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reign, valued at $4,84 ; the French franc, valued at 18 cents 6
mills ; and* the five-franc piece, valued at $0.93.

Although the currency of the United States is in dollars,
cents and mills, yet in some of the States accounts are still
kept in pounds, shillings and pence.

In all the States the shilling is reckoned at 12 pence, the
pound at 20 shillings, and the dollar at 100 cents.

The following table shows the number of shillings in a dol-
lar, the value of 1 in dollars, and the value of $1 in the
fraction of a pound ?



In English currency,


4s. bd. - 1=$4.84 :


, and$l= T .-i- T .


In N. E., Ya , Ky., (


C ^1 &31


, ,


Tenn., j


$ 5,


an * ^TtT-


In N. Y., Ohio, N. [






Carolina-, j


8s. - l=$2 2 ,


and $1 |.


In N. J., Pa., Del., [
Md., )


Ts. &d. - J61=$2|,


and$l= f


In S. Carolina &Ga.


4s. Sd. - l:=$4f,


and $!=.,&.


In Canada & Nova )
Scotia, j


5., - 1=*,


and $!=: l.


368. What arc coins?


V/hat arc they called ?


Wliat is made "



legal tender?



26 tt REDUCTION OF CURRENCIES.



REDUCTION OF CURRENCIES.

270. Reduction of Currencies is changing their denomina-
tions without changing their values.

There are two cases of the Reduction of Currencies :

1st. To change a currency in pounds, shillings and pence,

to United States currency.

2d. To change United States currency to pounds, shillings

and pence.

271. To reduce pounds, shillings and pence to United
States currency.

1. What is the value of <3 12s. Qd., New England cur-
rency, in United States money.

OPERATION.

ANALYSIS. Since l = $3i the 3 12s. Qd.=3.G%5

number of dollars in 3 12s. Gd.= rlnllc in ^1 - 31

3.625, will be equal to 3.625

taken 3^ times : that is, to $12,08 : 1.2084"

hence, 10.875

Ans. $12.083 +

Multiply the amount reduced to pounds and the decimals of
a pound by the number of dollars in a pound, and the product
will be the answer.

272. To reduce United States money to pounds, shillings
and pence.

1. What is the value of $375.81, in pounds, shillings and
pence, New York currency ?

ANALYSIS. Since $!=, the

number of pounds in $375.87 will bo OPERATION.

equal to this number taken times : $375.87 X -? =<150 348

that is, equal to 150.348=150 6s. =^E150 6s Hid

. : hence,



200. What is currency ? How many kinds arc there ? What foreign
coins are most used in this country? What are the denominations of
United States currency ? What denominations are sometimes used in
the States ?

270. What is reduction of currencies ? How many kinds of reduc-
tion arc there ? What arc they ?

271. What is the rule for reducing from pounds, shillings rind pence
to United States money ?



EXCHANGE. 265

Multiply the amount by that fraction of a pound which
denotes the value q/ 1 $1, and the product will be the answer in
pounds and decimals of a pound.

EXAMPLES

1. What is the value of 127 18s. 6d., New England
currency, in United States money ?

2. What is the value of $2863.75 in pounds, shillings and
pence, Pennsylvania currency ?

3. What is the value of 459 3s. Qd., Georgia currency, in
United States money ?

4. What is the value of $973.28 in pounds, shillings and
pence, North Carolina currency ?

5. What is the value in United States money of 637 18s.
8d., Canada currency ?

6. Reduce $102.85 to English money ; to Canada cur-
rency ; to New England currency ; to New York currency ;
to Pennsylvania currency ; to South Carolina currency.

7. Reduce 51 13s. OJtf. English money ; 62 10s. Can-
ada currency ; 75 New England currency ; 100 New
York currency ; 193 15s. Pennsylvania currency ; and 58
6s. 7Jrf. Georgia currency, to United States money.

EXCHANGE.

273. EXCHANGE denotes the payment of a sum of money
by a person residing in one place to a person residing in an-
other. The payment is usually made by means of a bill of
exchange.

