and farthings possess the second and third places; observing to increase the second place by 5, if the shillings be odd; and the third place by }, when the farthings exceed 12; and by 2, when they exceed 36. EXAMPLES. 1. Find the decimal of 15s. 8^d. by inspection. 2. Find by inspection the decimal expression of 16s. 4£d. and 13s. 10|d. Ans. 819 and '694. 3. Value the following sums by inspection, and find their total, viz. 19s. ll^d. + 6s. 2d. + 42s. 8d. + Is. 10id. + |d.+ 11d. Ans. 2'042 the total. CASE IV. To find the value of any given decimal in terms of the integer. RULE. 1. Multiply the decimal by the number of parts in the next less denomination, and cut off as many places for a re and consequently take the place of lOths in the decimal; but when they are odd, their half will always consist of two figures, the first of which will be half the even number, next less, and the second a 5; and this confirms the rule as far as it respects shillings. Again, farthings are so many 960tHs of a pound; and had it happened, that 1000, instead of 960, had made a pound, it is plain any number of farthings would have made so many thousandths, and might have taken their place in the decimal accordingly. But 960, increased by part of itself, is=1000; consequently any number of farthings, increased by their part, will be an exact decimal expression for them. Whence} if th# mainder on the right as there are places in the given decimal. 2. Multiply the remainder by the parts in the next inferior denomination, and cut off for a remainder as before. 3. Proceed in this manner through all the parts of the integer, and the several denominations, standing on the left, make the answer. EXAMPLES. f. Find the value of 37623 of a pound. 20 7-52460 6'29520 1'18080 Ans. 7s. 6d. 2. What is the value of r625 of a shilling? 3. What is the value of '83229161.?* Ans. ? d. Ans. 16s. 7±d. 4. What is the value of '6725cwt.? Ans. 2qrs. 19lb. 5oz. 5. What is the value of r67 of a league? Ans. 2mls. 3pls. 1yd. 3in. lb. c. 6. What is the value of '61 of a tun of wine? Ans. 2hhd. 27gal. 2qt. lpt. 7. What is the value of 461 of a chaldron of coals? Ans. 16bu. 2pe. 8. What is the value of '42857 of a month? Ans. lw. 4d. 23h. 59' 56". CASE V. To find the value of any decimal of a pound by inspection. RULE. Double the first figure or place of tenths for shillings, and if the second be 5 or more than 5 reckon another shilnumber of farthings be more than 12, a part is greater than , and therefore 1 must be added; and when the number of farthings is more than 37, a part is greater than 1|, for which 2 must be added; and thus the rule is shown t» be right, ling; then call the figures in the second and third places, af ter 5, if contained, is deducted, so many farthings; abating 1, when they are above twelve; and 2, when above 36; and the result is the answer. EXAMPLES. 1. Find the value of '785\. by inspection. Is. for 5 in the place of tenths. for the excess of 12, abated. 15s. 84d. the answer. 2. Find the value of 8751. by inspection. Ans. 17s. 6d. 3. Value the following decimals by inspection, and find their sum, viz. 927l. + 3511. + 203l. + 0611. + '021. + 0091. Ans. 11. lis. 51d. FEDERAL MONEY.* The denominations of Federal Money, as determined by an Act of Congress, Aug. 8, 1786, are in a decimal ratio; and therefore may be properly introduced in this place. * The coins of federal money are two of gold, four of silver, and two of copper. The gold coins are called an eagle and halfeagle; the silver, a dollar, half-dollar, double dime, and dime; and the copper, a cent and half-cent. The standard for gold and silver is eleven parts fine and one part alloy. The weight of fine gold in the eagle is 246'268 grains; of fine silver in the dojlar, 375 64 grains; of copper in 100 cents, 2ilb. avoirdupois, The fine gold in the half-eagle is half the weight of that in the eagle; the fine silver in the half-dollar, half the weight of that in the dollar, &c. The denominations less than a dollar are expressive of their values: thus, mill is an abbreviation of mille, a thousand, for 1000 mills are equal to 1 dollar; cent, of centum, a hun A mill, which is the lowest money of account, is 001 o£ & dollar, which is the money unit. A number of dollars, as 754, may be read 754 dollars, or 75 eagles, 4 dollars; and decimal parts of a dollar, as 365, dred, for 100 cents are equal to 1 dollar; a dime is the French of tithe, the tenth part, for 10 dimes are equal to 1 dollar. The mint-price of uncoined gold, 11 parts being fine and 1 part alloy, is 209 dollars, 7 dimes, and 7 cents per lb. Troy weight; and the mint-price of uncoined silver, 11 parts being fine and part alloy, is 9 dollars, 9 dimes, and 2 cents, per lb. Troy. In Mr. Pike's "Complete System of Arithmetic," may be seen "Rules for reducing the Federal Coin, and the Currencies of the several United States; also English, Irish, Canada, Nova-Scotia, Livres Tournois, and Spanish milled dollars, each to the par of all the others." It may pe sufficient here to observe respecting the currencies of the several States, that a dollar is equal to 6s. in New-England and Virginia; 8s. in New-York and North-CaVolina; 7s. 6d. in New-Jersey, Pennsylvania, Delaware, and Maryland; and 4s. 8d. in South-Carolina and Georgia. The English standard for gold is 22 carats of fine gold, and 2 carats of copper, which is the same as 11 parts fine and 1 part alloy. The English standard for silver is 18oz. 2dwt. of fine silver, and 18dwt. of copper; so that the proportion of alloy in their silver is less than in their gold. When either gold or siK Ver is finer or coarser than standard, the variation from standard is estimated by carats and grains of a carat in gold, and by penny-weights in silver. Alloy is used in gold and silver to harden them. NOTE. Carat is not any certain weight or quantity, but Of any weight or quantity; and the minters and goldsmiths divide Jt into 4 equal parts, called grains of a carat. may be read 3 dimes, 6 cents, 5 mills, or 36 cents) 5 mills, or 365 mills; and others in a similar manner. Addition^ subtraction, multiplication, and division of federal money are performed just as in decimal fractions; and consequently with more ease than in any other kind of money. EXAMPLES. 1. Add 2 dollars, 4 dimes, 6 cents, 4D. 2d., 4d. 9c., IE. 3D. 5c. 7m., 3c. 9m., ID. 2d. 8c. lm,, and 2E. 4D. 7d. 8c. 2m. together. (2) (3) E. D. d. c. m. E. D. d. c. m. 畫畫 3 2 1 . 039 281 6 1 782 7 8 9 6 34 1 03 70 308 17 8 231 7. Multiply 3D. 4d. 5c. lm. by ID. 2d. 3c. 2m. |