RULE. The burthensrof similar built shijos 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 burthen of another ship, whose keel is 100 feet long? T.cwt. qrs. lb. As 75 x 75.x 75:300 : : 100 x 100 x 100:711 2 0 24+ DUODECIMALS, CROSS MULTIPLICATION, IS a rule made use of by workmen and artificers in cast ing up the contents of their work. RULE. 1. Under the mulplicand write the corresponding deno. minations 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; ob serving to carry an unit for every 12, from each lower 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 righ; 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. 4 6 97 39 58 97 FEET, INCRES AND SECONDS. F. I. [tiplier =prod. by the feet in the mul7 3 4 6 11 =ditto by the inches. 2 5 1 6 =ditto by the seconds. How many square feet in a board 16 feet 9 inches long, and 2 feet 3 inches wide ? By Duodecimals. By Decimals. F. 1. 16 9=16,75 feet. 2 3 2 3=2,25 33 6 8375 F. 1. Ans. 37 8 3 T 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 fect; of which make half a cord, and 128 a cord. EXAMPLE How many solid feet are contained in a load of wood. 7 feet 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 st. 3 in.= 2.25; then, 7,5 x 4,167=31,2525 X2,25=70,318125 solid feet, Ans. 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 half a cord, which is called 4 feet of wood; but if the breadth of the load be less than 4 feet, its beight 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 Diodecimals. By Decimals. F. in. F. 3,75 9 4 6 9,375 F. in. 4 8 3 4,6875=487 or half a cord and 8+ inches over. The foregoing method is concise and easy to those who are well acquainted with Duodecimals, but the following table will give tho content of any inad of wood, by inspection only, sufficiently exact for common practice; which will be found ver konvenient. A TABLE of Breadth, Height, and Content. Inches. 7 16|31|47|62| 1 3 4 6 8 9 10 12 13 14 8 16 32 48 64 1 3 4 5 7 8 9 11 12 13 15 9 17334966|| 1 31 41 6 7 8 9 11 12 14 15 10 ||173451 68|| 2 3 4 6 7 9 10 11 13 14 16 11 ||1835 53 70! 2 3 4 6 7 9 10 12 13!15 16 3 0 1836,5472 21 3.5 6 8 9 11 12 14 15 17 1 19|37|56|74|| 2 3 5 6 8 9 11 12 14 16 17 2 ||1938|57|76| 21 3 5 6 8 10 11 13 14 16 17 3 1939 59 781 2 3 5 7 8/10 11 13 15 16 18 4 ||20.40 60 80 1 2 3 35 7 8 10 12 13 15 17 18 5 21 41 62 82|| 2 3 3 5 7! 7! 8 10 12 14 16 17|19 6 1|2142|6384 2 4 5 7 9 11 12 14 16 18 19 7 122 4364/86|| 2 4 5 7 9 11 13 14 16 18 20 8 22 4466.881 2 4 6 7 9 11 13 15 17 18 20 9 ||23 45 68|90|| 2 4 6 7 9 11 13 15 17 19 21 10 123 4669 921 2 4 6 7 9 11 13 15 17 19 21 11 ||23|47 70 94 2 4 6 8 10 12 14 16 18 20 22 4 0 24/4872/96|| 21.41 6 8/10/12 14 16 18 20 22 TO USE THE FOREGOING TABLE, First measure the breadth and height of your load to the nearest average inch; then find the breadth in the left hand column of the table, then move to the right on the same line till you come under the height in feet, and you will have the content in inches, answering the feet, to which add the content of the inches on the right and divide the sum by 12, and you will have the true content of the load in feet and inches. Note.The contents answering the inches being always small, may be added by inspection. EXAMPLES. 1. Admit a load of wood is 3 feet 4 inches wide, and 2 feet 10 inches high, required the content. Thus, against 3 feet 4 inches, and under 2 feet, stands 40 inches ; and under 10 inches at top, stands 17 inches: then 40+17557, true content in inches, which divide by 12, gives 4 leet 9 inches, the answer. 2. The breadth being 3 feet, and height 2 feet 8 inches; roquired the conLent. Thus, with breadth 3 feet 0 inches, and under 2 feet atop, stands 38 inches; and under 8 inches, stands 12 inches: now 36 and 12 make 48, the answer in inches; and 48–712=4 feet, or just half a cord. 3. Admit the breadth to be 3 feet '1 inches, and height 3 feet 9 inches; required the content. Under 3 feet at top, stands 70; and under 9 inches, is 18: 70 and 18, mah 88-;-12=7 feet 4 inches, or 7 ft. I qr. 2 inches, the answer. TABLE 1. Showing the amount of £l, or $1, at 5 and 6 per cent. per annum, Compound Interest, for 20 years. Yrs.15 per cent. 6 per cent. Yrs.15 per cent. 6 per cent. 1 1,05000 1,06000 11 1,71034 | 1,89829 2 1,10250 1,12360 12 1,79585 | 2,01219 3 1,15762 1,19101 13 1,88565 | 2,13292 4 | 1,21550 1,26247 14 1,97993 2,26090 5 1,27628 1,33822 15 / 2,07893 2,39655 6 1,34009 1,41851 16 2,18287 2,54727 7 1,40710 1,50363 17 2,29201 2,69277 8 1,47745 1,59384 18 2,40661 | 2,85433 9 1,55132 1,68947 19 | 2,52695 3,02559 10 1,62889 1,79084 20 2,65329 3,20713 VII. The weights of the coins of the United States, pwt. grs. Eagles, 11 6 Standard 5 15 Gold. 2 193 17 8 Half-Dollars, 8 16 Standard 4 8 Silver. 1 204 Cents, 8 16 Half-Cents, } Copper. 4 8 The standard for gold coin is 11 parts pure gold, ani one part alloy--the alloy to consist of silver and copper The standard for silver coin is 1485 parts fine to 179 parti alloy-the alloy to be wholly copper. 173 |