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Def. 1. Exchange is the rule by which the money of one country is changed to that of another.

Def. 2. The par of exchange is the intrinsic value of the coin of one country expressed in terms of the coin of another.

Def. 3. The course of exchange at any time is the sum, which at that time, is given in one coinage for a sum in another.

Def. 4. By arbitration of exchange is meant the determining the course of exchange between two places, from the known rates between each of the two and other places. Arbitration is called Simple or Compound, according as three only or more than three places are mentioned.

Rules. Questions in Exchange may be worked by Practice or Proportion; questions in Simple Arbitration by Proportion, and in Compound by the Rule called

The Chain Rule, Beginning with one of the places between which the course of exchange is required, write down a series of equations expressing the courses of exchange between the several places which are mentioned, always putting on the left hand the same denomination of coin, as appeared in the preceding equation on the right. Multiply together all the numbers on the right hand side, and all but the first on the left hand side ; divide the first product by the second; the result will be the amount of coinage of the last mentioned place equal to the given amount of that first mentioned.

EXAMPLES. 1. Exchange £735 for francs at 24.25 fr. for £1.

24.25 francs =£1

735

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2. Exchange £520 : 15:0 for Prussian dollars at 6 dollars 25 groschen

per £1.

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Ans. 355831 Pr. dol. = 3558 Pr. dol. 134 groschen.

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3. Exchange 3864 florins at Amsterdam with Naples at 80} florins for ducats. As 804 f. 3864 fi.

40 ducats

Ans.
3864 x 40
Ans. =

ducats
801
3864 X 80

ducats
161
= 24 X 80 ducats = 1920 ducats.

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4. Bills on Paris, bought in London at 25 francs 40 cents, are sold in Hamburg at 187 francs per 100 marks : what is the exchange between London and Hamburg ? As 187 francs 25 francs 40 cents

100 marks

Ans.
25.40 X 100
Ans. =

marks
187
2540

marks
187

109 = 13

marks
187

61
- 13 marks 9- sch.

187

5. A bill upon Hamburg is bought at 13 marks 103 sch. per £1 sterling, and sold in Amsterdam at 35% florins per 40 Banco marks; if the proceeds are there laid out in bills upon Genoa at 471 florins per 100 lire, and these again sold in Paris at 1 per cent. discount, what is the rate of exchange between London and Paris.

£1

= 1331 marks
40 marks = 35% florins
471 florins = 100 lire
100 lire = 99 francs

21
.. £ X 40 X 471 X 100 = 13– X 351 X 100 X 99 francs

32

437 x 71 x 99 or £1 X 1890

francs 32 X 2

437 x 71 x 11
£1 =

francs
32 X 2 X 210
345667

francs
13440

113
= 25 frs. 71 cent. Ans.

672

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Def. Barter is the Rule by which is determined what quantity of one article is equivalent in value to a given quantity of another; or what must be the quality of an article that a given quantity of it may be equivalent in value to a given quantity of another.

I. TO FIND THE QUANTITY OF ONE ARTICLE EQUIVALENT IN VALUE TO

A GIVEN QUANTITY OF ANOTHER ARTICLE.

Rule. Find the value of the goods received, and thence determine the quantity of goods exchanged, which may be had for the same money. Or work by the Chain Rule as in Exchanges.

EXAMPLES. 1. How many yards of silk velvet at 158. a yard may be exchanged for 125 yards of satin at 10s. 6d. a yard ? Value of satin = 10s. 70. X 125 = £65: 12:6 = £65%

653 525 .. No. of yards of velvet=

= 871 Ans.

6 2. Bought 2 cwt. 3 qrs. 16lbs. of sugar at £3 : 5:0 per cwt. and paid half in cash, and the rest in cloth at 14s. 6d. per yard; how much money did I pay, and how many yards of cloth ?

£. 8. d.
3 5 0 = value of 1 cwt. Value of cloth =£4: 14:04
2

=945 s.

Price per yard - 147 .
6 100
2 cwt.

9436 2qrs.=fcwt. 1 12 6

... No. of yards lqr.={cwt. 0 16 3

141 16lbs.=cwt. 0 9 39

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2 qrs. Iqr.

