NOTE. Every multiplier is an abstract number, because it merely indicates how many expressions of the multiplicand are required. Literally it is absurd to say "3 feet times 3 feet," and that is not our mental process in obtaining area. Neither do we mean "3 times 3 linear feet are 9 square feet," for that is untrue, because 3 times 3 linear feet are 9 linear feet. We mean merely that area contains as many units of area as there are abstract units in the product of the number of units of length by the number of units of breadth. ENGLISH AND UNITED STATES SURFACE MEASURE. 1. COMMON TABLE. Irregular scale of values. 144 square inches, (sq. in.,) make 1 square foot, 9 square feet, sq. ft. sq. yd. 30 square yards, or 272 square feet, 40 square rods, or perches, 4 roods, or 160 sq. rds., 640 acres, UNIT EQUIVALENTS. } 1 (sq. rd., pole,} P. or perch, NOTE 1.-Let the pupil illustrate upon the slate or blackboard the statements of the table. NOTE 2. Although the parties to any contract of work can estimate that work in any units that suit their convenience, yet artisans are accustomed to estimate their work mostly as follows: 1. Glazing and stone-cutting, by the ceiling,} 3. Flooring, partitioning, roofing, by the square, of 10 ft. square, or square foot. square yard. 100 square feet. 4. Bricklaying is generally estimated by the thousand bricks, but sometimes by the square yard, or the square of 100 square feet, provided that the work is 1 foot, or 14 bricks thick. 5. In measuring irregular work, such as mouldings, cornices, and curved surfaces in general, artisans seek to estimate the whole surface. This implies that the quantity of that surface is obtained in the units of square measure, which are flat. This is found in mouldings which are straight by making the measuring line follow all the irregularities crosswise, for one dimension, and the length is the other. In spherical and other curves, the surface is found by the rules of mensuration. 2. SURVEYORS' SURFACE MEASURE. Art. 214. Surveyors' Square Measure is used in computing the area of land, or other surveyed surfaces. NOTE. This table is based on the supposition that the chain used is Gunter's chain. If another chain is used, a table adapted to it may be easily constructed, by Art. 213. 3. METRIC SURFACE MEASURE. Art. 215. The standard of surface measure, for large surfaces, in the Metric System, is the are, (pronounced air.) It equals a square decametre, that is, a square surface, each of whose sides is 10 metres long, and is, therefore, equal to 100 square metres. It is mostly used in expressing the surface of land and water. TABLE. Regular scale of values, 100. 100 centares, (marked c.a.,) make 1 are, NOTE 1.-Centare (pronounced cent'air) is sometimes written centiare, (pronounced cent'e air.) NOTE 2. The denominations milliare, deciare, decare, kilare, and myriare are not used. A centare being a square metre, an are can be represented by a square whose side is 10 metres long, and a hectare by a square whose side is 10 times 10 metres, that is, 100 metres long. But a deciare, which would be 10 square metres of surface, cannot be represented by a square whose side is a whole number of metres. The same is true of a decare, a surface of 1000 square metres, and of a kilare, a surface of 100,000 square metres. NOTE 3.-For general purposes it is customary to express surface by the square of some denomination of linear measure. TABLE. Regular scale of values, 100. 100 sq. metres, (M2) equal 1 sq. decametre, marked D.M.' 119.6 sq. yds. 1 m.m.2 = .00155 NUMERATION. Art. 216. To read a mixed number in metric square measure, either read it as a mixed decimal of its denomination, or read the integral part as a whole number of its denomination, and the fractional part either as a decimal of that denomination, or as a whole number of its lowest denomination. NOTE.-Remember that each denomination occupies two decimal places. ILLUSTRATION.-The number 5.604237K.M." may be read as 5 square kilometres and 604237 millionths, or 5 square kilometres and 604237 square metres. III. MEASURE OF VOLUME. Art. 217. The volume of any thing is the quantity of space which it occupies. It is measured by the product of three dimensions at right angles to each other. It is often called solidity, or content, or bulk. The measure of volume is often called solid measure, in reference to solidity, the thing measured. It is also called cubic measure, because the units used in expressions of volume are cubes. A cube is a body bounded by six squares. Therefore its length, breadth, and thickness are equal. A cube takes its name from the length of one of its edges. Thus, a cubic inch is a cube each of whose edges is an inch long, or whose sides are square inches; a cubic foot is a cube each of whose edges is a foot long, or whose sides are each a square foot, &c. Art. 218. Any six-sided body, whose sides are rectangles,* contains as many cubic units of a certain name as the product of the linear units of the same name in its length, by those in its breadth, by those in its thickness. * Such a body is called a rectangular parallelopipedon. = 1 yd. X 1 yd. X 1 yd. 1 cu. yd., and 3 ft. X 3 ft. X 3 ft. = 27 cu. ft. Figure 1 represents a rectangular six-sided body, 6 inches long, 2 inches broad, and 2 inches high. Therefore one row of cubes = 12 represents 6 cubic inches, the bottom layer of 2 rows 2 X 6 cubic inches, and 2 layers 2 X 12 24 cubic inches. = Figure 2 represents a cubic yard, 3 feet long, 3 feet broad, and 3 feet high. Therefore one row of cubes represents 3 cubic feet, the bottom layer of 3 rows 3 X 3 9 cubic feet, and 3 layers 3 X 9 = 27 cubic feet. ENGLISH AND UNITED STATES CUBIC MEASURE. 1. COMMON TABLE. Irregular scale of values. 1728 cubic inches, (cu. in.,) make 1 cubic foot, 27 cubic feet, = cu. ft. 1 cubic yard, cu. yd. NOTE 1.-A cord of wood is 128 cubic feet. A pile of wood 8 ft. long, 4 ft. wide, and 4 ft. high, contains a cord, because 8 ft. X 4 ft. X 4 feet = 128 cu. ft. A cordfoot is one foot in length of such a pile, being 1 ft. long, 4 ft. wide, and 4 ft. high, 1 CORD equal to 16 cu. ft. Hence 8 cord feet make a cord. NOTE 2.-A foot in board measure is 1 ft. long, 1 ft. broad, and 1 inch thick; that is, it is a foot square of an inch board. |