26o 



INDUCTION. 



antecedents which had been over- 

 looked, 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, on the Method of Difference) 

 we have ascertained the causes of some 

 of these effects, or the effects of some 

 of these causes ; and are thence ap- 

 prised 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, which 

 now, without any fresh experiments, 

 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 ABC, 

 ab 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 separ- 

 ately what effect they must produce 

 in the case ABC where they act to- 

 gether. Of the two instances, there- 

 fore, 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, pro- 

 vided the previous inductions, those 

 which gave the effects of A and B, 

 were obtained by the same infallible 

 method, and provided we are certain 

 that C is the only antecedent to which 

 the residual phenomenon c can be re- 

 ferred ; the only agent of which we 

 had not already calculated and sub- 

 ducted the effect. But as we can 

 never be quite certain of this, the 

 evidence derived from the Method of 

 Residues is not complete unless we 



can obtain C artificially and try it sepal 

 rately, or unless its agency, when once 

 suggested, can be accounted for, and 

 proved deductively, from known laws. 

 Even with these reservations, the 

 Method of Residues is one of the most 

 important among our instruments of 

 discovery. Of all the methods of in- 

 vestigating laws of nature, this is the 

 most fertile in unexpected result* : 

 often informing us of sequences in 

 which neither the cause nor the effect 

 were sufficiently conspicuous to at- 

 tract of themselves the attention of 

 observers. The agent C may be an 

 obscure circumstance, not likely to 

 have been perceived unless sought 

 for, nor likely to have been sought 

 for until attention had been awakened 

 by the insufficiency of the obvious 

 causes to account for the whole of 

 the effect. And c may be so dis- 

 guised by its intermixture with a and 

 b, that it would scarcely have pre- 

 sented itself spontaneously as a sub- 

 ject of separate study. Of these uses 

 of the method we shall presently cite 

 some remarkable examples. The canon 

 of the Method of Residues is as fol- 

 lows : — 



Fourth Canon. 



Subduct from any phenomenon such 

 part as is knoivn by previous induc- 

 tions to be the effect of certain ante- 

 cedents, and the residue of the pheno- 

 menon is the effect of the remaining 

 antecedents. 



§ 6. There remains a class of laws 

 which it is impracticable to ascertain 

 by any of the three methods which 

 I have attempted to characterise, 

 namely, the laws of those Permanent 

 Causes, or indestructible natural 

 agents, which it is impossible either 

 to exclude or to isolate ; which we 

 can neither hinder from being pre- 

 sent, nor contrive that they shall be 

 present alone. It would appear at 

 first sight that we could by no means 

 separate the effects of these agents 

 from the effects of those other pheno- 

 mena with which they cannot be pre- 



