BY THE SLIDING RULE. As the length upon C : 12 upon D :: girth upon D: content ироп 0. EXAMPLES. 1. A piece of timber is 93 feet long, and the quarter girth is 39 inches; what is the solidity ? By Decimals. Hence 3.25/x 9.75=10.5625 x 9.75=102.984375 cubic feet=solidity required. By Cross Multiplication. ft. in. 9 9 10 6 9 95 0 9 102 11 9 9=solidity. As 94 upon BY THE SLIDING RULE. upon upon D: 103 upon C, the content. 2. The length of a tree is 25 feet, and the girth throughout 21 fect; what is its solidity ? Ans. 9 feet 9 inches. 3. The length of a tree is 141 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. с في 12.5664 by only about part of * Let c=circumference, and l=length, as before. 2c47 c47 =content of the tree 5 5 20.5 12.5 according to the rule. And the true content is as was before shown. 12.5664 1 190 the whole, and is therefore sufficiently near the truth for any practid 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 it of the product: from this last number subtract of itself, and the remainder will be the answer. cl 7 8 1 For of er very nearly;=(98 xcl= 12.566488 88 cl cal of 11 which is the same as the rule, and differs 8 11' from the truth by only 1 foot in 2300. P1 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 9 feet long, and } of the girth is 2.6 feet; what is the solidity ? By Decimals. 2.6 156 52 6.76 3380 4732 6084 65.9100 2 Here 2.61* x 9.75 X 2=131.8200=content. BY THE SLIDING RULE. As 19.15 upon upon D:. 31} in. upon D : 132 the content upon C. 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 : Dry oak A table of the specific gravities of bodies. Fine gold 19630 Brick 2000 Standard gold 18888 Light earth 1984 Quicksilver 14000 Solid gunpowder 1745 Lead 11325 Sand 1520 Fine silver 11091 Pitch 1150 Standard silver 10535 Dry box-wood 1030 Copper 9000 Sea water 1030 Gun metal 8784 Common water 1000 Cast brass 8000 925 Steel 7850 Gunpowder, shaken 922 Iron 7645 Dry ash 800 Cast iron 7425 Dry maple 755 Tin 7320 600 Marble 2700 Dry fir 550 Common stone 2520 Cork 240 Loam 2160 Air 17 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 |