THE FOUR EXPERIMENTAL METHODS. 223 



tried with T) and E, but without B and C, and that the effect is ade. 

 Then wo may rouson thus : b and c are not effects of A, for they were 

 not produced hy it in the second experiment; nor are .cZ 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 cannot 

 have been the effect of B or C, since it was produced where they 

 were not; nor of D or K, since it was produced where they were not. 

 Therefore it is the effect of A. 



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

 substance and an oil. This combination being tried under several 

 varieties of circumstance resembling each other in nothing else, the 

 results agree in the production of a greasy and detersive or saponaceous 

 substance : it is therefore coiu'duded 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, ;vve have only 

 the. resource of observation without experiment: we cannot take a 

 phenomenon of which we know not the origin, and try to find its mode 

 of production by producing it ; if we succeeded in suqli a random trial 

 it could only be by accident. But if we can observe a in two different 

 combinations, aic and ade; and if we know, or can discover, that the 

 antecedent circumstances in these cases respectively were ABC and 

 ADE; we may conclude by a reasoning similar to that in the pre- 

 ceding example, that A is the antecedent connected with the consequent 

 (i by a law of causation. B and G, we may say, cannot be causes of a, 

 since on its second occurrence they were not present ; nor are D and E, 

 for they were not present on its first occurrence. A, alone of the 

 five circumstances, was found among the antecedents of a in both 

 instances. 



For example, let the effect a be crystalizatioUi. We compare in- 

 stances in which bodies are known to assume crystaHne structure, but 

 which have no other point of agreement; and we find thdm to have 

 one, and as far as we can observe, only one, antecedent in common : 

 the deposition of a solid matter from a liquid state, either a state of 

 fusion or of solution. We conclude, therefore, that the solidification 

 of a substance from a liquid state is an invariable antecedent of its 

 crystalization. 



In this example we may go further, and say, it is not only the 

 invariable antecedent but the cause. For in tliis case we are able, 

 after detecting the antecedent A, to produce it artificially, and by 

 finding that a follows it, verify the result of our induction. The 

 importance of thus reversing the proof was. never more strikingly- 

 manifested than when, by keeping a phial of water charged with 

 siliceous particles undisturbed for years, a chemist (1 believe Dr. 

 Wollaston) succeeded in obtaining crystals of quartz ; and in the 

 equally interesting experiment in which Sir James Hall produced 

 artificial marble, by the cooling of its materials from fusion under 

 immense pressure : two admirable examples of the light which may 

 be thrown upon the most secret processes of nature by well-contrived 

 inten-ogation of her. 



But if we cannot artificially produce the phenomenon A, the con- 



