Example. - If a two-inch ball weighs 2 pounds, what is the diameter of a ball that weighs twice that?

2 pounds: 4 pounds :: 2x2x2 inches: (the cube of the answer).

To find the cubical contents or weight of any solid which is similar to a given solid.

Rule. - State the question as in proportion, and cube the given sides, diameters, circumferences, or altitudes: the fourth term of the proportion is the required answer.

Examples. - If a ball 4 inches in diameter weighs 50 pounds,, what is the weight of a ball 6 inches in diameter?

4x4x4: 6x6x6:: 50 pounds: (the answer).

If a three-inch cube weighs 7 pounds, what is the weight of a four-inch cube?

3x3x3: 4x4x4:: 7 pounds: (the answer).

Mensuration.

To find the Area of a Square or Parallelogram. - Multiply the length by the breadth.

To find the Area of a Tapering Board. - Multiply the length in feet, by the breadth of the middle in inches, and divide by 12; or add together the width of the ends in inches, and multiply the length by half of this sum, and divide by 12: the result is the number of square feet contained in the board.

To find the Area of a Rhombus or Rhomboid. - Multiply the length of the side, by the breadth measured square across.

To find the Area of any Triangle. - Multiply the base by half of the perpendicular, or multiply half the base by the perpendicular.

To find the Area of a Circle. - Multiply the square of the= diameter by .7854.

To find the Circumference of a Circle. - Multiply the diameter by:3.416.

To find the Surface Area of a Globe. - Multiply the circumference by the diameter.

To find the Solid Contents of a Globe. - Multiply the surface area by 1/6 of the diameter.

To find the Area of a Ring. - Multiply the sum of the inside and the outside diameters by their difference, and multiply the product thus obtained by .7854.

To find the Side of a Square containing the Same Area as a Given Circle. - Multiply the diameter by .886227.

To find the Side of an Inscribed Square. - Multiply the diameter by .707.

To find the Area of an Ellipse. - Multiply the longer diameter by the shorter, and multiply this product by .7854.

To find the Solid Contents of a Cylinder (as a log). - Multiply the area of the end by the length.

To find the Solid Contents of Pyramids or Cones. - Multiply the area of the base by 1/3 of the height.

To find the Cubical Contents of the Frustum of a Cone (practical application, find the cubical contents of a tapering, round log). - Multiply together the diameters of the large and of the small ends, and to the product add 1/3 of the square of the difference of the diameters; then multiply this sum by .7854, which will give the average area; multiply this area by the length, and the product will be the cubical contents.