her longitude 2° 30′ in a day, how many statute miles does she sail? Ans. 172.5 mi. 36. At $5.75 a cord, what is the value of a pile of wood, 160 yd. long, 5 ft. high, 4 ft. wide? Ans. $431.25. 37. How many acres, etc., in four rectangular pieces of land, the first of which is 990 ft. long by 880 yd. wide; the second, 450 ft. square; the third, 40 rd. by 440 yd.; and the fourth, 25 chains by 16 chains?

Ans. 124 A. 2 R. 23 sq. rd. 244 sq. yd. 38. How many minutes from 4 P. M., Dec. 6, 1872, to 4 P. M., July 23, 1873 ?

39. From 3 lb. 8 oz. 16 pwt. of silver, how many spoons weighing 34 pwt. each can be made?

40. If sound moves 1120 feet in a second, in how many seconds will a thunder-clap be heard from clouds 2 mi. 160 rd. distant? Ans. 11 sec.

41. Suppose a person's income to be 2d. every minute, what will be his income in pounds, shillings, and pence, for the three spring months? Ans. £1104. 42. How many gallons in 16017 gills, wine measure? 43. How many acres in the four Middle States, New York containing 47000 square miles, New Jersey 8320, Pennsylvania 46000, and Delaware 2120 ?

44. If 8 tons of phosphorus are required for tipping 40,000,000 matches, how many grains are needed for tipping 1 match? Ans. 24 gr.

45. If the distance from the earth to the sun is 91,430,000 miles, and if a railroad connected them, in what year, month, and day (allowing for leap-years), would a train. starting from the earth at noon, Jan. 1, 1874, and travelling 30 miles an hour, reach the sun? Ans. Sept. 5, 2221.

46. At 8 cents a pound, what is the cost of 1 T. 3 cwt. 15 lb. of nails? Ans. $185.20. 47. What is the capacity, in cubic inches, of an ice

house, 6 yd. high, 30 ft. long, and 18 feet wide; and what is the value of the ice it will hold, allowing a ton of ice to measure 36 cubic feet, and to be worth $3.50 ?

Last ans. $945.

48. Reduce 14 39 31 02 gr. 15 to grains.

49. If a barrel of flour were retailed in pounds Troy, in stead of pounds avoirdupois, how many pounds would it make?

50. How many bags holding 12 lb. 8 oz. can be filled from 10 bar, of salt bought at the N. Y. State works?

51. What is the distance of a star of the second magnitude, whose light is 28 years of 365 days in reaching the earth, light travelling at the rate of 185000 miles a second? Ans. 163468368000000 mi.

52. An apothecary puts up 10 lb. avoir. of Rochelle salts in ounce parcels. How many more parcels will he make, if he uses avoirdupois weight, than if he uses apothecaries'? Ans. 141 parcels.

53. How many hands, how many span, how many paces, how many lines, how many fathoms, how many cubits, are equivalent to 20 feet?

54. Reduce to nails 6 yards 1 quarter 1 sixteenth.

55. If 1 bu. 2 pk. of rye are required for sowing an acre, how many quarts are needed for sowing a rectangular field 484 feet by 270 ? Ans. 144 qt.

56. How many knots an hour does a vessel run, which sails due south, and changes her latitude 1' every 10 minutes?

5%. What cost 9 cwt. 15 lb. of cheese, at 11 c. a pound, Canada money?

58. If a cubic inch of distilled water weighs 252.458 gr., what is the weight of a cubic foot of distilled water, in pounds, etc., Troy; and what in pounds avoir.?

First ans. 75 lb. 8 oz. 16 pwt. 23.424 gr.

59. Reduce 19.61 chains to inches.

60. What is the weight in grains Troy of a diamond weighing 75 carats ?

61. How many grains in the following mixture: Pulverized cubebs, ss.; muriate of ammonia, 3 vij.; pulverized liquorice, white sugar, and gum-acacia, āā 3 iij.? Ans. Gr. 4980.

62. How many seconds are there in 4 solar years? 63. Reduce 3367 yd. to inches; to statute miles, etc.; to geographical miles. Last ans. About 1.66 geo. mi.

