THE DEDUCTIVE METHOD. 269 



of each, — a condition in most cases not to be fulfilled ; and even when 

 fulfilled, to niaki; the calculation transcends, in any but very simple 

 cases, the utmost power of mathematical science with its most modem 

 improvements. 



lliese objections truly have much weight, and would be altogether 

 unansweiable, if there were no test by which, when we employ the 

 Deductive Metlunl, we might judge whether an error of any of the 

 abt)ve di'scriptious had been committed or no. 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 have little other value than that of 

 guess-work. To warrant reliance upon the general conclusions arrived 

 at by' deduction, these conclusions must be found, on a careful com- 

 parison, to accord with the results of direct observation wherever it 

 can be had. If, when we have experience to compare with them, this 

 experience confirms them, we may safely ti-ust to them in other cases 

 of which our specific experience is yet to come. But if our deductions 

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

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

 nation can be shown to have existed, and where the effect has not 

 followed, we must be able to show (or at least to make a probable 

 surmise) what frustrated it : if we cannot, the theory is imperfect, and 

 not yet to be relied 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. 



It needs scarcely be observed, that 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 la^vs : that the 

 uniformities, whether complete or incomplete, which, were observed to 

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

 causes, were such as could not hut c^\6t if those be really the causes 

 by which the phenomena are produced. Thus it was very reasonably 

 deemed an essential requisite of any true theory pf the causes of the 

 celestial motions, that it should lead by deduction to Kepler's laws: 

 which, accordingly, the Newtcniian theory did. 



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

 by deduction, it is important that as many as possible of th^ empirical 

 laws of the phenomena should be ascertained, by a comparison of in- 

 stances, conformably to the Method of Agreement : as well as (it must 

 be added) that the phenomima themselves should be. described, in the 

 most comprehensive as well as accurate manner possible ; by collect- 

 ing from the observation of parts, the simplest possible correct expres- 

 sion for the corresponding wholes: as when the series of the observed 

 places of a planet was first expressed 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 I3.W from com- 



