In France, the assessment of spirit duties is made with the centesimal alcoholometer and tables of Gay-Lussac, which date from the year 1824. The range of the alcoholometer (areometer, hydrometer) extends from "water" to absolute alcohol, and is divided into 100 degrees, each degree representing 1 per cent. of absolute alcohol by volume at the temperature 15°. Three separate instruments are used to cover this range. One extends from 0° to 35°, the next from 35° to 70°, and the third from 70° to 100°. If the spirit tested is at the temperature 15°, the reading of the alcoholometer shows the' percentage of alcohol by volume directly: a reading of 40, for instance, indicates that the spirit contains 40 per cent. of alcohol by volume.

Raised to a temperature higher than 15°, the spirit will expand and become lighter; the alcoholometer therefore now sinks further than before. Conversely, at a temperature lower than 15° the instrument does not sink to so low a point as at 15°. The readings in such cases are termed ' apparent degrees," and Gay-Lussac's chief table (Table de la force reelle des liquides spiritueux) gives the true percentages of alcohol corresponding with these "apparent" or "observed" readings. The table shows also the corresponding correction for the change in volume which the spirituous liquid has undergone with the variation of temperature from the standard. The true quantity of alcohol can thus be calculated.

The alcohol used as the basis for constructing Gay-Lussac's tables had the specific gravity 07947 at 15°, referred to water at the same temperature as unity. In 1884, however, it was decreed that the graduation of alcoholometers should be based upon a new "table of the densities of mixtures of water and absolute alcohol ' drawn up by the National Bureau of Weights and Measures, in which table the specific gravity of the absolute alcohol is given as 79.433 at 15° in vacuo, water at the same temperature being taken as 100. The effect is to show slightly lower values than those of the original instruments, since a given percentage of the stronger alcohol (sp. gr. 0.79433) is equivalent to a higher percentage of the weaker alcohol (sp. gr. 0.7947). The maximum difference is 0.4 per cent.

With slight adaptations, Gay-Lussac's alcoholometer and tables are also used for fiscal purposes in Belgium, Norway, and Sweden. In Spain both Gay-Lussac's and an earlier French hydrometer (Cartier's) are employed.

Tralles's alcoholometer and tables were used in Germany during the greater part of the nineteenth century, and the instrument is still employed officially in Italy, and commercially in Russia. It is a glass areometer showing directly the percentage of alcohol by volume in a spirituous liquid at the standard temperature 15.6°. The alcohol taken as basis had the sp. gr. 0.7946 at 15-6o/15.6°. For use at temperatures other than the standard, tables were supplied.

Tralles's system has been superseded in Germany by the adoption of an alcoholometer graduated to show percentages of alcohol by weight at the standard temperature of 15°. The tables adopted are based upon the results of Mendeleeff's investigations. The official alcoholometers are made of glass, and contain a thermometer in the lower part, so that the one instrument shows both the temperature of the spirit and its alcoholic strength. Although the latter is taken by weight, for the purpose of charging duty the results are converted into volumes of absolute alcohol (at 15.6°) by means of tables which show the number of litres of absolute alcohol corresponding with any given number of kilograms of the spirit tested.

In what was formerly the Austrian Empire, Meisner's areometer is used for the assay of spirits. It is an instrument very similar to that of Tralles, but indicates percentages of alcohol both by weight and by volume. The alcohol on which the tables are based has the sp. gr. 0.795 at 12°/12° Reaumur (15°/15° C).

In Holland the official hydrometer is devised upon a different plan from any of the foregoing. The stem is graduated in terms of the volume of the instrument below the zero mark, each degree being one-hundredth part of this volume. The graduation is thus not arbitrary as with Sikes's instrument, nor does it show percentages of alcohol directly, like Gay-Lussac's or Tralles's alcoholometer. Tables are supplied which convert the indications of the instrument into percentage of alcohol by volume at 15°, but the standard adopted for fiscal charges is a "proof" spirit, which at 15° contains 50 per cent. by volume of absolute alcohol.

A metal hydrometer essentially similar to that of Sikes is used officially in Russia. It is graduated, however, in the reverse manner to Sikes's instrument, water being represented by zero on the Russian hydrometer, and strong spirit by 100. The zero mark, of course, is at the bottom of the stem. Tralles's alcohol is taken as the standard, the tables used with the instrument showing percentages by volume of this alcohol at 12 4/9° Reaumur (15.6° C).

In the United States, the Customs duties upon spirits were at one time levied in terms of alcohol percentages, but objections were made to this on the ground that it did not conform to trade usage, which was to buy and sell in terms of proof spirit. After inquiry, therefore, by a Committee appointed in the year 1866 to examine into the whole question of testing spirit strengths, it was decided that "the duties on all spirits shall be levied according to their equivalent in proof spirit." Tralles's alcohol was taken as the standard, and the United States proof spirit contains one-half of its volume of this alcohol at 156°. Gilpin's results were largely used in compiling the tables for use with the hydrometers, of which there is a series covering a range of graduations from 0 to 200. At the standard temperature 15.6° C. (60° F.), distilled water is represented by 0 on the hydrometer scale, proof spirit by 100, and Tralles's alcohol by 200.