NOTE. These tables are given for reference, and are not to be committed to memory. It may be well, however, to remember that a meter is 39.37 in.; a liter is 1.0567 liquid qt., or 0.908 dry qt.; and that a gram is 15.432 gr.; as by these equivalents all measures expressed in one system may be converted into the corresponding measures of the other system.

EXERCISE 97.

In the following problems take the equivalents from the Table of Equivalents, using three places of decimals, or four when the first decimal figure is zero, and add one to the last decimal figure when the next is 5 or more.

1. Reduce 25.55kg to pounds avoirdupois.

SOLUTION. Since 1kg = 2.205 lb., 25.55kg = 25.55 × 2.205 lb., or 56.33775 lb., that is, 56 lb. 5.4 oz.

2. Reduce 5 sq. yd. 6 sq. ft. 108 sq. in. to square meters. SOLUTION. 5 sq. yd. 6 sq. ft. 108 sq. in.

=

= 5.75 sq. yd. Since

1 sq. yd. = 0.836am, 5.75 sq. yd. = 5.75 × 0.8364m; that, is 4.807am.

3. Reduce 24 gal. to liters.

4. Reduce 10 lb. troy to kilograms.

5. Reduce 50.5 cu. yd. to cubic meters.

6.

7.

Reduce 12 A. 12 rd. to hektars.

8. Reduce 10 cd. to sters.

9. Reduce 4 cwt. 24 lb. to kilograms. 10. Reduce 25 bu. 2 pk. to hektoliters. 11. Express 15km in the common system. 12. Express 3ha in the common system. 13. Express 12.125cbm in the common system. 14. Express 101.251 in the common system. 15. Reduce 20.25h to liquid quarts; to dry quarts. 16. Express 5kg in troy weight.

17. Express 24st in the common system.

18. Express 62.54m in the common system.

19. Express 1001kg in avoirdupois weight.

20. Express 42 A. 100 sq. rd. in the metric system. 21. Find in acres, etc., the area of a rectangular field if it is 100m long and 75m broad.

22. Find the number of cubic meters in a rectangular box 2 yd. long, 3 ft. wide, and 21 ft. deep.

23. Find the number of cubic yards in a rectangular box 2m long, 75cm wide, and 50cm deep.

24. If a man walks 75m a minute, what is his rate in miles per hour?

25. If a cubic centimeter of cast iron weighs 7.1138, how many pounds does a cubic foot weigh?

26. How many steps 2 ft. 6 in. long will a man take in walking a kilometer?

27. Find the value of a carboy (17 qt.) of sulphuric acid, specific gravity 1.841, at 43 cents a kilogram.

28. Find the value of a carboy (171) of nitric acid, specific gravity 1.451, at 15 cents a pound.

29. If the specific gravity of sea water is 1.026, and that of olive oil is 0.915, what is the weight of a hektoliter of each in pounds and in kilograms?

30. Find the weight in pounds and in kilograms of 31 gal. of the best alcohol, specific gravity 0.792.

31. Find the weight in pounds and in kilograms of the air, specific gravity 0.00129206, in a room 7m long, 5m wide, and 3.5m high.

32. Find the weight in pounds and in kilograms of the air, specific gravity 0.00129206, in a room 23 ft. long, 16 ft. wide, and 10 ft. high.

33. What is the lifting force in kilograms and in pounds of a balloon that weighs 2kg, and contains 10,0001 of hydrogen gas, specific gravity 0.00008929 ?

NOTE. The lifting force is the weight of the air displaced by the balloon diminished by the weight of the hydrogen and the balloon.

34. What is the value at $4.50 a cord of a pile of wood 1.2m wide, 7m long, and 2m high?

35. How many miles will a train run in 1 hr. 28 min. at the rate of 50km an hour?

21 sec.,

36. Find the time it takes a train to run 31 mi. 180 yd. at the rate of 1 min. 25 sec. per kilometer.

37. What is the weight of 12 cu. yd. 16 cu. ft. 720 cu. in. of earth, .if a cubic meter weighs 1 t. 17 cwt.?

38. Find the weight in grams of a liter of mercury, if a cubic inch weighs 0.4925 of a pound avoirdupois.

39. How many yards of cloth, at $3.12 a meter, should be given in exchange for 15m at $2.75 a yard?

40. If a wine merchant buys 3h of wine for 1600 francs, what does a gallon cost him in United States money, if 25 francs are equivalent to $4.825?

41. A mill wheel is turned by a stream of water running at the rate of a yard a second in a channel 5 ft. wide and 9 in. deep. Find the weight in metric tons and in tons avoirdupois of the water supplied in 12 hr., if a cubic foot of water weighs 1000 oz.

EXERCISE 98.

In the following problems take the equivalents from the Table of Approximate Equivalents,

1

24

1. When water is heated from the freezing point to the boiling point it expands in volume. Find in kilograms the weight of a cubic foot of water at the freezing point and at the boiling point.

2. A circular plate of lead 8 in. in diameter and 2 in. thick is changed without loss into spherical shot each 1.25mm in radius. How many shot does it make ?

3. If of a yard of velvet costs $3, how many francs will of a meter cost?

4. Water expands in freezing, and a floating body displaces an amount of water equal in weight to the body. What is the volume in cubic meters and the weight in metric tons of an iceberg floating in the ocean, if the specific gravity of sea water is 1.026, and the part of the iceberg above the water is a rectangular solid 200 ft. long, 60 ft. wide, and 12 ft. high?

5. How many hektoliters of wheat will a rectangular bin hold 14 ft. long, 10 ft. wide, and 6 ft. high?

6. How many hektoliters of water will a cylindrical stand-pipe hold 70 ft. high and 35 ft. in diameter?

7. How many bushels of wheat will a rectangular bin hold 4m long, 3m wide, and 2.5m high?

8. How many gallons of water in a well 1.2m in diameter, if the depth of the water is 2m?

9. If 1 lb. troy of silver is worth $6.20, what is the value of a lump of silver weighing 2.64kg?

10. A pound of brass contains 3.3 cu. in., and a pound of antimony contains 6.27 cu. in. Find the weight in kilograms of a mass of 313 cu. in. that contains equal volumes of the two metals.