2. The gable ends of a barn are each 28 feet wide, and the perpendicular height of the ridge above the eaves is 7 feet; how many feet of boards will be required to board up both gables?

CASE V.

Ans. 196 feet.

463. To find the circumference or the diameter of a circle.

464. A Circle is a figure bounded by one uniform curved line.

465. The Circumference of a circle is the curved line bounding it.

466. The Diameter of a circle is a straight line passing through the center, and terminating in the circumference.

It is proved in geometry that in every circle the ratio between the diameter and the circumference is 3.1416+. Hence the

RULE. I. To find the circumference. Multiply the diameter by 3.1416.

II. To find the diameter. - Multiply the circumference by .3183.

EXAMPLES FOR PRACTICE.

1. What length of tire will it take to band a carriage wheel 5 feet in diameter ? Ans. 15 ft. 8.4+ in.

2. What is the circumference of a circular lake 721 rods in diameter ? Ans. 7 mi. 25 rds. 1.54 + ft. 3. What is the diameter of a circle 33 yards in circumference? Ans. 10.5yards.

CASE VI.

467. To find the area of a circle.

From the principles of geometry is derived the following

RULE. I. When both diameter and circumference are given; Multiply the diameter by the circumference, and divide the product by 4.

II. When the diameter is given;- Multiply the square of the diameter by .7854.

III. When the circumference is given; - Multiply the square of the circumference by .07958.

EXAMPLES FOR PRACTICE.

1. The diameter of a circle is 113, and the circumference 355; what is the area? Ans. 10028.75. 2. What is the diameter of a circular island containing 1 square mile of land? Ans. 1 mi. 41 rd. 1.3 ft.

3. A man has a circular garden requiring 84 rods of fencing to inclose it; how much land in the garden? Ans. 3 A. 81.5+ P.

able to drawing or remitting, the disadvantage is sometimes avoided, by means of a circuitous exchange on intermediate places between which the course is favorable.

DIRECT EXCHANGE.

97. Direct Exchange is confined to the two places between which the money is to be remitted.

598. There are always two methods of transmitting money between two places. Thus, if A is to receive money from B, 1st. A may draw on B, and sell the draft;

2d. B may remit a draft, made in favor of A.

NOTE. One person is said to draw on another person, when he is the maker of a draft addressed to that person.

CASE I.

599. To compute domestic exchange.

The course of exchange for inland bills, or drafts, is always expressed by the rate of premium or discount. Drafts on time, however, are subject to bank discount, like notes of hand, for the term of credit given. Hence, their cost is affected by both the course of exchange and the discount for time.

1. What will be the cost of the following draft, exchange on Boston being in Pittsburgh at 21 % premium?

$600.

PITTSBURGH, June 12, 1860. Sixty days after sight, pay to William Barnard, or order, six hundred dollars, value received, and charge the same to our

$1.012, cost of exchange for $1. $600 x 1.012 $607.20, Ans. ANALYSIS. From $1.0225, the $.0102, the bank discount of $1

course of exchange, we subtract for the specified time, and obtain

$1.015, the cost of exchange for $1; then $600 × 1.012= $607.20, the

cost of exchange for $600.

2. A commission merchant in Detroit wishes to remit to his employer in St. Louis, $512.36 by draft at 60 days; what is the face of the draft which he can purchase with this sum, exchange being at 1% discount?

OPERATION.

$18.015= $.985, course of exchange.

.01225, discount of $1.

$.97275, cost of exchange for $1.

$512.36.97275 = $532.18+, Ans.

ANALYSIS. From $.985, the course of exchange, we substract $.01225, the bank discount of $1 for the specified time, at the legal rate in Detroit, and obtain $.97275, the cost of exchange for $1;`and the face of the draft that will cost $512.36, will be as many dollars as $.97275 is contained times in 512.36, which is 532.18+, times. Hence we have the following

RULE. I. To find the cost of a draft, the face being given.. Multiply the face of the draft by the cost of exchange for $1. II. To find the face of a draft, the cost peing given.. the given cost by the cost of exchange for $1.

NOTE.

Divide

The cost of exchange for $i may always be found, by subtracting from the course of exchange the bank discount (at the legal rate where the draft is made), for the specified time. For sight drafts, the course of exchange is the cost of $1.

EXAMPLES FOR PRACTICE.

1. What must be paid in New York for a draft on Boston, at 30 days, for $5400, exchange being at % premium?

Ans. $5392.35 +.

2. What is the cost of sight exchange on New Orleans, for $3000, at 34% discount? 2402,50

3. What must be paid in Philadelphia for a draft on St. Paul drawn at 90 days, for $4800, the course of exchange being 1013 %? Ans. $4791.60.

4. A draft was purchased for $550.62, exchange being at a premium of 3%; what was the face? 32

5. An agent in Syracuse, N. Y., having $1324.74 due his employer, is instructed to remit the same by a draft drawn at 30 days; what will be the face of the draft, exchange being at 13 % premium? Ans. $1310.22-.

0125

138=178,22

178,22-5320-0335

EXCHANGE.

337

101225

6. My agent in Charleston, S. C., sells & house and lot for $7500, on commission of 1%, and remits to me the proceeds in a draft purchased at % premium; what sum do I receive from the sale of my property? 7354.75

7. A man in Hartford, Conn., has $4800 due him in Baltimore; how much more will he realize by making a draft for this sum on Baltimore and selling it at % discount, than by having a draft on Hartford remitted to him, purchased in Baltimore for this sum at % premium? Ans. $11.73.

8. The Merchants' Bank of New York having declared a dividend of 61%, a stockholder in Cincinnati drew on the bank for the sum due him, and sold the draft at a premium of 13 %, thus real8001 izing $508.75 from his dividend; how many shares did he own? 9. Sight exchange on New Orleans for $5000 cost $5075; what was the course of exchange? Ans. 1 % premium. 10. A man in Buffalo purchased a draft on St. Paul, Minn.. for $5320, drawn at 60 days, paying $5141.78; what was the course of exchange? Ans. 2% discount.

CASE II.

600. To compute foreign exchange.

601. The following standards of the decimal currency of the United States were established April 2, 1792.

In 1834, the eagle was reduced in weight to 258 grains, and in 1837 its fineness was fixed at 900 thousandths pure, which is likewise the present standard of purity for all the U. S. gold and silver coins. In 1837, also, the silver dollar was reduced in weight to 412.5 grains. In 1853, the silver half dollar was reduced in weight to 192 grains, and the smaller silver coins proportionally.

NOTE.

The object of the change in the silver coinage of the United States, made in 1853, was to prevent its exportation by raising the nominal value of silver above its foreign market value.

602. The intrinsic par of exchange between the United States and different countries, is given in the following