It is the relative abundance and scarcity of the moneys of various countries that makes up what we call the exchange.
The exchange is a setting of the current and transitory value of moneys.
Silver as a metal has a value like all other commodities, and it further has a value that comes from its ability to serve as the sign for other commodities ; and if it were but a simple commodity, there is little doubt that it would lose much of its price.
Silver as a money has a value which the prince can set in some respects, and has no way of setting in others.
The prince establishes a proportion between a quantity of silver as metal and the same quantity as money. Secondly, he sets the proportion among various metals used in coinage. Thirdly, he establishes the weight and purity of each coin. Finally, he gives to each coin this ideal value, of which I have spoken. I shall call the value of the money in these four respects positive value, because it can be set by law.
The moneys of each state have, in addition, a relative value, in the sense that they are compared with the moneys of other countries : it is this relative value which the exchange establishes. It depends a great deal on the positive value. It is set by the most general evaluation of traders, and cannot be set by the prince’s decree, because it varies constantly and depends on a thousand circumstances.
To set the relative value, the various nations will largely be guided by the one that has the most silver. If it has as much silver as all the others together, each will have little choice but to measure itself against that one ; this will cause them to make adjustments among themselves more or less as they have measured themselves against the principal nation.
In the present state of the world, it is Holland  which is the nation in question. Let us examine the exchange with respect to her.
In Holland there is a money called a florin : the florin is worth twenty sous or forty half-sous or groots.  To simplify things, let us imagine there are no florins in Holland, and that there are only groots : a man who has a thousand florins will have forty thousand groots, and so forth. Now the exchange with Holland consists in knowing how many groots each coin of the other countries will be worth ; and as in France we ordinarily count by the three-livre crown,  the exchange will ask how many groots a three-livre crown will be worth. If the exchange is at fifty-four, the three-livre crown will be worth fifty-four groots ; if it is at sixty, it will be worth sixty groots ; if silver is scarce in France, the three-livre crown will be worth more groots ; if it is plentiful, it will be worth fewer groots.
This scarcity or this abundance which results in the mutation of the exchange is not the real scarcity or abundance, it is a relative scarcity or abundance ; for exemple, when France has greater need of funds in Holland than the Dutch have in France, silver is called common in France and scarce in Holland, and vice versa.
Suppose the exchange with Holland were at fifty-four. If France and Holland constituted just one city, we would do what we do when we make change for a crown : the Frenchman would take three livres from his pocket, and the Dutchman would take fifty-four groots from his. But since there is some distance between Paris and Amsterdam, the person who gives me the fifty-four groots he has in Holland for my crown gives me a fifty-four-groot letter of exchange on Holland. We are no longer dealing with fifty-four groots, but with a fifty-four-groot letter ; thus, in order to gauge the scarcity or abundance of silver, one must know whether there are in France more fifty-four-groot letters destined for France than there are crowns destined for Holland.  If there are many letters offered by the Dutch and few crowns offered by the French, silver is scarce in France and common in Holland, and the exchange must rise, and for my crown I must be given more than fifty-four groots, or else I would not offer it, and vice versa.
It can be seen that the various operations of the exchange make up an account of credit and debit that must always be settled ; and that a debtor state no more discharges its debt with the others through the exchange than an individual pays a debt by changing money.
Suppose there are only three states in the world : France, Spain, and Holland ; that various Spanish individuals owe in France the value of one hundred thousand silver marks, and that various French individuals owe one hundred ten thousand marks in Spain ; and that some circumstance made everyone in Spain and in France suddenly wished to withdraw their money : what would the exchange operations do ? They would reciprocally acquit these two nations of the sum of one hundred thousand marks ; but France would still owe ten thousand marks in Spain, and the Spanish would still have letters on France for ten thousand marks, and France would have none at all on Spain.
Now if Holland were in an opposite situation with France, and owed her 10,000 marks, France could pay Spain in two ways : either by giving to her creditors in Spain letters on her Dutch debtors for 10,000 marks, or else by sending 10,000 silver marks in specie to Spain.
It follows from this that when a state needs to remit a sum of money in another country, it is indifferent by the nature of the thing whether silver is carted there or whether they take letters of exchange. The advantage of these two means of paying depends solely on the present circumstances : you have to see what at this moment will yield the most groots in Holland, of silver carried there in specie  or a letter on Holland in the same amount.
When the same purity and same weight of silver in France give me back the same weight and purity of silver in Holland, we say that the exchange is at par. In the present state of the monies, par is about fifty-four groots per crown  ; when the exchange goes over fifty-four groots, we will say it is high ; when it is below we will say it is low.
