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RULE.

The burthens of similar built ships are to each other as the cubes of their like dimensions.

EXAMPLE.

If a ship of 300 tons burthen be 75 feet long in the keel, I demand the burthen of another ship, whose keel is 100 feet long?

T.cwt.qrs.lb.

As 75x75x75: S00 :: 100×100×100: 711 2 0 24 +

CROSS MULTIPLICATION,

Is

a rule made use of by workmen and artificers in casting up the contents of their work.

RULE.

1. Under the multiplicand write the corresponding denominations of the multiplier.

DUODECIMALS,

OR

2. Multiply each terin into the multiplicand, beginning at the lowest, by the highest denomination in the multiplier, and write the result of each under its respective term; observing to carry an unit for every 12, from each lower denomination to its next superior.

F. I.

Multiply 7 S

By

4 7

3. In the same manner multiply all the multiplicand by the inches, or second denomination, in the multiplier, and set the result of each term one place removed to the right hand of those in the multiplicand.

4. Do the same with the seconds in the multiplier, setting the result of each term two places to the right hand of those in the multiplicand, &c.

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FEET, INCHES AND SECONDS.

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Product, 55 2 93 9 48 11 2 8 10.

-1

How many square feet in a board 16 feet 9 inches long, and 2 feet 3 inches wide By Duodecimals.

F. I.

16 9

2

3

33 6

8 11

By Decimals.

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6.6.

3350 S$50

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TO MEASURE LOADS OF WOOD.
RULE.

Multiply the length by the breadth, and the product by the depth or height, which will give the content in solid feet; of which 64 make half a cord, and 128 a cord.

EXAMPLE.

How many solid feet are contained in a load of wood. 7 feet 6 inches long, 4 feet 2 inches wide, and 2 feet S inches high?

=

7 ft. 6 in. 7,5 and 4 ft. 2 in.4,167 and 2 ft. S in= 2,25; then, 7,5x4,16731,2525×2,2570,518125 solid feel, Ans.

But loads of wood are commonly estimated by the foot, allowing the load to be 8 feet long, 4 feet wide, and then 2 feet high will make half a cord, which is called 4 feet of wood; but if the breadth of the load be less than 4 feet, its height must be increased so as to make half a cord, which is still called 4 feet of wood.

By measuring the breadth and heighth of the load, the content may be found by the following

RUIE.

Multiply the breadth by the height, and half the product will be the content in feet and inches.

EXAMPLE.

Required the content of a load of wood which is 5 feet 9 inches wide and 2 feet 6 inches high. ~ By Duodecimals. By Decimals.

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3,75

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750

94 6

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Ans. 4 8 S

4,68754 81, or half a cord and 81 inches over. The foregoing method is concise and easy to those who are well acquainted with Duodecimals, but the following Table will give the content of any load of wood, by inspection only, sufficiently exact for common practice; which will be found very convenient.

1875

A TABLE of Breadth, Height, and Content.

| Breadth. || Height in feet. fl. in.

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Inches.

1 2 3 4 12 545 | 6 |7 |8|9|10|11

2 6

7

8

9

10 |17|34|51|68|| 2 3 4

11

18355370

19365472

15 30 45 601245

3 4 5

1631 47 62
16/32/48/64
173349,66|| 134 6

3 4

5

6

3146

35 6

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TO USE THE FOREgoine table.

First measure the breadth and height of your load to the nearest average inch; then and the breadth in the left hand column of the table; then move to the right on the same line till you come under the height in feet, and you will have the content in laches, answering the feet, to which add the content of the inches on the right and divide the sum by 12, and you will have the true content of the load in feet and inches.

NOTE.-The contents answering the inches being always small, may be added by inspection.

EXAMPLES.

1. Admit a load of wood is 8 feet 4 inches wide, and 2 feet 10 inches high, required the content.

Thus, against 5 ft. 4 inches, and under 2 fect, stands 40 inches; and under 10 inches at top, stands 17 inches: then 40+ 17-57 true content in inches, which divide by 12 gives 4 feet 9 inches, the answer.

Why

2. The breadth being $ feet, and height 2 feet 8 inches, required the content.Thus, with breadth

feet 0 inches and under 2 feet

atop, stands 36 inches; and under 8 inches, stands 1£ inches now 36 and 12, make 48, the answer in inches ; and 48+12=4 feet, or just half a cord,

3. Admit the breadth to be 3 feet 11 inches, and height 5 feet 9 inches; required the content.

Under 3 feet at top, stands 70; and under 9 inches, is 18: 70 and 18, make 88÷12=7 feet 4 inches, or 7 ft. 1 qr. 2 inches, the answer.

i

TABLE I.

Showing the amount of £1, or 81, at 5 and 6 per cent. per annum, Compound Interest, for 20 years.

11

Trs. 15 per cent.16 per cent.]F ́rs. 15 per cent.16 per cent. 1,06000 31 | 1,71034 1,12360 12 1,79585

1,19104 13 1,88565

1,26247 14

1,97993

1,33822 15

2.07893

1,41854 16 2,48287

1 | 1,05000

2 1,10250

3

1,15762

5

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1,21550

1,27628

1,54009

1,40710 1,50363 17

1,59384 18

1,47745
1,55132
1,62889 1,79084 20

1.68947 19

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2,99201
2,40661

2.5 2695

2,65529

10

VII. The weights of the coins of the United States.

prot. gr.

11

6.

Eagles,
Half-Eagles,
Quarter-Eagles,
Dollars,
Half-Dollars,
Quarter-Dollars,
Dimes,
Half-Dimes,
Cests,
Half-Cents,

Copper.

4 8

The standard for gold coin is 11 parts pure gold and one part alloy the alloy to consist of silver and copper. The standard for silver coin is 1485 warts Ane to 179 parts alloy—the alloy to be whol

copper.

1,89829 2,01219

2,13292

2.26090

2,39655

2,34727

2.69277

2.85433

515

2 19

8

816

4 8
1171

201
8.16

17

3,02559

5.20715

Standard

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Standard
Silver.

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