RESULTS AND LIMITS OF SCIENTIFIC METHOD. 449 



The Divergent Scope for New Discovery. 



(in the writings of some recent philosophers, especially 

 of Auguste Comte, and in some degree John Stuart Mill, 

 there is an erroneous and hurtful tendency to represent 

 our knowledge as assuming an approximately complete 

 character. At least these and many other writers fail to 

 impress upon their readers a truth which I think cannot 

 be too constantly borne in mind, namely, that [the utmost 

 successes which our scientific method can accomplish will 

 not enable us to comprehend more than an infinitesimal 

 fraction of what there doubtless is to comprehend. Pro- 

 fessor Tyndall seems to me open to the same charge in a 

 less degree. He remarks 1 that we can probably never 

 bring natural phenomena completely under mathematical 

 laws, because the approach of our sciences towards com- 

 pleteness may perhaps be asymptotic, so that however far 

 we may go, there may still remain some facts not subject 

 to scientific explanation. He thus likens the supply of 

 novel phenomena to a convergent series, the earlier and 

 larger terms of which have been successfully disposed of, 

 so that only comparatively minor groups of phenomena 

 remain for future investigators to occupy themselves upon. 

 On the contrary, as it appears to me, the supply of new 

 and unexplained facts is divergent in extent, so that the 

 more we have explained, the more there is to explain. 

 The further we advance in any generalization, the more 

 numerous and intricate are the exceptional cases still 

 demanding further treatment. The experiments of Boyle, 

 Mariotte, Dalton, Gay-Lussac, and others, upon the 

 physical properties of gases might seem to have ex- 

 hausted that subject by showing that all gases obey the 



1 'Fragments of Science,' p. 362. 

 VOL. II. G g 