64. An apothecary buys 4 lb. avoir. of a certain drug, for $12.50 a pound, and retails it so as to bring him in $13.25 a pound apothecaries'. What is his profit on the whole ? Ans. $14.41.

65. At $1 a square yard, what will oil-cloth cost for a room 20 ft. by 18 ft. ?

66. How many bushels of potatoes can be put in a rectangular bin, 10 ft. long, 5 ft. wide, and 4 ft. high?

Ans. 160.7+ bu. 67. What is the profit or loss on 1 lb. 8 oz. avoir. of a drug bought for $2 an ounce avoir., and sold for $2.20 an ounce apothecaries'? Ans. 12 c. profit. 68. A rectangular lot of 25 acres is 100 rd. long; how broad is it? Ans. 40 rd.

Area = length breadth (Art. 333). Hence, if the area in square rods is divided by either factor in rods, the quotient will be the other factor in rods.

69. What length must be given to a rectangular lot 360 ft. wide, to make it contain 3 acres?

70. How wide is a rectangular strip of land having an area of 14 sq. mi. and a length of 2400 yd.?

71. What will it cost to carpet a room 13 ft. 6 in. wide and 24 ft. long, with carpeting & yd. wide, at $1.60 a yard? Ans. $76.80.

72. Sold 15 T. 4 cwt. wheat, at $1.75 a bushel; 36 T. 8 cwt. corn, at 65 c. a bushel; and 8T. oats, at 55 c. a bushel. What did the bill amount to? (Art. 323.)

Ans. $2007.25.

73. 450 bushels of wheat, averaging 57 bushel, changed hands in New York at $1.60 much did it bring?

lb. to the

bu. How

Ans. $690.

74. What will it cost to pave a court 36 ft. square, at $1.75 a square yard?

75. Change August 14th 15 h. 16 min., astronomical time, to civil time.

76. A rectangular cistern 4 ft. by 4 ft., and 12 ft. deep, will hold how many barrels ?

Ans. 45

bar.

77. Reduce to higher denominations 14524272 sq. in.; 189570 in. First ans. 2 A. 1 R. 10 sq. rd. 144 sq. yd. 78. Reduce to minims Cong. j. O.iij. f3 xij. f3 vj. 79. A grocer bought 3 bu. of chestnuts for $2.50 a bu., and retailed them at 12 c. a quart wine measure. What was his profit?

Ans. $5.91.

80. A surveyor finds the length of a rectangular farm to be 45 ch., and its width 36 ch. How much is it worth, at $30.50 an acre? Ans. $4941.

81. Of two rectangular pieces of land, respectively 50 ch. by 34 ch. and 70 rd. by 400 rd., which is the greater, and how much? Ans. The latter, by 5 acres. 82. A rectangular cistern, 4 feet in length and 3 feet in width, has a capacity of 8 cubic yards; what is its depth?

Capacity = length × breadth × depth (Art. 339). Hence, if the capacity in cubic feet is divided by the product of two of the factors in feet, the quotient will be the other factor in feet.

83. The horizontal section of a rectangular cistern being 15 sq. ft., how deep must it be to have a capacity of 6 cubic yards?

Ans. 104 ft.

84. What length must be given to a rectangular bin 5 ft. high and 6 ft. broad, that it may hold 250 bushels? Ans. 10 ft. 438 in.

85. How many squares of a certain length and breadth are contained in a surface three times as long and three times as broad?

86. A fieid containing 14 square chains is 198 feet broad; how long is it?

Reduction of Denominate Fractions.

373. A Common Fraction or a Decimal is called Denominate when it is used in connection with a denomination; as, lb., .9 of a mile.

374. A denominate fraction, whether common or decimal, is reduced, like an integer, to a lower denomination by multiplication, to a higher denomination by division.

Ex. 1.-Reduce £

to the common fraction, and £.0003 to the decimal, of a farthing.

Multiplying by 20 reduces pounds to shillings (Art. 366), multiplying by 12 reduces shillings to pence, multiplying by 4 reduces pence to farthings. Hence,

Prove by reducing the results back to the common fraction and decimal of a pound, as in Ex. 2.

Ex. 2.-Reduce sec. to the common fraction, and .138 sec. to the decimal, of an hour.