Coherence (units of measurement)

James Clerk Maxwell played a major role in developing the concept of a coherent CGS system and in extending the metric system to include electrical units.

A coherent system of units is a system of units of measurement used to express physical quantities, that does not use conversion factors in the definitions of its derived units.

A coherent derived unit is a derived unit that, for a given system of quantities and a chosen set of base units, is a product of powers of base units, with the proportionality factor being one.

This means that any equation relating numerical values (expressed in the units of the system) has the same form, including the same numerical factors, as the corresponding equation relating the relevant quantities. E.g. for kinetic energy, the quantity equation is E = (1/2) × m × v2. If m = 2 kg and v = 3 m/s, then the numerical value equation is 9 J = (1/2) × 2 kg × (3 m/s)2.

The concept of coherence was developed in the mid-nineteenth century by, among others, Lord Kelvin and James Clerk Maxwell, and promoted by the British Association for the Advancement of Science. The concept was initially applied to the systems of units called centimetre–gram–second (CGS) in 1873 and foot–pound–second (FPS) in 1875. The International System of Units (SI) was designed in 1960 to incorporate the principle of coherence.

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