64. How many feet board measure in 8 planks, 4 in. thick, 18 ft. long and 16 in. wide?

65. How many feet board measure in a stick of timber 1 ft. square and 20 ft. long?

66. How many feet board measure in 40 joists 10′′ × 2′′ and 12 ft. long?

Round logs are sold by the can be cut from them, acWhen logs do not exceed

314. To measure round logs. amount of square lumber that cording to calipers now in use. 16 ft. in length, the length and the diameter of the small end are taken, and a table stamped upon the calipers gives the number of feet board measure. This table may be

calculated as follows:

Express the diameter in inches, subtract twice the diameter from the square of the diameter, and 21 of the remainder will be the number of feet board measure in a log 10 ft. long.

The formula is 1 (d2 – 2d), in which d stands for the diameter of the log in inches.

Ex. Find the number of feet board measure in a log 16 ft. long and 20 inches in diameter.

18 of 189 302.4 ft. board measure. Ans.

By this rule find the number of feet board measure in :

67. A log 12 ft. long and 16 in. in diameter. 68. A log 13 ft. long and 12 in. in diameter.

69. A log 14 ft. long and 20 in. in diameter. 70. A log 15 ft. long and 15 in. in diameter.

315. Oak and other heavy timber.

Large heavy timber of hard wood is generally sold by the ton, signifying 50 cu. ft. or 600 ft. board measure.

316. To find the contents of a cask.

Subtract the diameter of one of the heads from the bung diameter expressed in inches, and multiply the difference by 0.65; to the product add the head diameter, and this will give the mean diameter.

Square the mean diameter and multiply it by the length in inches. Divide this product by 294. The quotient is the number of gallons the cask will hold.

71. Find the number of gallons contained in a cask of which the bung diameter is 24 in., head diameter 20 in., and the length 36 in.

72. Find the number of gallons contained in a cask of which the bung diameter is 30 in., head diameter 26 in., and the length 38 in.

317. To find the volume of an irregular body.

Immerse the body in a vessel full of water. Remove the body and calculate the amount of water displaced.

318. To find the surface of a sphere.

Multiply the square of the diameter by 3.1416.

73. How many square inches on the surface of a ball 4 in. in diameter?

74. How many square inches on the surface of a globe 18 in. in diameter ?

319. To find the volume of a sphere.

Multiply the cube of the diameter by 0.5236 (that is, of 3.1416).

75. Find the volume of a globe 2 ft. in diameter.

CHAPTER XV.

Ex. 164.

MISCELLANEOUS PROBLEMS.

1. Fifteen men and eight boys together earn $342 a week. If a boy's pay is half a man's pay, what are the daily wages of a man, and also of a boy?

2. A man divides $1622.50 among four persons so that the first has $40 more than the second, the second $60 more than the third, and the third $87.50 more than the fourth. Find the part of the fourth.

3. A family of six persons makes $8.75 a day, and works 304 days in the year. At the end of the year each member of the family puts $80 in a savings bank. Find the daily expense of the family.

4. A man bought 5.5 yds. of cloth for $35. In having a suit made from it, he found that he lacked 1.75 yds., which he procured at the price per yard of his first purchase. What is the cost of the suit if the trimmings cost $6.50 and the making $15?

5. A man has 76.25 yds. of linen, worth 44 cts. a yard, made into shirts. It takes 3.05 yds. for a shirt, and the price for making is 50 cts. a shirt. Find the cost of a shirt, and the number he has made.

6. A man's expenses from the first of January to the end. of October 17 are $1845.50. How much must he diminish his daily expense in order that the total expense for the year shall not exceed $2200?

7. A quart contains 1600 beans of average size, and a field is planted with 22 rows of 800 hills each, with 6 beans in a hill. The increase is tenfold.

What

is the value of the crop at $3 a bushel? (There are 32 quarts in a bushel.)

8. For making 25 gallons of ordinary beer 60 pounds of

barley and 0.5 of a pound of hops are needed. If the barley costs $1.50 for 60 pounds, and the hops cost 18 cents a pound, what is the profit to the brewer on a cask of 42 gallons if he sells it for $5 and reckons his labor $1.50?

9. A person receives his income quarterly.

The first

quarter he receives $533.25, the second $1535.20, the third $856.44, the fourth $ 725.19. His expenses for these quarters are respectively $686.60, $734.25, $589.15, $849.65. How much does he save for the year?

10. A hen lays on an average 120 eggs a year worth 24 cents a dozen. She eats a quart of barley every 5

days. The barley is worth 56 cents a bushel. What is the annual profit from this hen?

11. A square garden measuring on each side 40.50 yards is enclosed by three lines of galvanized iron wire. Eight yards of this wire weigh a pound, and it is worth 7.5 cents per pound. What is the cost of the wire?

12. A family composed of five persons consumes daily one pound of stale bread for each person, or 1.15 pounds of fresh bread. If bread is worth 5 cents a pound, find the annual saving which this family will make if it eats stale bread altogether.

13. It is estimated that in France 240,000 women and girls are employed in making lace. The annual production has a value of $13,000,000, and the value of the raw material is 0.27 of the value of the lace. Find the average daily wages of these women and girls, supposing that each works 240 days in the year.

14. The salt water which is obtained from the bottom of a mine of rock salt contains 0.09 of its weight of pure salt. What weight of salt water is it necessary to evaporate in order to obtain 4734 pounds of salt?

15. The weight of ashes from the burning of oak wood is 0.03 of the weight of the wood, and the weight of carbonate of potash contained in the ashes is 0.065 of the weight of the ashes. Find the weight of carbonate of potash from 1170 pounds of wood.

16. The weight of sugar from the sugar beet is nearly 0.06 of the weight of the beet. If an acre produces 30,000 pounds of beets that are sold at the rate of $2 a thousand pounds, how many acres of land is it necessary to sow to furnish beets to a sugar factory which produces 150,000 pounds of sugar a year, and what will the be value of the crop obtained?

17. If a workman has taken every day for the last 12 years two glasses of beer at 5 cents a glass, how much could he have saved if he had not indulged this habit, reckoning 365 days each year?

18. A woman has three children. She pays for each $15 a year for having their clothes made, $1.50 a month for mending, and $0.35 a week for washing. How much could she save in a year if she knew how to wash, make clothes, and mend?