CHAPTER XXI. EXCHANGE. THE term EXCHANGE in commerce, is generally employed to designate that species of mercantile transactions, by which the debts of individuals residing at a distance from their creditors, are cancelled without the transmission of money. A BILL OF EXCHANGE is an order addressed to some person at a distance, directing him to pay a certain sum to the person in whose favor the bill is drawn, or his order. The person who draws the bill, is called the drawer; the person in whose favor it is drawn, the remitter or payee; the person on whom it is drawn, the drawee. The drawer is also called the acceptor, when he has accepted, or engaged to pay the bills. Though Bills of Exchange are originally drawn by credi tors on their debtors, they are very rarely transmitted directly, but pass from hand to hand like any other circulating medium, and are bought and sold in the market. When the remitter disposes of a bill, he writes his name on the back, and is termed the indorser. If he indorses in favor of any particular individual, he gives a special indorsement, and the indorsee must also indorse the bill if he negotiates it. But if the indorsement is blank, the bill may be passed at pleasure from hand to hand. Every indorser, as well as the acceptor, is held responsible for the payment of the bill, and may be sued for its recovery. INLAND, or DOMESTIC EXCHANGE, includes the commercial transactions within the limits of one country. FOREIGN EXCHANGE relates to the transactions of one country with another. The TRUE PAR OF EXCHANGE is the value of the currency of one country estimated in the currency of another, by comparing the quantity of gold and silver in their respective coins. The exchange with England apparently furnishes an exception to this rule, the nominal par being $4.444 per £, while the actual value of the pound sterling, which is the real par, is about $4.87. Hence exchange on England is generally said to be from 8 to 10 per cent. above par. The COURSE OF EXCHANGE, or the fluctuation above or be low par, depends generally on the amounts due between different countries. Thus when the debts and credits between two countries are equal, the real exchange is at par. But if New York owes London more than London owes New York, there will be a greater demand for bills on London, and this demand will produce a rise in the price, or cause the bills to be at a premium The premium, however, can never exceed the cost of transporting specie; for if it did, all debts would be paid in money or merchandise, instead of bills of exchange. The nominal premium, however, may exceed the cost of remitting coin, when the nominal par is above the real par. The operation of Bills of Exchange, may be explained by a single example. If A. of Boston, owes B. of Paris, and C. of Paris owes D. of Boston, A. purchases in the market a bill upon Paris; that is, he buys of D. an order on his creditor C., to pay A. or his order, the amount desired. A. indorses the bill, and sends it to B., who receives payment from C. Thus the two debts are cancelled by a single remittance; the inconveni ence of exporting and re-importing coin is removed, and all danger of loss is obviated, by sending three bills, (called the First, Second, and Third of Exchange,) either of which being paid the others are void. An ACCEPTANCE is an engagement to pay the amount of the bill, and may be either absolute or qualified. An absolute acceptance binds the drawer when the bill becomes due, and in making it, the drawee usually writes "Accepted," and subscribes his name at the bottom, or across the body of the bill. A qualified acceptance implies some condition, as the sale of merchandise, &c., and does not bind the acceptor until the condition is complied with. If a bill is made payable at a certain time after sight, the acceptance should be dated. A bill should be presented for payment during the regular hours of business, on the day it becomes due. When acceptance or payment has been refused, the holder should give immediate notice to all the parties whom he in tends to hold responsible for the payment of the bill. This notice is usually accompanied with a PROTEST, which is an instrument prepared by a public notary, stating that acceptance or payment has been demanded and refused, and that the holder of the bill intends to recover any damages which he may sustain in consequence. In some places on the continent of Europe, banks of deposite are established, and exchanges are frequently made by transferring the amounts credited on the books of the bank from one person to another. The deposites on which these credits are based, are called banco, and they usually bear a premium above the ordinary currency of the country. This premium is called the agio. The comparative market value of gold and silver is constantly varying, and the