DIMENSION BOOK.

A. B.'s Copper Pan Gaged, 10 May, 1820.

The concluding process, that of tabling the Pan,

Thus have we given the true method of gaging and

inching a Pan in the form of the segment of a hollow sphere; but as Pans so accurately co-inciding with this shape are seldom to be met with, the diameters we have calculated by the pen, will, for the most part, have to be taken by admeasurement.

PROBLEM IV.

To Gage and Inch a Round Mash-Tun.

The most common form of a Mash Tun is that of the frustum of a cone standing on the greater base, and seldom differing much from a true frustum; but MashTuns of other forms are likewise occasionally met with.

METHOD OF GAGING A ROUND TUN.

From two cross diameters at the bottom, find the mean diameter, and multiply it by 707, for the side of the square to be inscribed at the bottom: then with a rule, or tape, extended to the number of inches in the product, inscribe the square; and from the four angles strike perpendiculars on the sides with a chalked line up to the mouth of the Tun. Next take the perpendicular depth; and at the middle of every 10 inches from the bottom, cross diameters. In case the depth of the Tun is not a multiple of ten inches, the last pair of cross diameters is to be taken at the middle of the excess above tens.

Of the several dimensions found by measure make a memorandum, and from the memorandum fill up the Dimension Book, calculating the areas at an inch

deep in Mash-Tun Gallons, and afterwards converting them to Quarters, Bushels, and Gallons.

The last step of all will be to inch the Tun by continually adding to each area, in quarters, bushels, and gallons, the content under it in the Tun.

EXAMPLE.

Let AKDMBTC be a Mash Tun resembling the frustum of a cone standing on its greater end, to be gaged and inched.

METHOD OF TAKING THE DIMENSIONS. Descend into the Tun, and from two cross diameters at the bottom, (which we shall suppose are 107 2 inches, and 106.8 inches,) find a mean diameter, which will in this case be 106 inches. Then multiply this mean by 707, and it will be,

107 mean diameter

Multiply by 707 constant decimal

749 7490

Product 75.649 side of the inscribed square.

Extending, therefore, a dimension-cane, or a tape, to 75.6 inches, inscribe a square in the circle forming the bottom of the Tun. Then with a chalked line strike perpendiculars on the sides, from the four angles of the square, up to the mouth.

Next, at five inches from the bottom make a mark on each of the chalk-lines, for the middle of the first ten inches, as at mn.

A rod being now laid diametrically across the mouth of the Tun from A to D, the perpendicular depth EF, is to be taken, which we can imagine to be 55 inches. The marks, for the ends of the several pairs of cross diameters, will consequently be as follows:

Second pair 15

Third
Fourth

Fifth Sixth

......

25

35

45

inches from the bottom, as at op. inches from the bottom, as at qr.

inches from the bottom, as at st.

inches from the bottom, as at væ.

2.5 inches from the mouth, as at iw.

The necessary dimensions having been all carefully taken, let the copy of the memorandum be as under:

Memorandum of A. B.'s Round Mash-Tun,