cask; but the rest being worse than he expected, he is willing to sell it at such a price per cask, that he may exactly make his purchase-money of the whole.' At what rate must he sell it?

(29.) A merchant bought 100 yards of velvet for 1127. at what rate must he sell it per yard to gain as much by the whole quantity as four yards are sold for?

(30.) Sold a quantity of Virginia snakeroot for 207. and by so doing lost 201. per cent. whereas I ought to have gained as much per cent. as the snakeroot cost. Quere my loss in point of trade?

(31) A tea-dealer purchased 120lb. of tea; of which he sold at 10s. 6d. per lb. but the rest, being damaged, he sold it at a loss of 37. 128. after which he found he had neither gained nor lost. What did the tea cost him per lb. and what was the damaged tea sold for?

(32.) My factor at Leghorn returned me 800 barrels of anchovies, each weighing 14lb. neat, worth 12 d. per lb. in lieu of 7490lb. of Virginia tobacco; by which consignment I find that I have gained 177. per cent. Pray what was the prime cost of a lb. of my tobacco to the factor?

(33.) A merchant sent goods to Boulogne to the va lue of 3475/. 158. by the sale of which he gained 407. sterling per cent.-The value of the goods he sent over and the gain were returned in commodities, by the sale of which in England he lost 15l. per cent. What was his gain at the last?

(34.) Sold a piece of cloth, containing 5000 ells Flemish, for 4250 guineas, and gained upon every yard of the prime cost of an English ell. What did the whole piece stand me in?

BARTER.

Definition. When merchants or tradesmen exchange one commodity for another, it is called Bartering; and, by the rule of proportion, the price and quantity of the goods so exchanged are determined, so that neither party may sustain a loss by such traffic.

Proposition 1. Given the price of an integer of any quantity of goods, to find the corresponding quantity of any other sort of goods, at any given price per integer.

Rule. Find the value of that commodity, whereof the quantity is given, by the Rule of Three, or Practice. Then, as the price of an integer of the required quantity of goods is to that integer, so is the value of the given quantity, found before, to the required quantity.

Note. Several questions that fall under this proposition may be solved, in the shortest manner, by the second rule of Compound Proportion, or by the Rule of Three Inverse.

Prop. 2. Given the price of an integer of any quantity of goods, to find the quantity of any other kind of goods, (at any given price per integer,) when part of the value is paid in money, or any other kind of merchandise.

Rule. Find the whole value of that commodity, whereof the quantity is given, by the Rule of Three, or Practice; from which subtract the sum of money to be paid down, or the value of the given quantity of goods in exchange. Then, as the price of an integer, of the required quantity of goods, is to that integer, so is the remaining value to be accounted for, to the required quantity.

Note. Several other propositions and rules in Barter are omitted as superfluous, the questions which they are intended to solve being of no real use; such as to find in what proportion one person ought to advance his goods to another who has raised his goods above their real. value, &c. For, in the real exchange of goods, when both parties have mentioned their ready-money prices, if one person's goods are advanced to a bartering price, the other person's must be advanced in the same proportion, and consequently the balance between them will remain exactly the same as if the ready-money price only had been used.

Examples to Proposition 1.

(1.) A and B barter; A has 34lb. of pepper at 13 d. per lb., B has ginger at 154d. per lb. How much ginger inust B give for A's pepper?

13×31=474 dividend, which divided by 154, the divisor, gives 3&lb.=3lb. 134 oz. as before.

Or,

13 d. 3lb.:: 15 d.*

Here it is evident that B must give A a less number of lbs. of ginger than he receives pepper, because the ginger is worth more per lh. Consequently,

133÷1513lb. or 3lb. 18oz. as above.

(2.) A would exchange 400 gallons of Jamaica rum, worth 7s. 9d. per gallon, with B for London porter, at 9d. a gallon; how many gallons of porter must A receive of B in exchange for his rum?

(3.) A hop-factor, A, exchanged 5cwt. 1qr. 10lb. of hops, at 2s. 44d. per lb. for wheat at 5s. 9d. per bushel, with a farmer B; what quantity of wheat did B give A for his hops?

