166 



SCIENCE. 



[Vol. IX., No. 211 



case, assume it as a cause, make further experi- 

 ments on this assumption, in the way described in 

 the ' method of experiment,' given aVtove. 



Causes may also be dealt with in our history 

 lessons in numberless ways, — especially when the 

 children are encouraged to bring their practical 

 knowledge of modern things to bear on things of 

 the past. The causes of the English settlement 

 in Britain, of the invasions of the Norsemen and 

 Danes, can be made fairly clear by the light of 

 modern emigration and immigration. Why the 

 English chose John for king, and their fellow-sub- 

 jects on the continent (at least some of them) 

 chose Arthur, will not be difficult for the children 

 to discover ; while, starting from our modern ag- 

 ricultural troubles, we may attempt a more elab- 

 orate chain of reasoning and accumulation of 

 causes in explanation of the peasant revolt in the 

 latter part of the fourteenth century. I do not 

 think it will be needful for me to go into detail, 

 — the demands of the peasants, the actual occur- 

 rences of the rebellion, and the events which im- 

 mediately preceded and followed it, will suggest 

 sufiScient causes to the teacher and his pupils, and 

 into these, investigation may then be made. Nor 

 need I point out how strikingly suggestive of an 

 explanation recent events have been, — distress of 

 a general character, agricultural distress and dis- 

 agreements, political discontent, the introduction 

 of the element of rowdyism, socialism, wanton 

 destruction of property by the regular London 

 mob ; even the guardians of order appear to have 

 been as paralyzed and useless in this town of Lon- 

 don on the one occasion as on the other. The 

 analogy is strikingly complete. But we must be 

 careful. Analogies are dangerous things, and are 

 wont to carry us too far, and to make us read into 

 a case evidence not really there. They should sug- 

 gest the direction and nature of our inquiries, 

 rather than be taken as in themselves sufficient 

 explanations. But, after ail, the great thing in 

 work of this kind is to choose our subject-matter 

 from common every-day events and things, or to 

 bring what we choose at once into as close a rela- 

 tion as is possible with every-day experience and 

 modern doings ; moreover, we need not exhaust, 

 or attempt to exhaust, all the causes for our phe- 

 nomena. Provided that the children are made 

 and hept keenly aware that there are other causes 

 besides those we are considering, we shall do no 

 harm in confining ourselves to the most promi- 

 nent. 



In the work we have been describing, we shall 

 gradually have advanced from individuals to 

 classes, — the statements at which we have been 

 arriving will have contained predicates more and 

 more general, and more and more abstract. Now 



we may begin to check and correct misstate- 

 ments, to curb exaggerations, and to encourage 

 the child to make more marked distinction be- 

 tween fancy and reality. We may begin some 

 simple deduction, consisting of the application of 

 some simple general principles, or general conclu- 

 sions, to the explanation and solution of particular 

 cases. Arithmetic and algebra — and, later, some 

 of our language work — will be found of great 

 assistance here. We could hardly begin with 

 any thing better, perhaps, than the deduction of 

 the rules for the multiplication and division of 

 vulgar fractions from the general principles that 

 regulate the nature of a vulgar fraction, and from 

 the general principles of multiplication and divis- 

 ion. 



The ways of doing this are numerous, and 

 familiar to every one : we, of course, generally be- 

 gin by establishing the rules referring to those 

 changes in the form of a fraction which do not 

 affect its value, and in making clear the fact that 

 the numerator and denominator of a fraction may 

 be treated as the dividend and divisor of a sum in 

 division ; or, to put it concisely, such an expres- 

 sion as f of 1 is tlje same as | of 3. But whatever 

 plan we adopt, of this we should take the gi-eat- 

 est care, — that our reasoning is strictly and hon- 

 estly deductive, and that its wording and its cogency 

 are both thoroughly understood and appreciated 

 by our pupils. This, however, is just the very 

 thing that teachers, as a rule, will not take the 

 trouble to do. They are in too great a hurry to 

 get to the working of sums, — the mechanical 

 manipulation of figures or symbols. This they 

 seem to look upon as the great end of arithmetic 

 work • and, when their pupils have applied a rule, 

 never clearly understood, to some hundred per- 

 fectly mechanical examples, the teacher \\i\\ 

 lead them on with the utmost complacency to an- 

 other mechanical exercise. Shall I be exaggerat- 

 ing if I say that more than half the teachers of 

 arithmetic to children are unable to explain clearly 

 to any one, when the time for explanation comes, 

 the principles of, say short division ? Not because 

 the matter is abstruse and difficult, but because 

 they have never thoiight it necessary to under- 

 stand those principles. 



The principles of the method of deduction, 

 however, v/ill come out more clearly in some of 

 the problems of algebra, — such as the theory of 

 indices, — and in simple propositions of theoretical 

 geometry. It is lamentable how seldom one gets 

 so easy a piece of reasoning as the theory of in- 

 dices clearly and correctly set forth by pupils whom 

 no diabolic complication of quantities and signs 

 and brackets can dismay. They can manipulate 

 almost any thing ; they can reason out nothing. 



