ART. 129.—British Units. The British unit commonly used is pound per cubic foot. The value one pound per cubic foot does not express the density of any substance, because the pound was not defined directly by the cubic foot and a standard substance. The pound, however, originally had a relation to the density of water; for, taking the ounce its sixteenth part, the density of water is very approximately

which gives

1000 oz. per cubic foot,

62.5 lb. per cubic foot.

The true value for the temperature of maximum density is 62.425 lbs. per cubic foot.

ART. 130.-Metric Units. In the case of the metric units, 1,000,000 grammes per cubic metre expresses the density of water, the million being introduced because the kilogramme was defined by the cubic decimetre. Thus 1 gramme per cubic centimetre expresses the density of water, and this is the unit in terms of which density is expressed in the C.G.S. system.

The density of pure water at 4°C. is, more exactly, 1·000013 gm. per cc. (See Art. 151.)

ART. 131.-Surface-density; Line-density. Suppose that a body has a uniform density throughout p M = L3. For a rectangular parallelepiped (Art. 93)

1 L3 L long by L broad by L thick ;

=

therefore, for any parallepiped within the body,

P M = L long by L broad by L thick.

If the body exist in the form of a plate of uniform thickness, then 1 L3 L2 surface by L thick;

and ..

or

=

Suppose that the thickness is d L, then the density is

dp M per L2 surface.

This is called surface-density, and the letter used to denote its general value is σ.

If the body exist in the form of a rod or wire of uniform crosssection, then

1 L3 L2 cross-section by L long,

=

and ... ρ M per L long = L2 cross-section.

The value of the cross-section gives the value of the line-density. Let it be a L2, then

ap M per L long.

A letter sometimes used to denote the general value of M per L long is λ.

ART. 132.-Rainfall. In the case of rainfall we have to consider a horizontal sheet of water. The density of water is

By a number of inches of rainfall is meant the number of inches of depth. An inch of depth is equivalent to 5.2 lbs. of water per foot of horizontal surface.

square

EXAMPLES.

Ex. 1. A cistern is 4 by 31 by 23 ft. What weight of water at 62 lbs. per cubic ft. can it hold?

Ex. 2. Gold can be beaten out to leaf of the thickness of 1/3800 mm.; platinum can be made into wire 1/20000 mm. thick. What is the surface-density of the gold leaf, and the line-density of the platinum wire.

1. A cubic foot of water weighs 1,000 oz. avoirdupois; required the relation of the kilogramme to the hundredweight.

2. A town of 241,000 inhabitants is supplied with water at the rate of 25 gallons per head per day; find the total supply both in volume and in mass for one year. 3. If the mass of a cubic inch of water be 252.5 grains, find the number of cubic inches in a ton of water.

4. The density of granite is 42 cwt. per cubic yard; what is it in lb. per cubic foot?

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 ton per cubic foot, and of lb. per square inch per foot.

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 106 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

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.

For example,

11.4 M of lead

M of water,

13.596 M of mercury = M of water,

15.96 M of oxygen M of 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