7. Required the superficial feet in the following lot of boards, viz. width. 9 inches 8. Required the content of the following pieces of timber in board measure, the length and side of the square being given. length. 30 feet 30 30 28 square. 9 23 16 feet. inches. 160 0 9. Required the solid content, or cubic feet in the follow 10. How many cubic feet in 4 stones, measuring, viz. length. 10 feet To find how much round timber will square to. Multiply. the girt by,225: or multiply the diameter by,7, or,71. To find the girt or circumference by the diameter. SayAs 1 is to 3,14159, or 3,14, or as 7 to 22, so is the diameter to the girt; and the reverse to find the diameter from the circumference. To find the quarter girt, take Deducting from the diameter will girt, nearly. EXAMPLE. Suppose a round stick to be 24 inches diameter, how much will it square to? is the girt? Ans. 17 inches. Round timber loses almost of its solidity by being squared, and the quarter girt makes about more than the side of the square would. The solid content being to that by the quarter girt as 9 to 7, and to the content, if squared, as 30 to 19. To find the Cubic Feet in Round Timber. RULE. Multiply the square of the girt by the length, from the product reject two figures to the right, and divide the remaining figures by 18, or more concisely by 3, and then by 6 for cubic feet. If by custom or agreement the quarter girt is taken, multiply the square of it by the length in feet, and divide by 144 for the content in cubic feet. EXAMPLES. 1. Required the content of a round log, the girt of which is 80 inches, and the length 26 feet. by the girt 80 quarter 20 inc. 80 6400 80X,225-18 in. for side 18 [of the square. 144 20 400 2. Required the contents of the following pieces of round 12)702 cub. ft. 58,6 if squared. "" 52 the mean of 5 diff. places ft. 20 39 " 51 " 35 - 28 Suppose the six pieces, last mentioned, were pine logs, brought by A. to a saw-mill, and when measured at the quar Ans. 25 161 50 311 65 41 45 621 49 40 ter girt, he sold them at $9 per thousand: Allowing as usual 115 feet to make a thousand feet of boards, and deducting one fourth for sawing, what was the amount? 8. Required the difference in the solid contents of the two following pieces of timber, equal in length and circumference, viz. One round piece, 24 feet long, and 60 inches in circumference. The other piece 24 feet long, 18 inches wide and 12 inches thick. Ans. 12 feet, the first being 48, and the other 36 cubic ft This difference accounts for the custom in N. England of paying one-third more for the hauling round timber from the forests to the ship-yards, than for that which is roughhewn; each being taken there at the quarter girt. RULES FOR PILLARS. 1. Multiply the square of of the girt by twice the length in feet, and divide by 144 for the content. 2. Multiply of the circumference by of the diameter, and the product by the length in feet, and divide the last product by 144 for the answer. 3 Multiply the square of the diameter by the length in feet, and that product by 11, and then divide by 14 for the solid content in feet. EXAMPLE. Required the content in cubic feet of a pillar, the diameter of which is 30 inches, equal to 94 inches girt, and the length 24 feet. To find the content of round or unsquared timber, whose ends or bases are unequal in circumference. RULE. To the products of the girts of the two bases, add of the square of the difference, the sum will be the square of the mean girt, then proceed as before. EXAMPLE. Required the solidity of a mast, the length of which is 72 feet, and the girt at one end is 57 inches, and at the other 38 inches. CIRCLES. To find the area of a circle from its circumference. Multiply its square by ,07958. And to find its area by the diameter, multiply its square by ,7854. To find the side of a square equal to any given superfices. RULE. The square root of the given area is the side required. If the diameters of circles be as 1 to 2, the circumferences will be in the same proportion. But the areas of the same circles will be as 1 to 4, or as the squares of their diameters. Therefore, while the circumference is twice as large, the area is four times as much. SPHERES OR GLOBES. The superfices of every sphere or globe is equal to four times the area of its greatest circle. Multiplying its diameter by its circumference will also give its convex surface. To find the solidity of a Sphere or Globe. Multiply the cube of its axis by,5236. Spheres are to each other as the cubes of their diameters; and their surfaces as the squares of their diameters. GAUGING. GAUGING teaches to find the content of any vessel by having the proper dimensions given, which are usually taken in inches and tenths of an inch. The Ale gallon is to the Wine gallon as 58 to 71 nearly. |