EXAMPLES.

CHAPTER I.

GENERAL MEASURES.

(See Sects. (7), (8), (9), Table II.)

1. A CISTERN is 2 metres long, 1.5 m. wide and 1 m. deep; how many litres of water will it contain?

2. How many pounds Troy are there in a kilogram? 3. If the value of g (the attractive force of gravity) at London is 32.1908 feet, what is it in metres?

4. It is 92000000 miles to the sun; how many kilometres is it?

5. Light travels 192000 miles a second; how many kilometres per second is that?

6. Sound travels 1130 feet in a second; how many metres per second is that?

7. Find the mass of a block of flint glass (A 3·5) 10 centimetres long and wide, and 2.857143 c.m. thick.

8. A block of steel (A 7·8) is 10 c.m. square and 1·8315 c.m. thick; find its mass.

9. Find the mass in tons of a ship which displaces 64240 cubic feet of sea-water (A 1·026).

10. The velocity of light is 3.004 × 108 metres per second, and it takes 8 minutes 13 seconds to pass from the sun to the earth. How many miles is the sun distant from the earth?

11. The latitude of Greenwich is 51° 28′ 40′′. Express this angle in seconds, and in degrees and decimals of a degree.

12. A geographical mile or knot is the distance subtended at the equator by an angle of l' at the centre of the earth. How many knots is it round the equator?

13. According to Bessel the polar radius of the earth is 20853657 feet, and the equatorial radius 20923600 feet. How many geographical miles in length is the great circle passing through the poles and Greenwich?

14. Using the data of the last question, find the volume of the earth in cubic feet, and if the density be 5.67 its mass in pounds.

15. A pressure of 1000 lbs. per square inch is how many kilos. per square millimetre ?

16.

(A 5-25)?

17.

(A 1·02) ?

What is the mass of a cubic metre of hematite

What is the mass of a cubic kilometre of sea-water

18. A nautical fathom is 6·0864 feet, what is its value in metres?

19. A piece of porcelain (A 2.3) is 10 c.m. square and 8.696 c.m. thick; find its mass in grams.

20. A round dolomite pillar (A 2.9) 1 m. across aud 10 m. high weighs how many kilograms?

21. Find the volume of 1000 grams of sea water (A 1.026).

22.

Find the mass of a cubic metre of anthracite (A1·4).

Find the mass of a glass (A 2·45) cylinder 2 decimetres high and 1 d.m. across.

23.

24. How many tons does a block of granite (A 2·7) 10 by 3 by 2 metres weigh?

25. The great pyramid (A 2·5) is 145 m. high, and the side of its square base is 658.3 m.; find its mass in tonnes. The surface of a sphere is 480 square yards; find its volume in cubic feet.

26.

27. A glass ball, weighing 7.7158 grams, 2 c.m. in diameter, just floats in a liquid. Find the density of the liquid.

28. A quantity of silver when placed in one pan of an untrue balance weighed 5 grams, but when placed in the other pan it weighed 6 grams. Find the true mass of the silver.

29.

The value found by Joule for the mechanical equivalent of heat was 772 foot-lbs. per 1° F. What is the value of J., taking as units 1° C., the kilogram, and the metre?

30. A glass ball counterpoised in air appeared to lose 5.6 grams when plunged into water, and 5·09 grams when plunged into turpentine. A crystal of copper sulphate, which weighed 11.69 grams in air, when plunged into turpentine appeared to lose 4.63 grams. Find the density of the turpentine and of the copper sulphate.

31.

When the mercury (A 13-596) barometer stands at 76 c.m., how high will one of glycerin (A 1-27) stand?

32. When the mercury (A 13.596) barometer stands at 760 m.m., how high would one of hydrogen sulphate (A 1.842) stand?

CHAPTER II.

MOLECULAR WEIGHTS.

(See Sect. 10.)

1. FIND the molecular weight of (i) carbon monoxide CO, (ii) magnesia MgO, (iii) lime CaO, (iv) silica SiO,, (v) alumina Al,O

2. Find the percentage of oxygen in each of the abovementioned bodies.

3. Find the molecular weight of (i) nitric oxide NO, (ii) sodium hydrate HNaO, (iii) ferric oxide Fe̟O̟„, (iv) chromium trioxide CrO,, (v) cadmium oxide CdO.

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4. Find the molecular weight of (i) antimony pentoxide Sb,O,, (ii) silver arsenate Ag,AsO,, (iii) barium sulphate BaSO, (iv) lead nitrate Pb2NO,, (v) potassium phosphate KPO

5. Find the molecular weight of (i) zinc sulphate ZnSO,. 7H2O, (ii) copper sulphate CuSO,. 5H,O, (iii) sodium sulphate Na,SO. 10H,O, (iv) nickel sulphate NiSO,. 7H,O, (v) manganous sulphate MnSO,. 4H2O.

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6. Find the molecular weight of (i) alcohol CHO, (ii) ether CH,,O, (iii) hydrogen acetate C,H,O,, (iv) hydrogen oxalate CH2O. 2H2O, (v) hydrogen tartrate CHO.

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7. Find the molecular weight of (i) glycerin C,H,O,, (ii) turpentine C10H16, (iii) aniline CH,N, (iv) hydrogen stearate CHO,, (v) cane-sugar C12H,,O,

18 36

12 22 11°

8. Find the molecular weight of (i) potassium chlorate KC1O,, (ii) borax Na BO,. 10H ̧0, (iii) strontium bromide SrBr.. 6H,0, (iv) barium carbonate BaCO,, (v) potassium dichromate K.Cr.O,

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9. Find the molecular weight of (i) potassium ferrocyanide K,FeC.N.. 3H,O, (ii) calcium fluosilicate CaSiF, (iii) sodium thiosulphate Na,S,O̟ ̧.5H ̧O, (iv) microcosmic salt NaNHHPО. 4H2O, (v) sodium nitroprusside Na FeCoNo (NO2), . 4H ̧0.

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