3. In 49A. 3R. 16p. how many square feet? 4. In 2171466 square feet how many acres? 5. What is the value of 365A. 3R. 17p. at $1.75 per square rod or pole? Ans. $102,439.75. 6. Sold a valuable piece of land, containing 3A. 1R. 30p., at $1.25 per square foot; what was received for the land? Ans. $187,171.87,5. 7. In a tract of land 12 miles square, how many square miles? How many acres? Ans. 92160 acres. 8. In 18A. OR. 16p. how many square feet? Ans. 788436 square feet. 9. Purchased 48A. 3R. 14p. of land for $2.25 per square rod, and sold the same for $3.15 per square rod; what did I gain by my bargain? Ans. $7032.60. CUBIC OR SOLID MEASURE. ART. 94. Cubic or Solid Measure is used in measuring such bodies or things as have length, breadth, and thickness; as timber, stone, &c. NOTE 1.-A pile of wood 8ft. in length, 4ft. in breadth, and 4ft. in height, contains a cord. Also, one ton of timber, as usually surveyed, contains 5092 cubic or solid feet. QUESTIONS. How do you divide by 272? Of what denomination is the remainder? How is the true remainder found?-Art. 94. For what is cubic measure used? Recite the table. What are the dimensions of a pile of wood containing 1 cord? How many solid feet does a ton of timber contain, as usually surveyed? NOTE 2.-A cube is a solid bounded by six square and equal sides. If the cube is 1 foot long, 1 foot wide, and 1 foot high, it is called a cubic or solid foot. If the cube is 3 feet long, 3 feet wide, and 3 feet thick, it is called a cubic or solid yard. 3ft = lyd 3 ft. 1 yd. 3ft.= 27 solid feet. Hence, To find the contents of a cubic or solid body, multiply its length, breadth, and thickness together. MENTAL EXERCISES. 1. In 2 cubic feet how many cubic inches? 1. In 48 cu. yd. and 15 cu. ft. how many cubic inches? 341 97 1311 feet. OPERATION. 48 yd. 15ft. 27 10488 2622 9177 1311 Ans. 226 5 4 0 8 inches. Now, since each side of a cubic yard, as represented in the diagram, contains 9 sq. ft. of surface (Art. 93), it is plain, if a block be cut off from one side, one foot thick, it can be divided into 9 solid blocks, with sides 1 foot in length, breadth, and thickness, and therefore will contain 9 solid feet; and since the whole block or cube is three feet thick, it must contain 3 times 927 feet; for 3ft. X 3ft. X In 4 cu. ft.? In 10 cu. yd.? In 96 c. ft.? In 160 cu. ft.? 2. In 2265408 cubic inches how many cubic yards? OPERATION. 1728) 226 5 4 0 8 cu. in. 27)1311 cu. ft. Ans. 48 yd. 15ft. QUESTIONS. What is a cube? How do you find the contents of a cube? Give the reason for the operation. Describe a cubic foot. How do you reduce a ton to cubic inches? Give the reason for the operation. How do you reduce cubic inches to cubic yards? Give the reason for the operation. 3. In 45 cords of wood how many cubic inches? 4. In 9953280 cubic inches how many cords of wood? 5. How many cubic feet in a pile of wood 15ft. long, 4ft. wide, and 64ft. high? How many cords? Ans. 3C. 6 cu. ft. 6. How many cubic inches in a block of marble 4ft. long 31ft. wide, and 2ft. thick? Ans. 44928. 7. In a room 14ft. long, 12ft. wide, and 8ft. high, how many cubic feet? Ans. 1344. 