The dollar is considered to be the unit money, and all denominations below are decimal parts of a dollar. Thus, 1 dime is .1, or of a dollar, 1 cent .01, or of a dollar, and 1 mill, .100 or rob of a dollar. The place next to dollars on the left hand, is eagles. Any number of dollars, as 475, may either be read 475 dollars, or 47 eagles, 5 dollars; and the decimal parts of a dollar, as .865 may be read 8 dimes, 6 cents, 5 mills, or 86 cents, 5 mills, or 865 mills. Hence a sum expressed in Federal Money, is a mixed number in Decimal Fractions, and may be managed as such. Thus 25 eagles, 8 dollars, 4 dimes, 6 cents and 3 mills are written 2 5 8. 6 3 or The usual way of reading sums in Federal Money is by naming only three of the denominations, namely, dollars, cents and mills. In this way, the above snm would be read 258 dollars, 46 cents,. and 3 mills. The real coins in Federal Money are two of gold, the Eagle and half eagle, four of silver, the dollar, half dollar, double dime, and dime, and two of copper, the cent and half cent. The mill is only imaginary, there being no piece of money of that denomination. Addition, Subtraction, Multiplication and Division of Federal Money, are performed by the rules already given for Addition, Subtraction, Multiplication and Division in Decimal Fractions, and to these the scholar is referred. To reduce New-England, &c. and New-York, &c. currencies to Federal Money.* RULE.-If there be shillings, pence and farthings in the given sum, reduce them to the decimal of a pound by inspection, (see Case III. Reduction of Decimals,) and place it at the right hand of the pounds. Divide the given sum thus prepared, by .3, if New-England, and by 4 if New-York currency, and the quotient, pointed according to the rule for the division of decimals, will be the answer in dollars, and the decimal of a dollar. If pounds only be given, annex ciphers in the place of the decimal, and proceed as above directed. * Virginia and Kentucky currency is the same as New-England; that of North-Carolina and Ohio, the same as New-York. There The reason of this rule will be obvious by considering that in N.E. currency, 6s. or of a pound, are equal to $1, and, or 3 of a pound; and that in N.Y. currency, 8s. or of a pound=1 dollar, and, or .4 of a pound. Hence, in the former case, there are evidently as many dollars in the pounds, as there are, and in the latter, as many as there are. fore, dividing the pounds by 3 in one case, and .4 in the other, and pointing according to the rule for the division of decimals, the quotient is evidently dollars and the decimal of a dollar.-If, after reducing the shillings, &c. to the decimal of a pound by inspection, the separatrix be removed one place to the right hand, the sum will be 2 shilling pieces and the decimal of a 2s. piece, and this divided by 3 and 4, as whole numbers will evidently give dollars and decimals of dollars in the two cases, because in the former, 3 two shillings, and in the latter, 4, are equal to a dollar. Case II. To reduce Federal Money to New-England, &c. to New-York, &c. currencies. RULE.-Multiply the given sum by .3 for New England currency, and by .4 for New-York currency, and the product, pointed according to the rule for the multiplication of decimals, will be pounds and the decimals of a pound. Then find the value of the decimal by inspection. (See Reduction of Decimals, Case V.) To reduce Pennsylvania, New-Jersey, Delaware and Maryland currency to Federal Money. RULE.t-Reduce the given sum to pence, and if there are farthings, for 1 qr. place 2 at the right hand of the pence; for 2 qrs. write 5, and for 3, write 7; but if there are no farthings, annex a cipher to the pence. Divide this sum by 9, and add the quotient to the dividend. From the sum point off three figures for cents and mills; those on the left hand will be dollars. *As this rule is the converse of the preceding, the truth of it must be sufficiently obvious from what has already been said. † A dollar in Pennsylvania, &c. currency, is 7s. 6d. 90d. which, increased by one ninth of itself, is 100 to the number of cents in a dollar. Hence the reason of the rule is obvious. To reduce Federal Money to Pennsylvania, &c. currency. Rule. If there be no mills in the given sum, reduce it to mills by annex. ing ciphers; from the sum subtract one tenth of itself, and the re mainder, excepting the right hand figure, will be pence, which must be reduced to pounds. If the figure cut off from the right hand be 2, call it 1qr. if 5, 2qrs. and if 7, 3qrs. If there be shillings, pence and farthings in the given sum, reduce *Here the shillings, pence, &c. are reduced to the decimal of a pound, and the whole multiplied by 4, because £1-4 dollars; a dollar in that currency being equal to 5 shillings. The currency of Nova Scotia is the same as Canada. |