Very considerable advances are supposed by many to have been recently made in school-books. These pretended improvements have often consisted more of show than of substance, and much remains yet to be done, although it is not to be denied that some advances have been made. In works of this kind, there was, in former times, too little adaptation to the comprehension of the youthful mind. In recent times, school-books have been made more simple and more intelligible to children, and it is questionable whether the tendency be not, at present, to an unprofitable childishness. It is not necessary to adopt all the familiarities of children, in order to be understood by them; and the language used in instructing them should always be a little in advance of their present attainments, that they may be continually raised to a higher standard. The Roman women were peculiarly attentive to the language of their children, and by habituating them from early childhood to a pure and elevated diction, they prepared them, under great disadvantages for education, compared with those which are now enjoyed, to be either themselves distinguished orators, or if not, to be capable of apprehending the beauties and feeling the force of the highest efforts of their orators.

In school-books, a great deal of noise and useless parade has been recently made about the introduction of the 'Analytic Method.' Many persons seem to consider this improvement to be like the exchange of the logic of Aristotle for that of Lord Bacon. The analytic method begins with the particular parts of a subject, and after having surveyed them in detail, combines them into a systematic whole; while the synthetic method takes a general view of a subject, and then proceeds to an examination in detail of its several parts. Now it is a well-established opinion in metaphysical philosophy, that while the analytical mode is the only true method for the discovery of truth not always known, the synthetic system has important advantages in teaching well-settled truth. That person must be a novice in the business of communicating instruction, who has not learned that a summary, general view of a subject is an important preparation for a profitable consideration of its several parts, and that great confusion will result from attention to particular parts, without some general and connected views of the whole subject.

A great improvement was supposed to have been made, some years since, in geography, by a new method of classification and arrangement. The subjects on which it treats were associated according to their relation to each other, and not according to their relation to a particular country. Thus, a chapter would be devoted to colleges, and these institutions would be treated of in connection with each other, throughout the world, instead of being separately treated of, when the particular country in which they are 'located' was under consideration. The author of this system was Mr. William C. Woodbridge, and his larger work contains, perhaps, a greater variety of valuable matter than any work on the subject, of equal size, in the language. His geography has had a circulation sufficiently wide to satisfy a reasonable ambition, or even cupidity itself. But it is questionable whether his system of classification is, after all, the best. One principle of association is laid hold of, while another and more important principle of association is abandoned. Location of place is every thing in geography; and an association of particular facts with the country to which they belong, is more important than an association of these facts with similar facts, in other parts of the world. After an abundant trial of this plan, it is believed that public opinion is reverting back to the old method of classification. Other geographies, on a different plan, have in a considerable measure superseded Woodbridge's smaller geography, while as yet no work has been produced on a different plan, which has sufficient merit to occupy the place of his larger geography, unless the recent work of Bradford, taken chiefly from Balbi's Geography, be of this character. This work will be found to be exceedingly rich in its materials, and peculiarly lucid in its arrangement.

Among the attempted improvements in arithmetic, what is generally denominated 'mental arithmetic,' stands conspicuous. That arithmetics in former times were too abstract, too little applied to the business of life, is undoubtedly true. To obviate this, mental arithmetic has been introduced. This exercise the scholar generally commences at the beginning of his course. A little of it might not be unprofitable; but it is believed that the tendency, at present, is to give it too great a prominence. It would seem as if, in the view of some writers on this subject, the first efforts of the child in numbers should be to invent to himself rules of arithmetic, a work to which he is utterly unequal. In some recent arithmetics, vulgar fractions will be found mingled, with simple addition, and the child will be required to solve difficult questions in the former, before he is well acquainted with the latter. This is altogether preposterous. Mental arithmetic has much less application to the business of life, than is often supposed. Few men of business rely very extensively on mental calculations, in preference to their pen or their slate, for two reasons. The one is, that in written calculations there is more certainty of correctness, and the other is, that they are incapable of inventing shorter and better rules for arriving at their results, than the rules of a good arithmetic. As an exercise of the mind, mental arithmetic may serve to sharpen the ingenuity, and give vigor to the faculties. But there is another exercise, which has been strangely overlooked by the writers of arithmetics for schools, which would be superior to it as a mental discipline, and that is, a demonstration of the rules of arithmetic, in which the reasons for every operation, in every rule, should be scientifically unfolded. The scholar would thus be led, in the true analytical method, to unravel the mental process by which the inventor of the rule arrived at it as a conclusion. Not more than two or three arithmetics, intended for common schools, have attempted this, in a general and scientific manner.

