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.
Therefore, when vessels have their sides composed of straight ribs, proceed ing in right lines from one to the other end of the conic frustum, the measure ment is easily made ; thus we may, with out difficulty, ascertain the contents of great coppers, mashing-tubs, corn-binns, and a great variety of similar vessels. But we rarely see casks of any description formed by the union of two frustrated cones ; their usual shape is more sphe roidal; that is, they have an arched or swelling course from the bung to the chimb or end ; consequently these con . tain more than such as are truly conical. This occasions the necessity for allowing something for the bulge or swell, and of taking the diameter at the centre, be the bung and the chimb, which diameter will give a true medium. The thickness of the cask may easily be as certained by aid of calibre compasses applied to the proper part. The length of the cask may be measured internally, by putting a rod or wand in at the tap hole, and the internal diameter may be taken in a similar way at the bung ; bat such can only be done when the cask is empty, or, at least, opened for the pur pose : whereas casks that are filled and sealed must often be measured ; for this purpose the calibre compasses are ex tremely useful, since they embrace the outside measure. To correct the com putation, we must usually allow an inch and a half in the whole length, and the same in the whole diameters at the hung and chimb, thus exteriorly taken, for the thickness of the cask itself. This deduc tion being made, we must compute ac cording to the form or swell of the staves. If they be much raised, we multiply the difference between the diameter at the bung, and at the end, by .7; if less raised, or swelling, we multiply the difference by .65 ; if nearly straight, by .6, and if rectilinear, or truly conical, by .55 ; the product added to the diameter at the end, or head, will give a mean diameter. Suppose the diameter within the bung to be 32 inches, at the head 24, and that the length within be 40 ; the difference be tween 32 and 24 is 8, which, multiplied by .7, gives 5.6 ; add thereto the diameter at the head, 24, and the medium will be 29.6; multiply by the length 40, and di vide by 359.05, and the quotient will be ale gallons 97.4. And thus, with the other multipliers, according to the apparent bulge or swell between the bung and the chimb, and according to wine or ale mea sure.