Densities and Specific Gravities

DEFINITION 1. - The density⁽¹⁾ of a substance at any temperature is the mass of a unit of volume of the substance at that temperature; thus the density of water at 4° C. is one gramme per cubic centimetre.

DEFINITION 2. - The specific gravity⁽¹⁾ of a substance at any temperature is the ratio of its density at that temperature to the density of some standard substance, generally the maximum density of water (i.e. the density of water at 4° C.).

DEFINITION 3. - The specific gravity of a body is the ratio of the mass of the body to the mass of an equal volume of some standard substance, generally water at 4° C.

It evidently follows from these definitions that, if ρ be the density of a substance, σ its specific gravity, and ω the maximum density of water, ρ=σω, and if M be the mass of a body consisting of the substance, whose volume is V, then M=Vρ=Vσω, and the mass of a volume of water equal to the volume of the body = Vω. The maximum density of water is 1 gramme per cubic centimetre. If we use the gramme as the unit of mass, and the cubic centimetre as the unit of volume, the numerical value of ω is unity and the equations we have written become ρ=σ and M=Vσ. Thus, the numerical value of the density of a substance on the C.G.S. system of units is the same as the number which expresses the specific gravity of the substance, this latter being of course a ratio, and therefore independent of units. And for the C.G.S. system of units, moreover, the numerical value of the mass of a body is equal to the number which expresses its volume multiplied by its specific gravity.

These relations are only true for the C.G.S. system, and any other systems in which the unit of mass is the mass of the unit of volume of water at 4° C.; but whatever be the system, the density of water at 4° C. is accurately known, although its numerical value may not be unity. Hence, in order to calculate the volume of a body whose mass is known, or vice versa, we require only to know its specific gravity, and hence the practical importance of determinations of specific gravity. It is generally an easy matter to determine experimentally the ratio of the mass of a body to the mass of an equal volume of water at the same temperature, but it would not be easy or convenient always to keep the water at its temperature of maximum density, throughout the experiment. The densities of bodies are therefore not usually experimentally compared directly with the maximum density of water in determining specific gravities, and the necessity for doing so is obviated by our knowing with great accuracy the density of water at different temperatures, (this is given in table 32); so that we are enabled, when we know the mass of a volume of water at any temperature, to calculate from the table the mass of the same volume at 4° C., and thus obtain the specific gravity required. We proceed to describe some of the practical methods in general use.

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It is unfortunate that in many physical text-books the terms "density" and "specific gravity" are used synonymously, the former being generally employed for gases and liquids, the latter for solids. It is quite evident that there are two very distinct ideas to be represented, namely (1) the mass of the unit of volume, a quantity whose liumerical value depends of course on the units chosen for measuring masses and volumes; and (2) the ratio of the mass of any volume to the mass of an equal volume of water at 4° C.; this quantity being a ratio, is altogether independent of units. There being now also two names, "density" and "specific gravity", it seems reasonable to assign the one name to the one idea and the other name to the other idea, as suggested by Maxwell, "Theory of Heat" (ed. 1872, p. 82). When there is no danger of confusion arising from using the term density when specific gravity is meant, there may be no harm in doing so, but beginners should be careful to use the two words strictly in the senses here defined.