330 INDUCTION. 



summing up the effects of many causes, unless we know accurately the 

 numerical law of each — a condition in most cases not to be fulfilled ; and 

 even when it is fulfilled, to make the calculation transcends, in any but 

 very simple cases, the utmost power of mathematical science with all its 

 most modern improvements. 



These objections have real weight, and would be altogether unanswer- 

 able, if there were no test by which, when we employ the Deductive Meth- 

 od, we might judge whether an error of any of the above descriptions had 

 been committed or not. Such a test, however, there is : and its application 

 forms, under the name of Verification, the third essential component part 

 of the Deductive Method ; without which all the results it can give iiave 

 little other value than that of conjecture. To warrant reliance on the gen- 

 eral conclusions arrived at by deduction, these conclusions must be found, 

 on careful comparison, to accord with the results of dii'ect observation 

 wherever it can be had. If, when we have experience to compare with 

 them, this experience confirms them, we may safely trust to them in other 

 cases of which our specific experience is yet to come. But if our deduc- 

 tions have led to the conclusion that from a particular combination of 

 causes a given effect would result, then in all known cases where that com- 

 bination can be shown to have existed, and where the effect has not follow- 

 ed, we must be able to show (or at least to make a probable surmise) what 

 frustrated it : if we can not, the theory is imperfect, and not yet to be re- 

 lied upon. Nor is the verification complete, unless some of the cases in 

 which the theory is borne out by the observed result are of at least 

 equal complexity with any other cases in which its application could be 

 called for. 



If direct observation and collation of instances have furnished us with any 

 empirical laws of the effect (whether true in all observed cases, or only true 

 for the most part), the most effectual verification of which the theory .could 

 be susceptible, would be, that it led deductively to those empirical laws; 

 that the uniformities, whether complete or incomplete, which wei'e observed 

 to exist among the phenomena, were accounted for by the laws of the causes 

 — were such as could not but exist if those be really the causes by which 

 the phenomena are produced. Thus it was very reasonably deemed an es- 

 sential requisite of any true theory of the causes of the celestial motions, 

 that it should lead by deduction to Kepler's laws ; which, accordingly, the 

 Newtonian theory did. 



In order, therefore, to facilitate the verification of theories obtained by 

 deduction, it is important that as many as possible of the empirical laws 

 of the phenomena should be ascertained, by a comparison of instances, con 

 formably to the Method of Agreement : as well as (it must be added) that 

 the phenomena themselves should be described, in the most comprehensive 

 as well as accurate manner possible; by collecting from the observation 

 of parts, the simplest possible correct expressions for the corresponding 

 wholes : as when the series of the observed places of a planet was first 

 expressed by a circle, then by a system of epicycles, and subsequently by 

 an ellipse. 



It is worth remarking, that complex instances which would have been 

 of no use for the discovery of the simple laws into which we ultimately 

 analyze their phenomena, nevertheless, when they have served to verify the 

 analysis, become additional evidence of the laws themselves. Although 

 we could not have got at the law from complex cases, still when the law, 

 got at otherwise, is found to be in accordance with the result of a complex 



