304 



INDUCTION. 



theory is imperfect, and not yet to be 

 relied upon. Nor is the verification 

 complete, unless some of the cases in 

 which the theory is borne out by the 

 observed result, are of at least equal 

 complexity with any other cases in 

 which its application could be called 

 for. 



If direct observation and collation 

 of instances have furnished us with 

 any empirical laws of the effect, 

 (whether true in all observed cases, or 

 only true for the most part,) the most 

 effectual verification of which the 

 theory could be susceptible would 

 be, that it led deductively to those 

 empirical laws ; that the uniformi- 

 ties, whether complete or incomplete, 

 which were observed to exist among 

 the phenomena were accounted for 

 by the laws of the causes — were such 

 as could not but exist if those be really 

 the causes by which the phenomena 

 are produced. Thus it was very 

 reasonably deemed an essential re- 

 quisite of any true theory of the 

 causes of the celestial motions, that 

 it should lead by deduction to Kep- 

 ler's laws ; which, accordingly, the 

 Newtonian theory did. 



In order, therefore, to facilitate the 

 verification of theories obtained by 

 deduction, it is important that as 

 many as possible of the empirical laws 

 of the phenomena should be ascer- 

 tained by a comparison of instances, 

 conformably to the Method of Agree- 

 ment, as well as (it must be added) 

 that the phenomena themselves should 

 be described, in the most compre- 

 hensive as well as accurate manner 

 possible, by collecting from the ob- 

 servation of parts the simplest possible 

 correct expressions for the corespond- 

 ing wholes : as when the series of the 

 observed places of a planet was first 

 expressed by a circle, then by a system 

 of epicycles, and subsequently by an 

 ellipse. 



It is worth remarking, that com- 

 plex instances which would have been 

 of no use for the discovery of the 

 simple laws into which we ultimately 

 jknalyse their pheaomena, neverthe- ] 



less, when they have served* to verify 

 the analysis, become additional evi- 

 dence of the laws themselves. Al- 

 though we could not have got at the 

 law from complex cases, still when 

 the law, got at otherwise, is found to 

 be in accordance with the result of a 

 complex case, that case becomes a 

 new experiment on the law, and helps 

 to confirm what it did not assist to 

 discover. It is a new trial of the 

 principle in a different set of circum- 

 stances ; and occasionally serves to 

 eliminate some circumstance not pre- 

 viously excluded, and the exclusion 

 of which might require an experiment 

 impossible to be executed. This was 

 strikingly conspicuous in the example 

 formerly quoted, in which the difference 

 between the observed and the calcu- 

 lated velocity of sound was ascertained 

 to result from the heat extricated by 

 the condensation which takes place in 

 each sonorous vibration. This was a 

 trial, in new circumstances, of the 

 law of the development of heat by com- 

 pression ; and it added materially to 

 the proof of the universality of that 

 law. Accordingly any law of nature 

 is deemed to have gained in point of 

 certainty by being found to explain 

 some compleec case which had not 

 previously been thought of in con- 

 nection with it ; and this indeed is a 

 consideration to which it is the habit 

 of scientific inquirers to attach rather 

 too much value than too little. 



To the Deductive Method, thus 

 characterised in its three constituent 

 parts, Induction, Ratiocination, and 

 Verification, the human mind is in- 

 debted for its most conspicuous 

 triumphs in the investigation of 

 nature. To it we owe all the theories 

 by which vast and complicated phe- 

 nomena are embraced under a few 

 simple laws, which, considered as the 

 laws of those great phenomena, could 

 never have been detected by their 

 direct study. We may form some 

 conception of what the method has 

 done for us from the case of the 

 celestial motions, one of the simplest 

 among the greater instances of the 



