BY THE SLIDING RULE. As the length upon C: 12 upon D:: girth upon D : content upon C. EXAMPLES. 1. A piece of timber is 9 feet long, and the quarter girth is 39 inches; what is the solidity? By Decimals. Here 39 in. 3.25 ft., and 9 ft.=9.75 ft. Hence 3.2529.75=10.5625 × 9.75=102.984375 cubic feet solidity required. 2. The length of a tree is 25 feet, and the girth throughout 2 fect; what is its solidity? Ans. 9 feet 9 inches. 3. The length of a tree is 14 feet, and its girth in the middle 3.15 feet; required the solidity? Ans. 9 feet nearly. 4. The girths of a tree in 4 different places are as follows in the first place 5 feet 9 inches, in the second, 4 feet 6 inches, in the third, 4 feet 9 inches, and in the fourth, 3 feet 9 inches; and the length of the whole tree is 15 feet; what is the solidity? Ans. 20 feet 7 inches. 5. An oak tree is 45 feet 7 inches long, and its quarter girth 3 feet 8 inches; what is the solid content, allowing for the bark? Ans. 515 feet, nearly. RULE II.* Multiply the square of one-fifth of the girth by twice the length, and the product will be the solidity, extremely near the truth. * Let c circumference, and l-length, as before. C Then X 음 5 5 according to the rule. 2c21 c2l 21 = And the true content is content of the tree as was before shown. the whole, and is therefore sufficiently near the truth for any prac tical purpose. This rule is full as easy in practice as the false one, and therefore ought to be generally used, since the ease of the other method is the only argument which is alleged for employing it. The following rule was given me by Mr. Burrow, and is a still nearer approximation. Rule.-Multiply the square of the circumference by the length, and take of the product: from this last number subtract of itself, and the remainder will be the answer. which is the same as the rule, and differs from the truth by only 1 foot in 2300. BY THE SLIDING RULE. As twice the length upon C: 12 upon D:: one-fifth of the girth upon D: content upon C. EXAMPLES. } 1. A piece of timber is 94 feet long, and of the girth is 2.6 feet; what is the solidity? 2. If the length of a tree be 24 feet, and the girth throughout 8 feet; what is the content? Ans. 123 feet, nearly. 3. If a tree girth 14 feet at the thicker end, and 2 feet at the smaller end; required the solidity when the length is 24 feet? Ans. 123 feet, nearly. 4. A tree girths in five different places as follows: in the first place 9.43 feet, in the second 7.92 feet, in the third 6.15 feet, in the fourth 4.74 feet, and in the fifth 3.16 feet; and the whole length is 174 feet; what is the solidity? Ans. 54.4249 feet. OF SPECIFIC GRAVITY. THE specific gravities of bodies are their relative weights, contained under the same given magnitude, as a cubic foot, a cubic inch, &c. The specific gravities of several sorts of bodies are expressed by the numbers annexed to their names in the following table: A table of the specific gravities of bodies. Fine gold Quicksilver Lead Fine silver Standard silver Gun metal 8784 - Note. As a cubic foot of water weighs just 1000 ounces Avoirdupois, the numbers in this table express not only the specific gravities of the several bodies, but also |