far. 4 48 960 d. 1 12 240 8. 1 20 1 NOTE 1. The symbol £. stands for the Latin word libra, signifying a pound; s. for solidus, a shilling; d. for denarius, a penny; gr. for quadrans, a quarter. NOTE 2.- Farthings are sometimes expressed in a fraction of a penny; thus, 1 far. =* d.; 2 far. = d.; 3 far. = d. NOTE 3. - The term sterling is probably from Easterling, the popular name of certain early German traders in England, whose money was noted for the purity of its quality. NOTE 4. — The English coins consist of the five-sovereign piece, the double-sovereign, the sovereign, and the half-sovereign, made of gold; the crown, the half-crown, florin, the shilling, the six-pence, the four-pence, the three-pence, the two-pence, the one-and-a-half-pence, and the penny, made of silver ; the penny, the half-penny, the farthing, and the half-farthing, made of copper. The sovereign represents the pound sterling, whose legal value in United States money is $4.84 ; and the florin represents one-tenth of the pound. The value of the English guinea is 21 shillings sterling. The guinea, the five-guinea, the half-guinea, the quarter-guinea, and the seven-shilling piece, are no longer coined. The English gold coins are now made of 11 parts of pure gold, and 1 part of copper, or some other alloy; and the silver coin, of 37 parts of pure sil. ver, and three parts of copper. The present standard weight of the sovereign is 12347} grains Troy; the crown, 43611 grains; the copper penny, 2913 grains. 128. To change numbers expressed in one or more denominations to their equivalents in one or more other denominations. OPERATION. Ex. 1. In 48£. 12s. 7d. 2far. how many farthings ? We multiply the 48 by 20, be48£. 1 2 s. 7 d. 2 far. cause 20 shillings make 1 pound, 20 and to this product we add the 12 shillings in the question, and obtain 9 7 2 shillings. 972 shillings. We then multiply 12 by 12, because 12 pence make 1 11 6 7 1 pence. shilling, and to the product we add the 7 pence, and obtain 11671 4 pence. Again, we multiply by 4, Ans. 4 6 6 8 6 farthings. because 4 farthings make 1 penny, and to this product we add the 2 farthings, and obtain 46686 farthings, the answer sought. OPERATION. Ex. 2. In 46686 farthings how many pounds ? We divide by 4, because 4 far4) 4 6 6 8 6 far. things make 1 penny, and the re sult is 11671 pence, and 2 farthings 1 2 ) 11 671 d. 2 far. remaining. We then divide by 12 20 ) 9 7 2 s. 7 d. because 12 pence make 1 shilling, and the result is 972 shillings, and 48 £. 1 2 s. 7 pence remaining. Lastly, we diAns. 48£. 12s. 7d. 2 far. vide by 20, because 20 shillings make i pound, and the result is 48 pounds, and 12 shillings remaining. By annexing to the last quotient the several remainders, we obtain 48£. 12s. 7d. 2far. as the required result. From these illustrations, for the two kinds of reduction, we deduce the following RULE. — For REDUCTION DESCENDING. Multiply the highest denomination given by the number of units required of the next lower denomination to make one in the denomination multiplied. To this product add the corresponding denomination of the multiplicand, if there be any. Proceed in this way, till the reduction is brought to the denomination required. FOR REDUCTION ASCENDING. Divide the lower denomination iven by the number of units required of that denomination to make one of the next higher. The quotient thus obtained divide in like manner, and so proceed until it is brought to the denomination required. The last quotient, with the several remainders, if there be any, annexed, will be the answer. EXAMPLES. 3. In 127£. 15s. 8d. how many farthings ? ? AVOIRDUPOIS WEIGHT. 129. Avoirdupois or Commercial Weight is used in weighing almost every kind of goods, and all metals except gold and silver. NOTE 1. — The oz. stands for onza, the Spanish for ounce, and in cwt. the c stands for centum, the Latin for one hundred, and wt for weight. NOTE 2. — The laws of most of the States, and common practice at the present time, make 25 pounds a quarter, as given in thc table. But formerly, 28 pounds were allowed to make a quarter, 112 pounds a hundred, and 2240 pounds a ton, as is still the standard of the United States government in collecting duties at the custom-houses. Note 3. — The term avoirdupois is from the French avoir du poid, signifying to have weight. NOTE 4. — - The standard avoirdupois pound of the United States is the weight, taken in the air, of 2770066 cubic inches of distilled water, at its maximum density, or when at a temperature of 3918. degrees Fahrenheit, the barometer being at 30 inches. It is the same as the Imperial poand avoirdupois of Great Britain, which is the weight of 2716166 cubic inches of distilled water at the temperature of 62 degrees. EXAMPLES. 