sum by the value of £1, ($4.84), the quotient will be the value in pounds and decimals of a pound. money. 4. Reduce £25 to U. S. Ans. $121. Ans. $74.536 Ans. $178.05+ Ans. £37. Ans. £25 14s. Ans. £206 12s. 23d.+ NOTE. The law of Congress, of July 31st, 1789, fixed the value of the pound sterling at $44, or $4.444, and $1. at 4s. Cd. As the then legal or nominal value of the pound was below its real value, such a per cent. was afterward added to the nominal as was necessary to make it express the real value. As it requires nearly 9 per cent. of $4.444 to be added to it, to make $4.84, when sterling funds or bills are estimated at $14 to a pound, and are 9 per cent. premium, they are really only at par. ART. 272. In buying or selling exchange on England, it is still customary to regard the pound as $44, and then to add the % premium. 1. What must be paid for a bill of exchange on London of £200, at 9 % premium? SOLUTION. £200 X 44 $888.888; $888.888.09=$80 premium; $388.888 +$80-$968.888 Ans. 2. What for a bill of exchange on Liverpool of £150, at 8% premium? Ans. $720. 3. What for a bill of exchange on London of £80 10s., at 91% premium? Ans. $391.76+ ART. 273. Previous to the adoption of Federal or U. S. Money, in 1786, accounts were kept in pounds, shillings, pence, and farthings. Owing to the fact that the Colonies had issued bills of credit, REVIEW.-270. How compute interest on sterling money? 271. How reduce sterling to U. S. Money? How reduce U. S. to sterling money? 271. NOTE. What was the legal value of the pound sterling in 1789 f How was the real value found from this? which depreciated more or less, the value of a colonial £ was less than that of a £ sterling. The depreciation being greater in some colonies than in others, gave rise to the different State currencies. Thus, 8s. In New England, Va., Ky., and Tenn., 6s. or £3=$1. or £=$1. 7s. 6d. or £ $1. 4s. 8d. or £$1. 5s. or £ 1 =$1. The process of changing any sum of U. S. Money to either of these currencies, or the reverse, involves the same principles as the exchanging of sterling money. Hence, to reduce U. S. Money to the currency of a State, Multiply the given sum, expressed in dollars, by the value of $1 expressed in the fraction of a pound; the product will be the value in pounds and decimals of a pound. To reduce a State currency to U. S. Money, Express the given sum in pounds and decimals of a pound, then divide this by the value of $1 expressed in the fraction of a pound; the quotient will be the value in dollars. 1. Reduce $120.50 to N. Eng. currency. 2. $75.25 to N. York currency. 3. $98 to Penn. currency. ANSWERS. 3s. £36 £30 2s. £36 15s. $102.50 4. £30 15s. N. E. currency to dollars. . 5. £25 17s. N. Y. currency to dollars. $64.625 6. £29 8s. Georgia currency to dollars. $126.00 NOTE. Any sum, in one currency, may be changed to that of another, by Sim. Proportion (Art. 203); or by short methods. Thus, since 6 shillings New England currency are equal to 8 shillings New York currency, to change the former to the latter, ADD one-third of the sum; to change the latter to the former, SUBTRACT one-fourth of the sum. REVIEW.-272. In buying or selling bills of exchange, how make the calculations? 273. In what were accounts kept previous to 1786 ? ART. 274. Any currency may be reduced to U. S. Money, or U. S. Money to any currency, by multiplication or division, as in Art. 271, when the value of a unit of the foreign currency expressed in U. S. Money is known. The unit of French money is the franc, its value being $0.186 Bills of exchange on France are bought and sold at a certain number of francs to the dollar. EXAMPLE. -At $1 for 5.30 francs, what will be the cost of a Bill on Paris for 1166 francs? Ans. $220. In "Ray's Higher Arithmetic" may be found a complete table of all foreign coins, with their value in U. S. Money; also, valuable information respecting