Among the improvements in regard to text-books for schools, many familiar treatises on general science stand conspicuous. School-literature is taking a wider range than formerly. Even in common schools, by the introduction of such a work as the 'Scientific Class-Book' as a reading-book, two important objects would be secured at the same time; while youth are learning to read with propriety, their minds will also be stored with many of the principles of natural philosophy, astronomy, chemistry, botany, and political economy, with other important subjects. Reading-books for schools have extensively been of that character usually denominated 'light reading.' But too much light reading, it should never be forgotten, is exceedingly well calculated to make light heads. Works for the youth of our schools, should be filled with substantial and systematic knowledge.

Among reading-books for schools, the Bible holds a distinguished place; and there is reason to apprehend that, of late years, it has been too often excluded from these institutions. Moral instruction in schools is of equal importance with that which is intellectual; and no means of moral instruction can be compared to the Scriptures. And even aside from their sublime doctrines, their pure morality, their immense practical bearing upon the heart and the life, there is no book where grandeur of thought is equally combined with simplicity of language, and where lofty ideas are so completely brought down to the comprehension of children. It will hence be found, that the reading of the Scriptures will be to them the most easy kind of reading, and well calculated to produce that natural tone and manner which constitute its perfection. They contain no high-sounding words, introduced to give a factitious dignity, where real dignity is wanting; no inversion, for the purpose of surrounding an idea with a mist, which may magnify its importance. Whether the whole Bible is used, or the New-Testament only, or extracts from different parts of the whole Scriptures, may be safely left to the decision of those who are charged with the selection of school-books. Several volumes of sacred extracts, well fitted to this object, have from time to time been made; and among them, one was executed, some years since, with great judgment and taste, by Dr. McKean, Professor of Rhetoric and Oratory in Harvard University, and another, more recently, by Dr. Porter, President of the Andover Theological Seminary.

To undertake to discuss, at large, the subject of school-literature, or the merits of the more prominent text-books for schools, would greatly exceed the limits of this paper. But it is a subject of great importance, and one of which no person should be ignorant, who has any concern in the management of schools. Such is the ignorance of many teachers, and even of the most intelligent men in the community, in regard to school-books, that many works of this kind have obtained a circulation to which they are not entitled. No person of general information should suffer himself to be uninformed in regard to school-literature. School books need a literary censorship, very different from that to which they have hitherto been subject. If all the literati of the country were well versed in this matter, and would bring their opinions to bear on school-authors, a public opinion might be formed which would fix the seal of approbation on valuable school-books, and a mark of censure, which would help to consign them to speedy oblivion, on those of a different description. If teachers should not be suffered to instruct without having their qualifications put to a strict test, still less should text-books be introduced into schools, until they have undergone a still more rigid scrutiny, by persons competent to decide on their merits.

It has been suggested, in some of the public prints, that it should be the business of the superintendent of common schools to select text-books for the common schools in the state of New-York. It is questionable whether any single man could be found, to whom it would be safe to trust this important concern. De Witt Clinton himself, were he now living, would be unequal to the work, unless he were to qualify himself for it by an attention to the subject, such as he never gave. He, in conjunction with other distinguished literary men, recommended 'Bartlett's National School Manual,' a work containing many good things, but exceedingly defective as a whole. Like Pharaoh's lean kine, it is calculated to devour all other school-books, but after having done so, it would be a meagre skeleton still. The truth is, that a great majority of the most distinguished literary men in the country have devoted so little attention to school-literature, that on their recommendation of school-books but little reliance can be placed. But such ought not to be the case; for the subject is too important to be delivered over to less competent hands.

A systematic arrangement and vigilant inspection of schools, stands intimately connected with their prosperity. They are a complicated concern, and like all such concerns, they require great and systematic attention. School-houses must be provided, fitted up with neatness and convenience, and worthy of the names of temples of science. It is disgraceful to science, to have mean and incommodious school-houses, in the midst of commodious or splendid dwelling-houses. They should be well lighted, have convenient benches and desks, and at the proper season, be easily and comfortably warmed. Every teacher knows how important these things are to the successful prosecution of the business of a school. If the school-room be hung round with maps and charts, and scientific diagrams, it will be so much the better. According to the laws of association by which the course of thought in the human mind is regulated, these things will take a strong hold of the susceptible minds of children, awaken a scientific curiosity, and divert them from their play to the proper business of the school-room, as well as afford valuable aids to the teacher in the business of instruction.

A number of well-qualified and laborious inspectors constitute an essential part of every good school organization. It should be the business of these inspectors to examine into the qualifications of teachers, and to see in what manner the business of instruction is carried on. No teacher should be employed, until his qualifications have been put to a rigid test. In the case of public schools, this should be done by public authority; and in private schools, the patrons should select a suitable number of persons, competent to perform this work. 'Good recommendations,' as they are called, are obtained with such facility, and given, even by persons of respectability, with so much carelessness, that comparatively but little reliance can be placed on them.