In the preceding bill of exchange Messrs. Cubbedge & Hazlehurst are the drawers, N. B. Browne is the drawee, and J. B. Lippincott & Co. are the payees.

EXAMPLES.

1. A manufacturer in Providence wishes to send $7857 to Mobile, exchange being at a premium of 11%; what must he Day for a check?

Analysis. 1 per cent. of $7857 is $117.85. Adding $117.85, the premium, to $7857, we have $7974.851 as the price of the check. Ans. $7974.85.

2. What would be the cost of a draft at St. Paul, Minn., on Boston for $6472, at 15 per cent. premium?

Ans. $6577.17.

3. Exchange being at a discount of 12 per cent., what would be the cost in Savannah, Ga., of a check for $1256, on Rutland, Vt.? Ans. $1234.02.

4. A merchant in New Orleans wishes to pay $4528 in Philadelphia, exchange being 21 per cent.

must he pay for a check?

premium; what Ans. $4624.22.

5. What would be the cost of a check at Newark, N. J., on Vicksburg, Miss., for $4856.40, at 7 of 1 per cent. discount? Ans. $4813.9065.

FOREIGN BILLS OF EXCHANGE.

ART. 302. Bills of exchange are called FOREIGN when the drawer and drawee live in different countries; for example, when one lives in the United States and the other in England. ART. 303. In order that debts between foreign countries may be paid, it is necessary to know how much money of one country is equivalent to a specified sum in another country. If a citizen of New York wished to pay a debt of 450 pounds sterling in England, he must be able to tell how many dollars

and cents in New York would be required to make 450 pounds sterling in England. The process used is called REDUCTION OF CURRENCY.

EXCHANGE BETWEEN THE UNITED STATES AND ENGLAND.

ART. 304. Bills of exchange on England are drawn in pounds sterling, shillings, pence and farthings. The pound sterling is represented by a gold coin called a sovereign, and its custom-house value in the United States is $4.84. A law of Congress in 1789 fixed the value of the pound sterling at $4.443, and this continued to be the value up to 1834. It will be seen that $4.84, the custom-house value of the pound sterling, is 9 per cent. above the old par value of $4.444. Hence, when it is said that bills of exchange on England are at a premium of 9 per cent., it must be borne in mind that the pound sterling is reckoned at $4.443, and that exchange is really at par, taking the custom-house value as the standard.

Ex. 1. A merchant in Baltimore purchased a bill of exchange on Liverpool for £456 12s. at 9 per cent. premium; how much in gold did he pay for the bill?

=

Since £1 =

Analysis. £1 $4.443 at the old par value; and £456 12s. £456.6. $4.444, then £456.6 will be worth 456.6 times as much $2029.334; taking 9 per cent.

=

off $2029.33, we have $182.64, which added to $2029.33 gives $2211.97 as the price of the bill.

The operation might have been shortened thus: £456 12s = £456.6

$4.444$44$40.

=

Then $40456.6 $2029.33 at the old par value, and $2029.33 .09 = 182.64, the premium at 9 per cent. Ans. $2211.97 = price of the bill.

2. A merchant in Philadelphia owes $3630.24 for cutlery in Sheffield, England; for how many pounds sterling must he

purchase a bill to pay the debt, exchange being at a premium of 8 per cent.?

Analysis. £1 $4.444; and taking 8% of $4.444, we have $0.35§; adding this to $4.443, we get $4.80 as the commercial value of £1. Now, as it requires $4.80 to purchase £1, it follows that $3630.24 will purchase as many pounds as $4.80 is contained times in $3630.24, which gives £756.3, or £756 6s. Ans. £756 6s.

3. Exchange being at 9% premium, what would be the cost of a bill purchased in Cincinnati to pay £648 16s. in Birmingham? Ans. $3143.07.

4. When exchange is at 101 per cent. premium what would be the face of a bill on Manchester which could be purchased in Mobile for $4040.05? Ans. £824 10s.

