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Therefore the guilders are only 56. And by the same reasoning, the true differences of the second line in the first, and of the third line in the second table may be discovered; but the others being of a different nature, the method for them may be demonstrated by the third line in the first table, where 76 French crowns of 6 livres are worth a little more than 375s. sterling; therefore 100%. sterling, must accordingly make the French money less, and to find the real value of 456 livres in shillings sterling, say,

Fr. Cro.

d.

Fr. Cro.

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As 1000 of 3 liv.-3 or of a shill.76 of 6 livres to the sum sought.

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which must be added to 375 shillings to make the true value of

6000

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A Comparison between fine Gold and Silver.

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I shall not treat here of the comparison made between gold and silver by the ancient Greeks and Romans, but commence my account of it much nearer our own times. Agricola says that a hundred years before he wrote, or about 1440, one part of pure gold was given in Germany for thirteen similar parts of pure silver. In the year 1457, it was regarded as a settled price, that had, notwithstanding the several alterations in the coins, subsisted for some time; the giving 84 pennings of Landsberg money for a guilder of the Rhine, 100 of these pennings weighing a mark of Erfurt, the standard was 24 pennyweights; if the mark of Nuremberg weighed at that time 152 engels, the mark of Erfurt would be about 149 engels that weight, or the guilder of the Rhine 23 of fine silver. In the year 1461, the mark of silver at Erfurt contained 7, Rhenish guilders, or the value of the said guilder a little less than 214 engels pure silver. In the year 1528, a mark of fine gold of Nuremberg was worth 95 guilders of the Rhine, and a mark of fine silver a little more than 8+ guilders of the Rhine called golden ones not coined; so that 11 marks of pure silver were worth one mark of pure gold. In the golden guilder of the Rhine there were 2 engels that weight of fine gold, or the guilder of the Rhine at that time was esteemed as 14 ounce of pure silver; from that time to the present, the price of gold in regard to that of silver is augmented in these parts, about an author asserts, that in 1390, gold, in respect to silver, had four times less value than in 1687, but the error proceeded from this, that he made no difference between the present Holland guilder and the ancient one of the Rhine.

In 1717, the coined silver in England was on such a footing, that 15 marks of pure silver was of the same value with a mark of pure gold; in France 15 marks of fine silver was reckoned as a mark of fine gold; in Holland 143 marks: in the East Indies, in some places, 12 marks; as in the kingdom of Siam in 1688. "Description du dit Royaume, par M. de la Loubere," p. 221, Amst. 1770. And in China and Japan about

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• Dan. Angelocra, doctri. de ponder. monet. cap. 2. p. 28 and 29, Francf. A. 1628. Id. de pretio metallorum, p. 29. Hartungi Kamermeisteri Annales Erfurtenses, col. 1223. Vide Menkenii Scriptor. Rerum German. tome 3. Leips. A. 1730. a Id. Col. 1186. d Angelocra, P. de pretio metal. p. 47. Id. p. 26. ex Agri'col. 'Annal. Erfurt. col. 1231. Angelocrat. p. 65. ex Bilib. Pirkheim. Estimatio priscorum nummorum. Angelocra, ex Agricol. et Airckh. p. 34 and 65. * Simon de Uries Groot. Historisch Magazyn, p. 580, Amst.

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p. 1688.

10 marks. Supposing the value of silver to be settled, that of gold it is seen was greater in England than elsewhere; strangers made their payments in that metal; but because silver was more valuable abroad, the English sent their's to foreigners; and for this reason the silver coin became so scarce at home, as to occasion the diminishing the value of the guinea, by lowering it to 21 shillings, as has been before observed; for by trade, gold and silver would naturally pass from those countries where their value was less, to them where it was higher.

