516 INDUCTION. 



correct expressions for the corresponding 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 complex instances which 

 would have been of no use for the discovery of the simple 

 laws into which we ultimately analyse their phenomena, 

 nevertheless, when they have served to verify the analysis, 

 become additional evidence of the laws themselves. Although 

 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 circumstances ; and occasionally serves to 

 eliminate some circumstance not previously 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 calculated 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 univer- 

 sality of that law. Accordingly any law of nature is deemed 

 to have gained in point of certainty, by being found to explain 

 some complex case which had not previously been thought of 

 in connexion 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 characterized in its three 

 constituent parts, Induction, Ratiocination, and Verifica- 

 tion, the human mind is indebted for its most conspicuous 

 triumphs in the investigation of nature. To it we owe all 

 the theories by which vast and complicated phenomena 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 