mint value is differently estimated by different governments. Thus, in England the relative worth of the two metals is as 1 to 14.29, in France, as 1 to 15.52, and in the United States, as 1 to 15.99. In England, silver is so much overvalued, that it would banish the gold coins from circulation, were there not a statute providing that gold only shall be legal tender in all payments of more than 40 shillings. The relative value of the precious metals should always be considered, in estimating the true par of exchange with any country. DOMESTIC EXCHANGE. Inland Exchange is usually effected by checks or Drafts, similar in form to the following: $1275.25 Philadelphia, June 3, 1844. Sixty days from date, pay to James N. Lewis, or order, Twelve Hundred and Seventy-Five Dollars and Twenty-Five Cents, and charge the same to my account. William Morris. To Markham & Jones, The premium or discount on drafts, may be owing either to a difference in the value of the circulating medium, or to fluctuations in the demand. The English denominations of shillings and pence, are still retained in this country to some extent. At the forma. tion of the Constitution, the continental currency had suffered a greater depreciation in some of the colonies than in others. Thus, while a pound in New England was worth $3.33}, in Pennsylvania it was but $2.66}, and in New York but $2.50. The value in Federal Money, of the old currencies of the different States, is as follows: A shilling of New England, Virginia, Kentucky, or Tennessee, is 163 cents. A shilling of New York or North Carolina, is 12 cents. A shilling of New Jersey, Pennsylvania, Delaware, or Maryland, is 13 cents. A shilling of South Carolina, or Georgia, is 21 cents. CHAPTER XXII. DIVISIBILITY OF NUMBERS. EVERY number that cannot be divided by any other number, (except 1,) without a remainder, is called a PRIME NUMBER. Two or more numbers that have no common divisor, are said to be prime to each other. Every prime number is prime to all other numbers except its own multiples. There are no known means of determining at once whether a proposed number is a prime, but the following properties and rules will enable us to determine all the divisors of any number. 1. 2 is a factor of all numbers terminated by 0, 2, 4, 6, or 8. For, as 2 will divide 10, it will also divide any number of tens, or any number of tens plus 2, 4, 6, or 8. Numbers divisible by 2 are called EVEN,-all others, ODD numbers. 2. 5 is a factor of all numbers terminated by 0 or 5. For, as 5 will divide 10, it will also divide any number of tens, or any number of tens plus 5. 3. 3, or 9, is a factor of all numbers in which the sum of the figures is exactly divisible by 3, or 9. For, if from any power of 10, as 10, 100, 1000, &c., we subtract 1, the remainder consists entirely of 9's, and is, therefore, divisible by both 3 and 9. Hence, any power of 10 is divisible by 3 and 9 with 1 remainder, therefore, any number of tens, hundreds, thousands, &c., diminished by as many units, will be divisible by 3 and by 9. Let us, then, examine the number 34794. 3 ten thousands 3; 4 thousands 4; 7 hundreds-7; 9 tens-9; and 4 units-4; each divided by 3 or 9, give no remainder. Therefore, 34794—3—4—7—9—4, is divisible by 3 and by 9, and if the sum of the numbers sub. tracted, or in other words, the sum of the digits, is similarly divisible, the number itself will be so. 4. 11 is a factor of all numbers in which the sum of the odd digits, (the 1st, 3d, 5th, &c.,) and the sum of the even digits, (the 2d, 4th, 6th, &c.,) are equal, or their difference is some multiple of 11. For any number of tens, thousands, hundred thousands, &c., (which represent the even digits,) increased by as many units, will be divisible by 11. Any number of hundreds, ten thousands, millions, &c., (which represent the odd digits,) diminished by as many units, will also be divisible by 11. Take, then, the number 635173. 6 hundred thousands + 6; 3 ten thousands · -3; 5 thousands + 5; 1 hundred 1; 707; and 3 3; each divided by 11 give no remainder. Therefore, 635173 18+ 7 or 635173 11, is divisible by 11, and 635173 itself must be so. 5. 4 is a factor of all numbers, in which the two terminating figures are divisible by 4. For, as 4 will divide 100, it will also divide any number of hundreds, or any number of hundreds plus any number of units divisible by 4. 6. 25 is a factor of all numbers terminated by 25, 50, 75, or two zeroes. For, as 25 will divide 100, it will also divide any number of hundreds, or any number of hundreds plus 25, 50, or 75. 7. Every number that is divisible by two or more numbers prime to each other, is divisible by their product. Take for example, 105 which is divisible by both 3 and 5. This number may be resolved into the factors 5 × 21; 5 × 21 must, therefore, be divisible by 3. But as 3 will not divide |