2. Divide 93gal. Iqt. by 11 ; by 19. 3. How many barrels, each holding 2bu. 3qt. can be filled with 41bu. 2pk. of apples ? 4. Divide 119 Cong. 15 f3 3f3 by 28. 10. How many house lots, each containing 1A. 1R. 15r. can be made from a piece of land 219r. long, and 63r. wide ? 11. Divide 37 6' 6" by 9; by 13. 13. In d' of 287yd. 3qr. 2na. 2in. how many yards and decimals of a yd.? 14. What is the value of g of 7631 piastres 35 paras, at 8 cents a piastre ? 15. Subtract 91 francs 63 centimes from 1720 fr. 11c., divide the remainder by 81, and find the value of the quotient, at 18cts. a franc. DUODECIMALS. DUODECIMALS are compound numbers, in which each denomination is iż of the one above it. They are used in square and cubic measure. The denominations of Duodecimals are, the foot, or unit, the inch, or prime, marked ('), the second, or twelfth of a prime ("), the third, or twelfth of a second (""), the fourth (''), and so on. These marks are called indices. Duodecimals are added and subtracted in the same manner as other compound numbers, but multiplication and division, when both numbers contain duodecimals, present some difficulties. The product of units by units is units; units by primes give primes, units by seconds give seconds, &c. Primes by primes give seconds ; primes by seconds give thirds, &c. Generally, to the product of any two denominations, we must annex as many indices as there are in both factors. For example, 5" x 5"" is the same as is of 11x of 1 of 12 of 12. In one factor, the denominator 12 is contained twice, in the other, four times; then in their product it will be contained six times, which will be represented by 25''. For a similar reason, in division we subtract the indices of the divisor from those of the divi. dend. Then 32"" ;-8"=4". EXAMPLES FOR THE BOARD. 2066 66 2 " 3' 7" What is the product of 2 3' 7" by 9 5’ 9" 5' 11" 11"? We write the units' figure of the multiplier under the right-hand figure 8' 3" of the multiplicand, because the pro11' 5' 11" duct of any denomination by units is 2' 1" 3'"' 5'' of the same value. The product by 21 6 9' 10" 21" 5' 12ths will be 12 times smaller than that by units, the product by seconds, 12 times smaller than that by primes, and so on. We therefore write the first figure of each product under the figure by which we multiply, as in simple multiplication. When any product, or the sum of any column, is greater than 12, we reduce it to its value in higher denominations, and carry the quotient to the next column at the left. Divide 21 “ 9' 10" 2" 5''"' by 9 “ 5' 11". 9" 5' 11") 21 9' 10'' 2" 5''"(2 " 3' 7"'. 9 (units) is con18 66 11' 10" tained in 21 (units) 2 (units) times. 2 " 10' 0' 2" Multiplying and 2 6 4' 5" 9" subtracting, we have a remainder 5' 6" 5' 5"" 5' 6' 5" 5" 2“ 10' 0''. Bringing down the 21 we reduce 2 - 10' to primes, and find 34' contain 9, 3' times. Multiplying and subtracting as before, we have a remainder 5' 6" 5'", to which we annex the 5''" of the dividend. 5'6''=66" which contain 9, 7" times. Multiplying by 7", there is no remainder ; the quotient is therefore, 2 " 3' 7". These operations are so analogous to those of Simple Multiplication and Division, that they require no separate rules. 1. How many feet, &c., are there in 6 boards, each of which is 13 11' long, and 1 9' wide ? 2. How many yards of carpeting that is 2 10' wide, will cover a floor 16 feet long and 13 6' wide ? 3. A carpenter has four boards, the first of which is 12ft. long and 2ft. wide; the second, 11 9' long and 1 9 wide; the third, 12 7: long and i 11' wide, and the fourth, 13 2' long and 1 wide. How many square feet are there in the whole ? 4. How many cubic feet in a wall 19ft. 6in. long, 2ft. 3in. thick, and 4ft. bin. high ? 5. How many cubic feet of wood in a pile 16 3' long, 4 6' wide, and 8 feet high? 6. The number of square feet, &c., in a floor, is 166 9' 6" 3''' 9'', and the length of the room is 17 11' 3". What is the breadth ? 