NOTE.-On debts or judgments in favor of the United States, interest .s computed at the rate of 6 per cent. per annum.

In order, therefore, to change the preceding currencies to United States money, the shillings, pence, and farthings, if there be any, must first be reduced to decimals of a pound, and annexed to the pounds.

RULE. Divide the pounds by the value of a dollar in the given currency, EXPRESSED BY A FRACTION OF A POUND; that is, to change the old New England currency to United States money, divide by; because 6 shillings is of a pound.

To change the old currency of New York, &c., to United States money, divide by 10; because 8 shillings is of a pound.

To change the old currency of Pennsylvania, &c., to United States money, divide by ; because 7 shillings and 6 pence is of a pound.

To change the old currency of South Carolina and Georgia to United States money, divide by : because 4 shillings and 8 pence is of a pound.

To change Canada and Nova Scotia currency to United States money, divide by ; because 5 shillings is of a pound.

The old method of changing English sterling money to United States money was, to divide the pounds by, and the quotient was dollars; and, to change dollars into English sterling money, to multiply the dollars by, and the product was pounds sterling. But, as will be seen by a note on page 151, this process does not give the present value of a pound sterling.

EXAMPLES.

1. Change 18£. 4s. 6d. of the old New England currency to United States money.

In this example we reduce the 4 shillings and 6 pence to a decimal of a pound, which we find to be .225. This decimal we annex to the pounds, and multiply the 18.225£. by 10, and divide by 3, and it produces the answer, $ 60.75. The reason for this process has already been shown.

2. Change $60.75 to the old currency of New England. 18£. 4s. 6d. Ans.

$60.75 X 1

= 18.225 =

The decimal .225 is reduced to shillings and pence by Case IV. of Decimal Fractions.

3. Change 78£. 7s. 6d. of the land to United States money.

old currency of New Eng

Ans. $261.25.

4. Change $261.25 to the old currency of New England.

Ans. 78£. 7s. 6d.

5. Change 46£. 16s. 6d. of the old currency of New York to United States money. Ans. $117.06. 6. Change $117.06 to the old currency of New York. Ans. 46£. 16s, 6d.

7. Change 387. of the old currency of Pennsylvania to United States money. Ans. $1032. 8. Change $1032 to the old currency of Pennsylvania, Delaware, and Maryland.

Ans. 387£.

Ans. $54.

9. Change 12£. 12s. of the old currency of South Carolina and Georgia to United States money. 10. Change $54 to the old currency of South Carolina and Georgia. Ans. 12. 12s.

11. Change 128. 18s. 6d. of Canada and Nova Scotia to United States money.

Ans. $515.70.

12. Change $515.70 to Canada and Nova Scotia curAns. 128. 18s. 6d.

rency.

NOTE. — From time immemorial

has been given in all our arithmetics as the value of the pound sterling in United States Money. It is time the error was corrected.

The nominal par of exchange with London, as expressed in reports of exchange, is 109.496+, or very nearly 109, being 93 above the computed par of $4.4443, represented by 100.

The Bank of England was established in 1694, by a company who advanced a loan of £1,200,000 sterling to government. Specie payment was suspended in 1797, and resumed, by act of Parliament, May 1, 1823.

The term Sterling is derived from the Easterlings, who were expert refiners from the eastern part of Germany, who came into England and first established the standard proportion of silver, 11oz. 2dwt. fine silver, and 18dwt. alloy. The first sterling was coined in 1216. In the reign of Charles the Second (1666) a new gold coinage was minted, called Guincas, from the country from which the gold was originally brought. In 1816 (150 years after) the guinea was superseded by a new coin, called the sovereign, which represents the pound sterling. The guinea (old coinage) weighs 1293gr., standard. The sovereign (new coinage) weighs 123gr., standard. The standard legal fineness of gold in England is The standard of silver is 11oz. 2dwt. == 1000 The sovereign contains precisely 1135gr. of pure gold.

9163

22 carats, or 1000.

900

912

The coinage of the United States is regulated by Congress. By the last act of Congress, January 18, 1837, the standard for both gold and silver was fixed at 1000, that is, suppose any of our gold or silver coin to be divided into 1000 equal parts, 900 of those parts are pure gold or silver, and 100 parts are alloy.

By this act the eagle weighs 258gr. Troy, standard.

Containing,
And

232.2gr. pure gold,
25.8gr. alloy.

