Emory and Company, Exchange Brokers, Baltimore, sold the following drafts. No. 1, $1500 at 3 per cent. below par 1. Pin Philadelphia owes L of Liverpool £349 19s. 3 d. sterling, to pay which he buys a bill at 24 per cent. below par; what must he pay in United States currency? Example shewing the use of Table 2d.' 2. A Factor in Philadelphia, owes a merchant in Dublin £1500 sterling, to pay which he buys a bill at 4 per cent. above par; how many dollars did that bill cost him? Ans. $69331. Let these examples be proved, by reducing them to sterling money. 3. A merchant in Bordeaux owes a merchant in Philadelphia, the nett proceeds of a consignment, amounting to $750.16, how many francs must he draw for, if exchange be at 19 cents per franc? Ans. 3948 frs. 21 cts. 4. What must be paid in New York for an invoice of goods, charged at 591 florins 17 stivers, allowing the exchange at 40 cents per florin, or 2 cents per stiver, and advancing on the invoice 60 per cent.? Ans. $378.78+ CIRCULAR EXCHANGE. CASE VII. 1. London was ordered to remit to Paris 1000 crowns at 32d. sterling per crown, and to draw for the value upon Amsterdam, at 36s. 6d. Flemish per pound sterling; but when the order came up, bills on Paris were at 321d. sterling per crown, what must be the rate of exchange with Amsterdam to compensate the advance on the remittance? Ans. 36s. 2d. * 2. If the exchange in Hamburgh on London, at 2 usance be 33, what should it be at sight, reckoning 1 per cent. for the time? Ans. 33s. 4d. 3. Suppose L of London has orders from P of Paris to remit to him at 23 livres 12 sous, (20 sous being equal to one livre) and to draw for the amount on A of Leghorn, at the exchange of 53d per dollar, but L finds the exchange of London on Paris is 24 livres-At what rate of exchange should he draw on Leghorn to fulfil the order? Ans. 52 4. A merchant in Baltimore shipped a quantity of flour which, when disposed of, amounted to 1040 milreas 500 reas, and received in return 17 pipes of wine, how much was the wine per pipe? Ans. $80. INVOLUTON, OR THE METHOD OF RAISING POWERS. 1. The first power of any number is unity multiplied by such number. 2. The second power of a number is found by multiplying any number by itself. *The term usance is French, and signifies the usage of different countries, in relation to the payment of bills: usances vary from 14 days to 1, 2 and 3 months after the date of a bill. EXAMPLES. Let 2 be raised to all the successive powers, from the 2d to the 5th. 2 × 2 =4 square of second power. 2 × 2 × 2 = 8 cube or third power. 2 × 2 × 2 × 2 = 16 biquadrate or 4th power. 2 × 2 × 2 × 2 × 2 32, 5th power. 1. A floor is 12 feet square, how many feet of boards does it contain? 2. In a plantation 300 perches square, how many perches does it contain? TABLE OF POWERS. Ans. 144 ft. Ans. 90000. Roots Squares. Cubes. 4th pow. 5th pow. 6th pow. 7th pow. 8th pow. 9th pr. 1. To extract the Square Root prepare the number for extraction by pointing it from units place, into periods of two figures each. 2. Find by involution or for convenience sake in the table, a square nearest to the first, subtract and bring down the next period, which place to the right of the remainder for a dividend. 3. Double the quotient figure for a divisor, and try how often it is contained in all the figures of the dividend except the one, on its right. 4. Place this in the quotient for a second figure of the root, as well as to the right of the divisor. 5. Multiply by this quotient figure as in division, the product subtract as before, and to the difference bring down the third period. 6. Proceed in like manner, still doubling the quotient figures for a new divisor, and bringing down another period each time for a new dividend, until the whole is completed. EXAMPLE. 1. What is the square root of 10, 34, 26, 56? (3216 9 62)134 124 641)1026 641 6426)38556 2. Extract the square root of 151321? Ans. 389 rt. 3. CC of 2985984? "1728 rt. 4. 66 66 " of 23097636? " 4806 rt. CASE II. In extracting the root of whole numbers and decimals, one half the number of decimal figures must be pointed out in the quotient. 1. What is the square root of 3271.4007? Ans. 57.19 + 2. 66 66 of 4.372594? 66 2.091 + 66 CASE III. To extract the Square Root of a mixed number. RULE 1.-Reduce the fractional part of the mixed number to its lowest term, and then the mixed number to an improper fraction. 2. Extract the roots of the numerator and denominator for a new numerator and denominator. 3. If the mixed number given be a surd, reduce the fractional part to a decimal, annex it to the whole number, and extract the square root. 1. What is the square root of 421? Ans. 61. 66 7. CASE IV. To extract the Square Root of a fraction. RULE. Reduce the fraction to its lowest terms, then extract the square root of the numerator for a new numerator, and the denominator for a new denominator. 1. What is the square root of 2. What is the square root of CASE V. 70 To extract the Square Root of a Surd. Ans. 3. 66 t. RULE. Reduce the surd to a decimal, and extract the root thereof. RULE. Multiply the two numbers together, and extract the square root of the product for a mean proportional. 1. Suppose A. in a school room sits 4 feet from a hot stove, and B. 9 feet from the same, how much warmer is A. than B? Ans. 6 times. 2. Two ships sail from the same port, one goes due North 128 miles, the other due East 72, how far are the ships asunder? Ans. 146.86 miles. CASE VII. The base and perpendicular given to find the hypothenuse. 1. The top of a castle is 45 yards high, and is surrounded with a ditch 60 yards broad, what length must a ladder be to reach from the outside of the ditch to the top of the castle? Ans. 75 yds. 2. The wall of a fort is 25 feet high, which is surrounded by a moat 30 feet in breadth, I want to know the length of a ladder that will reach from the outside of the moat to the top of the wall? Ans. 39.05 ft. |