Exchange for £1000. New York, May 16, 1856. Thirty days after sight of this first of exchange (second and third of the same tenor and date unpaid), pay J. W. Hathaway & Co., or order, London, one thousand pounds sterling, value received, and place the same to my account. To BATES, BARING, & Co., London. OPERATION. RUFUS W. KING. $40 X 1.095 $4.8663; 1000 X 4.8663 = $ 4866.66. = × We multiply $40, the nominal value of a pound, by 1.095, the given rate, decimally expressed, and obtain $ 4.866 as the cost of a pound at that rate; and 1000 multiplied by the number denoting this cost gives $ 4866.66% as the cost of the bill. RULE. Multiply the face of the bill by the cost of one pound at the given rate of exchange, and the product will be the cost in dollars. NOTE. When there are in the given sum, shillings, pence, or farthings, they must be reduced to a decimal of a pound. EXAMPLES FOR PRACTICE. 2. A merchant in Boston wishes to purchase a bill of 572£ 10s., on Liverpool, the premium being 8 per cent.; what will it cost him in dollars and cents? Ans. $2760.723. 3. If J. C. Sherman, of Chicago, should 1200£, exchange being at 94 per cent., what the bill in United States money? remit to London will be the cost of Ans. $5826.66. 267. To find the face of a bill on England, which can be purchased for a given sum. Ex. 1. When exchange is at 9 per cent. premium, what will be the amount of a bill on London which I can purchase for $4866.66 ? OPERATION. $41.095 $4.8663; 4866.664.866 = Ans. 1000£. 266. The rule for finding the cost of a bill on England in United States currency? 267. The rule for finding the face of a bill on England, which can be purchased for a given sum of United States currency?. We find, as by Art. 266, the cost of one pound at the given rate of exchange. The given sum, $ 4866.663, we divide by the cost of one pound, and obtain 1000£ as the required face of the bill. RULE. Divide the given sum by the cost of one pound at the given rate of exchange, and the quotient will be the face of the bill in pounds. EXAMPLES FOR PRACTICE. 2. J. Reed, of Cincinnati, proposes to make a remittance to Liverpool of $1640, exchange being at 8 per cent. premium ; what will be the face of the bill he can remit for that sum? Ans. 340£ 1s. 10d. 3. A merchant wishes to remit $500 to England, exchange being at 10 per cent. premium; what will be the face of the bill he can purchase for that sum? Ans. 102£ 5s. 5d.+. EXCHANGE ON FRANCE. 268. In France accounts are kept in francs and centimes. The centimes are hundredths of a frapc. All bills of exchange on France are drawn in francs, and are bought, sold, and quoted as at a certain number of francs to the dollar. 269. To find the cost of a bill on France. Divide the face of the bill by the cost of one dollar in francs, and the quotient will be the cost in dollars. EXAMPLES FOR PRACTICE. Ex. 1. What must be paid, in United States currency, for a bill on Paris of 2380 francs, exchange being 5.15 francs per dollar? Ans. $462.13+. 2. How many dollars will purchase a bill on Havre of 30000 francs, exchange being 5.17 francs per dollar? Ans. $5797.10+. 3. What is the cost of a bill on Paris of 62500 francs, exchange being 5.12 francs per dollar? Ans. $12207.03+. 270. To find the face of a bill on France, which can be purchased for a given sum. 268. How are accounts kept in France? How are all bills of exchange on France drawn? - 269. How do you find the cost in United States currency of a bill on France? -270. How do you find the face of a bill on France, which can be purchased for a given sum of United States money ? Multiply the given sum by the cost of one dollar in francs, and the product will be the face of the bill in francs. Ex. 1. Alfred Walker, of New York, pays $2500 for a bill on Paris, exchange being 5.12 francs per dollar. face of the bill in francs? What was the Ans. 12800. 2. When exchange on France is at 5.13 francs per dollar, a bill of how many francs should $700 purchase? Ans. 3591. 3. Morton and Blanchard, of Boston, wish to remit $675 to Paris, exchange being 5.16 francs per dollar; what will be the face of the bill of exchange they can purchase with the money? Ans. 3483 francs. DUODECIMALS. 271.* Duodecimals are a kind of compound numbers in which the unit, or foot, is divided into 12 equal parts, and each of these parts into 12 other equal parts, and so on; thus, 2, 144, &c. Duodecimals decrease from left to right, according to a scale of 12 (Art. 82; note). The different orders, or denominations are distinguished from each other by accents, called indices placed at the right of the figures. Thus, 1 inch or prime, equal to of a foot, is written 1 in. or 1'. 