have become the melancholy objects of penury and distress through the same neglect. The best interest of youth would be essentially promoted, were this important branch of science introduced into our schools, and to constitute a prominent part of their education. The work, with its trifling errors, is now presented to the public in full confidence that it will meet the acceptance it deserves. It claims no preference to the numerous publications on this subject. The author asks that patronage only, to which it is entitled by its real merits. And if, kind reader, you can find a better treatise, freely adopt it; "At si non rectius invenire potes, hoc utere mecum ;" And in either case it will be perfectly satisfactory to THE AUTHOR. Boston, September 30, 1818. The following typographical errors have escaped timely attention, which the reader is respectfully requested to correct on the margin of the page referred to in the table of ERRATA. Page 16-Exam. 7, multiplicand, for 84 read 48. 20-Exam. 9, dividend, for 467 read 464. 26-Dry measure, for 4 gals. read 2 gals. 29-Question 18, insert 2 yds. 30-Exam. 30, after 37, insert 15. 33-Question 13, insert cwt. after 9 1-2, also, lb. after 31920. 33 15, Ans. for drs. read oz. 40-Exam. 11, Long measure, subtrahend, for 2 yds. read 4 yds. 43-Exam. 12, Time, in Ans. for 3 weeks read 0. 63-Note first, for numerator read denominator, and for denom. read numerator. 64-Question 6, for divided read multiplied. 67-Case II, line 4, for left read right. 67-Exam. 4, dele the second 2, 80-Exam. 12, in quotient, for 75 read 25. 109-Exam. 26, for 14d. read 4d. 114-Question 5, in Ans. for 86,6 2-3 read 85,5 5-9. 117-Exam. 13, Ans. for 59 gals. read 62 gals. 156-Line 7th from top, for 00 read 700. 172-Line 9th from bottom, dele 0 in dividend. 181 and 182, for proportion read proposition. 256-Personal accounts, first line, for Dr. read Cr. also in second line, for Cr. read Ds. 290-Dr. Sugar, for 589 read 549. 4-Preface, remark 5, for simplicity read similarity. 40-Exam. 10, for scru. grs. read drs. scru. 48-Exam. 4, Ans. for 1-2 read 1-4. 58-Case IX. for denominator read numerator. 78-Exam. 2, dele 0 in dividend, also 7 in quotient. 96-Second method, top line, in dollars insert 8. 167-Exchange, France, for 4 6d. sterl. exchange at par. read 2 6d. sterling. 192-Ans. 4, decimal, dele second 3. Boston, October 8th, 1818. AT the Annual Meeting of the "ASSOCIATED INSTRUCTERS OF YOUTH IN THE TOWN OF BOSTON AND ELSEWHERE," the following Report of a Committee was made and accepted, viz : "The Committee appointed by the Association to examine a Treatise, entitled, Practical Arithmetic, and a short System of Book-keeping,' by DANIEL STANIFORD, A. M.. have attended to that service, and after a careful examination, are of opinion, that it is a work, better calculated to facilitate the progress of youth, in these useful and important sciences, than any. treatise of the kind, of which we have any knowledge. Signed, JONA. SNELLING, Committee. A true copy from the records and files of the Association. Attest, THOS. PAYSON, Sec. A. I. Y. THE undersigned having attentively examined a treatise on "Bookkeeping," By Daniel Staniford, A. M. are of opinion that it is better calculated to give pupils a knowledge of the rudiments of this important science, then any one of the kind we have hitherto seen. The introduction contains a large number of valuable rules for journalizing and posting, which are too often omitted in treatises of this kind; and the several accounts in the Waste-book are so judiciously arranged as examples to each rule, that they may be readily comprehended by the learner. We sincerely hope that it will have a general circulation in our schools and academies. J. COTTING, Explanation of the Characters used in the following Work. 11+1x + Equal. The sign of equality; as 4 qrs. 1 cwt. · Divided by. The sign of Division ; as, 12÷4=3. Division is likewise expressed by numbers placed in the form of a fraction; as 27=9. Letters also placed in the form of a fraction signify that the upper letters are to be divided by the lower. : :: : The sign of Proportion; as 4: 8; 12: 24, that is, as 4 is to 8, so is 12 to 24. 72, or 32, Signifies the second power, or square. 13, or 43, Signifies the third power, or cube. ✔ Signifies the square root. 34 Signifies the cube root. Note: The number belonging to the above signs of powers, and roots, is called the index or exponent. A line or vinculum, drawn over several numbers, signifies, that the numbers under it are to be considered jointly; as 8-3+4=1 but without the line, 8-3+4=9. PRACTICAL ARITHMETIC. ARITHMETIC is the art of computing by numbers. Number is that which answers directly to the question, "How many?" and is either an unit, a multitude of units, part or parts of an unit, or a mixt expression. The whole art of Arithmetic is comprehended in the various operations of the five following rules, viz. 1. Numeration, or Notation. 2. Addition. 3. Subtraction. 4. Multiplication. 5. Division. Practical Arithmetic is the application of the preceding fundamental rules, so as to be most useful in business. NUMERATION. NUMERATION teaches to read, or write, any number. All numbers are expressed by ten characters, ures, or digits, viz. 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. first are called significant figures; the last, a nought. called figThe nine cipher, or The cipher is of no value when it stands alone, or at the left hand of a whole number; but, when annexed to any significant figure, it increases its value ten-fold. The simple value of any figure may be known by inspeetion, and the following table plainly shows the local value of any figure from the place of units towards the left hand, as far as may answer every purpose of calculation. RULE. There are three periods; the first on the right hand, Units; the second Thousands; and the third Mil lions, each of which consists of three places or figures. Reckon the third figure of each period, from the left hand, so many Hundreds, the next Tens, and the other, so many Units, of what is written over them; as the first period on the left hand, read thus, Nine hundred eighty-seven millions; the second period, Six hundred fifty-four thousands; and the other period, Three hundred and twenty-one units. It is obvious, that numbers increase in a ten-fold propor tion from the right hand towards the left; that is, any |