IS when the price of each simple is given, also the quantity of one of them, and the mean rate, to find the several quantities of the rest in proportion to that given.

RULE.

1. Take the difference between each price and the mean rate as in the last rule.

2. As the difference of that simple whose quantity is given: is to the known quantity :: so is any other difference: to the quantity of its opposite name.

EXAMPLES.

(5) How much tea at 6s. 6d., 7s. 6d. and 9s. per lb. must be taken to be mixed with 36 lb. at 12s. per lb. that the mixture may be worth 8s. per lb.

(6) A tobacconist has by him 120 lb. of fine Oronoko tobacco, worth 2s. 6d. a pound; to this he would mix York river ditto at 20d. and other inferior tobaccos at 18d. and 15d. a pound, as will make up a mixture answerable to 2s. a pound. What will this parcel weigh?

XXIX. ALLIGATION TOTAL

IS when the price of each simple is given, as also the mean. rate, and what quantity of the compound, to find how much. of each sort will make that quantity.

RULE.

1. Take the difference between each price and the mean rate, as before.

2. Say, as the sum of these differences : is to the whole quantity of the mixture :: so is each particular difference; to its particular quantity.

EXAMPLES.

(7) How much gold of 16, of 18, and 23 carats fine, must be mixed together, to form a composition of 60 oz. of 20 carats fine?

(8) A grocer has by him 4 sorts of green tea, viz. of 5s. 6s, 8s. and 9s. per lb.; out of these he is inclined to mix up a canister, containing net, a hundred and a half, so as to make the commodity worth 7s. per pound. In what proportion must those teas be taken?

XXX. EXCHANGE

IS the receiving in one country for the value paid in another.

The par of exchange is always fixed and certain, it being at the intrinsic value of any foreign money compared with sterling: but the course of exchange between any two countries rises and falls upon various occasions.

But as it would be both needless and endless to write of every kind of exchange, so I shall only give a few examples of the exchange of England with some of the chief countries of Europe.

Exchange is either performed by Sec. XII. or XV. and sometimes most expeditiously by the latter.

1st. With FRANCE.

They keep their accounts at Paris, Lyons, and Rouen, in livres, sols, and deniers, and exchange by the crown of three livres Tournois, or 60 sols French, and give pence sterling, more or less, for this exchange crown, which is equal to 4s. 6d. at par.

As 1 crown: is to the given rate :: so is the given French sum: to the sterling required; or by the rules given in Practice.

Case 2. To change sterling money into French.

RULE.

As the rate of Exchange: is to 1 crown :: so is the sterling sum: to the French required.

Note. The same rule must be observed with most of the following countries.

EXAMPLES.

(1) What sterling money must be paid in London, to receive in Paris 500 crowns; exchange at 56d. per crown?

(2) How many crowns must be paid at Paris, to receive in London 1161. 13s. 4d. the exchange at 56d. per crown? (3) Change 640 crowns, 12 sols, 8 deniers, at 54+d. per

crown, into sterling.

(4) Change 145l. 7s. 71⁄2d. sterling, into French crowns, exchange at 544d. per crown.

2d. With SPAIN.

They keep their accounts at Madrid, Cadiz, and Seville, in dollars, rials, and maravedies, and exchange by the piece of

eight, which is equal to 4s. 6d. at par.

4 Maravedies vellon, or

Quarta.

24 Maravedies plate

8 Quartas, or

8 Rials of plate

Piece of eight or dollar.

N. B. A rial vellon is of a

17 rial of plate, and of a

256

piastre.

EXAMPLES.

(5) Change 8561. 6s. 8d. into Spanish money, exchange at

56d. per piece of eight.

(6) If I pay in Seville 1426 pieces of eight, 4 rials, 26 maravedies, what may I draw my bill for on London, exchange at 544d. per piece of eight?

3d. With Italy.

In Italy they keep their accounts, at Genoa and Leghorn, in livres, sols, and deniers, and exchange by the piece of eight

or dollar, which is equal to 4s. 6d. at par.

At Florence the exchange is by ducatoons, and at Venice by

ducats, divided as follows, viz.

(7) Genoa is indebted to London 640 dollars. For how much sterling may London draw on Genoa, the exchange at 52d. per dollar?

(8) If a merchant remit 1381. 13s. 4d. sterling to Leghorn, how many dollars will he receive there, the exchange at 52d. per dollar?

Note.-In St. George's bank, at Genoa, accounts are kept in piastres or pezzoes, which are divided into soldi and denari, as the pound sterling.

But some merchants keep their accounts in lires, or liras, soldi, and denari, divided as before. This money is only one fifth in value of the bank money.

(9) Change 8644 pez. into sterling money, exchange at 471⁄2d. per pezzo.

(10) London is indebted to Genoa 1710l. 16s. 4d. For how many pezzoes may Genoa draw on London, the exchange at 47 d. per pez.?

4th. With PORTUGAL.

They keep their accounts in Lisbon, Oporto, &c. in reas,

and exchange on the milrea; and London gives from 5s. to 5s. 6d. for the same.

EXAMPLES.

(11) A merchant at Lisbon being desirous to remit to his correspondent at London 4760 milreas, exchange at 64d. per milrea, how much sterling must be paid in London?

(12) How many milreas will 15661. 6s. 8d. amount to, exchange at 64d. per milrea?

5th. With HOLLAND, FLANDERS, and GERMANY.

In these places, their accounts are kept sometimes in pounds, shillings, and pence, as in England; and sometimes in guilders, stivers, and pennings. The money of Holland and Flanders is distinguished by the name of Flemish, and the exchange is made with London, from 30 to 38 shillings Flemish, per pound sterling.

To change Flemish money into sterling; and, on the contrary, sterling into Flemish, is the same with that of France; only what was French there will be Flemish here.

To reduce Flemish pounds, shillings, and pence, into guilders.

RULE.

Reduce them into pence Flemish, then divide by 40 (because 40d. are equal to one guilder), and the quotient will be guilders; and the remainder (if any) divide by 2 (because 2d. is equal to one stiver), and the quotient will