the tun, when dry, so much water as will just cover the bot tom; for by this means a level is obtained, by the help of which it will be easy to ascertain how far up the surface of the liquor will reach when the tun is full. Then find the content of that part between the surface of the drip and the furface of the liquor when the tun is full; to which add the drip or fall, and the fum will be the content of the tun. Next, divide the difference of the head and bottom diameters by the depth, and the quotient is a common addend for 1 inch from top to bottom, by which you may find the diameter in the middle of every 10 inches of the depth. EXAMPLE. Let the bottom diameter of a conical veffel be 98 inches, top diameter 80, and depth 40 inches; it is requi red to find how much it will hold upon every inch, and to table the fame. Bottom diameter 8818 98 80 And 40)18.00(.45 the addend. Now, 5, 15, 25, and 35 are the inches which fall in the middle of every 10 inches; if these numbers be multiplied by the addend, the products will fhew how much ought to be added to the diameters at thofe depths. Thus, 80 top diameter. 2.25 Gall. B. F. 82.25 diameter at 5 inches deep, its area is 18.84=0 2 Gall, 1.84 80 top diameter. 6.75 86.75 diameter at 15 inches deep, its area is 20.96=0 2 80 top diameter. 2 3.96 11.25 91.25 diameter at 25 inches deep, its area is 23.19=0 6.29 95.75 diameter at 35 inches deep, its area is 25.530 3 0.03 The fum of these areas are which, multiplied by 10, gives 885.2 gallons, the content of the tun. 88.52 Now, 18.84 gallons, which is o bar 2 fir. 1.84 gall. is the common area to the firft 10 inches; and, for the next 10 inches, 20.96 gall. which is o bar. 2 fir. 3.96. And fo on for the rest. The operation will be as follows. Victuallers, who brew but little at a brewing, generally cool their worts in tubs. In order to ascertain the quantity of worts, the gauger ought to have the area of each tub marked upon it, otherwise to number the tubs, and enter the number and area of each tub in his stock-book. PROBLEM VIII. Fig. 1. To gauge a copper with a rifing crown, and make allowance for the fame. RULE. Take a fmall cord and let it reprefent the diameter of the head, and, by a plumb-line, find Ee, Gg, the greatest and leaft depths of the copper. Note Ae, Find the content of CDFE, confidered as the fruftum of a cone; then find the content of the crown, being reckoned a fpherical fegment; fubtract the latter from the former, and the remainder will fhew the quantity of liquor ncceflary to cover the crown. Then find the content of the copper from the crown upwards, take the diameter of every 4, 6, or 10 inches, and infert them, together with their correfponding areas (in barrels, firkins, and gallons) in a table; then multiply each of these areas by their diftance, and the fum of the products will be the content after the crown is covered. A very good and ready method to find how much liquor will cover the crown, is, to measure in as much water as will just cover it. EXAMPLE. The more curved the fides of the copper are, the more mean diameters and areas you ought to take. EXAMPLE. Suppofe the figure ABFE to represent a copper, and ExFgE its rifing crown, AB=90, CD=82, Ae=5, it is plain that AB—2 × Ae=90-10=EF, Ee=30, and Gg=27, confequently gx=3. To cover the crown. In the core CDFE, the diameter' CD=82, EF-80, and gx=3, its content in gallons, &c. is The bafe diameter 80, and height' Gall. B F. Gall. 54-782 I 2 3-778 of the crown 3, its content in ale 26.737 = 0 gallons, &c. will be The liquor that will cover the crown is 3 1.235 28.945 0 3 2.543 The crown being thus covered, it now remains to find the content of the copper from the crown upwards, the depth being 27 inches. In order to this, take the diameter in the middle of every 10 inches from the top, and infert each against the parts of the depth, as in the following table. Find the area of each in ale gallons, by Problem IV. and infert thefe areas, each against its corresponding diameter, as in column third; also the contents of the feveral parts of the depth are placed in the fourth column. And these contents, being reduced to barrels, firkins, gallons, are inferted in the last column, as follows. Parts |