Example. In a bin with hopper the box is 5 ft. long, 5 ft. wide, 4 ft. 9 in. deep. The hopper (pyramid) is 2 ft. 6 in. deep. What is the capacity?

Capacity of bin and hopper =

181.25 cu. ft. =

146.16 bu. To find the volume of a combined round cylinder and cone that is, the capacity of a steep tank with hopper and similar vessels (approximate formula).

Add the volumes of the cylinder and of the cone.

Example. In a steep tank, the tank proper (cylinder) measures 6 ft. diameter and 4 ft. depth, the hopper (inverted cone) 2 ft. depth. What is the capacity?

Vol. of cylinder 6 × 0.7854 = 28.2744 X 4 = 113.0976 cu. ft. Vol. of cone = 63 X 0.7854 X % =

Capacity of steep tank and hopper =

18.8496 cu. ft.

131.9372 cu. ft. = 106.4 bu.

The brew-kettle is a vessel of wholly irregular shape, from a geometrical point of view. Its shape varies according to the requirements of the brewery, sometimes being broader and more shallow, and again deeper and more slender. The measurements given in the subjoined table are not intended to give the net contents of kettles, but the net brewing capacity, according to the methods customary among coppersmiths, which are almost entirely empirical. Thus, for a 100-barrel kettle, the bottom

diameter (B) is 8 feet 6 inches, the largest diameter (A) is 10 feet 6 inches. This gives a mean diameter of 9 feet 6 inches. The height of the shell (D) is 6 feet. Treating the vessel like a

=

cylinder of the mean diameter of 9 feet 6 inches, the capacity is (9′ 6′′)2 X 0.7854 X 6 = 425.29 cubic feet 102.73 barrels of 31 gallons. The bottom below B is not figured at all, allowance being made for boiling down. Out of a copper of this size some brew

ers will turn out 115 barrels, some 110, some only 100. Architects and coppersmiths generally specify kettles large enough to allow for all methods of brewing.

It is possible to get approximate figures on the contents of a kettle by taking inside measurements at A and B and the height Dand figuring as above; then adding thereto the contents of the

bottom calculated as a spherical segment, according to this formula: Square the radius (or 2 diameter) of circle B, multiply by 3; to the product add the square of the height (C) of the segment; multiply this sum by the height (C), and this last product by 0.5236. The formula accordingly for the whole kettle would be, for inside measurements:

(A + B) × 0.78:4 X D +[()*X3+ C2] XCX 0.5236.

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There is no way of calculating the capacity of a kettle, or of any other vessel, for that matter, with mathematical accuracy. The only strictly accurate test is to fill the vessel with water and measure its contents by a meter.

Customary dimensions and capacities of kettles, fermenting and stock tubs, round and oval casks:

The standard in common commercial use in the United States is the "avoirdupois" or "commercial" pound, which contains 7,000 grains and is practically identical with the British avoirdupois pound, which is the weight of 27,7015 cubic inches of distilled water in air at 39.2° F. with a barometer of 3c inches. While the pound is the theoretical standard, the practical unit is the grain, which is equal in Troy, apothecaries' and avoirdupois or commercial weight.

MEASURES OF CAPACITY.

The measures of capacity in use in the United States have no exact equivalent in the measures of any other country. While many names are derived from the British, and, in some cases, are identical with the same, their values, as a rule, are quite different.

The units of capacity are the "gallon" for liquids and the "bushel" for dry measure.

The "standard liquid gallon" of the United States contains 231 cubic inches and is equal to 8.3389 pounds avoirdupois of pure water at 39.2° F. at a barometer of 30 inches. The "half peck" or "dry gallon" contains 268.8 cubic inches. The "imperial gallon" of Great Britain contains 277.274 cubic inches, being the volume occupied by 10 pounds of water weighed in air at 62° F. and 30 inches barometric pressure, and is equal to about 1.2 United States liquid gallons.

The "standard struck bushel" of the United States contains 2150.42 cubic inches (the old British Winchester struck bushel). or 1.2445 cubic feet, or 77.6274 pounds avoirdupois of pure water at 39.2° F. It is a cylindrical measure 181⁄2 inches in diameter and 8 inches deep.

A "heaped bushel," which is like the foregoing, with a heaped cone not less than 6 inches high, is equal to 14 struck bushels. The "imperial bushel" of Great Britain contains 2216.192 cubic inches, or 1.2837 cubic feet.

The United States "standard barrel" contains 31 gallons. The United States "beer barrel," according to the Internal Revenue laws of the United States, contains 31 gallons even. This should be used to measure water tanks, coppers, coolers, etc., as well as chip casks, fermenting tubs, etc.

METRIC SYSTEM.

The metric system is compulsory in France, Germany, Austria Hungary, Belgium, Spain, Portugal, Italy, Norway, Sweden. Switzerland, Servia, Roumania, Mexico, Brazil, Peru, Venezuela and the Argentine Republic. It is legalized but not compulsory in the United States (act of 1866), Great Britain, Denmark and Japan. In the United States, however, and in Great Britain, both custom and the greater convenience of com putation-aside from notation-in the duodecimal over the decimal system have prevailed to maintain the old customary standards in common use. The Federal government has furnished exact metric standards to the several states. The metric sys tem is used extensively in scientific work, as it requires no adaptation of different national standards, and thus facilitates the mutual exchange of scientific research in different countries The metric unit is the meter, which was intended to be the

I

ten-millionth part (10000,000) of the earth's quadrant, i. e., of that part of a meridian from either pole to the equator. After this length was obtained and a set of standards prepared and deposited in the archives of France, it was discovered that errors were made in the calculations. Nevertheless, the standards were left undisturbed.

The metric measures of surface and capacity are the squares and cubes of the meter, its decimal fractions or multiples. The metric unit of weight is the gram, being the weight of a cubic centimeter of pure water at 39.2° F.

By convention among the leading nations of the world an international bureau of weights and measures has been created. with its seat near Paris, which has prepared two ingots of pure platinum-iridium. From one of these a number of standard kilograms have been made, and from the other a number of standard meter bars, both derived from the standards in the French archives. Certain of these copies were preserved as international standards, and others were distributed among the contributory governments. Those sent to the United States are in the possession of the Coast and Geodetic Survey. These copies of the international prototype meter and kilogram form the basis of official metrology in the United States.