32 PHYSICAL SCIENCE 



relations between them by the methods of logic, 

 with no necessary intention of elucidating the 

 phenomena of Nature. Except when inventing 

 new methods, the mathematician is a calculating 

 machine. His conclusions are, or ought to be, 

 contained implicitly in the premises he uses. He 

 develops the premises, discovers their full meaning, 

 and elaborates their consequences, in a way quite 

 beyond the unaided power of thought, which, 

 without the guiding rules and generalisations of 

 mathematical analysis, would be lost in the maze 

 of complications. But the mathematician lives in 

 a purely conceptual sphere, and mathematics is 

 but the higher development of symbolic logic. 



Taking, then, a new-born hypothesis, its con- 

 sequences are deduced by logical common-sense 

 reasoning ; and, where such reasoning cannot see 

 its way unaided, by the help of mathematical 

 analysis. The results thus obtained are then 

 used by the observer or experimenter, who tests 

 by the use of old, or the determination of new 

 data, the truth of the formula by every possible 

 means. Its relations to other ascertained prin- 

 ciples, its power of correlating hitherto uncon- 

 nected phenomena, are examined in turn. From 

 consideration of its significance, we gain sug- 

 gestions for further observation, if possible for 

 future experiment. Such experiments, undertaken 

 with the express purpose in view, are probably 

 better adapted to test the formula than the 

 observations previously accumulated. If the 

 concordance is complete as far as the accuracy 

 of experiment can go, the formula becomes, in 

 the then state of knowledge, an accepted theory. 

 Whatever this means, such a generalisation will. 



