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To change sterling to the currency of South Carolina, or Georgia--Multiply by 28, and divide the product

by 27.

by 28.

Examples. 1. In £1115: 10 6. sterling, how much currency of South Carolina, &c.?:

Ans. £ 1156 16 91 2. In £6358 11 74 sterling, how much currency of South Carolina, or Georgia? Ans. £ 6549 1 827

To change the currency of South Carolina, or Georgia, to sterling

Multiply by 27, and divide the product

EXAMPLES 1. 'In £1156 16 91 currency of South Carolina, ør Georgia, how much sterling? Ans. £1115 10 6.

2. In £6594 1 877 currency of South Carolina, or Gebrgia; how much sterling?'. "Ans. £6358 1171

To change federal money to the currency of Canada, Nova Scotia, Brunswick, &c.

Multiply dollars by 5, gives shillings, which may be Multiply.cents by 60, gives pence, it reduc. to their Multiply mills by 240 gives farthings, S proper terms. To change the currencies of Canada, Nova Scotia, and New Brunswick, to federal money:

Divide shillings by 5 for dollars, pence by 60, and farthings by 240.

ALLIGATION MEDIAL :.

Teaches how to find the meani price of several articles mixed, by having the quantity and value of the several articles mixed, given.

Rule. Find the quantity and value of the whole mixturé, then say, as the whole composition, or mixture, is to its total value, so is any part of the composition, to its mean-price or value.

EXAMPLES. 1 A grocer mixed 2cwt. of sugar at 89 per.cwt, and 1 cw at $7 per cwt. andicwt. at $10 per cwt; what is the value of 1 cwt. of this mixture ?

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Ans. $9 2. A refiner mixed 3lb. of gold, of 22 carats fine, with 3lb. of 20 carats fine, I demand the fineness of this mixture.

Ans, 21 carats. 3. A farmer mixed 19 bushels of wheat, at i dol.:

per bushel, and 40 bushels of rye, at 66 cts, per bushel, and 11. bushels of barley, at 50 cents per bushel; what is a bushel of this mixture worth?

Ans. $0,72,74 4. A vintner mixed 5 gallons of Canary, at dol. 1,30, with 6 gallons of Malaga, at dol. 1,20, and 4 gallons of white wine, at 1 dol. per gallon ; what is a gallon of this mixture worth?

Ans. dol. 1,18. To prove questions in this rule, find the value of the whole mixture at the mean price, and if it agrees with the total value of the several quantities at their respective rates, the work is right,

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ALLIGATION ALTERNATE

Teaches how, from the prices of several articles given, to find how much of each must be mixed, to bear a certain price proposed. RULE. Place the prices

4) prices. one over the other, and the mean pri: 7

6 of the proposed price against them,

8( several as in the margin.

10 articl. Link the several prices together, so that one greater than the mean vi price may be coupled to another 1:3 8 which is less ; thus,

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6

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Take the difference between each price, and the mean price, and set them down alternately, and they will be the quantities required.

EXAMPLES 1. How much wheat at I dol. rye at 66 cents, and barley at 50 cents per bushel, must be mixed to make the mixture worth 75 cents per bushel ?

wheat
1,00

9+25=34
mean price 75. rye

66) 25 = 25 barley 50° 25 =25

34 bushels of wheat.
Ans.

do.

rye.

25 do. barley. This is proved by Alligation Medial, thus,

34 bushels at I dol. is $34,00
25 rye at 66 cents, 16,50
25 barley at 50 cents, 12,50

{

25

84

84)6300(75 cents, proof.

588

420
420

2. How much canary wine, at dol. 1,50 per gallon, Malaga at dol. 1,20, and white wine at i dol. must be mixed together, that the mixture may be worth dol. 1,30 per gallon ? :

2 gallons of Canary. Ans. 1 do.

Malaga.

1 do. White wine. 3. How much sugar at 9 dols. per cwt. al 7 dols. per cwt. and at 10 dols. per cwt. must be mixed together, tbat 'the mixture may be worth 9 dols. per cwt ?

2 cwt. at $9 Ans. I do. at 7

2 do. at 10 NOTE. Other cases in Alligation-might be treated of but as they are of no real advantage, they are omitted.

DUODECIMALS. Duodecimals are fractions of a foot, or of an inch, or of any part of an inch, having 12 for their denominators, useful in measuring mechanics' work, bales, boxes, &c. NOTATION OF DUODECIMALS.

F. 1. " Duodecimals are written thus: 5 7 2 5 8 &c. and are read thus : 5 feet, 7 inches, 2 seconds, 5'thirds, 8 fourths, &c.

NOTE. Some call the inches primes, and then the above

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would stand thus :

5 y 2 5 8 &c.

ADDITION OF DUODECIMALS.
NOTE. 12 fourths,

I third.
12 thirds,

1 second

make 12 seconds,

1 inch.
12 inches,

I foot.
EXAMPLES.

F.
25 17 2 5 7 43 6 3 5 6 73 4 6 17
46 2 7 3 5 36 4 7 4 3 47 7 2 8 2
65 5 3 6 2 24 2 2 6 9 36 37 5 9
56.4 6 4 6 63 1 9 2 6 24 5 4 96
74 4 9:6 4 56 5 8 6 5 25 7 5 10 4
56 9 4 8 6 63 7 4 7 8 52 4 9 3 9
31 6 8 5 9 75 9 9 5 2 63 8 4 6 2

F.

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F.

356 4 6 4 3

SUBTRACTION OF DUODECIMALS.

EXAMPLES.
F.

F.
From 97 1 3 5 7 57 3 6 9 4 637 1 7 3 6
Subtract 39 9 6 1 3 31 9 373 9 1 6 1

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Remains 57 9 9 4 4

Proof,

97 7 3 5 7

MULTIPLICATION OF DUODECIMALS.

By some called Cross Multiplication.

Note 1. Feet multiplied by feet produce feet, Feet multiplied by inches, or inches by feet, produce inches. Feet multiplied by seconds, or seconds by feet, produce seconds. Inches multiplied by inches, produce seconds. Inches multiplied by seconds, or seconds by inches, produce thirds. Seconds multiplied by seconds, produce fourths, &c.

Note 2. The multiplicand must be multiplied by each denomination in the multiplier, and the several products added together, to obtain the true product.

Note 3. Sometimes it is easier to take parts, as in practice, with the less denominations instead of multiplying.

EXAMPLES

F.'
1. Multiply 767 3
Ву

3 6 4

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Ans.=270 2 10 11 In this example I begin by multiplying by 3, saying 3 times 3 are 9 seconds, which I set down under the seconds ; then say, 3 times 7 are 21 minutes, which is 9 more than 12 ; I set down the 9 under the minutes, and carry one for the 12, to the next denomination, saying 3 times 6 are. 18, and 1 that I carry will make it 19 feet ; this being the highest denomination, I set down all over 10, viz. 9, and carry one for the ten to the next, saying, 3 times 7 are 21, and 11 carry makes 22 ; this being the left hand, or last figure to multiply, I set the whole down, viz. 22. I now come to the figure 6 in the multiplier, standing in the place of inches, and say 6 times 3 are 18, this is 6 over 12, and as inches and seconds multiplied together, produce thirds, I set down 6 in the place of thirds, and carry one to the next, &c.

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