GHEAT VALUE OF EXHAUSTIVE RESEARCH. 199 



from usual ones, we obtain a clue to the more general 

 truth involved ; this is effected by first obtaining a suffi- 

 cient number of exceptional ones, classifying them accord- 

 ing to their similarities, and then making the comparison. 

 But as in most researches only one, or a very few of such 

 instances, are met with at first, we arrive at the more true 

 explanation by means of the indirect method of inference, 

 i.e., by showing that of all the possible explanations the 

 one assigned is the on]y one which agrees with all the cir- 

 cumstances. If the exceptional cases are sufficient in 

 number, they may even include a still more exceptional 

 instance which cannot be accounted for by the new explana- 

 tion ; and in that case, we imagine an additional set of 

 hypotheses, and test them in a similar manner, and thus 

 arrive at a still wider law or principle ; and in this way 

 it is that exceptions of the exceptions disclose the most 

 hidden conditions, and are signs of the greatest truths. 



Even a single exception may thus prove the existence 

 of a more general law. In such cases, we may either state 

 the less general truth, and include in the statement all the 

 exceptions ; or we may state the more general one which 

 includes the exceptions. Thus we may, with regard to 

 the phenomenon of the expansion of bodies by heat, either 

 say, all bodies expand when heated, except water at its 

 freezing point ; iodide of silver at 300 C. ; fusible alloy 

 at a particular temperature, &c., or we may (if we are 

 able) state the molecular condition or principle which 

 determines the result in all the instances. 



Exceptional cases are often only apparently so, even to 

 our imperfect statements of laws. In consequence of our 

 ignorance and very incomplete insight, many facts are not 

 really exceptional which appear so. Sometimes they are 

 only extreme, conspicuous, or peculiar instances of the 

 operation of known laws. In other cases they are merely 



