Note. The dimensions and areas are transferred to the specimen of the Dimension Book, at the end of this Section. To find the content. Contents. 39.1 first 10 inches. 57.9 second 10 inches. 8.38 x 12=100.56 upper 12 inches. 2. How many ale gallons are contained in the foregoing guile-tun, when the depth of the liquor is 27.8 inAns. 162.364 ale gallons. ches? 3. The side of a square, pyramidical guile-tun, at 5 inches from the bottom, measures 49.2; at 15 inches from the bottom, 52.3; at 25 inches from the bottom, 55.2; at 35 inches from the bottom, 58.4; at 46 inches from the bottom, 61.2 inches; required the area of each section, and the whole content, in ale gallons; its perpendicular depth being 52 inches... Note. The first four diniensions are taken in the middle of every 10 inches; but the fifth dimension is taken in the middle of the last 12 inches of the depth. Ans. The area of the first section is 8.58, the second section 9.70, the third section 10.81, the fourth section 12.09, and the fifth section 13.28 ale gallons; hence we find the whole content of the tun to be 571.16 ale gallons. PROBLEM XI. To gauge and fix a guile-tun in the form of the frustum of a rectangular pyramid, or a prismoid. To take the dimensions. With some convenient instrument take the perpendicu lar depth of the vessel; also, measure the mean length and breadth in the middle of every 6, 8, or 10 inches; and enter all the dimensions in your Note Book. Note. Measure both sides of the vessel, divide the sum by. 2, and take the quotient for the mean length. The mean breadth must be found in the same manner. To find the area and content. RULE. Multiply the mean length of each section by the mean breadth; divide each product by 282; and the quotients will be the areas of the respective sections, in ale gallons. Multiply the area of each section by its respective perpendicular depth; and the sum of the products will be the whole content of the tun, in ale gallons. EXAMPLES. 1. The perpendicular depth of a guile-tun, in the form of the frustum of a rectangular pyramid, is 30 inches; the mean length and breadth, taken at 5 inches from the bottom, measure 36 and 26 inches; at 15 inches from the bottom, 42 and 32 inches; and at 25 inches from the bottom, 48 and 38 inches; required the area of each sec tion, and the whole content, in ale gallons. BY THE PEN. To find the area. Inches. 36 length. 216 72 Divisor 282)936(3.319 area in ale gallons. Also, 42 x 32-282-1344-282=4.765 ale gallons, the area of the second section; and 48 x 38-282-1824÷282 6.468 ale gallons, the area of the third section. BY THE SLIDING RULE. As the square divisor on A, is to the length on B; so is the breadth on A, to the area on B. The dimensions and areas will appear in the Note Book, as below. NOTE BOOK. A. B.'s Sq. Guile Tun, No. 2, gauged March 12, 1821. Note. The dimensions and areas are transferred to the specimen of the Dimension Book, at the end of this Section. 2. How many ale gallons are contained in the fore going guile tun, when the depth of the liquor is 26.3 inches? Ans. 121.661 ale gallons. 3. The perpendicular depth of a guile-tun, in the form of a prismoid, is 40 inches; the mean length and breadth, taken at 5 inches from the bottom, measure 56.4 and 41.2 inches; at 15 inches from the bottom, 60.8 and 44.8 in ches; at 25 inches from the bottom, 65.7 and 48.6; and at 35 inches from the bottom, 71.2 and 51.9; required the area of each section, and the whole content in ale gallons. Ans. The area of the first section is 8.24, the second 9.66, the third 11.32, and the fourth 13.10 ale gallons: hence we find the whole content of the tun to be 423.2 ale gallons. REMARK. Having given the methods of gauging and fixing all kinds of guile-tuns that generally occur in victuallery, it only remains to observe, that if a guile-tun should be met with whose base is a triangle, a trapezium, a trapezoid, &c. &c. such dimensions must be taken as will give the areas of horizontal sections in the middle of every 6, 8, or 10 inches of the perpendicular depth. Then multiply each area by its corresponding depth; and the sum of the products will be the whole content of the tun. (See the Remark at the end of Prob. V.) PROBLEM XII. The method of gauging by-tubs. By-tubs are such vessels as are not fixed in the Officer's Dimension Book. They are generally small, of various and irregular forms; and used by victuallers for cooling their wort, or for working small quantities of beer, when the fixed vessels are too full. To take the dimensions. Whatever be the form of the vessel, such mean dimen Dd sions must be taken as are most likely to give the true content of the liquor. Thus, if the vessel be a parallel. opipedon, measure the mean length and breadth; if it be a cylinder, measure the mean diameter; if it be the frustum of a right cone, measure the mean diameter, at half the perpendicular depth of the liquor, in order to reduce the vessel to a cylinder; and if it be the frustum of an elliptical cone, measure the mean transverse and conjugate diameters, at half the perpendicular depth of the liquor; and when their difference is not great, take half their sum for a mean circular diameter, thus reducing the vessel to a cylinder. Also, in every case, take the mean perpendicular depth of the liquor; and enter all the di mensions in a vacant column of your Survey Book. Note 1. In order to find a mean diameter at half the perpendicular depth of the liquor contained in a vessel in the form of the frustum of a right cone, standing upon its less base, place a rod perpendicularly to the bottom of the vessel, and touching the side; then the distance between the other side of the vessel and the rod, measured at the surface of the liquor, will be the mean diameter sought.-By a similar process you may obtain the mean transverse and conjugate diameters, at half the perpendicular depth of the liquor contained in a vessel in the form of the frustum of an elliptical cone. 2. The foregoing method of reducing a vessel in the form of the frustum of a right cone, or an elliptical cone to a cylinder, is not mathematically correct; but it is generally adopted in practice, because the content of the liquor can be found by the Sliding Rule, without finding the area of the vessel. To find the content. RULES. BY THE PEN. 1. When the vessel is a parallelopipedon, multiply the mean length, breadth, and depth continually together; divide the last product by 282; and the quotient will be the content in ale gallons. 2. When the vessel is a cylinder, or the frustum of a cone reduced to a cylinder, multiply the square of the mean diameter by the depth of the liquor; divide the |