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# Gauging

## diameter, measure, inches, ale, length, contents, vessels, bung, medium and multiply

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GAUGING, is the art of ascertaining the contents of casks, vats, and other re gularly formed vessels, either in wine measure, which leas 231 cubic inches to the gallon ; in ale measure, whioh has 282 to the gallon ; or in corn measure, which has 2150.42 cubic inches to the bushel. To find the contents of a vessel of a rec tilinear form, you must ascertain the number of square inches on its surface, which being divided by the foregoing numbers (according as you use wine, ale, or corn measure,) will give the contents in gallons. But in this we suppose the vessel to be only one inch in depth ; if more, the number of inches from the surface to the bottom must become a second agent in the calculation. Thus, ifa cooler be a parallelogram of 250 inches long, and 84.5 broad, these measure ments being multiplied together, will give an area of 21.125 inches, which being di vided by 282, the number of inches in an ale gallon, the result will be 74.9 gallons: or if the product had been divided by .003546, the quotient would have been 74.90925, which is much the same. We have in this case supposed the area to have perpendicular sides, only one inch in depth. If tl-le sides be six inches deep, the foregoing result, viz. 74.9, should be multiplied by 6 ; which would then give 449.4 gallons to be the measurement of the cooler. Where the sides shelve in, as in most tubs, or project out as in bell casks, regularly increasing or de creasing from the top to the bottom, the whole length at top and the whole length at bottom must be added together, and be halved, so as to give the medium length ; and the same to find a medium of the two breadths at top and bottom. These medi ums being multiplied together will give an are a,w hich, being multiplied by the depth in inches, will spew the true contents, in either wine, ale, or corn measure, accord ing to the divisor used. When the bot tom shelves equally, the measurement at the centre will be a true medium ; but if the bottom is uneven and irregular, you must take various measurements in differ ent parts ; then add the whole together, and divide by the number of measure ments, or dips, and the quotient will, in general, be a fair medium. If the vessel is triangular,.pentagonal, or anywise poly angular, the area must be ascertained by the ordinary rules in GEOXETRY, which see.

In circular vessels you must multiply the square of the diameter by .002785 for ale, or .003399 for wine : divide the former measure by 359.05, the latter by 294.12, and the quotients will be ale or wine gal lons respectively.

Where you have an oval vessel to mea sure, ascertain the transverse or longest diameter, and the cojugate, or shortest diameter; multiply them together and di vide as. above.

Prismatic vessels are measured accord ing to the first explanation, and frustrated or pyramidical vessels are disposed of in the same manner as those whose side or sides regularly augment, or vice versa. Truncated cones, likewise, come under the same rule ; only treating their termi nations as circles, instead of computing them as squares, or rectilinear bases.

The following very easy mode of ascer taining the contents of a conic frustum is given by the ingenious Newton. Mul tiply each diameter (i. e. of top and bot tom) by itself; then the one by the other, and the aggregate of those products by the altitude ; multiply also the last pro duct by 78539, (the superficial content of a circle whose diameter is 1000) ; a third part of the product is the measure of the frustum.