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Gauging is measuring the capacity of casks and other round vessels. When a round vessel has the same diameter throughout, it is said to be cylindrical, or like a cylinder. The area of a cylinder is equal to square of the diameter x.7854 x height. Hence, if we take the dimensions of diameter and height in inches, to find the number of gallons we must divide the product by 231, the number of inches in a gallon. But 54.0034. Hence,

To find how many gallons a cylindrical vessel will contain,

Multiply by .0034 the product of the square of the diameter in inches by the height in inches.

Thus, a can 4 ft. high, and 12 in. in diameter, will contain 144 x 48 x .0034-23.5008=231 gals. To find how many gallons a cask will contain, Multiply by .0034 the product of the square of half the sum of the diameters, at head and bung, by the length.

Thus, a cask 22 inches in diameter at the head, and 26 inches at the bung, and 36 inches long, would contain (2622)2 x 36 x .0034-70.5024 gals.

If the cask be not full, to find the contents, stand it on end, take the height of the liquid as the height of the cask, and proceed as before.

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If beer gallons be required, multiply by 282 =.0028, nearly.

To find the capacity in bushels. Multiply by

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To find the capacity of a box or bin in bushels. Multiply together the length, breadth and height in feet, and the product by or .8.

Thus a bin 12 ft. long, 2 ft. wide, and 3 ft. high, contains 12 × 2 × 3 ×.8=57.6 bu.

To find the size of a bin necessary to hold a given number of bushels. Increase the number of bushels by one-fourth and resolve into three factors. These will be the length, breadth, and height required.

SPECIAL GOVERNMENT RULES.

NOTE.—Casks are of four varieties, according to the curvature of the staves. Their contents or capacity is estimated by using gauging instruments and extensive tables adapted to the different measurements and varieties.

To estimate the capacity of cisterns or tubs.

1ST RULE.—Multiply together the mean diameter in inches, the decimal .0034, and the depth in inches; the product will indicate the number of wine gallons.

2D RULE.-Find this sum of the square of the top diameter, the square of the bottom diameter, and four times the square of the middle diameter; one-sixth of the sum will equal the square of the true mean diameter, and this quotient multiplied by the height will give the capacity in cylindrical inches. To get wine gallons, divide by 294.

NOTES.-1. The measurements are to be made in inches and tenths of an inch.

2. A cylindrical inch is the volume of a cylinder one inch in diameter and one inch high, and is equal to .785398+ cu. in.

3D RULE.-Divide the outside mean circumference by 3.1416; from the quotient subtract twice the thickness of the staves; the remainder will be the mean diameter; then proceed as in the 1st Rule.

SPECIFIC GRAVITY.

The ratio of the weight of a certain volume of a given substance to the weight of the same volume of pure water at a temperature of 60°, is called the specific gravity of the substance. Thus a cubic foot of marble weighs about 2716 ounces; and a cubic foot of water, 1000 ounces. Hence, the specific gravity of marble is 18, or 2.716. Hence, to find the weight of a mass of iron, stone, wood, etc., we have only to find its dimensions in cubic feet, and multiply by one thousand times the specific gravity of the substance. The result will be the weight in ounces.

A table of many familiar substances is given below. Gases are compared with air instead of water. They are indicated by italics.

Chemical Elements.

The earth, with everything upon it, is formed out of certain substances, which, as they cannot be analyzed into component substances, are called Chemical Elements. There are some 65 of these at present discovered, but the more important are familiar metals, like iron and copper, the gases oxygen, nitrogen, hydrogen, etc., and such substances as carbon, sulphur, and phosphorus.

In the table below, the elements are distinguished from other substances by having their symbols and their atomic weights given. The symbols are

simply the initials of their Latin names: thus Au for aurum, Latin for gold. H,SO,, the symbol of sulphuric acid, shows that the elements which make it up are hydrogen, sulphur, and oxygen. The small figures indicate the proportion of the parts. Thus in sulphuric acid, there are two parts of hydrogen, to one of sulphur and four of oxygen. Where the elements are connected by the sign, they are simply mixed, but not combined. Thus the air, N1+0, is a mixture of four parts of nitrogen to one of oxygen.

The atomic weight indicates the proportionate weight of the single combining part of each element. To find the proportionate weights of the elements in nitrate of silver, AgNO,, we multiply the number of parts of each element by the atomic weight of that element, Thus:

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The proportion of silver in nitrate of silver is therefore 198, or, 6353. It would take 108 ounces of silver to make 170 ounces of nitrate of silver.

The constituents of many well-known substances are given below. It is hoped that the tables may prove useful. In many cases, only approximations can be given in a treatise like this.

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