Our gold coinage, then, is 213 carats fine; our silver coinage is 10oz. 16dwt. fine, 6dwt. short of sterling fineness, which is 11oz. 2dwt. The American dollar weighs 4124gr., standard, containing 3714gr. pure silver, and 414gr. alloy. The alloy in our gold coins is mostly silver, and in our silver coin it is copper.

2295

The ratio of gold to silver in our coinage is 153322 to 1,- that is, whatever an ounce of silver may be worth, an ounce of gold is worth 153322 times as much.

3520000

The pound sterling under the above act, as represented by the sovereign of legal weight and fineness, is 723303 exactly, $4.866+, which is the real gold par with London.

=

TO REDUCE STERLING MONEY TO UNITED STATES

RULE.

MONEY.

·Express the shillings, pence, and farthings decimally; then multiply sterling by 723303, 3520000, and the product will be dollars, &c.

NOTE. - This rule supposes the sovereign, which represents the pound sterling, to be fine, and to contain 1135gr. of pure gold. But the sovereign falls a little short of its legal weight and fineness. So that its

real value in our currency does not vary essentially from $4.84. This is the value assigned to it by act of Congress, in calculating ad valorem duties in our custom-houses on goods imported from England, which are invoiced in sterling money. Therefore, multiply sterling by $4.84 and we shall have the custom-house and market par value of sovereigns or pounds sterling.

N. B.- $4.444 never represented the true value of the pound sterling in the United States currency.

Under the act of Congress of the 2d of April, 1792, establishing the mint and regulating the coins of the United States, the value of the pound sterling was $4.56+

By the act of Congress of the 28th of June, 1834, called the Gold Bill, the value of the pound or sovereign was $4.871. By the act of Congress of the 18th of January, 1837, supplementary to the act of 1834, the value of the pound sterling becomes $723303 +$4.86423303. Sovereigns are usually valued at $4.85 at the banks.

3520000

=

SECTION XXX.

INFINITE OR CIRCULATING DECIMALS.*

DEFINITIONS.

1. DECIMALS produced from Vulgar Fractions, whose denominators do not measure their numerators, and distinguished by the continual repetition of the same figure or figures, are called infinite or circulating decimals.

2. The circulating figures, that is, those that are continually repeated, are called repetends. If only the same figure is repeated, it is called a single repetend, as .11111 or .5555, and is expressed by writing the figure repeated with a point over it. Thus .11111 is denoted by .1, and .5555 by .5.

3. If the same figures circulate alternately, it is called a compound repetend, as .475475475, and is distinguished by putting a point over the first and last repeating figures; thus, .475475475 is written .475.

4. When other figures arise before those which circulate, it is called a mixed repetend; as .1246, or .17835.

5. Similar repetends begin at the same place; as .3 and .¤; or 5.123 and 3.478.

* Infinite or circulating decimals being less important for use than many other rules, and somewhat difficult in their operation, the student can omit them until he reviews the Arithmetic.

6. Dissimilar repetends begin at different places; as .986 and .4625.

7. Conterminous repetends end at the same place; as .631 and .465.

8. Similar and conterminous repetends begin and end at the same place; as .1728 and .4987.

REDUCTION OF CIRCULATING DECIMALS.

CASE I.

To reduce a simple repetend to its equivalent vulgar fraction. If a unit with ciphers annexed to it be divided by 9 ad infinitum, the quotient will be one continually; that is, if be reduced to a decimal, it will produce the circulate .1; and since .1 is the decimal equivalent to §,.2 will be equivalent to , .3 to 8, and so on, till .9 is equal to or 1. Therefore every single repetend is equal to a vulgar fraction, whose numerator is the repeating figure, and denominator 9. Again,, or, being reduced to decimals, makes .01010101, and .001001001 ad infinitum,=.01 and .001; that is, = .01, and = .001; consequently.02, and = .002; and, as the same will hold universally, we deduce the following

RULE. - Make the given decimal the numerator, and let the denominator be a number consisting of as many nines as there are recurring places in the repetend.

If there be integral figures in the circulate, as many ciphers must be annexed to the numerator as the highest place of the repetend is distant from the decimal point.

EXAMPLES.

1. Required the least vulgar fraction equal to .6 and .123.

2. Reduce .3 to its equivalent vulgar fraction.
3. Reduce 1.62 to its equivalent vulgar fraction.

Ans.

Ans..

Ans. 144.

4. Reduce .769230 to its equivalent vulgar fraction.

CASE II.

Ans. 1.

To reduce a mixed repetend to its equivalent vulgar fraction.