called the Par of Arbitration, between any number of places corresponds with, or is equivalent to, any assigned rates between each of them and another place: and a knowledge of this subject will enable a person to judge how he may remit his money from one place to another with the greatest advantage.

Arbitration is styled simple or compound, according as three or more places are concerned.

Ex. If the exchange between Amsterdam and Paris be 54d. for 1 crown, and between Amsterdam and London be 33s. 9d. for £1; what is the par of exchange or the arbitrated price between Paris and London?

that is, 32d. per crown is the arbitrated price between London and Paris.

If we arrange the equalities so that the first term of one shall always be of the same kind as the second of that which immediately precedes it, as follows:

1 crown at Paris = 54 pence at Amsterdam,

405 pence at Amsterdam 240 pence in London,

=

and multiply together the corresponding terms retaining the names only of the first and last countries and their denominations of money, we shall have

405 crowns at Paris = 54 × 240 pence in London:

and therefore 1 crown at Paris =

54 × 240 d.

405

= 32 in London,

=

as before and a proceeding of this kind is distinguished by the name of the Chain Rule, from the connection of the first and last terms being ascertained through those which are intermediate.

Examples for Practice.

(1) How much English money is equivalent to 1785 francs 6 decimes, at 24 francs per pound sterling?

Answer: £74. 8s.

(2) Reduce £156. 15s. to francs, the exchange being at 23.5 francs per pound sterling.

Answer: 3683.625 francs.

(3) If £100 be due from London to Paris when £1 is worth 25 francs: what sum must be remitted when a guinea is exchanged for 27 francs?

Answer: £97. 4s. 5§d.

(4) If the course of exchange between London and Amsterdam be 33s. 6d. Flemish per pound sterling and between London and Lisbon be 50d. sterling per milree : find the arbitrated rate of exchange between Amsterdam and Lisbon.

Answer: 833d. Flemish per milree.

(5) A person in London owes another at Petersburg 500 rubles, exchange at 40d. sterling per ruble: but remits to Paris at 24 francs per pound sterling; thence to Lisbon at 500 rees for 3 francs; thence to Amsterdam at 20 stivers per crusado of 400 rees and thence to Petersburg at 25 stivers per ruble: find the arbitrated rate between London and Petersburg and the gain or loss by the circuitous mode of remittance.

Answers: 30d. per ruble and the gain is £20. 16s. 8d.

(6) The rates of exchange being £1 = 25.4 francs, 3.75 francs = 105 kreutzen, 60 kreutzen = 1 florin and the cost of travelling in Germany being 13 florins per German mile which is equal to 4 English miles: find the expense, in English money, of travelling 381 English miles in Germany.

Answer: £10. 14s. 3 d.

163. The Course of Exchange between two countries fluctuates according to circumstances which cannot be entered into here; but the lower the course of exchange, the more favourable is it to the country in whose money it is estimated, and vice versa.

Thus, between London and Amsterdam, when the course of exchange is 9 guilders per pound sterling, it will evidently require more sterling money to pay a debt in Amsterdam and fewer guilders to discharge one in London, than if the course of exchange were 11 guilders: for, the merchant of Amsterdam has to buy pounds sterling to remit to London and the London merchant has to sell pounds sterling in order to purchase guilders for a remittance to Amsterdam. The exchanges may therefore be considered favourable to this country, when the courses of exchange run high in foreign countries with which it trades, and vice versa.

The reader is referred to the last Edition of Dr. KELLY'S Universal Cambist for practical information on this subject.

MISCELLANEOUS QUESTIONS.

164. In this section are presented a few miscellaneous Questions which could not with propriety be arranged under any of the preceding heads and are still of too much importance to be passed over without notice, in a work like the present.

Qu. 1. How many dozens of wine at £2 a dozen must be given in exchange for 27 yards of broad cloth at 32s. a yard?

The price of the cloth is 27 × 32 = 864s. :

whence, 40s. 864s. 1 doz.: 21 doz.; that is, 213 dozens of wine are of equal value with 27 yards of cloth.

Questions of this kind are termed instances of Barter and Truck.

Qu. 2. If a grocer by selling tea at 6s. 6d. a pound clear one-sixth of the money: what will he clear per cent. by selling it at 7s. a pound?

Here, of 6s. 6d. = 1s. 1d. ; whence 5s. 5d. is the price per lb. the tea cost him: therefore

5s. 5d. 7s.

and £129. 4s. 71d.

f. is the increased value of £100 at this rate: that is, the gain per cent. is £29. 4s. 74d. ï3ƒ.

Qu. 3. A person loses at the rate of 10 per cent. by selling cloth at 15s. a yard: how ought it to have been sold to gain 20 per cent.?

Since he loses oth part, he receives only 9 parts out of 10 or 90 parts out of 100: whence,

the prime cost of 1 yard: for the same reason, we have

or £1 is the price per yard, in order to realize a profit of 20 per cent.

Questions of this description are classed under the heads, Profit and Loss, Loss and Gain and Per-centage.

QU. 4. Required the neat weight of 27 cwt. 1 qr. 14lbs., tare being allowed at the rate of 16lbs. per cwt. Here, by the rules of Practice, we have

Questions of this nature are usually inserted under a Rule called Tare and Tret, which comprises all allowances made upon goods on any ground whatever, whether by custom or by special agreement.

Qu. 5. If two men A and B together can perform a piece of work in 10 days and A by himself can do it in 18 days: what time will it take B to do it?

Assuming 1 to represent the piece of work, we have

Qu. 6. Three agents A, B, C can produce a given effect in 12 hours; also, A and B can produce it in 16 hours and A and C in 18 hours: in what time can each of them produce it separately?

effect produced by A and B in 1 hour:

and therefore 1 12 hours: 48 hours,

the time in which C alone can produce it:

1

again, = effect produced by A and C in 1 hour:

18

the time in which B alone can produce it:

= effect produced by A, B and C in 1 hour:

the time in which A can produce the effect proposed.

Qu. 7. Distribute £200 among A, B, C and D, so that B may receive as much as A, C as much as A and B together and D as much as A, B and C together.