ILLUSTRATIONS OF THE LOGIC OF SCIENCE. 477 



propositions of geometry ; only, in that case, if he takes a fancy to read 

 Euclid, he will do well to skip whatever he finds with A, B, C, etc., for, 

 if he reads attentively that disagreeable matter, the freedom of his opin- 

 ion about geometry may unhappily be lost forever. 



How many people there are who are incapable of putting to their 

 own consciences this question, " Do I want to know how the fact stands, 

 or not ? " 



The rules which have thus far been laid down for induction and hy- 

 pothesis are such as are absolutely essential. There are many other 

 maxims expressing particular contrivances for making synthetic infer- 

 ences strong, which are extremely valuable and should not be neglect- 

 ed. Such are, for example, Mr. Mill's four methods. Nevertheless, in 

 the total neglect of these, inductions and hypotheses may and some- 

 times do attain the greatest force. 



IV. 



Classifications in all cases perfectly satisfactory hardly exist. Even 

 in regard to the great distinction between explicative and arapliative 

 inferences, examples could be found which seem to lie upon the border 

 between the two classes, and to partake in some respects of the charac- 

 ters of either. The same thing is true of the distinction between 

 induction and hypothesis. In the main, it is broad and decided. By 

 induction, we conclude that facts, similar to observed facts, are true in 

 cases not examined. By hypothesis, we conclude the existence of a 

 fact quite different from anything observed, from which, according to 

 known laws, something observed would necessarily result. The former, 

 is reasoning from particulars to the general law ; the latter, from effect 

 to cause. The former classifies, the latter explains. It is only in some 

 special cases that there can be more than a momentary doubt to which 

 category a given inference belongs. One exception is where we ob- 

 serve, not facts similar under similar circumstances, but facts different 

 under different circumstances the difference of the former having, 

 however, a definite relation to the difference of the latter. Such infer- 

 ences, which are really inductions, sometimes present nevertheless some 

 indubitable resemblances to hypotheses. 



Knowing that water expands by heat, we make a number of ob- 

 servations of the volume of a constant mass of water at different tem- 

 peratures. The scrutiny of a few of these suggests a form of alge- 

 braical formula which will approximately express the relation of the 

 volume to the temperature. It may be, for instance, that v being the 

 relative volume, and t the temperature, the few observations examined 

 indicate a relation of the form 



v = 1 + at + bt 2 + ct\ 



Upon examining observations at other temperatures taken at random, 

 this idea is confirmed ; and we draw the inductive conclusion that all 



