THE POUR EXrERIMENTAL METHODS. 229 



tleiit of the otlier, and corroborating it. But it is not ecjuivalcnt to a 

 proof" by the direct JNIethod of Difleroncc. For the requisitions of the 

 Method of Diffcreace are not satisfied, unless we can be quite sure 

 either that the instances affirmative of a agree in no antecedent what- 

 ever but A, or that the instances negative of « agi'ce in nothing but tlie 

 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 tke two 

 sets of instances sepaiately would then be sufficient to prove causation. 

 This indirect method, therefore, can only be viewed as a great exten- 

 sion and improvement of the Method of Agreement, but not as partici- 

 pating in the moi'e cogent nature of the Method of Diflerence. The 

 tbllovving luay be stated as its canon : — 



Third Canon. 



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

 one circumstance in common, while two or more instances in which it does 

 not occur have nothing in common save the absence of that circumstance ; 

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

 effect, or cause, or a necessary ^tart of the cause, of the jihenomenon. 



We shall presently show that the Joint Method of Agreement and 

 Difference constitutes, in another respect not yet adverted to, an im- 

 provement upon the common Method of Agreement, namely, in being 

 unatfected by a characteristic imperfection of that method, tlie nature 

 of which still remains to be pointed out. But as we cannot enter into 

 this exposition without introducing a new element of complexity into 

 this long and intricate discussion, I shall postJ)one it to the next chapter, 

 and shall at once proceed to the 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 

 Residues. Its pi'inciple is very simple. Subducting from any given 

 phenomenon all the portions which by virtue of preceding inductions, 

 can be assigned to known causes, the remainder will be the elfeot of 

 the antecedents which liad 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 h c, and that by previous inductions, (founded, we 

 will suppose, upon the ^Method of Dirterence,) 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 efiect of A is a, and that the 

 effect of B is b. Subti-acting the sum of these effects from the total 

 phenomenon, there remains c, which now, without any fresh experi- 

 ment, we may know to be the effect of C. This Method of llesiddes 

 is in ti-uth a peculiar modification of the Method of Difference. If the 

 instance ABC, ahc, coidd have been compared with a single instance 

 AB, ab, we should have proved C to be the cause of c, by the com- 

 mon process of the Method of Diffei'ence. In the present case, how- 

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

 the causes A and B, and to infer from the effects which ihey produce 



