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NOTE.-If it is required to make one which is 2, 3, 4, 5 or 6, &c. time less than the given one: divide the cube of the given side by the number mentioned in the question, and extract the root of the quotient; the root is the answer sought.

Examples.

1. There is a box that is 3 feet high, 3 feet long, and 3 feet wide; I demand the side of another which shall contain 4 times the quantity.

feet.

3X8X327X41084·7 nearly Ans.

2. There is a box that is 4 feet wide, 4 feet high and 4 feet long; I demand the side of another that shall contain of the quantity.

Ans, 2 ft.

PROBLEM III.

To find the side of a cubical box that shall contain a quan. tity equal to any given solidity.

RULE. The cube root of the given solidity is the side of a box that will contain the same quantity.

Examples.

1. There is a cylindrical cistern that contains 3204 solid inches; I demand the side of a cubical box, that shall contain the same quantity.

3/3204 = 1-4-74 in. Ans.

2. The side of a cubical cistern, that shall hold just as much liquor as a cask whose solid content is 255.19.1.196 inches, is required.

3/25519 1196 =

29.44† in. Ans,

REDUCTION OF COINS.

Under this head it may be thought necessary to say something relative to the former currency of the Unit ed States, before the FEDERAL CURRENCY was adopted.

In all the states, accompts were kept in pounds, shillings, pence, and farthings; but the value of these sevcral denominations were different, in different states.

They all reckoned, 4 farthings to 1 penny, 12 pence to 1 shilling, 20 shillings to 1 pound.

For the benefit of those who may have retained the former method of keeping accompts, and wish to know the value of the same in Federal Money, the following rules are inserted,

The former currency of New-Hampshire, Vermont, Mas-
sachusetts, Connecticut, and Rhode Island reduced
to dollars, cents, &c.

When the sum to be reduced is pounds only. RULE-Annex a cypher to the pounds, divide by 3, the quotient is dollars; if there is a remainder, annex three cyphers, continue dividing, the quotient will be dimes, cents, and mills; 6 shillings is equal to, of 2o.

Examples.

1. It is required to reduce 621 pounds, into dollars, 62103 $2070 Ans.

&c.

2. It is required to reduce 6.19 into dollars, dimes, cents and mills. 6.190.000 ÷ 3 = :863:333+ Ans. 3. It is required to reduce £.121 to dols. dimes cents, &c. Ans. $403.333t. 4. It is required to reduce £.16 to dols. dimes, cents, Ans. $53.333t.

&c.

When the sum to be reduced consists of pounds, shillings, pence and farthings.

RULE. To the pounds annex half the number of shillings, and 2 cyphers in decimals, if the shillings are even; if they are odd, annex the greatest even half, and 5 tenths and one cypher in decimals; if there are pence and farthings in the sum, reduce the pence to farthings, observing to increase the sum by 1 if it exceed 12, and by 2 if it exceed 37; add the farthings, thus increased, in the place of tenths and hundreths, divide the whole by 3, the quotient is cents.

1A

Examples.

1. Reduce 63 10s. 11 d. to dols. cents, and mills.

35.00
48

35 48 3811:826† Ans:

2. Reduce 617 19s. 11 d. to dols. cents, and mills.

179.50
$49

179,99÷3—859.999† Ans.

To change dols. cts. &c. to the former currency of New Hampshire, Vermont, Massachusetts, Rhode

Island and Connecticut.

RULE. When the sum to be reduced is dollars; multiply the dollars by 3; double the right hand figure of the product for shillings; the remaining figures are pounds. If the sum to be reduced is dols. cts. and mills, multiply the whole by 3, point off 4 figures from the right for decimals; the rest of the product is pouuds; (note, if mills are not named in the sum, three figures only must be pointed off;) find the value of the decimal part by multiplying by 20; 12 and 4; observing to point off for decimals each time of multiplying; and the sums standing on the left of the separatrix will be shillings, pence and farthings.

Examples.

1. It is required to reduce $251 to lawful money. 251X3=£75 68. Ans. 2. It is required to reduce $9529 to lawful money. 9529X3=62858 14s. Ans. 3. It is required to reduce $192 to lawful money. 192×3=657 128. Ans.

4. It is required to reduce $999 to lawful money. £299 148. Ansi

1. It is required to reduce $99 67 cts. to lawful money.

[blocks in formation]

2. It is required to reduce $67.90 to lawful mo

ney•,

Ans. 201. 78. 4jd.

3. It is required to reduce $99.999 to lawful money. Ans. 29. 19s. 114td. 4. It is required to reduce $61.276 to lawful moAns. 18. 7s. 74td..

ney.

To reduce the former currency of New-York and NorthCarolina to dols. cts. c. and the contrary.

RUEE Prepare the sum to be reduced exactly as in New-Hampshire, Massachusetts, &c. and divide by 4 instead of 3, the quotient is cents; a dollar in New-York is equal to 8s.

Examples.

1. Reduce £9 16s. to dollars, and cents, &c.

98÷4=$2450 Ans.

2. Reduce £230 10s. to dollars, and cents, &c.

2305÷4=$576-25 Ans.

3. Reduce 219 15s. 4 d. to dollars, cents, &c.

2197.50
18

[blocks in formation]

4. Reduce £419 10s. to dollars, cents, &c.

$1048.75 Ans. Change dollars, &c. to New-York and North Carolina currency.

RULE.-Proceed as in New-Hampshire currency, &c. only multiply by 4 instead of 3; the value of a dollar is equal to four tenths of a pound.

Examples.

1. Change 842 dols. to New-York currency, &c.

842
4

£336 16s. Ans.

2. Change $114-25 to North-Carolina curren Ans. £45 14s.

cy, &c.

New-Jersey, Delaware, Pennsylvania, and Maryland currencies reduced to the present currency of the United States, and the contrary.

1

RULE. Multiply the given sum (if it is pounds only,) by 8, and divide the product by 3; the quo tient is dollars. If the sum is pounds, shillings and pence, reduce the whole to pence, and add one ninth of the whole to itself, the sum will be cents; a dollar in these states is equal to 7s. 6d., or pound.

Examples.

of a

1. It is required to reduce £942 to dollars, &c.

942
8

3)7536

$2512 Ans.

2. It is required to reduce £961 19s. 6d. to dol

lars, &c.

Ans. $2565.31 cts.

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