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[Vol. IX., No. 207 



will always happen in all like cases. This is a 

 habit, or a tendency, not to be encouraged, but to 

 be corrected. The experience of children can 

 never be very great, — never sufficient for a very- 

 wide generalization : and to allow them to draw 

 conclusions from insufficient experience, however 

 right our wider experience may have shown that 

 conclusion to be, is to allow them to form a very 

 bad habit indeed. Are we, then, to exclude in- 

 ductive reasoning from the schoolroom ? By no 

 means. Inductions vary almost infinitely in 

 their degrees of generalization, from the narrow 

 inductions with which children themselves spon- 

 taneously begin, such as 'Flies, die,' to the 

 law of gravitation. Let us follow nature's 

 hint, and restrict our pupils' work at first to 

 the narrower kinds. We shall then be fairly 

 safe, especially if we are careful, as we should be, 

 to afford the young inquirer every possible oppor- 

 tunity of testing and correcting his conclusions. 

 I need scarcely point out here that the inductions 

 of mathematics will be at first even more useful 

 to us than those of physical science. In mathe- 

 matics the premises are so carefully restricted, 

 and the applications of the conclusions so strictly 

 narrowed, that within their assigned bounds our 

 inductions are absolutely true ; so much so, that 

 Mill refused to regard them as real inductions at 

 all. Moreover, we can test them exhaustively, — 

 I will not say exhaustingly, — and so make per- 

 fectly clear their truth and value. In grammar 

 also, especially in that of the mother-tongue, the 

 inductions are simple and easily made, and the 

 means for testing their accuracy are always ready 

 to hand. Again, the way in which children earli- 

 est show their curiosity is in seeking for causes. 

 They have a strong tendency to look upon every 

 thing as having a cause and a purpose. Here, 

 then, is another valuable hint of nature as to the 

 kind of work we should choose. Many easy ex- 

 ercises of the kind we require are to be obtained 

 from among the simpler phenomena of nature, or 

 from mathematics, and even history. The dis- 

 covery of causes is, however, often a very difficult 

 process, and always implies a method of proced- 

 ure. For a discussion and exposition of this, I 

 must refer you to two excellent chapters in Mr. 

 Jevons's little book (chapters xxviii. and xxix). 

 For convenience sake, I shall quote here Mill's can- 

 ons which bear on this matter, and which are to 

 be found in the chapters referred to. The first is 

 the rule for the method of agreement: "If two 

 or more instances of the phenomenon under in- 

 vestigation have only one circumstance in com- 

 mon, the circumstance in which alone all the 

 instances agree is the cause (or effect) of the 

 given phenomenon ; " or, more briefly, the sole 



invariable antecedent of a phenomenon is prob- 

 ably its cause. The next refers to the method of 

 difference. It runs: "If an instance in which 

 the phenomenon under investigation occurs, and 

 an instance in which it does not occur, have 

 every circumstance in common save one, that one 

 occurring only in the former, the circumstance 

 in which alone the two instances differ is the 

 effect or the cause, or an indispensable part of 

 the cause, of the phenomenon." ^ As Mr. Jevons 

 remarks, this is essentially the great method of 

 experiment, and its utility mainly depends upon 

 the precaution of only varying one circumstance 

 at a time, all other circumstances being main- 

 tained just as they were. Thomson and Tait re- 

 mark (iVa^itraZ philosophy, vol. i. p. 307), "In all 

 cases when a particular agent or cause is to be 

 studied, experiments should be arranged in such 

 a way as to lead, if possible, to results depending 

 on it alone ; or, if this cannot be done, thev should 

 be arranged in such a way as to increase the ef- 

 fects due to the cause to be studied till these so 

 far exceed the unavoidable concomitants that the 

 latter may be considered as only disturbing, not 

 essentially modifying, the effects of the principal 

 agent." The next canon refers to a joint method 

 of agreement and difference : "If two or more 

 instances in which the phenomenon occurs have 

 only one circumstance in common, while two or 

 more instances in which it does not occur have 

 nothing in common save the absence of that cir- 

 cumstance, the circumstance in which alone the 

 two sets of instances (always or invariably) differ 

 is the effect, or the cause, or an indispensable part 

 of the cause, of the phenomenon." The next 

 canon relates to what may be called the method 

 of concomitant variations: "Whatever phenom- 

 enon varies in any manner, whenever another 

 phenomenon varies in some particular manner, is 

 either a cause or an effect of that phenomenon, or 

 is connected with it through some fact of causa- 

 tion." Lastly, I will quote the canon relating to 

 what Mill called the method of residues: "Sub- 

 duct from any phenomenon such part as is known 

 by previous inductions to be the effect of certain 

 antecedents, and the residue of the phenomenon 

 is the effect of the remaining antecedents." Those 

 who desire more than Mr. Jevons gives, may find 

 it in Mill's ' System of logic ' (book iii. chapters 8, 

 9, 10). 



1 So, when we are trying experiments on condensation, 

 — of steam, for instance, — we find that a plate held in the 

 steam condenses some of it. What causes this 7 Perhaps 

 the coldness of the plate's surface. Well, then, let us heat 

 the plate and try: resalt, no condensation. Let us make 

 the plate very cold by placing it for a little while in the 

 freezing mixture. What is the result now? Increased 

 condensation. Probahly, then, cold produces condensation. 

 And so on, through a number of other experiments. 



