weight at 112 pounds, and the ton at 2240 pounds, and they are so reckoned at the present time in Great Britain as well as in the standard of the United States government. Most of the states of the Union have, however, passed laws fixing the values as in the table, and they are almost always so reckoned by merchants in buying and selling. 35. Troy Weight. (a.) The weight used in weighing gold, silver, and precious stones is called Troy Weight. This weight is also used in philosophical experiments. (b.) In this weight, lb. stands for pound, oz. for ounce, dwt. for pennyweight, and gr. for grain. Illustration. 13 pounds, 7 ounces, 18 pennyweights, 23 grains, may lb. oz. dwt. gr. be expressed thus: 13 lb. 7 oz. 18 dwt. 23 gr.; or thus: 13 7 18 23. (c.) The "carat," which equals four grains, is used in weighing diamonds. The term carat is also used in stating the fineness of gold, and means the twenty-fourth part of any weight of gold or gold alloy. Pure gold is “24 carats fine." Gold is 22 carats fine when of it is pure gold and 22 is alloy. 36. Apothecaries' Weight. (a.) The weight used in compounding or mixing medicines is called Apothecaries' Weight. Physicians write their prescriptions in this weight, but medicines are bought and sold by Avoirdupois Weight. TABLE OF APOTHECARIES' WEIGHT. 20 grains = 1 scruple. 3 scruples 8 drams 1 dram. 1 ounce. 12 ounces = 1 pound. To mark the denominations of this weight, we use the fol lowing characters, viz.: lb for pound, 3 for ounce, 3 for dram, for scruple, and gr. for grain. For example: 563 43 29 17 grs., would be read as 5 pounds, 6 ounces, 4 drams, 2 scruples, and 17 grains. 37. Comparison of Troy, Avoirdupois, and Apothecaries' Weights. (a.) The only difference between Troy Weight and Apothecaries' Weight is, that in the former the ounce is divided into pennyweights and grains, while in the latter it is divided into drams, scruples, and grains. The pound, ounce, and grain are the same in both weights. (b.) The value of denominations of the same name in Avoirdupois' and Troy Weights differs very materially, as may be seen from the following table, which shows the value in Troy grains of each denomination we have given in the preceding tables of weights. (c.) From the above table we should find by calculation that 144 lb. Av. = 175 lb. Tr., and 192 oz. Av. 175 oz. Tr. Therefore, 1 lb. Av. = 11 or 134 lb. Tr., and 1 oz. Av. = 131⁄2 oz. Tr. (d.) Which is the heavier, and why, 1. A pound of gold or a pound of feathers? 4. An ounce of gold or an ounce of feathers? 38. Long Measure. (a.) Distances in any direction are measured by Long (b.) In this measure, le. stands for league, m. for mile, fur. for furlong, rd. for rod, yd. for yard, ft. for foot, and in. for inches. (c.) Surveyors usually measure distances by means of a chain 4 rods in length, called Gunter's chain, or the Surveyor's chain. This chain contains 100 equal links; 25 links will, therefore, equal 1 rod, and 1 link will equal 7 39. Cloth Measure. inches. (a.) This measure is used for measuring cloth, ribbons, &c. (b.) In this measure, yd. stands for yard, qr. for quarter, and na. for nail. (c.) The yard and inch are the same in length as the yard and inch in Long Measure. 40. Square Measure. (a.) Square Measure is used for measuring surfaces. As true ideas of the nature of the right angle, rectangle, and square are essential to a just appreciation of this measure, we insert the following definitions and illustrations, leaving it with the teacher to give such others as he may deem necessary. (b.) When two lines meet at a point, their difference in direction is called the angle of the two lines. The point where they meet is called the vertex of the angle. D FIG. 1. B (c.) In this figure, the lines marked B A and B C form an angle whose vertex is at B. In reading an angle, the letter at the vertex is always made the middle one. The angle in Fig. 1 may be read either as the angle A B C, or as the angle C B A. FIG. 2. A B C (d.) In this figure there are two angles, viz., DBA and A B C. The first is the difference in direction of the two lines A B and D B, and the second is the difference in direction of the two lines A B and B C. It is evident that the first angle is larger than the second. (e.) When the two angles formed by one straight line meeting another are equal to each other, they are called right angles, and the two lines are said to be perpendicular to each other. FIG. 3. D A B (f) Suppose that the straight line D B should so meet the straight line A C as to make the adjacent angles A B D and D B C equal to each other; then A B D and D B C will each of them be right angles, and D B and A C will be perpendicular to each other. (g.) An angle greater than a right angle is called an obtuse (blunt) angle, and one less than a right angle is called an acute (sharp) angle. In Fig. 2, D BA is an obtuse angle, and A B C is an acute angle. In Fig. 1, A B C is an acute angle. (h.) A four-sided figure, having all its angles right angles, is called a rectangle. (i.) A rectangle, having all its sides equal, is called a square. A square, then, has four equal sides and four equal angles. Figs. 4 and 5 represent rectangles. Fig. 5 also represents a square. FIG. 5. FIG. 4. (j.) If a square measures a foot on each side, it is called a square foot; if it measures a yard on a side, it is called a square yard, &c. A square unit, or superficial unit, then, is any surface equivalent to a square 1 unit long and 1 unit wide. (k.) All surfaces are measured by Square Measure, that is, by the number of squares of a given size to which they are equivalent. Thus, a surface contains 5 square feet when it is equivalent to 5 squares, each measuring 1 foot on a side. (1. In this measure, Sq. M. stands for square mile, A. for acre, R. for rood, sq. rd. for square rod, sq. yd. for square yard, sq. ft. for square foot, and sq. in. for square inch. NOTE. Since a surface a unit long and a unit wide contains a square |