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3 X 3 X 3 X 4 =108 Divisor 37% 37% 37% 37=1874161 Subtrahend
37 X 374 37X 4 =202612 Divisor 376 X 376 x 370 X 376= 19987173376 Subtrahend.
DUODECIMALS, or Cross Multiplication, is a rule made ufe of in measuring and computing the dimensions of the several parts of build. ings; it is likewile used to find ships'tonnage and the contents of bales, cales, &c.
Dimensions are taken in feet, inches, and parts. Artificers' work is computed by different measures, viz. Glazing, and masons' fiat work, by the foot ; Painting, paving, plastering, &c. by the yard ; Partitioning, flooring, roofing, tiling, &c, by the square of 100 feet; Brick-work, &c. by the rod of 16 feet, whose square is 2724. The contents of bales, cases, &c, by the ton of 49
Cubic feet. The tonnage of ships, by the ton of 95 feet.
RULE FOR MULTIPLYING DUODECIMALLY. 1. Under the multiplicand write the corresponding denominations of the multiplier.
2. Multiply each term in the multiplicand, (beginning at the lowest) by the feet in the multiplier ; write each result under its respective term, observing to carry an unit from each lower denomination to its superior.
3. In the same manner, multiply the multiplicand by the inches in the multiplier, and write the result of each term, one place more to the right hand of them, in the multiplicand.
4 Work in the same manner with the other parts in the multiplier, setting the result of each term two places to the right hand of those in the multiplicand, and fo on for thirds, fourths, &c.
5. Proceed in the like manner with all the rest of the denominations, and their sum will give the answer required.
2. Multiply 9 feet 6 inches by 4 feet 9 inches.
3. What is the price of a marble flab, whose length is
feet 7 inches, and breadth 1 foot 10 inches, at i dollar per foot ?
Ans, io dols. 23 cts.
4. There is a house with three tiers of windows, 3 in a tier, the height of the first tier is 7 feet 10 inches, of the second 6 feet 8 inches, and of the third 5 feet 4 inches, and the breadth of each is 3
feet 11 inches; what will the glazing come to, at 14d. per foot ?
Ans. £.13 11S. 101d.
5. If a house measures within the walls 52 feet 8 inches in length, and
39 feet 6 inches in breadth, and the roof be of a true pitch, or the rafters of the breadth of the building, what will it come to, roofing at ios, 6d. per square ?
Anf. £.12 125, 11 d.
APPLICATION OF DUODECIMALS.
To find how many cubic or solid square feet (in order to ascertain
the freight) are contained in cases, bales, &c. that is, how many cubic feet ihey will take up in a ship.
2. Suppose the dimensions of a bale to be 7 feet 6 inches, 3 feet 3 inches, and a foot 10 inches ; what is the folid content ?
What is the freight of a bale containing 65 feet 9 inches, at 15 dollars per ton of 40 feet ?
3. A merchant imports from London 6 bales of the following dimensions, viz.
Length Height. Depth.
2 8 5.
2 8 1 8 What are the folid contents, and how much will the freight amount to, at 20 dollars per ton ? The contents are viz.
I 2 5
Ans. 35 dols. 79 cts, .
To find Ships' Tonnage by Carpenters'- Measure. RULE. For single decked vessels, multiply the length, breadth at the main beam, and depth of the hold together, and divide the produet by 95
EXAMPLE. What is the tonnage of a single decked vessel, whole length is 60 feet, breadth 20 feet, and depth 8 feet?
60 length. 20 breadth.
This is the usual method of tonnaging a fingle-decked veffel, having the deck bolted to the wale. But if it be required that the dock bo bolted at any height above the wale, the custom is to pay the car. penter for one half of the additional height, to which the deck may be thus raised ; that is, one half of the difference being added to the former depth, gives the depth to be used in calculating the tonnage
EXAMPLE. A merchant, after having contrated with a carpenter to build a single-decked vessel of 60 feet keel, 20 feet beam, and 8 feet hold, delires that the deck be laid for 10 feet hold ; required the tonnage to be paid for.
Rule. For a double-decked vessel, take half the breadth of the main beam for the depth of the hold, and work as for a fingle-decked vefsel.
EXAMPLES. 1. What is the tonnage of a double-decked vessel, whose length is 65 feet, and breadth 21 feet 6 inches ?
95)15023 1(15811 21 6 breadth.