# System of Units

## System of Units

a set of fundamental and derived units that pertains to some system of quantities and is formed in accordance with accepted principles. A system of units is constructed on the basis of physical theories that reflect the interrelationship existing in nature between physical quantities. When the units of a system are defined, the physical relations used are arranged in a sequence such that each succeeding expression contains only one new quantity. This method permits the unit of a physical quantity to be defined in terms of previously defined units and, in the final analysis, in terms of the fundamental (independent) units of the system (*see*UNITS, PHYSICAL).

The first systems of units employed units of length and mass as the fundamental units—for example, the foot and the English pound in Great Britain and the arshin and the *funt* (Russian pound) in Russia. These systems included multiple and fractional units that had their own names, such as the yard and inch in the English system and the *sazhen’, vershok*, and *fut* (foot) in the Russian system. Complicated sets of derived units were thus created. The difference in the national systems of units was an inconvenience for trade and industry. In response to this problem, the idea of the metric system arose in France in the 18th century. The metric system has been the basis for the international standardization of the units of length (the meter), mass (the kilogram), and the principal derived units—the units of area, volume and density.

In the 19th century K. F. Gauss and W. E. Weber proposed a system of units for electrical and magnetic quantities that was called absolute by Gauss. The fundamental units of the system were the millimeter, the milligram, and the second. The derived units were defined by equations expressing the relations between the quantities in simplest form—that is, the numerical coefficients were equal to unity. Systems defined in this way were later called coherent.

In the second half of the 19th century the British Association for the Advancement of Science adopted two systems of units: the centimeter-gram-second (cgs) electrostatic system and the cgs electromagnetic system (*see*). This act stimulated the creation of other systems of units, for example, the Gaussian system, the meter-kilogram-force system, and the meter-ton-second system. The Italian physicist G. Giorgi proposed in 1901 a system of units based on the meter, the kilogram, the second, and one electrical unit; the ampere was subsequently chosen as the electrical unit (*see*METER-KILOGRAM-SECOND-AMPERE SYSTEM). The Giorgi system included such widely used practical units as the ampere, volt, ohm, watt, joule, farad, and henry. The Giorgi system formed the basis for the International System of Units (SI), which was approved by the Eleventh General Conference of Weights and Measures in 1960. The International System has seven base units: the meter, kilogram, second, ampere, kelvin, mole, and candela. The creation of the system improved the outlook for a general standardization of units. Many countries decided to adopt the system or to give it preference.

Besides the practical systems of units, physics makes use of systems that are based on universal physical constants, such as the speed of propagation of light in a vacuum, the charge of an electron, and Planck’s constant (*see*NATURAL SYSTEMS OF UNITS).

### REFERENCES

Burdun, G. D.*Edinitsy fizicheskikh velichin*, 4th ed. Moscow, 1967.

Burdun, G. D.

*Spravochnikpo Mezhdunarodnoi sisteme edinits*. Moscow, 1971.

Burdun, G. D., and B. N. Markov.

*Osnovy metrologii*. Moscow, 1972.

K. P. SHIROKOV