1 second 1 third 1 fourth 12 fourths make 1"". 12 seconds 12 inches or primes make 1'. 66 1ft. NOTE. The foot expresses 12 linear inches, 144 square inches, or 1728 cubic inches, according to the measure in which the duodecimal is employed. Duodecimals are less used in practice than formerly, since all examples in duodecimals can be readily performed by common or decimal fractions. ADDITION AND SUBTRACTION. 272.* Duodecimals are added and subtracted in the same manner as compound numbers. 271. What are duodecimals? How do duodecimals decrease from left to right? How are the different denominations distinguished from each other? 272. How are duodecimals added and subtracted? EXAMPLES FOR PRACTICE. 1. Add together 12ft. 6' 9", 14ft. 7′ 8′′, 165ft. 11′ 10′′. Ans. 193ft. 2' 3". 2. Add together 182ft. 11′ 2′′ 4"", 127ft. 7′ 8′′ 11′′ 291ft. 5' 11" 10". Ans. 602ft. 0' 11" 1"". 3. From 204ft. 7' 9" take 114ft. 10' 6". Ans. 89ft. 9' 3". 4. From 397ft. 9' 6" 11" 7" take 201ft. 11' 7" 8" 10""". Ans. 195ft. 9' 11" 2" 9" MULTIPLICATION AND DIVISION. 273.* The denomination of the product of any two duodecimals. Ex. 1. What is the product of 9ft. multiplied by 3ft.? 2. What is the product of 7ft. multiplied by 6'? Ans. 3ft. 6'. 5' 3. What is the product of 5' multiplied by 4'? Ans. 1' 8". 4. What is the product of 9' multiplied by 11""? = OPERATION. Ans. 8" 3". 9', 99; Thus, feet multiplied by a number denoting feet produce feet; feet, by primes produce primes; primes, by primes produce seconds, &c.; and the several products are of the same denomination as denoted by the sum of the indices of the numbers multiplied together. Hence, When two numbers are multiplied together, the sum of their indices annexed to their product denotes its denomination. 274.* To multiply duodecimals together. Ex. 1. Multiply 8ft. 6in. by 3ft. 7in. Ans. 30ft. 5' 6". 273. How is the denomination of the product denoted when duodecimals are multiplied together? OPERATION. 8ft. 6' 3ft. 7' We first multiply each of the terms in the multiplicand by the 7' in the multiplier; thus, 6' X 7' 42" = 3' and 6". Writing the 6" below, one place to the right, we add the 3' to the product of 8ft. × 7' = 59%= 4ft. and 11', which we write down. We then multiply by the 3ft., thus: 6' X 3 18' 1ft. and 6'. We write the 6' under primes in the other partial product, and add the 1ft. to the product of the 8ft. X3, making 25ft, which we write down. The partial products being added, we obtain 30ft. 5' 6". 2 5ft. 4ft. 1 1'6" 3 Oft. NOTE. The notation of feet, primes, seconds, &c., of the multiplier is retained in the operation to note the different order of units. RULE. Write the multiplier under the multiplicand, so that the same denominations shall stand in the same column. Beginning at the right hand, multiply each term in the multiplicand by each term of the multiplier, and give each term of the product the proper index, observing to carry 1 for every 12 from each lower denomination to the next higher. The sum of the several partial products will be the product required. EXAMPLES FOR PRACTICE. 2. Multiply 8ft. 3in. by 7ft. 9in. 3. Multiply 12ft. 9' by 9ft. 11'. Ans. 63ft. 11' 3". Ans. 126ft. 5' 3". 4. My garden is 18 rods long and 10 rods wide; a ditch is dug round it 2 feet wide and 3 feet deep; but the ditch not being of a sufficient breadth and depth, I have caused it to be dug 1 foot deeper, and, outside, 1ft. 6in. wider. How many solid feet will it be necessary to remove? Ans. 7540. 5. I have a room 12 feet long, 11 feet wide, and 74 feet high. In it are two doors, 6 feet 6 inches high, and 30 inches wide, and the mop-boards are 8 inches high. There are 3 windows, 3 feet 6 inches wide, and 5 feet 6 inches high; how many square yards of paper will it require to cover the walls? Ans. 25 sq. yd. 275.* To divide one duodecimal by another. Ex. 1. A certain aisle contains 68ft. 10' 8" of floor. The width of the floor being 2ft. 8', what is its length? OPERATION. 2ft. 8') 6 8ft. 10' 8" (2 5ft. 10' 6 6ft. 8' 2ft. 2ft. 2' 8" Ans. 25ft. 10'. We first divide the 68ft. by the divisor, and obtain 25ft. for the quotient. We multiply the entire divisor by the 25, and subtract the product, 66ft. 8', from the corresponding portion of the dividend, and ob 274. The rule for the multiplication of duodecimals? |