53 52 3.1237 3.1356 3.1476 3.1595 3.2439 3.2560 3.2682 3.2803 3.2926 54 3.3663 3.3786 3.3910 3.4034 3.4159 55 3.4909 3.5035 3-5161 3-5288 3.5414 3.1715 56 3.6179 3.6307 3.6435 3.6564 3.6693 57 3.7471 3.7601 3.7732 3.7863 3.7994 58 3.8785 3.8918 3.9051 3.9184 3.9318 59 4.0123 4.0258 4.0393 4.0528 4.0664 60 EXAMPLE TO ILLUSTRATE THE USE OF THE TABLE. Required the content of a Cask of the First Variety, in wine gallons, and in ale gallons, the head diameter being 30.3 inches, the bung diameter 40.5 inches, and the length of the Cask 50 inches. SOLUTION. Head diameter 30.3 inches... 1·0405 tabular number Bung diameter 40.5 inches... 1·8589 tabular number Repeat the last... 1.8589 tabular number Sum 4.7583 Multiply by 50 length Content in wine gallons 237.9150 product. The content in ale gallons will be nine-elevenths of this content; that is, 237-9 wine gallons Multiply by 9 according to rule Divide by 11) 2141·1 Quotient 194-6 content in ale gallons. OF ULLAGING. When a Cask is partly filled, the vacuity or space unoccupied by the liquor is termed the DRY ULLAGE, and the content of liquor actually in the Cask is called the WET ULLAGE of the Cask. By this definition it is evident that there will be two cases of Ullaging Casks; the first when the Cask is in a horizontal position, or lying on its bulge, and the second when the Cask stands on its head or end. Of all the methods yet proposed for readily ascertaining the Ullage of a Cask in either of those positions, the best is by the lines of Segments on the Sliding Rule: all others are too intricate and tedious for practical use. It ought here to be mentioned that a valuable set of Ullage Tables by BOYDELL are to be had, in which the Ullage of Casks may be discovered at once by inspection. It was our design to give a set of Tables of this description, though on a plan different from BOYDELL'S, in the present work; the enormous extent, however, to which these Tables must have carried the work, would have rendered it so expensive and ponderous, as in a great measure to defeat its utility, and we have consequently with reluctance abandoned the intention yet nothing essentially requisite in this branch of Cask Gaging shall be omitted. PROBLEM I. To find the Ullage of a Cask Lying. In Ullaging any Cask it is necessary first to know the content of the Cask when full. This being known, measure the bung diameter with your gaging-rod, and DD observe the number of inches either wet or dry. Then set the bung-diameter on the segment-lying slide B, to 100 on the line SEGMENT LYING, and opposite to the number of wet inches on B, observe the number on the line SEGMENT LYING; which number reserve. Again, set 100 on A, to the content of the Cask on B, and against the reserved number on A, will be the WET ULLAGE on B. If the dry Ullage be sought, dry inches instead of wet, are in the first part of the operation to be taken on the slide B. It is manifest that the dry and wet Ullages of any Cask must together be equal to the whole content of the Cask, and hence we have a sure means of proving the correctness of every Ullage. EXAMPLE. Let ABCDE be a Cask partly filled, whereof the whole content when full is 150 gallons, given to be ullaged on its bulge. |