568. Allowing 7 ft. as a cow's length from horns to tail, how much more surface may she graze, if a rope 35 ft. long

be tied to her tail instead of to her horns?

569. A table has the shape of a regular octagon, side 3 ft.; and another table has the shape of a regular hexagon, side 4 ft. What will it cost to paint both their surfaces, at 8 cents per square inch?

570. A single circular valve is required to replace three smaller ones containing severally 10, 20, and 30 sq. in. Find its diameter.

571. A boiler needs a safety-valve 10 in. in diameter, but has only an 8-in. one. Find the diameter of a second valve required to make up the deficiency.

572. A measuring wheel is 34 ft. diameter, and turns exactly 168 times in going round a circular pond. Find the area of the pond.

573. How must a circular lot of land 343 ft. diameter be laid out so that a fish-pond in the centre, a flower-garden round the pond, and a walk around the garden, may each occupy of the entire area ?

574. The piston of a pump is 16 in. in diameter, and moves through a space of 46 in. How many cubic feet of water will be thrown out by 1000 strokes?

575. A body is placed under water in a right cylinder 60 in. in diameter, and the level of the water is observed to rise 30 in. Find the volume of the body.

576. How much will a brass cylinder weigh under water if the height is 10 in., and the diameter of the base is 7 in.? Brass is 7.8 times heavier than water, and a body when immersed in water loses a weight equal to the weight of the water displaced.

CHAPTER VIII.

MISCELLANEOUS EXERCISES.

1. The chief items of expense in converting 450 bu. of Dakota wheat into bread ready for sale in Boston, according to Mr. Atkinson's book on "The Distribution of Products," are as follows: price paid the Dakota farmer for the wheat, 80 cents per bushel; railroad freights, $200; milling at Minneapolis into 100 bbls. of flour, $50; cost of barrels, $40; commissions and cartage, $30; total cost of converting 100 bbls. of flour into 30,000 lbs. of bread, $420. If each loaf of bread weighs 14 lbs. and is sold for 8 cents, what per cent profit can a Boston baker clear above all expenses by buying Dakota wheat and converting it into bread?

2. The change in the deposits in the savings banks of Massachusetts between 1865 and 1885 is shown by the following figures:

291,488,

1885.

1,941,465.

848,787.

Number of accounts, Total amount deposited, $59,936,482, $274,998,412. Find for each date the average deposit on each account, and also the average deposit per head of population.

3. A man has 50 qts. of wine which cost him 62 cents per quart. After adding 12 qts. of water, he wishes to sell it so as to make 25% on his outlay. What should be his selling price?

4. In round numbers the population of this country was 34,750,000 in 1865, and 57,000,000 in 1885. The total grain crop was 1,127,500,000 bu. in 1865, and 3,000,000,000 bu. in 1885. Which has increased more rapidly during the period between the dates mentioned, the population or the production of grain? If the number of bushels of grain per head in 1865 be represented by a line 1 in. long, how long a line would represent the number of bushels per head in 1885?

5. The wheat crop of the United States in 1884 was in round numbers 500,000,000 bu. Land of good quality in Texas will produce 20 bu. of wheat per acre. The area of Texas is 275,000 sq. mi. very nearly. How much good land would be required to raise the entire wheat crop of 1884, and what per cent of the area of Texas would suffice for this purpose?

6. The cotton factories of the world now require about 12,000,000 bales of cotton. Good land in Texas produces 1 bale to the acre, and Texas contains in round numbers 275,000 sq. mi. What per cent of the area of Texas would be sufficient for producing all the cotton required?

7. The wages of mechanics in Massachusetts are now (1886) about 25% higher than in 1860, and the prices of things are on an average about 20% lower. If a mechanic now receives $90 per month, how much money could he save in a year, supposing that he saved nothing in 1860, and that he has the same standard of living now as then, with no additional expenses?

8. When water is heated from the freezing-point to the boiling-point it expands in volume. If a cubic foot of water at the freezing-point weigh 621 lbs., what will a cubic foot of boiling water weigh?

9. A merchant imports to New York goods which cost him £616 sterling in London. He pays an ad valorem duty of 12% on the goods, and a commission of 7% to agents for selling them. The goods realize $7800. What is the merchant's net gain, the pound sterling being equal to $4.86?

10. A circular plate of lead 8 in. diameter and 2 in. thick is converted without loss into spherical shot each 0.05 in. radius. How many shot does it make?

11. A tailor buys 38 yds. of cloth at $2.45 per yard. Sponging causes a shrinkage of 4%. What must be his selling price in order that he may gain 10%?

12. Two men perform a piece of work in 18 dys., and receive for it $189. One of the men was absent 5 dys. What amount of money should each man receive?

13. Six men undertake to do a piece of work in 15 dys. They work 10 hrs. a day, but at the end of 8 dys. they find that only half of the work is accomplished. How many hours a day must they work during the remaining time in order to finish the work in the time agreed upon?

14. A wine merchant imported 1315 gals. of wine at a cost of $3.33 per gallon. After adding water in the ratio. of a quart of water to each gallon of wine, he bottled the wine in bottles costing 5 cents each and holding a pint and a half. At what price per bottle must he sell the wine in order to make 50% profit on his money?

15. Five men have performed a piece of work in 20 dys., and have received for it $521.50. One of the men was absent 5 dys., and another was absent 2 dys. Another man receives 50 cents a day extra for directing the work. What should each man receive?

16. A milliner bought 275 bonnets at $14.40 apiece. She sold of them at 15% advance, and the rest at $13.75 each. What did she make by the transaction?

17. Hay costs $22 per ton, and oats cost 80 cents per bushel. If 1 horse eat daily 20 lbs. of hay and 8 qts. of oats, what will it cost to feed 10 horses from Dec. 1, 1889, to Mar. 31, 1890, both dates included?

18. A boy sells paper at 20 cents a quire, and 6 pens for 5 cents. The paper costs him $3.25 per ream of 20 quires, and the pens cost $1.10 per box containing 18 doz. What is his profit in selling 80 reams of paper and 30 boxes of pens?

19. An ore contains 18% of pure lead, but 14% of this lead is lost in reducing the ore. What weight of ore must be treated in order to obtain 1 t. of pure lead?

20. A hall is lighted by 58 gas-jets every evening except Sunday from 5.45 P.M. to midnight; each jet burns 6 cu. ft. per hour. The price of the gas is $1.25 per 1000 cu. ft. Find the cost of lighting the hall for the month of January, if the month begins on Friday.

21. From a pipe full of wine of the contents are drawn away, and then 35 gals. are added. The pipe is then just half full. How many gallons will it hold?

22. If a wheel revolves 91 times in 33 sec., times will it revolve in 5 hrs.?

how many

23. If ₫ of a yard of velvet cost $3, what will 1⁄2 of a yard cost?

24. A locomotive travels of a certain distance in 3 hrs. In how many hours will it travel at the same rate of the same distance?