Art. 12. The length, breadth and depth of any square bex being given, to find how many bushels it will contain. RULE. Multiply the length by the breadth, and that product by the depth, divide the last product by 2150,425 the solid inches in a statute bushel, and the quotient will be the answer EXAMPLE. There is a square box, the length of its bottom is 50 inches, breadth of ditto 40 inches, and its depth is 60 inches ; how many bushels of corn will it hold ? 50X40X60--2150,425–55,84+ or 55 bushels three pecks. Ans. Art. 13. The dimensions of the walls of a brick build ing being given, to find how many bricks are necessary to build it. RULE From the whole circumference of the wall measured round on the outside, subtract four times its thickness, then multiply the remainder by the height, and that pro duct by the thickness of the wall, gives the solid content of the whole wall ; which multiplied by the number of bricks contained in a solid foot gives the answer. EXAMPLE. How many bricks 8 inches long, 4 inches wide, and 21 inches thick, will it take to build a house 44 feet long, 40 feet wide, and 20 feet high, and the walls to be one foot thick ? 8X4X2,5=80 solid inches in a brick, then 1728:80 --21,6 bricks in a solid foot. 44+40+44+40=168 feet, whole length of wall. 4 four times the thickness. 3280 solid feet in the whole wall. Multiply by 21,6 bricks in a solid foot. Product, 70848 bricks, Anse Art. 14. To find the tonage of a ship. RULE. Multiply the length of the keel by the breadth of the beam, and that product by the depth of the hold, and divide the last product by 95, and the quotient is the tonage.. EXAMPLE Suppose a ship 72 feet by the keel, and 24 feet by the beam, and 12 feet deep; what is the tonage? 72X24X12--95=218,2+tons. Ans. RULE II. Multiply the length of the keel by the breadth of the beam, and that product by half the breadth of the beam. and divide by 95. EXAMPLE. A ship 84 feet by the keel, 28 feet by the beam ; what in the tonnage ? 84X28X14:95=350,29 tons. Ans ART. 15. From the proof of any cable, to find the strength of another. RULE. Is to the weight of its anchor ; EXAMPLES. 1. If a cable 6 inches about, require an anchor of 21 cwt. of what weight must an anchor be for a 12 inch cable As 6x6x6 : 24cwt. : : 12x12x12 : 18cwt. Ans. 2. If a 12 inch cable require an anchor of 18 cwt. what must the circumference of a cable be, for an anchor of 21 cwt. ? cwt. cut. in. As 18 : 12x12x12 2,25 : 216 216–6 Ans. ART. 16. Having the dimensions of two similar built ships of a different capacity, with the burthen of one of them, to find the burthen of the other. RULE. The burtnens of similar built ships are to each other, as the cubes of their like dimensions. EXAMPLE If a ship of 300 tons burthen be 75 feet long in the keel, I demand the larthen of another ship, whose keel is 100 feet long? T. cut. qrs. Ib. As 75x75x75 : 300 :: 100X100X100 : 711 2 0 24+ DUODECIMALS, OR CROSS MULTIPLICATION, IS S a rule made use of by workmen and artificers in casting up the contents of their work. RULE. 1. Under the multiplicand write the corresponding denominations of the multiplier. 2. Multiply each term into the multiplicand, beginning at the lowest, by the highest denomination in the multiplier, and write the result of each under its respective term : observing to carry an unit for every 12, from each-lower de nomination to its next superior. 3. In the same manner multiply all the multiplicand by the inches, or second denomination, in the multiplier, and set the result of each term one place removed to the right hand of those in the multiplicand. 4. Do the same with the seconds in the multiplier, setting the result of each term two places to the right hand oo those in the multiplicand, &c. EXAMPLES. 3 9 5 8 9 7 How many square feet in a board 16 feet 9 inches long, and 2 feet 3 inches wide ? By Duodecimals. By Decimals. F. da 16 9=16.75 feet. 3 2 3=2,25 '33 6 8375 3350 3350 on F. 1. Ans. 37,6875–87 Ans. 37 8 3 TO MEASURE LOADS OF WOOD. RULE. Multiply the length by the breadth, and the product by the depth or height, which will give the content in solid feet; of which 64 make half a cord, and 128 a cord. EXAMPLE. How many solid feet are contained in a load of wood, 7 fert 6 inches long, 4 feet 2 inches wide, and 2 feet 3 inches high ? 7 ft. 6 in.=7,5 and 4 ft. 2 in. =4,167 and 2 ft. 3 in. 2,25; then, 7,5X4,167 =31,2525X2,25=70,318125 solid feet, Aris. But loads of wood are commonly estimated by the foot, allowing the load to be 8 feet long, 4 feet wide, and then 2 feet high will make hali a cord, which is called 4 feet of wood; but if the breadth of the load be less than 4 feet, its height must be increased so as to make half a cord, which is still called 4 feet of wood. By measuring the breadth and height of the load, the content may be found by the following RULE. Multiply the breadth by the height and half the product will be the content in feet and inches. EXAMPLE. Required the content of a load of wood which is 3 feet 9 inches wide and 2 feet 6 inches high. By Duodecimals. By Decimals. F. in. F. 3 9 3,75 2 6 2,5 4 9 4 6 9,375 F. in. Ans. 4 8 3 4,687534 81, or half a cord and 84 inches over. The foregoing method is concise and easy to those who are well-scquainted with Duodecimals, but the following Table will give the content of any load of wood, by inspection only, sufficiently exact for como practice ; which will be foand very convenient. |