By the Sliding Rule. Set the bung diameter upon C to 100 on the line marked Seg. Ly. or SL; then against the wet inches on C, you will have a segment on the line SL, which call a fourth number. Set 100 on the line marked A, to the content of the cask upon B; then against the fourth number on A, is the quantity of liquor in the cask, upon B. EXAMPLES. 1. The length of a cask is 30, the bung diameter 24, the head diameter 18, and the wet inches 15; what is the ullage in ale gallons? Here 1524 = .625, which exceeds .500 by .125, one-fourth part of which is .03125; then .625 +.03125 = .65625, the multiplier. By the last Problem, the whole content of the cask is 38.75 ale gallons; then 38.75 × .65625 = 25.4296875 ale gallons, the ullage required. As 24 On A. As 100 100 :: 15: 67, a fourth number. On B. On A. On B. 38.75 :: 67: 252 gallons. 2. Let the dimensions and content be the same as in the last example; what is the ullage in ale gallons, for 9 wet inches? Here 924 .375, which is less than .500 by .125, one-fourth part of which is .03125; then .375 .03125 = .34375, the multiplier; hence 38.75 x .34375 = 13.3203125 ale gallons, the ullage required. Note. If we add 25.429, the ullage of the first example, to 15 3%, the ullage of the second; we obtain 38.73, the whole content of the Cask By the Sliding Rule. On C. On SL. As 24 100 :: On A. On B. As 100 On C. On SL. 9: 32.5, a fourth number. On A. On B. 38.75 :: 32.5: 12.6 gallons. 3. The length of a cask is 32, the bung diameter 25.6, the head diameter 19.2, and the wet inches 15.8; what is the ullage in ale and wine gallons? Ans. 30.4315577 ale, and 37.194126 wine gallons. MISCELLANEOUS QUESTIONS CONCERNING GAUGING. 1. THE perpendicular depth of a vessel in the form of a parallelopipedon is 52, its breadth 75, and the diagonal of its bottom 125 inches; what is its content in ale gallons? Ans. 1382.9787 gallons. 2. A vessel in the form of a parallelopipedon contains 675 ale gallons; its length is 85, and its breadth 64 inches; what is its depth? Ans. 34.9908 inches. 3. The diagonal of a cylindrical vessel is 45, and its diameter 27 inches; what is its lons? 4. The greatest diameter of a the frustum of a cone, is 96, the its slant height 51 inches; how will it contain? content in wine galAns. 89.2653 gallons. vessel in the form of least diameter 48, and many gallons of ale Ans. 673.8718 gallons. 5. A reservoir measures 144 inches in length, 122 in breadth, and 85 in depth; how long will a person be in filling it with water, by means of a pump; supposing he makes 30 strokes in a minute, and lifts 3 pints of water at each stroke? Ans. 7 hours, 50.695 minutes. 6. The slant height of a cistern in the form of the frustum of a square pyramid is 153, the perpendicular height 135, and the side of the less end 92 inches; what is its content in ale gallons? Ans. 13702.9787 gallons. 7. The altitude of a vessel in the form of a hexago nal prism is 60, and the side of its base 30 inches; what is its content in Winchester bushels? Ans. 65.254 bushels. 8. The greatest depth of the liquor in a cylindrical vessel, placed upon an inclined plane, is 38 inches, the least depth 32 inches, and the diameter of the vessel 36 inches; how many ale gallons does it contain ? Ans. 126.3509 gallons. 9. The transverse diameter of an elliptical bath measures 144, the conjugate 112, and the depth 60 inches; how many gallons, ale measure, will it contain ? Ans. 2695.0917 gallons. 10. If the internal diameter of a hollow sphere be 100 inches; how many bushels of corn, Winchester measure, will it hold? Ans. 243.5348 bushels. 11. The top diameter of a conical vessel measures 32, and its slant height 34 inches; how many gallons of wine will it contain? Ans. 34.816 gallons. 12. The top diameter and depth of a vessel, in the form of the greater segment of a globe, are 32 inches each; how many ale gallons will it hold?` Ans. 106.4727 gallons. 13. If the linear side of each Platonic body be 30 inches; required their respective contents in wine gallons. Ans. The content of the tetraedron is 13.7748, the hexaedron 116.8831, the octaedron 55.0992, the dodecaedron 895.6892, and the icosaedron 255.0033 wine gal lons. 14. Two porters agreed to drink off a pot of strong beer at two pulls, or a draught each; now, the first having given it a black eye, as it is called, or drunk till the surface of the liquor just touched the opposite edge of the bottom, gave the remaining part to the other; what was the difference of their shares, supposing the pot was the frustum of a cone, whose top diameter was 3.7, bottom diameter 4.23, and perpendicular depth 5.7 inches? Ans: 7.06511 cubic inches. 15. At Konigstein, near Dresden, in Germany, is a cask whose head diameter is 25, bung diameter 26, and perpendicular altitude 28 feet; how many gallons of wine will it contain? Ans. The content found by Rule II, Problem X., is 1076401 gallons, which exceeds the content of the cask at Heidelberg, by 376551 gallons. See Example 4, Problem III. Nole. Those who wish to see this subject more fully treated, are referred to Nesbit's and Little's Treatise on Practical Guaging. REMARK. The Konigstein Cask was begun in the year 1722, and finished in 1725, under the direction of General Kyaw; and is considered to be the largest cask in the world. It consists of 157 staves, each 8 inches in thickness; and one of its heads is composed of 26, and the other of 28- boards. The top or upper head of this enormous cask is railed round, and affords sufficient room for twenty persons to regale themselves; and there are several sorts of large goblets, called, "Welcome Cups," offered to strangers, who are invited to drink by a Latin inscription, which in English is as follows: "Welcome, Traveller, and admire this Monument, dedicated to Festivity, in order to exhilarate the Mind with a cheerful Glass, in the year 1725, by FREDERIC AUGUSTUS, King of Poland, and elector of Saxony, the Father of his Country, the TITUS of his Age, the Delight of Mankind: Drink, therefore, to the Health of the Sovereign, the Country, the Electoral Family, and Baron KYAW, Governor of Konigstein; and if thou be able, according to the Dignity of this Cask, the most capacious of all Casks, drink to the Prosperity of the whole Universe; so farewell." THE METHOD OF COMPUTING DISTANCES BY THE VELOCITY OF SOUND. THE velocity of sound, or the space through which it is propagated in a given time, has been very dif ferently estimated by Authors who have written upon this subject. Roberval states it at the rate of 560 feet in a second of time; Gassendus at 1473; Musenne at 1474; Duhamel, in the History of the Academy of Sciences at Paris, at 1338; Newton at 968; Derham, in whose measure Flamstead and Halley acquiesce, at 1142. The reason of this variety is ascribed, by Derham, partly to some of those gentlemen using strings and plummets instead of regular pendulums; partly to the too small distance between the sonorous body and the place of observation; and partly to no regard being paid to the winds. By the account since published by M. Cassini de |