144 THE PRINCIPLES OF SCIENCE. 



usually be in operation at the same time, the effects of 

 which are complicated together. The only modes of dis 

 covery consist either in exhaustively trying a great number 

 of supposed laws, a, process which is exhaustive in more 

 senses than one, or else by carefully contemplating the 

 effects, endeavouring to remember cases in which like 

 effects followed from known laws. However we accom 

 plish the discovery, it must be done by the more or less 

 apparent application of the direct process of deduction. 



The Logical Abecedarium illustrates induction as well as 

 it does deduction. In the Indirect process of Inference we 

 found that from certain propositions we could infaUibly 

 determine the combinations of terms agreeing with those 

 premises. The inductive problem is just the inverse. 

 Having given certain combinations of terms, we need to 

 ascertain the propositions with which they are consistent, 

 and from which they may have proceeded. Now if the 

 reader contemplates the following combinations 



ABC abC 



aBC abc, 



he will probably remember at once that they belong to the 

 premises A = AB, B = BC. If not, he will require a few 

 trials before he meets with the right answer, and every 

 trial will consist in assuming certain laws and observing 

 whether the deduced results agree with the data. To test 

 the facility with which he can solve this inductive pro 

 blem, let him casually strike out any of the combinations, 

 say of the fourth column of the Abecedarium (p. 109), and 

 say what laws the remaining combinations obey, observing 

 that every one of the letter-terms and their negatives 

 ought to appear in order to avoid self-contradiction in the 

 premises (pp. 88, 128). Let him say, for instance, what 

 laws are embodied in the combinations 

 ABC aBC 



