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Extract the square root of the sum of the squares of the other two sides.
15. To find the base or the perpendicular of a rightangled triangle, Extract the square root of the difference between the square of the hypotenuse and the square of the other side.
475. CONTENTS OF SOLIDS.
1. To find the solid contents of a rectangular solid, Multiply the length, width, and thickness together.
2. To find either dimension of a rectangular solid, Divide the solid contents by the product of the other two dimensions.
3. To find the solid contents of a cylinder, Multiply the area of the base by the altitude. 4. To find the solid contents of a sphere,
1. Multiply the cube of the diameter by .5236. Or,
2. Multiply the surface by one third of the radius. 5. To find the solid contents of a cone or pyramid, Multiply the area of the base by one third of the altitude.
6. To find the solid contents of the frustum of a cone or pyramid, To the sum of the areas of the two bases, add the square root of their product, and multiply the result by one third of the altitude.
7. To measure timber, as planks, joists, etc., by board measure, Find the number of square feet in one surface, and multiply the result by the thickness in inches.
476. A Foreign Bill of Exchange is a draft drawn in one country and payable in another. (Art. 328.)
Foreign Bills are expressed in the currency of the country on which they are drawn. They are issued in sets of three, of the same tenor and date, called the First, Second, and Third of Exchange, and are sent by different mails to avoid delay in case of miscarriage, When one is paid, the others are void.
477. The Par of Exchange is the comparative value of the currencies of two countries. (Art. 329.)
The commercial value of foreign exchange may be higher, equal to, or lower than the par of exchange. A bill payable in sixty days costs less than a bill payable on sight, or in three days, called “short sight.”
The commercial or quoted value of exchange is used in finding the cost of a foreign bill.
EXCHANGE ON ENGLAND.
478. Bills between the United States and England are expressed in sterling money, and are drawn on London. They are called Sterling Bills.
The legal or par value of a pound sterling is $1.8665, and the custom-house value is $4.84. The commercial or exchange value is now quoted in dollars and cents, gold,
1. What will a bill on London for £448 11s. cost in New York, when sterling exchange is quoted at 4.863 ?
£448 11s. £448.55.
$4.863 X 448.55 $2182.943, cost of bill in gold. Since £1 is worth $4.863, £448.55 are worth $4.863 X 448.55, which is $2182.943.
2. What will a sterling bill for £219 10s. 6d. cost in New York, when sterling exchange is quoted at 4.911?
3. What will a bill on London for £200 12s., payable in 60 days, cost in New York in currency, when sterling exchange is quoted at 4.853, and gold at 113}?
$4.856 X 200.6 $974.1136, cost in gold ;
4. What will a sight draft on London for £300 8s. cost in New York in currency, when sterling exchange is quoted at 4.88, and gold at 1144 ?
5. What will a sight draft on London for £250 cost a merchant in Cincinnati, in currency, when sterling exchange is quoted at 4.86, gold at 1103, and the broker's commission is $% of cost of draft in New York ?
6. What will be the cost of the following bill in currency, when sterling exchange is quoted at 4.851, and gold at 1.094?
NEW YORK, Jan. 10, 1876. Sixty days after sight of this First of Exchange (Second and Third of same tenor and date unpaid) pay to the order of Wilson, Hinkle & Co. One Thousand Pounds, value received, and charge to account of
AUGUST BELMONT & Co. To Brown, Shipley & Co.,
To Brown, Shimon.com.}
7. What amount of sterling exchange can be bought for $1080.45 in gold, when sterling exchange is quoted at 4.90?
$1080.45 - $4.90 = 220.5; £220.5
8. How large a draft on London can be bought in Chicago for $2195.475 in gold, when sterling exchange is quoted at 4.863, and the broker's commission is 1 % of cost of draft in New York ?
9. How large a sight draft on London can be bought in New York for $1291.62 in currency, when sterling exchange is quoted at 4.89}, and gold at 1.10?
479. RULES.— 1. To find the cost of sterling exchange, Multiply the cost of £1 by the number of pounds denoting the face of the bill.
NOTE:-When the face of the bill contains shillings and pence, reduce them to the decimal of a pound. (Art. 171.)
2. To find the amount of sterling exchange that can be bought for a given sum of United States money, Divide the given sum of money by the cost of £1 of exchange.
EXCHANGE ON FRANCE.
480. The New York quotations of exchange on Paris give the number of francs and centimes which are equal in exchange to $1 of United States money (gold). The centimes are usually expressed as hundredths.
Quotations on Antwerp and Switzerland are also in francs. Quotations on Amsterdam are in guilders, worth about 41 cents.
The value of a franc (Louis Napoleon) is $.192 nearly, $1 being equal to 5 francs and 145 centimes. The custom-linuse value is $.193.
1. What will be the cost of a bill on Paris for 3870 fr., when Paris exchange is quoted in New York at 5.16 ?
3870 fr. ; 5.16 fr. 750; $1 X 750 = $750. Since $1 will buy 5.16 fr., it will take as many times $1 to buy 3870 fr. as 5.16 fr. is contained times in 3870 fr., which is 750.
2. What will a draft on Paris for 6475 fr. cost in New York, when Paris exchange is quoted at 5.18?
3. What will a bill on Paris for 5330 fr. cost in New York in currency, when Paris exchange is quoted at 5.123, and gold at 1083 ?
4. What amount of exchange on Paris can be bought for $1500, when Paris exchange is quoted at 5.14!?
5. How large a draft on Paris can be bought in New York for $2584 in currency, when Paris exchange is quoted at 5.163, and gold at 1.061?
6. What will be the cost of a bill on Antwerp for 64187 fr., when exchange is quoted at 5.131 ?
7. What amount of exchange on Switzerland can be bought for $741 in currency, when exchange is quoted at 5.15, and gold at 1.14?
481. RULES.-1. To find the cost of exchange on Paris, Divide the number of francs in the face of the bill by the number of francs that equal $1 of exchange.
2. To find the amount of exchange on Paris that can be bought for a given sum of money, Multiply the number of francs that equal $1 of exchange by the number denoting the given sum of money.
EXCHANGE ON GERMANY.
482. Exchange on Germany is quoted at so many cents per
The par value of a reichsmark, the new German coin, is $.243, or about 11 francs.
1. What will be the cost of a sight bill on Hamburg for 2240 reichsmarks, when exchange is quoted in New York at .961?
$.961 X 2240 • 4 = $539, cost.