A BILL OF EXCHANGE is an order from one person to another
directing the payment to a third person named therein of a
certain sum of money :

1. He who writes the open letter of request is called the
drawer or maker of the bill.

2. The person to whom it is directed is called the draw'ee.



272. What is the rule for reducing from United States money to
pounds, shillings and pence ?

273. What does exchange denote ? How is the payment generally
made ? What is a bill of exchange ? Who is the drawer ? Who the
drawee ? Who the buyer or remitter ?



266 FOREIGN BILLS.

3. The person to whom the money is ordered to be paid is
called the payee ; and

4. Any person who purchases a bill of exchange is called
the buyer or remitter.

274. A bill of exchange is called an inland bill, when the
drawer and drawee both reside in the same country ; and when
they reside in different countries, it is called a foreign bill.

Exchange is said to be at par, when an amount at the
place from which it is remitted will pay an equal amount at
the place to which it is remitted. Exchange is said to be at
a premium, or above par, when the sum to be remitted will
pay less at the place to which it is remitted ; and at a dis-
count, or below par, when it will pay more.

EXAMPLES.

1. A merchant at Chicago wishes to pay a bill in New
York amounting to $3675, and finds that exchange is 1J per
cent premium : what must he pay for his bill?

2. A merchant in Philadelphia wishes to remit to Charles-
ton $8756.50, and finds exchange to be 1 per cent below par ;
what must he pay for the bill ?

3. A merchant in Mobile wishes to pay in New York
$6584, and exchange is 2| per cent premium : how much
must he pay for such a bill '{

4. A merchant in Boston wishes to pay in New Orleans
$4653.75 ; exchange between Boston and New Orleans is 1J
per cent below par : what must he pay for a bill ?

5. A merchant in New York has $3690 which he wishes
to remit to Cincinnati ; the exchange is 1 \ per cent below
par : what will be the amount of his bill ?

FOREIGN BILLS.

275. A Foreign Bill of Exchange is one in which the
drawer and drawee live in different countries.

NOTE. In all Bills of Exchange on England, the sterling is
the unit or base, and is still reckoned at its former value of $4$
= $4.4444 -f, instead of its present value $4.84.

274. When is a bill of exchange said to be inland ? When foreign ?
When is exchange said to be at par ? When at a premium ? When
at a discount ?



FOREIGN BILLS. 267

Hence, 1 =$4.4444 -f

Add 9 per cent, .3999

Gives the present value of 1 $4.8443.

Hence, the true par value of Exchange on England is
9 per cent on the nominal base.

1. A merchant in New York wishes to remit to England
a' bill of Exchange for 125 15s. Qd : how much must he
pay for this bill when exchange is at 9J per cent premium?

125 15s. 6d. ...... =125.775

Add 9| per cent .....

gives amount in 's, at $4f==



NOTE. The pounds and decimals of a pound are reduced to
dollars by multiplying by 40 and dividing by 9 giving, in this
case, $612.105.

RULE. I. Reduce the amount of the bill to pounds and
decimals of a pound, and then add the premium of exchange.

II. Multiply the result by 40 and divide the product by
9 : the quotient will be the answer in United States Money.

2. A merchant shipped 100 bales of cotton to Liverpool,
each weighing 450 pounds. They were sold at *l\d. per
pound, and the freight and charges amounted to 187 10s.
He sold his bill of exchange at 9} per cent premium : how
much should he receive in United States Money ?

3. There were shipped from Norfolk, Ya., to Liverpool,
Sbhhd. of tobacco, each weighing 450 pounds. It was sold
at Liverpool for l^^d. per pound, and the expenses of freight
and commissions were 92 Is. Sd. If exchange in New
York is at a premium of 9J per cent, what should the owner
receive for the bill of exchange, in United States Money ?

276. The unit or base of the French Currency is the French
franc, of the value of 18 cents 6 mills. The franc is divided into
tenths, called decimes, corresponding to our dimes, and into
centimes corresponding to cents. Thus, 5.12 is read, 5 francs
and 12 centimes.

