See GEOMETRY.

GAUGING-Rod, an instrument used in gauging or measuring the contents of any vessel. That usually employed is the four-foot gauging-rod. It is com- monly made of box, and consists of four rules, each a foot long and about three-eighths of an inch square, joined together by three brass joints; by which means the rod is rendered four feet long when the four rules are quite opened, and but one foot when they are all folded together. On the first face of this rod, marked 4, are placed two diagonal lines; one for beer and the other for wine: by means of which the content of any common vessel in beer or wine gallons may be rea- dily found, by putting the rod in at the bung-hole of the vessel till it meets the intersection of the head of Gauging, the vessel with the flaves opposite to the bung-hole. For distinction of this line, there is written thereon, beer and wine gallons. On the second face, 5, are a plate of inches and the gauge-line; which is a line ex- pressing the areas of circles, whose diameters are the corresponding inches in ale-gallons. At the beginning is written, ale area. On the third face, 6, are three scales of lines; the first, at the end of which is written hoghead, is for finding how many gallons there are in a hoghead when it is not full, lying with its axis par- allel to the horizon. The second line, at the end of which is written B. L. signifying a butt lying, is for the same use as that for the hoghead. The third line is to find how much liquor is wanting to fill up a butt when it is standing; at the end of it is written B. S. signifying a butt standing. In the half of the fourth face of the gauging-rod, 7, there are three scales of lines, to find the wants in a firkin, kilderkin, and bar- rel, lying with their areas parallel to the horizon. They are distinguished by letters F. K. B. signifying a firkin, kilderkin, and barrel.

Use of the diagonal lines on this rod. To find the content of a vessel in beer or wine gallons, put the braided end of the gauging-rod into the bung-hole of the cask, with the diagonal lines upwards, and thrust this braided end to the meeting of the head and flaves; then with chalk make a mark at the middle of the bung-hole of the vessel, and also on the diagonal lines of the rod, right against, over one another, when the braided end is thrust home to the head and flaves: then turn the gauging-rod to the other end of the vessel, and thrust the braided end home to the end, as before. Lastly, see if the mark made on the gauging-rod come even with the mark made on the bung-hole when the rod was thrust to the other end; which if it be, the mark made on the diagonal lines will, on the same lines, show the whole content of the cask in beer or wine gallons.

If the mark made on the bung-hole be not right against that made on the rod when you put it the other way, then right against the mark made on the bung-hole make another on the diagonal lines; and the division on the diagonal line between the two chalks will show the vessel's whole contents in beer or wine gallons. Thus, e.g., if the diagonal line of a vessel be 28 inches four-tenths, its contents in beer gal- lons will be near 51, and in wine gallons 62.

If a vessel be open, as a half-barrel, tun, or copper, and the measure from the middle on one side to the head and flaves be 38 inches, the diagonal line gives 122 beer-gallons; half of which, viz. 61, is the con- tent of the open half tub.

If you have a large vessel, as a tun or copper, and the diagonal line taken by a long rule proves 70 inches; the content of that vessel may be found thus: Every inch at the beginning-end of the diagonal-line call ten inches. Thus ten inches becomes 100 inches; and every tenth of a gallon call 100 gallons; and every whole gallon call 1000 gallons.

Example. At 44.8 inches on the diagonal beer- line is 200 gallons; so that 4 inches 48 parts, now called 44 inches 8-tenths, is just two-tenths of a gallon, now called 200 gallons: so also if the diagonal line be 76 inches and 7-tenths, a close cask of such diagonal will GAU

will hold 1000 beer-gallons; but an open cask but half so much, viz., 500 beer-gallons.

Use of the Gauge-Line. To find the content of any cylindrical vessel in ale-gallons: seek the diameter of the vessel in inches, and just against it on the gauge-line is the quantity of ale-gallons contained in one inch deep; this multiplied by the length of the cylinder will give its content in ale-gallons.

For example, suppose the length of the vessel 32.06, and the diameter of its base 25 inches; to find what is the content in ale-gallons? Right against 25 inches on the gauge-line is one gallon and 745 of a gallon; which multiplied by 32.06, the length, gives 55.9447 gallons for the content of the vessel.

The bung diameter of a hogshead being 25 inches, the head diameter 22 inches, and the length 32.06 inches; to find the quantity of ale-gallons contained in it? Seek 25, the bung diameter, on the line of inches; and right against it on the gauge-line you will find 1.745: take one-third of it, which is .580, and set it down twice: seek 22 inches in the head diameter, and against it you will find on the gauge-line 1.356; one-third of which added to twice .580, gives 1.6096; which multiplied by the length 32.06, the product will be 51.603776, the content in ale-gallons. Note, this operation supposes, that the aforesaid hogshead is in the figure of the middle frustum of a spheroid.

The use of the lines on the two other faces of the rod is very easy; you need only put it downright into the bung-hole (if the vessel you desire to know the quantity of ale-gallons contained therein be lying) to the opposite slaves; and then where the surface of the liquor cuts any one of the lines appropriated to that vessel, will be the number of gallons contained in that vessel.