ARTICLE VII.

To find the solid contents of a cube.*

RULE.

Multiply the length of one side by itself, and multiply the product by the same length, that is, by the same multiplier; the last product will be the solid contents of

the cube.

EXAMPLES.

1. How many solid feet are contained in a cube, or solid block of 6 equal sides, each side being 3 feet in length, and 3 in breadth?

3X3X3=27 solid or cubick feet. Ans. When the contents are required of right angled solids, whose length, breadth, &c., are not equal; multiply the length by the breadth, and that product by the thickness- -the product will be the answer.

2. Required the contents of a load of wood, whose length is 8 feet, breadth 4 feet, and height or thickness 4 feet. 8X4X4 128 solid feet, or 1 cord. Ans. 3. Required the contents of a stone 16 feet in length, 11 in breadth, and 1 foot in thickness.

16.5X1.5X1=24.75 solid feet, or 1 perch. Ans. Note.-Solids whose dimensions are in feet and inches, are more easily measured by Duodecimals.

ARTICLE VIII.

To find the contents of a prism.

A prism is an angular figure, generally of three equal sides, whose ends are in the form of triangles. It resembles a fife of three sides, whose whole length is of equal bigness.

RULE.

Find the area or superficial contents of one end as of any other triangle, then multiply the area by the length of the prism, and the product will be the solidity.

EXAMPLE.

What are the solid contents of a prism, the sides of the triangles of which measure 13 inches, the perpen

* A cube is a solid body of equal sides, each of which is an exact square:

dicular extending from one of its angles to its opposite side, 12 inches, and its length 18 inches? 13X12=156÷÷2=78X18-1404 cubick inches. Ans.

ARTICLE IX.

To find the contents of a cylinder.

A cylinder is a long round body, all its length being of equal bigness, like a round ruler.

RULE.

Find the area of one end, by the rule for finding the area of a circle, then multiply it by the length, and the product will be the answer.

EXAMPLE.

What is the solidity of a cypher, the area of one end of which contains 2.40 square feet, and its length being 12.5 feet? 2.40X12.5=30 solid feet, Ans.

ARTICLE X.

To find the solid contents of a round stick of timber, which is of a true taper from the larger to the smaller end.

RULE.

Find the area of both ends; add the two areas together, and reserve the sum; multiply the area of the larger end by the area of the smaller end, extract the square root of the product, add the root to the reserved sum, then multiply this sum by one third the length of the stick, and the product will be the solidity.

Note. As this method requires considerable labour, the following has been preferred for common use, though not quite so accurate.

RULE.

Girt the stick near the middle, but a little nearer to the larger than to the smaller end; this will give the circumference at that place. Find the diameter by the circumference; multiply the circumference and diameter together; then multiply one fourth of the product by the length, and the answer will be nearly the solid

contents.

EXAMPLE.

What is the solidity of a round stick of timber that

is 10 feet long, and its circumference near the middle is

Multiply the cube of the diameter by 5236, the product will be the solid contents. Or, multiply the superficial contents, or surface, by one sixth part of the surface. Or, multiply the cube of the diameter by 11, and divide the product by 21-in either case the product will be the solidity.

EXAMPLES.

1. What are the solid contents of a globe whose di'ameter is 14 inches?

14×14×14=2744×.5236=1436.7584

cubick inches. Ans. 2. How many solid miles are contained in the earth, or globe, which we inhabit?

Suppose the diameter to be 7954 miles; then, 7954X 7954X7954-503218686664 the cube of the earth's axis, or diameter; then,

503218686664.5236=263485304337

Note. The solidity of a globe may be found by the circumference, thus-Multiply the cube of the circumference by .016887-the product will be the contents.

PRACTICAL QUESTIONS.

1. A cannon ball goes about 1500 feet in a second of time. Moving at that rate, what time would it take in going from the earth to the sun; admitting the distance to be 100 millions of miles, and the year to contain 365 days, 6 hours? Ans. 10,4808

13149.

2. A young man spent of his fortune in 3 months, of the remainder in 12 months more, after which he had £410 left. What was the amount of his fortune? Ans. £956 13s. 4d. 3. What number is that, from which if you take & of , and to the remainder add of, the sum will be 10? Ans. 10 2240

4. What part of 3, is a third part of 2? Ans.. 5. If 20 men can perform a piece of work in 12 days, how many will accomplish another thrice as large, in one fifth of the time? Ans. 300.

6. A person making his will, gave to one child 13 of his estate, and the rest to another. When these legacies were paid, the one proved to be £600 more than the other. What was the worth of the whole estate? Ans. £2000.

7. The clocks of Italy go on to 24 hours; how many strokes do they strike in one complete revolution of the index? Ans. 300.

8. What quantity of water must be added to a pipe of wine, valued at £33, to bring the first cost to 4s. 6d. per gallon? Ans. 20 gallons. 9. A younger brother received £6300, which was of his elder brother's portion. What was the whole estate? Ans. £14400. 10. What number is that which being divided by 2, or 3, 4, 5, or 6, will leave 1 remainder, but which if divided by 7 will leave no remainder? Ans. 721.

11. What is the least number that can be divided by the nine digits without a remainder? Ans. 2520. 12. How many bushels of wheat, at $1.12 per bushel, can I have for $81.76?

Ans. 73.

13. What will 27 cwt. of iron come to, at $4.56 per cwt.? Ans. $123.12. 14. When a man's yearly income is 949 dollars, how much is it per day?

Ans. $2.60. 15. My factor sends me word he has bought goods to the value of £500. 13s. 6d. upon my account; what will his commission come to at 31 per cent.?

Ans. £17. 10s. 51d

16. How many yards of cloth, at 17s. 6d. per yard, can I have for 13 cwt. 2 qrs. of wool, at 14d. per lb.? Ans. 100 yards, 31 qrs. 17. There is a cellar dug that is 12 feet every way, in length, breadth, and depth; how many solid feet of earth were taken out of it? Ans. 1728. 18. If of an ounce cost of a shilling, what will of a lb. cost?

Ans. 17s. 6d. 19. If of a gallon cost § of a £. what will & of a tun 32 cost?

Ans. £105. 20. If of a ship be worth £3740, what is the worth of the whole? Ans. £9973. 6s. 8d. 21. What is the commission on $2176.50, at 21 per cent.? Ans. $54.413. 22. In a certain orchard of the trees bear apples, pears, plums, 60 of them peaches, and 40 cherries; how many trees are in the orchard?

Ans. 1200.

23. If A travel by mail at the rate of 8 miles an hour, and when he is 50 miles on his way, B start from the same place that A did, and travel on horseback the same road at 10 miles an hour, how long and how far will B travel to come up with A?

Ans. 25 hours, and 250 miles. 24. Bought a quantity of cloth for 750 dollars, of which I found to be inferior which I had to sell at 1 dollar 25 cents per yard, and by this I lost 100 dollars: what must I sell the rest at per yard that I shall lose nothing by the whole? Ans. $3.151.

25. If the Earth goes round the sun in 365 days, 5 hours, 48 minutes, 49 seconds, and its distance from the sun 95000000 miles, what must be the distance of the planet Mercury from the Sun, admitting the time of its revolution round the Sun to be 87 days, 23 hours, 15 minutes, 40 seconds?

Note. The planets describe equal areas in equal times: therefore, as the square of the time of the revolution of one planet, round the Sun, is to the square of the time of the revolution of any other planet, so is the cube of the distance of one planet from the Sun, to the cube of the distance of any other from the Sun.