in the form of a spheroid, contain, whose fixed axis is 100, and revolving 60 inches ? Anf. 668.4 ale gallons, 816.4 wine gallons, and 87.6 malt bushels. Ex. 2. Required the content of the parabolic conoid in ale and wine gallons, the height being 30, and diameter of its base 20. Anj. 16.7 ale gallons, and 20.4 wine gallons. Ex. 3. Required the content of the hyperbolic conoid, the bare being 100 inches, and altitude 60 inches. Anf. 696.2 ale gallons, and 850 wine gallons. Ex. 4. Required the content of a parabolic spindle whose length is 60 inches, and greatest diameter is 64, in ale and wine gallons. Anf. 103.02 ale gallons, and 125.7 wine gallons. INCHING Tuns and Coolers. The practical method of gauging any fixed tun of copper, and of making a table to fhew what it will hold at every inch deep First, You must know that most (if not all) brewers tuns are so fixed as to lean a little, for conveniency of cleansing their drink, which is usually called the drip, or full of the tun. Now, the drip, or fall, is the hoof of such a solid as the tun is suppofed to represent. The beft and readiest way is to measure into XX the the tun, when dry, so much water as will just cover the boto 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 surface of the liquor when the tun is full; to which add the drip or fall, and the sum 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 to inches of the depth. EXAMPLE. Let the bottom diameter of a conical vefsel be 98 inches, top diameter 80, and depth 40 inches; it is required to find how much it will hold upon every inch, and to table the same. Bottom diameter 98 80 And 40)18.00(-45 the addend. 18 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 those depths. Thus, 80 top diameter. 2.25 Gall. B. F. Gall. 82.25 diameter at 5 inches deep, its area is 18.8450 1.84 80 top diameter 6.75 86.75 diameter at 15 inches deep, its area is 20.96=0 2 3.90 80 top diameter. 11.25 91.25 diameter at 25 inches deep, its area is 23.1930 2 6.29 8c top diameter. 15.75 95.75 diameter at 35 inches deep, its area is 25.53=3 0.03 The sum of these areas are 88.52 which, multiplied by 10, gives 885.2 gal. lons, the content of the tun. Now, 18.84 gallons, which is o bar 2 fir. 1.84 gall. is the common area to the first 10 inches; and, for the next 10 inches, 20.96 gall. which is o bar. 2 fir. 3.96. And so on for the reit. The operation will be as follows. 4.18 2 2 2 20 0.38 7.10 14 1.84 2.70 6.19 4 2 2 2 0,18 3 0.03 22 ABSTRACT. In. Bar. Fir. Gall. O 26 1.20 1 25 7.86 2 24 3 6.02 3 24 I 4 23 3 2.34 5 23 I 0.50 6 22 2 7.16 7 22 O 5.32 8 21 2 3.48 9 21 0 104 10 i 8.30 19 3 4.34 12 19 I 13 18 2 4.92 14 18 O 0.96 15 17 I 5.50 16 16 3 1.54 17 16 6.08 18 15 2 2.12 19 14. 3 6.66 20 14 I 2.70 21 13 2 5.01 22 12 3 7:32 23 1 1.13 24 II 2 3.44 25 1o 3 5.75 20) JO 8.00 27 9 2 1 87 28 8 29 8 6.49 30 7 0.30 31 6 0.27 6 O 0.24 33 5 I 1.21 34 4 2 0.18 35 3 3 0.15 3 0.12 37 2 I 0.09 2 o.co 39 3 0. c.co ! 2 Victualiers, 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 rising crown, and make allowance for the same. RULE. Take a small cord and let it represent 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, considered as the frustum of a cone; then find the content of the crown, being reckoned a spherical segment; subtract the latter from the former, and the remainder will fhew the quantity of liquor neceffary 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 insert them, together with their corresponding arcas (in barrels, firkins, and gallons) in a table; then multiply each of these areas by their distance, and the sum 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 sides of the coprer are, the more mcan diameters and arcas you ouglie to take. |