also relative density, relative mass density
The dimensionless ratio of the mass of a volume of an object substance to the mass of the same volume of a reference substance, i.e. the ratio of their respective mass densities. Usually the reference substance is water at its densest (close to 4°C) with the object substance being measured at 20°C, but dry air at
In addition to the simple numeric ratio, various scales have been adopted for the expression of relative volumic mass, often to express it in a manner more easily converted to some consequent use but just as often in a manner whose only convenience seems to be the construction of the instrument.
[ISO 649-1 and -2:1981 Laboratory Glassware - Density Hydrometers for General Purposes] Many are utterly arbitrary from a user's viewpoint. Most of them are expressed as degrees, including using the familiar ° symbol. Thus any measurement in such a generic unit is meaningless unless qualified as to the scale employed, though there is some favour for its general use meaning 100 times the relative volumic mass (with a better symbol than ° or degree to signify it).
The measurement of aqueous solutions and mixtures has a long history relative to the taxation of alcoholic drinks, the distinct difference in the relative densities of water and alcohol providing a ready means for assessment of alcoholic content in a beverage. More subtly, the measurement of the relative volumic mass of the mash from which a beer is made provided a fair indication of its alcohol potential, while the difference between readings at the start and end of brewing translated well into alcohol content. (The retention of solids precludes a simpler measurement.) This last, dealing with solutions denser than water, was the pioneering area of such densitometry.
An aqueous solution of sugar may have a relative volumic mass close to 1.5 (1 L can contain over 1.3 kg of dissolved sugar). Typical brewing mashes start around 1.05 to 1.09, and are stopped 0.02 to 0.05 lower. Interestingly, the drop in value multiplied by a hundred is close to the resulting percentage alcohol content by volume. That percentage is wanted to one decimal place, so the relative volumic mass is taken to three places. The term degree of gravity is used for the specific gravity (i.e. relative volumic mass) difference multiplied by one thousand, either the difference from 1 for a mash or other solution (i.e. 55° means a relative volumic mass of 1.055) or a drop (e.g. 55° when from 1.085 to 1.030). Divided by 3.86, the degree of gravity gives a measure of percentage solids by mass. The Brix scale is just such measure, specifically the percentage by mass of sucrose in water solution, at 17.5°C.
For sugar solutions more generally, and similar denser-than-water solutions, the Twaddell scale measures specific gravity by degrees that equal a half percentage point relative to water at its densest (4°C), e.g. 1.12 becomes 24°Tw. The twin Baumé scales provide for unlimited application, with arbitrary values escalating by about 1 per step of 0.07 away from the reference value of 1 in specific gravity, from 0° Baumé in the heavier scale, and from 10° for the lesser volumic mass of water; at 10° Réaumur (12.5°C, 54.5°F). The scale of the degree API (API gravity) is structured identically with the lighter Baumé but for a temperature of 60°F; readings are about 1% greater.
Wines and distilled spirits have specific gravities of less than 1. The best-known measure for hard liquor is proof. This term relates any sample to a standard that is regarded as 100, the resulting measure being expressed as either percentage proof or degree proof in absolute terms, or, as under or over proof, relative to 100. In the UK the historic standard is a mixture with 57.1% alcohol by volume; in the USA it is 50%. Proof figures equal the change in overall volume that would produce a mixture of proof 100, a useful factor for proportional taxation. Various hydrometers have been used as measuring tools for proof, each typically with a bevy of alternative weights and its own scale.
[Glazebrook R. T. (ed.) Dictionary of Applied Physics Vol. 3: Meteorology, Metrology and Measuring Apparatus (London: Macmillan, 1923)] The Sikes, developed by the Royal Society, was probably the first to encompass the problems of temperature by incorporating tables for converting its readings into proof, but its scale was peculiar in having its zero at 66.7% over proof (UK); its 100 was at the maximal specific gravity, i.e. pure water in this context. Subsequent extension above 66.7% brought the Sikes ‘A’ and ‘B’ scales.
For wines, several competing schemes have persisted into the contemporary world. The most preferable of these is the Gay-Lussac. Widely used in the French-speaking world, this scale is effectively the percentage of alcohol by volume, expressed in degrees that are percentage points, so is just half the US proof and 0.571 times the UK proof; that is, with the traditional Gay-Lussac scale used at 15°C, just 1 degree Fahrenheit below the 60°F that applies to proof. The modern consensus favours using the Gay-Lussac internationally at 20°C, which increases the figures by about 0.2 in mid-range. The Tralles scheme used in Russia is essentially the same as the traditional Gay-Lussac, but set at 60°F. The Windisch scale of Germany differs distinctly in being percentage point by mass. The Cartier scale of Spain is, in contrast, utterly arbitrary in every way, going from 10° at 0% alcohol to 44° at 100%, in irregular steps, with about 19.5° for 50% alcohol by volume (US 100 proof) and 26.5° for 70% (US 40 over proof).
