46. If 17 T. 15 cwt. 62 lb. of iron cost $1333.593, how much will 1 ton cost? 47. How many wine gallons will a tank hold, that is 4 ft. long by 3 ft. wide, and 13 ft. deep? Ans. 187 gal. 48. What will be the cost of 300 bushels of wheat at 9s. 4d. per bushel, Michigan currency? 49 What will be the cost in Missouri currency? Ans. $350. 1 50. What will be the cost in Delaware currency ? 51. What will be the cost in Georgia currency? Ans. $600. 52. What will be the cost in Canada currency? 53. Bought the following bill of goods in Boston: 6 yd. Irish linen 12 " flannel 8" calico 9 "ribbon Ars. $560. 6 gal. molasses What was the amount of the bill? Ans. $21.76 +. 54. How many pipes of Madeira are equal to 22 pipes of sherry? 55. A cubic foot of distilled water weighs 1000 ounces avoirdupois; what is the weight of a wine gallon? Ans. 8 lb. 542 oz. 56. There is a house 45 feet long, and each of the two sides of the roof is 22 feet wide. Allowing each shingle to be 4 inches wide and 15 inches long, and to lie one third to the weather, how many half-thousand bunches will be required to cover the roof? Ans. 28,5 64 57. A cistern measures 4 ft. 6 in. square, and 6 ft. deep; how many hogsheads of water will it hold? 58. If the driving wheels of a locomotive be 18 ft. 9 in. in circumference, and make 3 revolutions in a second, how long will the locomotive be in running 150 miles? Ans. 8 h. 54 min. 40 sec. 59 In traveling, when I arrived at Louisville my watch, which was exactly right at the beginning of my journey, and a correct P timekeeper, was 1 h. 6 min. 52 sec. fast; from what direction had I come, and how far? Ans. From the east, 16° 43'. 60. How many U. S. bushels will a bin contain that is 8.5 ft. long, 4.25 ft. wide, and 3 ft. deep? 61. Reduce 3 hhd. 9 gal. 3 qt. wine measure to Imperial gallons. Ans. 165.5807+ Imp❜l gal. 62. A man owns a piece of land which is 105 ch. 85 1. long, and 40 ch. 15 1. wide; how many acres does it contain? 63. A and B own a farm together; A owns of it and B the remainder, and the difference between their shares is 15 A. 68 P. How much is B's share? Ans. 38 A. 911 P. 64. At $3.40 per square, what will be the cost of tinning both sides of a roof 40 ft. in length, and whose rafters are 20 ft. 6 in. long? Ans. $55.76. 65. What is the value of a farm 189.5 rd. long and 150 rd. wide, at $31 per acre? 66. Reduce 9.75 tons of hewn timber to feet, board measure, that is, 1 inch thick. Ans. 5850 ft. 67. How many wine gallons will a tank contain that is 4 ft. long, 34 ft. wide, and 29 ft. deep? Ans. 29947 gal. 68. If a load of wood be 12 ft. long, and 3 ft. 6 in. wide, how high must it be to make a cord? 69. In a school room 32 ft. long, 18 ft. wide, and 12 ft. 6 in. high, are 60 pupils, each breathing 10 cu. ft. of air in a minute. In how long a time will they breathe as much air as the room contains? 70. A man has a piece of land 2013 rods long and 41 rods wide, which he wishes to lay out into square lots of the greatest possible size. How many lots will there be? Ans. 396. 71. A man has 4 pieces of land containing 4 A. 140 P., 6 A. 132 P., 9 A. 120 P., and 11 A. 112 P. respectively. It is re quired to divide each piece into the largest sized building lots possible, each lot containing the same area, and an exact number of square rods. How much land will each lot contain? Ans. 156 P. DUODECIMALS. 387. Duodecimals are the parts of a unit resulting from continually dividing by 12; as 1, 2, 1, 1728, etc. In practice, duodecimals are applied to the measurement of extension, the foot being taken as the unit. In the duodecimal divisions of a foot, the different orders of units are related as follows: of a foot, or 1 in. linear measure. Tof a foot, or 1" square 68 1′ (inch or prime).......... is 2 12 fourths, (""), 12 thirds 12 seconds 66 12 primes, SCALE-uniformly 12. The marks NOTES. 1. Duodecimals are really common fractions, and can always be treated as such; but usually their denominators are not expressed, and they are treated as compound numbers. 