164 THE PRINCIPLES OF SCIENCE. 



of practical application in science. The purely logical 

 inverse problem, whereby we pass from combinations to 

 their laws, is solved in the preceding pages, as far as it 

 is likely to be for a long time to come ; and it is almost 

 impossible that it should ever be carried more than a 

 single step further. 



Distinction between Perfect and Imperfect Induction. 



We cannot proceed further with advantage, before 

 noticing the extreme difference which exists between 

 cases of perfect and those of imperfect induction. We 

 call an induction perfect when all the objects or combi- 

 nations of events which can possibly come under the class 

 treated have been examined. But in the majority of 

 cases it is impossible to collect together, or in any way to 

 investigate, the properties of all portions of a substance or 

 of all the individuals of a race. The number of objects 

 would often be practically infinite, and the greater part of 

 them might be beyond our reach, in the interior of the 

 earth, or in the most distant parts of the Universe. In all 

 such cases induction is said to be imperfect, and affected 

 by more or less uncertainty. As some writers have fallen 

 into much error concerning the functions and relative 

 importance of these two branches of reasoning, I shall 

 have to point out that 



1. Perfect Induction is a process absolutely requisite, 



both in the performance of imperfect induction and 

 in the treatment of large bodies of facts of which 

 our knowledge is complete. 



2. Imperfect Induction is founded on Perfect Induction, 



but involves another process of inference of a 

 widely different character. 



It is certain that if I can draw any inference at all 

 concerning objects not examined, it must be done on the 



