the centre and side, as EwF: then, disregarding the crown, cross diameters at stated depths are to be taken as in the preceding Coppers.

EXAMPLE.

Let ABCD be a Copper to be gaged and inched, of which the fall of the bottom is very inconsiderable.

Lay a rod diametrically across the mouth from A to D, and along the rod slide a plumb-line, till the lead hangs over F, half-way between the centre of the bottom and the side.

The distance between E and F, which let be 40.6 inches, must be considered as the mean depth of the Copper.

Cross diameters are now to be taken five inches from the mouth, as at mn; then at 10 inches lower, as at xz; and again 10 inches lower, as at rs. Now

setting off ten inches downwards from rs, there remain 5 inches and 6 tenths. But the last pair of cross diameters would not, in this case, be exactly in the middle of the last division, (for we cannot well take cross diameters in the middle of the remaining 6 tenths, so as to consider the ten inches above, as a division,) wherefore we make, at five inches below rs, a faint mark as at w, and take cross diameters half way betwixt w and the bottom, as at vi.

These being all the necessary dimensions, we enter them, one by one, in the Memorandum Book, as we take them, and shall suppose them to stand as follows:

Memorandum of A. B.'s Copper, No. 4, Gaged,

From this memorandum we make the following entry in the Dimension Book, and with which we shall conclude this first problem, having sufficiently explained and illustrated the method of inching or tabling a Copper, in PROBLEM I., to which the reader may, whenever either a difficulty or a doubt occurs, advantageously refer.

DIMENSION BOOK.

A. B.'s Copper, No. 4, Gaged, 10 May, 1820.

Copper-Backs are vessels with flat bottoms, generally rectilineal, and constructed sometimes of copper but more frequently of wood, placed horizontally over the mouth of a Copper, so that the steam from the Copper may impart a portion of its heat to the liquor in the Back, and thus prepare it for the purposes to which it is subsequently to be applied.

The most common form of a Copper-Back is a quadrilateral with two adjutments in front, between which is the entrance to the mouth of the Copper, with a firm door (when on a large scale) to prevent the steam from issuing out in this direction, and to secure its action more completely on the Back over the Copper.

METHOD OF GAGING.

Divide the base into such geometrical figures as can be most easily and conveniently measured with the fewest dimensions, on the principles fully explained in the First and Second Sections of MENSURATION. Then take the lengths of the necessary lines, carefully noting them in a memorandum.

Next chuse a constant dipping place by the side of the Back, to which you can at all times approach without labour or interruption. The dipping place having been chosen, cause liquor to be admitted into the back, till the bottom is just covered, and take the depth of the liquor at the dipping place: after which, draw the whole off into a vessel of known capacity.

Lastly, observe whether the sides of the Back are all perpendicular or nearly so, and conclude with calculating the area, at an inch deep, in ale gallons, adding it first to the drip (if any) and then continually to the sum, in barrels, firkins, and gallons, for wet inches; leaving all odd tenths on the depth, at the top.

EXAMPLE.

Let ABFHELOK be a Copper-Back with a flat bottom and perpendicular sides, to be gaged and inched.

Prolong the line EL both ways to C and D, then draw the diagonals EF, and KL; after which, demit on them the perpendiculars DG, HI, CN, OM.

Having performed this operation with a chalked line on the base of the Back, take the length and breadth of the parallelogram ABCD, with the lengths of the two diagonals, and the four perpendiculars; and let these eight dimensions be as follows: