22. A hip has the bottom 2 ft. 6 in. square, the top 3 ft. 6 in. square, the height 2 ft. 6 in.; what is the cost of lining it with zinc at 20 per sq. ft.? How many bu. will it hold? Ans. $7.37; 18.24 bu.

23. How many cu. ft. in a telegraph pole 40 ft. long, 18 in. in diameter at the base, and 8 in. in diameter at top? Ans. 38.6883 cu. ft. 24. How much map-surface on a school globe 12 inches in diame ter; and how many cubic inches of material are there in it, if it is a hollow sphere 1 in. thick? Ans. 452.3904 sq. in.; 381.1808 cu. in. 25. A room 24 ft. 6 in. long, 13 ft. 4 in. wide, is flooded with water 8 in. deep; what is the weight of the water? Ans. 5104 lb.

26. A circular room, of which the diameter is 25 ft., and height of wall 14 ft., is covered with a hemispherical dome, what is the cost of plastering the wall and dome at 254 per sq. ft.? Ans. $520.323. 27. How many dozen boxes of perfumery, 2 in. on each side, can be packed in a rectangular box whose dimensions are respectively 1 ft. 6 in., 1 ft., and 8 in.? Ans. 18 doz. 28. A cubic inch of gold is hammered out to cover a square (10C sq. ft.); what is its thickness? Ans. .000069 inch.

29. An ice house is 40 ft. long, 30 ft. wide, and 20 ft. deep; what area of ice 6 in. thick, will be required from a pond to fill it? What would it weigh at 56 lb. the cu. ft.? Ans. 48000 sq. ft.; 1344000 lb.

30. A company wish to excavate a canal 25 miles long, with an average width of 9 yards, and an average depth of 5 ft. 6 in.; how long will it take 500 men to do the work, if each man averages 12 cubic yards a day? Ans, 121 days.

31. If the men are paid $1.50 each per day, and the contractor estimates 5% profit, what proposal will he make for digging the above canal? Ans. $95287.50.

32. If 50 cubic feet of air are required per person in a well-ventilated room, how many persons can safely remain in a room 60 ft. long, 40 ft. wide, and 12 ft. high? Ans. 576 persons.

33. The cost of a cube of metal, at $12 per cubic inch, is $4116; find the cost of gilding it over at 24 per square inch.

Ans. $5.88.

34. A cast-iron garden roller is 40 in. long, 22 in. in diameter, and the iron is in. thick; required its weight, if a cubic inch of iron weighs 4 ounces. Ans. 576.5321 lb.

35. If a cannon ball, 6 in. in diameter, is melted and cast in a con cal mould 6 in. in diameter at the base, what is the length of the cone ? Ans. 12 in.

36. A railroad embankment has an average depth, for 5 miles, of 12 feet, width at top 8 yards, and at bottom 12 yards; what was the cost of carting at 150 per load (cu. yd.) ? Ans. $52800

APPENDIX.

THE METRIC SYSTEM

OF WEIGHTS AND MEASURES.

NOTE TO TEACHER-The Metric System may be omitted by classes whose time for arithmetic is limited, at the option of the teacher.

INTRODUCTION.

THE old system of weights and measures in our country is irregular, difficult to learn, and inconvenient to apply. The same is true with the old systems of all nations. Originating by chance, rather than by science, they lacked the simplicity of law; and were, therefore, irregular and chaotic.

In 1795, France adopted a system of weights and measures called the Metric System, based upon the decimal method of notation, all the divisions and multiples being by 10. It was regarded as so great an improvement upon the old methods that it has since been introduced into Spain, Belgium, Portugal, Switzerland, Holland, Italy, Germany, Austria, Sweden, Denmark, Greece, Mexico, Brazil, and by most of the South American States, and in the most of these countries its use is compulsory. In 1864, the British Parliament passed an act permitting its use throughout the empire whenever parties should agree to use it.

The introduction of the Metric System into this country had been long recommended by scientific men, and by such statesman as Madison, Jefferson, John Quincy Adams, etc. In 1866, through the influence of Charles Sumner, Congress authorized its use in the United States, and provided for its introduction into the post-offices for the weighing of letters and papers. To facilitate its adoption, a convenient standard of comparison was furnished, by making the new five-cent piece five grams in weight and one fiftieth of a meter, or two centimeters, in diameter. This system will, without doubt, in a few years be in general use in this country.

The advantages of the Metric System are numerous and important. 1. It is easily learned; a school-boy can learn it in a single afternoon. 2. It is easily applied, all the operations being the same as in simple numbers.

3. It does away with addition, subtraction, multiplication, division, and reduction of compound numbers.

4. It will facilitate commerce, giving the nations a universal system of weights and measures.

785. The Metric System of weights and measures is based upon the decimal system of notation.

786. In this system we first establish the unit of each measure, and then derive the other denominations by taking decimal multiples and divisions of the unit.

787. Names.- We first name the unit of any measure and then derive the other denominations by adding prefixes to the unit name.

788. The higher denominations are expressed by prefixing to the name of the unit

The lower denominations are expressed by prefixing to the name of unit

789. Units.-The following are the different units, with

790. The Meter is the unit of length. It is the ten millionth part of the distance from the equator to the poles, and equals 39.37 inches, or 3.28 feet.

TABLE.

10 millimeters (mm.) equal 1 centimeter,

cm.

NOTES.-1. The meer is very nearly 3 feet 3 inches and 3 eighths of an Inch in length, which may be easily remembered as the rule of three threes. 2. Cloth, etc., are measured by the meter; very small distances, by the millimeter; great distances, by the kilometer.

3. The 5-cent piece of 1866 is very nearly of a meter in diameter; hence its diameter is about of a decimeter, or 2 centimeters. It was ordered to be of a meter in diameter, but owing to the composition of the alloy it was necessary to make its diameter a little greater; 48.6 nickel 5-cent pieces laid side by side measure one meter.

4. A decimeter is about 4 inches: a kilometer, about 200 rods, or § of a mile; a millimeter, about of an inch. The inch is about 24 centimeters; the foot, 8 decimeters; the rod, 5 meters; the mile, 1600 meters, or 16 hectometers.

MENTAL EXERCISES.

1. How many centimeters in a meter? 2. How many millimeters in a meter?

3. How many decimeters in a decameter? 4. How many meters in a hectometer?

5. How many meters in a kilometer?

MEASURES OF SURFACE.

791. The Are is the unit of surface used to measure land. The are is a square decameter. It equals 119.6 sq.

yd., or 0.0247 acre.

TABLE.

10 milliares (ma.) equal 1 centiare, ca.

NOTES.-1. The are, centiure, and hectare, are the denominations princi cipally used, as these are exact squares. The centiare is a square whose side is 1 meter; the hectare is a square whose side is 100 meters.

The are 100 square meters. The centiare = 1 square meter,

The hectare

10,000 square meters.

2. The deciare is not a square, it is merely the tenth of an are; the decar not a square, it is merely ten ares.

3. A hectare equals nearly 2 acres; a centiare equals nearly 1f sq. yd. An acre is very nearly 40 ares.

MEASURES OF OTHER SURFACES.

792. All surfaces besides land are measured by the ¿quare meter, square decimeter, etc. The measures are shown by the following table:

TABLE.

100 sq. millimeters (mm.2) = 1 sq. centimeter, cm.

100 sq. centimeters

100 sq. decimeters

=

1 sq. meter,

M.2 NOTE.-TLe measures higher than these are not generally used. The usual method of notation is to write aq. before the denomination; but I suggest as an abbreviation that we indicate the square by an exponent.

MENTAL EXERCISES.

1. How many centiares in an are?

2. How many ares in a hectare?

3. How many square meters in an are?
4. How many square decimeters in an are?
5. How many ares in 640 square meters?

MEASURES OF VOLUME.

793. The Stere is the unit of volume. It is a cubis meter, and equals 35.3166 cubic ft., or 1.308 cu. yd.

NOTE.-Wood is measured by this measure. The stere, decistere, and lecastere are principally used. 3.6 steres, or 36 decisteres, very nearly equal the common cord.

MEASURES OF OTHER VOLUMES.

794. Other solid bodies are usually measured by the cubic meter and its divisions. The measures are shown by the following table:

TABLE.

=

1000 cubic millimeters (mm.3) 1 cubic centimeter, cm. 8

1000 cubic centimeters

1000 cubic decimeters

=1 cubic decimeter, dm. =1 cubic meter,

M.*