33. If a board be 16 in. broad, what length of it will make 7 sq. ft.? Ans. 5 ft. 34. If a hogshead contain 10 cubic feet, how many more gallons of dry measure will it contain than of beer measure? 35. How many tons in a stick of hewn timber 60 ft. long, and 1 ft. 9 in. by 1 ft. 1 in.? Ans. 2.275 tons.

71

81

bu. + of of 31 qt. from 5 bu. 331 qt.

36. Subtract

37. What is the difference between

Ans. 163 pk.

of 5 sq. mi. 250 A. 3 R.,

and 3 times 456 A. 3 R. 14 P. 25 sq. yd.?

Ans. 2 sq. mi. 254 A. 2 R. 26 P. 24§ sq. yd. 38. How many pounds of silver, Troy weight, are equivalent in value to 5.6 lb. of gold by the English government standard? Ans. 80 lb. 2 pwt. 19.2768 gr.

39. If a piece of gold is pure, how many carats fine is it? 40. In gold 16 carats fine what part is pure, and what part is alloy ?

41. A man having a piece of land containing 3844 A., divided it between his two sons, giving to the elder 22 A. 1 R. 20 P. more than to the younger; how many acres did he give to each?

Ans. 203 A. 2 R. 14 P., elder; 181 A. 0 R. 34 P., younger. 42. 4000 bushels of corn in Illinois is equal to how many bushels in New York? Ans. 3586, bu.

43. The market value being the same in both States, a farmer in New Jersey exchanged 110 bu. of cloverseed, worth $4 a bushel, with a farmer in New York for corn, worth $ a bushel, which he sold in his own State for cash. The exchange being made by weight, in whose favor was the difference, and how much in cash value?

Ans. The N. J. farmer gained 694 bu. corn, worth $46. 44. The great pyramid of Cheops measures 763.4 feet on each side of its base, which is square. How many acres does it cover? 45. The roof of a house is 42 ft. long, and each side 20 ft. 6 in. wide; what will the roofing cost at $4.62 a square?

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 33 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.

50. What will be the cost in Delaware currency? 1.

51. What will be the cost in Georgia currency? Ans. $600. 52. What will be the cost in Canada currency? Ans. $560. 53. Bought the following bill of goods in Boston:

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. 54 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. 285.

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. 3 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

Р

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 34 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 l. 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. 1 R. 28 P. How much is B's share? Ans. 38 A. 2 R. 111 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, 31 ft. wide, and 29 ft. deep? Ans. 2994 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. 3 R. 20 P., 6 A. 3 R. 12 P., 9 A. 3 R., and 11 A. 2 R. 32 P. respectively. It is required 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, 12, 144, 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:

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′′′′. Ans. 443 ft. 7′ 8′′ 6"".

3. From 36 ft. 7' 11" take 12 ft. 9' 5". 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.

=

=

= 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. 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?