.455.347759 .471.363715.487.379700 .456.348755.472.364713.488 .380700 Note. The use of the foregoing Table is given in Problem XV., Rule II.; and the method of constructing it may be seen in Moss's Gauging, page 92, PART V. MENSURATION OF SOLIDS APPLIED TO GAUGING. DEFINITIONS OF SOLIDS. 1. A SOLID is a figure which generally consists of three dimensions; viz. length, breadth, and thickness. 2. The measurement of a solid is called its solidity, capacity, or content. 3. The contents of solids are estimated by a cube whose side is one inch, one foot, one yard, &c. called the measuring-unit; hence the solidity of a body is said to be so many cubic inches, feet, yards, &c. as are contained in that body. In Gauging, however, the contents of all vessels are reduced to ale gallons, wine gallons, malt bushels, &c. &c. 4. A cube is a solid having six equal square sides, 5. A parallelopipedon is a solid having six rectangular sides, every opposite two of which are equal and parallel. 6. A prism is a solid whose ends are two equal, parallel, and similar plane figures; and its sides rectangles. It is called a triangular prism when its ends are triangles; a square prism, when its ends are squares; a pentagonal prism, when its ends are pentagons, &c. 7. A cylinder is a solid conceived to be described by the revolution of a right-angled parallelogram about one of its sides, which remains fixed, and is called the axis of the cylinder; or it is a solid whose ends are parallel circles, and its sides right-lines. Note. When the parallel ends of a solid are bounded by dissimilar that is, when one end is bounded by an ellipse and the other by a circle, the figure is called a cylindroid. curves; 8. A pyramid is a solid the base of which is any plane figure whatever, and its sides are triangles, meeting in a point, called the vertex of the pyramid 9. A cone is a solid conceived to be described by the revolution of a right-angled triangle about one of its legs, which remains fixed, and is called the axis of the cone; or it is a pyramid of an infinite number of sides, having a circle for its base. Note. When the base of a cone is an ellipse, the solid is called an elliptical cone. 10. The frustum of a pyramid or cone is that part which remains when the top is cut off by a plane parallel to the base. The part cut off is called a segment. 11. A wedge is a solid whose base is a rectangle, its two ends plane triangles, and its two opposite sides ter minate in an edge. 12. A prismoid is a solid whose bases or ends are two right-angled parallelograms, being parallel but not simi lar to each other; and its sides four plane trapezoids. 13. A sphere or globe is a solid conceived to be formed by the rotation of a semi-circle about its diameter, which remains fixed, and is called the axis or diameter; or it is a solid bounded by one continued convex surface, every part of which is equally distant from a point within, called the centre. 14. The segment of a sphere is any part of it cut off by a plane. If the plane pass through the centre, it will divide the sphere into two equal parts called hemispheres. 15. The zone of a sphere is a part intercepted between two parallel planes, and if these planes be equally distant from the centre, it is called the middle zone of the sphere. 16. A circular spindle is a solid conceived to be formed by the revolution of a circular segment about its chord, which remains fixed. 17. Cylindrical hoofs or ungulas are solids formed by cutting a cylinder in different directions, and may be divided into six varieties; viz. 1st, when the cutting plane is parallel to the axis of the cylinder, and passes through both ends; 2nd, when the plane is oblique to the axis, and passes through both ends; 3rd, when the plane passes obliquely through the sides; 4th, when the plane enters the side, passes through the base, and makes the circular segment of the base less than a semi-circle; 5th, when the plane enters the side, passes through the base, and makes the segment of the base a semi-circle; and 6th, when the plane enters the side, passes through the P |