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For the mean depth.
490 X 368X5.6=1009792 cubic inches
5.6 mean depth.
By the Sliding Rule.
Set the mean depth on MD to the length on N, and against the breadth on the line A is the content on the line B.
His instrument is two feet in length, much used in taking dimensions, and in casting up the contents. One of its fides is provided with a sider, or slip, both sides of which are divided in the same logarithmic manner with one of the fides of the rule. On the other side of the slider is another line, marked the girt line, and is useful in cafting up solids. Besides, at the divisions 17.15, and 18.95, are marked w. G. and A. G. the wine and ale gauge points, for the purpose of gauging wine and ale by this rule.
This rule is so well known, that it is unnecessary to give a tedious description of its properties or construction. We shall only give a few rules to thew its utility,
PROB. I. To multiply any two numbers.
Rule. Set i on the slip to one of the factors on the stock, and over against the other factor on the flip you have the product on the stock.
Pros. II. To divide by the fiding rule.
Rule. Set the divisor on the flip to the dividend on the stock, and against s on the flip you have the quotient on the stock.
PROB. III. To square a number by the slide ruk.
RULE. Set i on the flip to the given number on the stock, and against the given number on the flip you have the square on the stock.
PROB. IV. To extract the square root by the sliding rule.
RULE. Set i or 100 on the flip to I or in on the girt line, and over against the given number on the Nip you have the root on the girt line.
Prob. V. To perform the rule of three by the siding rule.
Rule. Set the first term on the slip to second term on the stock, and over against the third ferm on the flip you have the answer on the stock.
PROB. VI. To caß up fuperficies by the fliding rule.
Rule, Set the breadth in inches on the flip to 12 on the stock, and against the length in feet on the stock you have the content on the flip in square feet and decimal parts.
PROB. VII. To find the solid content of Squared timber.
Rule. Set the length in feet on the lip to 12 on the girt line, and against the fide of the square in inches on the girt line is the content in solid teet on the flip.
PROB. VIII. To find the. folid content of four-sided timber, whose
base is an oblong; that is, whose breadth is greater than its thicknefs.
Rule. Multiply the breadth by the thickness by Prob. I. and extract the square root of their product by Prob. 4. With
this square root, as the fide of the square, work as directed in Prob. 7. and you have the answer.
MEASURING OF BOARD AND TIMBER.
To find the superficial content of a board or plank.
Multiply the length by the breadth, and the product is the area.
RULE 2. If the board is tapering, add the breadth of both ends together, and multiply half the fum by the length for the area,
Required the area of a plank 15 inches broad and 18 feet long
Decimally Duo-decimally. By Reduction
I=216 Breadth 1.25
22 6 And
1443240(22 feet. 22.50 Ant
By the Slide rule.
Set 15, the breadth in inches, on the flip, to 12 on the stock, and opposite to 18, the length in feet, on the stock, you have 22; feet on the flip.
Ex. 2. Required the content of a plank 16 feet 3 inches long, and 18 inches broad. Ànf. 24 feet 4 inch. 6 parts. Ex. 3.- of a plank 22 feet long 194 inches broad.
Anf. 36 feet 11 inch. 7 parts 6" Ex. 4.-30 feet long and 14 inches broad.
Anf. 35 feet 4 inch. 8 parts. Ex. 5.--25% feet long and 19 inches broad.
Anf. 39 feet to inch. 2 parts. Ex. 6.-341 feet long and 21 inches broad.
Anf. 60 feet 4 inch. 6 parts. Ex. 7.-27feet long and 151 inches broad.
Anf: 35 feet 2 inch. 4 parts 6". Ex. 8.-327' feet long and 13. inches broad.
Anf. 35 feet 5 inch. I part 3". Ex. 9.-231 feet long and to inches broad.
Anf. 19 feet 3 inches 3 parts. 5" Ex. 10.-12 feet long and 9 inches broad.
Anf. 9 feet 2 inch. 3 parts. -10 feet long and 6 inches broad.
Anf. 5 feet 2 inches. Ex. 12.-1515 feet long and 84 inches broad.
Anf. 10 feet 4 inches 5 parts 3". Ex. 13.-197's feet long and 8 inches broad.
Anf. 12 feet 84 inches. Ex. 14.29 feet long and 22 inches broad.
Anf. 53 feet 2 inches. Ex. 15.-_-321 feet long and 16 inches broad.
Ans. 52 feet 8 inches.