exchange with all civilized nations. XXII. DUODECIMALS. ART. 275. Duodecimals are a peculiar order of fractions, which increase and decrease in a twelve-fold ratio. Their name, from the Latin duodecim, signifies twelve. The unit, 1 foot, is divided into 12 equal parts, called inches, or primes, marked thus, ('). Each inch, or prime, is divided into 12 equal parts, called seconds, marked ("). Each second, into 12 equal parts, called thirds, ('''). Each third, into 12 equal parts, called fourths, (''''). The marks,"","","", called indices, show the different parts. Duodecimals are added and subtracted like Compound Numbers; 12 units of each order making a unit of the next higher. ART. 276. MULTIPLICATION. Duodecimals are used in the measurement of surfaces and solids, as boards, solid walls, &c. 1. Find the superficial contents of a board 7ft. 5in. long, and 4ft. 3in. wide. Length, multiplied by breadth, gives the superficial contents. SOLUTION.-5' of a foot; therefore, 5' X4 ft. ΤΣ 5X4=29=20 inches, which is 1 ft. 8 in.; write the inches or primes in the order of primes, and carry the 1 ft. Next, 7 ft. X 4 ft. 28 ft., to which add the 1 ft. carried, the sum is 29 ft.; which write in the order of feet. Again, 55, and 3'3; therefore, 3 - 12 in the order of seconds, and carry the 1 in. ft. OPERATION. 3"; write the 3 sec. Next, 7 ft. x 3 in. = 7× 3 = 2121′, and 1' carried, make 221 ft. 10. Writing these in their orders, and adding the two products, the entire product is 31 ft. 6′ 3′′. The product of any two denominations, is of that denomination denoted by the sum of their indices; thus, 3'× 5′ = 15′′, 3'X7=21′, 7′′X4'===28"". Hence, Feet multiplied by feet, Inches multiplied by seconds, give (square) feet. give seconds. give thirds. Seconds multiplied by seconds, give fourths, and so on. REVIEW.-273. Why was the value of a colonial pound less than that of a pound sterling? How reduce U. S. Money to a State currency? 273. How reduce a State currency to U. S. Money? 275. What are duodecimals? Whence their name? What are Primes? Seconds? Thirds? Fourths? Repeat the table. What are indices? What part of a foot is 1'? 1? 1"? 1? How are duodecimals added and subtracted? Rule for Multiplication.-1. Write the multiplier under the multiplicand, placing units of the same order under each other. 2. Multiply, first by the feet, next by the inches, and so on, recollecting that the product will be of that denomination denoted by the sum of their indices. 3. Add the several partial products together, and their sum will be the required product. The primes of the product of two duodecimal factors, are neither linear nor square in., but twelfths of a sq. ft. The primes of the product of three duodecimal factors, are twelfths of a cu. ft. 2. How many square feet in a board 5 ft. 3in. long, and 1 ft. 5 in. wide? Ans. 7 sq. ft. 5' 3". 3. Multiply 5 ft. 7 in. by 1 ft. 10 in. Ans. 10 sq. ft. 2′10′′. 8 ft. 6 in. 9"x7 ft. 3 in. 4. 5. 8ft. 4 in. 6"x2 ft. 7 in. 4". Ans. 62 sq. ft. 11" 3"". Ans. 21 sq. ft. 10′ 5′′. 6. 4ft. 5' 6"x2 ft. 3' 5". Ans. 10 sq. ft. 2' 2" 9"" """. Another method of solution found in "Ray's Higher Arithmetic." XXIII. INVOLUTION. ART. 277. INVOLUTION is the multiplication of a number by itself one or more times. A POWER is the product obtained by involution. The ROOT, or first power, is the number multiplied. If the number be taken twice as a factor, the product is the second power; 3X3=9, is the 2d power of 3. If the number be taken 3 times as a factor, the product is the 3d power; 2X2X2=8, is the 3d power of 2. REVIEW.-276. For what are duodecimals used? Of what denomination is the product of any two denominations? What is the product of feet by feet? Feet by inches? Inches by inches? Inches by seconds? Seconds by seconds? Rule for multiplication? What do the primes of the product of two duodecimal factors represent? Of three? |