5. A broker in Richmond, Va., sold a bill of exchange on London, the face of which was for £864 4s. 6d.; how much did he receive for the bill, exchange being at 10% premium? Ans. $4225.10.

EXCHANGE ON FRANCE.

ART. 305. In France the currency is reckoned in francs and centimes. Centimes are hundredths of a franc. Thus, 5.24 francs may be read, 5 francs 24 centimes. The custom-house

value of the franc is 18 cents. The commercial value is not uniform, but, like the pound sterling, it fluctuates with the state of trade. Bills of exchange on France are bought and sold at a certain number of francs and centimes to the dollar.

Ex. 1. A merchant of St. Louis, Mo., buys a bill of exchange on Paris for $4275, exchange being 5.25 francs to the dollar; what is the face of his bill in francs and centimes?

2. A silk merchant in New York owes 12969 francs in Lyons, and buys a bill of exchange, the rate being 5 francs 24 centimes to the dollar; what must he pay for his bill? Analysis. Since 5.24 francs = $1, there will be as many dollars as 5.24 is contained times in 12969, which gives $2475. Ans. $2475.

3. A wine merchant in New Orleans wishes to remit a bill of $4273 to Bordeaux, exchange being 5 francs 31 centimes to the dollar; what must be the face of his bill of exchange? Ans. 22689.63fr.

4. Exchange on Rouen being 5 francs 35 centimes to the dollar, how many dollars would be required to buy a bill of exchange covering 13096.80 francs? Ans. $2448. 5. A merchant in Louisville, Ky., owes $3256 in Marseilles; exchange being 5.32 francs to the dollar, what must be the face of his bill of exchange to pay the debt?

Ans. 17321.92fr. NOTE. For more minute information respecting Exchange consult "Sanford's Higher Analytical Arithmetic."

DUODECIMALS.

ARTICLE 306. DUODECIMALS are a peculiar kind of compound quantities which decrease from left to right uniformly. in a twelvefold ratio. They derive their name from the Latin word duodecim, meaning twelve. They are used in the measurement of surfaces and solids, as plastering, painting and

masonry.

ART. 307. The denominations of Duodecimals are feet, inches or primes, seconds, thirds, fourths, etc., which are dis tinguished from each other by certain marks called INDICES.

Thus, inches or primes are marked ('), seconds are marked ("), thirds (""), fourths (""), etc.

ART. 308. The foot is always taken as the unit, whether it

be linear, square, or cubic measure, and the several denominations have the relations indicated below.

1' =
1" = of 1' =

of a foot.

1728 of a foot.

=

of a foot.

1" = 1⁄2 of 1" of

=

of 1ft. = 1"" = of 1" = 1 of 12 of 1ft. 15 1715

ART. 309. In Duodecimals, 12 of any lower denomination make one of the next higher, or one of a higher is equivalent

to 12 of the next lower. Hence,

12 fourths ("") make 1 third, ("")

12 thirds ("")

1 second, (").

12 seconds (")

1 prime, ().

ART. 310. Duodecimals may be added or subtracted in the same manner as compound quantities.

EXAMPLES.

1. What is the sum of 35ft. 8' 10", 27ft. 6' 9" and 32ft. 5' 8"?

Ans. 95ft. 9' 3". 2. Add together 213ft. 7′ 9′′ 8", 124ft. 8' 10" 7"" and 185ft.

9' 7" 6"".
3. From 186ft. 5' 8" 10" subtract 128ft, 9′ 6′′ 5′′.

Ans. 524ft. 2' 3" 9"".

Ans. 57ft. 8' 2" 5"".

4. From 323ft. 5' 4" 7"" 6" take 185ft. 8' 2" 9" 4""".

Ans. 137ft. 9' 1" 10" 2""

MULTIPLICATION OF DUODECIMALS.

ART. 311. Plasterers, painters, carpenters and rock-masons employ duodecimals in estimating their work. One of the most common applications is in measuring lumber.