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, I demand the burthen of another ship, whose keel is 100 feet long? T.cwt.qrs.lb. As 75x75x75 : 300 :: 100×100×100: 711 2 0 24+ 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 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 right hand of those in the multiplicam. 4. Do the same with the seconds in the multiplier, set. ting the result of each term two places to the right hand of those in the multiplicand, &c. How many square feet in a board 16 feet 9 inches long, and 2 feet 3 inches wide? By Duodecimals. F. I. 16 9 2 3 33 6 4 2 3 Ans. 37 SS 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 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 ft. 5 in= 2,25; then, 7,5×4,167 $1,2525×2,2570,318125 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 height must be increased so as to make half a cord, which is still called 4 feet of wood. By measuring the breadth and heighth 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. 84 inches over. The foregoing method is concise and easy to those who are well quainted with Duodecimals, but the following Table will give the content of any load of wood, by inspection only, sufficiently exact for common practice; which will be found very convenient. ft. in. 2 6 A TABLE of Breadth, Height, and Content. Breadth. || Height in feet. 1234 Inches. 1|2|3 | 4 | 5 | 6 | 7 | 8 | 9 |10|11| |15|30|45|60|| 1245 7910111214 6 7 2243 648624517 8 9111214/15) 9 10111314|16| 9101213,15 16 9|11|12|14|1517] 9 11 12 14 16|17| 8 10 11 13 141617 8101113,151618 8 10 12 13 15|17|18| 10 12 14 161719 8 9 11 1214161819) 1123 47 70194 4 6 8 10 12 14 16 18 20 22 4 0 24487296|| 2|46|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 cortent 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 8 feet 4 inches wide, and 2 feet 10 inches high; required the content.- es; Thus, against 3 ft. 4 inches, and under 2 feet, stands 40 inchand under 10 inches at top, stands 17 inches: then 40-+17-57 true content in inches, which divide by 12 gives 4 feet 9 inches, the answer. 2. The breadth being 8 feet, and height 2 feet 8 inches; required the content. Thus, with breadth 3 feet 0 inches, and under 2 feet atop, stands 36 inches; and under 8 inches, stands 12 inches: now 56 and 12, make 48, the answer in inches; and 48 12 4 feet, or just half a cord. 3. Admit the breadth to be S feet 11 inches, and height 5 feet 9 inches; required the content. Under 3 feet at top, stands 70; and under 9 inches, is 18: 70 and 18, make 88÷÷12-7 feet 4 inches, or 7 ft. 1 qr. 2 inches, the answer. TABLE I. Showing the amount of £1, or 31, at 5 and 6 per cent. per annum, Compound Interest, for 20 years. Trs. 15 per cent.6 per cent.|Frs. 15 per cent.16 per cent. 6749 1,34009 1,41851 16 2,18287 2,54727 1,40710 1,50363 17 2,29201 2,69277 8 1,47745 1,59384 18 1,68947 19 1,55132 VII. The weights of the coins of the United State 2,52695 3,02559 2,653 29 3.20713 Eagles, pwt. gr. Standard Half-Eagles, 5 15 Gold. Quarter-Eagles, 2 19 Dollars, 17 8 The standard for gold coin is 11 parts pure gold, and one part alloy--the alloy to consist of silver and copper. The standard for silver coin is 1495 parts fine to 179 parts alloy—the alloy to be whollly copper. |