(4.) How many yards of cloth, at 18s. 6d. per yard, must I give for 5000 yards of baize, at 13 d. per yard? (5.) A delivered 6 hogsheads of brandy, at 6s. 8d. per gallon, to B for 252 yards of cloth; what ought the cloth to be worth per yard?

(6.) A has 288 ells of cloth, worth 18. 3d. per ell, which he would barter with B for cheese at 19s. per cwt. what weight of cheese ought B to give for the cloth?

(7.) A and B bartered; A had 14cwt. 3qrs. of sugar, worth 17. 178. per cwt. which he bartered for wine worth 38. 9d. per gallon; how much wine did A receive?

(8.) A chandler and a butcher trade as follows: the butcher has 3cwt. 2qr. 16lb. of tallow at 17. 17s. 4d. per cwt. and the chandler rates his candles at 5s. 2d. per dozen. How many lbs. of candles must the chandler give the butcher for his tallow?

Examples to Prop. 2.

(9.) A and B barter as follows: A has 41 cwt. of hops at 30s. per cwt. for which B gives him 207. in ready mo

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ney, and the rest in sugar at 6d. per lb. What quantity of sugar must B give Ã?

(10.) A and B barter; A has 750 yards of canvas, worth 10d. per yard, for which B gives him 475 yards of serge at 11 d. per yard, and the balance in cotton at 3s. per yard; how many yards of cotton must A receive?

10d. 41 750

3s. 1yd. 81. 9s. 91d. : 56yds. 27qrs. answer.

(11.) A has 700 gallons of rum at 4s. 6d. per gallon, for which B gives him 27 guineas in money, and the rest in cotton at 11 d. per lb.; how much cotton must A receive?

(12.) A has 57qrs. 6bush. of corn, worth 17. 118. 6d. per quarter, for which B will give 14cwt. 3qr. 18lb. of sugar at 41. 14s. per cwt. and the balance in raisins at 7d. per lb. Should these persons barter, what quantity of raisins ought B to give A?

(13.) A has 27 cwt. of cheese, worth 17. 11s. 4d. per cwt., and B has 25 pieces of cloth, worth 17. 19s. 10žd. per piece; should these persons barter together, to whom will the balance, if any, be due?

CLASS II.

(14.) A gave B 120 yards of Kersey, 34 yards of which cost 158. 9d. for stockings at 7s. per pair, and hats at 6s. 6d. each; B gave A as many hats as pairs of stock. ings; how many of each did he give?

(15.) Two merchants have various kinds of goods to barter: A has 735 yards of India silk, worth 8s. 6d. per yard, 532 canes worth 3s. each, and 16 pieces of muslin worth 41. each; B has scarlet eloth worth 17. per yard, glass manufacture at 1s. 8d. per lb. and a finer kind at 2s. 4d. per lb. How many yards of cloth and pounds of each sort of glass must B give A, admitting that he gives as many pounds of each sort of glass as he gives yards of cloth?

(16.) A merchant, A, of London, sent 8752 yards of cloth, worth 17. 11s. 6d. per yard, to B in Jamaica ; and desired him to return him of the value in sugar at 17. 15s. 6d. per cwt. of the value in pepper at 71. 3s. 9d. per cwt. and the rest in rum at 5s. 6d. per gallon. Each merchant ran the risk, and paid the charges of the commodity he sent over; pray what quantity of sugar, pepper, and rum, did A receive.

(17.) A and B barter; A has 24 puncheons of rum, worth 4s. 9d. per gallon; for which B gives him 150 guineas in cash, and 714 yards of cloth. What ought B's cloth to be worth per yard?

When

(18.) A bartered tobacco, worth 3s. 4d. per lb. at 3s. 9d. per lb. with B for tea at 6s. 3d. per lb. A sold the tea, he found himself a gainer of 17l. 6s. 8d. per cent. and in the whole 87. 10s. 8d. What did A sell the tea for per lb. and what quantity of tobacco and tea were bartered?

EXCHANGE.

Definition 1. By Exchange is meant the bartering, or exchanging, the money of one place for that of another, by means of an instrument in writing, called a Bill of Exchange; and consists in finding what quantity of the money of one city or country will be equal to any given sum of another, according to a given course of exchange.

2. The Course of Exchange is the value agreed upon by merchants, or their factors; and is continually fluctuating above or below the Par of Exchange, according as the demand for bills is greater or less.

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