xxxi.] LIMITS OF SCIENTIFIC METHOD. 753 



impress upon their readers a truth which 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. 1 Professor Tyndall 

 seems to me open to the same charge in a less degree. He 

 remarks 2 that we can probably never bring natural pheno- 

 mena completely under mathematical laws, because the 

 approach of our sciences towards completeness may 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 con- 

 vergent series, the earlier and larger terms of which have 

 been successfully disposed of, so that comparatively minor 

 groups of phenomena alone 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 generalisation, 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 exhausted that 

 subject by showing that all gases obey the same laws 

 as regards temperature, pressure, and volume. But in 

 reality these laws are only approximately true, and the 

 divergences afford a wide and quite unexhausted field for 

 further generalisation. The recent discoveries of Professor 

 Andrews have summed up some of these exceptional facts 

 under a wider generalisation, but in reality they have 

 opened to us vast new regions of interesting inquiry, and 

 they leave wholly untouched the question why one gas 

 behaves differently from another. 



1 Mr. C. J. Monroe objects that in this statement I do injustice 

 to Comte, who, he thinks, did impress upon his readers the inade- 

 quacy of our mental powers compared with the vastness of the subject 

 matter of science. The error of Comte, he holds, was in maintaining 

 that science had been carried about as far as it is worth while to 

 carry it, which is a different matter. In either case, Comte's position 

 is so untenable that I am content to leave the question undecided. 



2 Fragments of Science, p. 362. 



3 