In 1000 Dutch ducats there are 334 carats 9, grains of pure gold, and if these are worth 5250 guilders, how much shall 24 carats be worth? and the answer will be 367 guilders and 7 stivers, the value of a mark of pure gold in coin. We have before found by the Dutch 3 guilder pieces that a mark of 11 pennyweights pure is worth 23 guilders and 7 stivers current money; and the mark of fine silver has been found worth a little less than 25 guilders and 9 stivers. In the same manner it is said, if 21 carats of pure gold are esteemed in France at 720 livres, how much shall 24 carats be worth? and, if 11-pennyweights of fine silver are worth 49 livres, how much shall 12 pennyweights be worth? By division it will be found as follows; supposing that in the English silver coin there had been no alteration made since 1717.

In

England 15 marks 1 ounce 134 engels,

France 14 marks 5 ounces 13 engels, fine silver for 1 mark of fine gold.
Holland 14 marks 6 ounces 4 engels,

From whence it is seen that Mr. Dernis, page 2, and Mr. Wiertz are not exact, because they say, that the proportion between pure gold and silver in Holland is fixed at 14; and it is also found in this last-mentioned author, page 491, that the mark of fine gold is fixed in Holland at 355 guilders current money, which is very true, but if the value of a ducat is taken to be 5 guilders 5 stivers, as it commonly passes, there is an agio of 6 per cent. in the specie of ducats; I know very well that these rise and fall a trifle; but the agio on gold must not be neglected, otherwise the ducat is never worth above 4 guilders 19 stivers.

This I think sufficient to give an idea of the par of monies, and I shall finish it with an instance of an arithmetical question abbreviated, concerning Spanish wool; as it is something curious, and may be instructive.

It is known to all concerned in that trade, that the wools of Germany and Poland are sold at Amsterdam with an allowance of fifteen months' discount, and one per cent. for prompt payment; for which the merchants deduct exactly a tenth; and for thosc of Spain 24lb. are always allowed for tare on 175lb. besides a deduction of twenty-one months' discount, and one per cent, for prompt payment; and in order to investigate a shorter method for calculating these abatements on the Spanish wools than has hitherto been practised, without neglecting the fraction which is often found in the tare, our author, Mr. Samuel Ricard, invented the following rule:

Rule.

1st. Multiply the pounds by the price, and from the product subtract a quarter part, Land the remainder will be expressed by A.

2d. Take 1 per mil. from A. and the 10th must be deducted; the remainder will be B. The difference of A. B. will be the sum sought for, which will surpass the true answer upon 11000 guilders about half a stiver.

3d. To correct this, there must be taken away from the guilders of B. †, and sub

tract as many deniers as there are of guilders for the remainder, and it will come to about 1 denier too little on 1,000,000 guilders' worth of wool.

Example.

It is demanded how much ought to be paid for some bales of wool, which weigh, after the tare marked on the bales is deducted, 9975lb. tare 24lb. on 175lb. and each lb. at 314 stivers, with twenty-one months' discount, and one per cent. for prompt pay. ment? the answer is 11,772 guilders, 6 stivers, and 12 deniers.

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OF ARBITRATIONS OF EXCHANGE.

ARBITRATION, a construction of the French word Arbitrage, in exchanges, has been Science des variously defined by the several authors who have treated of it.

la Port,

Negocians.

Sam. Ri

One says it is a combination or conjunction made of many exchanges, to find out

card,Traité what place is the most advantageous to remit or draw on.

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Another describes it, by saying it is only the foresight of a considerable advantage Commerce. which a merchant shall receive from a remittance or draught, made on one place preferably to another.

J. Laru,

P. 545.

Mons. de
Mondotte-

A third construes it to be a truck which two bankers mutually make of their bills Buy Traité upon different parts, at a conditional price and course of exchange.

trages. Mr. J. P. Ri

card, le

N goce d'Amster

dam, p. 810.

According to a fourth, it is the negociation of a sum in exchange, once or oftener repeated, on which a person does not determine till after having examined by several rules, which method will turn best to account.

And though these several distinctions are couched in different terms, they seem, if rightly considered, to have the same meaning, whereof some may be counted the text on which the others serve as comments or expositions.

Before any person applies himself to the study of this subject, it is necessary that he should be well skilled in all the practical operations, in regard to the reducing of the

sterling money of England into the foreign monies of exchange, and of account of all places of Europe, according to the direct courses of exchange established for these pur poses, and vice versa.

