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These difficulties, with others, arising from the manner in which the study is pursued, and the want of capacity in the instructers, render arithmetic, instead of a most simple and practical thing, one of the most irksome and unintelligible that can be presented to the young mind. Mr Colburn's book is liable to none of these objections. A child sees, at once, from the examples, that arithmetic is something which he can understand, and which will be of use to him.

In another respect, this book is likely to do a great deal of good. It contains excellent instruction for teachers. Directions are often as much required for them as for their pupils. The discipline of the infant mind is almost the only thing for directing which no apprenticeship, no experience, and very little information are in this country, at least, supposed to be required.* A man is often deemed capable of teaching, for the very reason that he has shown himself incapable of any thing else. The only part of us, which is immortal, is abandoned to the care of such as are unable to do aught for the body; and he who has no memory, nor taste, nor power of reasoning himself, is to communicate them, or develop and show the best means of improving them, in another. Now and then, a poor student in college, who was waked from the lethargy of ignorance by the pressure of adversity, and has been nursed in her arms, who has learned how to teach from the necessity of teaching himself, may stumble upon a natural method; and even then he is compelled to abandon his hope of improvement, from finding books, and the habits of his pupils and common opinion, opposed to him. These are obstacles which it is not easy to overcome. There are no books which contain the results of the experience of others. These have not been recorded in our language; and a person, on beginning to instruct, is very much in the condition of one who should begin an art or profession, which had never been exercised before. He is ignorant of the material he is to work upon, the instrument he is to use, and the effect to be produced. To such a person, the practical views contained in Mr Colburn's

* In many parts of Germany there are excellent schools for schoolmasters. An institution of this kind, of high repute, is supported by the grand duke of Saxe-Weimar. This is a state of about 200,000 inhabitants. How does the support of the institution of which we speak, in its little metropolis, compare with the Vandal proposal made in the legislature of Massachusetts, at its last session, to abridge the provisions made by our laws for the support of education!

sensible preface, and the directions in the key will be of great

use.

These directions and the arrangement of the examples are so excellent, that one hardly need understand the subject previously; if he will but go straight forward in the path pointed out, he will teach exceedingly well.

There are two ways in which the book may be used. The first is with the plates which accompany it, and which are intended for children who are beginning the study. These render the solution of questions practical, as well as the questions themselves. We shall not describe the use of these, nor the particular parts of the plan, which has already been published under the disguise of a disgusting book by Neef. It is sufficient to observe, that the difficulties are so introduced, that one only occupies the attention of the pupil at once. After having gone through the examples with the plates, which may be done by children of eight or nine years, the pupil will be able, by means of the plates, to solve readily and intelligibly, most of the questions that commonly occur, in which the numbers are small.

The same examples, in the same order, proposed to be solved without the slate, or any other mechanical assistance whatever, furnish an intellectual exercise, which may be of great use to pupils in any stage of their education.

We have no doubt that Mr Colburn's book will do much to effect an important change in the common mode of teaching arithmetic; and of its speedy adoption the rapid sale of the first edition, and its great intrinsic merit, give the highest promise. We understand that a second edition, still farther improved, is in the press; and that the author intends to publish another little volume for the especial use of older pupils.

We hope Mr Colburn will go on in making school books, and, by furnishing one upon a similar plan, for geometry, for drawing, and for algebra, will afford the means of giving instruction in the better sort of schools an entirely new character.

ART. XXIII.—A Discourse on the Early History of Pennsylvania; being an Annual Oration delivered before the American Philosophical Society, held at Philadelphia, for promoting useful Knowledge, June 6, 1821. By Peter S. Du Ponceau, LL. D.

THE history of almost every people begins in fable. It is not in the first weak struggles of a barbarous tribe, for ascendancy over its neighbors, that the future conquerors of mankind are to be discerned; nor is it in the execution of petty schemes of traffic or plunder, that we can foresee an opulent maritime power, which is to cover the sea with her ships, and the land with monuments of her commercial splendor. Great as may be the destinies of the infant nation, there is nothing to arrest attention in the obscure events of her early growth, as she slowly and painfully emerges from insignificance, until her subsequent wealth, power, and refinement have imparted an interest to the minutest incidents of her primitive history. Then it is that the poet seeks to flatter the pride of his countrymen, and to excite his own imagination by swelling the little chieftains of his ancestry into heroes, and peopling the dark void of his country's origin with demigods, whose pretensions, like objects viewed through mist, are magnified by the very darkness in which they are enveloped. To the rhapsodies of the bard succeed the legends of the annalist, or the researches of the antiquary, each supplying the defect of authentic records by fanciful reasonings, by conjectures whose far-fetched ingenuity is not always enough to redeem them from the imputation of folly and falsehood, and by vain attempts to throw light upon that which the unsparing hand of time has long since consigned to perpetual oblivion. Such are the thousand mystical tales, which Herodotus received from the Egyptian priests. Such are the apocryphal expeditions, wars, and conquests of the Greeks, and the deities, whose combats and intrigues have, at least, furnished the subject of many a beautiful fiction to Homer, Hesiod, or Apollonius. Such too, there is reason to believe, is no small part of the history of the kings of Rome, which Livy confesses to rest upon slender proofs, and which Dionysius and Plutarch narrate with a particularity more suspicious than even the silence of older historians. The same cloud of uncertainty hangs over the rise of the mo