7. What is the price of a pile of wood 128ft. long, 8 9' wide, and 6 3' high, at $6.25 per cord ? 8. How much plastering is there in the ceiling of a room 21 4' long and 18 7'6" wide ? 9. How many square feet of glass in 8 windows, of 12 panes each, each pane being 1 1' long and 9' wide ? 10. Add 4 0' 3", 18 5', and 3 8' 2", subtract from the sum 13 5' 11", multiply the remainder by 5 times 4 2' 4", and divide the product by 4 2' 6". MISCELLANEOUS EXAMPLES. 1. 316%. + 24.59+1197–78,45 *12 -961= ? 2. In a certain farm that is 142.5 rods long, and 1193 rods wide, there is a pond containing 13 acres. How many acres are not covered by water? 3. The pyramid of Cheops measures 763.4 feet on each side of its base. How many acres does it cover ? 4. A farmer purchased 49A, 3R. 31r. of woodland, 565 A. of pasture, 119A. 27r. of meadow, and 38 A. of tillage. What did he give for the whole, at $28.50 per acre ?. 5. A mason builds a wall 14 11' 3" long, 2ft. thick, and 4 6' high. What will he receive for the whole, at $0.75 per foot ? 6. What would be the weight of a gold wire that would reach from Boston to Liverpool, estimating the distance at 2997m. 3fur. 28r., and the weight of the wire at 180ogr. avoirdupois, per foot? 7. The wheel of a carriage measures 13.625 feet in circumference. How many times will it revolve in going 963 miles ? 8. How many Wine gallons will fill a cubical box that is 9.7 feet long, 4ft. 5in. wide, and 83 feet high? How many Imperial gallons ? 9. What is the cost of 97. 11cwt. 3qr. of sugar, at 5d. 3qr. per pound? 10. How many bottles, each holding 10. 14f3. 28m, may be filled with 29 Cong. of mixture, and how much will be left ? 11. What part of £279 11s. is £31 9s. 62d. ? 12. How many bushels of potatoes at 2s. 6d. per bushel, will pay for 49%yd. of cloth, at £1} per yard ! 13. How many times will a seconds' pendulum tick in 3 Y. 19d. 4h.? 14. What must I pay for 3 yd. of cloth, if 25 yd. cost 433 cents ? 15. I have a tea-spoon that holds 28 drops of water. How many times must it be filled to give me llb. 12oz. of water ? 16. When wood is $5.375 per cord, wh must I рау for 19 loads, each measuring 8.3ft, long, 3.5ft. wide, and 4.25ft. high? 17. Divide .019 of .00386 by 3 of 269.03. 18. A grocer purchased 194cwt. of sugar, at 61 cents a pound, and sold the whole for $156.75. How much did he gain by the sale ? 19. Bought 95yd. 3qr. 2na. of broadcloth, at $3.50 per yard. For how much must I sell the whole to gain $35.75 ? 20. What is the least common multiple of 130, 546, 156, and 182? 21. What is the greatest common divisor of 111, 222, 333, 444, 555, 666, 777, 888, 999999 and 74 ? 22. If 47 yards of calico cost 51 shillings, what is the price of one yard ? 23. How many acres of land in a field that is 73, rods long, and 494 rods wide ? 24. If from a piece of broadcloth containing of s of 32; yards, i of of 49 yards be cut, how many yards, quarters, &c., will be left ? 25. James Anthony bought of Oliver Edwards, 126 pounds of rice, at 41 cents per pound. barrel. 26. If į of 15 bushels of wheat cost $11], what is the price of i bushel ? 27. Multiply in one line 6784.5 by 321. 29. A labourer received $1614.00 for 3y. 115 d. wages. How much was that per day? 30. If 137 yards of broadcloth cost $628, what will be the cost of 1 yard? Of 70 yards ? 31. How many arithmetics that are worth $7.50 per dozen, can I buy for $105 ? 32. 74.6 x 361.8-261.537=? 33. Bought 11e. 3C.ft. of wood, for $57.25. At what price must I sell it per cord, in order to gain $9.75 on the whole ? 34. Reduce to a common denominator s of of z of , of li, 315, and 231 35. What is the sum of 194, 27, of į of ã of 8, 128, and 6311? 36. How much must I give for 49 T. 5cwt. lqr. of flour, at $4.875 per barrel of 196 pounds ? 37. A farmer sold 54 tons of hay at $4.50 per bundle, |