Also, that he should be acquainted with the methods of converting sterling money into the monies of exchange, and of account, of all other places of commerce, wherewith England has no direct established courses of exchange, but is under the necessity of making use of the intermediate exchange of other places: together with the nature of the agios, and the manner of converting their bank monies into current, and the

reverse.

That he should be able to calculate the par of all foreign monies throughout Europe with those of every distinct country, either according to the direct, or intermediate exchange, which makes a much greater variety of cases, than those who are not thoroughly acquainted with this extensive subject can imagine.

It is necessary likewise, as a preliminary to the practice of arbitration of exchanges, to know the intrinsic value of foreign coins, according to the most accurate assays which have been made for that purpose.

Finally, it is requisite to understand the general natural causes of the rise and fall of the courses of exchange between nation and nation, or between one trading city and another in the same nation.

Arbitrations are divided by the writers on them into simple and compound, of which I shall succinctly give some examples, and endeavour, as plainly as I can, to illustrate such rules for their operation as may render it easy both to the apprehension and performance; my predecessors having consigned me this task by unanimously leaving the solution of their questions too much in the dark to be comprehended by most of their readers, as they have contented themselves with replying to the queries, without showing their method of performing, and have thereby rendered abortive their pretended design of conveying instruction; which could no otherwise be done than by a delivery of their ideas and conceptions in such a manner as might leave them open, and easy to be followed and practised.

A simple, or single, arbitration, is to be wrought by the direct, or inverted, rule of three; and to distinguish which of these rules is to be used in working any question relative thereto, it must be observed:

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1. That an arbitration must be cyphered by the direct rule of three when the first term of stating is more than the third, and that the quotient is less than the middle term. And,

2. This rule must be used when the first term is less than the third, and the quotient is more than the middle one.

And the two following remarks will show when the indirect, or inverted, rule, is to be followed:

1st. The question must be worked by the inverted rule of three when the first term is less than the third, and the quotient less than the middle number.

2d. The operation must be by this rule, when the first term is more than the third, and the quotient more than the middle term.

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And whether the arbitrations be simple or compound, a price of exchange must always be supposed, when a reimbursement is ordered on any other place than that from whence it is directed.

Whatsoever number of figures enter into a compound arbitration question, the first and last must be of the same species, and the rules must be commenced by the species sought for.

These maxims being well understood, and applied to the examples, will facilitate the operation of the rules of arbitration to those who pay any attention to them.

And as the use of some characters instead of words will considerably abbreviate the work in the solution of the subsequent examples, I have employed them to this purpose, and shall here explain them once for all.

× signifies multiplied by, as 10 × 54, is 10 multiplied by 54.

24 x 67 x 19

A number above a line, with another under it, specifies that the uppermost must be divided by that beneath, or the numerator by the denominator, from whence 15 x 28 x 1 signifies, that 24 multiplied by 67, multiplied by 19, must be divided by 15 multiplied by 28, multiplied by 12; and denotes, that 54 is to be divided by 234, increased by.

54

23445

= signifies, equal to, as 10 = 5 × 2 = 8 × 4. This premised, I proceed to my proposed

First Example.

A. of Lyons orders B. of Cadiz to draw upon him at 76 sols per dollar, provided at the same time he can remit him on London, at 42d. sterling also per dollar, but as B. drew at 75, it is demanded at what exchange he may remit on London to complete this order; and this is answered by the direct rule of three as follows: If 76 sols give 42d. sterling, what shall 754 sols give?

42.

150

300

21

76)3171(41&&d. ster, answer.

304

131

76

55

Second Example.

A. of Oporto had orders to draw on Rouen, at 490 rees per crown of 60 sols, provided he could at the same time remit on Leghorn at 770 rees per dollar; but as on receipt of the said order he could get no more for his bill than 488 rees, it is demanded at what price he ought to remit on Leghorn, to recompense the said diminution in his draughts; which is solved by the inverted rule of three, in the following manner:

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