S uts. The interest of 50 collars for 6 months, is 1 50 And, the interest of 1 dol. 50 cts. for 6 months, is 4 Ans. Rebate, 81 46 2. What is the rebate of 150l. for 7 months, at 5 per cent. ? fr. s. d. Interest of 1501. for 7 months, is 4 7 6 Interest of 41. is. 6d. for 7 months, is 2 61 Ans. 64 4 115 nearly. By the above Rule, those who use interest tables in ther counting-houses, have only to deduct the interest of the interest, and the remainder is the discount. a A concise Rule to redure the currencies of the different States, ?chiere a dollar is an even number of shillings, to Federal Honey. RULE I. Bring the given sum into a decimal expression by in spection, (as in Problem I. page 87) then divide the whole by ,3 in New England and by ,4 in New-York currency, and the quotient will be dollars, cente, &c. 1. Reduce 541. 8. Sid. New-England currency, to Federad Money. ,5)54,415 decimally expressed. EXAMPLES. Ans. $181,38 cts. 2. Reduce 7s. 113d. New England currency, to Fede. ral Money. 7s. 1134.=£0,599 then, ,3),599 Brs. $1,33 3. Reiluce 5131. 16s. 10d. New-York, &c. currency to Federal Miuney. ,4)515,842 decimal Ans. 81284,601 4. Reduce 19s. 53d. New-York, &c. currency, to Fede. ral money. ,4)0,974 decimal of 19s. 53d.' Money. 82,434 Ans. 5. Reduce 641. New-England currency, to Federal ,5)64000 decimal expression., $215,534 Ans. Note. By the foregoing rule you may carry on the decimal to any degree of exactness; but in ordinary prac-. tice, the following Contraction may be useful. RULE II. To the shillings contained in the given sun, arinex o times the given pence, increasing the product by %; then dividle the whole by the number of shillings contained in a dollar, and the quotient will be cents. EXAMPLES. 1. Reduce 45s. 60. New-England currency, to Fede. ral Money 6x8+2 50 to be annexed. 8 cts. 758 cents. =7,58. 2. Reduce 21. 10s. 9d. New-York, &c. currency, to Federal Money. 9x8+2=74 to be annexed. Then 8) 5074 Or thus, 8)50,74 8 cts. Ans. 634 cents.=6 34 86,34 Ans. N. B. When there are no pence in the given sum, you must annex two cyphers to the shillings; then divide as before, &c. S. Reduce 31. 5s. New-England currency, to Federal Money. Sl. 58.65s. . Then 6)6500 Ens 1086 cents AND SOME USEFUL RULES, SOLIDS. SECTION I. OF SUPERFICIES. The superficies or area of any plane surface, is composed 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 in length make 1 foot of long measure, there. fore, 12x12=144, the square inches in a superficiai 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 product 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 ? 20x20=400 feet, the Answer. 2. Suppose a square lot of land measures 26 rods on each side, how many acres doth it contain ? Note.-160 square rods make an acre. 36r. the Answer. ART. .. To measure a Parallelogram, or lopg 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 ft. long, and 54 wide; how many square feet of ground are contained in it? Ans. 96 x 54=5184 square feet. 2. A lot of land, in form of a long square, is 120 rode in length, and 60 rods wide ; how many acres are in it? 120 X 60-7200 sq. rods, then, 7220 =45 acres, Ans. 3. If a board or plank be 21 feet long, and 18 inches broad; how many square feet are contained in it: 18 inches=1,5 feet, then 21x1,5=31,5 Ins. Or, in measuring boards, you may multiply the length ju feet by the breadth ,n inches, and divide by 12, the quotient will give the answer in square feet, &ic. Thus, in the foregoing example, 21x18+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 will 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 rightIines.* RULE. Níultiply 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 side is 32 inches, and the perpendicular height: 14 inches. 32x7=224 square inches, the Answer. 2. There is a triangular or three cornered lot of land whose base or longest side is 51 } rods; the perpendicular froin the corner opposite the base, measures 44 rods; how many acres doth it contain ? 51,5 X 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 perpendicular, by marking it doux on a slate, poper, &c. TO MEASURE A CIRCLE. Art. 4. The diameter of a Circle being given, to find the Circumference. RULE. As 7 :.is to 22 : : so is the given diameter : to the circumference. Or, more exactly, As 113 : is to 355 :: &c. the diameter is found inversely. NOTE. -The diameter is a right line draw across the circle through its centre. EXAMPLES, 1. What is the circumference of a wheel whose diam. eter is 4 feet?--As 7 : 22 : :4 : 12,57 the circumfe.. Tence. 2. What is, the circumference of a circle whose diame. ter is 35 ?--As 7 : 22 : : 35': 110 Ans.--and inversely as 22 : 7 :: 110 : 55, the diameter, &c. ART. 5. To find the area of a Circle. RULE. Multiply half the diameter by half the circumference, and the product is the area ; or if the diameter is given withont 'the circumference, multiply the square of the diameter by ,7854 and the product will be the area. EXAMPLES 1. Required the area of a circle whose diameter is ra inches, and circumference 57,7 inches. 18,85=half the circumference, 6-half the diameter, 119,10 area in square inches. 2. Requires the area of a circular garden whose diameter is 11 rods? ,7854 By the second method, 11x11 = 121 Ans. 93,0334 rods. SECTION 2. OF SOLIDS. Solids arc estimated by the solid inch, solid foot, &c. 1728 of these inches, that is 12x12x12 make 1 cubic 0x solid foot. |