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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 =

wt. in air / wt. of equal volume of water = wt. in air / ((wt. in air) - (wt. in water))

(c) Solids Lighter than Water.—This will require a sinker to hold the body under water. Weigh the solid in air (w). Weigh the sinker in water (s). Attach the sinker to the solid and weigh both in water (w´). The specific gravity equals

(wt. of solid in air)/(loss in wt. of solid in water) or w/((w + s) - w´)

The apparent loss of weight of the solid is equal to the sum of its weight in air plus the weight of the sinker in water, less the combined weight of both in water.

(d) The Density of a Liquid by a Hydrometer.—One may also easily find the density of any liquid by Archimedes' Principle. If one takes the rod described in Art. 46, and places it in water, the number of cubic centimeters of water it displaces indicates its weight in grams. On placing the rod in another liquid in which it floats, it will of course displace its own weight and the height to which the liquid rises on the scale gives the volume. By dividing the weight of the rod as shown by its position in water by the volume of the liquid displaced we obtain the density of the liquid. Commercial hydrometers for testing the density of milk, alcohol and other liquids are made of glass of the form shown in Fig. 28. The long narrow stem permits small differences in volume to be noticed, hence they are more accurate than the rod described in the preceding paragraph. For convenience this rod contains a paper scale, so that when the height of the liquid on the stem is noted, the density is read at once.