5. A ton of stone measures 13 cubic feet; what is the weight in kilogrammes of a cubic metre of the stone?

6. Reduce pound per cubic foot to gramme per cubic centimetre.

7. The density of water is 62.4 lb. per cubic foot; what is its bulkiness?

8. How many cubic feet of coal must be taken by a steamer going on a ten days' voyage, having engines of 1,000 horse-power? Rate of consumption of coal is 7 lbs. per horse-power per hour, and the bulkiness of the coal is 40 cubic feet per ton.

9. The density of granite is 160 lbs. per cubic foot; a paving block is 4 inch wide by 9 inch deep by 12 inch long. Find the number of tons required to pave a street one mile long and 20 yards broad, allowing an interval of ten per cent. between the blocks.

10. The average density of gunpowder is 5268 oz. per cubic inch; find the amount required to fill a boring of 14 inch diameter and one yard long.

11. The density of water is 036 lb. per cubic inch; express it in terms of per cubic foot, and of lb. per square inch per foot.

ton

12. Given that the density of iron rail is 10'08 lb. per yard per square inch; find the mass required for 100 miles when the section of the rail is 6 square inches.

13. The population of Great Britain in 1881 was 35,262,762, and the area is 120,830 square miles; what is the average density of the population?

14. Given that the line density of a round bar of cast iron is 2:45 lb. per foot per inch diam. square, what is the weight of a pipe 2 yards long, having a bore of 16 inches, and a thickness of inch?

15. A flat bar of iron, 4 inch broad, and § of an inch thick, has a linear density 9·91 lb. per foot; deduce the value of lb. per inch broad per eighth-inch thick per foot long.

16. The line-density of steel wire of 23 inch circumference is 4 lb. per fathom; what is the line-density of wire of the same material 23 inch in circumference?

17. Express the density of wrought iron in the form of, first, lbs. per square foot per inch thick; second, lbs. per linear yard per square inch section; third, lbs. per foot run per inch diameter square.

18. Given 10'6 bricks per square foot surface per brick thick; find the superficial area given by 10,000 bricks in a wall 2 bricks thick.

19. Transform the density of water given as 62 425 lbs. per cubic foot into the form suitable for calculations of rainfall, namely, pound per square mile per inch of rainfall, and pound per acre per inch of rainfall.

20. A cubic foot of copper, weighing 560 lbs., is rolled into a square bar 40 feet long. An exact cube is cut from the bar, what is its mass to four decimals of a pound?

21. Find the mass of zinc required to cover a rectangular roof 30 feet long by 20 feet broad, having a slope of 3 to 1, the superficial density of the covering being 7 cwt. per 100 square feet.

SECTION XXIV.-SPECIFIC MASS.

ART. 133.-Relative Density. Let the densities of two substances A and B be

and

We deduce

or

m M of A = V,

n M of B = V.

m M of A = n M of B, m/n M of Д = M of B.

This rate expresses the density of A relatively to that of B, or the number of units of mass of A which are equivalent in volume to one unit of mass of B.

Different substances may thus be compared with one standard substance. Solids and liquids are compared with water; gases with air or with hydrogen.

Equivalences are of two kinds-absolute and relative. Density is an example of the former kind, and relative density of the latter kind.

ART. 134.-Specific Mass and Specific Gravity. The density of a substance relatively to that of a standard substance is properly called Specific Mass. It is usually called Specific Gravity, as a consequence of not distinguishing weight from mass. These ideas are different; their numerical values, however, are the same, because the weight of a body is proportional to its mass, and is independent of its physical constitution.

By taking the reciprocals

Woods.

Alloys.

Solid Metals.

we deduce

1/m V of AM,

1/n V of BM,

n/m ▼ of A = V of B.

This expresses the relative bulkiness which is the reciprocal of the relative density.

Ex. 1. A cubic foot of fresh water weighs 62.4 lbs., find in cubic feet the space occupied by one ton of sea water.

62.4 lbs. of fresh water cubic foot,

1.026 lbs. of salt water

= lb. of fresh water,

Ex. 2. Sodium has to alcohol the relative density 1.23, and alcohol has to water the relative density 79; what is the density of sodium relatively to water?

Observation-In order that two relative equivalences may be combined in this manner, they must of course be equivalences in the same respect; and the conclusion is an equivalence in the same respect.

Ex. 3. Eleven cubic inches of iron weigh as much as seven cubic inches of lead, and the price per ton of lead is £15, of iron £4. The value of a certain block of lead is 367. 17s. 11d., what would be the value of a block of iron of the same size?

Ex. 4. The specific gravity of gold is 19.3, that of silver is 10.4. What is the composition of an alloy of gold and silver whose specific gravity is 17.6, no change of volume being supposed to accompany the combination of the metals ?

Let the composition by volume of the alloy be

a V gold + b V silver = a + b V alloy,

19.3 M per V, 10.4 M per V;

therefore the composition by mass is

19.3 a M gold + 10·4 6 M silver = 19·3 a + 10·4 b M alloy. Hence the density of the alloy is