275. What is a foreign bill of exchange ? In bills on England, wh.it
is the unit, or base? What is the exchange value of the sterling ?
How much is the true value above the commercial value of the ster-
ling? How do you find the value of a bill in English currency in
United States mo'ney?



268 DUTIES.

All bills of exchange on France are drawn in francs.
Exchange is quoted in New York at so many francs and
centimes to the dollar.

1. What will be the value of a bill of exchange for 4^36
francs, at 5,25 to the dollar ?

ANALYSIS. Since 1 dollar will buy

5.25 francs, the bill will cost as many OPERATION.

dollars as 5.25 is contained timesin the 5.25)4536($864 Ans
amount of the bill ; hence,

Divide the amount of the bill by the value of$l in francs:
the quotient is the amount to be paid in dollars.

2. What will be the amount to be paid, United States
money, for a bill of exchange on Paris, of 6530 francs,
exchange being 5.14 francs per dollar ?

3. What will be the amount to be paid in United States
money for a bill of exchange on Paris of 10262 francs, ex-
change being 5.09 francs per dollar ?

4. What will be the value in United States money of a
bill for 87595 francs, at 5.16 francs per dollar?

DUTIES.

277. Persons who bring goods or merchandise into the
United States, from foreign countries, are required to land
them at particular places or Ports, called Ports of Entry, and
to pay a certain amount of their value, called a Duty. This
duty is imposed by the General Government, and must be
the same on the same articles of merchandise, in every part
of the United States.

Besides the duties on merchandise, vessels employed in
commerce are required, by law, to pay certain sums for the
privilege of entering the ports. These sums are large or
small, in proportion to the size or tonnage of the vessels.
The moneys arising from duties and tonnage, are called
revenues.

276. What is the unit or base of the French currency ? What is its
value? How is it divided ? In what currency arc French bills of ex-
change drawn ?

277. What is a port of entry? What is a duty? By whom are duties
imposed ? What charges are vessels required to pay ? What are the
moneys arising from duties and tonnage called ?



DUTIES. 269

278. The revenues of the country are under the general
direction of the Secretary of the Treasury, and to secure their
faithful collection, the government has appointed various
officers at each port of entry or place where goods may be
landed.

279. The office established by the government at any port
of entry is called a Custom House, and the officers attached
to it are called Custom House Officers.

280. All duties levied by law on goods imported into the
United States, are collected at the various custom houses, and
are of two kinds, Specific and Ad valorem.

A specific duty is a certain sum on a particular kind of
goods named ; as so much per square yard on cotton or wool-
len cloths, so much per ton weight on iron, or so much per
gallon on molasses.

An ad valorem duty is such a per cent on the actual cost
of the goods in the country from which they are imported.
Thus, an ad valorem duty of 15 per cent on English cloth, is
a duty of 15 per cent on the cost of cloths imported from Eng-
land.

281. The laws of Congress provide, that the cargoes of all
vessels freighted with foreign goods or merchandise shall be
weighed or gauged by the custom house officers at the port to
which they are consigned. As duties are only to be paid on
the articles, and not on the boxes, casks and bags which con-
tain them, certain deductions are made from the weights and
measures, called Allowances.

Gross Weight is the whole weight of the goods, together
with that of the hogshead, barrel, box, bag, &c., which con-
tains them.

L ; __^____

278. Under whose direction are the revenues of the country ?

279. What is a custom house ? What are the officers attached to it
called ?

280. Where are the duties collected ? How many kinds are there,
and what are they called ? What is a specific duty ? An ad valorem
duty ?

281. What do the laws of Congress direct in relation to foreign
goods? Why are deductions made from their weight? What are
these deductions called ? What is gross weight ? What is draft ?
What is the greatest draft allowed ? ' What is tare ? What arc the
different kinds of tare ? What allowances are made on liquors ?



270 DUTIES.

Draft is an allowance from the gross weight on account of
waste, where there is not actual tare.

On 112/6. it is 1/6.

