478 INDUCTION. 



which they were deduced, " have almost invariably 

 failed to support the theoretical structures which have 

 been erected on them." 



Under this uncertainty, the conclusion we may 

 draw from the concomitant variations of a and A, to 

 the existence of an invariable and exclusive connexion 

 between them, or to the permanency of the same 

 numerical relation between their variations when the 

 quantities are much greater or smaller than those 

 which we have had the means of observing, cannot 

 be considered to rest upon a complete induction. All 

 that in such a case can be regarded as proved on the 

 subject of causation, is that there is some connexion 

 between the two phenomena ; that A, or something 

 which can influence A, must be one of the causes 

 which collectively determine a. We may, however, 

 feel assured that the relation which we have observed 

 to exist between the variations of A and a, will hold 

 true in all cases which fall between the same extreme 

 limits ; that is, wherever the utmost increase or 

 diminution in which the result has been found by 

 observation to coincide with the law, is not exceeded. 



The four methods which it has now been attempted 

 to describe, are the only possible modes of experimen- 

 tal inquiry, of direct induction a posteriori, as distin- 

 guished from deduction : at least I know not, nor am 

 able to conceive, any others. And even of these, the 

 Method of Residues, as we have seen, is not indepen- 

 dent of deduction ; though, as it requires specific 

 experience in addition, it may, without impropriety, 

 be included among methods of direct observation and 

 experiment. 



These, then, with such assistance as can be 

 obtained from Deduction, compose the available 

 resources of the human mind for ascertaining the 



