Coherence (units of measurement)

A coherent derived unit is defined as a derived unit that, for a given system of quantities and for a chosen set of base units, is a product of powers of base units with no other proportionality factor than one. The concept of coherence was developed in the mid-nineteenth century by, amongst others, Kelvin and James Clerk Maxwell and promoted by the British Association for the Advancement of Science. The concept was initially applied to the centimetre–gram–second (CGS) and the foot–pound–second systems (FPS) of units in 1873 and 1875 respectively. The International System of Units (1960) was designed around the system of coherence.

In SI, which is a coherent system, the unit of power is the watt which is defined as one joule per second. In the US customary system of measurement, which is non-coherent, the unit of power is the horsepower which is defined as 550 foot-pounds per second (the pound in this context being the pound-force); similarly the gallon is not equal to a cubic yard (nor is it the cube of any length unit).

The earliest units of measure devised by humanity bore no relationship to each other. As both humanity's understanding of philosophical concepts and the organisation of society developed, so units of measurement were standardised - first particular units of measure had the same value across a community then different units of the same quantity (for example feet and inches) were given a fixed relationship. Apart from Ancient China where the units of capacity and of mass are linked to red millet seed, there is little evidence of the linking of different quantities until the Age of Reason.

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