12. 2. The word duodecimal is derived from the Latin term duodecim, signifying ADDITION AND SUBTRACTION. 388. Duodecimals are added and subtracted in the same manner as compound numbers. EXAMPLES FOR PRACTICE. 1. Add 12 ft. 7' 8", 15 ft. 3' 5", 17 ft. 9′ 7′′. Ans. 45 ft. 8' 8". 2. Add 136 ft. 11' 6" 8"", 145 ft. 10′ 8′′ 5"", 160 ft. 9′ 5′′ 5"". 3. From 36 ft. 7' 11" take 12 ft. 9' 5". Ans. 443 ft. 7′ 8′′ 6"". Ans. 23 ft. 10′ 6′′. 4. A certain room required 300 sq. yd. 2 sq. ft. 5′ of plastering. The walls required 50 sq. yd. 1 sq. ft. 7′ 4′′, 62 sq. yd. 5′ 3′′, 48 sq. yd. 2 sq. ft., and 42 sq. yd. 2 sq. ft. 3' 4", respectively. Required the area of the ceiling. Ans. 97 sq. yd. 5 sq. ft. 1' 1". MULTIPLICATION. 389. In the multiplication of duodecimals, the product of two dimensions is area, and the product of three dimensions is solidity (282, 286). The product of any two orders is of the order denoted by the sum of their indices. 390. 1. Multiply 9 ft. 8' by 4 ft. 7'. OPERATION. יד 9 ft. 8' 4 ft. 5 ft. 7' 8" 44 ft. 3' 8", Ans. 38 ft. 8' = ANALYSIS. Beginning at the right, 8' x 7' 56' 4′ 8′′; writing the 8" one place to the right, we reserve the 4' to be added to the next product. Then, 9 ft. x 7+ 4′ = 675 ft. 7', which we write in the places of feet and primes. Next multiplying by 4 ft., we have 8' x 4 ft. := 32′ = 2 ft. 8′; writing the 8' in the place of primes, we reserve the 2 ft. to be added to the next product. Then, 9 ft. x 4 ft.+ 2 ft. 38 ft., which we write in the place of feet. Adding the partial products, we have 44 ft. 3′ 8′′ for the product required. Hence the RULE. I. Write the several terms of the multiplier under the corresponding terms of the multiplicand. II. Multiply each term of the multiplicand by each term of the multiplier, beginning with the lowest term in each, and call the product of any two orders, the order denoted by the sum of their indices, carrying 1 for every 12. III. Add the partial products; their sum will be the required answer. EXAMPLES FOR PRACTICE. 1. How many square feet in a floor 16 ft. 8' wide, and 18 ft. 5' long? 2. How much wood in a pile 4 ft. wide, 3 ft. 8' high, and 23 ft. 7' long? 3. If a floor be 79 ft. 8' by 38 ft. 11', how many square yards does it contain? Ans. 344 yd. 4 ft. 4′ 4′′. 4. If a block of marble be 7 ft. 6' long, 3 ft. 3' wide, and 1 ft. 10' thick, what are the solid contents? Ans. 44 ft. 8' 3". 5. How many solid feet in 7 sticks of timber, each 56 ft. long, 11 inches wide, and 10 inches thick? Ans. 299 ft. 5' 4". 6. How many feet of boards will it require to inclose a building 60 ft. 6' long, 40 ft. 3' wide, 22 ft. high, and each side of the roof 24 ft. 2', allowing 523 ft. 3' for the gables, and making no deduction for doors and windows? Ans. 7880 ft. 5'. CONTRACTED METHOD. 391. The method of contracting the multiplication of decimals may be applied to duodecimals, the 'only modification being in carrying according to the duodecimal, instead of the decimal, scale. 1. Multiply 7 ft. 3' 5" 8" by 2 ft. 4' 7" 9"", rejecting all denominations below seconds in the product. OPERATION. 7 ft. 3' 5" 8"" 9" 7" 4' 2 ft 14 ft. 6' 11" 2 ft. 5' 2" 4' 3" 5" ANALYSIS. We write 2 ft., the units of the multiplier, under the lowest order to be reserved in the product, and the other terms at the left, with their order reversed. Then it is obvious that the product of each term by the one above it is seconds. Hence we multiply each term of the multiplier into the terms above and to the left of it in the multiplicand, carrying from the rejected terms, thus; in multiplying by 2 ft., we have 8′′ × 2 ft. 16/= 1' 4'', which being nearer 1′′ than 2′′, gives 1" to be carried to the first contracted product. In multiplying by 4', we have 5′′ × 4′ = 20'' = 1'' 8''', which being nearer 2 than 1, gives 2 to be carried to the second contracted product, and so on. = 17 ft. 4' 9", Ans. EXAMPLES. FOR PRACTICE. 1. Multiply 7 ft. 3' 4" 5"" by 5 ft. 8' 6", extending the product only to primes. Ans. 41 ft. 7'± |