LEDGER ACCOUNTS. 123. The principal book of accounts among merchants is called a ledger. In it are brought together scattered items of accounts, often making long columns. As a rapid way of finding the amounts, accountants generally add more than one column at a single operation (Art. 48). The examples below may be added both by the usual method and by that which is more rapid. 3. $ 4. 1. $ cts. 2. COMPOUND NUMBERS. 124. A COMPOUND NUMBER is a collection of concrete units of different denominations; as, 5 pounds and 6 ounces; 4 feet and 5 inches. 125. A scale expresses the law of relation between the different units of a number. The different units of simple numbers have a uniform tenfold increase from lower to higher orders, and a like decrease from higher to lower orders. They, therefore, are said to have a uniform scale. In compound numbers, the names of different measuring units (Art. 9) are included in the expression of a single quantity, so that the relation of the units of one order to those of another is that of a varying scale; as in the expression of pounds, shillings, and pence, it is 4, 12, and 20. REDUCTION OF COMPOUND NUMBERS. 126. REDUCTION is the process of changing numbers from one denomination to another, without altering their values. It is of two kinds, Reduction Descending and Reduction Ascending. Reduction Descending is changing numbers of a higher denomination to a lower denomination; as pounds to shillings, &c. It is performed by multiplication. Reduction Ascending is changing numbers of a lower denomination to a higher denomination; as farthings to pence, &c. It is the reverse of Reduction Descending, and is performed by division. ENGLISH MONEY. 127. English or Sterling Money is the currency of Eng NOTE 1. The symbol £. stands for the Latin word libra, signifying a pound; s. for solidus, a shilling; d. for denarius, a penny; qr. for quadrans, a quarter. NOTE 2. thus, 1 far. NOTE 3. Farthings are sometimes expressed in a fraction of a penny; = d.; 2 far. = 1⁄2 d.; 3 far. = 2 d. = 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 doublesovereign, the sovereign, and the half-sovereign, made of gold; the crown, the half-crown, the shilling, the six-pence, the four-pence, the three-pence, the twopence, 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. 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 guinea is so called because the gold of which the first guineas were made was brought from Guinea, in Africa. 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 silver, and 3 parts of copper. The present standard weight of the sovereign is 123111 grains Troy; the crown, 436 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. Ex. 1. In 48£. 12s. 7d. 2far. how many farthings? OPERATION. 972 shillings. We multiply the 48 by 20, be48 £. 12 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 972 shillings. We then multiply by 12, because 12 pence make 1 shilling, and to the product we add the 7 pence, and obtain 11671 pence. Again, we multiply by 4, because 4 farthings make 1 penny, and to this product we add the 2 farthings, and obtain 46686 farthings, the answer sought. 11671 pence. Ans. 4 6 6 8 6 farthings. Ex. 2. In 46686 farthings how many pounds? OPERATION. 4) 4 6 6 8 6 far. We divide by 4, because 4 farthings make 1 penny, and the result is 11671 pence, and 2 farthings remaining. We then divide by 12 because 12 pence make 1 shilling, and the result is 972 shillings, and 7 pence remaining. Lastly, we divide by 20, because 20 shillings make 1 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. 48 £. 12 s. Ans. 48£. 12s. 7d. 2 far. 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 given by the number of units required of that denomination to make one of the next higher. The quotient thus obtained divide as before, 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? 4. In 122672 farthings how many pounds? 5. How many farthings in 28£. 19s. 11d. 3 far. ? 6. How many pounds in 27839 farthings? 7. In 378£. how many pence? 8. In 90720 pence how many pounds? 9. Reduce 967 guineas to pounds. 10. Reduce 1015£. 7s. to guineas. 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 cut. 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 the 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 277015 cubic inches of distilled water, at its maximum density, or when at a temperature of 39,83 degrees Fahrenheit, the barometer being at 30 inches. It is the same as the Imperial pound avoirdupois of Great Britain, which is the weight of 2774 cubic inches of distilled water at the temperature of 62 degrees. 100 10000 EXAMPLES. 1. In 165T. 13cwt. 3qr. 19lb. 14oz. how many ounces? 2. In 5302318 ounces how many tons? 3. If a load of hay weigh 3T. 16cwt. 2qr. 18lb., required the weight in ounces. 4. In 122688 ounces how many tons? 5. Required the number of drams in 2T. 17cwt. 3qr. 16lb. 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. 20lb. of sugar cost at 9 cents per pound? Ans. $179.55. |