From 112 to 224 < 2,

224 to 336 ' 3,

336 to 1120 ' 4,

1120 to 2016 ' 7,

Above 2016 any weight ' 9 ;
consequently, 9/6. is the greatest draft allowed.

Tare is an allowance made for the weight of the boxes,
barrels, or bags containing the commodity, and is of three
kinds : 1st, Legal tare, or such as is established by law ; 2d,
Customary tare, or such as is established by the custom among
merchants ; and 3c?, Actual tare, or such as is found by re-
moving the goods and actually weighing the boxes or casks
in which they are contained.

On liquors in casks, customary tare is sometimes allowed
on the supposition that the cask is not full, or what is called
its actual wants; and then an allowance of 5 per cent for
leakage.

A tare of 10 per cent is allowed on porter, ale and beer, in
bottles, on account of breakage, and 5 per cent on all other
liquors in bottles. At the custom house, bottles of the com-
mon size are estimated to contain 2J gallons the dozen.

NOTE. For table8 of Tare and Duty, see Ogden on the Tariff
of 1842.

EXAMPLES.

1. What will be the duty on 125 cartons of ribbons, each
containing 48 pieces, and each piece weighing 802. net, and
paying a duty of $2.50 per pound ?

2. What will be the duty on 225 bags of coffee, each weigh-
ing: gross 160/6., invoiced at 6 cents per pound ; 2 per cent
being the legal rate of tare, and 20 per cent the duty ?

3. What duty must be paid on 275 dozen bottles of claret,
estimated to contain 2J gallons per dozen, 5 per cent beinar
allowed for breakage, and the duty being 35 cents per gallon?

4. A merchant/ imports 175 cases of indigo, each case
weighing 196/fo?. gross ; 15 per cent is the customary rate of
tare, and the duty 5 cents per pound : what duty must he
pay on the whole ?



ALLIGATION MEDIAL. 271



ALLIGATION MEDIAL.

282. ALLIGATION MEDIAL is the process of finding the
price of a mixture when the quantity of each simple and its
price are known.

1. A merchant mixes Sib. of tea, worth 75 cents a pound,
with 16/6. worth $1.02 a pound : what is the price of the
mixture per pound ?

ANALYSIS. The quantity, 8lb. of OPERATION.

tea, at 75 cents a pound, costs $6 ; 8/6. at 75cte.=$ 6 00

and 16. at $1.03 costs $16.32 : 16/6 at $1 Q2 = $16.32

hence, the mixture, = 24lb,, costs \ .

$22.32 ; and the price of lib. of the 24 24)22.32

mixture is found by dividing this $0 93
cost by 24 : hence, to find the price of the mixture,

I. Find the cost of the entire mixture :

II. Divide the entire cost of the mixture by the sum of
the simples, and the quotient will be the price of the mixture.

EXAMPLES.

1. A farmer mixes 30 bushels of wheat worth 5s. per
bushel, with 72 bushels of rye at 3s. per bushel, and with
60 bushels of barley worth 2s. per bushel : what should be
the price of a bushel of the mixture ?

2. A wine merchant mixes 15 gallons of wine at $1 per
gallon with 25 gallons of brandy worth 75 ceuts per gallon :
what should be the price of a gallon of the compound ?

3. A grocer mixes 40 gallons of whisky worth 31 cents
per gallon with 3 gallons of water which costs nothing : what
should be the price of a gallon of the mixture ?

4. A goldsmith melts together 2/6. of gold of 22 carats
fine, 602:. of 20 carats fine, and 6oz. of 16 carats fine : what
is the fineness of the mixture ?

5. On a certain day the mercury in the thermometer was
observed to average the following heights : from 6 in the
morning to 9, 64 ; from 9 to 12, 74 ; from 12 to 3, 84 ;
and from 3 to 6, 70 : what was the mean temperature of
the day ?

282. What is Alligation Medial ? What is the rule for determining
the price of the mixture ?



272



ALLIGATION ALTERNATE.



ALLIGATION ALTERNATE.

