EXAMP. 1. If London remit 1000 l. Sterling to Spain, by way of Holland, at 35 s. Flemish per l. Sterling; thence to France, at 58 d. Flemish per crown; thence to Venice, at 100 crowns per 60 ducats; and thence to Spain, at 360 mervadies per ducat; how many piastres, of 272 mervadies, will the 1000 l. Sterling amount to in Spain?

Antecedents. Consequents. Abridged.
1 l. Sterling = 35 s. or 420 d. Fl. 1 = 210
58 d. Flemish = 1 crown France 29 = 1
100 crowns France = 60 ducats Venice 1 = 30
1 ducat Venice = 360 mervadies Spain 1 = 45
272 mervadies = 1 piastre 17 = 1
How many piastres = 1000 l. Sterling = 10

In order to abridge the terms, divide 58 and 420 by 2, and you have the new antecedent 29, and the new consequent 210; reject two ciphers in 100 and 1000; divide 272 and 360 by 8, and you have 34 and 45; divide 34 and 60 by 2, and you have 17 and 30; and the whole will stand abridged as above.

Then, 29 \times 17 = 493 divisor; and, 210 \times 30 \times 45 \times 10 = 2835000 dividend; and, 493)2835000(5750\frac{1}{2} piastres. Ans.

Or, the consequents may be connected with the sign of multiplication, and placed over a line by way of numerator; and the antecedents, connected in the same manner, may be placed under the line, by way of denominator; and then abridged, as follows:

\begin{aligned} \frac{420 \times 60 \times 360 \times 100}{58 \times 100 \times 272} &= \frac{210 \times 60 = 360 \times 10}{29 \times 1 \times 272} \\ &= \frac{210 \times 60 \times 45 \times 100}{29 \times 34} = \frac{210 \times 30 \times 45 \times 10}{29 \times 17} \\ &= \frac{2835000}{493} \end{aligned}

And, 493)2835000(5750\frac{1}{2} piastres. Ans.

The placing the terms by way of antecedent and consequent, and working as the rules direct, save so many statings of the rule of three, and greatly shortens the operation. The proportions at large for the above question would stand as under.

L. St. d. Fl. L. St. d. Fl.
If 1 : 420 :: 1000 : 420000
d. Fl. Cr. d. Fl. Cr. Cr.
If 58 : 1 :: 420000 : 7241\frac{1}{2}

Cr.

Cr. Duc. Cr. Duc.
If 100 : 60 724\frac{1}{2} 4344\frac{1}{2}
Duc. Mer. Duc. Mer.
If 1 : 360 4344\frac{1}{2} 1564137\frac{1}{2}
Mer. Piaft. Mer. Piaft.
If 272 : 1 1564137\frac{1}{2} 5750\frac{1}{2}

If we suppose the course of direct exchange to Spain to be 42\frac{1}{2} d. Sterling per piaftre, the 1000l. remitted would only amount to 5647\frac{1}{2} piaftres; and, consequently, 103 piaftres are gained by the negotiation; that is, about 2 per cent.

2. A banker in Amsterdam remits to London 400 l. Flemish; first to France at 56 d. Flemish per crown; from France to Venice at 100 crowns per 60 ducats; from Venice to Hamburg at 100 d. Flemish per ducat; from Hamburg to Lisbon at 50 d. Flemish per crusade of 400 rees; and, lastly, from Lisbon to London at 64 d. Sterling per milree: How much Sterling money will the remittance amount to? and how much will be gained or saved, supposing the direct exchange from Holland to London at 36 s. 10 d. Flemish per l. Sterling?

Antecedents.      Consequents.

56 d. Flem. = 1 crown
100 crowns = 60 ducats.
1 ducat = 100 d. Flem.
50 d. Flem. = 400 rees.
1000 rees = 64 d. Sterling.

How many d. Ster. = 400l. or 96000 d. Flemish?

This, in the fractional form, will stand as follows.

\frac{60 \times 100 \times 400 \times 64 \times 96000}{56 \times 100 \times 50 \times 1000} = \frac{368640}{7}, \text{ and} 7)368640(52662\frac{6}{7} \text{ d. Ster.} = 219\text{l. } 8\text{s. } 6\frac{6}{7}\text{d. St. Ans.}

To find how much the exchange from Amsterdam directly to London, at 36 s. 10 d. Flemish per l. Sterling, will amount to, say,

s. d. d. Fl. l. St. d. Fl. l. s. d. St.
36 10 If 442 : 1 96000 : 217 3 10\frac{1}{2}
12 219 8 6\frac{1}{2}
442 Gained or saved, 2 4 8\frac{1}{2}

In the above example, the par of arbitration, or the arbitrated price, between London and Amsterdam, viz. the number of Flemish pence given for 1 l. Sterling, may be found thus:

Make 64 d. Sterling, the price of the milree, the first antecedent; then all the former consequents will become antecedents, and all the antecedents will become consequents. Place 240, the pence in 1 l. Sterling, as the last consequent, and then proceed as taught above, viz.

Antecedents. Consequents.
64 d. Ster. = 1000 rees.
400 rees = 50 d. Flem.
100 d. Flem. = 1 ducat.
60 ducats = 100 crowns.
1 crown = 56 d. Flem.

How many d. Flem. = 240 d. Ster.?

\frac{1000 \times 50 \times 100 \times 56 \times 240}{64 \times 400 \times 100 \times 60} = \frac{875}{2}, \text{ and}
2)875(437\frac{1}{2} \text{ d.} = 36\text{s. } 5\frac{1}{2}\text{d. Flem. per l. Ster. Ans.}

Or the arbitrated price may be found from the answer to the question, by saying,

d. Ster. d. Flem. d. St.
If 368640 : 96000 240
7 7
672000
240
2688
1344

d. s. d. Flem.

368640)161280000(437\frac{1}{2} = 36\text{s. } 5\frac{1}{2}\text{d. as before.}

The work may be proved by the arbitrated price thus: As 1 l. Sterling to 36 s. 5\frac{1}{2} d. Flemish, so 219 l. 8 s. 6\frac{6}{7} d. Sterling to 400l. Flemish.

The arbitrated price compared with the direct course shows whether the direct or circular remittance will be most advantageous, and how much. Thus the banker at Amsterdam will think it better exchange to receive 1 l. Sterling for 36 s. 5\frac{1}{2} d. Flemish, than for 36 s. 10 d. Flemish.

EXCHANGE signifies also a place in most considerable trading cities, wherein the merchants, negotiants, agents, bankers, brokers, interpreters, and other persons concerned in commerce, meet on certain days, and at certain times thereof, to confer and treat together of matters relating to exchanges, remittances, payments, adventures, assurances, freightments, and other mercantile negotiations, both by sea and land.