last half century. It has fundamentally 

 changed the ideas of those who study the so-called laboratory subjects 

 in which observation with artificially constructed materials goes hand 

 in hand with the framing of laws and hypotheses, but it has changed 

 the study of mathematics in an even more fundamental manner. In the 

 past, geometry and arithmetic were suggested by observation and 

 practical needs and the development of both with symbolic representa- 

 tion proceeded on lines which were dictated by the problems which 

 arose. The methods of discovery in working forward were not es- 

 sentially different from those of an observational science, except per- 

 haps that the testing of a new law was unnecessary on account of the 



