deep. Wherefore at three inches above the crown, having first inscribed a square, and drawn four perpendicular lines on the sides as directed in page 330, we are to take a pair of cross diameters; and at six inches. higher, another pair; and so on, at six-inch distances, till six pair of diameters have been taken. Lastly, we are to admit water into the Still to cover the crown, the quantity of which, requisite for this purpose, we can suppose is 28 wine gallons. A memorandum of every particular having been carefully noted, we make the following entry, in which the Dimensions are, we can imagine, those found by measurement, and faithfully copied from the memorandum. DIMENSION BOOK. A. B.'s Wash Still, No. 1, Gaged, 10 May, 1820. NOTE. The content of the spherical frustum is found by PROB. XX. page 215, MENSURATION. The next process is to tabulate or inch the Still all the way down from the collar to the crown. But before this can be done we are to ascertain by calculation, the diameters of the globular frustum at every inch as follows: [See page 331.] 2) 60 greater diameter 30 radius of the base Multiply by 30 radius of the base Product 900 square of half GH. 12.5 × 12.5 = 156.25 square of half EF. Remainder 743.75 8×8 = 64.00 square of the altitude 8+8 16) 679-75 (42-48 inches. Hence the distance of D from the centre of the sphere is 42.48 inches. Wherefore, to obtain the diameter of the sphere, it will be Again, 52 semi-diameter Subtract 42.48 distance of D from the centre Remainder 9.52 Subtract 8 altitude of the frustum Remainder 1.52 altitude of the segment cut off. Now the diameters of the frustum at the top and bottom being known, we need only calculate the seven following diameters: [See page 275.] Inches 104-2.5-101.5 Multiply by 2.5 Diam. Dry ia Inches Inches Product 253.75 whereof twice the sq. root is 31.8 1 104--3.5-100.5 Multiply by 3.5 Product 351-75 whereof twice the sq. root is 37.5 2 104-4.599.5 Multiply by 4.5 Product 447-75 whereof twice the sq. root is 42.3 3 104-5.598.5 Multiply by 5.5 Product 541.75 whereof twice the sq. root is 46.5 4 Product 633.75 whereof twice the sq. root is 50.3 5 Product 723.75 whereof twice the sq. root is 53.8 6 Product 811.75 whereof twice the sq. root is 56.9 7 -- All the diameters throughout the Still being now known, we may proceed to construct the Table, by taking half the sum of every pair of contiguous diameters in the globular part, for the mean diameter at the middle of every inch; and consequently the several means will be, First inch......28.4 inches......... 2.74 gallons Third...........39.9 inches......... 541 gallons Fifth............484 inches......... 7.96 gallons Sixth............52.0 inches......... 9 19 gallons Sum 58.05 gallons. With these mean diameters we have entered the Table of Circular Areas in Wine Gallons, to ascertain by inspection the content at every inch of the globular part. It will here be seen that the whole content of the spherical frustum has lost about half a gallon in being tabled, but this trifling discrepancy is unavoidable, and may in a great degree be owing to the retention of so few decimal places in the operation. We have here carried the Table to 18 dry inches only, being convinced that this process is sufficiently under |