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Title:  The compendious measurer: being a brief, yet comprehensive, treatise on mensuration and practical geometry. ... Adapted to the use of schools ... By Charles Hutton, ...
Author: Hutton, Charles, 1737-1823.
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By the Sliding Rule.Set 40 on C to 46.4 on D; then against24 on D stands 10.532 on D stands 19.057½ on D stands 62.0sum 91.5 ale gallons.Set 40 on C to 42.0 on D; then against24 on D stands 13.032 on D stands 23.257½ on D stands 75.0sum 111.2 wine gallons.Ex. 2. What is the content of a cask whose length is 20, the bung diameter being 16, the head diameter 12, and the diameter in the middle between them 14⅜?Answer 11.4479 ale gallons,Answer 13.9010 wine gallons.PROBLEM XVII. To find the Content of any Cask from Three Dimensions only.Add into one sum 39 times the square of the bung diameter, 25 times the square of the head diameter, and 26 times the product of the two diameters; then multi∣ply the sum by the length, and the product again by .00034/9 for ale gallons, or by .00034/11 or .00003 1/11 for wine gallons.EXAMPLES.1. Required the content of a cask whose length is 40, and the bung and head diameters 32 and 24.0