by, not understood. If we cannot understand that which wise and thoughtful men have written and have understood in the ages which have preceded us, we have not unfolded in us that intellectual element, in virtue of which men so reasoned. Our reason is not educed; we are, in that respect, uneducated.

108 And when the study of works of reasoning, by the aid of commentators, is likened to the study of Aristotle in the middle ages, we are to recollect that, in those periods, the works of Aristotle were studied, not as reasoning, but as authority. The commentators were employed in interpreting his dogmas, not in explaining his arguments. Aristotle himself is remarkable for the want of real mathematical insight, in the mathematical illustrations which he has introduced; and when the sway of that which passed for his philosophy was overthrown, the main instrument in the reform was, that mathematical education of man which we are here recommending, and which can only be carried on by the study of mathematical works occupying a permanent place in education on account of their real truth and excellence.

109 We have already mentioned the fear which, in speaking of education, men sometimes express; that fixed subjects of educational study should become an exercise for the memory, rather than for the intellect; the forms of speech, which seem to contain the knowledge required, being, in fact, retained by rote, and uttered with no real intelligence. We have stated that this fear is one with very little foundation; since one or two very simple questions will at once ascertain whether the student really understands the language which he pretends to translate, or the reasoning which he pretends to give. We may add, that if, in such employments, especially with slow intellects, memory and repeated attention come in for a share of the student's success in performing his task, we are not on

that account to suppose that the reason is left unculti vated. The truth is, that, in most persons, it is only by such exertions of memory and attention that the reason can be cultivated. To overcome the difficulties of a long train of mathematical reasoning, is one of the best ways of cultivating the reason; but to do this, is, with most persons, a matter of time and thought; and of memory also; for while the student is attending to one part of the chain, he loses, for the moment, his clear apprehension of the other; and only bears it in mind as what he had before proved. But by successive efforts of this kind, the whole becomes clear, and the reason acquires the power of grasping the whole at once. And thus the reason is educated by means of the memory. And the same is the case, not unfrequently, with the interpretation of difficult passages in ancient authors. Such interpretations, accepted at first upon authority, and retained in the memory, are afterwards made more fully intelligible by similar examples, till at last they are seen to belong to the genius of the language. Such exercises of memory and attention are the necessary means of intellectual culture. It is, no doubt, possible that the comment or the interpretation may be lodged in the memory, without producing any effect upon the reason; and in this case, it is an acquisition of small value. But then, in this case, it is also possible that the mind may be one to which it is difficult to impart anything much more valuable. The reason may be so inert and obscure in its operations, that the education of that faculty cannot proceed very prosperously by any process. The exercise of the memory may lead to the best developement of the mental faculties which their native constitution will permit. The case in which it is most likely that the employment of the memory will lead to no real education of the mental faculties, is when the memory is employed principally, not upon

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