16 lbs.

2)98 09 = 2 cwt. 3 qrs. 16 lbs.
£4 14 0,4 = value paid in cash

= value of goods bartered

812

393 =6—

812

The same example worked by the Chain Rule.
Quantity of cloth required = 1 cwt. 1 qr. 22 lbs. sugar = 162 lbs. sugar.

112 lbs. sugar = 65 shillings
20. shillings =) yard cloth.

162 X 65 162 X 65
. . Quantity of cloth =

yards of cloth
112 X 212 56 X 29
81 X 65 5265

28 X 29 812

393
= 6- yards of cloth.

812

II.

TO DETERMINE THE QUALITY OF AN ARTICLE, OF WHICH A GIVEN QUANTITY IS EXCHANGED FOR A GIVEN QUANTITY OF ANOTHER.

Rule. Find the value of the goods received, and divide it by the number of units in the quantity exchanged; the result will be the price of an unit of the quantity.

EXAMPLES. 1. Exchanged 84 gallons of brandy, at 24s. per gailon, for 504 yards of silk; what was the price of the silk per yard ? Value of brandy = 84 X 24 s. = 2016 s.

2016 .. Price per yard of silk =

S. = 4s. 504

2. Received in barter a cow valued at 6 guineas, 20 sheep valued at 2 guineas, £100 in cash, and 150 quarters of barley, for 110 quarters of wheat at 69s. per quarter; what was the price of the barley per quarter ?

Value of wheat = 110 X 698. = £379 : 10:0

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III.

THE NETT AND BARTERING PRICES OF ONE ARTICLE BEING GIVEN, TO DETERMINE THE BARTERING PRICE OF ANOTHER, THE NETT PRICE BEING KNOWN, OR vice versa.

Rule. State: as the nett price of one is to its bartering price, so is the nett price of the other to its bartering price. Or as the bartering price of one is to its nett price, so is the bartering price of the other to its nett price.

EXAMPLE. The nett price of an article is 5s. but in barter is raised to 58. 4d. What should be the bartering price of an article, valued at 3s. Od. ready money? As 5's. 51 s.

3 s.

Ans.
16 15
Ans. =- - X -58. = 4s.

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Def. Alligation is the Rule by which is determined the rate of value of a mixture, from the rates of the ingredients of which it is composed.

Rule. Multiply the quantities of each ingredient, expressed in terms of the same unit, by the rates also expressed in the same unit; divide the sum of the products by the sum of the quantities; the quotient will be the price of an unit of quantity in terms of an unit of price.

EXAMPLE. A wine merchant mixes 30 gallons of wine at 158.a gallon with 40 gallons at 16s.; and with 24 gallons at 17s. 6d.; what will be the price of the mixture?

galls. 30 x 15 = 450 = cost of 30

94)1510(163 40 X 16 = 640 = cost of 40

94 24 x 36 = 420 = cost of 24

570 Whole cost=1510 = cost of 94

564

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Def. 1. Lines are measured by considering how often they contain a certain length, called the lineal unit.

Def. 2. Surfaces are measured by considering how often they contain a certain surface, called the superficial or square unit, which is a square, whose side is equal to the lineal unit.

Def. 3. Solids are measured by considering how often they contain a certain solid, called the solid, or cubic unit, which is a cube, whose faces are equal to the square unit.

Def. 4. The dimensions of a magnitude are its length, breadth, and thickness.-A line is of one, a surface of two, a solid of three, dimensions.

Obs. The Rules of Mensuration are Rules which enable us to find, by lineal measurements of the dimensions of a magnitude, the extent of its surface, and its capacity or solid content. These Rules are too numerous for insertion here. The Rules for finding the area of a rectangle, and the content of a rectangular parallelopiped are as follows.

I. TO FIND THE AREA OF A RECTANGLE.

Rule. Multiply the units in the length by the units in the breadth, the result is the number of square units in the area.

This operation may be conducted either (1) by expressing the length and breadth in terms of the same unit, fractional or integral ; or (2) by the

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