dern nations of Europe, whose minstrels will point out to you, in the obscure and broken traditions of their forefathers, some Trojan hero like Brute, or Scandinavian god like Odin, to render their first beginning illustrious.

The only exceptions to this are in the case of colonies. planted in a foreign country by populous and flourishing nations, which, being at the time in possession of arts and literature, can transmit to posterity an account of the origin of their colonies, of the causes which led to their establishment, and of the distinguished individuals who communicated dignity and splendor to the enterprise. If such a colony should outlive the perils and hardships to which its commencement was exposed, if it should gradually rise up to the rank of a powerful empire, capable of coping successfully even with the people which gave it birth, and if, having attained the strength and robustness of manhood, it should throw off the dominion of its parent state, and boldly place itself among the independent nations of the earth, it may then look back with sentiments of honorable pride upon the patriots who founded it in the wilderness, the heroes who defended it from hostile aggression, and the statesmen by whom it was lifted up to its subsequent elevation and grandeur.

We, therefore, who trace the very beginning of our national being to a period when mankind had already become polished by civilization; who sprang from a land where science was even then fostered and flourishing; whose progenitors brought with them across the ocean a share of the knowledge, refinement and letters of their contemporaries in Europe; and who, from the first morning that an American sun rose upon our fathers to light them on amid the unexplored deserts of the west, down to the day which is now passing over our heads, have never ceased to consult our own glory, and the good of those who are to come after us, by cultivating literature and science, we have no occasion to call upon the doubtful aid of fiction for the celebration of our ancestry, devoid as it is of the false brilliancy which a series of deified heroes may have thrown upon the lineage of Europeans. The curious and learned, indeed, may contend for the rival claims of Spain or Portugal, of England or France, to the dominion of the new world; they may dispute on the priority of the voyages of Vespucci or Columbus to this continent; they may speculate on the expeditions of Biron from Norway, or of Madoc from New Series, No. 10.

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Wales; or they may ascend higher, and amuse themselves with seeking for the Νήσοι Μακάρων, the Blessed Isles of Pindar, or the Atlantis of Plato, in the fertile regions of tropical America; but their discussions, strikingly as they tend to show how many of the events which to-day are notorious and important, are forgotten among the vicissitudes of to-morrow, do not shake the credibility of the general facts of our early history, nor cast any doubtfulness upon the characters and deeds of those, who laid the foundations of our public prosperity.

We have been led into this course of reflection by the perusal of Mr Du Ponceau's eloquent discourse on the early history of Pennsylvania, and especially by his remarks on the character of William Penn, in which, if he displays an enthusiastic admiration of this great apostle of peace, it is certainly an enthusiasm equally honorable to his head and to his heart.

If I had not already trespassed too much upon your patience,' he observes, I would with delight pass in review before you some more, at least, of the interesting traits with which this history abounds, and which an abler pen than mine will, I hope, at no distant day, fully delineate. Above all, I should love to dwell on the great character of our immortal founder, and to point out, by numerous examples, that astonishing ascendancy over the minds of the mass of mankind, which enabled him to raise a flourishing commonwealth by means of all others the most apparently inadequate. To acquire and secure the possession of an extensive country, inhabited by numerous tribes of warlike savages, without arms, without forts, without the use or even the demonstration of physical force, was an experiment which none but a superior mind would have conceived, which none but a masterspirit could have successfully executed. Yet this experiment succeeded in a manner that has justly excited the astonishment of the whole world. "Of all the colonies that ever existed," says Ebeling, "none was ever founded on so philanthropic a plan, none was so deeply impressed with the character of its founder, none practised in a greater degree the principles of toleration, liberty and peace, and none rose and flourished more rapidly than Pennsylvania. She was the youngest of the British colonies established before the eighteenth century, but it was not long before she surpassed most of her elder sisters in population, agriculture, and general prosperity."* This our author justly ascribes to the genius of William Penn, who, disdaining vulgar means, dared to Geschichte von Pennsylvania, in his Erdbeschreibung und Geschichte von America, v. vi.'

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