278 INDUCTION. 



aration for discussing the methods of direct induction ; a preparation ren- 

 dei'ing superfluous much that must otherwise have been introduced, with 

 some inconvenience, into the heart of that discussion. To the consideration 

 of these methods we now proceed. 



CHAPTER VIII. 



OF THE FOUR METHODS OF EXPERIMENTAL INQUIRY. 



§ 1. The simplest and most obvious modes of singling out from among 

 the circumstances which precede or follow a phenomenon, those with which 

 it is really connected by an invariable law, are two in number. One is, by 

 comparing together different instances in which the phenomenon occurs. 

 The other is, by comparing instances in which the phenomenon does occur, 

 with instances in other respects similar in which it does not. These two 

 methods may be respectively denominated, the Method of Agreement, and 

 the Method of Difference. 



In illustrating these methods, it will be necessary to bear in mind the 

 twofold character of inquiries into the laws of phenomena; which may 

 be either inquiries into the cause of a given effect, or into the effects or 

 properties of a given cause. We shall consider the methods in their ap- 

 plication to either order of investigation, and shall draw our examples 

 equally from both. 



We shall denote antecedents by the large letters of the alphabet, and 

 the consequents cori'esponding to them by the small. Let A, then, be an 

 agent or cause, and let the object of our inquiry be to ascertain what are 

 the effects of this cause. If we can either find, or produce, the agent A in 

 such varieties of circumstances that the different cases have no circumstance 

 in common except A; then whatever effect we find to be produced in all 

 our trials, is indicated as the effect of A. Suppose, for example, that A is 

 tried along with B and C, and that the effect is a h c; and suppose that 

 A is next tried with D and E, but without B and C, and that the effect is 

 ade. Then we may reason thus : h and c are not effects of A, for they were 

 not produced by it in the second experiment; nor are (? and e, for they 

 were not produced in the first. Whatever is really the effect of A must 

 have been produced in both instances; now this condition is fulfilled by 

 no circumstance except a. The phenomenon a can not have been the ef- 

 fect of B or C, since it was produced where they were not; nor of D or E, 

 since it Avas produced where they were not. Therefore it is the effect 

 of A. 



For example, let the .antecedent A be the contact of an alkaline sub- 

 stance and an oil. This combination being tried under several varieties 

 of circumstances, resembling each other in nothing else, the results agree in 

 the production of a greasy and detersive or saponaceous substance : it is 

 therefore concluded that the combination of an oil and an alkali causes the 

 production of a soap. It is thus we inquire, by the Method of Agreement, 

 into the effect of a given cause. 



In a similar manner we may inquire into the cause of a given effect. 

 Let a be the effect. Here, as shown in the last chapter, we have only the 

 resource of observation without experiment : we can not take a phenome- 

 non of which we know not the origin, and try to find its mode of produc- 



