tracting from the whole content the inch area in Barrels, Firkins, and Gallons, as already clearly explained.

PROBLEM XV.

To Gage and Inch a Guile-Tun with Tapering

Straight Sides.

1. If the base be rectangular, from two lengths find a mean length, and from two breadths a mean breadth of the Tun at the middle of every ten inches on the depth, beginning at the mouth: then multiply each length by the corresponding breadth, and divide the product by 282, the number of cubic inches in an ale gallon: the several quotients will be the content for an inch deep, respectively, throughout the ten-inch division of the Tun, to which the particular mean length and mean breadth refer. Next the drip is to be found as already directed, and afterwards the whole content, precisely in the manner of a Copper. See page 231. Lastly, a Table for dry inches is to be constructed as illustrated in page 234.

2. If the Tun or Vat be circular, take cross diameters at the middle of every ten inches from the mouth, and find the arithmetical mean between each pair of diameters, by adding them together, and dividing by 2: then enter the Table of Circular Areas in Ale, with this mean, and take out the content answering to it, which note in a memorandum. Next find the drip (the method of doing which has already been explained) and fix the dipping place. In all other

respects proceed as directed for the Tun with a rectangular base in the beginning of this problem.

EXAMPLE OF A ROUND GUILE-TUN WITH TAPERING

SIDES.

Let the following diagram represent a round GuileTun, or Working-Vat, with tapering sides, to be gaged and inched.

Lay a rod diametrically across the mouth of the Tun, and take the perpendicular depth; then strike four vertical lines with chalk, centrally opposite to each other, from the mouth of the Tun to the bottom. Next, begin at the mouth, and set off 5 inches on each of the chalk-lines, for the extremities of the uppermost pair of cross diameters. Which repeat at every ten inches below the first marks, so long as five

inches clear remain at the bottom: but as soon as one of the ten-inch distances would leave less than 5 inches clear below it, forbear to mark this ten-inch distance, and instead of it make a mark at 5 inches below the last ten marked. Then half way between this five-inch mark and the bottom, make a mark on each of the lines for cross diameters at the middle of this lowermost division of the Tun.

As this will be more intelligible by assuming an appropriate depth for the Tun before us, we shall suppose its depth to be, by admeasurement, 134.6 inches.

Here the cross diameters will be respectively at the following distances from the mouth:

And now no ten-inch division remains; wherefore, a mark being made on each of the four lines, at 5

inches below the last marks respectively, that is, at 130 inches from the mouth, there will be 4.6 inches remaining over, at the bottom: but the half of 4.6 inches is 2.3 inches, the distance from the bottom at which the lowermost two cross diameters are to be taken.

Hence the fourteenth pair of cross diameters will be at 132.3 inches from the mouth, and thus we bring the odd tenths in the depth to the bottom, as we ought to do for dry inches.

As the method of finding the drip, and of tabling a circular Tun with tapering sides, has been amply illustrated in some of the foregoing problems, further instructions would be a waste of time. We shall, therefore, only once more remind the young officer, that in all Working Vats or Guile-Tuns the Tabulation must be for Dry Inches.

PROBLEM XVI.

To Gage and Inch a Round Guile Tun with Bending

Sides.

Lay a straight rod across the mouth of the Tun, and with a rule or dimension-cane, take the perpendicular depth: then in the middle of every six inches, counting either from the bottom or top, where there are no odd tenths on the depth, take cross diameters; and record your proceedings and measurements in a memorandum, with the mean between each pair of diameters. Lastly, make an entry in the Dimension Book, precisely in the same way as in the preceding problems, having ascertained, as already directed, the drip of the Tun.

EXAMPLE.

Let the following diagram represent a Guile Tun with bending sides, given to be gaged and inched.

Lay a straight rod across the mouth, and take the depth of the Tun, which let be 40 inches. Then at 3 inches from the bottom take a pair of cross diameters, and 6 inches higher, another pair: also, 6 inches higher a third pair; and so on at six-inch distances, till six pair of cross diameters have been taken; when it will be found that only seven inches are left between the last pair and the mouth: but of these seven inches three belong to the division of the Tun, to which the last pair of cross diameters refers. Consequently the uppermost division of the Tun will be only four inches in depth, and therefore a pair of diameters taken two inches from the mouth will be at the middle of this division.