WM. P. SMITH, _Preceptor of Mathematics and Natural Philosophy, No. 152, South Tenth Street._ * * * * * SIR--I have carefully examined "The New Federal Calculator, or Scholar's Assistant," by Thomas T. Smiley, on which you politely requested my opinion; and freely acknowledge that I think it better calculated for the use of the United States schools and counting-houses than any book on the subject that I have seen. The author's arrangement of the four primary rules is, in my opinion, a judicious and laudable innovation, claiming the merit of improvement; as it brings together the rules nearest related in their nature and uses. His questions upon the rules throughout, appear to me to be admirably calculated to elicit the exertions of the learner. But above all, the preference he has given to the currency of his own country, in its numerous examples, has stamped a value upon this little work, which I believe has not fallen to the lot of any other book of the kind, as yet offered to the American public. I am, sir, yours respectfully, JOHN MACKAY. _Charleston, (S. C.) March 29, 1825._ * * * * * _From the United States Gazette._ Among the numerous publications of the present day, devoted to the improvement of youth, we have noticed a new edition of Smiley's Arithmetic, just published by J. Grigg. The general arrangement of this book is an improvement upon the Arithmetics in present use, being more systematic, and according to the affinities of different rules. The chief advantage of the present over the first edition, is a correction of several typographical errors, a circumstance which will render it peculiarly acceptable to teachers. In referring to the merits of this little work, it is proper to mention that a greater portion of its pages are devoted to Federal calculation, than is generally allowed in primary works in this branch of study. The heavy tax of time and patience which our youth are now compelled to pay to the errors of their ancestors, by performing the various operations of pounds, shillings, and pence, should be remitted, and we are glad to notice that the Federal computation is becoming the prominent practice of school arithmetic. In recommending Mr. Smiley's book to the notice of parents and teachers, we believe that we invite their attention to a work that will really prove an "assistant" to them, and a "_guide_" to their interesting charge. * * * * *