Wherefore it will be, W.G. divisor 231) 12280 (53-16 wine gallons. A. G. divisor 282) 12280 (43.54 ale gallons. M.B. divisor 2150) 12280 (5.71 malt bushels. Various other methods of determining the area of a curvilineal space have been proposed, and put in practice; but none of them has been found to apply so generally to every kind of curve, or with equal facility to give so accurate results, as the above. To enlarge on them, therefore, would be foreign to our purpose. PROBLEM XVIII. To determine the Content, for an Inch Deep, of an Irregular plane Figure. RULE. Divide the given figure into figures that can be measured by the foregoing problems, and having determined each of the figures, add the several contents in cubic inches together, and divide the sum by the number of cubic inches in the proposed integer. EXAMPLE. Let ABCDEFGH be an irregular plane figure, of which the content, for an inch in depth, is required in wine gallons, ale gallons, and malt bushels. After a little inspection, a very rational way of dividing the given figure, appears to be as follows: Find the centre K of the circular curve HG, and complete the sector GHKF. HK seems to be parallel to AB; let, therefore, these two lines be prolonged to L and M. It now appears that BL is parallel to CD, and that KM is parallel to FE. Wherefore take the perpendicular breadths xv, no, rs; and the three figures BCDL, AqML, FKME, come all under the description of figures in PROB. VII. The dimensions necessary to be known, and which we shall suppose known, are the following: 2) 200 sum brought over 100 half sum Multiply by 28 perpendicular rs. Product 2800 cubic inches in KFEM. 2) 66 arc GH. 33 half the arc Multiply by 90 radius GH. Product 2970 cubic inches in the sector. These four figures constituting the whole of the given figure, it will be, 2016 content of BCDL. 4368 content of AqML. 2800 content of KFEM. 2970 content of the sector GHK. W.G. divisor 231)12154 (52.61 wine gallons. A. G. divisor 282)12154 (43.10 ale gallons. M. B. divisor 2150)12154 (5.65 malt bushels. It has been stated in the First Section that no general Rule can be given for the division of irregular figures into compartments. The results, however, will in every way, be the same, or nearly the same; and to obtain these in the shortest and easiest way is the only DESIDERATUM. |