283. ALLIGATION ALTERNATE is the process of finding what
proportions must be taken of each of several simples, whose
prices are known, to form a compound of a given price. It
is the opposite of Alligation Medial, and may be proved by it.

284. To find the proportional parfe.

1. A farmer would mix oats at 3s. a bushel, rye at 6s., and
wheat at 9s. a bushel, so that the mixture shall be worth 5
shillings a bushel : what proportion must be taken of each
sort?



OPERATION,



oats, 3



5 -j rye,



wheat, 9



A.



B.



c.


D.


E.


2


1


3




2


2


1




1



ANALYSIS. On every bushel put into the mixture, whose price
is less than the mean price, there will be a gain ; on every bushel
whose price is greater than the mean price, there will be a loss ;
and since there is to be neither gain nor loss by the mixture, the
gains and losses must balance each other.

A bushel of oats, when put into the mixture, will bring 5 shil-
lings, giving a gain of 2 shillings ; and to gain 1 shilling, we must
take half as much, or \ a bushel, which we write in column A.

On 1 bushel of wheat there will be a loss of 4 shillings ; and
to make a loss of 1 shilling, we must take of a bushel, which
we also write in column A : i and are called proportional
numbers.

Again : comparing the oats and rye, there is a gain of 2 shil-
lings on every bushel of oats, and a loss of 1 shilling on every
bushel of rye : to gain 1 shilling on the oats, we take \ a bushel,
and to lose 1 shilling on the rye, we take 1 bushel : these num-
bers are written in column B. Two simples, thus compared, are
called a couplet : in one, the price of unity is less tJian the mean
price, and in the other it is greater.

If, every time we take i a bushel of oats we take ^ of a bushel
of wheat, the gain and loss will balance ; and if every time we
take ^ a bushel of oats we take 1 bushel of rye, the gain and loss



283. What is Alligation Alternate ?

J284. How do you lind the proportional numbers/*



ALLIGATION ALTERNATE.



273



will balance : hence, if tTie proportional numbers of a couplet be
multiplied by any number, the gain and loss denoted by the products,
will balance.

When the proportional numbers, in any column, are fractional
(as in columns A and B), multiply them by the least common
multiple of their denominators, and write the products in new
columns C and D. Then, add the numbers in columns C and D,
standing opposite each simple, and if their sums have a common
factor, reject it : the last result Will be the proportional numbers.

RULE. I. Write the prices or qualities of the simples in a
column, beginning with the lowest, and the mean price or
quality at the left.

II. Opposite the first simple write the part which must be
taken to gain 1 of the mean price, and opposite the other simple
of the couplet, write the part which must be taken to lose 1 of
the mean price, and do the same for each simple.

III, W hen the proportional numbers are fractional, reduce
them to integral numbers, and then add those which stand oppo-
site the same single: if the sums have a common factor, reject
it : the result will denote the proportional parts.

2. A merchant would mix wines worth 16s., 18s., and 22s.
per gallon, in such a way, that the mixture may be worth
20s. per gallon : what are the proportional parts ?



OPERATION. .




A.


B.


C.


D.


E.


(161

204l8 J
(22




1
1


1

i


1


1
1


1
1
3


PROOF.


1 gallon, at 16 shillings, == 16s.
1 gallon, at 18 shillings, = 18s.
3 gallon, at 22 shillings, = 66s.



5) 100 (2 Os., mean price.

N'OTE. The answers to the last, and to all similar questions,
will be infinite in number, for two reasons:

1st. If the proportional numbers in column E be multiplied by
any number, integral or fractional, the products will denote pro-
portional parts of the simples.

2d. If the proportional numbers of any couplet be multiplied by
18



274: ALLIGATION ALTERNATE.

any number, the gain and loss in that couplet will still balance,
and the proportional numbers in the final result will be changed.

3. What proportions of tea, at 24 cents, 30 cents, 33 cents
and 36 cents a pound, must be mixed together so that the
mixture shall be worth 32 cents a pound ?

4. What proportions of coffee at IQcts., 20cts. and 28cfe.
per pound, must be mixed together so that the compound
shall be worth 24ds. per pound ?

