pupil should read it, 36 and 9, 65 and 7, 52 and I, &c. 3. Name the product of every successive pair of figures as fast as you can repeat them. Thus, in the seventh line, say 48, 32, 12, 21, &c. Next, taking three figures, increase the product of the first and second by the third, and name the result without any helping word. Thus, 68437 will suggest the following exercise: 6 times 8 and 4; 8 times 4 and 3; 4 times 3 and 7. 4. Divide each row by all the numbers up to 12, naming the quotient and remainder only. Thus, dividing 21402 by 6, say 3 and 3, 5 and 4, 6 and 4, 7. The readiest way to divide by 11, is by repeating the multiple of 11, and the figure which, added to it, will make up the number divided. Thus, in dividing 43645 by 11, say 33 and 10, 99 and 7, 66 and 8, 77 and 8. Always use the pence table in dividing by 12. Thus, taking the figures 54798, we get 54d., 4s. 6d. ; 67d., 5s. 7d.; 79d., 6s. 7d. ; 78d., 6s. 6d. ; but the pupil should only name the results, 4 and 6 pence, 5 and 7 pence, 6 and 7 pence, &c., or 4 and 6, 5 and 7, &c. SECTION V.- -WEIGHTS. Troy Weight. Troy Weight is used in weighing gold, silver, and other articles of a costly nature, in philosophical experiments, and generally where great accuracy is required. Apothecaries' Weight. Apothecaries' Weight is used in mixing medicines. The grain, ounce, and pound, are the same as the Troy grain, ounce, and pound. 20 grains (gr.) make 1 scruple (sc: or 9). 3 scruples I dram (dr: or 3). Avoirdupois Weight is used in weighing common goods. The pound Avoirdupois weighs 7,000 grains Troy; and the pound Troy weighs 5,760 grains Troy. 16 drams (dr.) make 1 ounce (oz.). Lineal Measure, or, as it is sometimes called, Long Measure, is used in measuring lines or distances. 12 inches (in.) make I foot (ft.). 3 feet 5 yards 4 poles 40 poles 1 yard (yd.). 8 furlongs (or rl 3 miles The following are sometimes used :— 3 barley-corns (b. c.) make 1 inch. 4 inches 9 inches 18 inches 6 feet 100 links Cloth Measure. Cloth Measure is used in measuring cloth and other goods sold by the yard. For this purpose the yard is divided into halves, quarters, eighths, and sixteenths. Superficial or Square Measure. A square is a figure having four equal sides, and all its angles right angles. Area or superficies is the surface enclosed by any given lines; as the area of a floor, a field, &c. I square yd. = 9 square ft. A square yard is a figure enclosed by four straight lines of 1 yard or 3 feet each. Its area is 3 × 3, or 9 square feet. In the same way it may be shown that a square foot contains 12 x 12, or 144 square inches; and a square pole, 51 × 51, or 30 square yards. 144 square inches (sq. in.) make I square foot (sq. ft.). 9 square feet 30 square yards I square yard (sq. yd.). This measure is used in measuring flooring, paving, &c., and the following for Land Measure. 40 square poles make 1 rood (r.). 4 roods I acre (a.). 100,000 square links Solid or Cubic Measure. A cube is a solid enclosed by six equal square I cubic yard 27 cubic feet. sides. For instance, a box having six equal square sides, or a die, to play with, is a cube. The content of a solid is the space enclosed by any given surfaces. A cubic yard is a solid whose length, breadth, and thickness are each 1 yard, or 3 feet, and the content is 3 × 3 × 3, or 27 cubic feet. In the same way it may be shown that a cubic foot contains 12 x 12 x 12, or 1,728 cubic inches. The length, breadth, and thickness of cubic or solid bodies-such as timber, stone, &c.—are measured by lineal measure; and these dimensions multiplied together give the solid content 1,728 cubic inches (c. in.) make 1 cubic fcot (c. ft.). 27 cubic feet (c. ft.) I cubic yard (c. yd.). N.B.-A cubic foot of water weighs 1,000 ounces avoirdupois. Measure of Capacity. When one vessel holds more than another, it is said to have greater capacity; the word capacity here signifying room or space. Measures of capacity may be divided into two classes-Measures of Liquids, and Measures of Dry Goods. Liquid Measures.-Wine Measure. Wine Measure is used in measuring wines, and all other liquids except malt liquors and water. |