PROBLEM II. To find the solid content of Square timber. RULE. Multiply the three dimensions continually, and the last product will be the folidity. EXAMPLE I. Required the solid content of a tree 18 feet long, and 18 inches the side of the square. Set 18 feet, the length, on the fin, to 12 on the girt line, and and against 18, the fide of the square, in inches, on the girt line, is 40s on the flip, which is the answer in feet and frac tional parts. Ex. 2. Required the content, when the length is 19 feet, fide of the square 9 inches. Anf. ic feet 8 inch. 6 pts. Ex. 3.- the length 24 feet, side of the square 14 inches. Ans. 32 feet 8 inches. Ex. 4.-231 feet, side of the square 30 inches. Anf. 146 feet 10 inch. 6 pts. Ex. 5.-14; feet, side of the square 15 inches. . Anf. 17 feet 11 inches. Ex. 6. 22 feet, side of the square 12 inches. Anf. 22 feet , inches. Ex. 7.—15 feet, side of the square 10 inches. Anf. 10 feet 6 inch. 4 pts. 8". Ex. 8._-24 t'I feet, side of the square 2 feet. Anf. 96 feet 4 inchesa Ex. .-- 28 feet, side of the square ii inches. Anf. 23 feet 10 inch. 6 pts. 1" 6". Ex. 10.0 feet, fide of the square 141 inches. Ans: 12 feet i inchi Ex. 11.6 feet, the side of the square 3 feet. Anf. 54 feet. Ex. 12.-8feet, side of the square 14 inches. Anf. 10 feet 11 inches: Squared timber, whose breadth is greater than the thickness, may be truly cast up by the above rule with as much expedition as with any other. Unskillful measurers, however, generally add the breadth and thickness together, and they consider half their fum as the side of the square, and work accordingly; but this method is false ; and the greater the difference between the breadth and thickness is, the error thence resulting will be the more considerable ; and in every case of this kind the result is greater than the truth. EXAMPLE I. Required the solidity of a log whose length is 191 feet, breadth 32, and thickness 20 inches. The true method. The common method. Decimally. Duodecimally, F. F. lo, 32 3)19.5 20 2.6 8 19 6 2 By the Sliding rule. Set the rule and lip even at the ends; and over against the area area of the base on the slip you have the side of the square ori the girt line; then the folidity is found, as above. Ex. 2. How many cubic feet are in a log of wood 40 feet 6 inches long, the base being 32 inches by 20? Anf. 180 fcet. Ex. 3. Required the content of a log of wood, whose length is 13. feet, and base 10 inches by 8. Anf. 7 feet 4 in. 4 pts. Ex. 4. How many cubic fect are in a plank 12 feet long, I foot broad, and 6 inches thick? Anf. 16 feet 9 in. 3 pts. 10" Ex. 5. How many cubic feet are in a plank 20 feet long, the base being 30 inches by 20 ? Anf. 83 feet 4 inches. Ex. 6. How many cubic feet are in a log, whose length is 15 feet 9 inches, the breadth being 12 inches by 5 ? Auf. 6 feet 6 inches 9 pts. Es. 7. Required the solidity of a tree, 10, feet long, the. bafe being 15 inches by 9. Anf. 9 feet 10 in. I prt. 6" Fx. 3. Required the content of a log 16 feet long, 30 inches broad, and 18 thick. Anf. 50 feet. 9. Required the folidity of a piank 19 feet 3 inches long, 9 inches broad, and 6 inches thick. Anf: 7 feet 2 in. 7 pts. 6". Ex. 10. How many cubic feet are in a plank 17 feet long, its base being 14 inches by 7 ? Anf. 11 feet 6 in. 10 parts. Ex. 11. Required the content of a plank whose length is. 151 feet, breadth 10 inches, and thickness 8 inches. Anf. 8 feet 7 inches 4 parts. Ex. 12. Required the folidity of a plank whose length is 19 Scet 10 inches, breadth 15 inches, and thickness 12 inches. Anf. 24 feet 9 inches 6 parts, PROBLEM III. To find the folidity of round or unsquared timber. RULE, RULE, common way. Multiply the square of of the circumference by the length, and the product will be the folidity. EXAMPLE, I. Required the folidity of a tree whofe length is 32 feet, and girt 6 inches. Set the length in feet on the lip to 12 on the girt line, anul over against the side of the square, (which is of the girt) on the girt line, you have the content on the flip. Now, if we consider the tree a cylinder, its folidity may be found as follows. |