# Centimeter-Gram-Second System

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## centimeter-gram-second system

[¦sent·ə‚mēd·ər ¦gram ′sek·ənd ‚sis·təm]## Centimeter-Gram-Second System

(cgs system), the system of units of physical quantities that is based on the three fundamental units of the centimeter for length, the gram for mass, and the second for time.

In 1861 the British Association for the Advancement of Science appointed a committee on electrical standards, whose membership included such leading physicists of the day as W. Thomson (Lord Kelvin), J. Maxwell, and C. Wheatstone. The committee proposed that a system of units based on fundamental units of length, mass, and time be adopted for mechanics and electrodynamics. Ten years later, the association formed a new committee, which made a final choice of the centimeter, gram, and second as the fundamental units. The First International Congress of Electricians, which was held in Paris in 1881, also adopted the cgs system. Since then, the system has been widely used in scientific research. Since the introduction of the International System of Units (SI), the use of cgs units has been permitted alongside SI units in physics and astronomy.

With respect to mechanical measurements, the most important derived units in the cgs system are as follows: speed, cm/sec; acceleration, cm/sec^{2}; force, dyne (dyn); pressure, dyn/cm^{2}; work and energy, erg; power, erg/sec; dynamic viscosity, poise (P); and kinematic viscosity, stokes (St).

For electrodynamics, two cgs systems—the cgs electromagnetic system and the cgs electrostatic system—were originally adopted. The electromagnetic system is based on Coulomb’s law of the force between two point magnetic poles, and the electrostatic system on Coulomb’s law of the force between two point electric charges. In the cgs electromagnetic system, the permeability of empty space μ_{0} is dimensionless and is taken as 1. The permittivity of empty space ɛ_{0} = 1/c^{2} sec^{2}/cm^{2}, where *c* = (2.99792458 ± 0.000000012) X 10^{10} is the numerical value of the speed of light in cm/sec. The cgs electromagnetic system includes the following units: magnetic flux, maxwell (Mx); magnetic flux density, gauss (G); magnetic field strength, oersted (Oe); and magnetomotive force, gilbert (Gb). Special names have not been adopted for the electrical units in this system.

In the cgs electrostatic system, ɛ_{0} = 1, and μ_{0} = 1/*c*^{2} sec^{2}/cm^{2}. The electrical units of this system have not been given special names. Their sizes are in general inconvenient for measurements, and they are used primarily in theoretical work.

Elements of the electromagnetic and electrostatic cgs systems are mixed in the Gaussian system, which has become the most widely used system in the second half of the 20th century. In this system, μ_{0} = 1, and ɛ_{0} = 1. The magnetic units of this

Table 1. Relations between the most important cgs units and the corresponding SI units^{1} | ||||
---|---|---|---|---|

Quantity | SI system | cgs electromagnetic system | cgs electrostatic system | Gaussian system |

^{1}In table, c is the numerical value of the speed of light in cm/sec | ||||

Force..................... | 1 N | 10^{-5}N | 10^{-5}N | 10^{-5}N |

Work, energy ................ | 1 J | 10^{-7}J | 10^{-7}J | 10^{-7}J |

Dynamic viscosity ............. | 1 N.sec/m^{2} | 0.1 N.sec/m^{2} | 0.1 N.sec/m^{2} | 0.1 N.sec/m^{2} |

Kinematic viscosity ............ | 1 m^{2}/sec | 10^{-4}m^{2}/sec | 10^{-4} m^{2}/sec | 10^{-4}m^{2}/sec |

Current.................... | 1A | 10A | 10/c A | 10/c A |

Electric charge.......... | 1C | 10C | 10/cC | 10/cC |

Electric potential.............. | 1V | 10^{-8}V | 10^{-8}c V | l0^{-8}c V |

Electric resistance............. | 1Ω | 10^{-9} Ω | 10^{-9}C^{2}Ω | 10^{-9}C^{2}Ω |

Electric capacitance ........... | 1F | 10^{9}F | l0^{9}/c^{2} F | l0^{9}/c^{2} F |

Magnetic field strength .......... | 1 A/m | 10^{3}/(4π) A/m | 10^{3}/(4πc) A/m | 10^{3}/(4π) A/m |

Magnetic flux density ........... | 1T | 10^{-4}T | 10^{-4}cT | 10^{-4} T |

Magnetic flux ................ | 1 Wb | 10^{-8} Wb | 10^{-8}c Wb | 10^{-8} W |

system are identical to those of the cgs electromagnetic system, and the electrical units are identical to those of the cgs electrostatic system.

Table 1 shows the relations between the most important units of the three cgs systems and the corresponding SI units.

### REFERENCE

Burdun, G. D.*Spravochnik po Mezhdunarodnoi sisteme edinits*. Moscow, 1971.

K. P. SHIROKOV