Hydrometer
A hydrometer is an instrument used to measure the specific gravity (or relative density) of liquids; that is, the ratio of the density of the liquid to the density of water.
A hydrometer is usually made of glass and consists of a cylindrical stem and a bulb weighted with mercury or lead shot to make it float upright. The liquid to be tested is poured into a tall jar, and the hydrometer is gently lowered into the liquid until it floats freely. The point at which the surface of the liquid touches the stem of the hydrometer is noted. Hydrometers usually contain a paper scale inside the stem, so that the specific gravity can be read directly.
The operation of the hydrometer is based on the Archimedes principle that a solid suspended in a liquid will be buoyed up by a force equal to the weight of the liquid displaced. Thus, the lower the density of the substance, the lower the hydrometer will sink. (See also Relative density and hydrometers.) Some historians credit Hypatia of Alexandria with the invention of the hydrometer although there is little evidence to support this.
In light liquids such as kerosene, gasoline, and alcohol, the hydrometer will sink deeper, and in heavy liquids such as brine, milk, and acids it will not sink so far. In fact, it is usual to have two separate instruments, one for heavy liquids, on which the mark 1.000 for water is near the top of the stem, and one for light liquids, on which the mark 1.000 is near the bottom. In many industries a set of hydrometers is used  covering specific gravity ranges of 1.00.95, 0.950.9 etc  to provide more precise measurements.

# Commercial uses
Because the commercial value of many liquids, including sugar solutions, sulfuric acid, and alcohol beverages such as beer and wine, depends directly on the specific gravity, hydrometers are used extensively.
A lactometer is a hydrometer used to test milk. The specific gravity of milk does not give a conclusive indication of its composition since milk contains a variety of substances that are either heavier or lighter than water. Additional tests for fat content are necessary to determine overall composition.
An alcoholometer is a hydrometer which is used for determining the alcoholic strength of liquids.  It is also known as a proof & traille hydrometer.
A saccharometer is a hydrometer used for determining the amount of sugar in a solution. It is primarily used by brewers and winemakers.
A thermohydrometer is a hydrometer that has a thermometer enclosed in the float section.
For measuring the density of petroleum products, like fuel oils, the specimen is usually heated in a temperature jacket with a thermometer placed behind it since density is dependent on temperature. Light oils are placed in cooling jackets, typically at 15oC.
Very light oils with many volatile components are measured in a variable volume container using a floating piston sampling device to minimize light end losses.

# Soil analysis
A hydrometer analysis is the process by which fine-grained soils, silts and clays, are graded. Hydrometer analysis is performed if the grain sizes are too small for sieve analysis. The basis for this test is Stoke's Law for falling spheres in a viscous fluid in which the terminal velocity of fall depends on the grain diameter and the densities of the grain in suspension and of the fluid. The grain diameter thus can be calculated from a knowledge of the distance and time of fall. The hydrometer also determines the specific gravity (or density) of the suspension, and this enables the percentage of particles of a certain equivalent particle diameter to be calculated.