3. A gentleman consented to have his daughter married on New Year's day, and agreed to give her one dollar towards her portion, promising to double it, on the first day of every month for one year, what was her portion? Ans. $4095. 4. A thresher wrought 20 days and received for the first day's labour 4 grains of wheat; for the second 12; for the third 36, &c, how much did his wages amount to, allowing 7680 grains to make a pint, and the whole to be disposed of at $1 per bushel? Ans. $14187. 5. A sum of money is to be divided among 10 persons, the first is to have $10, the second $30 and so on in three fold proportion; what will the last have? Ans. $196830. DUODECIMALS. This rule is of great use to carpenters, joiners, &c. The name is derived from the latin words duo, 12 and decem, 10, and as the ratio is 12, it may with propriety be termed Duodecimals. As the French and other European nations divide their inch into 12 equal lines, so our American artificers, suppose the inch to be divided as follows: DENOMINATIONS OF DUODECIMALS. 1 foot, I F F. 1. " Add 642.11.8.8 Add 6464.10.9 436.10.6.4 4243. 9.4 Add 6468.10.5 4864. 9.3 Add 9346. 7.3 4842. 9.4 3464.11.6 MULTIPLICATION.-Observe the following rules. F 1. 2.1 11.0 12.10.0 2. Multiply 8 feet 6 inches by 14 feet 9 inches. Ans. 125 ft. * in. 6 s. CASE II. Rule.-Multiply by the component parts, as in compound multiplication, and take parts for the inches as in practice. 1. Multiply 208 feet 8 inches 4 seconds, by 24 feet 3 inches 9 seconds. F. 1. » 6 x 4 5073.10.7.3 Answer. 2. Multiply 4 feet 7 inches by 6 feet 4 inches. Ans. 29 ft. 0. in 4 s. 3. How many square feet are in a floor 48 ft. 6 in. long, by 24 ft. 3 in. broad? Aus. 1176 ft. 1 in. 6 s. 4. How many cubic feet of stone work are contained in 9 walls, each 30 ft. 6 in. long, 9 ft. 8 in. high and 2 ft. thick? Ans. 5307 ft. 5. How many cubic feet in a cellar 30 ft. 3 in. long, 27 ft. 6 in. broad, and 8 ft. deep? Ans. 6655 ft. 6. What is the content of a marble slab 6 ft. 7 in. long, 2 ft. broad, and 1 ft. 9 in. thick? Ans. 23 ft. O in. 6 7. What is the superficial content of a stone 4 ft. 9 in. long, and 3 ft. 9. in. broad? Ans. 18 ft. O in. 1 s. 6 t. MENSURATION. IMPORTANT TO SHIP BUILDERS. A concise Rule to find the length of Masts. RULE 1.-Multiply the length of the keel by 2, and divide the product by 3, and then to the quotient add the breadth of the beam, and the sum will be the length of the main mast. 1. Suppose a ship to be 84 feet by the keel, and 31 ft. by the beam, what is the length of her mast? Ans. 87 ft. 2. Suppose a ship to be 108 feet by the keel, and 40 feet by the beam, what is the length of her main mast? Ans. 112 feet. ANOTHER METHOD. When the length and thickness of Masts is required in yards. RULE.—Add the breadth of the beam and the depth of the hold in feet together, and divide the sum by 1.5, and the quotient will be the length of the main mast in yards. 1. Admit a ship whose keel in length is 73 feet, and the breadth of the beam 28.5 feet, and the depth of the hold 12 feet, what is the length of her main mast? Feet. Ans. 81 feet. Breadth of the beam, 28.5 Depth of the hold, 12.0 1.5)40.5(27 yards or 81 feet. Now to find the thickness, it is customary to allows of the length in feet for the thickness in inches; in that case, a main mast 81 feet long, must be 27 inches thick. 2. If a ship of 100 tons be 44 feet long at the keel, of what length must the keel of a ship be that carries 220 tons? tons. tons. Say as 100 : 220 : : 443 (85184) 187404.80, whose cube root is 57.226, the length of the keel sought. To find Ship's Tonnage by Carpenter's Measure. Rule.--For single-decked vessels, multiply the length and breadth at the main beam, and depth of the hold together, and divide the product by 95. For double-decked vessels, take half the breadth of the main beam, and work as above directed. 1. What is the tonnage of a single decked vessel, whose length is 60 feet, breadth 20, and depth 8 feet? Ans. 101 is tons. 95 2. What is the tonnage of a double-decked vessel, whose length is 65 feet, breadth 21 feet 6 inches, and depth 10 feet 9 inches? Ans. 1581} tons. TO FIND GOVERNMENT TONNAGE. GOVERNMENT RULE.If the vessel be double-decked, take the length thereof from the fore part of the main stem to the after part of the stern-post above the upper deck; the breadth thereof at the broadest part above the main wales, half of which breadth shall be accounted the depth of such vessel, and then deduct from the length of the breadth; multiply the remainder by the breadth, and the product by the depth, and divide this last product by 95, the quotient whereof shall be deemed the true contents or tonnage of such ship or vessel; and if such ship or vessel be single-decked, take the length and breadth, as above directed, deduct from the said length of the breadth, and take the depth from the under side of the deck-plank to the ceiling in the hold, and the multiply and divide as aforesaid, and the quotient shall be deemed the tonnage.” 1. What is the government tonnage of a single-decked vessel, whose length is 69 feet 6 inches, breadth 22 feet 6 inches, and depth 8 feet 6 inches? F. I. F. I. Illustration of the rule 69.6 breadth 22.6 Deduct 13.6 3 107 10 1232.0 6 in. is į 28.0 feet. tons. feet 1260 X 8.6 = 11216 2. Required the tonnage of a single decked vessel, by carpenter's measure, whose length is 70 feet 6 inches, breadth 24 feet 8 inches, and depth 9 feet 10 inches? Ans. 180 tons. 3. What is the Government tonnage of a double-decked vessel of the following dimensions: length 82 feet 3 inches, breadth 24 feet 3 inches, and depth 12 feet 1.1 inches? Ans. 20973 tons. BOARD OR LUMBER MEASURE. RULE:~Multiply the length in feet by its breadth in inches, and divide by 12 for the content. 1. What is the content of a board 24 feet long and 8 inches wide? Ans. 16 ft. 2. What is the content of a board 30 feet by 16 inches? Ans. 40. |