utmost, have given the whole solar system to the child, for his first lesson in geography. This is called setting up landmarks, and getting a general knowledge of the subject; but so far from that, in my view, it is getting no knowledge at all. It is only a confusion of words, without any definite meaning attached to them.

The subject is begun precisely at the wrong end. If it is addressed to the understanding of the young learner, this arrangement seems to presume, that he will take a deeper interest in, and better comprehend the general features of the world, embracing its largest mountains and rivers, and the characters of nations, of whose existence he has never before heard, than of the roads, hills, and rivers of his own neighbourhood, and the boundaries of his own town, county, or state. Besides, he can get no adequate idea of the magnitude of the largest mountains and rivers in the world, except by comparing them with the mountains and rivers, which he has seen, and of which he has formed some definite idea.

In forming a conception of a distant mountain or river, which we have never seen, we proceed precisely as we do in forming a conception of any other magnitude. We fix upon something of the same kind, which is known, as a unit of measure; and then compare and discover the relation of what is known, with what is unknown. So the child could form some idea of a mountain twice as high as the hill before his eyes; or he could form a tolerable

conception of a river, three times as long and as broad, as the brook, which runs before his father's door, or the river, he may, perhaps, have seen in a neighbouring town; but tell him, at once, the Himmaleh mountains in Asia, are 25,669 feet high; and the river Amazon, in South America, extends 3500 miles in length, and empties into the ocean on the equator, from a mouth of 150 miles wide, and I am much mistaken, if he forms the least conception of what he is told.

The correct plan for an elementary geography, would begin nearer home, with a description, and if practicable, with a map of the town, in which the young learner lives. Or if that is too particular for general use, the instructer must supply the description; and the map begin with his own county, or state, in which he will of course be most interested. From this he may proceed to his whole country or kingdom, and thence to more general divisions of the earth. The map will of course be reduced in its scale, and the descriptions grow less and less minute, as the places are farther removed; or from any cause, are less interesting. If I have remarked with freedom on the state of books upon this subject, it has been without reference to persons, and with the single motive of inducing those authors, to whom we are already indebted for many improvements, to examine their plans, and see if one cannot be adopted, more consonant to the principles of the youthful mind.

LETTER VI.

It would be easy to multiply examples of the inductive method of communicating knowledge upon other subjects, but I shall confine myself to one more. Arithmetick deserves the place, both because it affords an opportunity to obviate some of the prejudices, which exist against it, as a study for young learners; and at the same time, to examine the leading features of a system, already before the publick, and written upon the principle to be illustrated. Improvements in the method of teaching numbers have been more slowly made, than in any other branch of elementary instruction. This can hardly be accounted for, except that the subject has always been considered one of peculiar and intrinsick difficulties, which could not be encountered successfully, but by those few minds, favoured of Heaven, with a sort of mathematical inspiration.

Under such discouraging impressions, we need not be surprised, that no one has appeared to convince the publick by example, that the subject is not so intrinsically difficult, as has been imagined; in fact, that it is completely level to any capacity, which can comprehend any subject. The consequence of the miserable state of the books, has been, that while all

other branches have been gaining ground, and been better and better taught, arithmetick has lost, what other branches have gained; and instead of being best and most successfully taught, as its importance demands, it has been the worst, and most carelessly taught.

No adequate reason can be assigned for the declining interest of arithmetick in our schools, for the last twenty years, but the vast disparity in improvements in the books on this, and other subjects. Some variety exists in the great abundance of elementary arithmeticks, but the same general principle of communicating knowledge pervades them all. This principle is wrong. It is wrong, first, because it does not give the best knowledge of the subject; and it is wrong, secondly, because it does not afford the best discipline to the mind. These are the only purposes, for which an elementary book is studied; and a failure in both or either of these points, is capital, and fatal to the branch to be taught. The systems have been formed, no doubt, by good mathematicians, but the object of a school book, as has been before observed, is not to reduce the science to the fewest general principles, and state those principles, as a philosopher would arrange and state them for his own convenience. Adaptation to the mind, which is acquiring the science, must be ever kept in view, by the writer of a school book, which is destined to answer the only purposes for which it is written.

The plan of all arithmeticks, till quite lately, has

been, to state the principle or rule to be taught in the most concise manner possible, and then arrange under it, examples of its application. This is called the synthetick, in contradistinction to the analytic method, which begins with examples, and at length arrives at a rule. Now the first part of the process by synthesis, cannot be said to give the best, if it can be said to give any knowledge of the subject. For, what is a learner wiser after he has committed the general principle or rule to his memory? And it is impossible for him to do any thing more, without presupposing in him some knowledge of the subject. This operation in itself can, certainly, give him no knowledge; because it is an abstract principle, stated in terms, of which he has probably never heard. And if he has no ideas attached to the principal terms, of which the sentence is composed, he cannot understand the relation of the ideas, intended to be expressed in the sentence.

Should the learner, therefore, after committing a rule to his memory, be able to solve a question under it, the operation must be merely mechanical. He begins as the rule directs, and when he has read or said a sentence, he puts his finger upon the place, lest he should do the same thing again, and conforms literally with his direction. This done, he proceeds to read another sentence, and in like manner to comply with its direction, and at length out comes the answer. If any pupil is able to do better, than I have described, it is not because the rule, he has