COMPOUND INTEREST BY DECIMALS.

TABLE showing the amount of $1, or £1, at 5 and 6 per cent. per annum, compound interest, from 1 year to 20 years.

RULE 1.-Multiply the given principal continually by the amount of one dollar, or one pound, for one year, at the rate per cent. given, until the number of multiplications be equal to the given number of years. the last product will be the amount for the whole time; from which subtract the given principal, and the remainder will be the compound interest.

Or,

RULE 2.-Multiply the amount of one dollar, or one pound, for the given number of years, by the given principal, the product will be the amount required; from which subtract the given principal, and the remainder will be the compound interest.

EXAMPLES.

1. What will be the amount and compound interest of $500 for 3 years, at 6 per cent.?

By rule 1. $500 × 1.06 X 1-06 × 1·06=$595.508 Amt. 95.508 Comp. Int.

$595.508-500

=

By rule 2. Amount of one dollar for 3 years 1∙191016

218. What is the method of computing compound interest by decimals?

2. What will be the compound interest of £320 for 4 years, at & per cent. ?

Ans. £68 19s. 2d. 3.52 qrs. Rule 1.

3. What will $50 amount to in 20 years, at 6 per cent. compound interest? Ans. $160.35675. Rule 2.

4. What will be the compound interest of $1500 for 15 years, at 6 per cent. ?

Ans. $2094-837. Rule 2.

DUODECIMALS;*

OR

CROSS MULTIPLICATION.

THE rule of Duodecimals is particularly useful to Workmen and Artificers, in casting up the contents of their work.

The denominations are feet, inches or primes, seconds, thirds, fourths, fifths, &c. there being no limit to the division.

12 fifths, (marked") are 1 fourth, ("")

12 fourths

1 third, (")

1 second, (")

1 inch or prime, (')

1 foot (ft.)

Glaziers' and Masons' work is measured by the foot.

Painting, plastering, and paving are done by the yard. Partitioning, flooring, slating, rough boarding, by the square of 100 feet.

Stone and brick work by the rod of 16 feet, whose square is 2724. Bricks also are laid by the thousand.

*Duodecimals are a species of compound numbers, decreasing in an uniform ratio of 12, from a greater denomination to a less; hence their name.

219. What are Duodecimals?220. What is the use of duodecimals?— -221. What are the denominations used in duodecimals?

RULE.

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

2. Multiply each term in the multiplicand, beginning at the lowest, by the feet 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 superior.

3. In the same manner multiply the multiplicand, by the inches in the multiplier, and write the result of each term in the multiplicand, thus multiplied, one place to the right hand in the product.

4. Proceed in the same manner with the other parts in the multiplier, which if seconds, write the result two places to the right hand; if thirds, three places, &c. and their sum will be the answer required.

NOTE.-Feet multiplied by feet give feet-Feet multiplied by inches give inches-Feet multiplied by seconds give seconds-Inches multiplied by inches give seconds--Inches multiplied by seconds give thirds-Seconds multiplied by seconds give fourths.

EXAMPLE.

Multiply 7 feet, 3 inches, 2 seconds, by 1 foot, 7 inches and 3 seconds.

"

F. L.
732
173

Prod. by the feet, 7 3 2 " do. by primes, 4 2 10 2 do. by seconds,

1996

Here we multiply the 7f. 3in. 2" by the 1f. in the multiplier, which gives seconds, inches and feet. We next multiply the same 7f. 3in. 2" by the 7in. saying 7 times 2 are 14 which is once 12 and 2 over, which (2) we set down one place to the right hand, that is, in ` the place of thirds, and carry one to the next place, and proceed in the same manner with the other terms. Lastly, we multiply the multiplicand by the 3′′ saying 3 times 2 are 6, which we set down two places to the right hand and so proceed with the other terms of the multiplicand. The sum of all the products is the answer.

11 7 9 11 6

222. What is the rule?

APPLICATION AND USE OF DUODECIMALS.

I. To find the superficial contents of boards, &c. where length and breadth only are considered.

RULE.-Multiply the length by the breadth, and the product will be the superficial content.

NOTE. If the board or plank is tapering, add the width of both ends together, and take half the sum for the mean width, which multiplied by the length, will give the contents.

EXAMPLES.

1. How many feet in a board 10 feet 7 inches long, and 9 inches wide? Ans. 7ft. 11' 3"

2. What number of feet are there in a floor 16 feet 6 inches long, and 12 feet 8 inches wide?

Ans. 209 feet.

II. To find the solid content of timber, stone, bales, trunks, &c.

RULE.-Multiply the length by the breadth, and the product by the depth or thickness; the last product will be the content in solid or cubick feet, and parts of a foot.

EXAMPLES.

1. How many cubick feet in a stick of timber 12 feet 10 inches long, 1 foot 7 inches wide, and 1 foot 9 inches thick ?

Ans. 35ft. 6. 8." 6.""

2. How many cubick feet, and perches of 242 feet, are there in a cellar wall, 130 feet 8 inches long, 8 feet high, and 2 feet 9 inches thick?

NOTE.-Bricklayers value their work at the rate of a brick and a half thick; and if the thickness of the wall is more or less, it must be reduced to that thickness, which may be done by the following

223. What is the rule for measuring boards by duodecimals ?—224. What is the rule for finding the solid content of timber, stone, &c.?

RULE.--Multiply the area of the wall by the number of the half bricks in the thickness of the wall, the product divided by 3 will give the area.

III. To measure drains, vaults, dikes, cellars, &c.

RULE. Multiply the length, width and depth in feet together, and divide by 216.

NOTE--Diggers work by the square of 6 feet long, wide and deep, making 216 cubic feet to a square.

EXAMPLES.

1. The re is a drain 200 feet long, 3 feet wide, and 5 feet deep; how many squares does it contain?

Ans. 18 squares.

216

2. How many squares are in a vault 8 feet square, and 91 feet deep? Ans. 22 squares.

IV. To measure wood.

RULE.--Multiply the length by the width, and the product by the height, the last product will be the content in cubick feet, and parts of a foot, which are brought into cords by dividing them by 128, or into cord wood feet by dividing by 16.

NOTE.-A cord of wood is a pile 8 feet long, 4 feet wide, and 4 feet high, containing 128 cubick feet, or 8 feet of cord wood. A foot of cord wood is a pile 4 feet long, 4 feet wide, and 1 foot high, containing 16 cubick feet.

EXAMPLES.

1. How many cords are there in a pile of wood 176 feet long, 3 feet 9 inches wide, and 4 feet 3 inches high?

Ans. 2111 cords.

225. What is the rule for measuring drains, vaults, &?—226. What is the rule for measuring wood duodecimally?