part of the tun which is to be tabulated. With the plumb-line, transfer this perpendicular from the surface of the water at m, to the side of the vessel at G; at which point make a mark; and then measure the diameter G B.

Quarter the tun as before directed; and parallel to the diameter G B, measure cross diameters in the middle of every 6, 8, or 10 inches, as at a a, b b, c c, &c. &c.; from these cross diameters find mean diameters; then determine the areas of the several sections; and the whole content of the figure D E B G, to which add the content of the ungula D CE; and the sum will be the quantity of liquor that the vessel will contain, when thus placed in an oblique position.

Note 1. When any circular vessel is placed in an inclining position, all the sections that are taken parallel to the horizontal surface of the liquor, required to cover the bottom, will be ellipses; but as the difference of their diameters will always be small, they may be reduced to circles, by taking half the sum of the diameters for a mean diameter. (See Definitions 17, 18, 20, and 21, Part V.)

2. It is scarcely necessary to observe that after the perpendicular depths of Вn, and G m have been determined, the water that was poured into the vessel, to cover its bottom, must be drawn off, before you can, with convenience, measure the cross diameters.

3. The method of tabling the tun for dry inches, is shewn in Prob lein II.; and for wet inches, in Problem III, of this Section.

4. When it is intended to table the tun for wet inches, cross diame ters must be taken in the middle of every 6, 8, or 10 inches from the diameter D E, towards the top of the vessel. (See Prob. VI., of the first Section.)

Observations on finding a dipping-place.

As the lines Bn and G m, are both perpendicular to the line D E, supposed to be formed by the surface of the liquor required to cover the bottom of the vessel, it is evident that the dipping-place may be either at B or G; but as the perpendicular G m is intercepted by the side of the vessel, at G; it is obvious that the depth, in either wet or dry inches, may be most conveniently measured from the top of the tun, in the perpendicular direction of

Bn.

If the tun be tabulated for wet inches, the gauging rod, in taking the depth, will come in contact with the bottom of the vessel, at r; consequently, the depth nr, of the drip, must be ascertained, which let us suppose to be 2 inches; then the number of gallons required to cover the bottom, will be the content at 2 inches deep; and this content added to the area of the first section, will be the content at 3 inches deep; and thus we may obtain the content at every inch of the perpendicular depth Bn.

EXAMPLES.

EXAM. 1.

The dimensions of the guile-tun A B C D, in the form of the frustum of a cone, standing upon its greater base, are contained in the following Note Book; it is required to tabulate the vessel for dry inches, as practised in the Excise.

NOTE BOOK.

A.B.'s Round Guile Tun, No. 1, gauged Aug.24, 1821.

Having found the areas of the several sections, and the contents of the different divisions, as before directed; we hence form the Dimension Book, as below.

A. B.'s Round Guile Tun, No. 1, gauged Aug. 24, 1821.

Depths

Mean Areas Contents

Areas. in Dia- in in in Inches. meters. Gallons. Gallons. B. F. G.

10

10

10

Contents.

in

B. F. G.

92.3 23.7271237.27102 5.7271 623.271 93.7 24.4520244.523 0 2 6.4523 6 3 1.523 95.9 25.6140256.140 0 2 7.6140 7 0 4.140 98.5 27.0217270.217 0 3 0.0217 7 2 0.217 102.4 29.2039292.039 03 2.2039 8 04.039 10 105.6 31.0577 310.577 0 3 4.0577 8 2 4.577

10

10

62

2 Drip. Drip.

16.500 Per measure.0 17.500

Whole Content. 1627.267 Whole content. 45 0 7.267

THE METHOD OF TABULATING THE FOREGOING GUILETUN FOR DRY INCHES.

3

43 0 8.0857

0 2 15.7271

7 40 2 3.1773 11 37 3 6.5437
02 5.7271
02 6.4523

In this manner the content, at every dry inch, may be obtained; and the Learner is required to continue the above process; and form a Table Book. (See the Key to this Work.)

EXAM. 2.

Admitting the dimensions of the foregoing guile-tun to be taken from the bottom upwards; it is required to tabulate the vessel for wet inches; as practised in the Excise.

DIMENSION BOOK.

A. B.'s Round Guile Tun, No. 1, gauged Aug. 24, 1821.

Mean Areas Contents Areas

in

in

Contents in

Dia- in meters. Gallons. Gallons. B.F. G. B. F. G.

92.3 23.7271 237.271 025.7271 623.271 93.7 24.4523 244.523 026.4523 6 31.523 95.9 25.6140 256.140 027.6140 7 04.140 98.5 27.0217270.217 030.0217 7 20.217 102.4 29.2039292.039 103 2.2039 8 04.039 105.6 31.0577310.577 034.0577 8 24.577

10

Drip Drip by Measure.

62 Depth. Whole Content. 1627.267 wholecontent. 450 7.267

THE METHOD OF TABULATING THE FOREGOING GUILE. TUN FOR WET INCHES.

In the same manner the content may be obtained at at every wet inch; and the Learner is required to con tinue the process, and form a Table Book.

Note. As the depth of the drip is 2 inches, it is evident that the content of the drip added to the area of the first Section, will be the content of the tun at 3 inches, &c. &c. as in the above Table. (See the observations on finding a dipping-place.)

Το

gauge

PROBLEM X.

and inch a circular guile-tun with curved sides, and make an allowance for the drip or fall.

Directions for taking the dimensions, &c. &c.

Pour in water to cover the bottom, as directed in the last Problem; then quarter the tun, and measure cross diameters in the middle of every 6 or 8 inches. From these cross diameters find mean diameters; then determine the areas of the several sections, the contents of the different divisions; and tabulate the vessel, either for wet or dry inches, as directed in the foregoing Problems. (See Problem VII. of the first Section.)