If the justness of this view of the subject be admitted, there necessarily results the following conclusion: viz., that if any one branch of Mathematics exists, which is not calculated to produce these benefits, that branch ought immediately to be rejected as a subject of Academical Education. Now, I think it will be allowed by all those, who are acquainted with mathematical studies, that Analytics answer to this description, and that they, who devote their attention to this branch of Mathematics, will never find the advantages it confers, at all answerable to the time that it consumes.

I. Analytics have not, like Geometry, any tendency to inure the mind to those habits of thinking, which are so useful in the studies of after life. This, perhaps, is not strictly true of their first principles; for, when rigorously demonstrated, they are as well calculated to improve the mind in reasoning, as the proofs of Geometrical propositions; but, when these principles are once established, and certain rules and expressions are deduced from them, the application of these rules and expressions has no further influence in strengthening the powers of the understanding. Dr. Watson, the late Bishop of Landaff, has mentioned in his memoirs, that, during the period of his undergraduateship, he was in the habit, while walking, of going over in his mind the most intricate propositions in Euclid and Newton, and that, by frequent practice, he was able to accomplish this laborious task, without the assistance of the figures. It was, doubtless, this mental exercise, that laid the

foundation of that strength of mind, and clearness of reasoning, by which he was afterwards so eminently distinguished. Now, I would ask, does the study of Analytics afford the means of such discipline as this? Can the Analytical student retrace in his mind his former calculations, and, when pen, ink, and paper, are removed, deduce, by the mere power of his intellect those conclusions, which he has once found to be the result of his own working? Analytics have been well defined to be "the art of reasoning without thinking;" their superiority over Geometry consists in this, that, by using the symbols they afford, and working according to known rules and established principles, we may arrive at the knowledge of truths, to which Geometry alone would never have been able to conduct us. But this very circumstance, which constitutes their excellence in a mathematical point of view, renders them unfit for a subject of Academical education. We want to teach the students, who come to the University, to reason and to think, by calling their attention to a subject, which requires thought; but it is the peculiar use of Analytics, that they supersede the necessity of thinking.

II. Analytics have not, like Geometry, any tendency to make us better able to arrange and combine our ideas. They do, indeed, teach us to combine and arrange the Algebraical symbols we make use of, but they go no further. It is often the case, that when the Analytical student has been filling whole sheets with his calculations, and, in his

own estimation, has been doing great things, his reasoning powers have all the while remained inactive; and though he may at length have arrived at some important conclusion, yet, during his progress, he has exerted no higher mental faculties, than those, which would have been called forth in working some of the long and tedious examples to the common rules of Arithmetic. This will, perhaps, account for the fact, that Analytics are so much the favourite branch of study with the rising generation of mathematicians. They know the important conclusions, to which Mathematics lead, and they wish to arrive at them themselves; but still the labour of thinking is disagreeably fatiguing, and they, therefore, prefer displaying the ingenuity with which they can manœuvre the Algebraic symbols, to pursuing a Geometrical demonstration through all its intricate details. But, while thus employed, it is manifest, that they are not in any way preparing themselves for the studies of after life; the difficulties of the law are not to be cleared, the doctrines of religion are not to be deduced by an ingenious application of symbols, but by frequent and careful meditation upon the ideas, which the study of those subjects suggests.

III. Analytics have not, like Geometry, any tendency to give us that power over our ideas, which enables us to express them in clear and perspicuous language. In this assertion I think I am fully borne out by the style, in which the works of some of the greatest Analytical writers are composed. The writings of Lacroix, for instance, are doubtless adb

mirable in their way, and eminently useful to those, who intend to make Mathematics the study of their life. The estimation, in which his name is generally held, would lead us to imagine, that his works must exhibit a most favourable specimen of Analytical reasoning. But were we to appeal to the good sense of any one, who has diligently read the three large volumes, in which Lacroix has developed the principles of the Differential and Integral Calculus, and to ask him, whether he thought, that the attentive study of this work, would enable any one afterwards to reason more justly, and to express his ideas more clearly upon other subjects, I thir.k he would immediately and unhesitatingly answer, No! It seems, in short, as if a familiar acquaintance with Analytical subtleties, had a natural tendency to destroy all relish for that plain and straight-forward method of reasoning, by which alone the truths of science can be made accessible to common understandings. And thus it is, that while English Mathematicians have been increasing the quantity of general knowledge by elementary treatises, concisely and clearly written, while, by the judicious manner in which they unfold the subject, they gradually prepare the mind of the student for the reception of deeper truths; the French, on the contrary, by the mysterious and profound nature of those demonstrations, which they apply even to the simplest theorems, seem, as if they laboured to shut the avenues of science against those, who are not prepared to devote their whole lives to its pursuit. The merit of the English Mathematicians consists

in their being able to familiarize the remote; but it is the fault of the French, that they are too fond of estranging the familiar. Now, since it is in our nature to acquire those habits of thinking, and to imitate those modes of expressing our thoughts, which we find in the authors, with whose works we are most familiar, the study of Analytics must rather disqualify, than prepare us, for the duties of any future profession. He, who is called to the bar, must not only be able to understand the intricacies of the law, but he must also be able to adapt his explanation of them to the understandings of common men; he who is called to the Church, must set forth the doctrines of religion in such a manner, as to be understood by those, who know nothing of the refinements of learning. That student, therefore, who by studying the French Analytical writers, has at length acquired their obscure and confused manner of thinking, and their extreme fondness for those subtleties, which they deem elegant refinements, will, (if he ever enters the world) enter it with a mind that must be re-modelled, with a taste that must be corrected, and without a clearness of perception that must be acquired, before he can ever expect to become eminent, or even useful, in his profession. There is, however, something in the plain straight-forward method of Geometrical reasoning, peculiarly adapted to prepare the mind for the clear arrangement and expression of its thoughts. In composition, before we begin the construction of a sentence, we must first, as it were, take a distinct view of the ideas we are going to