of stock operations, the arbitration of exchanges, may be treated in algebraic forms, and from them alone any valuable practical rules can be derived. The last of these is not yet an object of business among us, but the time is approaching, when, in intelligent hands, it will be the surest and safest mode of employing capital. To facilitate the calculations of this important branch of business, a synopsis of algebraic formula, and tables of logarithms, lie upon the desk of every banker of Europe.

To return to general views of education:—it is in the logic of the ancient geometers that we are to find that exercise which is finally efficient in bringing the reasoning faculty to its proper state of development. We are willing indeed to admit that there may occasionally be found persons of strong and masculine genius, who write their native language with force and even purity, yet who have not received a liberal education; but such instances are so rare, as like all other exceptions to be the most convincing proofs of the general rule. On the other hand, a classical education will create even in inferior minds the faculty of the easy and elegant expression of thought. But the proof of the value of mathematical studies is even more conclusive; for we can quote no instance, in any author of modern date, of a long sustained and convincing logical reasoning, carried on by any person, who had not in his youth imbibed the spirit of the ancient geometers. We are aware that there are now shorter roads to proficiency in mathematics, and that modern metaphysical subtilty has affected to discover omissions and inaccuracies in the foundation of some of the more important trains of ancient geometric argument; but we must say, that here we might be disposed to admit of the physical argument, that where the inference is true, and all the steps that lead to it unexceptionable, the basis cannot be defective. We would allude more particularly to the ancient theory of parallel lines, which modern geometers seem to concur in admitting to be incomplete, and for which no adequate substitute has been proposed. To this refinement we would oppose the single objection, that more than twenty centuries had read and considered this theory, and that it was not until the taste which could fully appreciate the whole merit of the geometric method of the ancients had begun to decline, that we find its accuracy doubted.

The fashion of the day has led to the substitution of various treatises, more valuable perhaps in their application to higher studies than the Elements of Euclid. Among these the treatise of Legendre has had the most success, probably from its having been chosen by Harvard University, and since adopted at West Point. Considering as we do the science of mathematics rather as a part, though doubtless a most important one of a liberal education, than as to be studied for its own sake, except

by those who are to profess it, we cannot but object to the substitution of this treatise for the ancient one.

We would urge with all our strength the importance of elementary mathematics in every system of liberal education; because their value seems to be equally misapprehended by those who are mathematicians and those who are not; by those who consider the learning of the schools as intended to be a training of the mind, and those who look upon education with no other view than the limited one of the direct application of it to useful purposes. The mathematics have no doubt the most extensive useful applications of any branch of study; every art and every science derive from them some, if not all of the most important principles, but all are not called upon to know the science on which their practice is founded, while many men never have occasion in after life to use even its most remote inferences. Our estimate of the value of mathematical learning coincides with that of the great statesman of Holland, who, when asked of what use the geometrical studies, to which a great portion of his youth had been devoted, were to him, replied, "they have passed from my memory to my judgment."

Such is indeed the real and useful object of all elementary education; to occupy the youthful mind in such a manner as gradually to form habits of thought and application; to fit it to engage in the business of life with an intelligence and acuteness that will enable it to foil the devices of low cunning, which the ignorant mistake for wisdom; to prepare it, if need be, for the study of the more elevated sciences, or the pursuit of literature; and in a more especial manner, to enable it to appreciate the wisdom, the power, and the beneficence of the deity.

Here the direct objects of an early education may be considered as ceasing. Other branches there are, collateral and less important in mental discipline, but which their more immediate utility will not permit us to pass over. No man can be considered as educated, who is unacquainted with the political and natural divisions of the globe he inhabits; with the history of his race, of his native country, and of those from which its civilization and population are derived; with the scientific principles on which the arts that distinguish civilized man from the savage are founded; with the structure and laws that govern the universe; and above all with his duties as a man, a citizen, and an accountable being.

Much might be said in respect to the manner in which these ought to be taught, and the space they ought to fill in elementary education. But our prescribed limits will not permit us to dilate on these heads. Suffice it to say, that a good teacher will in them all endeavour to impress upon his pupil's mind clear and accurate ideas, instead of a mere recollection of words; and VOL. VI. NO. 11.

22.

that the utmost that can be done in any institution, is to establish a solid foundation, on which the labours of after life are to erect the superstructure.

With those who wish to overturn the established system of education, the modern languages rank next in importance to the applied sciences. We place both of these in a high rank, but we make both the result and object of a good education, instead of considering them as the means. We are satisfied, that as a general rule, no high or even useful attainment in science is to be reached by those who have not laid the foundation deep in language and the mathematics; and while we deem any modern language inferior to the Latin as the first that is to be studied, we know that when the latter is once attained, no difficulty remains in reaching the literature of the former. A few lessons will enable a classical scholar to read with ease the prose writers of France, Spain, Portugal, and Italy. The first of these nations has no poetic dialect, and that of the three last, however valuable in a point of view purely literary, is not a matter to be considered in an education which is merely intended to be useful. To speak and pronounce with fluency and elegance, to write with idiomatic accuracy any modern language, is an acquisition of far greater difficulty; practice alone can give so much, and hence they can form no part of an elementary education, but must be left to the taste, the future pursuits, and opportunities of the pupil. While, then, we would be far from rejecting any of them as a branch of collegiate education, we would neither make them imperative, nor admit them as substitutes for the studies we have urged as more immediately necessary.