To know whether the state gains or loses in a certain exchange situation, we have to consider it as debtor, as creditor, as seller, and as buyer. When the exchange is below par, it loses as debtor, gains as creditor, loses as buyer, and gains as seller. It is clear that it loses as debtor : for example, France owing Holland a certain number of groots, the less its crown is worth in groots, the more crowns it will take her to pay ; contrariwise, if France is owed a certain number of groots, the less each crown is worth in groots, the more crowns she will receive. The state again loses as buyer, for it still takes the same number of groots to buy the same quantity of merchandise, and when the rate drops, each French crown yields fewer groots. For the same reason, the state gains as seller : I sell my merchandise in Holland for the same number of groots as I had been selling it ; I will therefore have more French crowns in France when I obtain a crown with fifty groots than when I have to have fifty-four to get the same crown ; for the other state, all of this will be reversed. If Holland owes a certain number of crowns, she will gain, and if we owe them to her, she will lose ; if she sells, she will lose ; if she buys, she will gain.
Yet we must pursue this. When the exchange is above par, for example if it is at fifty instead of being at fifty-four, it should happen that France, sending through the exchange fifty-four thousand crowns to Holland, would buy only fifty thousand worth of merchandise ; and that on the other hand Holland, sending the value of fifty thousand crowns to France, would buy fifty-four thousand worth, which would make a difference of eight fifty-fourths, or more than a one-seventh loss for France : so one-seventh more would have to be sent to Holland in silver or in merchandise than we did when the exchange was at par ; and with the problem constantly increasing, since such a debt would make the exchange fall further, France would ultimately be ruined. It seems, I say, that this should happen : and it does not, because of the principle I have already established elsewhere,  which is that states always tend to balance their accounts and procure their liberation ; thus they borrow only in proportion to what they can pay, and buy only as they sell ; and taking the above example, if the exchange falls in France from fifty-four to fifty, the Dutchman who was buying French merchandise for a thousand crowns and was paying fifty-four thousand groots for them, would now pay only fifty thousand if the Frenchman would consent to that ; but the French merchandise will rise imperceptibly, and the profit will be shared between the Frenchman and the Dutchman : for when a dealer can gain, he readily shares his profit ; there will thus be a communication of profit between the Frenchman and the Dutchman. In the same way, the Frenchman who was buying merchandise from Holland for fifty-four thousand groots, and was paying for them with a thousand crowns when the rate was fifty-four, would be required to add one-seventh more French crowns to buy the same merchandise ; but the French merchant who will be aware of the loss he would sustain will wish to pay less for the merchandise from Holland ; there will therefore be a communication of loss between the French merchant and the Dutch merchant, the state will step imperceptibly into the balance, and the drop in the exchange rate will not have all the disadvantages that might have been foreseen.
When the rate is below par, a dealer can remit his funds in foreign countries without diminishing his fortune, because when he recalls them he gets back what he has lost ; but a prince who sends to foreign countries nothing but silver that is never to return always loses.
When dealers do a great deal of business in a country, the rate invariably rises. That is because they contract many engagements and buy considerable merchandise, and they draw on the foreign country to pay for them.
If a prince accumulates large quantities of silver in his state, silver may be scarce there in reality, and common relatively : for example, if at the same time this state had to pay for considerable merchandise in the foreign country, the rate would fall, even though silver was scarce.
The exchange in all marketplaces always tends to settle at a certain proportion, and this is in the nature of the thing itself. If the exchange from Ireland to England is below par, and that of England to Holland also below par, that of Ireland to Holland will be even lower, in other words in compound ratio of Ireland to England and England to Holland ; for a Dutchman who can send for his funds indirectly from Ireland through England will be unwilling to pay more to send for them directly. That, I say, is how it should be ; yet it is not exactly that way : there are always circumstances which make things vary, and the difference between the profit that can be got from one market or from another is the art and particular skill of bankers, which are not at issue here.
When a state ups its coin, for example when it calls six livres or two crowns what it was calling only three livres or one crown, this new denomination, which adds nothing real to the crown, should not obtain a single additional groots through the exchange. For the two new crowns one should receive only the same quantity of groots as the former one crown brought ; and if that is not the case, it is not the effect of the naming itself, but the effect it produces as new and the effect it has as sudden. The exchange holds to business in course, and only makes an adjustment after a certain time.
