achievement of the Examination-hall, but the daily exercise of the Lecture-room. The sympathy with the past and present generations of cultured men, which a good education implies, cannot be proved by any transient test of Question and Answer. It must be nurtured and brought into view by the constant intercourse of intelligent men, occupied in intellectual pursuits, and conscious of the working of each other's minds upon a common object. The prospect of an examination may stimulate the attention in such exercises; but it cannot make either individual study or private tuition produce the effect of such exercises, and answer as a substitute for them, in the course of Education.

176 Examinations, as to their subjects, are either special or general: special, when they refer to a prescribed and limited range of subjects, as for instance, certain selected classical works, or certain branches of mathematics and no other: general, when they include the whole body of approved classical authors, the examinee not knowing beforehand from what work the passages proposed to him will be taken; or the whole course of mathematics, from the lowest to the highest portions.

Special Examinations are very useful auxiliaries to the Teaching by Lectures which takes place in Colleges. An Examination in the subject of the Lectures, known as appointed to come on when the Lectures are over, tends strongly to fix attention upon the Lectures: always supposing, as we have already said, that a due correspondence between the Examinations and the Lectures is secured. And a series of Examinations on the successive portions of a good course of Mathematical study, and on a good series of Classical works, including poetry, history, and philosophy, would be a very valuable part of a liberal education, if thus combined with a corresponding series of Lectures. Even if the University or the Colleges were to provide and

enforce such Examinations only, without the corresponding Lectures, the series would form a sort of Education; for each subject would, in a greater or less degree, lead to the next; and would be prevented from entirely slipping out of the mind after it was once learnt, by its being in some measure connected with the next, and involved in it.

177 But if the University have none but General Examinations, it must be considered as abdicating the function of teaching altogether. A University conducted on such a system, is no longer an Educating, but only a Prize-awarding Body. When the University assumes this character, it is natural that ambitious persons who resort to it should try to go through all their course of study before they come to the University, and should wish, while they are there, to employ themselves only in competitions for Prizes; and in such processes of "getting up" their subjects, by their own exertions, or by the aid of Private Tutors, as may be likely to lead to the attainment of Prizes. So far as this becomes the case with a University, all the machinery of Collegiate and Professorial Lectures, with the other features of College life, are extraneous to the main business of the University. How remote such a condition of things is from that which has always been conceived to exist in the Universities of Oxford and Cambridge, I need not attempt to explain to my readers. Those bodies have always been considered as eminently and characteristically Educating Bodies ; and it is only recently and partially that the other character, of mere Prize-awarding Bodies, has become so prominent, as to make it necessary to draw attention to the dangers which may arise to the older office, from the operation of the newer.

SECT. 4. Of the Relation between the University System and School Teaching.

178 Since the Universities of Oxford and Cambridge are Educating Bodies, and are to be maintained as such, the previous preparation of those who are sent to these Universities ought to be conducted upon this supposition. If the Universities of Oxford and Cambridge were, like the University of London, bodies whose sole function it was to award prizes, confer degrees, and the like; it would be sufficient if schools, and early teachers of boys going to the University, prepared them to be examined. But since young men are sent to Oxford and Cambridge, not merely to show what they have learnt, but also to learn; the teaching of schools should have, for one of its objects, to fit them for being, while at the Universities, further educated. And this view of the relation of our Schools to our Universities will suggest some important maxims with regard to the general conduct of the studies of young men. For instance, this being the case, the object of schoolmasters and early Tutors ought to be, not to carry their pupils through all the subjects of University teaching, from the lowest to the highest, so much as to teach them thoroughly well in the lower subjects, and to prepare them by a good fundamental instruction for a progress in the higher subjects, when the University course brings them to that stage. The school course should not, as soon as the schoolboy has acquired an imperfect and limited knowledge of Latin, urge him on as fast as possible in Greek, carrying him into the most difficult authors, and requiring him to write Greek verse and Greek prose. The aim ought rather to be to secure a very exact and tolerably extensive knowledge of the Latin authors; for instance, Virgil, Ovid, Horace, Terence, Cæsar, Sallust, Cicero; and to consider a thorough acquaintance with these

authors as more essential than a like knowledge of the Greek writers. The writing of Latin prose ought to be sedulously cultivated at school, for it is only by practice that any excellence and facility in this exercise can be acquired; and the same may be said of composition in Latin verse, where there appears to be time and talent for this accomplishment. To sacrifice these parts of scholarship to the practice of composition in Greek prose and verse, with a view to University prizes, is a complete perversion of the business of Education, and must interfere with the genuine classical culture of the student.

179 And in the same manner, in the mathematical portion of school teaching, the object ought to be, not so much to teach what will fit the pupil for the University Examinations as for the College Lectures. And as the basis of all real progress in mathematics, the boy ought to acquire a good knowledge of Arithmetic and a habit of performing the common operations of Arithmetic, and of applying the rules in a correct and intelligent manner. This acquirement appears to be often neglected at our most eminent classical schools. Such a neglect is much to be regretted; for the want of this acquirement is a great practical misfortune, and is often severely felt in after life. Many persons who are supposed to have received the best education which the country affords, are, in all matters of numerical calculation, ignorant and helpless, in a manner which places them, in this respect, far below the members of the middle class, educated as they usually are. We are here, however, concerned, not so much with the practical evils arising from the neglect of Arithmetic in our higher education, as with the effect of this neglect in making all sound mathematical education at a later period impossible. And this evil is in no degree remedied by employing the schoolboy on some of the subjects which enter into the University course, as

Geometry and Algebra. These he may speedily learn when he arrives at the University, if he have been properly grounded in mathematical habits: but Arithmetic he cannot then learn to any purpose. Arithmetic is a matter of habit, and can be learnt only by longcontinued practice. For some years of boyhood there ought to be a daily appropriation of time to this object. Geometry and Algebra do not require so much time. Geometry is a matter of reasoning; and when the proofs are once understood, the student has little more to do. And although Algebra requires, like Arithmetic, the habits of performing operations on symbols, the operations of Algebra are learnt with comparative ease, when those of Arithmetic are already familiar.

180 Indeed we may say that, in general, boyhood is fitted for the formation of practical Habits, and that the aptitude to attend to general Reasonings comes with more advanced youth. In the most natural course of public education, at School we learn to do, at College we learn reasons why we do. At School we learn to construe and to cipher; at College we are invited to follow the speculations of Philologers, and to attend to the proofs of the rules of Arithmetic. And the tastes of boys, for the most part, correspond to this distribution of employments. They can learn to perform and apply the rules of Arithmetic, and they take a pleasure in the correctness of their operations, and in the manner in which the rules verify themselves; but they find it irksome to follow the reasoning of Euclid, where the interest is entirely of a speculative kind. The interest which belongs to demonstration, as demonstration, comes at a later period, when the speculative powers, in their turn, begin to unfold themselves, and to seek their due employment.

181 Perhaps, too, the interest of demonstration is greater when the truth proved is one with which we are already familiar in practice; as when the reasons