RULE. Multiply the principal, in cents, by the number of days and point off five figures to the right hand of the product which will give the interest for the given time, in shillings and decimals of a shilling, very nearly. $cts. EXAMPLES. S. A note for 65 dollars, 31 cents, has been on interest 25 days; how much is the interest thereof in New-England currency? s. d. qrs. Ans. 65,31-6531 × 25-1,63275=1 7 2 REMARKS.-In the above, and likewise in the preceding practical Rules, (page 115) the interest is confined at 6 per cent. which admits of a variety of short methods of casting: and when the rate of interest is 7 per cent. as estalished in New-York, &c. you may first cast the interest at 3 per cent. and add thereto one sixth of itself, and the sum ill be the interest at 7 per ct., which perhaps, many times will be found more convenient than the general rule of cast ng interest. EXAMPLE. Required the interest of 751. for 5 months, at 7 per cent S. 7,5 for 1 month. 5 £. s. d. 37,5-1 17 6 for 5 months at 6 per cent. Ans. £2 3 9 for ditto at 7 per cent. A SHORT METHOD FOR FINDING THE REBATE OF ANY GIVEN SUM, FOR MONTHS AND DAYS. RULE.-Diminish the interest of the given sum for the time by its own interest, and this gives the Rebate very nearly. EXAMPLES. 1. What is the rebate of 50 dollars, for 6 mouths, at 6 per cent. ? The interest of 50 dollars for 6 months, is And, the interest of 1 dol. 50 cts. for 6 months, is Ans. Rebate, $1 44 2. What is the rebate of 150 for 7 months, at 5 pe cent. ? Interest of 1501. for 7 months, is £. s. d. Ans. £4 4 11 nearly By the above Rule, those who use interest tables in their counting-houses, have only to deduct the interest of the in terest, and the remainder is the discount. A concise Rule to reduce the currencies of the different States, where a dollar is an even number of shillings, to Federal Money. RULE. I.-Bring the given sum into a decimal expression by inspection, (as in Problem I. page 80) then divide the whole by 3 in New-England, and by,4 in New-York currency, and the quotient will be dollars, cents, &c. EXAMPLES. 1. Reduce 541. 8s. 31d. New-England currency, to fo leral money. ,3)54,415 decimally expressed. Ans. $181,38 cts. 2. Reduce 7s. 113d. New-England currency, to federal noney. 7s. 11 d. £0,399 then,,3),399 Ans $1,33 3. Reduce 5137. 16s. 10d. New-York, &c. currency, to federal money. ,4)513,842 decimal. Ans. $1284,60 4. Reduce 19. 53d. New-York, &c. currency, to Fedeal Money. ,4)0,974 decimal of 19s. 53d. $2,43 Ans. 5. Reduce 647. New-England currency, to Federal Money. ,3)64000 decimal expression. $213,33 Ans. NOTE. By the foregoing rule you may carry on the decimal to any degree of exactness; but in ordinary practice, the following Contraction may be useful. RULE II. To the shillings contained in the given sum, annex 8 times the given pence, increasing the product by 2; then divide the whole by the number of shillings contained in a dollar, and the quotient will be cents. EXAMPLES. 1. Reduce 45s. 6d. New-England currency, to Federal Money. 6×8+2=50 to be annexed. 6)45,50 or 6)4550 $7,583 Ans. 758 cents. $ cls. 7,58 2. Reduce 27. 10s. 9d. New-York, &c. currency, to 9×8+2=74 to be annexed. l'ederal Money. Then 8)5074 Or thus, 8)50,74 $cts. 634 cents. 6 34 Ans. $6,34 Ans. N. B. When there are no pence in the given sum, you must annex two ciphers to the shillings; then divide as be fore, &c. 3. Reduce 31. 5s. New-England currency, to Federal Morey 31. 3s --65s. Then 6)6500 Ans. 1083 cents. SOME USEFUL RULES, FOR FINDING THE CONTENTS OF SUPERFICES AND SOLIDS. SECTION 1.-OF SUPERFICES. The superfices or area of any plane surface, is compor sed or made up of squares, either greater or less, according to the different measures by which the dimensions of the figure are taken or measured :—and because 12 inches it length make I foot of long measure, therefore, 12×12=144 the square inches in a superficial foot, &c. ART. I. To find the area of a square having equal sides RULE. Multiply the side of the square into itself and the prcduct will be the area, or content. EXAMPLES. 1. How many square feet of boards are contained in the floor of a room which is 20 feet square? 20 × 20-400 feet, the Answer. 2. Suppose a square lot of land measures 26 rods c each side, how many acres doth it contain? NOTE.-160 square rods make an acre. Therefore, 26×26=676 sq. rods, and 676÷160=4 a 36 r. the Answer". " ART. 2. To measure a parallelogram, or long square. RULE. Multiply the length by the breadth, and the product will be the area, or superficial content. EXAMPLES. 1. A certain garden, in form of a long square, is 96 feet long, and 54 wide; how many square feet of ground are contained in it? Ans. 96x54-5184 square feet. 2. A lot of land, in form of a long square, is 120 rods in ength, and 60 rods wide; how many acres are in it? 120 × 60-7200 sq. rods, then 7200. 7200=45 acres. Ans. 3. If a board or plank be 21 feet long, and 18 inches road; how many square feet are contained in it? 18 inches 1,5 feet, then, 21×1,5=31,5 Ans. Or, in measuring boards, you may multiply the length in 'eet by the breadth in inches, and divide by 12, the quoient will give the answer in square feet, &c. Thus, in the foregoing example, 21 x 18÷12=31,5 as before. 4. If a board be 8 inches wide, how much in length will make a square foot? RULE.-Divide 144-by the breadth, thus, 8)144 Ans. 18 in. 5. If a piece of land be 5 rods wide, how many rods in length will make an acre? RULE.-Divide 160 by the breadth, and the quotient wil be the length required, thus, 5)160 Ans. 32 rods in length. ART. 3. To measure a triangle. Definition. A triangle is any three cornered figure which is bounded by three right lines.* RULE. Multiply the base of the given triangle into half its perpendicular height, or half the base into the whole perpendicular, and the product will be the area. EXAMPLES. 1. Required the area of a triangle whose base or longest vide is 32 inches, and the perpendicular height 14 inches. 32×7=224 square inches the Answer. 2. There is a triangular or three cornered lot of land whose base or longest side is 511⁄2 rods; the perpendicular from the corner opposite the base measures 44 rods; how many acres doth it contain? 51,5×22=1133 square rods,=7 acres, 13 rods. * A Triangle may be either right angled or oblique; in either case the teacher can easily give the scholar a right idea of the base and perpendicu las, by marking it down on the slate, paper, &c. |