EXAMPLES. 1. Two merchants made a company; A put in 200 dollars for 5 months, and B 150 dollars for 6 months, and they gain 70 dollars; what share of the profit belongs to each? 200 X 5: 1000. 150×6=900. And 1000+900: 1000 :: 70: 3616 A's share. 1000+900 900 :: 70: 33 B's share. 2. Three merchants join trade; A puts in 500 dollars for 3 months, B 600 for 4 months, and C 700 for 5 months; what share of 200 dollars gain should each have? the shares are in proportion to the products of stock and time. This may be demonstrated simply as follows, viz. Suppose 100 dollars in trade 12 months, gain 20 dollars, 50 dollars in 6 months, at the same rate, will gain 5 dollars; and both together 25 dollars. For, 100×12: 50×6:: 20:5 Again, by composition, and 20+5=25. 100x12+50×6: 100×12 :: 25: 20 gain of $100 in 12m. And 100×12+50×6: 50×6:: 25: 5 gain of $50 in 6m. From which, the reason of the rule, and its correctness of principle, is evident. EXCHANGE. Exchange, in an arithmetical sense, is the method of reducing the money, weights and measures of one country into that of another; but particularly in fixing the momentary and actual value of money. Gold and silver, as metals, have their intrinsic value; but, as they are capable of becoming the sign or medium. by which merchandize may be estimated, they may receive an additional value. Certain specific values may be given to the coins or other monies of a nation, by authority of its own government, to fix their currency amongst the subjects of that nation; but with other nations, the value of money is fixed by the current course of commerce, and the general opinion of merchants, according to the accidental circumstances of trade, money transactions between nations and the state of their public credit.. The mutability of the course of exchange is not real, but relative; for instance, when Philadelphia has greater occasion for funds in Savanna, than Savanna has in Philadelphia, though the price of the specie of both places bear a fixed proportional value to each other, yet when there is not a credit in Savanna equal to the debit, the price of bills, (not of money,) will rise of course at Philadelphia. If the balance of trade be reciprocal between foreign. countries, or between different sections of the same country, there will be enough of bills in the one to settle accounts with the other; in which case exchange will be at par. But if a nation, or one section of country, supplies another with more than it purchases, there will be a balance against that other; to discharge which, the money or bills of exchange on that nation, or section of country, naturally rises above par, and puts those against whom the balance of trade stands, below par; which constitutes the course of exchange. The course of exchange between two nations, publicly proclaims the state of commerce be-tween them, and shews which of them is indebted to the other. The nation that is in debt, as well as an individual, suffers a disadvantage both in commerce and money negociations.. The balance of trade naturally imports specie, and renders money at home more valuable abroad. On the contrary, when the balance is against a nation, its specie is exported, and becomes thereby of less value. A bill of exchange, is a written order, delivered in one place for value received there (according to the rate of exchange agreed upon) for the like value to be paid to the holder of the bill, in the place upon which it is drawn. When the money received for a bill of exchange, is equal in value to the money paid for it, exchange is then at par, or equal. The course of exchange, is the fluctuation of par. Usance, is a particular time specified for the payment. of a bill of exchange, after acceptance, being in some places 30 days, in others 60, 90, &c. DOMESTIC EXCHANGE. Domestic exchange, is a method by which the current value of money in one state, is changed to that of another. The keeping of accounts, all over the United States, is now partly the same; they being principally kept in dollars and cents. But I shall subjoin something upon the currency of the different states, as it formerly was, viz. The value of the Federal dollar, in the currency of the different states, stands thus: By deducting from the current value of a dollar in New-Jersey, Pennsylvania, Delaware, and Maryland, the remainder will be equal to the current value of the dollar, in each of the eight named states to the left of this page above, viz. the nominal value only. 6s. 8 These are all the nominal current values for the dollar in the respective states. And to reduce 4 8d. the nominal value of a number of dollars in the 7 6 states where 6s. goes for the dollar, to the nominal value, where 8s. are equal to a dollar; § reduced, becomes 2, and 1-1. Therefore to make of 6s. dollars, 8s. dollars, of their number must be added; and to make of 8s. dollars, those of 6s., of their number must be deducted. To reduce 4s. 8d. dollars, to 6s. dollars, we have 4s. 8d. =56d. and 6s. 72d.; hence 6-7, and 1-7-3. There fore, to make 4s. 8d. dollars out of 6s. dollars, parts of the latter must be deducted; if to make 6s. dollars out of 4s. 8d. dollars, multiply by 9 and divide by 7. To make of 6s. dollars, dollars of 7s. 6d. we have 6s. 72d. and 7s. 6d.=90d.; hence 12, and 1-3=3; therefore, to make 6s. dollars, 7s. 6d. dollars, multiply by 5 and divide by 4; and to make 7s. 6d. dollars, dollars of 6s., deduct. In a similar manner, rules can be made for every possible case. In the following page is a table of coins which formerly passed current in the United States of North America; but since November 1st, 1819, by act of congress, all gold coins of Britain, Portugal, France, and Spain, as well as other foreign gold coins, are prohibited from being a lawful tender for the payment of debts or demands. Silver coins of those countries are under the same restrictions, since April 29th; 1821. |