The subjects of which we have hitherto spoken, are in their nature purely elementary. We cannot conceive intelligence to exist, without the acquisition of the greater part of them. But the education afforded by a college or university is not to stop at the elements. Higher studies must be introduced, to occupy the time that intervenes between youth and manhood-between the years when parental caution would exclude the pupil from too close a contact with the world, and those in which a professional noviciate can be entered upon to advantage, or the society of men enjoyed. Among such studies stand pre-eminent the Greek language and the higher mathematics. The former opens the door to the most perfect literature the world has ever known, to the finest models of style, and exquisite instances of taste; the latter are boundless in their useful applications, and so much a matter of liberal knowledge, that we consider an acquaintance with their language at least, as indispensable in every scheme of finished education.

In the study of the higher mathematics, the method of the ancients must now be abandoned. The analytic course of reason

1829.]

ing opens shorter and better roads to all the truths and practical applications of the science; and from the moment the elements are acquired, any deviation from this, the most direct path, is sheer waste of time and opportunities. Single equations, deduced by short and perspicuous processes, involve the expression of truths, that would occupy pages even to express in the Synthetic method, and volumes to contain their demonstrations.

The study of rhetoric, and practice in English composition, will next become valuable, although we do not ascribe to them the high rank they hold in some systems of education. The latter is in truth rather the mechanical application of knowledge, than a mode of acquiring it. Good writing consists in the expression of clear and well-defined ideas in terse and apposite language; the former quality is attainable only by a knowledge of the subject; the latter by practice, of which the best is the verbal translation from some other language. Rhetoric teaches us to name, and even gives us rules for using, the tools, but without the materials the mere tools are of no value. In short,

"Bene scribendi sapere est et principium et fons."

If a delicate English ear does, or at least affects to, perceive even in our best authors the marks of a foreign origin, precisely as those of a former age detected similar faults in Hume and Robertson; if our most distinguished poets frequently fail to reach the spirit of the poetic idiom, is it not because we study our language in dictionaries and grammars, and neglect the only true road to elegance of style, frequent and copious translation from the classic writers?

Such was not the case when the value of a classic education was better understood. If before the revolution fewer were well educated, yet in those few the groundwork was better laid, and hence the state papers of the early congress were worthy of the splendid eulogy of Chatham, and equalled in force, in elegance, and in purity, the productions of the best cotemporary writers. of England, although those were Johnson and Goldsmith.

ART. VIII. The Diplomacy of the United States. Being an Account of the Foreign Relations of the Country, from the First Treaty with France, in 1778, to the present time. Second Edition, with Additions. By THEODORE LYMAN, Jr.; 2 vols. 8vo. pp. 470 and 517. Wells & Lilly. Boston:

1828.

FEW subjects possess more intrinsic interest to Americans, than the history of our diplomacy, including as it does that of all our foreign relations-our disputed boundaries and their settlementthe spoliations suffered, and the reparations obtained or sought by us; our acquisition of territory, and the terms of it; our commercial intercourse with other countries, and the treaties which regulate it; our maritime rights-their violation and vindication; the causes of war and the conditions of peace; finally, the general policy pursued by our government, and the circumstances by which that policy has been, or is likely to be, changed or affected. Topics of this nature are important in every country; in our own especially, it is indispensable that their discussion should be frequent and open, and that public opinion should be enlightened and decided on the great questions arising on them.

In its design, therefore, this work is excellent; and we are tempted, in consideration of that, to overlook many of the faults in its arrangement and execution. The author's opinions are generally sound, and his facts authentic; but his reasonings are not strongly presented, nor is his narrative remarkable for perspicuity; it is rather for his intention, than the fulfilment of it, that he deserves our thanks.

In a review of our negotiations, from the Declaration of Independence to the present day, there will be found much of what Americans may regard with just pride, in the general ability, directness, frankness, sagacity, and vigour of our state papers. They are remarkable for these qualities, and for the almost total absence of that duplicity, cunning, and Machiavelism, which are held contemptible in private life, and ought to be considered equally so in public transactions.

Our diplomatic history may be divided into four periods, the first of them including our negotiations during the war of independence, and immediately subsequent, down to the commencement of the wars of the French revolution: the second extending through the course of those wars, to the Treaty of Ghent ; the third ending at our acknowledgment of the independence of the Spanish American States; and the fourth coming down to the present time.

Our first diplomatic appearance at the courts of Europe, was