and elevated feelings naturally express their conceptions. For the most perfect exhibition of this, the world is indebted to the Romans.

When this extraordinary people retired from the scene of history, a change appears to have taken place in the character of our species. A different religion, new maxims of conduct, and new models of excellence prevailed. Such a people is not likely to exist again. Human nature has there submitted to an experiment never to be repeated.

JUVENILE STUDIES.

In tenui labor.

ON a former occasion some remarks were offered upon the difficulty and disadvantage of teaching grammar at so early a period as it is commonly attempted. The rules of that art, like those of rhetorick and logick, have been derived from the practice of the best speakers and writers. They are, therefore, subsequent to an extensive knowledge of words and phrases, and a practical acquaintance with construction. It may be said that language makes grammar, but we know of no way that grammar can make a language.

Reasons were also stated, why arithmetick, and some other branches, should precede the study of grammar in a course of elementary instruction. The present portion of this essay will be employed in pointing out what seems to be the best mode of teaching the former. The reader must not expect that a complete system of rules for this purpose, will be proposed at this time. Such hints as experience. has suggested, shall be submitted to the candor and judgment of parents and teachers. On this

subject we want facts, rather than speculation. When a sufficient number of these shall have been noticed and preserved by intelligent and careful observers, we may then hope for a plan of instruction, more complete and philosophical, and a generation of men more perfect than has yet existed; then may we hope to approximate to that perfection in the science of education and of morals, which has been attained in physicks by applying the principles of Bacon. If the following remarks have any value, it consists in the practical character, which they may be found to possess.

The

Arithmetick must be taught by example. method of invention is the best method of instruction. It begins with particular instances, and proceeds by induction to general rules. But all examples will not be equally proper for the young beginner. They should be the most simple and familiar, involving only such terms and numbers, as he is already acquainted with. He should be led on from the easiest to less easy, and finally by a just gradation to the most difficult; or, as a sage has said upon another subject, per notiora ad ignota, et non per ignota ad ignotius. In most treatises of arithmetick this method, so natural and so pleasing, is completely reversed.

A long rule, the last thing we arrived at in the process of invention, meets the learner, like a Cerberus, at the threshold; and unless he is favoured of the gods,

he cannot get well over it: unless Nature, kinder than the Sybil, comes uncalled to be his guide, it is impossible that he should without injury pass this terror of all tyros. Then follows a long and perhaps complex example, in which the learner is lost, as in a labyrinth; not being beforehand possessed of the principle, which would serve as a clue to conduct his uncertain and tardy steps. Should he apply to his teacher, he does not always receive any efficient aid. The principle is not always, as it should be, explained and demonstrated to him, but only the operation performed for him. The operation, when long, is rather a manual, than mental labour; and assistance in that merely, leaves a lad about as little qualified to encounter new difficulties, as he was before. The mind, and especially the young mind, will not long endure what is perplexing and painful. It soon becomes weary and impatient, and turns to other objects; nor will it be easily induced to approach again the source of its uneasiness. In this manner a prejudice is often imbibed against the study of the mathematicks, which it is always difficult, and often impossible afterwards to remove.

Instead of this, let the learner have the most simple questions proposed to him at first, and let such, increasing a little in difficulty, be continued, till he can invent as well as answer them. To begin with addition, supposing numeration to have been previously learnt. If you put together the four quarters of an

apple or a dollar, what will they make? Ten dimes, what will they make? Four pecks? Let a great number and variety of such questions be put, and the learner will soon see that the parts of any thing taken together are equal to the whole. This is the essential idea of addition. If proper illustrations are employed, he will immediately obtain some idea of the utility of the operation. A hundred cents, reduced to the compass of a dollar, are rendered more convenient for use: and four pecks, or three pecks and eight quarts put together, than those quantities separate. The principle. and object being thus explained, proceed to abstract numbers; and let simple questions be again proposed. Five added to two is equal to what? 7 added to 9? and so on, as far as possible, without any external help, performing the whole in the mind. This exercise, besides making the learner acquainted with the subject immediately before him, will have another excellent effect. It will accustom him to abstract and purely intellectual operations, one of the great objects of all instruction; and as he finds it more and more difficult, and at last nearly impracticable to proceed, when the numbers are many and large, he will receive with surprise and satisfaction the aid which the decimal ratio affords.

To teach the method of carrying for ten, numeration must have been perfectly learnt. The truth of it will be readily perceived. It may be well illustrated,