the press. To adapt this work to the easy use of Instructers, I have endeavoured 10 simplify the definitions and rules, so as to render them as familiar and concise as the nature of the subject admits. At the same time, I have very considerably enlarged the Original System, by the insertion of a far greater number of practical examples, especially in the ground-rules, and by the introduction of many new rules, in order to furnish our Schools with a methodical and comprehensive Treatise of Practical Arithmetic. Works of this kind have too ofien abounded with abstruse and intricate questions, more puzzling than beneficial to the learner. And some authors have dwelt 100 much on those of a trifling nature, which, when understood, afford no useful knowledge. To avoid these extremes, to feed and invigorate the mind, and thus form our youth for entering, with fair promise, on the pursuits of active life, have been my principal aims, in preparing this edition for Most of the former demonstrations have been omitted, as being little suited to enlighten the pupil, and as excluding, in such compends, matter much more conducive to the purpose of bis instruction. The book-keeping, also, has been somewhat abridged, for the admission of other matter; yet enough, it is conceived, has been retained to give the student no very imperfect idea of this branch of learning. Besides what has been substituted in place of this excluded maiter, no fewer than 51 pages have been added to the last edition. To the whole have been prefixed brief questions on all the most important parts of Arithmetic. But, instead of entering into a detail of these enlargements, I beg leave to refer the reader tu the iable of contents, or to the pages of the work itself. During the many years that I have devoted to the instruction of youth in Arithmetic, I have used various systems, all of which have just claims to scientific merit. The authors, however, have, generally, appeared to be deficient in an important point-the practical teacher's experience. They have been much too sparing of examples, more especially in the first rules. The consequence is, that the scholar is hurried through these fundamental rules faster than his comprehension and proficiency would justify: To obviale this ob. jection, has been another design in the present undertaking. Considering that, to attain a thorough knowledge of vulgar fractions, is usually too difficult a task for young students, whose progress in Arithmetic has extended only to compound division, and that the difficulty frequently results in their utter discouragement; I have, therefore, deemed it most adviseable and advantagcous to transfer these fractions (except iwo or three problems introductory to decimals) beyond equation of payments. But, as decimul fractions may be more easily acquired, are more simple, useful, and necessary, and are sooner wanted in the practical branches of numbers, I have thought it expedient to let them occupy that part of the work which they did in former editions. The other rules l have likewise aimed so to arrange, as 10 give precedence to those which are most simple and necessary, introducing the more abstruse and difficult parts last. The teacher, however, will not consider himself as being obliged to adhere strictly to this arrangement. He can, notwithstanding, take the rules in such order as he may conceive to be D. R. the most proper. } 12||Rule of Three in Vul. Frac. 160 15||Rule of Three in Dec. Frac. 161 25 Simple Interest in Decimals, 163 Compound Interest in Decimals, 167 37 or $1, at 5 and 6 per cent. Annuities at compound interest, 168 73||Application and Use of the Roots of Powers in general, 179 114|Permutation and Combination, 193 117|| Measurement of Grindstones, 201 127|| Ships' Tounage and Length of Masts, Weight of Anchor a Cable Federal Money, Addition, Subtraction, Multiplication, Division, Fractions, Double, Simple Interest, Short Practical Rules, To compute Interest on Notes, Bonds, &c. Compound Interest, Cominission, Insurance, Discount, Annuities at Simple Interest, Equation of Payments, Exchange, LA Topics for Examination in the Arithmetic. What says ure. What is Arithmetic ? What are the four fundamental Rules for its opera- Long Measure. Squure Measure. Cubic Measure, Dry Measure. Name its How expressed ? ? What to that of Great Britain ? What does the Rule of Three leach? Why so named? Why called Golden Rule? Give the rules, and notes for its operation. What is Practice? What the rule in Case first ? What says Case second, and what its rule? What are Tare and Tret ?" De. fine all its terms. When is Case first used, and what its rule ? When Case second, and what the rule ? Case third, and what the rule ? Fourth, and what the rule? What does the Double Rule of Three teach? How many terns in its questions? How distinguished ? Give the rule and notes. What is Conjoined Proportion? When is Case first used, and what ils rules ? When Case second, and what its rule? What is Barter? Its rule? What Loss and Gain ? In what instruct Merchants and traders ? How its questions solved? What its general law? What is Fellowship? Its use? What Single Fellowship? Its Rule? How proved ? What Double Fellowship ? Its Rule? What is Interest ? What the legal interest ? Define its terms. How many kinds ? What Simple? Its Rule and Note? Tell the Table of Aliquot Parts? What the Rule for Months, at 6 per cent. ? For days at ditto? What the Short Practical Rule for pounds, &c. at ditto ? How serve at 5 or 7 per cent. ? What the Short Rule for Federal Money, at 6 per cent. ? How proceed at 5 or 7 per cent.? What the first Rule to compute Interest on Notes, &c. having Endorsements? How the Rule contracted ? What the Rule in Massachusetts ? What Compound Interest ? What the Rule? What Commission and Brokerage? Whai Insurance ? What Discount ? What Present Worth ? What the Rules? What the Rule when there are several surns to be paid, kic.? What an Annuity ? How in Arrears ? What meant by Amount ? What by Present worth ? How is the Amount found at Simple Interest? How the Present Worth? What Equation of payments ? What the Rule? What known by Exchange? Tell the Table. What the Rules ? How many kinds of Vulgar Fractions ? What a Proper one ? Improper ? Single? Compound ? Mixed? How turn a whole number to a Fraction? What a Compler one? What does a fraction denote? What ils value equal to ? What meant by Common Measure? What by Common Multiple?' Give the Rules of Problem first. Of Problem second. What is Reduction of Vulgar Fractions ? Repeat the last part of the rule in Case first. What the Rule in Case second ? What in Case third ? In Case fourth ? Those in Case fifth? Tell the rule in Case si.xlh ? What the rule in Case eighth ? What are the rule and notes in Addition of Vulgar Fractions ? What in Subtraction? What in Multiplication? What in Division ? How do you proceed in the Rule of Three" in Vulgar Fractions How in the Rule of Three in Decimals ? How in the Double Rule of Three in Vulgar Fractions ? Tell the Table of Ratios in Simple Interest by Decimals. What is Ratio? How do you find the Interest ? What the Rule in Case second ? In Case third? Case fourth ? How find Interest for Days? How calculated on Cash Accounts where partial Payments are made ? How find Compound Interest by Decimals? How find Amount of an Annuity at Compound 'Interest? How its Present Worth at ditto? What is Involution ? What the first Power ? What the second? The third ? The fourth? What Evolution or Extraction of Roots ? What the Root ? Can the Root of any num. ber be found ? How approximate towards it ? What are Roois called ? What is a Square? What extracting the Square Root? What the Rules ? What when a Vulgar Fraction ? What the Rules in its Application and Use? Whal a Cube? What is, to extract the Cube Root ? What the Rule ? Wbat the note, proposition, and rule in its Application and Use? What the Rules to extract Roots generally? What the Note? When are Numbers in Arithmetical Progression? What form increasing? What decreasing ? How named? What TERMS given ? What found? What the whole num ber called? What Problem first and rule ? Second and rule? Ithird and rule? When are numbers in Geometrical Progression? What called ratio ? What Problem first and rulé ? What Problem second, Case first and rules ? What Case second, rules and note ? What does Alligation teach? How distinguished? What Alligation Medial? What the rule ? What Alternate? What the rules ? What Position ? How many kinds ? What taught by Single Position? What the rule? What by Double Position ? What the rules and note ? What Permutation? What Combination! What Problem first and rule ? Problem second and rule ? Problem third and rule ? How are Gi indstones sold? How are their Contents found? What is Superficial Measure? How made up ? What is measured by it? What Case first and rule ? Case second and rule? What the Note ? 'What a Triangle ? How ils Surfuce measured. How the Superficies of Joists and Planks found ? How measure irregular Surfaces? What a Circle ? How find circumference if diameter be given ? How diameter if circumference be given ? How find Area ? How, if circumference alone be given? How find diameder by the area ? How circumference by the area ? What is a Sector ? How measured? By Rule second? What a Segment of a Circle? How find its area ? How measure a regular Polygon? How describe an ellipse or oval ? How find its area ? What is a Sphere or Globe? How find its area ? How are solids measured ? What is a Cube? How measured ? What Case second and rule? What noted? What Case third and rule ? What a Cylinder ? How measured? What Case fifth and rule ? Case sixth and rule? Case seventh and rule? What is a Čone or Pyramid? How its solidity found? What the Note? What a frustum of a Cone? How find ils solidity, if a square pyramid? How, if a triangular pyramid ? How, if a circular pyramid, or cone? What is a Globe? How find its solid content ? Frustum of a sphere? How find its solid content ? What is Gauging ? What its rule and notes? How use the Sliding rule? How gauge round tubs ? How a square vessel ? What the Note? How find a ship's I'onnage ? What the Noie?. What Section fifth and rule? Section sixih and rule ? How find the solidity of Wood and Bark? How find the Cords in a pile of either? What the principal rules in Assessing Taxes? What the general Rules in commom Book-keeping ? What a |