old, but upon new points of literature and science : for, in such a case, the traditional knowledge which alone can make the new advances fully intelligible, being wanting, the phrases which express the novel views, and the processes which are supposed to replace the ancient demonstrations, will really be mere formalities;-extraneous matters contained in the memory as a repository, but not assimilated by mental operations, and converted into intellectual nutriment.

110 The opposition between information merely accumulated in the memory by labour, on the one side; and acts of understanding and reasoning on the other, is often dwelt upon as very important in directing the conduct of education; and no doubt is so. But, as we have seen, the relation of these operations is misconceived, if it is conceived as a mere contrast: for the labour of attention and the exercise of memory are the means by which we form active habits of reasoning and expressing reasons. Juvenile views of education are especially apt to fasten upon and to exaggerate this contrast. Schoolboys and very young students, and those of them especially who are most impatient of steady thought and continued labour, find an easy gratification of their self-complacency in identifying all intellectual labour with the want of originality and vivacity of mind. It is their practice to affix terms of grotesque contempt to the mental habits which they thus wish to depreciate and some of these terms are sometimes used indiscriminately for all exercise of the memory, whether in its necessary educational functions, or in that forced preparation for examinations which is, as we shall see, a pernicious vice in educational systems. For instance, the former as well as the latter is sometimes, by thoughtless people, called cramming. Such terms, once put in circulation, exercise an almost unbounded sway over the young men's minds, and deprive them of the use of reason on these subjects. The

contemptuous phrases so used seem to remove at once all intellectual dignity and value from the subject of such satire, in the eyes of the young satirist. We may pass by this schoolboy trick, as too shallow to cause any confusion. But that it can succeed even with boys, shows how necessary it is to estimate duly the office of labour, industry, and attention, in the business of education.

111 Even with men, as well as with schoolboys, contempt and ridicule, directed towards one or another part of the methods of education, may interfere with a sound judgment on the subject. The methods of education which have been in use through all ages have had their technical terms, rules, and customs. All methods which are to be applied to great numbers of learners by ordinary teachers, must have such technicalities. But all technicalities, detached from their use and meaning, are easily made objects of ridicule and contempt. The technicalities of education, which are rendered familiar to the boy before he can understand their purpose, may easily provoke a smile in the man; especially if, in a more advanced season of life, he finds that his understanding retains its hold of the subject in other ways than by means of these technicalities. Hence one man speaks with ridicule of the Rules of Arithmetic as commonly given; for instance, the Rule of Three Inverse, the Rule of Five, Alligation, Barter, and the like. Another laughs at the technicalities of the common grammars; gerunds in di, do, and dum; supines in um, and u; deponent and impersonal verbs; and so on. We are not at all concerned to maintain that these are essential or important parts of education; but that which it is necessary for us to recollect is, that some such technicalities as these are essential parts of every general method of education;-that such technicalities are not at all necessarily useless because they do not explain themselves, or because they depend upon

views which are fanciful, or even false;-and that in the course of education, boys must often learn and apply technical phrases and technical rules, before they can understand them. It usually happens that boys who are made to learn and apply rules, begin to see the meaning of the rules, when their habits of thought are further unfolded; and though this may lead their friends or themselves to suppose that the rules at first were of no value to them, this supposition would be a great mistake. Boys can easily learn to apply rules, before they can easily learn to understand them; and are likely to understand them the better, from being already familiar with the mode in which they are applied. The memory may be brought into extensive action, before the understanding can; and may be made to assist powerfully in unfolding the understanding, by supplying it with materials to operate upon. If no boy was allowed to learn anything of which he did not, at the time, understand the reason, no general system of teaching could be applied; the progress of learners must be slow and irregular; and after all, there is no ground to believe that boys so taught would understand their rules better than those who begin by applying, and end by understanding the reasons of them. For it can admit of no doubt that to understand the rules and their reasons at a subsequent period is a necessary portion of the system of education to which they belong. To make the student understand fully both the rules of arithmetic and grammar, and their reasons, is an important step in that higher education which succeeds the education of the schoolboy. But on this ground, no valid argument against any particular form of such rules can be drawn from the ridicule to which they are subject, as being unintelligible to the boys who use them.

112 Nor is it, as we have said, any sufficient condemnation of such rules and technical expressions, that

they are founded on fanciful, or even false opinions. It may be true, that supines are mere nouns; that deponents are really passive verbs; and the like: yet no disadvantage arises from the use of such terms as supines and deponents to mark those cases. Or rather, it would be a great disadvantage that the learner should not know the meaning of such terms; so as to be able to understand those grammatical discussions in which they are employed. It may be that many of the Rules given in the common books of Arithmetic are arbitrary and superfluous, and that they might all be reduced, with advantage, to a smaller number. As they are given, they serve at least to classify and multiply examples of numerical operations, and are themselves multiplied examples of the simpler and more comprehensive principles to which the student is afterwards to be led, when his mind is matured and prepared for dealing with such principles. The boy learns rules as rules, which he can do easily and well; and the youth learns reasons and principles all the more easily, because the process of learning rules has preceded. But these considerations belong rather to the mode of teaching, which will be a subject for our attention hereafter.

113 It may be said that by thus defending and commending the use of the rules and technicalities belonging to the old methods of teaching, we do not adequately appreciate the great recent improvements in education; the new views of grammar and of the relations of language, and of the foundations and reasons of arithmetic, algebra, and geometry;—and the simplicity and clearness which have been introduced into the teaching of these subjects. To this I reply, that the new views of the fundamental principles, both of philology and of mathematics which have recently been published, have been, as I believe, very efficacious in promoting a better understanding of those subjects; but that they have not produced this effect merely in virtue

of their being better views, superseding worse, but in virtue of their being the results of the activity of thought and research of the Teachers. For though technical phrases and rules and maxims may be very useful instruments of education before they are fully understood by the learners, they cannot be used with any great efficacy for such purposes, except they are understood by the Teachers: and the new views of recent speculators, regarding language and antiquities, geometry and algebra, have been the results of their endeavours to ascertain fully the significance, truth, and foundations of the doctrines which the traditional forms of classical and mathematical literature take for granted. Precisely because the new doctrines are expressions of advances towards clear insight and full conviction in the minds of the Teachers, they are better doctrines for them, and enable them to teach better, than, without such an intellectual movement going on among them, they could have done. Such a mental advance will make their instructions both more rationally sound, and more zealous and persevering, than they would otherwise be. I believe it will be found that this is the source of any greater effectiveness of modern systems of teaching classics and mathematics which may have occurred, rather than any virtue inherent in the new methods themselves. When the expressions which convey the new views have come, in their turn, to be familiar technicalities, dimly understood; and when the new methods are applied by a number of teachers, of ordinary zeal and intelligence, to learners of all variable degrees of capacity, it is probable that the average success of the new methods will not be much greater than that of the old ones; and certainly it does not appear likely that the new methods will produce better scholars and better mathematicians, either in the most eminent cases or on the average, than the old methods produced. There appears to be no disadvantage, but rather a con