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(6.) Portland, May 16, 1857. Mr. J. C. Porter,
Bought of Willard & Hale,
17 bbl. Canada Flour,- at $8.25
50 lbs. Duponts Eagle Gunpowder, u .50
140" Sheet Zinc, ".08£
120" Prussian Blue, ".63
Willard & Hale.
(7.) New Fork, July 11, 1856.
Mr. JOHK CUMMINGS,
Bought of Lord & Secomb,
E. T. Lowe,
for Lord & Secomb. 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.
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, pence, and farthings, 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.
127. English or Sterling Money is the currency of England.
Note 1. — The symbol £. stands for the Latin word libra, signifying a pound; s. for sulidus, a shilling; d. for denarius, a penny; qr. for quadrans, a quarter.
Note 2. — Farthings are sometimes expressed in a fraction of a penny; thus, 1 far. = i d.; 2 far. = 4 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 $'4.84; and the florin represents one-tenth of the pound.
The value of the English guinea is 21 shillings sterling. The guinea, the five-guinea, the half-guinea, the quarter-guinea, and the seven-shilling piece, are no longer coined.
The English gold coins are now made of 11 parts of pure gold, and 1 part of copper, or some other alloy; and the silver coin, of 37 parts of pure sil* ver, and three parts of copper.
The present standard weight of the sovereign is 123^^- grains Troy; the crown, 436^ grains; the copper penny, 291$ 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. We multiply the 48 by 20, be
4 8 £. 1 2 s. 7 d. 2 far. cause 20 shillings make 1 pound,
2 0 and to this product we add the 12
—— shillings in the question, and obtain
9 7 2 shillings. n72 shillings. We then multiply
1 2 by 12, because 12 pence make 1
i , (• 7 i shilling, and to the product we add
1 i o / i pence. the 7 pence and obtain n671
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 .
Ex. 2. In 46686 farthings how many pounds?
orERation. We divide by 4, because 4 far
4 ) 4 6 6 8 6 far. things make 1 penny, and the re
n , „ e suit is 11671 pence, and 2 farthings
1 2 ) 1 1 G7 1 d. i tar. remaining. We then divide by 12
2 0) 9 7 2 s. 7 d. because 12 pence make 1 shilling,
and the result is 972 shillings, and
4 8 £. 1 2 s. 7 pence remaining. Lastly, we di
Ans. 48£. 12s. 7d. 2 far. vide *J 20, bemuse 20 shillings
make 1 pound, and the result is 48 pounds, and 12 shillings remaining. By annexing to the last quotient the several remaindei-s, we obtain 48£. 12s. 7d. 2far. as the required result.
From these illustrations, for the two kinds of reduction, we deduce the following
Rule.— Foil 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 (lie 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.
3. In 127£. 15s. 8d. how many farthings?
4. In 122672 farthings how many pounds?
5. How many farthings in 28£. 19s. lid. 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.
129. Avoirdupois or Commercial Weight is used in weighing almost every kind of goods, and all metals except gold and silver.