This section is from the book "The English And American Mechanic", by B. Frank Van Cleve. Also available from Amazon: The English And American Mechanic.
To find the contents of the occupied part of a lying cask in gallons.
Divide the depth of the liquid, or wet inches, by the bung-diameter, and if the quotient is under .5, deduct from the quotient one-fourth of what it is less than .5, and multiply the remainder by the whole capacity of the cask; this product will be the number of gallons in the cask. But if the quotient exceeds -6, add one-fourth of that excess to the quotient, and multiply the sum by the whole capacity of the cask ; this product will be the number of gallons.
Suppose the bung-diameter of a cask, on its bilge, is 32 inches, and the whole contents of the cask 118.80 U. S. standard gallons; required the ullage of 16 wet inches.
32) 15.00 (.46875 .5 - .46875 = .03125 / .4 = .0078125 .46876 - .0078125 = .4609375 X 118.80 = 54.759375 U. S. gallons.
Required the ullage of 17 wet inches in a cask of the above capacity.
32) 17.00 (.53125 - .5 = 03125 / .4 = .0078125 + .53125 = .6390625 X 118 80 = 64040626 U. S. gallons.
64.040625 + 64.769375 = 118.80 gallons.
 
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