DUODECIMALS. DUODECIMALSs, or Cross Multiplication, is a rule made use of in measuring and computing the dimensions of the several parts of buildings; it is likewise used to find ships' tonnage and. the contents of bales, cases, &c. Dimensions are taken in feet, inches, and parts. Artificers' work is computed by different measures, viz. Glazing, and masons' flat work, by the foot; Painting, paving, plastering, &c. by the yard. Partitioning, flooring, roofing, tiling, &c. by the square of 100 ft. Brick-work, &c. by the rod of 16 feet, whose square is 2724. The contents of bales, cases, &c. by the ton of 40 cubic feet. The tonnage of ships, by the ton of 95 feet. RULE FOR MULTIPLYING DUODECIMALLY. 1. Under the multiplicand write the corresponding denom inations of the multiplier. 2. Multiply each term in the multiplicand, (beginning at the lowest) by the teet in the multiplier; write each result under each 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, oneplace 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 so 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. EXAMPLES. 1. Multiply 4 feet 9 inches by 8 inches.. 2. Multiply 9 feet 6 inches by 4 feet 9 inches. 3. What is the price of a marble slab, whose length is 5 feet 7 inches, and breadth 1 foot 10 inches, at 1 dollar per foot? Ans. 10 dols. 23 cents. 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. 10žd. 5. If a house measures within the walls 52 feet 8 inches in length, and 30 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 10s. 6d. per square? Ans. £.12 12s. 112. 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 they will take up in a ship. EXAMPLES. 1. Suppose the dimensions of a bale to be 7 feet 6 inches, 3 fect 3 inches, and 1 foot 10 inches ; what is the solid content? 2. 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 follow ing dimensions, viz. What are the solid content, and how much will the freight amount to, at 20 dollars per ton ? The contents are, viz. ft. in. Feet. To find Ship's Tonnage by Carpenter's Measure. RULE. For single decked vessels, multiply the length, breadth at the main beam, and depth of the hold together, and divide the product by 95. EXAMPLE. What is the tonnage of a single decked vessel, whose length is 60 feet, breadth 20 feet, and depth 8 feet? 60 length This is the usual method of tonnaging a single-decked vessel, having the deck bolted to the waie. But if it be required that the deck be bolted at any height above the wale, the custom is to pay the carpenter for one half of the addrional height, to which the deck may be thus rai-ed; that is, one half of the diference being added to the former depth gives the depth to be used in calculating the tonnage. EXAMPLE. A merchant, after having contracted with a carpenter to build a single-decked vessel of 60 feet keel, 20 feet beam, and 8 feet hold, desires that the deck be laid for 10 feet hold; required the tonnage to be paid for ? 60 length RULE. For a double-decked vessel, takę half the breadth of the main beam for the depth of the hold, and work as for a single decked vessel. 1. EXAMPLES. What is the tonnage of a double-decked vessel, whose length is 65 feet, and breadth 21 feet 6 inches ? |