48. Density.—The density of a substance is often used as a test of its purity. Archimedes in testing King Hiero's crown to find out if it were made of pure gold determined first its density. It is by such tests that the purity of milk, of alcohol, of gold, and a great variety of substances is often determined.
Knowledge of methods of finding density is of value to everyone and should be included in the education of every student. The density of a substance is the mass of unit volume of the substance. In the metric system, for example, the density of a substance is the mass in grams per 1 ccm. Taking water, 1 ccm. weighs 1 gr. or its density is therefore 1 g. to the cubic centimeter. A cubic centimeter of aluminium weighs 2.7 g. Its density therefore is 2.7 g. per ccm.
49. Specific Gravity.—Specific gravity is the ratio of the weight of any volume of a substance to the weight of an equal volume of water. Its meaning is not quite the same as that of density, since specific gravity is always a ratio, i.e., an abstract number, as 2.7. Density of a substance is a concrete number, as 2.7 grams per ccm. In the metric system the density of water is one gram per cubic centimeter, therefore we have:
Density (g. per ccm.) = (numerically) specific gravity.
In the English system, the density of water is 62.4 pounds per cubic foot, therefore in this system we have:
Density (lbs. per cu. ft.) = (numerically) 62.4 × sp. gr.
50. Methods for Finding Density and Specific Gravity
(a) Regular Solids.—Solids of regular shapes such as cubes, spheres, etc., whose volumes may be readily found by measurement, may be weighed. The mass divided by the volume gives the density, or D = Mμ/v.
(b) Irregular Solids.—with these the volume cannot be found by measurement but may be obtained by Archimedes' Principle. Weigh the solid first in the air and then in water. The apparent loss of weight equals the weight of the equal volume of water displaced. From this the volume may be found. And then the density equals mass/volume; the specific gravity =