2. A piece of timber being 16 inches broad, 11 inches thick, and 20 feet long, to find the content ? Breadth 16 inches. Prod. 176 X 20=3520 then, 3520-144=24,4 feet, the Anscer. 3. A piece of timber 15 inches broad, 8 inches thick, and 25 feet long ; how many solid feet doth it contain ! Ans. 20,8 + feet. ART. 8. When the breadth and thickness of a piece of timber are given in inches, to find how much in length will make a solid foot, RULE. Divide 1728 by the product of the breadth and depth, and the quotient will be the length making a solid foot. EXAMPLES 1. If a piece of timber be 11 inches broad and 8 inches deep, how many inches in length will make a solid foot ? 11 X8=88)1728(19,6 inches. Ans. 2. If a piece of timber be 18 inches broad and 14 inches deep, how many inches in length will make a solid foot ? 18x14=252 divisor, then 252)1728(6,8 inches. Ans. ART. 9. To measure a Cylinder. Definition.--A cylinder is a round body whose bases are circles, like a round column or stick of timber, of equal bigness from end to end. RULE. Multiply the square of the diameter of the end by ,7854 which gives the area of the base ; then multiply the area of the base by the length, and the product will be the solid content. EXAMPLE What is the solid content of a round stick of timber of equal bigness from end to end, whose diameter is 18 in ches, and length 20 feet ! 18.in.=1,5 ft. X1,5 Square 2,25 X,7854=1,76715 area of the base. X 20 length. Ans. 35,34300 solid content Or, 18 inches. 18 inches. 324x,7854251,4696 inches, area of the base. 20 length in feet. 144)5089,3920(35,343 solid feet. Ans. ART. 10. To find how many solid feet a round stick of timber, equally thick from end to end, will contain when hewn square. RULE. Multiply twice the square of its semi-diameter in inches by the length in feet, then divide the product by 144, and the quotient will be the answer. EXAMPLES. If the diameter of a round stick of timber be 22 inch es and its length 20 feet, how many solid feet will it contain when hewn square ? 11X11 X2 X20--144=33,6 + feet, the solidity when hewn square. Art. 11. To find how many feet of square edged boards of a given thickness, can be şawn from a log of a given diameter. RULE. Find the solid content of the log, when made square. by the last article-Then say, As the thickness of the board including the saw calf: is to the solid seet : : So. is 12 (inches) to the number of feet of boards. EXAMPLES How many feet of square edged boards, 17 inch thick, including the saw calf, can be sawn from a log 20 feet long and 24 inches diameter ? 12X12 X2 x 20- 144240 feet, solid content, As 1 1: 40 ; : 12 : 384 feet, the Ana. Art. 12. The length, breadth, and depth of any square box 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 ansiyer. 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? 50 X 40 X 60-2150,425=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 inultiplied by the number of bricks contained in a solid foot gives the answer. How many bricks 8 inches long, 4 inches wide, and 2} inches thick, will it take to build a house 44 feet long, 40 feet wide, and twenty feet high, and the walls to be one foot thick ? 8X4X2,5=30 solid inches in a brick, then 1728--80 =21, 6 bricks in a solid foot. 44 X 40 X 44 X40=168 feet, whole length of wall. 4 times the thickness. EXAMPLE. 164 remains. Multiply by Multiply by 3280 solid feet in the whole wall 21,6 bricks in a solid foot 70948 bricks. Arse 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 ? 72 X24X12;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. A ship 84 feet by the keel, 28 feet by the beam; what is the tonage ? 84 X 28 X 14; 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; EXAMPLE EXAMPLES. 1. If a cable 6. inches about, require an anchor of 2 cwt, of what weight must an anchor be for a 12 inch cable As 6 X6 X6 : 2fcut. : : 12X12X12 : 18cut. 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 24 cwt.? cwt. cut. in. As 18: 12X12X12 : 2,25 : 2161216=6 Ars. ART., 16. Having the dimensions of two similar / ilt ships of a different capacity, with the burthen of to of them, to find the barthen of the other, 3 RULE. The burthens 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, 1 demand the burthen of another ship, whose keel is 100 feet long? T. cit. ib. As 15X75X75 : 300;: 100 x 100 x 100 :7112 0 24+ qrs. OR DUODECIMALS, CROSS MULTIPLICATION, Is 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 a unit for every 12, from each lovrer denomination 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 of those in the multiplicand, &c. EXAMPLES. |