To find the ullage, or quantity of liquor deficient in a cask, we have the following rule. Take the diameter at the bung, and ascertain the number of inches and parts that are dry ; say that of 29 inches 13 be dry ; also that the whole cask measures 80 gallons. Divide the dry inches 13 by 29, the bung diameter ; the quotient will be .148; find the two first figures, .44 under V. S. in the annexed table, and its sequent will be .4238, to which add a proportional part for the 8, and the whole sequent will be .4343, which, multiplied by the contents of the cask, will shew a deficiency of 34.664 gallons. This mea surement, however, applies to cylinders only ; if the cask be conical, you must find the mean diameter, which should be deducted from that at the bung; and not ing half the difference, which is to be de ducted from the wet inches, and reserved Then, as the mean diameter is to 100, so is the reserved difference to a versed line in the table : and if the segment (to be found in the table, be multiplied, as be fore shown, into the contents, the product. will be the quantity of liquor in the cask.
Example. Let the bung-diameter be 32, the mean-diameter 29.6, and the whole measure 97.4 gallons : say there be 19 inches wet : From 32.0 From 90 deduct 29.6 take 1.2 remain 2_4 remain 17.8 reserved.
its half is 1.2 Now as 29.6 is to 100, so is 17.8 to .60, the versed sine. The segment to 60 is .6265; which, multiplied by 97.4, the whole contents, the product gives 61 gal lons of liquor remaining. By working upon the dry inches, you would have found the ullage, or deficiency.
By such simple means we may ascer tain the dimensions of most vessels in common use ; we may, indeed, ordinarily estimate the diameters of casks to be in the proportion of 7 at the chimb for 10 at the bung, which gives a medium of 8.5.
But gaugers are, in general, provided with a neat, compact instrument, in form of a folding rule, whereby the measure ment of a cask's interior may be taken with sufficient accuracy. This instrument
consists of four pieces, each a foot long and about three-eighths of an inch square. It has three brass joints, for the purpose of folding. On one face is a double line of ,diagonals, one appropriated to wine, the other to beer measure. By inserting the lower end of the rod at the bung of the cask, and directing it obliquely so as to touch the junction of the head and stave, and noting the figures which stand oppo site the centre of the interior of the bung-hole, the measurement is taken: in this process care must be taken to mea sure towards both chimbs, because a cask has not always the bung truly centrical : when any difference appears,the medium of the two measurements serves as a standard. Open vessels may be measured in the same way, by measuring the ob lique line from the surface or one side to the bottom of the other side ; but only half the quantity shewn on the scale is to be taken for the contents. There is also a scale for cylindrical vessels, which shews the contents of one inch deep in any given area or diameter.
We must remark, that complete accu racy is not to be expected from this rod, however justly it may have been gradu ated : because the curves of staves, as has been shewn. vary so much, as to render some exclusive attention to that circum stance absolutely necessary ; it being a point which cannot be determined by the rod or rule. The guagers in excise offi ces usually understand, at sight, if any unusual curve exists, andfail not to make allowance for such anomalies. The wine merchants, however, for many years, got the start of them, by causing the staves to be hollowed out considerably, indeed.
as far as could be done with safety, leav ing the bungholes and the ends of the staves of their ordinary thickness. By this device many gallons escaped paying duty while the vender, selling by the gal lon, lost nothing, though he saved freight in proportion to the quantity of wood scooped from the interior face.