EXAMP

EXAMP. 1. If London remit 1000l. sterling to Spain, by way of Holland, at 35s. Flemish per pound sterling; thence to France, at 58d. 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 1000l. sterling amount to in Spain?

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 $\backslash times$ 17 = 493 divisor; and 210 $\backslash times$ 30 $\backslash times$ 45 $\backslash times$ 10 = 2835000 dividend; and, 493) 2835000(5750$\backslash frac\{1\}\{2\}$ 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:

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

The placing the terms by way of antecedent and consequent,

Exchange. frequent, and working as the rules direct, saves so many statings of the rule of three, and greatly shortens the operation. The proportions at large for the above question would be stated as under.

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

2. A banker in Amsterdam remits to London 400l. Flemish; first to France at 56d. Flemish per crown; from France to Venice, at 100 crowns per 60 ducats; from Venice to Hamburg, at 100d. Flemish per ducat; from Hamburg to Lisbon, at 50d. Flemish per crusade of 400 rees; and, lastly, from Lisbon to London at 64d. sterling per millree: 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 36s. 10d. Flemish per pound sterling?

Antecedents. Consequents.

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

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

7) 368640 (52662$\backslash frac\{1\}\{2\}$d. ster. = 219l. 8s. 6$\backslash frac\{1\}\{2\}$d. ster. Ans.)

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

442 Gained or saved; 2 4 8$\backslash frac\{1\}\{2\}$

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

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

Antecedents. Consequents.

How many d. Flem. = 240 ster.?

2) 875 (437$\backslash frac\{1\}\{2\}$d. = 36s. 5$\backslash frac\{1\}\{2\}$d. Flem. per l. ster. Ans.)

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

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

The work may be proved by the arbitrated price thus: As 1l. sterling to 36s. 5$\backslash frac\{1\}\{2\}$d. Flemish, so 219l. 8s. 6$\backslash frac\{1\}\{2\}$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 1l. sterling for 36s. 5$\backslash frac\{1\}\{2\}$d. Flemish, than for 36s. 10d. Flemish.