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vertex, perpendicular to the base, is called the hight of the pyramid.

RULE.-Find the area of the base, whether round, square, oblong, or triangular, by some one of the foregoing rules, as the case may be; then multiply this area by one-third of the hight, and the product will be the solid content of the pyramid.

EXAMPLES.

1. What is the content of a true-tapered round stick of timber, 24 feet perpendicular length, 15 inches diameter at one end, and a point at the other? 15x15x,7854×8

144

9,8175 solid feet, Ans.

To find the solid content of a frustum af a cone. What is the solid content of a tapering round stick of timber, whose greatest diameter is 13 inches, the least 61⁄2 inches, and whose length is 24 feet, calculating it by both rules?

RULE. 2-Multiply each diameter into itself; multiply one diameter by the other; multiply the sum of these products by the lengths; annex two ciphers to the product, and divide it by 382; the quotient will be the content, which divide by 144 for feet as in other cases.

(13X13)+(6,5×6,5)+(13×6,5)×2400

382

1858,115

And 1858,115÷144—12,903¡-ft, Ans.

To find the content of timber in a tree, multiply the square of of the circumference at the middle of the tree, in inches, by twice the length in feet, and the product divided by 144 will be the content, extremely near the truth. In oak, an allowance of or must be made for the bark, if on the tree; in other wood, less trees of irregular growth, must be measured in parts.

To find the solid content of a frustum or segment of a globe.

DEFINITION. The frustum of a globe is any part cut off by a plane.

RULE. To three times the square of the semi-diameter of the base, add the square of the hight; multiply this sum by the hight, and the product again by .5236; the last product will be the solid content.

EXAMPLE.

If the hight of a coal-pit, at the chimney, be 9 feet, and the diameter at the bottom be 24 feet, how many cords of wood does it contain, allowing nothing for the chimney?

24÷2-12-h'fdiam. 12x12X3-432. 9X9=81

And 432-+81X9X,5236

18,886+cords, Ans.

128 solid feet in a cord.

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QUESTION.-A stick of timber is carried by three men, one carries at the end, and the other two with a lever, How far should the lever be placed from the other end, that each man may carry equally?

RULE. Divide the length of the stick by 4, and the quotient is the answer.

There is a stick of timber, 30 feet long, to be carried by 3 men: one carries at the end, the other two carry by a lever; how far must the lever be placed from the other end, that each may carry equally? Ans. 7 feet from the end.

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Gauging is the art of measuring the capacity of casks and vessels of any form. In commerce, most of the gauging is done by the use of the diagonal rod, which gives only approximate results, but sufficiently accurate for ordinary purposes.

Ullage is the difference between the actual contents of a vessel and its capacity, or that part which is empty.

To measure small cylindrical vessels.

RULE.-Multiply the square of the diameter, in inches, by 34, and that by the height, in inches, and point off four figures; the result will be the capacity, in wine gallons and decimals of a gallon. For beer gallons multiply by 28 instead of 34.

EXAMFLE.-A can measures 15 inches in diame ter, and is 2 feet 2 inches in height. How many gal lons will it contain? 15 × 15 = 225

5850; 5850 × 34

26 height =

= 19.8900. Ans. 19 galls.

=

Casks are usually regarded as the two equal frustums of a cone, and are very accurately gauged by three dimensions as follows:

To measure a cask by three dimensions.

1st. Add the bung and head diameters in inches, and divide by 2 for the mean diameter.

2d. Multiply the square of the mean diameter by the length of the cask in inches.

3d. Multiply the last product by .0034 for wine gallons, .0028 for beer gallons.

EXAMPLE. How many wine gallons in a cask, the bung diameter of which is 22 inches, the head diameter 20 inches, and the length 32 inches?

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Note. If the cask is not full, stand it on the end, and multiply by the height of the liquid, instead of the length of the cask, for actual contents

When the cask is much bilged or rounded from the bung to the head, a more accurate way is to gange by four dimensions, as follows:

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