Whenever a state, instead of simply upping its money by law, mints new coinage in order to make a strong money into a weaker money, it happens that while the operation is under way there are two kinds of money : the strong one which is the old one, and the weak one which is the new ; and as the strong one is banned, and accepted only at the mint, and letters of exchange must consequently be paid in new specie, it seems the exchange ought to be set in terms of the new specie. If, for instance, the depreciation in France were by half, and the former three-livre crown yielded sixty groots in Holland, the new crown ought to yield only thirty groots ; in another way, it seems that exchange ought to be determined by the value of the old specie, because the banker who has money and who accepts letters is obliged to carry old specie to the mint to get new specie for it, on which he loses ; the exchange will therefore assume a value between the value of the new specie and that of the old ; the value of the old specie is falling, so to speak, both because there is already some new specie in circulation and because the banker cannot insist, it being in his interest to get the old money quickly out of his till so he can put it to work, and even being forced to do it to make his payments ; on the other hand, the value of the new specie rises, so to speak, because the banker with some of the new specie finds himself in a circumstance where, as we shall show, he can obtain some of the old specie at great advantage ; the exchange will therefore settle, as I have said, between the new specie and the old. At that point, bankers benefit by getting the old specie out of the state, because in that way they obtain the same advantage that an exchange determined by the old specie would yield, in other words, many groots in Holland ; and they have a return at a rate set between the new specie and the old specie, which is to say, lower, which procures many crowns in France.
I shall assume that three livres of old specie yield at the present rate forty-five groots, and that by carrying this same crown to Holland you get sixty ; but with a forty-five-groot letter you will obtain a three-livre crown in France, which, taken in old specie to Holland, would also yield sixty groots ; all of the old specie will therefore leave the state that is reminting, and the profit will go to the bankers.
Correcting this will make a new operation mandatory. The state which is reminting will itself send a large quantity of old specie into the nation that regulates the exchange ; and thus obtaining a credit, it will make the rate rise to the point where very nearly as many groots will be obtained by exchanging a three-livre crown as would have been by sending one of three livres in old specie outside the country. I say very nearly because, when the profit is modest, no one will be tempted to send specie out, because of the transportation costs and the risks of confiscation.
It will be helpful to give a very clear idea of this. Mr. Bernard,  or any other banker whom the state wishes to use, proposes his letters on Holland, and offers them at one, two, or three groots higher than the current rate of exchange ; he has made a provision in foreign countries by means of old specie which he continually had transported ; he has thus brought the rate up to the point we have just said ; meanwhile, by dint of issuing his letters, he grabs up all the new specie, and forces the other bankers who have payments to make to take their old specie to the mint ; and moreover, as he has quietly taken all the silver, he obliges the other bankers in their turn to give him letters at a very high exchange rate : the profit in the end compensates him in large part for his loss at the beginning.
It will be clear that during this whole operation the state must suffer a violent crisis. Silver will become very scarce, first because most of it must be banned ; second, because part of it must be transported to foreign countries ; third, because everyone will hoard it, no one wanting to leave to the prince a profit they hope to have themselves. It is dangerous to do it slowly ; it is dangerous to do it swiftly. If the gain anticipated is immoderate, the drawbacks increase in proportion.
We have seen above that when the exchange was lower than the specie, there was a profit in sending money away ; for the same reason, when it is higher than the specie, there is a profit in bringing it back.
But there is one case where a profit is had by sending specie awau even though the exchange is at par : that is when it is sent abroad to be relabelled or melted down. When it has returned, the profit from the money is realized whether by using it in that country, or by taking letters of exchange for use abroad.
If it happened that a company was set up in a state with a very considerable number of shares, and these shares had been made in a few months to rise twenty or twenty-five times beyond their initial repurchase value, and this same state had established a bank the bills of which had to function as currency, and the numerical value of these bills was prodigious in order to to correspond to the prodigious money value of the shares (this is Mr. Law’s System), it would follow from the nature of the thing that these shares and bills vanish in the same way they had established themselves. The shares could not have been made to rise all of a sudden to twenty or twenty-five times their original value without providing many people with the means of obtaining immense riches on paper : everyone would seek to assure his fortune ; and since the exchange offers the easiest path for liquifying it or sending it wherever one wishes, one would constantly be remitting a part of one’s holdings to the nation that regulates the exchange. A continual project of remitting to foreign countries would cause the exchange to drop. Let us suppose that at the time of the System, in the relationship between the purity and the weight of silver money, the rate of exchange were forty groots per crown : when limitless paper had become money, no one would have been willing to offer more than thirty-nine groots per crown, then thirty-eight, thirty-seven, and so on. That went so far that the offer was down to eight groots, and finally there was no more exchange at all.
It was the exchange which in this case was supposed to set the proportion of silver to paper in France. Supposing that, by the weight and purity of the silver, the paper three-livre crown was worth forty groots, and that, the exchange taking place in paper, the paper crown of three livres was worth but eight groots, the difference was four-fifths. The paper three-livre crown was therefore worth four-fifths less than the three-livre crown in silver.