8. What will 9080 cubic feet of ship-timber cost, at $11.50 per ton? Ans. $2610.50 WINE OR LIQUID MEASURE. ART. 95. Wine or Liquid Measure is used in measuring all kinds of liquids, except, in some places, beer, ale, porter, and milk. NOTE 1. By laws of Massachusetts, 32 gallons make 1 barrel. In some states 31 gallons, and in others from 28 to 32 gallons, make 1 barrel. 42 gallons make 1 tierce, and 2 tierces, 1 puncheon. NOTE 2.-The term hogshead is often applied to any large cask that may contain from 50 to 120 gallons, or more. NOTE 3.-The Standard Unit of Liquid Measure adopted by the government of the United States is the Winchester Wine Gallon, which contains 231 cubic inches. It has the name Winchester, from its standard having been formerly kept at Winchester, England. The Imperial Gallon, now adopted in Great Britain, contains 277274 cubic inches; so that 6 Winchester gallons make about 5 Imperial gallons. QUESTIONS. - Art. 95. For what is wine or liquid measure used? Repeat the table. How many gallons make a barrel? How many a tierce? How many a puncheon? How is the term hogshead often applied? What is the standard unit of liquid measure? MENTAL EXERCISES. 1. In 3 pints how many gills? In 5 pints? In 9 pints? 2. In 4 quarts how many pints? In 6 quarts? In 8 quarts? 3. In 5 gallons how many quarts? In 7 gallons? 4. How many gallons in 12 quarts? In 18 quarts? EXERCISES FOR THE SLATE. 1. In 47 tuns of wine how many gills? OPERATION. 47 tuns. 4 hhd. 1 188 hogsheads. 564 1128 11844 gallons. 4 47376 quarts. 94752 pints. 2 Pints (pt.) 4 Quarts 54 Gallons = Ans. 379008 gills. 3. Reduce 197 tuns 3hhd. 60gal. 3qu. 1pt. to gills. 4. In 1596604 gills how many tuns? 5. What will 7 hogsheads of wine cost, at 5 cents a pint? 6. What cost 18 tuns 1hhd. 47gal. of oil, at $1.25 per gallon? Ans. $5807.50. gal. 1 54 BEER MEASURE. ART. 96. Beer Measure is used in measuring beer, ale, porter, and milk. TABLE. make 66 66 2. In 379008 gills how many tuns? OPERATION. 4) 379008 gi. • 2)94752 pt. 4)47376 qt. 63)11844 gal. 4) 1 8 8 hhd. Ans. 47 tuns. 1 Quart, 1 Hogshead, qt. 1 4 216 QUESTION.-Art. 96. Repeat the table of beer measure. qt. gal. hhd. pt. 2 8 432 NOTE 1. The gallon of beer measure contains 282 cubic inches; and as has been usually reckoned, 36 gallons equal 1 barrel; 2 hogsheads, or 108 gallons, 1 butt; 2 butts, or 216 gallons, 1 tun. 1 gallon beer measure 1gall. 1pt. 3 gi. wine measure. = NOTE 2. Beer Measure is becoming obsolete. Milk and malt liquors, at the present time, are bought and sold, very generally, by wine or liquid measure. 1. How many quarts in 76 hogsheads? OPERATION. ch. 1 304 7 6 hhd. 54 EXERCISES FOR THE SLATE. 380 4104 gallons. 4 2 Pints (pt.) 8 Quarts 4 Pecks 8 Bushels 36 Bushels = Ans. 16416 quarts. 3. In 4 tuns 1hhd. 17gal. 1pt. how many pints? 4. How many tuns in 7481 pints? 5. What cost 7hhd. 18gal. of beer at 4 cents a quart? Ans. $63.36. 6. At 15 cents per gallon, what will 18hhds. of ale cost? Ans. $145.80. DRY MEASURE. ART. 97. This measure is used in measuring grain, fruit salt, coal, &c. bu. 1 = 36 = TABLE. 2. In 16416 quarts how many hogsheads?" make "66 66 60 66 pk. 1 4 144 OPERATION. 4) 16416 qt. 54) 410 4 gal. Ans. 7 6 hhd. QUESTIONS. How many cubic inches does the beer gallon contain? How do you reduce hogsheads to quarts? How do you reduce quarts to hogsheads? Art. 97. For what is dry measure used? Repeat the table. |