To find the contents of the occupied part of a lying cask in gallons.

Rule. - 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 .5, 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.

Example i.-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 15 wet inches.

32) 15.00 (.46875 .5 - .46875= .03125 ÷ 4 = .0078125 .46875 - .0078125 =.4609375 X 118.80 = 54.759375 U. S. Gallons.

Example ii.-Required the ullage of 17 wet inches in a cask of the above capacity?

32) 17.00 (.53125 - .5 = .03125 ÷ 4 = .0078125 + .53125 =.5390625 X 118.80 = 64.040625 U. S. Gallons.

Proof - 64.040625 + 54.759375 = 118.80 gallons.

To find the ullage of a filled part of a standing Cask, in gallons.

Rule. - Divide the depth of the liquid, or wet inches, by the length of the cask; then, if the quotient is less than .5, deduct from the quotient one-tenth 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. But if the quotient exceeds .5, add one-tenth of that excess to the quotient, and multiply the sum, by the whole capacity of the cask, this product will be the ullage, or contents in U. S. standard gallons.

Example. - Suppose a cask, 40 inches in length, and the capacity 118.80 gallons, as above: required the ullage of 21 wet inches ?

40) 21.000 (.525 -.5 = .025 ÷10= .0025+ .525 =.5275 X 118.80 = 62.667 U. S. Gallons.

.Note. - Formerly the British Wine and Ale Gallon measures were similar to those now used in the United States and British Colonies.

The following Tables exhibit the comparative value between the United States and the present British measures.

 U. S. measure for wine, spirits, etc. British (Im.) measure. galls. qts. I>ts. gills. 42 galls. = 1 Pierce = :34 3 1 3 63 = l hogsh = :52 1 1 3 126 = 1 pipe, = 104 3 1 3 252 = 1 fun, = 209 3 1 2
 U. S. measure for ale and beer. British (Im.) measure. trails. qts. pts. gills. 9 galls, = 1 firkin, = 9 0 1 1 36 = 1 barrel 36 2 0 3 54 = 1 hogsh 54 3 1 1 103 = 1 butt, = 109 3 0 3

To convert Imperial Gallons into United States Wine Gallons multiply the imperial by 1.2. To convert U. S. Gallons into Imperial multiply the U. Stales Wine gallons by 833.

51 U. S. Ale Gallons equal 60 Imperial Gallons, therefore to convert one into other add or deduct 1-G0lh.