area of a cube is equal to six times the square of its diameter. Cube: Cubic contents = D3 Superficial area = 6D2 To find the cubic contents of a rectangular solidFig. 70. Multiplying together the length, width and height will give the cubic contents of the rectangular solid. To find the superficial area of a rectangular solid. Multiply the width by the sum of the height and length and add to it the product of the height multiplied by the length, twice this sum is the superficial area of the rectangular solid. K -D Fig. 70. Rectangular solid: ---7-- Fig. 71. Cubic contents = D X H XL Superficial area = 2 (D (H+L) +HL) To find the cubic contents of a pyramid-Fig. 71. Multiply the area of the base by one-third the perpen dicular height and the product will be the cubic contents of the pyramid. To find the superficial area of a pyramid. Multiply the circumference of the base by half the slant height and to this add the area of the base, the sum will be the superficial area. MENSURATION OF TRIANGLES. To find the base of a right-angle triangle when the perpendicular and the hypothenuse are given-Fig. 72. Ι K--B--→ Subtract the square of the perpendicular from the square of the hypothenuse, the square root of the difference is equal to the length of the base. Base Hypotenuse2-Perpendicular2 or B=√C2—H2 To find the perpendicular of a right-angle triangle when the base and hypothenuse are given. Subtract the square of the base from the square of the hypothenuse, the square root of the difference is equal to the length of the perpendicular. Perpendicular v/Hypotenuse2-Base2 or H=√/C2—B2 To find the hypothenuse of a right-angle triangle when the base and the perpendicular are given. The square root of the sum of the squares of the base and the perpendicular is equal to the length of the hypoth enuse. Hypotenuse-Base2+Perpendicular2 C=√ B2+H2 To find the perpendicular height of any oblique angled triangle-Fig. 73. From half the sum of the three sides of the triangle, subtract each side severally. Multiply the half sum and the three remainders to Fig. 73. gether and twice the square root of the result divided by the base of the triangle will be the height of the perpendicular. To find the area of any oblique angled triangle when only the three sides are given. From half the sum of the three sides, subtract each side severally. Multiply the half sum and the three remainders together and the square root of the product is equal to the area required. Area S(S-A) (S-B) (S-C) To find the height of the perpendicular and the two sides of any triangle inscribed in a semi-circle, when -D- Rig. 74. the base of the triangle and the location of the perpendicular are given-Fig. 74. PROPERTIES OF METALS AND ALLOYS. The properties of the common metals and alloys are well marked, and the different degrees in which these qualities are possessed by the different metals and alloys render each better adapted for certain purposes than the others. These properties are: Metallic lustre, Tenacity, Ductility, Malleability, Conductivity, Fusibility, Specific gravity. Each of these qualities is of special value in its place. The capacity for taking a polish in brightening, and planishing, and finishing copper and tinned goods. Tenacity, or the strength of a metal or alloy to resist stress, pressure, pulling, bending in vessels, bars, rods, wires. Ductility, or the capacity for drawing out, upon which properly the art of wire-drawing is based. Without Malleability it would be impossible to roll thin sheets, or to flatten or raise them into curved forms. The good Conducting power of metals for heat renders them suitable for warming and domestic purposes, while their power of conducting electricity is a property of equal value, as bearing on wires and plates. Fusibility lies at the basis of all casting, but though the sheet-metal worker is but slightly interested in this branch, a knowledge of the fusibility of alloys is essential to the practice of brazing and soldering. The Specific gravities or relative weights of the metals is an important property, even from the point of view of the |