The characteristics of the "New Arithmetic," which have given the work so great populari y, are too well known to require any notice here. These, it is believed, vill be found in the new work in an improved form.

One of the peculiar characteristics of the new work is a more natural and philosophical arra: gement. After the consideration of simple whole numbers, that of simp e fractional numbers should evidently be introduced, since a part of a thing needs to be considered quite as frequently as a whole thing. Again; since the money unit of the federal currency is divided decimally, Federal Money certainly ought not to precede Decimal Fractions. I has been thought best to consider it in connection with decimals. Then follow Compound Numbers, both integral and fractional, the reductions preceding the other operations, as they necessarily must. Pe centage is made a general subject, under which are embraced many particulars. The articles on Proportion, Alligation, and the Progressions v ill be found well calculated to make pupils thoroughly acquainted wit these interesting but difficult subjects.

Čare has been taken to avoid an arbitrary arrangement, whereby the processes will be purely mechanical to the learner. If, for instance, all the reductions in com non fractions precede the other operations, the pupil will have occasic 1 to divide one fraction by another long before he shall have learned the method of doing it, and must proceed by a rule, to himself perfectly ur intelligible. The studied aim has been through out the entire work to enable the ordinary pupil to understand every thing as he advances. The author is yet to be convinced that mentai discipline will be prom sted, or any desirable end be subserved, by conducting the pupil thro gh blind, mechanical processes. Just so far as he can understand, ar d no farther, is there prospect of benefit. No good results from pre enting things, however excellent in themselves, if they are beyond the comprehension of the learner.

Those teachers who prefer to examine their classes by questions, will find that little will esc pe the pupil's attention, who shall correctly answer all those in the present work, while teachers who practise the far superior method of recitation by analysis, will find the work admirably adapted to their purpose.

The examples, it is hoped, will require very full applications of the principles.

Many antiquated things, which it has been fashionable to copy in arithmetics, from time immemorial, have been omitted or improved, while new and practical matter has been introduced. A Key to this revision is in progress.

With these remarks, the work is submitted to the candid examination of the public, by THE AUTHOR.

Keene, N. II, February, 1848.

SUGGESTIONS TO TEACHERS.

1

THE writer compies with the request of the venerable author of " Adums' Arithmetic," to preface the new work wit a few suggestions to nis associates in the work of instruction. Though he has been engaged for sometime past in assisting to make the work better fitted to accomplish its design, he is perfectly satisfied that mprovement in school education is rather to be sought in improved use of the books which we now have, than in making better books. Better arithmeticians would be made by the book as it was before the prese it revision, using it as it might be used, than will probably be made in 1 ost cases with the new work, even though the former were very defec ive, the latter perfect. Exertion, then, to bring teachers to a higher s andard, will be more effective in improving school education, than a y efforts at improving school books can possibly be. It is here where the g eat improvement must be sought. Without the cooperation of competer teachers, the greatest excellences in any book will remain unnoticed, nd unimproved. Pupils will frequently complain that they have never found one that could explain some particular thing, of which a full explanation is given in the book which they have ever used, and their a tention only needed to have been called to the explanation.

Then let teachers make themselves, in the first place, thoroughly acquainted with arithmetic. The idea that they can "study and keep ahead of their classes," is an absurd one. The must have surveyed the whole field in order to conduct inquirers ove any part, or there will be liability to ruinous misdirection. Young teac ers are little aware of their deficiencies in knowledge, and still less ware of the injurious effects which these deficiencies exert upon pu] ls, who are often disgusted with school education, because they are n. ade to see in it so little that is meaning.

In the next place, let no previous familiarity ith the subject excuse teachers from carefully preparing each lesson before meeting their classes. Thereby alone will they feel that fresh less of interest, which will awaken a kindred interest among their pupil; and if on any occasion they are compelled to omit such preparatio, they will discover a declining of interest with their classes. Teachers who are obliged to have their books open, and watch the page while heir classes recite, are unfit for their work.

Pupils should be taught how to study. That, after all, is the great object of educating. The facilities for merely acquiring knowledge are abundant, if persons know how to improve them. The members of classes will often fail in recitation, not because ey have not tried, but have not known how to get their lesson. They eglect trying, because they can do so little to advantage. They may read over a statement in their book a dozen times, they say, but cannot remember it, — because they do not understand it. An hour spent with each pupil individually

in questioning him on the meaning of each sentence, which he may be required to read, will be of incalculable advantage.

When pupils shall have been taught how to study, let them be re quired to get their lessons, and recite them. If the present book is no thought by teachers to contain a sufficient description, and a sufficien explanation of everything, let them try to find one that does, for if pupils present themselves before the blackboard at the time of recitation, with the expectation that the teacher is to explain to the class, and help them through with what they cannot go through themselves, they will not feel that they must have studied themselves; and the paltry oralizing of the teacher will not be listened to, or if heard, will not be understood, or at best, not retained in memory. Pupils may be made to see things for the moment, while no abiding impression will remain on their minds. They will often proceed, in such a manner, through a book. and, with the mistaken idea that they understand its contents, the evil of superficialism may be perpetuated by them, perhaps, as teachers. Pupils will never have a sufficient understanding of a subject till they shall have studied it carefully themselves, and mastered each part by severe personal application.

Recitation by analysis will be found more conducive to thorough scholarship than adherence to any written questions. Let the class, or any member of the class, be able to commence at the beginning and go through with the entire lesson without any suggestion from the teacher, -a thing that is perfectly practicable and easily attainable. Let pupils be called on, at the pleasure of the teacher, in any part of the class, to go on with the recitation, even to proceed with it in the midst of a subject, the topic in no case ever being named by the teacher. They will thereby become accustomed to give their attention to the recitation, and they will be profited from it, besides securing habits of attention, which will be of incalculable value.

In fine, let arithmetic be studied properly, and more valuable mental discipline will be acquired from it, than is often attained from the whole course in mathematics usually assigned by college faculties. It is not the extent, but the value of acquisitions in mathematics, which is desirable.

W. B. B.