5. A goldsmith has gold of 16, of 18, of 23, and of 24 carats
fine : what part must be taken of each so that the mixture
shall be 21 carats fine?

6. What portion of brandy, at 14s. per gallon, of old Ma-
deira, at 24s per gallon, of new Madeira, at 21s. per gallon,
and of brandy, at 10s. per gallon, must be mixed together so
that the mixture shall be worth 18s. per gallon ?

285. When the quantity of one simple is given :

I. How much wheat, at 9s. a bushel, must be mixed with
20 bushels of oats worth 3 shillings a bushel, that the mix-
ture may be worth 5 shillings a bushel ?

ANALYSIS. Find the proportional numbers : they are 2 and 1 ;
hence, the ratio of the oats to the wheat is \ : therefore, there,
must be 10 bushels of wheat.

RULE. I. Find the proportional numbers, and write the
given single opposite its proportional number.

II. Multiply the given simple by the ratio which its propor-
tional number bears to each of the others, and the products
will denote the quantities to be taken of each.

EXAMPLES.

1. How much wine, at 5s., at 5s. Gd., and 6s. per gallon
must be mixed with 4 gallons, at 4s. per gallon, so that the
mixture shall be worth 5s. 4d. per gallon ?

2. A fanner would mix 14 bushels of wheat, at $1,20 per
bushel, with rye at 72c/s., barley at 48cs., and oats at 36c/s. :
how much must be taken of each sort to make the mixture
worth 64 cents per bushel ?

3. There is a mixture made of wheat at 4s. per bushel,
rye at 3s., barley at 2s., with 12 bushels of oats at l&d. per
bushel : how much is taken of each sort when the mixture is
worth 3s. Qd. ?



ALLIGATION ALTERNATE. 275

4. A distiller would mix 40^ro/. of French brandy at 12s.
per gallon, with English at Is. and spirits at 4s. per gallon :
what quantity must be taken of each sort that the mixture
may be afforded at 8s. per gallon ?

286. When the quantity of the mixture is given.

1. A merchant would make up a cask of wine containing
50 gallons, with wine worth 16s., 18s. and 22s. a gallon, in
such a way that the mixture may be worth 20s. a gallon :
much must he take of each sort ?



ANALYSIS. This is the same as example 2, except that the
quantity of the mixture is given. If the quantity of the mixture
be divided by 5, the sum of the proportional parts, the quotient
10 will show how many times each pwportional part must be taken
to make up 50 gallons : hence, there are 10 gallons of the first,
10 of the second, and 30 of the third : hence,

RULE. I. Find the proportional parts.

II. Divide the quantity of the mixture by the sum of the
proportional parts, and the quotient will denote how many
times each part is to be taken. Multiply this quotient by
the parts separately, and each product will denote the quan-
tity of the corresponding simple.

EXAMPLES.

1. A grocer has four sorts of sugar, worth 12c?., Wd., 6d
and 4:d. per pound ; he would make a mixture of 144 pounds
worth Sd. per pound : what quantity must be taken of each
sort?

2. A grocer having four sorts of tea, worth 5s., 6s., 8s. and
9s. per pound, wishes a mixture of 87 pounds worth 7s, per
pound : how much must he take of each sort ?

3. A silversmith has four sorts of gold, viz., of 24 carats
fine, of 22 carats fine, and of 20 carats fine, and of 15 carats fine :
he would make a mixture of 42oz. of 17 carats fine ; how
much must be taken of each sort ?

PROOF. All the examples of Alligation Medial may be
found by Alligation Alternate.

285. How do you find the quantity of each simple when the quantity
of one simple is known ?

386. How do you find the quantity of each simple when the quantity
of each mixture is known ?



276 INVOLUTION.

INVOLUTION.

287. A POWER is the product of equal factors. The equal
factor is called the root of the power.

The first power is the equal factor itself, or the root :
The second power is the product of the root by itself :


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Online LibraryCharles DaviesSchool arithmetic. Analytical and practical → online text (page 19 of 24)