ART. 91. SOLID OR CUBIC MEASURE: Used in measuring things having length, breadth, and thickness; as, timber, stone, earth. ART. 92. A Cube is a SOLID, having 6 equal faces, which are squares. If each side of a cube is 1 inch long, it is called a cubic inch; if each side is 3 feet (1 yard) long, as in the figure, it is a cubic or solid yard. 3 feet thick 3 feet long. 3 feet wide The base of a cube, being 1 square yard, contains 3X3=9 square feet; and 1 foot high on this base, contains 9 solid feet; 2 feet high contain 9×2=18 solid feet; 3 feet high contain 9×3=27 solid feet. Also, it may be shown that 1 solid or cubic foot contains 12×12×12=1728 solid or cubic inches. Hence, the number of small cubes in any large cube, is equal to the length, breadth, and thickness, multiplied together. ART. 93. Any solid, whose corners resemble a cube, is a rectangular solid: boxes and cellars are of this form. The solid contents of a rectangular solid are found, as in the cube, by multiplying together the length, breadth, and thickness. TABLE. 1728 cubic inches (cu. in.) make 1 cubic foot, marked cu. ft. 27 cubic feet 1 cubic yard, . cu.yd. 40 feet of round or 50 feet of town timber} 128 cubic feet 8X4×4-8 ft. 1 tun, long, 4 ft. wide, and 4ft. high. 1 cord, NOTE.-A cord foot, is 1 foot in length of the pile which makes a cord. It is 4 feet wide, 4 feet high, and 1 foot long; hence, it contains 16 cubic feet, and 8 cord feet make 1 cord. 1. Reduce 2 cu. yd. to cubic inches. 2. 28 cords of wood to cu. ft. Ans. 93312 cu. in. Ans. 3584 cu.ft. REVIEW. 91. For what is Cubic Measure used? 92. What is a cube? A cubic inch? Cubic yard? How many sq. ft. in one side of a cubic yard? How many cubic feet in a solid 3 ft. long, 3 ft. wide, and 1 ft. thick? If 2 ft. thick? If 3 ft. thick? 3. Reduce 34 cord of wood to C. ft. Ans. 272 C. ft. Ans. 221184 cu. in. Ans. 1 cu. yd. 10 cu. ft. 6. 492480 cu. in. to tn. round timber. Ans. 7 tn. 5 cu. ft. 7. How many cubic feet in a rectangular solid, 8 ft long, 5 ft. wide, 4 ft. thick? See Art. 93. Ans. 160 cu. ft. 8. How many cubic yards of excavation in a cellar 8 yd. long, 5 yd. wide, 2 yd. deep? Ans. 80 cu. yd. 9. How many cubic yards in a cellar, 18 feet long, 15 feet wide, 7 feet deep? Ans. 70 cu. yd. 10. In a pile of wood 40 feet long, 12 feet wide, and 8 feet high, how many cords? ART. 94. CLOTH MEASURE Ans. 30 C. Is used in measuring cloth, muslin, ribbons, tape, &c. 6 quarters 1 Ell Flemish, 1 Ell French, This is a species of long measure, the yard being 36 1. Reduce 19 yd. to nails. inches in both. Ans. 304 na. Ans. 168 na. Ans. 91 na. Ans. 264 na. Ans. 566 na. Ans. 9 yd. 3 qr. 3 na. Ans. 11 E. Fr. 5 qr. 3 na. Ans. 8 E. Fl. Reduce the yards to quarters; then the quarters to Ells Flem. REVIEW.-92. To what is the number of small cubes in any large cube equal? 93. What is a rectangular solid? How is the solid contents found? Repeat the Table. 94. For what is Cloth Measure used? Repeat the Table. Of what is Cloth Measure a species? 9. Reduce 9 yd. 3 qr. to Ells Flemish. Ans. 13 E. Fl. 10. 12 yd. 1 qr. to E. Fl. 11. 37 E. Fl. to yards. 12. 36 E. En. to Ells French. 13. 22 E. En. 4 qr. to Ells Fr. 14. 47 E. En. to yards. Ans. 16 E. Fl. 1 qr. ART. 95. WINE OR LIQUID MEASURE: For measuring all liquids except beer, milk, and ale The Standard Unit of Liquid Measure is a gallon of 231 cubic inches. REVIEW.-95. For what is Liquid Measure used? Repeat the Table. NOTE. What is the standard unit of Liquid Measure? 13. Reduce 30339 gi. to T. Ans. 3 T. 3hhd. 3 gal. 3 gi. 14. 10125 gi. to T. Ans. 1T. 1hhd. 1 gal. 1qt. 1pt. 1gi. 15. 3 puncheons to gills. 16. 5 pipes to quarts. 17. 5712 pt. to tierces. ART. 96. ALE OR BEER MEASURE Is generally used in measuring ale, beer, and milk. NOTE. The beer gallon contains 282 cubic inches. In most places ART. 97. TIME MEASURE. Time is a measured portion of duration. The parts into which time is divided are shown in this REVIEW.-96. For what is Beer Measure used? Repeat the Table. 97. What is Time? Repeat the Table. 3d Bk. 7 NOTE 1. The EXACT length of the SOLAR year is 365 days, 5 hours, 48 minutes, 48 seconds: but, is usually considered to be 365 days, 6 hours. Ilence, One year being regarded as 365 days, 6 hours, the odd 6 hours of each year, make, in 4 years, 24 hours, an additional day. This gives 366 days to every fourth year, called LEAP YEAR: and, All leap years may be exactly divided by 4; thus, 1848, 1852, 1856, are leap years; while 1847, 1850, 1855, are not so: and, The additional day in leap years is added to February, making this month 29 days, instead of 28, as in common years. NOTE 2.-The difference between the SOLAR year and 365 days and 6 hours, is about three-fourths of a day in 100 years, or 3 days in 400 years. Hence, For greater accuracy, it is agreed that of the centennial (hundredth) years, only those which are exactly divisible by 400 shall be leap years: thus, 1900 will be a common year, and 2000 a leap year. Teachers and advanced students will find interesting and instructive historic information on this subject in " Ray's Higher Arithmetic.” NOTE 3. The year, as used by civilized nations, is divided into 12 calendar months, and numbered in their order as follows: January, 1st month, 31 days. July, 7th month, 31 days Thirty days hath September, April, June, and November: All the rest have thirty-one, save February, which alone Hath twenty-eight; and one day more we add to it, one year in four. REVIEW.-97. NOTE 1. What is the exact length of the solar year? What are leap years? February has how many days in leap years? 2 Which of the centennial years are leap years? Why? 3. How is the year divided? Give the number of days in each month. |