1. In 165T. 13cwt. 3qr. 191b. 14oz. how many ounces? 2. In 5302318 ounces how many tons ? 3. If a load of hay weigh 3T. 16cwt. 2qr. 181b., required the weight in ounces. 4. In 122688 ounces how many tons ? 5. Required the number of drams in 2T. 17cwt. 3qr. 161b. 15oz. 13dr. 6. In 1482749 drams how many tons ? 7. What is the value of 7T. 17cwt. at 7 cents per pound? Ans. $ 1099.00. 8. What will 19cwt. 3qr. 201b. of sugar cost at 9 cents per pound? Ans. $ 179.55. TROY OR MINT WEIGHT. 130. Troy or Mint Weight is the weight used in weighing gold, silver, jewels, and liquors; and in philosophical experiments. TABLE. 24 Grains (gr.) make 1 Pennyweight, pwt. 20 Pennyweights 1 Ounce, 12 Ounces 1 Pound, lb. gr. pwt. 24 1 480 20 1 5760 240 OZ. oz. Ib. 12 Note 1. — Troy weight was introduced into Europe from Cairo in Egypt, in the 12th century, and was first adopted in Troyes, a city in France, where great fairs were held, whence it may have had its name. NOTE 2. A grain or corn of wheat, gathered out of the middle of the ear, was the origin of all the weights used in England. Of these grains, 32, well dried, were to make one pennyweight. But in later times it was thought sufficient to divide the same pennyweight into 24 equal parts, still called grains, being the least weight now in use, from which the rest are computed. NOTE 3. — - Diamonds and other precious stones are weighed by what is called Diamond Weight, of which 16 parts make 1 grain; 4 grains, 1 carat. 1 grain Diamond Weight is equal to 1 grains Troy, and 1 carat to 3} grains Troy. In weighing pearls, the pennyweight is divided into 30 grains instead of 24, so that 1 pearl grain is equal to grains Troy. The carat as a weight must not be confounded with the assay carat, a term whose use is to indicate a proportional part of a weight, as in expressing the fineness of gold, each carat means a twenty-fourth part of the entire mass used. Thus, pure gold is termed 24 carat gold, and gold that is not pure is termed 18 carat gold. 20 carat gold, &c., as its mass may be 18 twenty-fourths, 20 twenty-fourths, &c. pure gold. Each assay carat is subdivided into 4 assay grains, and each assay grain into 4 assay quarters. NOTE 4. — The Troy pound, the standard unit of weight adopted by the United States Mint, is the same as the Imperial Troy pound of Great Britain, and is equal to the weight, taken in the air, of 2276000 cubic inches of distilled water, at its maximum density, the barometer being at 30 inches. EXAMPLES 1. How many grains in 28lb. 11oz. 12pwt. 15gr. Troy? 2. In 166863 grains Troy how many pounds? 3. If a silver pitcher weigh 3lb. 10oz., what is its weight in grains ? 4. How many pounds Troy in 22080 grains ? 5. What is the value of 73lb. lloz. of standard silver at $0.062 per pennyweight ? 6. How many pounds of standard silver can be purchased for $ 1099.88, at the rate of $ 0.062 per pennyweight? 7. A Californian has 571b. 7oz. of pure gold. What is its value at $ 20.593} per ounce ? Ans. $14229.9013. 8. What is the value of a mass of standard gold weighing 191b. Coz. 16pwt. at 93 cents per pennyweight ? Ans. $ 4367.28. 9. I have a lump of pure silver weighing 131b. 9oz. What is its value at $ 1.385 70 per ounce ? Ans. $ 228.6404. APOTHECARIES' WEIGHT. 131. Apothecaries' Weight is used in mixing medical prescriptions. TABLE. 20 Grains (gr.) make 1 Scruple, sc. or Ə. 3 Scruples 1 Dram, dr. or 3. 8 Drams 1 Ounce, oz. or 3. 12 Ounces 1 Pound, Ib. or Ib. gr. 20 1 dr. 60 1 480 24 1 Ib. 5760 288 1 60. OZ. = Note 1. — In this weight the pound, ounce, and grain are the same as in Troy Weight. NOTE 2. — Medicines are usually bought and sold by Avoirdu pois Weight. NOTE 3. — In estimating the weight of fluids, 45 drops, or a common teaspoonful, make about 1 fluid dram; 2 common table-spoonfuls, about 1 fluid ounce; a wineglassful, about 13 fluid ounces; and a common teacupful, about 4 fluid ounces. EXAMPLES. 1. In 23lb 93 03 23 13gr. how many grains ? |