quired of all Candidates for Degrees, but which are now discontinued. Each of these Disputations turned on three Theses or Questions, of which, latterly at least, two were of a mathematical and the third of a moral nature. The Opponents adduced arguments in a logical form, and in Latin, against the Theses of the Respondent, which were generally taken from wellknown works, as those of Newton, or Cotes, or Wood; and these arguments the Respondent had to refute, or to take off, as it was called. This exercise was much facilitated by the general familiarity with the diagrams of Newton, Cotes and Wood, which then prevailed. It was eminently fitted, in my opinion, both to produce and to test a thorough acquaintance with the subjects thus disputed on; for the arguments were often very perplexing; and yet it was certain that, inasmuch as they seemed to contradict demonstrated truths, there must be some fallacy in them. To be able always to detect the fallacy at the moment, required both a very firm hold of the subject, and great clearness and quickness of mind. If I may be allowed to speak of my own tastes in reference to this matter, I must say that, both as Disputant and as Moderator, I always took a most lively interest in these exercises; and was never satisfied, after an argument had been brought, till I saw the fallacy. But these exercises gradually lost their interest for the students, because they were superseded, in their bearing upon University distinction, by the subsequent examinations of the same Students in the Senate-House. The Questionists' performances in the Schools produced no direct definite effect, and finally produced no effect at all, upon their places in the Tripos Paper. When matters came to this point, the Questionists went through the Disputations as a form, taking no thought about the meaning of the arguments which they read. The last time that I was Moderator, I tried in vain to lead, either the

Respondent or the Opponents, to understand the arguments, or to look for the fallacies of them.

170 Yet I am fully persuaded, as I have said, that to discover the solutions of such difficulties is an excellent mathematical discipline. It would, I think, be difficult to restore the Disputations in their ancient form, and even in any modified form. Men are now so unfamiliar with Latin, and Latin is so ill suited to express our modern mathematics, that the employment of that language for such a purpose is not to be thought of. Yet such Disputations could not be carried on with any degree of precision or coherency, without some technical forms of expression; and all the existing technical forms being Latin, it would not be easy to supersede them by English technicalities. We have seen that on this ground one of our classical scholars has been compelled to retain the Latin for his critical notes, whilst employing English for his notes of explanation*. Again: the technical forms employed in such Disputations must be logical forms; for the technicalities of Disputation are one of the main subjects of logic; but we are here very little acquainted with logic; nor would it, I think, be easy to revive the study of it to such an extent as a correct conduct of Disputations would require. I think, therefore, that any attempt at reviving the Mathematical Disputations of our Schools must be looked upon as chimerical.

171 But I think the same beneficial effect which these Disputations were fitted to produce upon the Questionists, along with the beneficial effects of oral examinations, of which I have before spoken, might be produced by another mode of proceeding. I have already intimated that the Moderator, in such disputations, may take the arguments out of the hands of the Opponent, and may himself put them to the Re

* Mr Shilleto's Demosthenes De falsa Legatione.

spondent, and require them to be answered. And the Examiner may, without the form of a Disputation, do the same thing. We may propound difficulties against the received doctrines of the subject which the examinee professes to have studied, and may require him to solve them. This indeed is a mode of oral examination which differs from common interrogations respecting received proofs, only in making the difficulties which are propounded to the examinee a little more elaborate than the obvious obscurities of a demonstration. By means of difficulties thus proposed to the examinee, both his possession of the subject in question, and his power of mathematical reasoning, may be very thoroughly tested. Such an examination may very well be made an important element in assigning to a student his place in the classes of mathematical honours. And such exercises being held in public, and attended by those who are afterwards to become candidates, may produce, in the mathematical portion of our System of Education, the benefits of an oral examination which we have spoken of as so desirable. We may afterwards speak more in detail of the mode in which this suggestion may be carried into effect.

172 With regard to the remaining objection, of those above mentioned, to a system of oral examination;-that such Examinations cannot be extended to the profounder parts of knowledge, and especially of mathematical knowledge;-undoubtedly the weight of the objection must be acknowledged; and from the undeniable force of this consideration, we are led to conclude that our system of examination ought not to be entirely oral; a conclusion to which we are led by several other considerations. We have already stated that an examination of any serious extent, if entirely oral, will require too great an expenditure of time to allow it to be applied to a great number of candidates: add to which, it is desirable, not only in analytical

mathematics, but in other subjects, that the examinee should be led to produce his knowledge, not only in the sudden shape of oral answers, but also in such a form as he can give it with more thought and deliberation, upon paper. It is not only necessary as a matter of convenience, but highly desirable on account of the exercise itself, that there should be portions of the examination in which the answers are given upon paper: and these may consist of translations of Latin and Greek passages into English; of dissertations on philology and antiquities; of proofs of mathematical propositions or solutions of problems proposed; of explanations of, and comments upon, the principles of such proofs. They may also contain translations out of English into Latin prose, or original Latin composition; and, in a moderate degree, according to the conditions of the examination, translations of Latin and Greek verse into English verse, of English verse into Latin and Greek verse; and perhaps the writing of Greek prose.

173 I will venture to suggest a step which may be taken in paper examinations, in addition to the usual practice; and which would, I think, give to paper examinations a considerable portion of the beneficial effect of oral examinations. The reasons which make it desirable that examinations should be public, hold for the publicity of the answers given by the examinees, as well as the questions proposed by the examiners. It appears very desirable that, in every Examination, the answers, or at least some of the best of them, should be made accessible to Students and to Teachers who wish to consult them. Such papers would be interesting and instructive to all concerned in the educational system; they would show the kind of knowledge required by the examiners, and afford examples of a certain degree of excellence in the requisite performance. 174 Among the reasons which have recommended

written examinations, besides the comparative ease of conducting them, which I have already mentioned, I may notice the manifest fairness of giving the same questions and exercises to all the candidates, which is easy in a written examination, but impossible in an examination conducted vivá voce; at least if the examination be a public one. In a public oral examination, even in the same subject, two candidates may have passages or questions of very various difficulty assigned them, however carefully the examiners may try to equalize the examination; and may, consequently, appear to be very unequally dealt with. And there is also an appearance of justice in the greater amount of time which the paper examination allows for the examiner to peruse, estimate, and compare the answers. The judgment formed of oral performances must, necessarily, be rapid, and may easily be conceived to be hasty and inaccurate.

175 These considerations naturally produced a favourable opinion of paper examinations; and to this has been added a belief, that such examinations are sufficient for the purposes of Education. It has been conceived, of late years, that Education consists in acquiring certain portions of knowledge, or, as it is called, Information; that a written examination may ascertain whether a man has acquired this Information; and that by acquiring such information in examinations at our Universities, we may secure the Education of our Students. But it will appear, from what has been said, that any Education, which deserves the name, cannot be so secured. Education, such as we have shown that it must be, to answer its higher purposes, consists, not in accumulating knowledge, but in educing the faculties of man. It does not consist in information, in the modern sense of the term, but in the formation of the mind. It requires, not merely occasional performances, but permanent habits; not merely the