464 INDUCTION. 



5. The first of these has been aptly denominated 

 the Method of Residues. Its principle is very simple. 

 Subducting from any given phenomenon all the por- 

 tions which, by virtue of preceding inductions, can be 

 assigned to known causes, the remainder will be the 

 effect of the antecedents which had been overlooked, 

 or of which the effect was as yet an unknown quantity. 



Suppose, as before, that we have the antecedents 

 ABC, followed by the consequents a b c, and that 

 by previous inductions, (founded, we will suppose, 

 upon the Method of Difference,) we have ascertained 

 the causes of some of these effects, or the effects of 

 some of these causes ; and are by this means apprised 

 that the effect of A is a, and that the effect of B is b. 

 Subtracting the sum of these effects from the total 

 phenomenon, there remains c t which now, without 

 any fresh experiment, we may know to be the effect 

 of C. This Method of Residues is in truth a peculiar 

 modification of the Method of Difference. If the 

 instance A B C, a b c, could have been compared with 

 a single instance A B, a b, we should have proved C 

 to be the cause of c, by the common process of the 

 Method of Difference. In the present case, however, 

 instead of a single instance A B, we have had to study 

 separately the causes A and B,, and to infer from the 

 effects which they produce separately, what effect 

 they must produce in the case ABC where they act 

 together. Of the two instances, therefore, which the 

 Method of Difference requires, the one positive, the 

 other negative, the negative one, or that in which 

 the given phenomenon is absent, is not the direct 

 result of observation and experiment, but has been 

 arrived at by deduction. As one of the forms of the 

 Method of Difference, the Method of Residues partakes 

 of its rigorous certainty, provided the previous indue- 



