7. How much wood in a load, which measures 10f. in length, 3ƒ 9in. in width, and 4f. 8in in height; and how much will it cost, at 1 dol. 33 cts. per cord? Ans. 1 cord, and 47 solid feet over; it will cost 1 doll. 81 cts. 8m. OR, we may multiply by the feet as already directed, and for the inches, take such parts of the multiplicand, &c, as the inches are aliquot or even parts of a foot, as done in the rule of Practice. 8. How many square feet in a board of 16 feet, 4 inches in length, and 2 feet, 8 inches wide? 6 inches is 16 4 2 8 32 8 2. 2 8 Ans. 43 282 8 6 8 HERE, in the first place I multiply the 16ft. 4in. by the feet (2) of the multiplier; the inches (8) not being an even part of a foot, I take such as are an even part; thus, 6in. is half a foot, therefore divide the multiplicand by 2 for 6 inches, and that quotient by 3, (2 in. is of 6 inches) for 2 inches, all which being added, give the product of 16 feet, 4 inches multiplied by 2ft. 8in. 9. ANOTHER board is 18 feet 9 inches in length, and 2 feet, 6 inches wide, how many square feet does it contain? By Practice. Ans. 46ft. 10in. 6". By Duodecimals. 10. THERE is a stock of 15 boards, 12 feet, 8 inches in length, and 13 inch es wide; how many feet of boards does the stock contain ? Ans. 205 feet, 10 inches. By Practice. By Duodecimals. SUPPLEMENT to Duodecimals. QUESTIONS. 1. Of what use are Duodecimals? To whom more especially are they useful? 2. IN what are dimensions taken? 3. How do you proceed in the multiplication of duodecimals ? 4. For what number do you carry ? 5. WHAT do you observe in regard to setting down the product different from what is common in the multiplication of other numbers ? 6. Of what term is the product which arises from the multiplication of feet by inches? Feet by seconds? Inches by inches? Inches by seconds? Seconds by seconds? 7. In what way can the operation be varied? THE Dimensions of Wainscotting, Paving, Plastering, and Painting are taken in Feet and Inches, and the content given in Yards. PAINTERS and JOINERS. To find the Dimensions of their work, take a line and apply one end of it to any corner of the room, then measure the room going into every corner with the line, till you come to the place where you first began; then see how many feet and inches the string contains; this call the Compass or Round, which multiplied into the height of the room, and the Product divided by 9, the Quotient will be the content in yards. EXAMPLES. 1. If the height of a room painted be 12f. 4in. and the compass 84f. 1lin. How many square yards does it contain ? Ans. 116Y. 3f. 3' 8" | 2. THERE is a room wainscotted the compass of which is 47f. 3' and the height 7f. 6' What is the content in square yards? Ans. 39 Y. 3f. 4′ 6′′ GLAZIERS work by the foot. To find the dimensions of their work, multiply the height of windows by their breadth. EXAMPLES. THERE is a house with 4 tiers of windows, and 4 windows in a tier; the height of the first tier is 6f. 8'; of the second, 5ƒ. 9'; of the third, 4f. 6′ ; and of the fourth, 3f. 10'; and the breadth of each is 3f. 5'; What will the glazing come to, at 19 cents per foot? Ans. 53 Dolls. 88 cents. § 9. Alligation. ALLIGATION is the method of mixing two or more simples of different qualities, so that the composition may be of a mean or middle quality. It is of two kinds, MEDIAL and ALTERNATE. ALLIGATION MEDIAL. ALLIGATION MEDIAL is when the quantities and prices of several things are given, to find the mean price of the mixture compounded of those things. RULE. As the sum of the quantities or whole composition is to their total value' so is any part of the composition to its value or mean price. EXAMPLES. 1. A FARMER mingled 19 bushels of wheat at 6s. per bushel, and 40 bushels of Rye, at 4s. per bushel, and 12 bushels of barley, at 3s. per bushel together; I demand what a bushel of this mixture is worth? Bush. OPERATION. £. 8. Bush. L. s. |