284 - INDUCTION. 



away a is removed along with it, we have by the one proposition ABC, 

 a b c, by the other B C, 6 c, the positive and negative instances Avhich the 

 Method of Difference requires. 



This method may be called the Indirect Method of Difference, or the 

 Joint Method of Agreement and Difference; and consists in a double em- 

 ployment of the Method of Agreement, each proof being independent of 

 the other, and corroborating it. But it is not equivalent to a proof by 

 the direct Method of Difference. For the requisitions of the Method of 

 Difference are not satisfied, unless we can be quite sure either that the in- 

 stances affirmative of a agree in no antecedent whatever but A, or that the 

 instances negative of a agree in nothing but the negation of A. Now, if it 

 were possible, which it never is, to have this assurance, we should not need 

 the joint method; for either of the two sets of instances separately would 

 theji be sufiicient to prove causation. This indirect method, therefore, can 

 only be regarded as a great extension and improvement of the Method of 

 , Agreement, but not as participating in the more cogent nature of the Meth- 

 od of Difference. The following may be stated as its canon : 



Third Caiston. 



If two or more instances in which the phenomenon occurs have only 

 one circumstance in common, while two or m,ore distances in which it does 

 not occur have nothing in commo7i save the absence of that circumstance, 

 the circumstance in which alone the two sets of instances differ, is the 

 effect, or the cause, or an indispensable part of the cause, of the phenomenon. 



We shall presently see that the Joint Method of Agreement and Differ- 

 ence constitutes, in another respect not yet adverted to, an improvement 

 upon the common Method of Agreement, namely, in being unaffected by 

 a characteristic impei'fection of that method, the nature of which still re- 

 mains to be pointed out. But as we can not enter into this exposition 

 without introducing a new element of complexity into this long and intri- 

 cate discussion, I shall postpone it to a subsequent chapter, and shall at 

 once proceed to a statement of two other methods, which will complete 

 the enumeration of the means which mankind possess for exploring the 

 laws of nature by specific observation and experience. 



§ 5. The first of these has been aptly denominated the Method of Resi- 

 dues. Its principle is very simple. Subducting from any given phenome- 

 non all the portions which, by virtue of preceding inductions, can be assignee! 

 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 6 c, and that by previous inductions (founded, we will sup- 

 pose, 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 A B C, a 6 c, could have been compared 

 with a single instance A B, « 6, 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 sep- 



